,transcriber's note3 ,a few typographical errors have been corrected3 they are listed at the end of the text4 ,in mathematical formulae the carat 77 and underscore 77 introduce superscripts or subscripts respectively1 of one character or a group enclosed in curly braces 7xyz74 ,elsewhere underscores delimit italics in the text1 and braces enclose the original page numbers thus #abc4 ,,by ,,augustus ,,de ,,morgan ,a ,,budget ,,of ,,paradoxes ,,reprinted ,,with ,,the ,,author',s ,,additions ,,from ,,the ,,athenaeum ,,second ,,edition ,,edited ,,by ,,david ,,eugene ,,smith ,,with ,a ,,new ,,introduction ,,by ,,ernest ,,nagel ,,professor ,,of ,,philosophy1 ,,columbia ,,university ,,unabridged ,,edition--,,two ,,volumes ,,bound ,,as ,,one ,volume ,,ii ,,dover ,,publications1 ,,inc41 ,,new ,,york 99 99 99 99 99 ,this new ,dover ,edition1 published in #aied1 is an unabridged republication of the ,second ,edition of #aiae1 with a new introduction by ,professor ,ernest ,nagel4 ,copyright #aied by ,dover ,publications1 ,inc4 ,manufactured in the ,united ,states of ,america 99 99 99 99 99 #a ,a ,,budget ,,of ,,paradoxes4 ,,volume ,,ii4 ,,on ,,some ,,philosophical ,,atheists4 ,with the general run of the philosophical atheists of the last century the notion of a ,god was an hypothesis4 ,there was left an admitted possibility that the vague somewhat which went by more names than one1 might be personal1 intelligent1 and superintendent4 ,in the works of ,laplace1#a who is sometimes called an atheist from his writings1 there is nothing from which such an inference can be drawn3 unless indeed a ,reverend ,fellow of the ,royal ,society may be held to be the fool who said in his heart1 etc41 etc41 if his contributions to the ,philosophical ,transactions go no higher than nature4 ,the following anecdote is well known in ,paris1 but has never been printed entire4 ,laplace once went in form to present some edition of his ,systeme du ,monde to the ,first ,consul1 or ,emperor4 ,napoleon1 whom some wags had told that this book contained no mention of the name of ,god1 and who was fond of putting embarrassing questions1 received it with--,m4 ,laplace1 they tell me you have written this large book on the system of the universe1 and have never even mentioned its ,creator4 ,laplace1 who1 though the most supple of politicians1 was as stiff as a martyr on every point of his philosophy or religion 7e4 g41 even under ,charles ,x he never concealed his dislike of the priests71 drew himself up and answered #b bluntly1 ,je n'avais pas besoin de cette hypothese-la4#b ,napoleon1 greatly amused1 told this reply to ,lagrange1 who exclaimed1 ,ah6 c'est une belle hypothese2 ca explique beaucoup de choses4#c ,it is commonly said that the last words of ,laplace were1 ,ce que nous connaissons est peu de chose2 ce que nous ignorons est immense4#d ,this looks like a parody on ,newton's pebbles3#e the following is the true account2 it comes to me through one remove from ,poisson4#f ,after the publication 7in #ahbe7 of the fifth volume of the ,mecanique ,celeste1 ,laplace became gradually weaker1 and with it musing and abstracted4 ,he thought much on the great problems of existence1 and often muttered to himself1 ,qu'est ce que c'est que tout cela6#g ,after many alternations1 he appeared at last so permanently prostrated that his family applied to his favorite pupil1 ,m4 ,poisson1 to try to get a word from him4 ,poisson paid a visit1 and after a few words of salutation1 said1 ,j'ai une bonne nouvelle a vous annoncer3 on a recu au ,bureau des ,longitudes une lettre d',allemagne annoncant que ,m4 ,bessel a verifie par l'observation vos decouvertes theoriques sur les satellites de ,jupiter4#h ,laplace opened his eyes and answered with deep #c gravity1 ,l'homme ne poursuit que des chimeres4#i ,he never spoke again4 ,his death took place ,march #e1 #ahbg4 ,the language used by the two great geometers illustrates what ,i have said3 a supreme and guiding intelligence--apart from a blind rule called nature of things--was an hypothesis4 ,the absolute denial of such a ruling power was not in the plan of the higher philosophers3 it was left for the smaller fry4 ,a round assertion of the non-existence of anything which stands in the way is the refuge of a certain class of minds3 but it succeeds only with things subjective2 the objective offers resistance4 ,a philosopher of the appropriative class tried it upon the constable who appropriated him3 ,i deny your existence1 said he2 ,come along all the same1 said the unpsychological policeman4 ,euler#aj was a believer in ,god1 downright and straightforward4 ,the following story is told by ,thiebault1#aa in his ,souvenirs de vingt ans de sejour a ,berlin1#ab published in his old age1 about #ahjd4 ,this volume was fully received as trustworthy2 and ,marshall ,mollendorff#ac told the ,duc de ,bassano#ad in #ahjg that it was the most veracious of books written by the most honest of men4 ,thiebault says that he has no personal knowledge of the truth of the story1 but #d that it was believed throughout the whole of the north of ,europe4 ,diderot#ae paid a visit to the ,russian ,court at the invitation of the ,empress4 ,he conversed very freely1 and gave the younger members of the ,court circle a good deal of lively atheism4 ,the ,empress was much amused1 but some of her councillors suggested that it might be desirable to check these expositions of doctrine4 ,the ,empress did not like to put a direct muzzle on her guest's tongue1 so the following plot was contrived4 ,diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of ,god1 and would give it him before all the ,court1 if he desired to hear it4 ,diderot gladly consented3 though the name of the mathematician is not given1 it was ,euler4 ,he advanced towards ,diderot1 and said gravely1 and in a tone of perfect conviction3 ,monsieur1 7a bn7 _/ n x1 donc ,dieu existe2 repondez6#af ,diderot1 to whom algebra was ,hebrew1 was embarrassed and disconcerted2 while peals of laughter rose on all sides4 ,he asked permission to return to ,france at once1 which was granted4 ,,rotation ,,of ,,the ,,moon4 ,an examination of the ,astronomical doctrine of the ,moon's rotation4 ,by ,j4 ,l4#ag ,edinburgh1 #ahdg1 #hvo4 ,a systematic attack of the character afterwards made with less skill and more notice by ,mr4 ,jellinger ,symons4 ,july #ahff1 ,j4 ,l4 appears as ,mr4 ,james ,laurie1 with a new pamphlet ,the ,astronomical doctrines of the ,moon's rotation 444 ,edinburgh4 ,of all the works ,i have seen on the question1 this is the most confident1 and the sorest4 #e ,a writer on astronomy said of ,mr4 ,jellinger ,symons1#ah ,of course he convinced no one who knew anything of the subject4 ,this ungenerous slur on the speculator's memory appears to have been keenly felt2 but its truth is admitted4 ,those who knew anything of the subject are the so-called men of science1 whose three ,p's were assailed2 prestige1 pride1 and prejudice3 this the author tries to effect for himself with three ,q's2 quibble1 quirk1 and quiddity4 ,he explains that the ,scribes and ,pharisees would not hear ,jesus1 and that the lordly bishop of ,rome will not cast his tiara and keys at the feet of the humble presbyter who now plays the part of pope in ,scotland4 ,i do not know whom he means3 but perhaps the friends of the presbyter-pope may consider this an ungenerous slur4 ,the best proof of the astronomer is just such as might have been expected from the merest of blockheads2 but as the giver is of course not a blockhead1 this circumstance shows how deeply blinded by prejudice he must be4 ,of course the paradoxers do not persuade any persons who know their subjects3 and so these ,scribes and ,pharisees reject the ,messiah4 ,we must suppose that the makers of this comparison are ,christians3 for if they thought the ,messiah an enthusiast or an impostor1 they would be absurd in comparing those who reject what they take for truth with others who once rejected what they take for falsehood4 ,and if ,christians1 they are both irreverent and blind to all analogy4 ,the ,messiah1 with ,his ,divine mission proved by miracles which all might see who chose to look1 is degraded into a prototype of ,james ,laurie1 ingeniously astronomizing upon ignorant geometry and false logic1 and comparing to blockheads those who expose his nonsense4 ,their comparison is as foolish as--supposing #f them ,christians--it is profane3 but1 like errors in general1 its other end points to truth4 ,there were ,pseudochrists and ,antichrists2 and a ,concordance would find the real forerunners of all the paradoxers4 ,but they are not so clever as the old false prophets3 there are none of whom we should be inclined to say that1 if it were possible1 they would deceive the very educated4 ,not an ,egyptian among them all can make uproar enough to collect four thousand men that are murderers--of common sense--to lead out into the wilderness4 ,nothing1 says the motto of this work1 is so difficult to destroy as the errors and false facts propagated by illustrious men whose words have authority4 ,i deny it altogether4 ,there are things much more difficult to destroy3 it is much more difficult to destroy the truths and real facts supported by such men4 ,and again1 it is much more difficult to prevent men of no authority from setting up false pretensions2 and it is much more difficult to destroy assertions of fancy speculation4 ,many an error of thought and learning has fallen before a gradual growth of thoughtful and learned opposition4 ,but such things as the quadrature of the circle1 etc41 are never put down4 ,and why8 ,because thought can influence thought1 but thought cannot influence self-conceit3 learning can annihilate learning3 but learning cannot annihilate ignorance4 ,a sword may cut through an iron bar2 and the severed ends will not reunite3 let it go through the air1 and the yielding substance is whole again in a moment4 ,miracles versus ,nature3 being an application of certain propositions in the theory of chances to the ,christian miracles4 ,by ,protimalethes4#ai ,cambridge1 #ahdg1 #hvo4 ,the theory1 as may be supposed1 is carried further than most students of the subject would hold defensible4 #g ,an astronomical ,lecture4 ,by the ,rev4 ,r4 ,wilson4#bj ,greenock1 #ahdg1 #abmo4 ,against the moon's rotation on her axis4 ,handed about in the streets in #ahdg3 ,i quote the whole3 ,important discovery in astronomy1 communicated to the ,astronomer ,royal1 ,december #bast1 #ahdf4 ,that the ,sun revolve round the ,planets in #begdh-b_/e years1 in consequence of the combined attraction of the planets and their satellites1 and that the ,earth revolve round the ,moon in #ah years and #bbh days4 ,d4 ,t4 ,,glazier altered with a pen into ,,glazion4 ,price one penny4 #ahdg4 ,in the ,united ,service ,magazine for ,september1 #ahdg1 ,mrs4 ,borron1#ba of ,shrewsbury1 published some remarks tending to impeach the fact that ,neptune1 the planet found by ,galle1#bb really was the planet which ,le ,verrier and ,adams#bc had a right to claim4 ,this was followed 7,september #ad7 by two pages1 separately circulated1 of ,further ,observations upon the ,planets ,neptune and ,uranus1 with a ,theory of ,perturbations2 and 7,october #ai1 #ahdh7 by three pages of ,a ,review of ,m4 ,leverrier's ,exposition4 ,several persons1 when the remarkable discovery was made1 contended that the planet actually discovered was an intruder2 and the future histories of the discovery must contain some account of this little afterpiece4 ,tim ,linkinwater's theory that there is no place like ,london for coincidences1 would have been utterly overthrown in favor of what they used to call the celestial spaces1 if there had been a planet which by chance was put #h near the place assigned to ,neptune at the time when the discovery was made4 ,,early ,,ideas ,,of ,,aviation4 ,aerial ,navigation2 containing a description of a proposed flying machine1 on a new principle4 ,by ,daedalus ,britannicus4 ,london1 #ahdg1 #hvo4 ,in #ahdb-dc a ,mr4 ,henson#bd had proposed what he called an aeronaut steam-engine1 and a ,bill was brought in to incorporate an ,aerial ,transit ,company4 ,the present plan is altogether different1 the moving power being the explosion of mixed hydrogen and air4 ,nothing came of it--not even a ,bill4 ,what the final destiny of the balloon may be no one knows3 it may reasonably be suspected that difficulties will at last be overcome4 ,darwin1#be in his ,botanic ,garden 7#agha71 has the following prophecy3 ,soon shall thy arm1 unconquered ,steam6 afar ,drag the slow barge1 or drive the rapid car2 ,or1 on wide-waving wings expanded1 bear ,the flying chariot through the fields of air4 ,darwin's contemporaries1 no doubt1 smiled pity on the poor man4 ,it is worth note that the two true prophecies have been fulfilled in a sense different from that of the predictions4 ,darwin was thinking of the suggestion of ,jonathan ,hulls1#bf when he spoke of dragging the slow barge3 it is only very recently that the steam-tug has been employed on the canals4 ,the car was to be driven1 not drawn1 and on the common roads4 ,perhaps1 the flying chariot will #i be something of a character which we cannot imagine1 even with the two prophecies and their fulfilments to help us4#bg ,,the ,,secret ,,of ,,the ,,universe ,,divulged4 ,a book for the public4 ,new ,discovery4 ,the causes of the circulation of the blood2 and the true nature of the planetary system4 ,london1 #ahdh1 #hvo4 ,light is the sustainer of motion both in the earth and in the blood4 ,the natural standard1 the pulse of a person in health1 four beats to one respiration1 gives the natural second1 which is the measure of the earth's progress in its daily revolution4 ,the ,greek fable of the ,titans is an elaborate exposition of the atomic theory3 but any attempt to convince learned classics would only meet their derision2 so much does long-fostered prejudice stand in the way of truth4 ,the author complains bitterly that men of science will not attend to him and others like him3 he observes1 that in the time occupied in declining1 a man of science might test the merits4 ,this is1 alas6 too true2 so well do applicants of this kind know how to stick on4 ,but every rule has its exception3 ,i have heard of one4 ,the late ,lord ,spencer#bh--the ,lord ,althorp of the ,house of ,commons--told me that a speculator once got access to him at the ,home ,office1 and was proceeding to unfold his way of serving the public4 ,i do not understand these things1 said ,lord ,althorp1 but ,i happen to have ---- 7naming an eminent engineer7 upstairs2 suppose you talk to him on the subject4 ,the discoverer went up1 and in half-an-hour returned1 and said1 ,i am very much obliged to your ,lordship for introducing me to ,mr4 ----2 he has convinced me #aj that ,i am quite wrong4 ,i supposed1 when ,i heard the story--but it would not have been seemly to say it--that ,lord ,a4 exhaled candor and sense1 which infected those who came within reach3 he would have done so1 if anybody4 ,,the ,,trisection ,,and ,,quadrature ,,again4 ,a method to trisect a series of angles having relation to each other2 also another to trisect any given angle4 ,by ,james ,sabben4 #ahdh 7two quarto pages74 ,the consequence of years of intense thought3 very likely1 and very sad4 #ahdh4 ,the following was sent to me in manuscript4 ,i give the whole of it3 ,quadrature of the ,circle4--,a quadrant is a curvilinear angle traversing round and at an equal distance from a given point1 called a center1 no two points in the curve being at the same angle1 but irreptitiously graduating from #ij to #fj4 ,it is therefore a mean angle of #ij and #fj1 which is #ge1 because it is more than #fj1 and less than #ij1 approximately from #fj to #ij1 and from #ij to #fj1 with equal generation in each irreptitious approximation1 therefore meeting in #ge1 and which is the mean angle of the quadrant4 ,or suppose a line drawn from a given point at #ij1 and from the same point at #fj4 ,let each of these lines revolve on this point toward each other at an equal ratio4 ,they will become one line at #ge1 and bisect the curve1 which is one-sixth of the entire circle4 ,the result1 taking #af as a diameter1 gives an area of #bja4jgbdjj1 and a circumference of #ej4bfha4 ,the original conception1 its natural harmony1 and the result1 to my own mind is a demonstrative truth1 which ,i presume it right to make known1 though perhaps at the hazard of unpleasant if not uncourteous remarks4 ,i have added punctuation3 the handwriting and spelling #aa are those of an educated person2 the word irreptitious is indubitable4 ,the whole is a natural curiosity4 ,the quadrature and exact area of the circle demonstrated4 ,by ,wm4 ,peters4 #hvo4 n4 d4 7circa #ahdh74bi ,suggestions as to the necessity for a revolution in philosophy2 and prospectus for the establishment of a new quarterly1 to be called the ,physical ,philosopher and ,heterodox ,review4 ,by ,q4 ,e4 ,d4 #hvo4 #ahdh4 ,these works are by one author1 who also published1 as appears by advertisement1 ,newton rescued from the precipitancy of his followers through a century and a half1#cj and ,dangers along a coast by correcting 7as it is called7 a ship's reckoning by bearings of the land at night fall1 or in a fog1 nearly out of print4 ,subscriptions are requested for a new edition4 ,the area of a circle is made four-fifths of the circumscribed square3 proved on an assumption which it is purposed to explain in a longer essay4#ca ,the author1 as ,q4 ,e4 ,d41 was in controversy with the ,athenaeum journal1 and criticised a correspondent1 ,d41 who wrote against a certain class of discoverers4 ,he believed the common theories of hydrostatics to be wrong1 and one of his questions was3 ,have you ever taken into account anent gravity and gravitation the fact that a five grain cube of cork will of itself half sink in the water1 whilst it will take #bj grains of brass1 which will sink of itself1 to pull under the other half8 ,fit this if you can1 friend ,d41 to your notions of gravity and specific gravity1 as applied to the construction of a universal law of gravitation4 ,this the ,athenaeum published--but without some ,italics1 for which the editor was sharply reproved1 as a sufficient #ab specimen of the quod erat ,d4 monstrandum3 on which the author remarks--,d1--,wherefore the e caret8 is it ,d apostrophe8 ,d'1 ,d',m1 ,d',mo1 ,d',monstrandum2 we cannot find the wit of it4 ,this ,i conjecture to contain an illusion to the name of the supposed author2 but whether ,de ,mocritus1 ,de ,mosthenes1 or ,de ,moivre was intended1 ,i am not willing to decide4 ,the ,scriptural ,calendar and ,chronological ,reformer1 for the statute year #ahdi4 ,including a review of recent publications on the ,sabbath question4 ,london1 #ahdi1 #abmo4#cb ,this is the almanac of a sect of ,christians who keep the ,jewish ,sabbath1 having a chapel at ,mill ,yard1 ,goodman's ,fields4 ,they wrote controversial works1 and perhaps do so still2 but ,i never chanced to see one4 ,geometry versus ,algebra2 or the trisection of an angle geometrically solved4 ,by ,w4 ,upton1 ,b4,a4#cc ,bath 7circa #ahdi74 #hvo4 ,the author published two tracts under this title1 containing different alleged proofs3 but neither gives any notice of the change4 ,both contain the same preface1 complaining of the ,british ,association for refusing to examine the production4 ,i suppose that the author1 finding his first proof wrong1 invented the second1 of which the ,association never had the offer2 and1 feeling sure that they would have equally refused to examine the second1 thought it justifiable to #ac present that second as the one which they had refused4 ,mr4 ,upton has discovered that the common way of finding the circumference is wrong1 would set it right if he had leisure1 and1 in the mean time1 has solved the problem of the duplication of the cube4 ,the trisector of an angle1 if he demand attention from any mathematician1 is bound to produce1 from his construction1 an expression for the sine or cosine of the third part of any angle1 in terms of the sine or cosine of the angle itself1 obtained by help of no higher than the square root4 ,the mathematician knows that such a thing cannot be2 but the trisector virtually says it can be1 and is bound to produce it1 to save time4 ,this is the misfortune of most of the solvers of the celebrated problems1 that they have not knowledge enough to present those consequences of their results by which they can be easily judged4 ,sometimes they have the knowledge and quibble out of the use of it4 ,in many cases a person makes an honest beginning and presents what he is sure is a solution4 ,by conference with others he at last feels uneasy1 fears the light1 and puts self-love in the way of it4 ,dishonesty sometimes follows4 ,the speculators are1 as a class1 very apt to imagine that the mathematicians are in fraudulent confederacy against them3 ,i ought rather to say that each one of them consents to the mode in which the rest are treated1 and fancies conspiracy against himself4 ,the mania of conspiracy is a very curious subject4 ,i do not mean these remarks to apply to the author before me4 ,one of ,mr4 ,upton's trisections1 if true1 would prove the truth of the following equation3 #c cos 7theta _/ #c7 #a root7#d - sin#btheta7 which is certainly false4#cd #ad ,in #aheb ,i examined a terrific construction1 at the request of the late ,dr4 ,wallich1#ce who was anxious to persuade a poor countryman of his1 that trisection of the angle was waste of time4 ,one of the principles was1 that magnitude and direction determine each other4 ,the construction was equivalent to the assertion that1 theta being any angle1 the cosine of its third part is sin #ctheta 4 cos7#etheta_/#b7 sin#b theta sin 7#etheta_/#b7 divided by the square root of sin#b #ctheta 4 cos#b 7#etheta_/#b7 sin#d theta sin #ctheta 4 sin #etheta 4 sin#b theta4 ,this is from my rough notes1 and ,i believe it is correct4#cf ,it is so nearly true1 unless the angle be very obtuse1 that common drawing1 applied to the construction1 will not detect the error4 ,there are many formulae of this kind3 and ,i have several times found a speculator who has discovered the corresponding construction1 has seen the approximate success of his drawing--often as great as absolute truth could give in graphical practice1--and has then set about his demonstration1 in which he always succeeds to his own content4 ,there is a trisection of which ,i have lost both cutting and reference3 ,i think it is in the ,united ,service ,journal4 ,i could not detect any error in it1 though certain there must #ae be one4 ,at least ,i discovered that two parts of the diagram were incompatible unless a certain point lay in line with two others1 by which the angle to be trisected--and which was trisected--was bound to be either #j deg4 or #ahj deg44 ,aug4 #bb1 #ahff4 ,mr4 ,upton sticks to his subject4 ,he has just published ,the ,uptonian ,trisection4 ,respectfully dedicated to the schoolmasters of the ,united ,kingdom4 ,it seems to be a new attempt4 ,he takes no notice of the sentence ,i have put in italics3 nor does he mention my notice of him1 unless he means to include me among those by whom he has been ridiculed and sneered at or branded as a brainless heretic4 ,i did neither one nor the other3 ,i thought ,mr4 ,upton a paradoxer to whom it was likely to be worth while to propound the definite assertion now in italics2 and ,mr4 ,upton does not find it convenient to take issue on the point4 ,he prefers general assertions about algebra4 ,so long as he cannot meet algebra on the above question1 he may issue as many respectful challenges to the mathematicians as he can find paper to write3 he will meet with no attention4 ,there is one trisection which is of more importance than that of the angle4 ,it is easy to get half the paper on which you write for margin2 or a quarter2 but very troublesome to get a third4 ,show us how1 easily and certainly1 to fold the paper into three1 and you will be a real benefactor to society4 ,early in the century there was a ,turkish trisector of the angle1 ,hussein ,effendi1 who published two methods4 ,he was the father of ,ameen ,bey1 who was well known in ,england thirty years ago as a most amiable and cultivated gentleman and an excellent mathematician4 ,he was then a student at ,cambridge2 and he died1 years ago1 in command of the army in ,syria4 ,hussein ,effendi was instructed in mathematics by ,ingliz ,selim ,effendi1 who translated a work #af of ,bonnycastle#cg into ,turkish4#ch ,this ,englishman was ,richard ,baily1 brother of ,francis ,baily#ci the astronomer1 who emigrated to ,turkey in his youth1 and adopted the manners of the ,turks1 but whether their religion also ,i never heard1 though ,i should suppose he did4 ,i now give the letters from the agricultural laborer and his friend1 described on page #ab1 ,vol4 ,i4 ,they are curiosities2 and the history of the quadrature can never be well written without some specimens of this kind3 ,doctor ,morgan1 ,sir4 ,permit me to address you ,brute ,creation may perhaps enjoy the faculty of beholding visible things with a more penitrating eye than ourselves4 ,but ,spiritual objects are as far out of their reach as though they had no being ,nearest therefore to the brute ,creation are those men who ,suppose themselves to be so far governed by external objects as to believe nothing but what they ,see and feel ,and ,can accomedate to their ,shallow understanding and ,imaginations ,my ,dear ,sir ,let us all ,consult ourselves by the wise proverb4 ,i believe that evry mans merit ability aught to be appreciated and valued ,in proportion to its worth utility ,in whatever ,state or ,circumstances they may fortunately or unfortunately be placed ,and happy it is for evry man to know his worth and place ,when a ,gentleman of your ,standing in ,society ,clad with those honors ,can not understand or ,solve a problem ,that is explicitly explained by words and ,letters and #ag mathematically operated by figuers ,he had best consult the wise proverd ,do that which thou ,canst understand and ,comprehend for thy good4 ,i would recommend that ,such ,gentleman ,change his business ,and appropriate his time and attention to a ,sunday ,school to ,learn what he ,could and keep the ,litle ,children form durting their ,close ,with ,sincere feelings of ,gratitude for your weakness and ,inability ,i am ,sir your ,superior in ,mathematics ---- #ahdi ,june th#bi4 ,dor ,morgin ,sir ,i wrote and ,sent my work to ,professor ---- of ---- ,state of ---- ,united ,states ,i am now in the possession of the facts that he highly approves of my work4 ,and ,says he will ,insure me ,reward in the ,states ,i write this that you may understand that ,i have knowledge of the unfair way that ,i am treated ,in my own nati ,county ,i am told and have reasons to believe that it is the ,clergy that treat me so unjust4 ,i am not ,desirous of heaping ,disonors upon my own nation4 ,but if ,i have to ,leave this kingdom without my ,just dues4 ,the world ,shall know how ,i am and have been treated4 ,i am ,sir ,desirous of my ,just dues ---- #ahdi ,july #c4 ,july #gth1 #ahdi4 ,sir1 ,i have been given to understand that a friend of mine one whom ,i shall never be ashamed to acknowledge as #ah such tho' lowly his origine2 nay not only not ashamed but proud of doing so for ,i am one of those who esteem and respect a man according to his ability and probity1 deeming with ,dr4 ,watts 'that the mind is the standard of the man1'#dj has laid before you and asked your opinion of his extraordinary performance1 viz4 the quadrature of the circle1 he did this with the firmest belief that you would not only treat the matter in a straightforward manner but with the conviction that from your known or supposed knowledge of mathematicks would have given an upright and honorable decision upon the subject2 but the question is have you done so8 ,could ,i say yes ,i would with the greatest of pleasure and have congratulated you upon your decision whatever it might have been but ,i am sorry to say that ,i cannot your letter is a paltry evasion1 you say 'that it is a great pity that you 7,mr4 ----7 should have attempted this 7the quadrature of the circle7 for your mathematical knowledge is not sufficient to make you know in what the problem consists1' you don't say in what it does consist according to your ideas1 oh6 no nothing of the sort1 you enter into no disquisition upon the subject in order to show where you think ,mr4 ---- is wrong and why you have not is simply--because you cannot--you know that he has done it and what is if ,i am not wrongly informed you have been heard to say so4 ,he has done what you nor any other mathematician as those who call themselves such have done4 ,and what is the reason that you will not candidly acknowledge to him as you have to others that he has squared the circle shall ,i tell you8 it is because he has performed the feat to obtain the glory of which mathematicians have battled from time immemorial that they might encircle their brows with a wreath of laurels far more glorious than ever conqueror won it is simply this that it is a poor man a #ai humble artisan who has gained that victory that you don't like to acknowledge it you don't like to be beaten and worse to acknowledge that you have miscalculated1 you have in short too small a soul to acknowledge that he is right4 ,i was asked my opinion and ,i gave it unhesitatingly in the affirmative and ,i am backed in my opinion not only by ,mr4 ---- a mathematician and watchmaker residing in the boro of ,southwark but by no less an authority than the ,professor of mathematics of ---- ,college ---- ---- ,united ,states ,mr4 ---- and ,i presume that he at least is your equal as an authority and ,mr4 ---- says that the government of the ,u4,s4 will recompense ,m4 ,d4 for the discovery he has made if so what a reflection upon ,old england the boasted land of freedom the nursery of arts and sciences that her sons are obliged to go to a foreign country to obtain that recompense to which they are justly entitled ,in conclusion ,i had to contradict an assertion you made to the effect that 'there is not nor ever was any reward offered by the government of this country for the discovery of the quadrature of the circle4' ,i beg to inform you that there was but that it having been deemed an impossibility the government has withdrawn it4 ,i do this upon no less an authority than the ,marquis of ,northampton4#da ,i am1 sir1 yours ---- ,dr4 ,morgan4 ,,the ,,moon',s ,,rotation4 ,notes on the ,kinematic ,effects of ,revolution and ,rotation1 with reference to the ,motions of the ,moon and of the earth4 ,by ,henry ,perigal1 ,jun4 ,esq4 ,london1 #ahdf-ahdi1 #hvo4 ,on the misuse of technical terms4 ,ambiguity of the terms ,rotation and ,revolution1 owing to the double meaning improperly #bj attributed to each of the words4 7,no date nor place1 but by ,mr4 ,perigal1#db ,i have no doubt1 and containing letters of #ahdi and #ahej47 ,the moon controversy4 ,facts v4 ,definitions4 ,by ,h4 ,p41 ,jun4 ,london1 #ahef1 #hvo4 7pp4 #d47 ,mr4 ,henry ,perigal helped me twenty years ago with the diagrams1 direct from the lathe to the wood1 for the article ,trochoidal ,curves1 in the ,penny ,cyclopaedia3 these cuts add very greatly to the value of the article1 which1 indeed1 could not have been made intelligible without them4 ,he has had many years' experience1 as an amateur turner1 in combination of double and triple circular motions1 and has published valuable diagrams in profusion4 ,a person to whom the double circular motion is familiar in the lathe naturally looks upon one circle moving upon another as in simple motion1 if the second circle be fixed to the revolving radius1 so that one and the same point of the moving circle travels upon the fixed circle4 ,mr4 ,perigal commenced his attack upon the moon for moving about her axis1 in the first of the tracts above1 ten years before ,mr4 ,jellinger ,symons2#dc but he did not think it necessary to make it a subject for the ,times newspaper4 ,his familiarity with combined motions enabled him to handle his arguments much better than ,mr4 ,j4 ,symons could do3 in fact1 he is the clearest assailant of the lot which turned out with ,mr4 ,j4 ,symons4 ,but he is as wrong as the rest4 ,the assault is now1 ,i suppose1 abandoned1 until it becomes epidemic again4 ,this it will do3 it is one of those fallacies which are very tempting4 ,there was a dispute on the subject in #agdh1 between ,james ,ferguson#dd and an anonymous opponent2 and ,i think there have been others4 #ba ,a poet appears in the field 7,july #ai1 #ahfc7 who calls himself ,cyclops1 and writes four octavo pages4 ,he makes a distinction between rotation and revolution2 and his doctrines and phrases are so like those of ,mr4 ,perigal that he is a follower at least4 ,one of his arguments has so often been used that it is worth while to cite it3 ,would ,mathematicals--forsooth-- ,if true1 have failed to prove its truth8 ,would not they--if they could--submit ,some overwhelming proofs of it8 ,but still it totters proofless6 ,hence ,there's strong presumptive evidence ,none do--or can--such proof profound ,because the dogma is unsound4 ,for1 were there means of doing so1 ,they would have proved it long ago4 ,this is only one of the alternatives4 ,proof requires a person who can give and a person who can receive4 ,i feel inspired to add the following3 ,a blind man said1 ,as to the ,sun1 ,i'll take my ,bible oath there's none2 ,for if there had been one to show ,they would have shown it long ago4 ,how came he such a goose to be8 ,did he not know he couldn't see8 ,not he6 ,the absurdity of the verses is in the argument4 ,the writer was not so ignorant or so dishonest as to affirm that nothing had been offered by the other side as proof2 accordingly1 his syllogism amounts to this3 ,if your proposition were true1 you could have given proof satisfactory to me2 but this you have not done1 therefore1 your proposition is not true4 ,the echoes of the moon-controversy reached ,benares in #aheg1 in which year was there published a pamphlet ,does the ,moon ,rotate8 in ,sanskrit and ,english4 ,the #bb arguments are much the same as those of the discussion at home4 ,,on ,,the ,,names ,,of ,,religious ,,bodies4 ,we see that there are paradoxers in argument as well as in assertion of fact3 my plan does not bring me much into contact with these2 but another instance may be useful4 ,sects1 whether religious or political1 give themselves names which1 in meaning1 are claimed also by their opponents2 loyal1 liberal1 conservative 7of good71 etc4 have been severally appropriated by parties4 ,whig and ,tory are unobjectionable names3 the first--which occurs in ,english ballad as well as in ,scotland--is sour milk2#de the second is a robber4 ,in theology1 the ,greek ,church is ,orthodox1 the ,roman is ,catholic1 the modern ,puritan is ,evangelical1 etc4 ,the word ,christian 7,vol4 ,i1 p4 #bdhdf7 is an instance4 ,when words begin1 they carry their meanings4 ,the ,jews1 who had their ,messiah to come1 and the followers of ,jesus of ,nazareth1 who took ,him for their ,messiah1 were both ,christians 7which means ,messianites73 the ,jews would never have invented the term to signify ,jesuans1 nor would the disciples have invented such an ambiguous term for themselves2 had they done so1 the ,jews would have disputed it1 as they would have done in later times if they had had fair play4 ,the ,jews of our day1 ,i see by their newspapers1 speak of ,jesus ,christ as the ,rabbi ,joshua4 ,but the #bc heathens1 who knew little or nothing about the ,jewish hope1 would naturally apply the term ,christians to the only followers of a ,messiah of whom they had heard4 ,for the ,jesuans invaded them in a missionary way2 while the ,jews did not attempt1 at least openly1 to make proselytes4 ,all such words as ,catholic1 etc41 are well enough as mere nomenclature2 and the world falls for the most part1 into any names which parties choose to give themselves4 ,silly people found inferences on this concession2 and1 as usually happens1 they can cite some of their betters4 ,st4 ,augustine1#dg a freakish arguer1 or1 to put it in the way of an old writer1 lectorem ne multiloquii taedio fastidiat1 ,punicis quibusdam argutiis recreare solet1#dh asks1 with triumph1 to what chapel a stranger would be directed1 if he inquired the way to the ,catholic assembly4 ,but the best exhibition of this kind in our own century is that made by the excellent ,dr4 ,john ,milner1#di in a work 7first published in #ahja or #ahjb7 which ,i suppose still circulates1 ,the ,end of ,religious ,controversy3 a startling title which1 so far as its truth is concerned1 might as well have been ,the floor of the bottomless pit4 ,this writer1 whom every one of his readers will swear to have been a worthy soul1 though many1 even of his own sect1 will not admire some of his logic1 speaks as follows3 ,letter xxv4 ,on the true ,church being ,catholic4 ,in treating of this third mark of the true ,church1 as expressed in our common creed1 ,i feel my spirits sink within me1 and ,i am almost tempted to throw away my pen in despair4 ,for what chance is there of opening the eyes of candid ,protestants to the other marks of the ,church1 if they are capable of keeping them shut to this8 ,every time they address the #bd ,god of ,truth1 either in solemn worship or in private devotion stretch of rhetoric1 they are forced1 each of them1 to repeat3 ,i believe in ,,the ,,catholic ,church1 and yet if ,i ask any of them the question3 ,are you a ,,catholic8 he is sure to answer me1 ,no1 ,i am a ,,protestant6 ,was there ever a more glaring instance of inconsistency and self-condemnation among rational beings6 ,john ,milner1 honest and true1 ,did what honest people still may do1 ,if they write for the many and not for the few1 ,but what by and bye they must eschew4 ,he shortened his clause2 and for a reason4 ,if he had used the whole epithet which he knew so well1 any one might have given his argument a half-turn4 ,had he written1 as he ought1 the ,holy ,catholic ,church and then argued as above1 some sly ,protestant would have parodied him with and yet if ,i ask any of them the question3 ,are you ,,holy8 he is sure to answer me ,no1 ,i am a ,,sinner4 ,to take the adjective from the ,church1 and apply it to the individual partisan1 is recognized slipslop1 but not ground of argument4 ,if ,dr4 ,m4 had asked his ,protestant whether he belonged to the ,catholic ,church1 the answer would have been ,yes1 but not to the ,roman branch4 ,when he put his question as he did1 he was rightly answered and in his own division4 ,this leaving out words is a common practice1 especially when the omitter is in authority1 and cannot be exposed4 ,a year or two ago a bishop wrote a snubbing letter to a poor parson1 who had complained that he was obliged1 in burial1 to send the worst of sinners to everlasting happiness4 ,the bishop sternly said1 hope#ej is not assurance4 #be ,could the clergyman have dared to answer1 he would have said1 ,no1 my ,lord6 but 'sure and certain hope' is as like assurance as a minikin man is like a dwarf4 ,sad to say1 a theologian must be illogical3 ,i feel sure that if you took the clearest headed writer on logic that ever lived1 and made a bishop of him1 he would be shamed by his own books in a twelvemonth4 ,milner's sophism is glaring3 but why should ,dr4 ,milner be wiser than ,st4 ,augustine1 one of his teachers8 ,i am tempted to let out the true derivation of the word ,catholic1 as exclusively applied to the ,church of ,rome4 ,all can find it who have access to the ,rituale of ,bonaventura ,piscator#ea 7lib4 i4 c4 #ab1 de nomine ,sacrae ,ecclesiae1 p4 #hg of the ,venice #bf folio of #aecg74 ,i am told that there is a ,rituale in the ,index ,expurgatorius1 but ,i have not thought it worth while to examine whether this be the one3 ,i am rather inclined to think1 as ,i have heard elsewhere1 that the book was held too dangerous for the faithful to know of it1 even by a prohibition3 it would not surprise me at all if ,roman ,christians should deny its existence4#eb ,it amuses me to give1 at a great distance of time1 a small ,rowland for a small ,oliver1#ec which ,i received1 de par l',eglise1#ed so far as lay in the ,oliver-carrier more than twenty years ago4 ,the following contribution of mine to ,notes and ,queries 7#c;d ,ser4 vi4 p4 #age1 ,aug4 #bg1 #ahfd7 will explain what ,i say4 ,there had been a complaint that a contributor had used the term ,papist1 which a very excellent dignitary of the ,papal system pronounced an offensive term3 ,,papist4 ,the term papist should be stripped of all except its etymological meaning1 and applied to those who give the higher and final authority to the declaration ex cathedra#ee of the ,pope4 ,see ,dr4 ,wiseman's#ef article1 ,catholic ,church1 in the ,penny ,cyclopaedia4 ,what is one to do about these names8 ,first1 it is clear that offence should1 when possible1 be avoided3 secondly1 no one must be required to give a name which favors any assumption made by those to whom it is given1 and not #bg granted by those who give it4 ,thus the subdivision which calls itself distinctly ,evangelical has no right to expect others to concede the title4 ,now the word ,catholic1 of course1 falls under this rule2 and even ,roman ,catholic may be refused to those who would restrict the word ,catholic to themselves4 ,roman ,christian is unobjectionable1 since the ,roman ,church does not deny the name of ,christian to those whom she calls heretics4 ,no one is bound in this matter by ,acts of ,parliament4 ,in many cases1 no doubt1 names which have offensive association are used merely by habit1 sometimes by hereditary transmission4 ,boswell records of ,johnson that he always used the words dissenting teacher1 refusing minister and clergyman to all but the recipients of episcopal ordination4 ,this distinctive phrase has been widely adopted3 it occurs in the ,index of #c;d ,s4 iv4 ,notes and ,queries4 ,here we find ,platts 7,rev4 ,john71 ,unitarian teacher1 #dab2 the article indexed has ,unitarian minister4 ,this1 of course is habit3 an intentional refusal of the word minister would never occur in an index4 ,i remember that1 when ,i first read about ,sam ,johnson's little bit of exclusiveness1 ,i said to myself3 ,teacher8 ,teacher8 surely ,i remember ,one who is often called teacher1 but never minister or clergyman3 have not the dissenters got the best of it8 ,when ,i said that the ,roman ,church concedes the epithet ,christians to ,protestants1 ,i did not mean that all its adherents do the same4 ,there is1 or was1 a ,roman newspaper1 the ,tablet1 which1 seven or eight years ago1 was one of the most virulent of the party journals4 ,in it ,i read1 referring to some complaint of grievance about mixed marriages1 that if ,christians would marry ,protestants they must take the consequences4 ,my memory notes this well2 because ,i recollected1 when ,i saw it1 that there was in the stable a horse fit to run in the curricle with this one4 ,about seventeen years ago an ,oxford ,m4 ,a41 who hated #bh mathematics like a genuine ,oxonian of the last century1 was writing on education1 and was compelled to give some countenance to the nasty subject4 ,he got out cleverly2 for he gave as his reason for the permission1 that man is an arithmetical1 geometrical1 and mechanical animal1 as well as a rational soul4 ,the ,tablet was founded by an old pupil of mine1 ,mr4 ,frederic ,lucas1#eg who availed himself of his knowledge of me to write some severe articles--even abusive1 ,i was told1 but ,i never saw them--against me1 for contributing to the ,dublin ,review1 and poking my heretic nose into orthodox places4 ,dr4 ,wiseman1 the editor1 came in for his share1 and ought to have got all4 ,who ever blamed the pig for intruding himself into the cabin when the door was left open8 ,when ,mr4 ,lucas was my pupil1 he was of the ,society of ,friends--in any article but this ,i should say ,quaker--and was quiet and gentlemanly1 as members of that ,church--in any article but this ,i should1 from mere habit1 say sect--usually are4 ,this is due to his memory2 for1 by all ,i heard1 when he changed his religion he ceased to be ,lucas couchant1 and became ,lucas rampant1 fanged and langued gules4 7,i looked into ,guillim#eh to see if my terms were right3 ,i could not find them2 but to prove ,i have been there1 ,i notice that he calls a violin a violent4 ,how comes the word to take this form87 ,i met with several ,roman ,christians1 born and bred1 who were very much annoyed at ,mr4 ,lucas and his doings2 and said some severe things about new converts needing kicking-straps4 #bi ,the mention of ,dr4 ,wiseman reminds me of another word1 appropriated by ,christians to themselves3 fides2#ei the ,roman faith is fides1 and nothing else2 and the adherents are fideles4#fj ,hereby hangs a retort4 ,when ,dr4 ,wiseman was first in ,england1 he gave a course of lectures in defence of his creed1 which were thought very convincing by those who were already convinced4 ,they determined to give him a medal1 and there was a very serious discussion about the legend4 ,dr4 ,wiseman told me himself that he had answered to his subscribers that he would not have the medal at all unless--7naming some ,italian authority1 whom ,i forget7 approved of the legend4 ,at last pro fide vindicata#fa was chosen3 this may be read either in a ,popish or heretical sense4 ,the feminine substantive fides means confidence1 trust1 7it is made to mean belief71 but fidis1 with the same ablative1 fide1 and also feminine1 is a fiddle-string4#fb ,if a ,latin writer had had to make a legend signifying ,for the defence of the fiddle-string1 he could not have done it otherwise1 in the terseness of a legend1 than by writing pro fide vindicata4 ,accordingly1 when a ,roman ,christian talks to you of the faith1 as a thing which is his and not yours1 you may say fiddle4 ,i have searched ,bonaventura ,piscator in vain for notice of this ambiguity4 ,but the ,greeks said fiddle2 according to ,suidas1#fc ,greek3 skindapsos#fd--;a word meaning a four stringed instrument played with a quill--was an exclamation of contemptuous dissent4 ,how the wits of different races jump6 #cj ,i am reminded of a case of fides vindicata1 which1 being in a public letter1 responding to a public invitation1 was not meant to be confidential4 ,some of the pupils of ,university ,college1 in which all subdivisions of religion are 7#ahff2 were1 #ahfg7 on a level1 have of course changed their views in after life1 and become adherents of various high churches4 ,on the occasion of a dinner of old students of the ,college1 convened by circular1 one of these students1 whether then ,roman or ,tractarian ,christian ,i do not remember1 not content with simply giving negative answer1 or none at all1 concocted a jorum of theological rebuke1 and sent it to the ,dinner ,committee4 ,heyday6 said one of them1 this man got out of bed backwards6 ,how is that8 said the rest4 ,why1 read his name backwards1 and you will see4 ,as thus read it was--,no grub6#fe ,,the ,,word ,,church4 ,to return to ,notes and ,queries4 ,the substitution in the 7editorial7 index of ,unitarian teacher1 for the contributor's ,unitarian minister1 struck me very much4 ,i have seldom found such things unmeaning4 ,but as the journal had always been free from editorial sectarianisms1--and very apt to check the contributorial1--,i could not be sure in this case4 ,true it was1 that the editor and publisher had been changed more than a year before2 but this was not of much force4 ,though one swallow does not make a summer1 ,i have generally found it show that summer is coming4 ,however1 thought ,i to myself1 if this be ,little ,shibboleth1 we shall have ,big ,shibboleth by-and-bye4 ,at last it came4 ,about a twelvemonth afterwards1 7#c;d ,s4 vii4 p4 #cf7 the following was the editorial answer to the question when the establishment was first called the ,church of ,england and ,ireland3 #ca ,that unmeaning clause1 ',the ,united ,church of ,england and ,ireland1' which occurs on the title-page of ,the ,book of ,common ,prayer1 was first used at the commencement of the present century4 ,the authority for this phrase is the fifth article of the ,union of #ahjj3 ',that the ,churches of ,england and ,ireland be united into one ,protestant 767 episcopal ,church1 to be called ,the ,united ,church of ,england and ,ireland4' ,of course1 churchmen are not responsible for the theology of ,acts of ,parliament1 especially those passed during the dark ages of the ,georgian era4 ,that is to say1 the journal gives its adhesion to the party which--under the assumed title of the ,church of ,england--claims for the endowed corporation for the support of religion rights which ,parliament cannot control1 and makes it1 in fact1 a power above the ,state4 ,the ,state has given an inch3 it calls this corporation by the name of the ,united ,church of ,england and ,ireland1 as if neither ,england nor ,ireland had any other ,church4 ,the corporation1 accordingly aspires to an ell4 ,but this the nation will only give with the aspiration prefixed4 ,to illustrate my allusion in a delicate way to polite ears1 ,i will relate what happened in a ,johnian lecture-room at ,cambridge1 some fifty years ago1 my informant being present4 ,a youth of undue aspirations was giving a proposition1 and at last said1 ,let ,e ,f be produced to ',l'3 ,not quite so far1 ,mr4 ----1 said the lecturer1 quietly1 to the great amusement of the class1 and the utter astonishment of the aspirant1 who knew no more than a ,tractarian the tendency of his construction4 ,this word ,church is made to have a very mystical meaning4 ,the following dialogue between ,ecclesiastes and ,haereticus1 which ,i cannot vouch for1 has often taken place in spirit1 if not in letter3 ,e4 ,the word ,church 7,greek3 ekklesia7#ff is never used in the ,new ,testament except generally or locally for that holy and mystical body to which the sacraments and the ordinances of ,christianity are entrusted4 #cb ,h4 ,indeed6 ,e4 ,it is beyond a doubt 7here he quoted half a dozen texts in support74 ,h4 ,do you mean that any doctrine or ordinance which was solemnly practised by the ,greek3 ekklesia is binding upon you and me8 ,e4 ,certainly1 unless we should be cut off from the congregation of the faithful4 ,h4 ,have you a couple of hours to spare8 ,e4 ,what for8 ,h4 ,if you have1 ,i propose we spend them in crying1 ,great is ,diana of the ,ephesians6 ,e4 ,what do you mean8 ,h4 ,you ought to know the solemn service of the ,greek3 ekklesia 7,acts xix4 #cb1 #da71 at ,ephesus2 which any one might take to be true ,church1 by the more part not knowing wherefore they were come together1 and which was dismissed1 after one of the most sensible sermons ever preached1 by the ,recorder4 ,e4 ,i see your meaning3 it is true1 there is that one exception6 ,h4 ,why1 the ,recorder's sermon itself contains another1 the ,greek3 ennomos ekklesia1#fg legislative assembly4 ,e4 ,ah6 the ,new ,testament can only be interpreted by the ,church6 ,h4 ,i see6 the ,church interprets itself into existence out of the ,new ,testament1 and then interprets the ,new ,testament out of existence into itself6 ,i look upon all the ,churches as fair game which declare of me that absque dubio in aeternum peribo2#fh not for their presumption towards ,god1 but for their personal insolence towards myself4 ,i find that their sectaries stare when ,i say this4 ,why6 they do not speak of you in particular6 ,these poor reasoners seem to think that there could be no meaning1 as against me1 unless it should be propounded that without doubt he shall perish everlastingly1 especially ,a4 ,de ,morgan4 ,but ,i hold1 with the schoolmen1 that ,omnis homo est animal in conjunction with ,sortes est homo amounts to ,sortes est animal4#fi ,but they do not mean it personally6 ,every universal proposition is #cc personal to every instance of the subject4 ,if this be not conceded1 then ,i retort1 in their own sense and manner1 ,whosoever would serve ,god1 before all things he must not pronounce ,god's decision upon his neighbor4 ,which decision1 except every one leave to ,god himself1 without doubt he is a bigoted noodle4 ,the reasoning habit of the educated community1 in four cases out of five1 permits universal propositions to be stated at one time1 and denied1 pro re nata1#gj at another4 ,before we proceed to consider any question involving physical principles1 we should set out with clear ideas of the naturally possible and impossible4 ,the eminent man who said this1 when wanting it for his views of mental education 767 never meant it for more than what was in hand1 never assumed it in the researches which will give him to posterity6 ,i have heard half-a-dozen defences of his having said this1 not one of which affirmed the truth of what was said4 ,a worthy clergyman wrote that if ,a4 ,b4 had said a certain thing the point in question would have been established4 ,it was shown to him that ,a4 ,b4 had said it1 to which the reply was a refusal to admit the point because ,a4 ,b4 said it in a second pamphlet and in answer to objections4 ,and ,i might give fifty such instances with very little search4 ,always assume more than you want2 because you cannot tell how much you may want3 put what is over into the didn't-mean-that basket1 or the extreme case what-not4 ,,protestant ,,and ,,papal ,,christendom4 ,something near forty years of examination of the theologies on and off--more years very much on than quite off--have given me a good title--to myself1 ,i ask no one else for leave--to make the following remarks3 ,a conclusion has premises1 facts or doctrines from proof or authority1 and mode of inference4 ,there may be invention or #cd falsehood of premise1 with good logic2 and there may be tenable premise1 followed by bad logic2 and there may be both false premise and bad logic4 ,the ,roman system has such a powerful manufactory of premises1 that bad logic is little wanted2 there is comparatively little of it4 ,the doctrine-forge of the ,roman ,church is one glorious compound of everything that could make ,heraclitus#ga sob and ,democritus#gb snigger4 ,but not the only one4 ,the ,protestants1 in tearing away from the ,church of ,rome1 took with them a fair quantity of the results of the ,roman forge1 which they could not bring themselves to give up4 ,they had more in them of ,martin than of ,jack4 ,but they would have no premises1 except from the ,new ,testament2 though some eked out with a few general ,councils4 ,the consequence is that they have been obliged to find such a logic as would bring the conclusions they require out of the canonical books4 ,and a queer logic it is2 nothing but the ,roman forge can be compared with the ,protestant loom4 ,the picking1 the patching1 the piecing1 which goes to the ,protestant termini ad quem1#gc would be as remarkable to the general eye1 as the ,roman manufacture of termini a quo1#gd if it were not that the world at large seizes the character of an asserted fact better than that of a mode of inference4 ,a grand step towards the deification of a lady1 made by alleged revelation #ahjj years after her death1 is of glaring evidence3 two or three additional shiffle-shuffles towards defence of saying the ,athanasian curse in church and unsaying it out of church1 are hardly noticed4 ,swift has bungled his satire where he makes ,peter a party to finding out what he wants1 totidem syllabis and totidem literis1 #ce when he cannot find it totidem verbis#ge ,this is ,protestant method3 the ,roman plan is viam faciam2 the ,protestant plan is viam inveniam4#gf ,the public at large begins to be conversant with the ways of wriggling out1 as shown in the interpretations of the damnatory parts of the ,athanasian ,creed1 the phrases of the ,burial ,service1 etc4 ,the time will come when the same public will begin to see the ways of wriggling in4 ,but one thing at a time3 neither ,papal ,rome nor ,protestant ,rome was built--nor will be pulled down--in a day4 ,the distinction above drawn between the two great antitheses of ,christendom may be illustrated as follows4 ,two sets of little general dealers lived opposite to one another3 all sold milk4 ,each vaunted its own produce3 one set said that the stuff on the other side the way was only chalk and water2 the other said that the opposites sold all sorts of filth1 of which calves' brain was the least nasty4 ,now the fact was that both sets sold milk1 and from the same dairy3 but adulterated with different sorts of dirty water3 and both honestly believed that the mixture was what they were meant to sell and ought to sell4 ,the great difference between them1 about which the apprentices fought each other like ,trojans1 was that the calves' brain men poured milk into the water1 and the chalk men poured water into the milk4 ,the ,greek and ,roman sects on one side1 the ,protestant sects on the other1 must all have churches3 the ,greek and ,roman sects pour the ,new ,testament into their churches2 the ,protestant sects pour their churches into the ,new ,testament4 ,the ,greek and ,roman insist upon the ,new ,testament being no more than part and parcel of their churches3 the ,protestant insist upon their churches being as much part and parcel of the ,new ,testament4 ,all dwell vehemently upon the doctrine that there must be milk #cf somewhere2 and each says--,i have it4 ,the doctrine is true3 and can be verified by any one who can and will go to the dairy for himself4 ,him will the several traders declare to have no milk at all4 ,they will bring their own wares1 and challenge a trial3 they want nothing but to name the judges4 ,to vary the metaphor1 those who have looked at ,christianity in open day1 know that all who see it through painted windows shut out much of the light of heaven and color the rest2 it matters nothing that the stains are shaped into what are meant for saints and angels4 ,but there is another side to the question4 ,to decompose any substance1 it must be placed between the poles of the battery4 ,now theology is but one pole2 philosophy is the other4 ,no one can make out the combinations of our day unless he read the writings both of the priest and the philosopher3 and if any one should hold the first word offensive1 ,i tell him that ,i mean both words to be significant4 ,in reading these writings1 he will need to bring both wires together to find out what it is all about4 ,time was when most priests were very explicit about the fate of philosophers1 and most philosophers were very candid about their opinion of priests4 ,but though some extremes of the old sorts still remain1 there is now1 in the middle1 such a fusion of the two pursuits that a plain man is wofully puzzled4 ,the theologian writes a philosophy which seems to tell us that the ,new ,testament is a system of psychology2 and the philosopher writes a ,christianity which is utterly unintelligible as to the question whether the ,resurrection be a fact or a transcendental allegory4 ,what between the theologian who assents to the ,athanasian denunciation in what seems the sense of no denunciation1 and the philosopher who parades a ,christianity which looks like no revelation1 there is a maze which threatens to have the only possible clue in the theory that everything is something else1 and nothing is anything at all4 ,but this is a paradox far beyond my handling3 it is a ,budget of itself4 #cg ,,religion ,,and ,,philosophy4 ,religion and ,philosophy1 the two best gifts of ,heaven1 set up in opposition to each other at the revival of letters2 and never did competing tradesmen more grossly misbehave4 ,bad wishes and bad names flew about like swarms of wasps4 ,the ,athanasian curses were intended against philosophers2 who1 had they been a corporation1 with state powers to protect them1 would have formulized a per contra4 ,but the tradesmen are beginning to combine3 they are civil to each other2 too civil by half4 ,i speak especially of ,great ,britain4 ,old theology has run off to ritualism1 much lamenting1 with no comfort except the discovery that the cloak ,paul left at ,troas was a chasuble4 ,philosophy1 which always had a little sense sewed up in its garments--to pay for its funeral8--has expended a trifle in accommodating itself to the new system4 ,but the two are poles of a battery2 and a question arises4 ,if ,peter ,piper picked a peck of pepper1 ,where is the peck of pepper ,peter ,piper picked8 ,if ,religion and ,philosophy be the two poles of a battery1 whose is the battery ,religion and ,philosophy have been made the poles of8 ,is the change in the relation of the wires any presumption of a removal of the managers8 ,we know pretty well who handled the instrument3 has he resigned or been#gg turned out8 ,has he been put under #ch restriction8 ,a fool may ask more questions than twenty sages can answer3 but there is hope2 for twenty sages cannot ask more questions than one reviewer can answer4 ,i should like to see the opposite sides employed upon the question1 ,what are the commoda1 and what the pericula1#gh of the current approximation of ,religion and ,philosophy8 ,all this is very profane and irreverent6 ,it has always been so held by those whose position demands such holding4 ,to describe the ,church as it is passes for assailing the ,church as it ought to be with all who cannot do without it4 ,in ,bedlam#gi a poor creature who fancied he was ,st4 ,paul1 was told by another patient that he was an impostor2 the first maniac lodged a complaint against the second for calling ,st4 ,paul an impostor1 which1 he argued1 with much appearance of sanity1 ought not to be permitted in a well regulated madhouse4 ,nothing could persuade him that he had missed the question1 which was whether he was ,st4 ,paul4 ,the same thing takes place in the world at large4 ,and especially must be noted the refusal to permit to the profane the millionth part of the licence assumed by the sacred4 ,i give a sound churchman the epitaph of ,st4 ,john ,long2 the usual pronunciation of whose name must be noted-- ,behold6 ye quacks1 the vengeance strong ,on deeds like yours impinging3 ,for here below lies ,st4 ,john ,long#hj ,who now must be long singeing4 ,how shameful to pronounce this of the poor man6 ,what1 ,mr4 ,orthodox6 may ,i not do in joke to one pretender what #ci you do in earnest--unless you quibble--to all the millions of the ,greek ,church1 and a great many others4 ,enough of you and your reasoning6 ,go and square the circle6 ,the few years which end with #ahfg have shown1 not merely the intermediate fusion of ,theology and ,philosophy of which ,i have spoken1 but much concentration of the two extremes1 which looks like a gathering of forces for some very hard fought ,armageddon4 ,extreme theology has been aiming at a high ,church in ,england1 which is to show a new front to all heresy3 and extreme philosophy is contriving a physical organization which is to think1 and to show that mind is a consequence of matter1 or thought a recreation of brain4 ,the physical speculators begin with a possible hypothesis1 in which they aim at explanation3 and so the bold aspirations of the author of the ,vestiges find standing-ground in the variation of species by natural selection4 ,some relics--so supposed--of extremely ancient men are brought to help the general cause4 ,only distant hints are given that by possibility it may end in the formation of all living organisms from a very few1 if not from one4 ,the better heads above mentioned know that their theory1 if true1 does not bear upon morals4 ,the formation of solar systems from a nebular hypothesis1 followed by organizations gradually emerging from some curious play of particles1 nay1 the very evolution of mind and thought from such an apparatus1 are all as consistent with a ,personal creative power to whom homage and obedience are due1 and who has declared himself1 as with a blind ,nature of ,things4 ,a pure materialist1 as to all things visible1 may be even a bigotted ,christian3 this is not frequent1 but it is possible4 ,there is a proverb which says1 ,a pig may fly1 but it isn't a likely bird4 ,but when the psychological speculator comes in1 he often undertakes to draw inferences from the physical conclusions1 by joining on his tremendous apparatus of a priori knowledge4 ,he deduces that he can do without a ,god3 he can deduce all things #dj without any such necessity4 ,with ,occam#ha and ,newton he will have no more causes than are necessary to explain phenomena to him3 and if by pure head-work combined with results of physical observation he can construct his universe1 he must be a very unphilosophical man who would encumber himself with a useless ,creator6 ,there is something tangible about my method1 says he2 yours is vague4 ,he requires it to be granted that his system is positive and that yours is impositive4 ,so reasoned the stage coachman when the railroads began to depose him--,if you're upset in a stage-coach1 why1 there you are6 but if you're upset on the railroad1 where are you8 ,the answer lies in another question1 ,which is most positive knowledge1 ,god deduced from man and his history1 or the postulates of the few who think they can reason a priori on the tacit assumption of unlimited command of data8 ,we are not yet come to the existence of a school of philosophers who explicitly deny a ,creator3 but we are on the way1 though common sense may interpose4 ,there are always straws which show the direction of the wind4 ,i have before me the printed letter of a medical man--to whose professional ability ,i have good testimony--who finds the vital principle in highly rarefied oxygen4 ,with the usual logic of such thinkers1 he dismisses the eternal personal identity because ,if soul1 spirit1 mind1 which are merely modes of sensation1 be the attribute or function of nerve-tissue1 it cannot possibly have any existence apart from its material organism6 ,how does he know this impossibility8 ,if all the mind we know be from nerve-tissue1 how does it appear that mind in other planets may not be another thing8 ,nay1 when we come to possibilities1 does not his own system give a queer one8 ,if highly rarefied oxygen be vital power1 more highly rarefied oxygen #da may be more vital and more powerful4 ,where is this to stop8 ,is it impossible that a finite quantity1 rarefied ad infinitum1 may be an ,omnipotent8 ,perhaps the true ,genesis1 when written1 will open with ,in the beginning was an imperial quart of oxygen at #fj deg4 of ,fahrenheit1 and the pressure of the atmosphere2 and this oxygen was infinitely rarefied2 and this oxygen became ,god4 ,for myself1 my aspirations as to this system are ,manichaean4 ,the quart of oxygen is the ,ormuzd1 or good principle3 another quart1 of hydrogen1 is the ,ahriman1 or evil principle6 ,my author says that his system explains ,freewill and ,immortality so obviously that it is difficult to read previous speculations with becoming gravity4 ,my deduction explains the conflict of good and evil with such clearness that no one can henceforward read the ,new ,testament with becoming reverence4 ,the surgeon whom ,i have described is an early bud which will probably be nipped by the frost and wither on the ground3 but there is a good crop coming4 ,material pneuma is destined to high functions2 and man is to read by gas-light4 ,,the ,,sun ,,an ,,electric ,,space4 ,the solar system truly solved2 demonstrating by the perfect harmony of the planets1 founded on the four universal laws1 the ,sun to be an electric space2 and a source of every natural production displayed throughout the solar system4 ,by ,james ,hopkins4#hb ,london1 #ahdi1 #hvo4 ,the author says3 ,i am satisfied that ,i have given the true laws constituting the ,sun to be space2 and ,i call upon those disposed to maintain the contrary1 to give true laws showing him to be a body3 until such can be satisfactorily established1 ,i have an undoubted claim to the credit of my theory1--,that the ,sun is an ,electric ,space1 fed and governed by the #db planets1 which have the property of attracting heat from it2 and the means of supplying the necessary pabulum by their degenerated air driven off towards the central space--the wonderful alembic in which it becomes transmuted to the revivifying necessities of continuous action2 and the central space or ,sun being perfectly electric1 has the counter property of repulsing the bodies that attract it4 ,how wonderful a conception6 ,how beautiful1 how magnificent an arrangement6 ,o ,centre6 ,o ,space6 ,o ,electric ,space6 ,,joseph ,,ady4 #ahdi4 ,joseph ,ady#hc is entitled to a place in this list of discoverers3 his great fault1 like that of some others1 lay in pushing his method too far4 ,he began by detecting unclaimed dividends1 and disclosing them to their right owners1 exacting his fee before he made his communication4 ,he then generalized into trying to get fees from all of the name belonging to a dividend2 and he gave mysterious hints of danger impending4 ,for instance1 he would write to a clergyman that a legal penalty was hanging over him2 and when the alarmed divine forwarded the sum required for disclosure1 he was favored with an extract from some old statute or canon1 never repealed1 forbidding a clergyman to be a member of a corporation1 and was reminded that he had insured his life in the ---- ,office1 which had a royal charter4 ,he was facetious1 was ,joseph3 he described himself in his circulars as personally known to ,sir ,peter ,laurie#hd and all other aldermen2 which was nearly true1 #dc as he had been before most of them on charges of false pretence2 but ,i believe he was nearly always within the law4 ,sir ,james ,duke1 when ,lord ,mayor1 having particularly displeased him by a decision1 his circulars of #ahdi contain the following3 ,should you have cause to complain of any party1 ,sir ,j4 ,duke has contrived a new law of evidence1 viz41 write to him1 he will consider your letter sufficient proof1 and make the parties complained of pay without judge or jury1 and will frank you from every expense4 ,i strongly suspect that ,joseph ,ady believed in himself4 ,he sometimes issued a second warning1 of a ,sibylline character3 ,should you find cause to complain of anybody1 my voluntary referee1 the ,rt4 ,hon4 ,sir ,peter ,laurie1 ,kt41 perpetual ,deputy ,lord ,mayor1 will see justice done you without any charge whatever3 he and his toady1 -- ---- ----4 ,the accursed of ,moses can hang any man3 thus1 by catching him alone and swearing ,naboth spake evil against ,god and the ,king4 ,therefore 767 ,i admit no strangers to a personal conference without a prepayment of #bjs4 each4 ,had you attended to my former notice you would have received twice as much3 neglect this and you will lose all4 ,,on ,,modern ,,astrology4 ,zadkiel's ,almanac for #ahdi4 ,nineteenth number4 ,raphael's ,prophetic ,almanac for #ahdi4 ,twenty-ninth number4 ,reasons for belief in judicial astrology1 and remarks on the dangerous character of popish priestcraft4 ,london1 #ahdi1 #abmo4 ,astronomy in a nutshell3 or the leading problems of the solar system solved by simple proportion only1 on the theory of magnetic attraction4 ,by ,lieut4 ,morrison1#he ,n4 ,n4 ,london 7s4 a47 #abmo4 #dd ,lieut4 ,morrison is ,zadkiel ,tao ,sze1 and declares himself in real earnest an astrologer4 ,there are a great many books on astrology1 but ,i have not felt interest enough to preserve many of them which have come in my way4 ,if anything ever had a fair trial1 it was astrology4 ,the idea itself is natural enough4 ,a human being1 set down on this earth1 without any tradition1 would probably suspect that the heavenly bodies had something to do with the guidance of affairs4 ,i think that any one who tries will ascertain that the planets do not prophesy3 but if he should find to the contrary1 he will of course go on asking4 ,a great many persons class together belief in astrology and belief in apparitions3 the two things differ in precisely the way in which a science of observation differs from a science of experiment4 ,many make the mistake which ,m4 le ,marquis made when he came too late1 and hoped ,m4 ,cassini#hf would do the eclipse over again for his ladies4 ,the apparition chooses its own time1 and comes as seldom or as often as it pleases1 be it departed spirit1 nervous derangement1 or imposition4 ,consequently it can only be observed1 and not experimented upon4 ,but the heavens1 if astrology be true1 are prophesying away day and night all the year round1 and about every body4 ,experiments can be made1 then1 except only on rare phenomena1 such as eclipses3 anybody may choose his time and his question4 ,this is the great difference3 and experiments were made1 century after century4 ,if astrology had been true1 it must have lasted in an ever-improving state4 ,if it be true1 it is a truth1 and a useful truth1 which had experience and prejudice both in its favor1 and yet lost ground as soon as astronomy1 its working tool1 began to improve4 #ahej4 ,a letter in the handwriting of an educated man1 dated from a street in which it must be taken that educated persons live1 is addressed to the ,secretary of the #de ,astronomical ,society about a matter on which the writer says his professional pursuit will enable him to give a satisfactory reply4 ,in a question before a court of law it is sworn on one side that the moon was shining at a certain hour of a certain night on a certain spot in ,london2 on the other side it is affirmed that she was clouded4 ,the ,secretary is requested to decide4 ,this is curious1 as the question is not astrological4 ,persons still send to ,greenwich1 now and then1 to have their fortunes told4 ,in one case1 not very many years ago1 a young gentleman begged to know who his wife was to be1 and what fee he was to remit4 ,sometimes the astronomer turns conjurer for fun1 and his prophesies are fulfilled4 ,it is related of ,flamsteed#hg that an old woman came to know the whereabouts of a bundle of linen which had strayed4 ,flamsteed drew a circle1 put a square into it1 and gravely pointed out a ditch1 near her cottage1 in which he said it would be found4 ,he meant to have given the woman a little good advice when she came back3 but she came back in great delight1 with the bundle in her hand1 found in the very place4 ,the late ,baron ,zach#hh received a letter from ,pons1#hi a successful finder of comets1 complaining that for a certain period he had found no comets1 though he had searched diligently4 ,zach1 a man of much sly humor1 told him that no spots had been seen on the sun for about the same time--which was true1--and assured him that when the spots came back1 the comets would come with them4 ,some time after he got a letter #df from ,pons1 who informed him with great satisfaction that he was quite right1 that very large spots had appeared on the sun1 and that he had found a fine comet shortly after4 ,i do not vouch for the first story1 but ,i have the second in ,zach's handwriting4 ,it would mend the joke exceedingly if some day a real relation should be established between comets and solar spots3 of late years good reason has been shown for advancing a connection between these spots and the earth's magnetism4#ij ,if the two things had been put to ,zach1 he would probably have chosen the comets4 ,here is a hint for a paradox3 the solar spots are the dead comets1 which have parted with their light and heat to feed the sun1 as was once suggested4 ,i should not wonder if ,i were too late1 and the thing had been actually maintained4 ,my list does not contain the twentieth part of the possible whole4 ,the mention of coincidences suggests an everlasting source of explanations1 applicable to all that is extraordinary4 ,the great paradox of coincidence is that of ,leibnitz1 known as the pre-established harmony1 or law of coincidences1 by which1 separately and independently1 the body receives impressions1 and the mind proceeds as if it had perceived them from without4 ,every sensation1 and the consequent state of the soul1 are independent things coincident in time by the pre-established law4 ,the philosopher could not otherwise account for the connection of mind and matter2 and he never goes by so vulgar a rule as ,whatever is1 is2 to him that which is not clear as to how1 is not at all4 ,philosophers in general1 who tolerate each other's theories much better than ,christians do each other's failings1 seldom revive ,leibnitz's fantasy3 they seem to act upon the maxim quoted by ,father ,eustace#ia from the #dg ,decretals1 ,facinora ostendi dum puniuntur1 flagitia autem abscondi debent4#ib ,the great ghost-paradox1 and its theory of coincidences1 will rise to the surface in the mind of every one4 ,but the use of the word coincidence is here at variance with its common meaning4 ,when ,a is constantly happening1 and also ,b1 the occurrence of ,a and ,b at the same moment is the mere coincidence which may be casualty4 ,but the case before us is that ,a is constantly happening1 while ,b1 when it does happen1 almost always happens with ,a1 and very rarely without it4 ,that is to say1 such is the phenomenon asserted3 and all who rationally refer it to casualty1 affirm that ,b is happening very often as well as ,a1 but that it is not thought worthy of being recorded except when ,a is simultaneous4 ,of course ,a is here a death1 and ,b the spectral appearance of the person who dies4 ,in talking of this subject it is necessary to put out of the question all who play fast and loose with their secret convictions3 these had better give us a reason1 when they feel internal pressure for explanation1 that there is no weathercock at ,kilve2 this would do for all cases4 ,but persons of real inquiry will see that first1 experience does not bear out the asserted frequency of the spectre1 without the alleged coincidence of death3 and secondly1 that if the crowd of purely casual spectres were so great that it is no wonder that1 now and then the person should have died at or near the moment1 we ought to expect a much larger proportion of cases in which the spectre should come at the moment of the death of one or another of all the cluster who are closely connected with the original of the spectre4 ,but this1 we know1 is almost without example4 ,it remains then1 for all1 who speculate at all1 to look upon the asserted phenomenon1 think what they may of it1 the thing which is to be explained1 as a connection in time of the death1 and the #dh simultaneous appearance of the dead4 ,any person the least used to the theory of probabilities will see that purely casual coincidence1 the wrong spectre being comparatively so rare that it may be said never to occur1 is not within the rational field of possibility4 ,the purely casual coincidence1 from which there is no escape except the actual doctrine of special providences1 carried down to a very low point of special intention1 requires a junction of the things the like of each of which is always happening4 ,i will give three instances which have occurred to myself within the last few years3 ,i solemnly vouch for the literal truth of every part of all three3 ,in ,august #ahfa1 ,m4 ,senarmont1#ic of the ,french ,institute1 wrote to me to the effect that ,fresnel#id had sent to ,england1 in or shortly after #ahbd1 a paper for translation and insertion in the ,european ,review1 which shortly afterwards expired4 ,the question was what had become of that paper4 ,i examined the ,review at the ,museum1 found no trace of the paper1 and wrote back to that effect at the ,museum1 adding that everything now depended on ascertaining the name of the editor1 and tracing his papers3 of this ,i thought there was no chance4 ,i posted this letter on my way home1 at a ,post ,office in the ,hampstead ,road at the junction with ,edward ,street1 on the opposite side of which is a bookstall4 ,lounging for a moment over the exposed books1 sicut meus est mos1#ie ,i saw1 within a few minutes of the posting of the letter1 a little catch-penny book of anecdotes of ,macaulay1 which ,i bought1 and ran over for a minute4 ,my eye was soon caught by this sentence3 ,one of the young fellows immediately wrote to the editor 7,mr4 ,walker7 #di of the ,european ,review4 ,i thus got the clue by which ,i ascertained that there was no chance of recovering ,fresnel's paper4 ,of the mention of current reviews1 not one in a thousand names the editor4 ,in the summer of #ahfe ,i made my first acquaintance with the tales of ,nathaniel ,hawthorne1 and the first ,i read was about the siege of ,boston in the ,war of ,independence4 ,i could not make it out3 everybody seemed to have got into somebody else's place4 ,i was beginning the second tale1 when a parcel arrived3 it was a lot of old pamphlets and other rubbish1 as he called it1 sent by a friend who had lately sold his books1 had not thought it worth while to send these things for sale1 but thought ,i might like to look at them and possibly keep some4 ,the first thing ,i looked at was a sheet which1 being opened1 displayed ,a plan of ,boston and its environs1 shewing the true situation of his ,majesty's army and also that of the rebels1 drawn by an engineer1 at ,boston ,oct4 #agge4 ,such detailed plans of current sieges being then uncommon1 it is explained that ,the principal part of this plan was surveyed by ,richard ,williams1 ,lieutenant at ,boston2 and sent over by the son of a nobleman to his father in town1 by whose permission it was published4 ,i immediately saw that my confusion arose from my supposing that the king's troops were besieging the rebels1 when it was just the other way4 ,april #a1 #ahec1 while engaged in making some notes on a logical point1 an idea occurred which was perfectly new to me1 on the mode of conciliating the notions omnipresence and indivisibility into parts4 ,what it was is no matter here3 suffice it that1 since it was published elsewhere 7in a paper on ,infinity1 ,camb4 ,phil4 ,trans4 vol4 xi4 p4 #a7 ,i have not had it produced to me4 ,i had just finished a paragraph on the subject1 when a parcel came in from a bookseller containing ,heywood's#if ,analysis of ,kant's ,critick1 #ahdd4 #ej ,on turning over the leaves ,i found 7p4 #aji7 the identical thought which up to this day1 ,i only know as in my own paper1 or in ,kant4 ,i feel sure ,i had not seen it before1 for it is in ,kant's first edition1 which was never translated to my knowledge2 and it does not appear in the later editions4 ,mr4 ,heywood gives some account of the first edition4 ,in the broadsheet which gave account of the dying scene of ,charles ,,ii1 it is said that the ,roman ,catholic priest was introduced by ,p4 ,m4 ,a4 ,c4 ,f4 ,the chain was this3 the ,duchess of ,portsmouth#ig applied to the ,duke of ,york1 who may have consulted his ,cordelier confessor1 ,mansuete1 about procuring a priest1 and the priest was smuggled into the king's room by the ,duchess and ,chiffinch4#ih ,now the letters are a verbal acrostic of ,pere ,mansuete a ,cordelier ,friar1 and a syllabic acrostic of ,ports,mouth and ,chif,finch4 ,this is a singular coincidence4 ,macaulay adopted the first interpretation1 preferring it to the second1 which ,i brought before him as the conjecture of a near relative of my own4 ,but ,mansuete is not mentioned in his narrative3 it may well be doubted whether the writer of a broadside for ,english readers would use ,pere instead of ,father4 ,and the person who really reminded the ,duke of the duty he owed to his brother1 was the ,duchess and not ,mansuete4 ,but my affair is only with the coincidence4 ,but there are coincidences which are really connected without the connection being known to those who find in them matter of astonishment4 ,presentiments furnish marked cases3 sometimes there is no mystery to those who have the clue4 ,in the ,gentleman's ,magazine 7vol4 #hj1 part #b1 p4 #cc7 we read1 the subject being presentiment of death1 as follows3 ,in #aggh1 to come nearer the recollection of #ea survivors1 at the taking of ,pondicherry1 ,captain ,john ,fletcher1 ,captain ,de ,morgan1 and ,lieutenant ,bosanquet1 each distinctly foretold his own death on the morning of his fate4 ,i have no doubt of all three2 and ,i knew it of my grandfather long before ,i read the above passage4 ,he saw that the battery he commanded was unduly exposed3 ,i think by the sap running through the fort when produced4 ,he represented this to the engineer officers1 and to the commander-in-chief2 the engineers denied the truth of the statement1 the commander believed them1 my grandfather quietly observed that he must make his will1 and the ,french fulfilled his prediction4 ,his will bore date the day of his death2 and ,i always thought it more remarkable than the fulfilment of the prophecy that a soldier should not consider any danger short of one like the above1 sufficient reason to make his will4 ,i suppose the other officers were similarly posted4 ,i am told that military men very often defer making their wills until just before an action3 but to face the ordinary risks intestate1 and to wait until speedy death must be the all but certain consequence of a stupid mistake1 is carrying the principle very far4 ,in the matter of coincidences there are1 as in other cases1 two wonderful extremes with every intermediate degree4 ,at one end we have the confident people who can attribute anything to casual coincidence2 who allow ,zadok ,imposture and ,nathan ,coincidence to anoint ,solomon ,selfconceit king4 ,at the other end we have those who see something very curious in any coincidence you please1 and whose minds yearn for a deep reason4 ,a speculator of this class happened to find that ,matthew viii4 #bh-cc and ,luke viii4 #bf-cc contain the same account1 that of the demons entering into the swine4 ,very odd6 chapters tallying1 and verses so nearly3 is the versification rightly managed8 ,examination is sure to show that there are monstrous inconsistencies in the mode of division1 which being corrected1 the verses tally as well as the chapters4 ,and then how comes it8 ,i cannot go on1 #eb for ,i have no gift at torturing a coincidence1 but ,i would lay twopence1 if ,i could make a bet--which ,i never did in all my life--that some one or more of my readers will try it4 ,some people say that the study of chances tends to awaken a spirit of gambling3 ,i suspect the contrary4 ,at any rate1 ,i myself1 the writer of a mathematical book and a comparatively popular book1 have never laid a bet nor played for a stake1 however small3 not one single time4 ,it is useful to record such instances as ,i have given1 with precision and on the solemn word of the recorder4 ,when such a story as that of ,flamsteed is told1 a priori assures us that it could not have been3 the story may have been a ben trovato1#ii but not the bundle4 ,it is also useful to establish some of the good jokes which all take for inventions4 ,my friend ,mr4 ,j4 ,bellingham ,inglis1#ajj before #ahjj1 saw the tobacconist's carriage with a sample of tobacco in a shield1 and the motto ,quid rides#aja 7,n4 ,q41 #c;d ,s4 i4 #bde74 ,his father was able to tell him all about it4 ,the tobacconist was ,jacob ,brandon1 well known to the elder ,mr4 ,inglis1 and the person who started the motto1 the instant he was asked for such a thing1 was ,harry ,calender of ,lloyd's1 a scholar and a wit4 ,my friend ,mr4 ,h4 ,crabb ,robinson#ajb remembers the ,king's ,counsel 7,samuel ,marryat7 who took the motto ,causes produce effects1 when his success enabled him to start a carriage4 ,the coincidences of errata are sometimes very remarkable3 it may be that the misprint has a sting4 ,the death of ,sir ,w4 ,hamilton#ajc of ,edinburgh was known in ,london on a ,thursday1 and the editor of the ,athenaeum wrote to #ec me in the afternoon for a short obituary notice to appear on ,saturday4 ,i dashed off the few lines which appeared without a moment to think3 and those of my readers who might perhaps think me capable of contriving errata with meaning will1 ,i am sure1 allow the hurry1 the occasion1 and my own peculiar relation to the departed1 as sufficient reasons for believing in my entire innocence4 ,of course ,i could not see a proof3 and two errata occurred4 ,the words addition to ,stewart#ajd require for addition to read edition of4 ,this represents what had been insisted on by the ,edinburgh publisher1 who1 frightened by the edition of ,reid1#aje had stipulated for a simple reprint without notes4 ,again principles of logic and mathematics required for mathematics read metaphysics4 ,no four words could be put together which would have so good a title to be ,hamilton's motto4 ,april #ahej1 found in the letter-box1 three loose leaves1 well printed and over punctuated1 being ,chapter ,,vi4 ,brethren1 lo ,i come1 holding forth the word of life1 for so ,i am commanded4444 ,chapter ,,vii4 ,hear my prayer1 ,o generations6 and walk by the way1 to drink the waters of the river4444 ,chapter ,,viii4 ,hearken o earth1 earth1 earth1 and the kings of the earth1 and their armies4444 ,a very large collection might be made of such apostolic writings4 ,they go on well enough in a misty--meant for mystical--imitation of ,st4 ,paul or the prophets1 until at last some prodigious want of keeping shows the education of the writer4 ,for example1 after half a page which might #ed pass for ,irving's#ajf preaching--though a person to whom it was presented as such would say that most likely the head and tail would make something more like head and tail of it--we are astounded by a declaration from the ,holy ,spirit1 speaking of himself1 that he is not ashamed of the ,gospel of ,christ4 ,it would be long before we should find in educated rhapsody--of which there are specimens enough--such a thing as a person of the ,trinity taking merit for moral courage enough to stand where ,st4 ,peter fell4 ,the following declaration comes next--,i will judge between cattle and cattle1 that use their tongues4 ,,the ,,figure ,,of ,,the ,,earth4 ,the figure of the earth4 ,by ,j4 ,l4 ,murphy1#ajg of ,birmingham4 7,london and ,birmingham1 #d pages1 #abmo47 7#ahej87 ,mr4 ,murphy invites attention and objection to some assertions1 as that the earth is prolate1 not oblate4 ,if the philosopher's conclusion be right1 then the pole is the center of a valley 767 thirteen miles deep4 ,hence it would be very warm4 ,it is answer enough to ask--,who knows that it is not8 999999 ,a paragraph in the ,,ms4 appears to have been inserted in this place by mistake4 ,it will be found in the ,appendix at the end of this volume4--,s4 ,e4 ,de ,m4 ,,perpetual ,,motion4 #ahea4 ,the following letter was written by one of a class of persons whom1 after much experience of them1 ,i #ee do not pronounce insane4 ,but in this case the second sentence gives a suspicion of actual delusion of the senses2 the third looks like that eye for the main chance which passes for sanity on the ,stock ,exchange and elsewhere3 #aeth ,sept4 #ahea4 ,gentlemen1--,i pray you take steps to make known that yesterday ,i completed my invention which will give motion to every country on the ,earth2--to move ,machinery6--the long sought in vain ',perpetual ,motion'66--,i was supported at the time by the ,queen and ,h4,r4,h4 ,prince ,albert4 ,if1 ,gentlemen1 you can advise me how to proceed to claim the reward1 if any is offered by the ,government1 or how to secure the ,,patent for the machine1 or in any way assist me by advice in this great work1 ,i shall most graciously acknowledge your consideration4 ,these are my convictions that my ,,several discoveries will be realized3 and this great one can be at once acted upon3 although at this moment it only exists in my mind1 from my knowledge of certain fixed principles in nature3--the ,machine ,i have not made1 as ,i only completed the discovery ,,yesterday1 ,sunday6 ,i have1 etc4 ---- ---- ,to the ,directors of the ,london ,university1 ,gower ,street4 ,,on ,,spiritualism4 ,the ,divine ,drama of ,history and ,civilisation4 ,by the ,rev4 ,james ,smith1 ,m4,a4#ajh ,london1 #ahed1 #hvo4 ,i have several books on that great paradox of our day1 ,spiritualism1 but ,i shall exclude all but three4 ,the bibliography of this subject is now very large4 ,the question is one both of evidence and speculation2--,are the facts #ef true8 ,are they caused by spirits8 ,these ,i shall not enter upon3 ,i shall merely recommend this work as that of a spiritualist who does not enter on the subject1 which he takes for granted1 but applies his derived views to the history of mankind with learning and thought4 ,mr4 ,smith was a man of a very peculiar turn of thinking4 ,he was1 when alive1 the editor1 or an editor1 of the ,family ,herald3 ,i say when alive1 to speak according to knowledge2 for1 if his own views be true1 he may have a hand in it still4 ,the answers to correspondents1 in his time1 were piquant and original above any ,i ever saw4 ,i think a very readable book might be made out of them1 resembling ,guesses at ,truth3 the turn given to an inquiry about morals1 religion1 or socials1 is often of the highest degree of unexpectedness2 the poor querist would find himself right in a most unpalatable way4 ,answers to correspondents1 in newspapers1 are very often the fag ends of literature4 ,i shall never forget the following4 ,a person was invited to name a rule without exception1 if he could3 he answered ,a man must be present when he is shaved4 ,a lady--what right have ladies to decide questions about shaving8--said this was not properly a rule2 and the oracle was consulted4 ,the editor agreed with the lady2 he said that a man must be present when he is shaved is not a rule1 but a fact4 ,among my anonymous communicants is one who states that ,i have done injustice to the ,rev4 ,james ,smith in referring to him as a spiritualist1 and placing his ,divine ,drama among paradoxes3 it is no paradox1 nor do spiritualistic views mar or weaken the execution of the design4 ,quite true3 for the design is to produce and enforce spiritualistic views2 and leather does not mar nor weaken a shoemaker's plan4 ,i knew ,mr4 ,smith well1 and have often talked to him on the subject3 but more testimony from me is unnecessary2 his book will speak for itself4 #eg ,his peculiar style will justify a little more quotation than is just necessary to prove the point4 ,looking at the battle of opinion now in progress1 we see that ,mr4 ,smith was a prescient3 7,p4 #ehh47 ,from the general review of parties in ,england1 it is evident that no country in the world is better prepared for the great ,battle of ,opinion4 ,where else can the battle be fought but where the armies are arrayed8 ,and here they all are1 ,greek1 ,roman1 ,anglican1 ,scotch1 ,lutheran1 ,calvinist1 ,established and ,territorial1 with ,baronial ,bishops1 and ,nonestablished of every grade--churches with living prophets and apostles1 and churches with dead prophets and apostles1 and apostolical churches without apostles1 and philosophies without either prophets or apostles1 and only wanting one more1 'the ,christian ,church1' like ,aaron's rod1 to swallow up and digest them all1 and then bud and flourish4 ,as if to prepare our minds for this desirable and inevitable consummation1 different parties have been favored with a revival of that very spirit of revelation by which the ,church itself was originally founded4 ,there is a complete series of spiritual revelations in ,england and the ,united ,states1 besides mesmeric phenomena that bear a resemblance to revelation1 and thus gradually open the mind of the philosophical and infidel classes1 as well as the professed believers of that old revelation which they never witnessed in living action1 to a better understanding of that ,law of ,nature 7for it is a ,law of ,nature7 in which all revelation originates and by which its spiritual communications are regulated4 ,mr4 ,smith proceeds to say that there are only thirty-five incorporated churches in ,england1 all formed from the ,new ,testament except five1 to each of which five he concedes a revelation of its own4 ,the five are the ,quakers1 the ,swedenborgians1 the ,southcottians1 the ,irvingites1 and the ,mormonites4 ,of ,joanna ,southcott he speaks as follows3 #eh 7,p4 #eib47 ,joanna ,southcott#aji is not very gallantly treated by the gentlemen of the ,press1 who1 we believe1 without knowing anything about her1 merely pick up their idea of her character from the rabble4 ,we once entertained the same rabble idea of her2 but having read her works--for we really have read them--we now regard her with great respect4 ,however1 there is a great abundance of chaff and straw to her grain2 but the grain is good1 and as we do not eat either the chaff or straw if we can avoid it1 nor even the raw grain1 but thrash it and winnow it1 and grind it and bake it1 we find it1 after undergoing this process1 not only very palatable1 but a special dainty of its kind4 ,but the husk is an insurmountable obstacle to those learned and educated gentlemen who judge of books entirely by the style and the grammar1 or those who eat grain as it grows1 like the cattle4 ,such men would reject all prological revelation2 for there never was and probably never will be a revelation by voice and vision communicated in classical manner4 ,it would be an invasion of the rights and prerogatives of ,humanity1 and as contrary to the ,divine and ,established order of mundane government1 as a field of quartern loaves or hot ,french rolls4 ,mr4 ,smith's book is spiritualism from beginning to end2 and my anonymous gainsayer1 honest of course1 is either ignorant of the work he thinks he has read1 or has a most remarkable development of the organ of imperception4 ,a ,,condensed ,,history ,,of ,,mathematics4 ,i cut the following from a ,sunday paper in #ahdi3 ,x4 ,y4--,the ,chaldeans began the mathematics1 in which the ,egyptians excelled4 ,then crossing the sea1 by means #ei of ,thales1#aaj the ,milesian1 they came into ,greece1 where they were improved very much by ,pythagoras1#aaa ,anaxagoras1#aab and ,anopides#aac of ,chios4 ,these were followed by ,briso1#aad ,antipho1 two circle-squarers2 where is ,euclid8 and ,hippocrates1#aae but the excellence of the algebraic art was begun by ,geber1#aaf an ,arabian astronomer1 and was carried on by ,cardanus1#aag ,tartaglia1#aah ,clavius1#aai1 ,stevinus1#abj ,ghetaldus1#aba ,herigenius1#abb ,fran4 ,van ,schooten meaning ,francis ,van ,schooten#abc1 ,florida de ,beaume1#abd etc4 ,bryso was a mistaken man4 ,antipho had the disadvantage of being in advance of his age4 ,he had the notion of which the modern geometry has made so much1 that of #fj a circle being the polygon of an infinitely great number of sides4 ,he could make no use of it1 but the notion itself made him a sophist in the eyes of ,aristotle1 ,eutocius1#abe etc4 ,geber1 an ,arab astronomer1 and a reputed conjurer in ,europe1 seems to have given his name to unintelligible language in the word gibberish4 ,at one time algebra was traced to him2 but very absurdly1 though ,i have heard it suggested that algebra and gibberish must have had one inventor4 ,any person who meddles with the circle may find himself the crane who was netted among the geese3 as ,antipho for one1 and ,olivier de ,serres#abf for another4 ,this last gentleman ascertained1 by weighing1 that the area of the circle is very nearly that of the square on the side of the inscribed equilateral triangle3 which it is1 as near as #c4afb 444 to #c4ada4444 ,he did not pretend to more than approximation2 but ,montucla and others misunderstood him1 and1 still worse1 misunderstood their own misunderstanding1 and made him say the circle was exactly double of the equilateral triangle4 ,he was let out of limbo by ,lacroix1 in a note to his edition of ,montucla's ,history of ,quadrature4 ,,st4 ,,vitus1 ,,patron ,,of ,,cyclometers4 ,quadratura del cerchio1 trisezione dell' angulo1 et duplicazione del cubo1 problemi geometricamente risolute e dimostrate dal ,reverendo ,arciprete di ,san ,vito ,d4 ,domenico ,anghera1#abg ,malta1 #ahed1 #hvo4 #fa ,equazioni geometriche1 estratte dalla lettera del ,rev4 ,arciprete 444 al ,professore ,pullicino#abh sulla quadratura del cerchio4 ,milan1 #ahee or #ahef1 #hvo4 ,il ,mediterraneo gazetta di ,malta1 #bf ,decembre #ahee1 ,no4 #iji3 also #iaa1 #iab1 #iac1 #iad1 #icf1 #ici4 ,the ,malta ,times1 ,tuesday1 #ith ,june #aheg4 ,misura esatta del cerchio1 dal ,rev4 ,d4 ,anghera4 ,malta1 #aheg1 #abmo4 ,quadrature of the circle 444 by the ,rev4 ,d4 ,anghera1 ,archpriest of ,st4 ,vito4 ,malta1 #aheh1 #abmo4 ,i have looked for ,st4 ,vitus in catalogues of saints1 but never found his legend1 though he figures as a day-mark in the oldest almanacs4 ,he must be properly accredited1 since he was an archpriest4 ,and ,i pronounce and ordain1 by right accruing from the trouble ,i have taken in this subject1 that he1 ,st4 ,vitus1 who leads his votaries a never-ending and unmeaning dance1 shall henceforth be held and taken to be the patron saint of the circle-squarer4 ,his day is the #aeth of ,june1 which is also that of ,st4 ,modestus1#abi with whom the said circle-squarer often has nothing to do4 ,and he must not put himself under the first saint with a slantendicular reference to the other1 as is much to be feared was done by the ,cardinal who came to govern ,england with a title containing ,st4 ,pudentiana1#acj who shares a day with ,st4 ,dunstan4 ,the ,archpriest of ,st4 ,vitus will have it that the square inscribed in a semicircle is half of the semicircle1 or the circumference #c-a_/e diameters4 ,he is active and able1 with #fb nothing wrong about him except his paradoxes4 ,in the second tract named he has given the testimonials of crowned heads and ministers1 etc4 as follows4 ,louis-,napoleon gives thanks4 ,the minister at ,turin refers it to the ,academy of ,sciences1 and hopes so much labor will be judged degna di pregio4#aca ,the ,vice-,chancellor of ,oxford--a blunt ,englishman--begs to say that the ,university has never proposed the problem1 as some affirm4 ,the ,prince ,regent of ,baden has received the work with lively interest4 ,the ,academy of ,vienna is not in a position to enter into the question4 ,the ,academy of ,turin offers the most distinct thanks4 ,the ,academy della ,crusca attends only to literature1 but gives thanks4 ,the ,queen of ,spain has received the work with the highest appreciation4 ,the ,university of ,salamanca gives infinite thanks1 and feels true satisfaction in having the book4 ,lord ,palmerston gives thanks1 by the hand of ,william ,san4 ,the ,viceroy of ,egypt1 not being yet up in ,italian1 will spend his first moments of leisure in studying the book1 when it shall have been translated into ,french3 in the mean time he congratulates the author upon his victory over a problem so long held insoluble4 ,all this is seriously published as a rate in aid of demonstration4 ,if these royal compliments cannot make the circumference of a circle about #b per cent4 larger than geometry will have it --which is all that is wanted--no wonder that thrones are shaky4 ,i am informed that the legend of ,st4 ,vitus is given by ,ribadeneira#acb in his lives of ,saints1 and that ,baronius1#acc in #fc his ,martyrologium ,romanum1 refers to several authors who have written concerning him4 ,there is an account in ,mrs4 ,jameson's#acd ,history of ,sacred and ,legendary ,art 7ed4 of #ahfc1 p4 #edd74 ,but it seems that ,st4 ,vitus is the patron saint of all dances2 so that ,i was not so far wrong in making him the protector of the cyclometers4 ,why he is represented with a cock is a disputed point1 which is now made clear3 next after gallus gallinaceus#ace himself1 there is no crower like the circle-squarer4 ,,celebrated ,,approximations ,,of pi4 ,the following is an extract from the ,english ,cyclopaedia1 ,art4 ,,tables3 #ahec4 ,william ,shanks1#acf ,contributions to ,mathematics1 comprising chiefly the ,rectification of the ,circle to #fjg ,places of ,tables1 ,london1 #ahec4 7,,quadrature ,,of ,,the ,,circle47 ,here is a table1 because it tabulates the results of the subordinate steps of this enormous calculation as far as #ebg decimals3 the remainder being added as results only during the printing4 ,for instance1 one step is the calculation of the reciprocal of #fja4efja2 and the result is given4 ,the number of pages required to describe these results is #hg4 ,mr4 ,shanks has also thrown off1 as chips or splinters1 the values of the base of ,napier's logarithms1 and of its logarithms of #b1 #c1 #e1 #aj1 to #acg decimals2 and the value of the modulus 4#dcdb 444 to #acf decimals3 with the #acth1 #beth1 #cgth 444 up to the #gbast powers of #b4 ,these tremendous stretches of calculation--at least we so call them in our day--are useful in several respects2 they prove more than #fd the capacity of this or that computer for labor and accuracy2 they show that there is in the community an increase of skill and courage4 ,we say in the community3 we fully believe that the unequalled turnip which every now and then appears in the newspapers is a sufficient presumption that the average turnip is growing bigger1 and the whole crop heavier4 ,all who know the history of the quadrature are aware that the several increases of numbers of decimals to which pi has been carried have been indications of a general increase in the power to calculate1 and in courage to face the labor4 ,here is a comparison of two different times4 ,in the day of ,cocker1#acg the pupil was directed to perform a common subtraction with a voice-accompaniment of this kind3 '#g from #d ,i cannot1 but add #aj1 #g from #ad remains #g1 set down #g and carry #a2 #h and #a which ,i carry is #i1 #i from #b ,i cannot1 etc4' ,we have before us the announcement of the following table1 undated1 as open to inspection at the ,crystal ,palace1 ,sydenham1 in two diagrams of #g ft4 #b in1 by #f ft4 #f in43 ',the figure #i involved into the #iabth power1 and antecedent powers or involutions1 containing upwards of #gc1jjj figures4 ,also1 the proofs of the above1 containing upwards of #adf1jjj figures4 ,by ,samuel ,fancourt1 of ,mincing ,lane1 ,london1 and completed by him in the year #ahcg1 at the age of sixteen4 ,n4,b4 ,the whole operation performed by simple arithmetic4' ,the young operator calculated by successive squaring the #b;d1 #dth1 #hth1 etc41 powers up to the #eabth1 with proof by division4 ,but #eaa multiplications by #i1 in the short 7or #aj-a7 way1 would have been much easier4 ,the #b;d1 #cb;d1 #fdth1 #abhth1 #befth1 and #eabth powers are given at the back of the announcement4 ,the powers of #b have been calculated for many purposes4 ,in ,vol4 ,,ii of his ,magia ,universalis ,naturae et ,artis1 ,herbipoli1 #afeh1 #dto1 the ,jesuit ,gaspar ,schott#ach having discovered1 on some grounds of theological #fe magic1 that the degrees of grace of the ,virgin ,mary were in number the #befth power of #b1 calculated that number4 ,whether or no his number correctly represented the result he announced1 he certainly calculated it rightly1 as we find by comparison with ,mr4 ,shanks4 ,there is a point about ,mr4 ,shanks's #fjh figures of the value of pi which attracts attention1 perhaps without deserving it4 ,it might be expected that1 in so many figures1 the nine digits and the cipher would occur each about the same number of times2 that is1 each about #fa times4 ,but the fact stands thus3 #c occurs #fh times2 #i and #b occur #fg times each2 #d occurs #fd times2 #a and #f occur #fb times each2 #j occurs #fj times2 #h occurs #eh times2 #e occurs #ef times2 and #g occurs only #dd times4 ,now1 if all the digits were equally likely1 and #fjh drawings were made1 it is #de to #a against the number of sevens being as distant from the probable average 7say #fa7 as #dd on one side or #gh on the other4 ,there must be some reason why the number #g is thus deprived of its fair share in the structure4 ,here is a field of speculation in which two branches of inquirers might unite4 ,there is but one number which is treated with an unfairness which is incredible as an accident2 and that number is the mystic number seven6 ,if the cyclometers and the apocalyptics would lay their heads together until they come to a unanimous verdict on this phenomenon1 and would publish nothing until they are of one mind1 they would earn the gratitude of their race4--,i was wrong3 it is the ,pyramid-speculator who should have been appealed to4 ,a correspondent of my friend ,prof4 ,piazzi ,smyth#aci notices that #c is the number of most frequency1 and that #c-a_/g is the nearest approximation to it in simple digits4 ,professor ,smyth himself1 whose word on ,egypt is paradox of a very high order1 backed by a great quantity of useful labor1 the results which will be made available by those who do not receive #ff the paradoxes1 is inclined to see confirmation for some of his theory in these phenomena4 ,,curious ,,calculations4 ,these paradoxes of calculation sometimes appear as illustrations of the value of a new method4 ,in #ahfc1 ,mr4 ,g4 ,suffield1#adj ,m4,a41 and ,mr4 ,j4 ,r4 ,lunn1#ada ,m4,a41 of ,clare ,college and of ,st4 ,john's ,college1 ,cambridge1 published the whole quotient of #ajjjj 444 divided by #gfii1 throughout the whole of one of the recurring periods1 having #gfih digits4 ,this was done in illustration of ,mr4 ,suffield's method of ,synthetic division4 ,another instance of computation carried to paradoxical length1 in order to illustrate a method1 is the solution of x#c - #bx #e1 the example given of ,newton's method1 on which all improvements have been tested4 ,in #ahca1 ,fourier's#adb posthumous work on equations showed #cc figures of solution1 got with enormous labor4 ,thinking this a good opportunity to illustrate the superiority of the method of ,w4 ,g4 ,horner1#adc not yet known in ,france1 and not much known in #fg ,england1 ,i proposed to one of my classes1 in #ahda1 to beat ,fourier on this point1 as a ,christmas exercise4 ,i received several answers1 agreeing with each other1 to #ej places of decimals4 ,in #ahdh1 ,i repeated the proposal1 requesting that #ej places might be exceeded3 ,i obtained answers of #ge1 #fe1 #fc1 #eh1 #eg1 and #eb places4 ,but one answer1 by ,mr4 ,w4 ,harris ,johnston1#add of ,dundalk1 and of the ,excise ,office1 went to #aja decimal places4 ,to test the accuracy of this1 ,i requested ,mr4 ,johnston to undertake another equation1 connected with the former one in a way which ,i did not explain4 ,his solution verified the former one1 but he was unable to see the connection1 even when his result was obtained4 ,my reader may be as much at a loss3 the two solutions are3 #b4jideeadhaedbcbfe444 #i4jeddheahdegfgcdj444 ,the results are published in the ,mathematician1 ,vol4 ,,iii1 p4 #bij4 ,in #ahea1 another pupil of mine1 ,mr4 ,j4 ,power ,hicks1#ade carried the result to #aeb decimal places1 without knowing what ,mr4 ,johnston had done4 ,the result is in the ,english ,cyclopaedia1 article ,,involution ,,and ,,evolution4 ,i remark that when ,i write the initial of a ,christian name1 the most usual name of that initial is understood4 ,i never saw the name of ,w4 ,g4 ,horner written at length1 until ,i applied to a relative of his1 who told me that he was1 as ,i supposed1 ,wm4 ,george1 but that he was named after a relative of that surname4 ,the square root of #b1 to #aaj decimal places1 was given #fh me in #aheb by my pupil1 ,mr4 ,william ,henry ,colvill1 now 7#ahfg7 ,civil ,surgeon at ,baghdad4 ,it was #a4dadbacefbcgcjiejdhhjafhhgbdbjifihjghe fif #gahgecgfidhjgcagffgigcgiijgcbdghdfbajgj c #hhejchgecdcbgfdaegbgcejachdfbc ,mr4 ,james ,steel#adf of ,birkenhead verified this by actual multiplication1 and produced #b - #behjdac _/ #ajaag as the square4 ,calcolo decidozzinale del ,barone ,silvio ,ferrari4 ,turin1 #ahed1 #dto4 ,this is a serious proposal to alter our numeral system and to count by twelves4 ,thus #aj would be twelve1 #aa thirteen1 etc41 two new symbols being invented for ten and eleven4 ,the names of numbers must of course be changed4 ,there are persons who think such changes practicable4 ,i thought this proposal absurd when ,i first saw it1 and ,i think so still3#adg but the one ,i shall presently describe beats it so completely in that point1 that ,i have not a smile left for this one4 ,,on ,,comets4 ,the successful and therefore probably true theory of ,comets4 ,london1 #ahed4 7#dpp4 duodecimo47 ,the author is the late ,mr4 ,peter ,legh1#adh of ,norbury ,booths ,hall1 ,knutsford1 who published for eight or ten #fi years the ,ombrological ,almanac1 a work of asserted discovery in meteorology4 ,the theory of comets is that the joint attraction of the new moon and several planets in the direction of the sun1 draws off the gases from the earth1 and forms these cometic meteors4 ,but how these meteors come to describe orbits round the sun1 and to become capable of having their returns predicted1 is not explained4 ,a ,,new ,,phase ,,of ,,mormonism4 ,the ,mormon1 ,new ,york1 ,saturday1 ,oct4 #bg1 #ahee4 ,a newspaper headed by a grand picture of starred and striped banners1 beehive1 and eagle surmounting it4 ,a scroll on each side3 on the left1 ,mormon creed4 ,mind your own business4 ,brigham ,young2#adi on the right1 ,given by inspiration of ,god4 ,joseph ,smith4#aej ,a leading article on the discoveries of ,prof4 ,orson ,pratt#aea says1 ,mormonism has long taken the lead in religion3 it will soon be in the van both in science and politics4 ,at the beginning of the paper is ,professor ,pratt's ,law of ,planetary ,rotation4 ,the cube roots of the densities of the planets are as the square roots of their periods of rotation4 ,the squares of the cube roots of the masses divided by the squares of the diameters are as the periods of rotation4 ,arithmetical verification attempted1 and the whole very modestly stated #gj and commented on4 ,dated ,g4 ,s4 ,l4 ,city1 ,utah ,ter41 ,aug4 #a1 #ahee4 ,if the creed1 as above1 be correctly given1 no wonder the ,mormonites are in such bad odor4 ,,mathematical ,,illustrations ,,of ,,doctrine4 ,the two estates2 or both worlds mathematically considered4 ,london1 #ahee1 small 7pp4 #af74 ,the author has published mathematical works with his name4 ,the present tract is intended to illustrate mathematically a point which may be guessed from the title4 ,but the symbols do very little in the way of illustration3 thus1 x being the present value of the future estate 7eternal happiness71 and a of all that this world can give1 the author impresses it on the mathematician that1 x being infinitely greater than a1 x a x1 so that a need not be considered4 ,this will not act much more powerfully on a mathematician by virtue of the symbols than if those same symbols had been dispensed with3 even though1 as the author adds1 ,it was this method of neglecting infinitely small quantities that ,sir ,isaac ,newton was indebted to for his greatest discoveries4 ,there has been a moderate quantity of well-meant attempt to enforce1 sometimes motive1 sometimes doctrine1 by arguments drawn from mathematics1 the proponents being persons unskilled in that science for the most part4 ,the ground is very dangerous3 for the illustration often turns the other way with greater power1 in a manner which requires only a little more knowledge to see4 ,i have1 in my life1 heard from the pulpit or read1 at least a dozen times1 that all sin is infinitely great1 proved as follows4 ,the greater the being1 the greater the sin of any offence against him3 therefore the offence committed against an infinite being is infinitely great4 ,now the mathematician1 of which the proposers of this argument are not aware1 is perfectly familiar with quantities which increase together1 and never cease increasing1 but so that one of them remains finite when #ga the other becomes infinite4 ,in fact1 the argument is a perfect non sequitur4#aeb ,those who propose it have in their minds1 though in a cloudy and indefinite form1 the idea of the increase of guilt being proportionate to the increase of greatness in the being offended4 ,but this it would never do to state3 for by such statement not only would the argument lose all that it has of the picturesque1 but the asserted premise would have no strong air of exact truth4 ,how could any one undertake to appeal to conscience to declare that an offence against a being #d-g_/aj times as great as another is exactly1 no more and no less1 #d-g_/aj times as great an offence against the other8 ,the infinite character of the offence against an infinite being is laid down in ,dryden's ,religio ,laici1#aec and is1 no doubt1 an old argument3 ,for1 granting we have sinned1 and that th' offence ,of man is made against ,omnipotence1 ,some price that bears proportion must be paid1 ,and infinite with infinite be weighed4 ,see then the ,deist lost2 remorse for vice ,not paid2 or1 paid1 inadequate in price4 ,dryden1 in the words bears proportion is in verse more accurate than most of the recent repeaters in prose4 ,and this is not the only case of the kind in his argumentative poetry4 ,my old friend1 the late ,dr4 ,olinthus ,gregory1#aed who was a sound and learned mathematician1 adopted this dangerous kind of illustration in his ,letters on the ,christian ,religion4 #gb ,he argued1 by parallel1 from what he supposed to be the necessarily mysterious nature of the impossible quantity of algebra to the necessarily mysterious nature of certain doctrines of his system of ,christianity4 ,but all the difficulty and mystery of the impossible quantity is now cleared away by the advance of algebraical thought3 and yet ,dr4 ,gregory's book continues to be sold1 and no doubt the illustration is still accepted as appropriate4 ,the mode of argument used by the author of the tract above named has a striking defect4 ,he talks of reducing this world and the next to present value1 as an actuary does with successive lives or next presentations4 ,does value make interest8 and if not1 why8 ,and if it do1 then the present value of an eternity is not infinitely great4 ,who is ignorant that a perpetual annuity at five per cent is worth only twenty years' purchase8 ,this point ought to be discussed by a person who treats heaven as a deferred perpetual annuity4 ,i do not ask him to do so1 and would rather he did not2 but if he will do it1 he must either deal with the question of discount1 or be asked the reason why4 ,when a very young man1 ,i was frequently exhorted to one or another view of religion by pastors and others who thought that a mathematical argument would be irresistible4 ,and ,i heard the following more than once1 and have since seen it in print1 ,i forget where4 ,since eternal happiness belonged to the particular views in question1 a benefit infinitely great1 then1 even if the probability of their arguments were small1 or even infinitely small1 yet the product of the chance and benefit1 according to the usual rule1 might give a result which no one ought in prudence to pass over4 ,they did not see that this applied to all systems as well as their own4 ,i take this argument to be the most perverse of all the perversions ,i have heard or read on the subject3 there is some high authority for it1 whom ,i forget4 ,the moral of all this is1 that such things as the preceding should be kept out of the way of those who are not #gc mathematicians1 because they do not understand the argument2 and of those who are1 because they do4 ,the high authority referred to above is ,pascal1 an early cultivator of mathematical probability1 and obviously too much enamoured of his new pursuit4 ,but he conceives himself bound to wager on one side or the other4 ,to the argument 7,pensees1 ch4 #g7aee that le juste est de ne point parier1 he answers1 ,oui3 mais il faut parier3 vous etes embarque2 et ne parier point que ,dieu est1 c'est parier qu'il n'est pas4#aef ,leaving ,pascal's argument to make its way with a person who1 being a sceptic1 is yet positive that the issue is salvation or perdition1 if a ,god there be1--for the case as put by ,pascal requires this1--,i shall merely observe that a person who elects to believe in ,god1 as the best chance of gain1 is not one who1 according to ,pascal's creed1 or any other worth naming1 will really secure that gain4 ,i wonder whether ,pascal's curious imagination ever presented to him in sleep his convert1 in the future state1 shaken out of a red-hot dice-box upon a red-hot hazard-table1 as perhaps he might have been1 if ,dante had been the later of the two4 ,the original idea is due to the elder ,arnobius1#aeg who1 as cited by ,bayle1#aeh speaks thus3 ,sed et ipse ,christus quae pollicetur1 non probat4 ,ita est4 ,nulla enim1 ut dixi1 futurorum potest existere comprobatio4 ,cum ergo haec sit conditio futurorum1 ut teneri et comprehendi nullius possint anticipationis attactu2 nonne #gd purior ratio est1 ex duobus incertis1 et in ambigua expectatione pendentibus1 id potius credere1 quod aliquas spes ferat1 quam omnino quod nullas8 ,in illo enim periculi nihil est1 si quod dicitur imminere1 cassum fiat et vacuum3 in hoc damnum est maximum1 id est salutis amissio1 si cum tempus advenerit aperiatur non fuisse mendacium4#aei ,really ,arnobius seems to have got as much out of the notion1 in the third century1 as if he had been fourteen centuries later1 with the arithmetic of chances to help him4 ,,novum ,,organum ,,moralium4 ,the ,sentinel1 vol4 ix4 no4 #bg4 ,london1 ,saturday1 ,may #bf1 #ahee4 ,this is the first ,london number of an ,irish paper1 ,protestant in politics4 ,it opens with ,suggestions on the subject of a ,novum ,organum ,moralium1 which is the application of algebra and the differential calculus to morals1 socials1 and politics4 ,there is also a leading article on the subject1 and some applications in notes to other articles4 ,a separate publication was afterwards made1 with the addition of a long ,preface2 the author being a clergyman who ,i presume must have been the editor of the ,sentinel4 ,suggestions as to the employment of a ,novum ,organum ,moralium4 ,or1 thoughts on the nature of the ,differential ,calculus1 and on the application of its principles to metaphysics1 with a view to the attainment of demonstration and certainty in moral1 #ge political and ecclesiastical affairs4 ,by ,tresham ,dames ,gregg1#afj ,chaplain of ,st4 ,mary's1 within the church of ,st4 ,nicholas intra muros1 ,dublin4 ,london1 #ahei1 #hvo4 7pp4 xl #cb74 ,i have a personal interest in this system1 as will appear from the following extract from the newspaper3 ,we were subsequently referred to ,de ,morgan's ,formal ,logic and ,boole's ,laws of ,thought#afa both very elaborate works1 and greatly in the direction taken by ourselves4 ,that the writers amazingly surpass us in learning we most willingly admit1 but we venture to pronounce of both their learned treatises1 that they deal with the subject in a mode that is scholastic to an excess4444 ,that their works have been for a considerable space of time before the world and effected nothing1 would argue that they have overlooked the vital nature of the theme4444 ,on the whole1 the writings of ,de ,morgan and ,boole go to the full justification of our principle without in any wise so trenching upon our ground as to render us open to reproach in claiming our ,calculus as a great discovery4444 ,but we renounce any paltry jealousy as to a matter so vast4 ,if ,de ,morgan and ,boole have had a priority in the case1 to them we cheerfully shall resign the glory and honor4 ,if such be the truth1 they have neither done justice to the discovery1 nor to themselves quite true4 ,they have1 under the circumstances1 acted like 'the foolish man1 who roasteth not that which he taketh #gf in hunting4444 ,it will be sufficient for us1 however1 to be the ,columbus of these great ,americi1 and popularize what they found1 if they found it4 ,we1 as from the mountain top1 will then become their trumpeters1 and cry glory to ,de ,morgan and glory to ,boole1 under ,him who is the source of all glory1 the only good and wise1 to ,whom be glory for ever6 ,if they be our predecessors in this matter1 they have1 under ,him1 taken moral questions out of the category of probabilities1 and rendered them perfectly certain4 ,in that case1 let their books be read by those who may doubt the principles this day laid before the world as a great discovery1 by our newspaper4 ,our cry shall be ,greek3 eurekasi6#afb ,let us hope that they will join us1 and henceforth keep their light sic from under their bushel4 ,for myself1 and for my old friend ,mr4 ,boole1 who ,i am sure would join me1 ,i disclaim both priority1 simultaneity1 and posteriority1 and request that nothing may be trumpeted from the mountain top except our abjuration of all community of thought or operation with this ,novum ,organum4 ,to such community we can make no more claim than ,americus could make to being the forerunner of ,columbus who popularized his discoveries4 ,we do not wish for any ,greek3 eurekasi and not even for ,greek3 heurekasi4 ,for self and ,boole1 ,i point out what would have convinced either of us that this house is divided against itself4 ,alpha being an apostolic element1 delta the doctrinal element1 and ,chi the body of the faithful1 the church is ,alpha delta ,chi1 we are told4 ,also1 that if ,alpha become negative1 or the ,apostolicity become ,diabolicity my words2 or if delta become negative1 and doctrine become heresy2 or if ,chi become negative1 that is1 if the faithful become unfaithful2 the church becomes negative1 the very opposite to what it ought to be4 ,for self and ,boole1 ,i admit this4 ,but--which is not noticed--if ,alpha and delta should both become negative1 diabolical origin #gg and heretical doctrine1 then the church1 ,alpha delta ,chi1 is still positive1 what it ought to be1 unless ,chi be also negative1 or the people unfaithful to it1 in which case it is a bad church4 ,now1 self and ,boole--though ,i admit ,i have not asked my partner--are of opinion that a diabolical church with false doctrine does harm when the people are faithful1 and can do good only when the people are unfaithful4 ,we may be wrong1 but this is what we do think4 ,accordingly1 we have caught nothing1 and can therefore roast nothing of our own3 ,i content myself with roasting a joint of ,mr4 ,gregg's larder4 ,these mathematical vagaries have uses which will justify a large amount of quotation3 and in a score of years this may perhaps be the only attainable record4 ,i therefore proceed4 ,after observing that by this calculus juries 7heaven help them6 say ,i7 can calculate damages almost to a nicety1 and further that it is made abundantly evident that c e x is the general expression for an individual1 it is noted that the number of the ,beast is not given in the ,revelation in words at length1 but as ,greek3 chxw'4#afc ,on this the following remark is made3 ,can it be possible that we have in this case a specimen given to us of the arithmetic of heaven1 and an expression revealed1 which indicates by its function of addibility1 the name of the church in question1 and of each member of it2 and by its function of multiplicability the doctrine1 the mission1 and the members of the great ,synagogue of ,apostacy8 ,we merely propound these questions2--we do not pretend to solve them4 ,after a translation in blank verse--a very pretty one--of the #ahth ,psalm1 the author proceeds as follows1 to render it into differential calculus3 #gh ,and the whole tells us just this1 that ,david did what he could4 ,he augmented those elements of his constitution which were 7exceptis excipiendis7#afd subject to himself1 and the ,almighty then augmented his personal qualities1 and his vocational status4 ,otherwise1 to throw the matter into the expression of our notation1 the variable e was augmented1 and c x rose proportionally4 ,the law of the variation1 according to our theory1 would be thus expressed4 ,the resultant was ,david the king c e x c r8 7who had been ,david the shepherd boy71 and from the conditions of the theorem we have du_/de ce7dx_/de7 ex7dc_/de7x cx which1 in the terms of ordinary language1 just means1 the increase of ,david's educational excellence or qualities--his piety1 his prayerfulness1 his humility1 obedience1 etc4--was so great1 that when multiplied by his original talent and position1 it produced a product so great as to be equal in its amount to royalty1 honor1 wealth1 and power1 etc43 in short1 to all the attributes of majesty4#afe ,the solution of the family problem is of high interest4 ,it is to determine the effect on the family in general from a change of conduct in one of them4 ,the person chosen is one of the maid-servants4 ,let c e x be the father2 c#a;e#ax#a the mother1 etc4 ,the family then consists of the maid's master1 her mistress1 her young master1 her young mistress1 and fellow servant4 ,now the master's calling 7or c7 is to exercise his share of control over this servant1 and mind the rest of his business3 call this remainder a1 and let his calling generally1 or all his affairs1 be to his maid-servant as m 3 y1 i4e41 y 7mz_/c72 444 #gi and this expression will represent his relation to the servant4 ,consequently1 c e x 7a mz_/c7e x2 otherwise 7a mz_/c7e x is the expression for the father when viewed as the girl's master4 ,i have no objection to repeat so far2 but ,i will not give the formula for the maid's relation to her young master2 for ,i am not quite sure that all young masters are to be trusted with it4 ,suffice it that the son will be affected directly as his influence over her1 and inversely as his vocational power3 if then he should have some influence and no vocational power1 the effect on him would be infinite4 ,this is dismal to think of4 ,further1 the formula brings out that if one servant improve1 the other must deteriorate1 and vice versa4 ,this is not the experience of most families3 and the author remarks as follows3 ,that is1 we should venture to say1 a very beautiful result1 and we may say it yielded us no little astonishment4 ,what our calculation might lead to we never dreamt of2 that it should educe a conclusion so recondite that our unassisted power never could have attained to1 and which1 if we could have conjectured it1 would have been at best the most distant probability1 that conclusion being itself1 as it would appear1 the quintessence of truth1 afforded us a measure of satisfaction that was not slight4 ,that the writings of ,mr4 ,boole and myself go to the full justification of this principle1 is only true in the sense in which the ,scotch use1 or did use1 the word justification4 ,a ,,tribute ,,to ,,boole4 ,the last number of this ,budget had stood in type for months1 waiting until there should be a little cessation of correspondence more connected with the things of the day4 #hj ,i had quite forgotten what it was to contain2 and little thought1 when ,i read the proof1 that my allusions to my friend ,mr4 ,boole1 then in life and health1 would not be printed till many weeks after his death4 ,had ,i remembered what my last number contained1 ,i should have added my expression of regret and admiration to the numerous obituary testimonials1 which this great loss to science has called forth4 ,the system of logic alluded to in the last number of this series is but one of many proofs of genius and patience combined4 ,i might legitimately have entered it among my paradoxes1 or things counter to general opinion3 but it is a paradox which1 like that of ,copernicus1 excited admiration from its first appearance4 ,that the symbolic processes of algebra1 invented as tools of numerical calculation1 should be competent to express every act of thought1 and to furnish the grammar and dictionary of an all-containing system of logic1 would not have been believed until it was proved4 ,when ,hobbes1#aff in the time of the ,commonwealth1 published his ,computation or ,logique1 he had a remote glimpse of some of the points which are placed in the light of day by ,mr4 ,boole4 ,the unity of the forms of thought in all the applications of reason1 however remotely separated1 will one day be matter of notoriety and common wonder3 and ,boole's name will be remembered in connection with one of the most important steps towards the attainment of this knowledge4 ,,decimals ,,run ,,riot4 ,the ,decimal ,system as a whole4 ,by ,dover ,statter4#afg ,london and ,liverpool1 #ahef1 #hvo4 #ha ,the proposition is to make everything decimal4 ,the day1 now #bd hours1 is to be made #aj hours4 ,the year is to have ten months1 ,unusber1 ,duober1 etc4 ,fortunately there are ten commandments1 so there will be neither addition to1 nor deduction from1 the moral law4 ,but the twelve apostles6 ,even rejecting ,judas1 there is a whole apostle of difficulty4 ,these points the author does not touch4 ,,on ,,phonetic ,,spelling4 ,the first book of ,phonetic ,reading4 ,london1 ,fred4 ,pitman1#afh ,phonetic ,depot1 #bj1 ,paternoster ,row1 #ahef1 #abmo4 ,the ,phonetic ,journal4 ,devoted to the propagation of phonetic reading1 phonetic longhand1 phonetic shorthand1 and phonetic printing4 ,no4 #df4 ,saturday1 #ae ,november #ahef4 ,vol4 #ae4 ,i write the titles of a couple out of several tracts which ,i have by me4 ,but the number of publications issued by the promoters of this spirited attempt is very large indeed4#afi ,the attempt itself has had no success with the mass of the public4 ,this ,i do not regret4 ,had the world found that the change was useful1 ,i should have gone contentedly with the stream2 but not without regretting our old language4 ,i admit the difficulties which our unpronounceable spelling puts in the way of learning to read3 and ,i have no doubt that1 as affirmed1 it is easier to teach children phonetically1 and afterwards to introduce them to our common system1 than to proceed in the usual way4 ,but by the usual way ,i mean proceeding by letters from the very beginning4 ,if1 which ,i am sure is a better plan1 children be taught at the commencement very much by complete words1 as if they were learning ,chinese1 and be gradually accustomed to #hb resolve the known words into letters1 a fraction1 perhaps a considerable one1 of the advantage of the phonetic system is destroyed4 ,it must be remembered that a phonetic system can only be an approximation4 ,the differences of pronunciation existing among educated persons are so great1 that1 on the phonetic system1 different persons ought to spell differently4 ,but the phonetic party have produced something which will immortalize their plan3 ,i mean their shorthand1 which has had a fraction of the success it deserves4 ,all who know anything of shorthand must see that nothing but a phonetic system can be worthy of the name3 and the system promulgated is skilfully done4 ,were ,i a young man ,i should apply myself to it systematically4 ,i believe this is the only system in which books were ever published4 ,i wish some one would contribute to a public journal a brief account of the dates and circumstances of the phonetic movement1 not forgetting a list of the books published in shorthand4 ,a child beginning to read by himself may owe terrible dreams and waking images of horror to our spelling1 as ,i did when six years old4 ,in one of the common poetry-books there is an admonition against confining little birds in cages1 and the child is asked what if a great giant1 amazingly strong1 were to take you away1 shut you up1 ,and feed you with vic-tu-als you ne-ver could bear4 ,the book was hyphened for the beginner's use2 and ,i had not the least idea that vic-tu-als were vittles3 by the sound of the word ,i judged they must be of iron2 and it entered into my soul4 ,the worst of the phonetic shorthand book is that they nowhere1 so far as ,i have seen1 give all the symbols1 in every stage of advancement1 together1 in one or following pages4 ,it is symbols and talk1 more symbols and more talk1 etc4 ,a universal view of the signs ought to begin the works4 #hc ,a ,,handful ,,of ,,little ,,paradoxers4 ,ombrological ,almanac4 ,seventeenth year4 ,an essay on ,anemology and ,ombrology4 ,by ,peter ,legh1#agj ,esq4 ,london1 #ahef1 #abmo4 ,mr4 ,legh1 already mentioned1 was an intelligent country gentleman1 and a legitimate speculator4 ,but the clue was not reserved for him4 ,the proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the circle4 ,by ,gen4 ,perronet ,thompson4 ,london1 #ahef1 #hvo4 7pp4 #d47 ,another attempt1 the third1 at this old difficulty1 which cannot be put into few words of explanation4#aga ,comets considered as volcanoes1 and the cause of their velocity and other phenomena thereby explained4 ,london 7circa #ahef71 #hvo4 ,the title explains the book better than the book explains the title4 #ahef4 ,a stranger applied to me to know what the ideas of a friend of his were worth upon the magnitude of the earth4 ,the matter being one involving points of antiquity1 ,i mentioned various persons whose speculations he seemed to have ignored2 among others1 ,thales4 ,the reply was1 ,i am instructed by the author to inform you that he is perfectly acquainted with the works of ,thales1 ,euclid1 ,archimedes1 444 ,i had some thought of asking whether he had used the ,elzevir edition of ,thales1#agb which is known to be very incomplete1 or that of ,professor ,niemand with the lections1 ,nirgend1 #ahbd1 #b vols4 folio2 just to see whether the #hd last would not have been the very edition he had read4 ,but ,i refrained1 in mercy4 ,the moon is the image of the ,earth1 and is not a solid body4 ,by ,the ,longitude4#agc 7,private ,circulation47 ,in five parts4 ,london1 #ahef1 #aheg1 #aheg2 ,calcutta1 #aheh1 #aheh1 #hvo4 ,the earth is brought to a focus2 it describes a looped orbit round the sun4 ,the eclipse of the sun is thus explained3 ,at the time of eclipses1 the image is more or less so directly before or behind the earth that1 in the case of new moon1 bright rays of the sun fall and bear upon the spot where the figure of the earth is brought to a focus1 that is1 bear upon the image of the earth1 when a darkness beyond is produced reaching to the earth1 and the sun becomes more or less eclipsed4 ,how the earth is brought to a focus we do not find stated4 ,writers of this kind always have the argument that some things which have been ridiculed at first have been finally established4 ,those who put into the lottery had the same kind of argument2 but were always answered by being reminded how many blanks there were to one prize4 ,i am loath to pronounce against anything3 but it does force itself upon me that the author of these tracts has drawn a blank4 ,,lunar ,,motion ,,again4 ,times1 ,april #f or #g1 #ahef4 ,the moon has no rotary motion4 ,a letter from ,mr4 ,jellinger ,symons1#agd inspector of schools1 which commenced a controversy of many letters and pamphlets4 ,this dispute comes on at intervals1 and will continue to do so4 ,it sometimes arises from inability to understand the character of simple rotation1 geometrically2 sometimes from not understanding the mechanical doctrine of rotation4 #he ,lunar ,motion4 ,the whole argument stated1 and illustrated by diagrams2 with letters from the ,astronomer ,royal4 ,by ,jellinger ,c4 ,symons4 ,london1 #ahef1 #hvo4 ,the ,astronomer ,royal endeavored to disentangle ,mr4 ,j4 ,c4 ,symons1 but failed4 ,mr4 ,airy#age can correct the error of a ship's compasses1 because he can put her head which way he pleases3 but this he cannot do with a speculator4 ,mr4 ,symons1 in this tract1 insinuated that the rotation of the moon is one of the silver shrines of the craftsmen4 ,to see a thing so clearly as to be satisfied that all who say they do not see it are telling wilful falsehood1 is the nature of man4 ,many of all sects find much comfort in it1 when they think of the others2 many unbelievers solace themselves with it against believers2 priests of old time founded the right of persecution upon it1 and of our time1 in some cases1 the right of slander3 many of the paradoxers make it an argument against students of science4 ,but ,i must say for men of science1 for the whole body1 that they are fully persuaded of the honesty of the paradoxers4 ,the simple truth is1 that all those ,i have mentioned1 believers1 unbelievers1 priests1 paradoxers1 are not so sure they are right in their points of difference that they can safely allow themselves to be persuaded of the honesty of opponents4 ,those who know demonstration are differently situated4 ,i suspect a train might be laid for the formation of a better habit in this way4 ,we know that ,suvaroff#agf taught his ,russians at ,ismail not to fear the ,turks by accustoming them to charge bundles of faggots dressed in turbans1 etc4 ,at which your wise men sneered in phrases witty1 ,he made no answer--but he took the city6 ,would it not be a good thing to exercise boys1 in pairs1 in the following dialogue3--,sir1 you are quite wrong6--,sir1 #hf ,i am sure you honestly think so6 ,this was suggested by what used to take place at ,cambridge in my day4 ,by statute1 every ,b4,a4 was obliged to perform a certain number of disputations1 and the father of the college had to affirm that it had been done4 ,some were performed in earnest3 the rest were huddled over as follows4 ,two candidates occupied the places of the respondent and the opponent3 ,recte statuit ,newtonus1 said the respondent3 ,recte non statuit ,newtonus1#agg said the opponent4 ,this was repeated the requisite number of times1 and counted for as many acts and opponencies4 ,the parties then changed places1 and each unsaid what he had said on the other side of the house3 ,i remember thinking that it was capital drill for the ,house of ,commons1 if any of us should ever get there4 ,the process was repeated with every pair of candidates4 ,the real disputations were very severe exercises4 ,i was badgered for two hours with arguments given and answered in ,latin1--or what we called ,latin--against ,newton's first section1 ,lagrange's#agh derived functions1 and ,locke#agi on innate principles4 ,and though ,i took off everything1 and was pronounced by the moderator to have disputed magno honore1#ahj ,i never had such a strain of thought in my life4 ,for the inferior opponents were made as sharp as their betters by their tutors1 who kept lists of queer objections1 drawn from all quarters4 ,the opponents used to meet the day before to compare their arguments1 that the same might not come twice over4 ,but1 after ,i left ,cambridge1 it became the fashion to invite the respondent to be present1 who therefore learnt all that was to be brought against him4 ,this made the whole thing a farce3 and the disputations were abolished4 #hg ,the ,doctrine of the ,moon's ,rotation1 considered in a letter to the ,astronomical ,censor of the ,athenaeum4 ,by ,jones ,l4 ,mac,elshender4#aha ,edinburgh1 #ahef1 #hvo4 ,this is an appeal to those cultivated persons who will read it to overrule the dicta of judges who would sacrifice truth and justice to professional rule1 or personal pique1 pride1 or prejudice2 meaning1 the great mass of those who have studied the subject4 ,but how8 ,suppose the cultivated persons were to side with the author1 would those who have conclusions to draw and applications to make consent to be wrong because the general body of intelligent men1 who make no special study of the subject1 are against them8 ,they would do no such thing3 they would request the general body of intelligent men to find their own astronomy1 and welcome4 ,but the truth is1 that this intelligent body knows better3 and no persons know better that they know better than the speculators themselves4 ,but suppose the general body were to combine1 in opposition to those who have studied4 ,of course all my list must be admitted to their trial2 and then arises the question whether both sides are to be heard4 ,if so1 the general body of the intelligent must hear all the established side have to say3 that is1 they must become just as much of students as the inculpated orthodox themselves4 ,and will they not then get into professional rule1 pique1 pride1 and prejudice1 as the others did8 ,but if1 which ,i suspect1 they are intended to judge as they are1 they will be in a rare difficulty4 ,all the paradoxers are of like pretensions3 they cannot1 as a class1 be right1 for each one contradicts a great many of the rest4 ,there will be the puzzle which silenced the crew of the cutter in ,marryat's novel of the ,dog ,fiend4#ahb ,a tog is a tog1 said ,jansen4--,yes1 replied another1 we all know a dog is a dog2 but the question is--,is this dog #hh a dog8 ,and this question would arise upon every dog of them all4 ,,zetetic ,,astronomy4 ,zetetic ,astronomy3 ,earth not a globe4 #aheg 7,broadsheet74 ,though only a traveling lecturer's advertisement1 there are so many arguments and quotations that it is a little pamphlet4 ,the lecturer gained great praise from provincial newspapers for his ingenuity in proving that the earth is a flat1 surrounded by ice4 ,some of the journals rather incline to the view3 but the ,leicester ,advertiser thinks that the statements would seem very seriously to invalidate some of the most important conclusions of modern astronomy1 while the ,norfolk ,herald is clear that there must be a great error on one side or the other4 ,this broadsheet is printed at ,aylesbury in #aheg1 and the lecturer calls himself ,parallax3 but at ,trowbridge1 in #ahdi1 he was ,s4 ,goulden4#ahc ,in this last advertisement is the following announcement3 ,a paper on the above subjects was read before the ,council and ,members of the ,royal ,astronomical ,society1 ,somerset ,house1 ,strand1 ,london 7,sir ,john ,f4 ,w4 ,herschel1#ahd ,president71 ,friday1 ,dec4 #h1 #ahdh4 ,no account of such a paper appears in the ,notice for that month3 ,i suspect that the above is ,mr4 ,s4 ,goulden's way of representing the following occurrence3 ,dec4 #h1 #ahdh1 the ,secretary of the ,astronomical ,society 7,de ,morgan by name7 said1 at the close of the proceedings1--,now1 gentlemen1 if you will promise not to tell the ,council1 ,i will read something for your amusement3 and he then read a few of the arguments which had been transmitted by the lecturer4 ,the fact is worth noting that from #ahdi to #aheg1 arguments on the roundness or flatness of the earth did itinerate4 ,i have #hi no doubt they did much good3 for very few persons have any distinct idea of the evidence for the rotundity of the earth4 ,the ,blackburn ,standard and ,preston ,guardian 7,dec4 #ab and #af1 #ahdi7 unite in stating that the lecturer ran away from his second lecture at ,burnley1 having been rather too hard pressed at the end of his first lecture to explain why the large hull of a ship disappeared before the sails4 ,the persons present and waiting for the second lecture assuaged their disappointment by concluding that the lecturer had slipped off the icy edge of his flat disk1 and that he would not be seen again till he peeped up on the opposite side4 ,but1 strange as it may appear1 the opposer of the earth's roundness has more of a case--or less of a want of case--than the arithmetical squarer of the circle4 ,the evidence that the earth is round is but cumulative and circumstantial3 scores of phenomena ask1 separately and independently1 what other explanation can be imagined except the sphericity of the earth4 ,the evidence for the earth's figure is tremendously powerful of its kind2 but the proof that the circumference is #c4adaeibfe444 times the diameter is of a higher kind1 being absolute mathematical demonstration4 ,the ,zetetic system still lives in lectures and books2 as it ought to do1 for there is no way of teaching a truth comparable to opposition4 ,the last ,i heard of it was in lectures at ,plymouth1 in ,october1 #ahfd4 ,since this time a prospectus has been issued of a work entitled ,the ,earth not a ,globe2 but whether it has been published ,i do not know4 ,the contents are as follows3 ,the ,earth a ,plane--,how circumnavigated4--,how time is lost or gained4--,why a ship's hull disappears 7when outward bound7 before the mast head4--,why the ,polar ,star sets when we proceed ,southward1 etc4--,why a pendulum vibrates with less velocity at the ,equator than #ij at the ,pole4--,the allowance for rotundity supposed to be made by surveyors1 not made in practice4--,measurement of ,arcs of the ,meridian unsatisfactory4--,degrees of ,longitude ,north and ,south of the ,equator considered4--,eclipses and ,earth's form considered4--,the ,earth no motion on axis or in orbit4--,how the ,sun moves above the ,earth's surface concentric with the ,north ,pole4--,cause of ,day and ,night1 ,winter and ,summer2 the long alternation of light and darkness at the ,pole4--,cause of the ,sun rising and setting4--,distance of the ,sun from ,london1 #d1jbh miles--,how measured4--,challenge to ,mathematicians4--,cause of ,tides4--,moon self-luminous1 ,,not a reflector4--,cause of ,solar and ,lunar eclipses4--,stars not worlds2 their distance4--,earth1 the only material world2 its true position in the universe2 its condition and ultimate destruction by fire 7#b ,peter iii471 etc4 ,i wish there were geoplatylogical lectures in every town2 in ,england 7platylogical1 in composition1 need not mean babbling74 ,the late ,mr4 ,henry ,archer#ahe would1 if alive1 be very much obliged to me for recording his vehement denial of the roundness of the earth3 he was excited if he heard any one call it a globe4 ,i cannot produce his proof from the ,pyramids1 and from some caves in ,arabia4 ,he had other curious notions1 of course3 ,i should no more believe that a flat earth was a man's only paradox1 than ,i should that ,dutens1#ahf the editor of ,leibnitz1 was eccentric only in supplying a tooth which he had lost by one which he found in an ,italian tomb1 and fully believed that it had once belonged to ,scipio ,africanus1 whose family vault was discovered1 it is supposed1 in #aghj4 ,mr4 ,archer is of note as #ia the suggester of the perforated border of the postage-stamps1 and1 ,i think1 of the way of doing it2 for this he got #djjjl4 reward4 ,he was a civil engineer4 7,august #bh1 #ahfe47 ,the ,zetetic ,astronomy has come into my hands4 ,when1 in #ahea1 ,i went to see the ,great ,exhibition1 ,i heard an organ played by a performer who seemed very desirous to exhibit one particular stop4 ,what do you think of that stop8 ,i was asked4--,that depends on the name of it1 said ,i4--,oh6 what can the name have to do with the sound8 'that which we call a rose1' etc4--,the name has everything to do with it3 if it be a flute-stop1 ,i think it very harsh2 but if it be a railway-whistle-stop1 ,i think it very sweet4 ,so as to this book3 if it be childish1 it is clever2 if it be mannish1 it is unusually foolish4 ,the flat earth1 floating tremulously on the sea2 the sun moving always over the flat1 giving day when near enough1 and night when too far off2 the self-luminous moon1 with a semi-transparent invisible moon1 created to give her an eclipse now and then2 the new law of perspective1 by which the vanishing of the hull before the masts1 usually thought to prove the earth globular1 really proves it flat2--all these and other things are well fitted to form exercises for a person who is learning the elements of astronomy4 ,the manner in which the sun dips into the sea1 especially in tropical climates1 upsets the whole4 ,mungo ,park1#ahg ,i think1 gives an ,african hypothesis which explains phenomena better than this4 ,the sun dips into the western ocean1 and the people there cut him in pieces1 fry him in a pan1 and then join him together again1 take him round the underway1 and set him up in the east4 ,i hope this book will be read1 and that many will be puzzled by it3 for there are many whose notions of astronomy deserve no better fate4 ,there is no subject on which there is so little #ib accurate conception as that of the motions of the heavenly bodies4 ,the author1 though confident in the extreme1 neither impeaches the honesty of those whose opinions he assails1 nor allots them any future inconvenience3 in these points he is worthy to live on a globe1 and to revolve in twenty-four hours4 7,october1 #ahff47 ,a follower appears1 in a work dedicated to the preceding author3 it is ,theoretical ,astronomy examined and exposed by ,common ,sense4 ,the author has #abh well-stuffed octavo pages4 ,i hope he will not be the last4 ,he prints the newspaper accounts of his work3 the ,church ,times says--not seeing how the satire might be retorted--,we never began to despair of ,scripture until we discovered that ',common ,sense' had taken up the cudgels in its defence4 ,this paper considers our author as the type of a ,protestant4 ,the author himself1 who gives a summary of his arguments in verse1 has one couplet which is worth quoting3 ,how is't that sailors1 bound to sea1 with a 'globe' would never start1 ,but in its place will always take ,mercator's#ahh ,,level chart6 ,to which ,i answer3 ,why1 really ,mr4 ,common ,sense1 you've never got so far ,as to think ,mercator's planisphere shows countries as they are2 ,it won't do to measure distances2 it points out how to steer1 ,but this distortion's not for you2 another is1 ,i fear4 ,the earth must be a cylinder1 if seaman's charts be true1 ,or else the boundaries1 right and left1 are one as well as two2 ,they contradict the notion that we dwell upon a plain1 ,for straight away1 without a turn1 will bring you home again4 ,there are various plane projections2 and each one has its use3 ,i wish a milder word would rhyme--but really you're a goose6 ,the great wish of persons who expose themselves as above1 is to be argued with1 and to be treated as reputable #ic and refutable opponents4 ,common ,sense reminds us that no amount of blatant ridicule will turn right into wrong4 ,he is perfectly correct3 but then no amount of bad argument will turn wrong into right4 ,these two things balance2 and we are just where we were3 but you should answer our arguments1 for whom1 ,i ask8 ,would reason convince this kind of reasoner8 ,the issue is a short and a clear one4 ,if these parties be what ,i contend they are1 then ridicule is made for them3 if not1 for what or for whom8 ,if they be right1 they are only passing through the appointed trial of all good things4 ,appeal is made to the future3 and my ,budget is intended to show samples of the long line of heroes who have fallen without victory1 each of whom had his day of confidence and his prophecy of success4 ,let the future decide3 they say roundly that the earth is flat2 ,i say flatly that it is round4 ,the paradoxers all want reason1 and not ridicule3 they are all accessible1 and would yield to conviction4 ,well then1 let them reason with one another6 ,they divide into squads1 each with a subject1 and as many different opinions as persons in each squad4 ,if they be really what they say they are1 the true man of each set can put down all the rest1 and can come crowned with glory and girdled with scalps1 to the attack on the orthodox misbelievers4 ,but they know1 to a man1 that the rest are not fit to be reasoned with3 they pay the regulars the compliment of believing that the only chance lies with them4 ,they think in their hearts1 each one for himself1 that ridicule is of fit appliance to the rest4 ,miranda4 ,a book divided into three parts1 entitled ,souls1 ,numbers1 ,stars1 on the ,neo-,christian ,religion 444 ,vol4 i4 ,london1 #aheh1 #ahei1 #ahfj4 #hvo4 ,the name of the author is ,filopanti4#ahi ,he announces himself as the #dith and last ,emanuel3 his immediate #id predecessors were ,emanuel ,washington1 ,emanuel ,newton1 and ,emanuel ,galileo4 ,he is to collect nations into one family4 ,he knows the transmigrations of the whole human race4 ,thus ,descartes became ,william ,,iii of ,england3 ,roger ,bacon became ,boccaccio4 ,but ,charles ,,ix1#aij in retribution for the massacre of ,st4 ,bartholomew1 was hanged in ,london under the name of ,barthelemy for the murder of ,collard3 and many of the ,protestants whom he killed as ,king of ,france were shouting at his death before the ,old ,bailey4 ,,the ,,sabbath--,,the ,,great ,,pyramid ,a ,letter to the members of the ,anglo-,biblical ,institute1 dated ,sept4 #g1 #aheh1 and signed ',herman ,heinfetter4'#aia 7,broadsheet47 ,this gentleman is well known to the readers of the ,athenaeum1 in which1 for nearly twenty years1 he has inserted1 as advertisements1 long arguments in favor of ,christians keeping the ,jewish ,sabbath1 beginning on ,friday ,evening4 ,the present letter maintains that1 by the force of the definite article1 the days of creation may not be consecutive1 but may have any time--millions of years--between them4 ,this ingenious way of reconciling the author of ,genesis and the indications of geology is worthy to be added to the list1 already pretty numerous4 ,mr4 ,heinfetter has taken such pains to make himself a public agitator1 that #ie ,i do not feel it to be any invasion of private life if ,i state that ,i have heard he is a large corn-dealer4 ,no doubt he is a member of the congregation whose almanac has already been described4 ,the great ,pyramid4 ,why was it built8 ,and who built it8 ,by ,john ,taylor1 #ahei1aib #abmo4 ,this work is very learned1 and may be referred to for the history of previous speculations4 ,it professes to connect the dimensions of the ,pyramid with a system of metrology which is supposed to have left strong traces in the systems of modern times2 showing the ,egyptians to have had good approximate knowledge of the dimensions of the earth1 and of the quadrature of the circle4 ,these are points on which coincidence is hard to distinguish from intention4 ,sir ,john ,herschel#aic noticed this work1 and gave several coincidences1 in the ,athenaeum1 ,nos4 #afif and #afig1 ,april #bh and ,may #e1 #ahfj3 and there are some remarks by ,mr4 ,taylor in ,no4 #agja1 ,june #b1 #ahfj4 ,mr4 ,taylor's most recent publication is-- ,the battle of the ,standards3 the ancient1 of four thousand years1 against the modern1 of the last fifty years--the less perfect of the two4 ,london1 #ahfd1 #abmo4 ,this is intended as an appendix to the work on the ,pyramid4 ,mr4 ,taylor distinctly attributes the original system to revelation1 of which he says the ,great ,pyramid is the record4 ,we are advancing1 he remarks1 towards the end of the ,christian dispensation1 and he adds that it is satisfactory to see that we retain the standards which were given by unwritten revelation #gjj years before ,moses4 ,this is lighting the candle at both ends2 for myself1 ,i shall not undertake to deny or affirm either what is said about the dark past or what is hinted about the dark future4 #if ,my old friend ,mr4 ,taylor is well known as the author of the argument which has convinced many1 even most1 that ,sir ,philip ,francis#aid was ,junius3 pamphlet1 #ahac2 supplement1 #ahag2 second edition ,the ,identity of ,junius with a distinguished living character established1 ,london1 #ahah1 #hvo4 ,he told me that ,sir ,philip ,francis1 in a short conversation with him1 made only this remark1 ,you may depend upon it you are quite mistaken3 the phrase appears to me remarkable2 it has an air of criticism on the book1 free from all personal denial4 ,he also mentioned that a hearer told him that ,sir ,philip said1 speaking of writers on the question1--,those fellows1 for half-a-crown1 would prove that ,jesus ,christ was ,junius4 ,mr4 ,taylor implies1 ,i think1 that he is the first who started the suggestion that ,sir ,philip ,francis was ,junius1 which ,i have no means either of confirming or refuting4 ,if it be so and ,i now know that ,mr4 ,taylor himself never heard of any predecessor1 the circumstance is very remarkable3 it is seldom indeed that the first proposer of any solution of a great and vexed question is the person who so nearly establishes his point in general opinion as ,mr4 ,taylor has done4 ,as to the ,junius question in general1 there is a little bit of the philosophy of horse-racing which may be usefully applied4 ,a man who is so confident of his horse that he places him far above any other1 may nevertheless1 and does1 refuse to give odds against all in the field3 for many small adverse chances united make a big chance for one or other of the opponents4 ,i suspect ,mr4 ,taylor has made it at least #bj to #a for ,francis against any one competitor who has been named3 but what the odds may be against the #ig whole field is more difficult to settle4 ,what if the real ,junius should be some person not yet named8 ,mr4 ,jopling1 ,leisure ,hour1 ,may #bc1 #ahfc1 relies on the porphyry coffer of the ,great ,pyramid1 in which he finds the most ancient and accurate standard of measure in existence4 ,i am shocked at being obliged to place a thoughtful and learned writer1 and an old friend1 before such a successor as he here meets with4 ,but chronological arrangement defies all other arrangement4 7,i had hoped that the preceding account would have met ,mr4 ,taylor's eye in print3 but he died during the last summer4 ,for a man of a very thoughtful and quiet temperament1 he had a curious turn for vexed questions4 ,but he reflected very long and very patiently before he published3 and all his works are valuable for their accurate learning1 whichever side the reader may take47 ,,mrs4 ,,elizabeth ,,cottle4 #ahei4 ,the ,cottle ,church4--,for more than twenty years printed papers have been sent about in the name of ,elizabeth ,cottle4#aie ,it is not so remarkable that such papers should be concocted as that they should circulate for such a length of time without attracting public attention4 ,eighty years ago ,mrs4 ,cottle might have rivalled ,lieut4 ,brothers or ,joanna ,southcott4#aif ,long hence1 when the now current volumes of our journals are well-ransacked works of reference1 those who look into them will be glad to see this #ih feature of our time3 ,i therefore make a few extracts1 faithfully copied as to type4 ,the ,italic is from the ,new ,testament2 the ,roman is the requisite interpretation3 ,robert ,cottle 'was numbered 7#eaif7 with the transgressors' at the back of the ,church in ,norwood ,cemetery1 ,may #ab1 #aheh--;,isa4 liii4 #ab4 ,the ,rev4 ,j4 ,g4 ,collinson1 ,minister of ,st4 ,james's ,church1 ,chapham1 the then district church1 before ,all ,saints was built1 read the funeral service over the ,sepulchre wherein never before man was laid4 ,hewn on the stone1 'at the mouth of the ,sepulchre1' is his name1--,robert ,cottle1 born at ,bristol1 ,june #b1 #aggd2 died at ,kirkstall ,lodge1 ,clapham ,park1 ,may #f1 #aheh4 ,and that day 7,may #ab1 #aheh7 was the preparation 7day and year for 'the ,,prepared place for you'--,cottleites---by the widowed mother of the ,father's house1 at ,kirkstall ,lodge--,john xiv4 #b1 #c74 ,and the ,sabbath 7,christmas ,day1 ,dec4 #be1 #ahei7 drew on 7for the resurrection of the ,christian body on 'the third ,protestant ,sun-day'--#a ,cor4 xv4 #ce74 ,why seek ye the living 7,god of the ,new ,jerusalem--,heb4 xii4 #bb2 ,rev4 iii4 #ab7 among the dead 7men73 he 7the ,god of ,jesus7 is not here 7in the grave71 but is risen 7in the person of the ,holy ,ghost1 from the supper of 'the dead in the second death' of ,paganism74 ,remember how he spake unto you 7in the church of the ,rev4 ,george ,clayton1#aig ,april #ad1 #ahci74 ,i will not drink henceforth 7at this last ,cottle supper7 of the fruit of this 7,trinity7 vine1 until that day 7,christmas ,day1 #ahei71 when ,i 7,elizabeth ,cottle7 drink it new with you 7,cottleites7 in my ,father's kingdom--,john xv4 ,if this 7,trinitarian7 cup may not pass away from me 7,elizabeth ,cottle1 ,april #ad1 #ahci71 except ,i drink it 7'new with you ,cottleites1 in my ,father's ,kingdom'71 thy will be done--,matt4 xxvi4 #bi1 #db1 #fd4 ',our ,father which art 7,god7 in ,heaven1' hallowed be thy name1 thy 7,cottle7 kingdom #ii come1 thy will be done in earth1 as it is 7done7 in 7the new7 ,heaven 7and new earth of the new name of ,cottle--,rev4 xxi4 #a2 iii4 #ab74 444 ,queen ,elizabeth1 from ,a4,d4 #aeeh to #aeff4 ,and this ,,word yet once more 7by a second ,elizabeth--the ,,word of his oath7 signifieth 7at ,john ,scott's baptism of the ,holy ,ghost7 the removing of those things 7those ,gods and those doctrines7 that are made 7according to the ,creeds and ,commandments of men7 that those things 7in the moral law of ,god7 which cannot be shaken 7as a rule of faith and practice7 may remain1 wherefore we receiving 7from ,elizabeth7 a kingdom 7of ,god17 which cannot be moved 7by ,satan7 let us have grace 7in his ,grace of ,canterbury7 whereby we may serve ,god acceptably 7with the acceptable sacrifice of ,elizabeth's body and blood of the communion of the ,holy ,ghost7 with reverence 7for truth7 and godly fear 7of the unpardonable sin of blasphemy against the ,holy ,ghost7 for our ,god 7the ,holy ,ghost7 is a consuming fire 7to the nation that will not serve him in the ,cottle ,church74 ,we cannot defend ourselves against the ,almighty1 and if ,he is our defence1 no nation can invade us4 ,in verse #d the ,church of ,st4 ,peter is in prison between four quaternions of soldiers--the ,holy ,alliance of #ahae4 ,rev4 vii4 i4 ,elizabeth1 the ,angel of the ,lord ,jesus appears to the ,jewish and ,christian body with the vision of prophecy to the ,rev4 ,geo4 ,clayton and his clerical brethren1 ,april #hth1 #ahci4 ,rhoda was the name of her maid at ,putney ,terrace who used to open the door to her ,peter1 the ,rev4 ,robert ,ashton1#aih the ,pastor of 'the little flock' 'of #abj names together1 assembled in an upper 7school7 room' at ,putney ,chapel1 to which little flock she gave the revelation 7,acts4 i4 #ac1 #ae7 of ,jesus the same ,king of the ,jews yesterday at the prayer meeting1 ,dec4 #ca1 #ahda1 and to-day1 #ajj ,jan4 #a1 #ahdb1 and for ever4 ,see book of ,life1 page #bd4 ,matt4 xviii4 #ai1 xxi4 #ac-af4 ,in verse #f the ,italian body of ,st4 ,peter is sleeping 'in the second death' between the two ,imperial soldiers of ,france and ,austria4 ,the ,emperor of ,france from ,jan4 #a1 to ,july #aa1 #ahei1 causes the ,italian chains of ,st4 ,peter to fall off from his ,imperial hands4 ,i say unto thee1 ,robert ,ashton1 thou art ,peter1 a stone1 and upon this rock1 of truth1 will ,i ,elizabeth1 the angel of ,jesus1 build my ,cottle ,church1 and the gates of hell1 the doors of ,st4 ,peter1 at ,rome1 shall not prevail against it--,matt4 xvi4 #ah4 ,rev4 iii4 #g-ab4 ,this will be enough for the purpose4 ,when any one who pleases can circulate new revelations of this kind1 uninterrupted and unattended to1 new revelations will cease to be a good investment of excentricity4 ,i take it for granted that the gentlemen whose names are mentioned have nothing to do with the circulars or their doctrines4 ,any lady who may happen to be intrusted with a revelation may nominate her own pastor1 or any other clergyman1 one of her apostles2 and it is difficult to say to what court the nominees can appeal to get the commission abrogated4 ,march #af1 #ahfe4 ,during the last two years the circulars have continued4 ,it is hinted that funds are low3 and two gentlemen who are represented as gone to ,bethlehem asylum in despair say that ,mrs4 ,cottle will spend all that she hath1 while ,her ,majesty's ,ministers are flourishing on the wages of sin4 ,the following is perhaps one of the most remarkable passages in the whole3 ,extol and magnify ,him 7,jehovah1 the ,everlasting ,god1 see the ,magnificat and ,luke i4 #de1 #df--fh--gc--gi71 that rideth 7by rail and steam over land and sea1 from his holy habitation at ,kirkstall ,lodge1 ,psa4 lxxvii4 #ai1 #bj71 upon the 7,cottle7 heavens1 as it were 7,sept4 #i1 #ahfd1 see pages #ba1 #agj71 upon an 7exercising1 ,psa4 cxxxi4 #a71 horse-7chair1 bought of ,mr4 ,john ,ward1 ,leicester-square74 #aja ,i have pretty good evidence that there is a clergyman who thinks ,mrs4 ,cottle a very sensible woman4 ,the ,cottle ,church4 ,had ,i chanced to light upon it at the time of writing1 ,i should certainly have given the following4 ,a printed letter to the ,western ,times1 by ,mr4 ,robert ,cottle1 was accompanied by a manuscript letter from ,mrs4 ,cottle1 apparently a circular4 ,the date was ,novr4 #ahec1 and the subject was the procedure against ,mr4 ,maurice#aii at ,king's ,college for doubting that ,god would punish human sins by an existence of torture lasting through years numbered by millions of millions of millions of millions 7repeat the word millions without end17 etc4 ,the memory of ,mr4 ,cottle has1 ,i think1 a right to the quotation3 he seems to have been no participator in the notions of his wife3 ,the clergy of the ,established ,church1 taken at the round number of #bj1jjj1 may1 in their first estate1 be likened to #bj1jjj gold blanks1 destined to become sovereigns1 in succession1--they are placed between the matrix of the ,mint1 when1 by the pressure of the screw1 they receive the impress that fits them to become part of the current coin of the realm4 ,in a way somewhat analogous this great body of the clergy have each passed through the crucibles of ,oxford and ,cambridge1--have been assayed by the ,bishop's chaplain1 touching the health of their souls1 and the validity of their call by the ,divine ,spirit1 and then the gentle pressure of a prelate's hand upon their heads2 and the words--',receive the ,holy ,ghost1' have1 in a brief space of time1 wrought a #ajb change in them1 much akin to the miracle of transubstantiation--the priests are completed1 and they become the current ecclesiastical coin of our country4 ,the whole body of clergy1 here spoken of1 have undergone the preliminary induction of baptism and confirmation2 and all have been duly ordained1 professing to hold one faith1 and to believe in the selfsame doctrines6 ,in short1 to be as identical as the #bj1jjj sovereigns1 if compared one with the other4 ,but mind is not malleable and ductile1 like gold2 and all the preparations of tests1 creeds1 and catechisms will not insure uniformity of belief4 ,no stamp of orthodoxy will produce the same impress on the minds of different men4 ,variety is manifest1 and patent1 upon everything mental and material4 ,the ,almighty has not created1 nor man fashioned1 two things alike6 ,how futile1 then1 is the attempt to shape and mould man's apprehension of divine truth by one fallible standard of man's invention6 ,if proof of this be required1 an appeal might be made to history and the experience of eighteen hundred years4 ,this is an argument of force against the reasonableness of expecting tens of thousands of educated readers of the ,new ,testament to find the doctrine above described in it4 ,the lady's argument against the doctrine itself is very striking4 ,speaking of an outcry on this matter among the ,dissenters against one of their body1 who was the son of the ,white ,stone 7,rev4 ii4 #ag71 or the ,roman cement-maker1 she says-- ,if the doctrine for which they so wickedly fight were true1 what would become of the black gentlemen for whose redemption ,i have been sacrificed from ,april #h #ahci4 ,there are certainly very curious points about this revelation4 ,there have been many surmises about the final restoration of the infernal spirits1 from the earliest ages of ,christianity until our own day3 a collection of them would be worth making4 ,on reading this in proof1 ,i see a possibility that by black gentlemen may be meant the clergy3 #ajc ,i suppose my first interpretation must have been suggested by context3 ,i leave the point to the reader's sagacity4 ,,james ,,smith1 ,,arch-,,paradoxer4 ,the ,problem of squaring the circle solved2 or1 the circumference and area of the circle discovered4 ,by ,james ,smith4#bjj ,london1 #ahei1 #hvo4 ,on the relations of a square inscribed in a circle4 ,read at the ,british ,association1 ,sept4 #ahei1 published in the ,liverpool ,courier1 ,oct4 #h1 #ahei1 and reprinted in broadsheet4 ,the question3 ,are there any commensurable relations between a circle and other ,geometrical figures8 ,answered by a member of the ,british ,association 444 ,london1 #ahfj1 #hvo4--,this has been translated into ,french by ,m4 ,armand ,grange1 ,bordeaux1 #ahfc1 #hvo4 ,the ,quadrature of the ,circle4 ,correspondence between an eminent mathematician and ,james ,smith1 ,esq4 7,member of the ,mersey ,docks and ,harbour ,board71 ,london1 #ahfa1 #hvo4 7pp4 #bjj74 ,letter to the 444 ,british ,association 444 by ,james ,smith1 ,esq4 ,liverpool1 #ahfa1 #hvo4 ,letter to the 444 ,british ,association 444 by ,james ,smith1 ,esq4 ,liverpool1 #ahfb1 #hvo4--,these letters the author promised to continue4 ,a ,nut to crack for the readers of ,professor ,de ,morgan's ',budget of ,paradoxes4' ,by ,james ,smith1 ,esq4 ,liverpool1 #ahfc1 #hvo4 ,paper read at the ,liverpool ,literary and ,philosophical ,society1 reported in the ,liverpool ,daily ,courier1 ,jan4 #bf1 #ahfd4 ,reprinted as a pamphlet4 ,the ,quadrature of the circle1 or the true ratio between the diameter and circumference geometrically and mathematically demonstrated4 ,by ,james ,smith1 ,esq4 ,liverpool1 #ahfe1 #hvo4 #ajd ,on the relations between the dimensions and distances of the ,sun1 ,moon1 and ,earth2 a paper read before the ,literary and ,philosophical ,society of ,liverpool1 ,jan4 #be1 #ahfd4 ,by ,james ,smith1 ,esq4 ,the ,british ,association in ,jeopardy1 and ,dr4 ,whewell1 the ,master of ,trinity1 in the stocks without hope of escape4 ,printed for the authors 7,j4 ,s4 confessed1 and also hidden under ,nauticus74 7,no date1 #ahfe74 ,the ,british ,association in ,jeopardy1 and ,professor ,de ,morgan in the ,pillory without hope of escape4 ,london1 #ahff1 #hvo4 ,when my work appeared in numbers1 ,i had not anything like an adequate idea of ,mr4 ,james ,smith's superiority to the rest of the world in the points in which he is superior4 ,he is beyond a doubt the ablest head at unreasoning1 and the greatest hand at writing it1 of all who have tried in our day to attach their names to an error4 ,common cyclometers sink into puny orthodoxy by his side4 ,the behavior of this singular character induces me to pay him the compliment which ,achilles paid ,hector1 to drag him round the walls again and again4 ,he was treated with unusual notice and in the most gentle manner4 ,the unnamed mathematician1 ,e4 ,m4 bestowed a volume of mild correspondence upon him2 ,rowan ,hamilton#bja quietly proved him wrong in a way accessible to an ordinary schoolboy2 ,whewell1#bjb as we shall see1 gave him the means of seeing himself wrong1 even more easily than by ,hamilton's method4 ,nothing would do2 it was small kick and silly fling at all2 and he exposed his conceit by alleging that he1 ,james ,smith1 had placed ,whewell in the stocks4 ,he will therefore be universally pronounced a proper object of the severest literary punishment3 but the opinion of all who can put two propositions together will be that of the many strokes ,i have given1 the hardest and most telling are my republications of his own attempts to reason4 ,he will come out of my hands in the position he ought #aje to hold1 the ,supreme ,pontiff of cyclometers1 the vicegerent of ,st4 ,vitus upon earth1 the ,mamamouchi of burlesque on inference4 ,i begin with a review of him which appeared in the ,athenaeum of ,may #aa1 #ahfa4 ,mr4 ,smith says ,i wrote it3 this ,i neither affirm nor deny2 to do either would be a sin against the editorial system elsewhere described4 ,many persons tell me they know me by my style2 let them form a guess3 ,i can only say that many have declared as above while fastening on me something which ,i had never seen nor heard of4 ,the ,quadrature of the ,circle3 ,correspondence between an ,eminent ,mathematician and ,james ,smith1 ,esq4 7,edinburgh1 ,oliver ,boyd2 ,london1 ,simpkin1 ,marshall ,co47 ,a few weeks ago we were in perpetual motion4 ,we did not then suppose that anything would tempt us on a circle-squaring expedition3 but the circumstances of the book above named have a peculiarity which induces us to give it a few words4 ,mr4 ,james ,smith1 a gentleman residing near ,liverpool1 was some years ago seized with the morbus cyclometricus4#bjc ,the symptoms soon took a defined form3 his circumference shrank into exactly #c-a_/h times his diameter1 instead of close to #c-af_/aac1 which the mathematician knows to be so near to truth that the error is hardly at the rate of a foot in #b1jjj miles4 ,this shrinking of the circumference remained until it became absolutely necessary that it should be examined by the ,british ,association4 ,this body1 which as ,mr4 ,james ,smith found to his sorrow1 has some interest in 'jealously guarding the mysteries of their profession1' refused at first to entertain the question4 ,on this ,mr4 ,smith changed his 'tactics' and the name of his paper1 and smuggled in the subject under the form of ',the ,relations of a ,circle inscribed in a ,square'6 ,the paper was thus forced upon the ,association1 for ,mr4 ,smith informs us that he #ajf 'gave the ,section to understand that he was not the man that would permit even the ,british ,association to trifle with him4' ,in other words1 the ,association bore with and were bored with the paper1 as the shortest way out of the matter4 ,mr4 ,smith also circulated a pamphlet4 ,some kind-hearted man1 who did not know the disorder as well as we do1 and who appears in ,mr4 ,smith's handsome octavo as ,e4 ,m4--the initials of 'eminent mathematician'--wrote to him and offered to show him in a page that he was all wrong4 ,mr4 ,smith thereupon opened a correspondence1 which is the bulk of the volume4 ,when the correspondence was far advanced1 ,mr4 ,smith announced his intention to publish4 ,his benevolent instructor--we mean in intention--protested against the publication1 saying ',i do not wish to be gibbeted to the world as having been foolish enough to enter upon what ,i feel now to have been a ridiculous enterprise4' ,for this ,mr4 ,smith cared nothing3 he persisted in the publication1 and the book is before us4 ,mr4 ,smith has had so much grace as to conceal his kind adviser's name under ,e4 ,m41 that is to say1 he has divided the wrong among all who may be suspected of having attempted so hopeless a task as that of putting a little sense into his head4 ,he has violated the decencies of private life4 ,against the will of the kind-hearted man who undertook his case1 he has published letters which were intended for no other purpose than to clear his poor head of a hopeless delusion4 ,he deserves the severest castigation2 and he will get it3 his abuse of confidence will stick by him all his days4 ,not that he has done his benefactor--in intention1 again--any harm4 ,the patience with which ,e4 ,m4 put the blunders into intelligible form1 and the perseverance with which he tried to find a cranny-hole for common reasoning to get in at1 are more than respectable3 they are admirable4 ,it is1 we can assure ,e4 ,m41 a good thing that the nature of the circle-squarer should be so completely exposed as in this volume4 ,the benefit which he intended ,mr4 ,james ,smith may be #ajg conferred upon others4 ,and we should very much like to know his name1 and if agreeable to him1 to publish it4 ,as to ,mr4 ,james ,smith1 we can only say this3 he is not mad4 ,madmen reason rightly upon wrong premises3 ,mr4 ,smith reasons wrongly upon no premises at all4 ,e4 ,m4 very soon found out that1 to all appearance1 ,mr4 ,smith got a circle of #c-a_/h times the diameter by making it the supposition to set out with that there was such a circle2 and then finding certain consequences which1 so it happened1 were not inconsistent with the supposition on which they were made4 ,error is sometimes self-consistent4 ,however1 ,e4 ,m41 to be quite sure of his ground1 wrote a short letter1 stating what he took to be ,mr4 ,smith's hypothesis1 containing the following3 ',on ,,ac as diameter1 describe the circle ,d1 which by hypothesis shall be equal to three and one-eighth times the length of ,,ac4444 ,i beg1 before proceeding further1 to ask whether ,i have rightly stated your argument4' ,to which ,mr4 ,smith replied3 ',you have stated my argument with perfect accuracy4' ,still ,e4 ,m4 went on1 and we could not help1 after the above1 taking these letters as the initials of ,everlasting ,mercy4 ,at last1 however1 when ,mr4 ,smith flatly denied that the area of the circle lies between those of the inscribed and circumscribed polygons1 ,e4 ,m4 was fairly beaten1 and gave up the task4 ,mr4 ,smith was left to write his preface1 to talk about the certain victory of truth--which1 oddly enough1 is the consolation of all hopelessly mistaken men2 to compare himself with ,galileo2 and to expose to the world the perverse behavior of the ,astronomer ,royal1 on whom he wanted to fasten a conversation1 and who replied1 ',it would be a waste of time1 ,sir1 to listen to anything you could have to say on such a subject4' ,having thus disposed of ,mr4 ,james ,smith1 we proceed to a few remarks on the subject3 it is one which a journal would never originate1 but which is rendered necessary from time to time by the attempts of the autopseustic to become #ajh heteropseustic4 ,to the mathematician we have nothing to say3 the question is1 what kind of assurance can be given to the world at large that the wicked mathematicians are not acting in concert to keep down their superior1 ,mr4 ,james ,smith1 the current ,galileo of the quadrature of the circle4 ,let us first observe that this question does not stand alone3 independently of the millions of similar problems which exist in higher mathematics1 the finding of the diagonal of a square has just the same difficulty1 namely1 the entrance of a pair of lines of which one cannot be definitely expressed by means of the other4 ,we will show the reader who is up to the multiplication-table how he may go on1 on1 on1 ever nearer1 never there1 in finding the diagonal of a square from the side4 ,write down the following rows of figures1 and more1 if you like1 in the way described3 #a #b #e #ab #bi #gj #afi #djh #ihe #a #c #g #ag #da #ii #bci #egg #acic ,after the second1 each number is made up of double the last increased by the last but one3 thus1 #e is #a more than twice #b1 #ab is #b more than twice #e1 #bci is #da more than twice #ii4 ,now1 take out two adjacent numbers from the upper line1 and the one below the first from the lower3 as #gj #afi #ii4 ,multiply together #ii and #afi1 giving #af1gca4 ,if1 then1 you will say that #gj diagonals are exactly equal to #ii sides1 you are in error about the diagonal1 but an error the amount of which is not so great as the #af1gcast part of the diagonal4 ,similarly1 to say that five diagonals make exactly seven sides does not involve an error of the #hdth part of the diagonal4 ,now1 why has not the question of crossing the square been as celebrated as that of squaring the circle8 ,merely because ,euclid demonstrated the impossibility of the first #aji question1 while that of the second was not demonstrated1 completely1 until the last century4 ,the mathematicians have many methods1 totally different from each other1 of arriving at one and the same result1 their celebrated approximation to the circumference of the circle4 ,an intrepid calculator has1 in our own time1 carried his approximation to what they call #fjg decimal places3 this has been done by ,mr4 ,shanks1#bjd of ,houghton-le-,spring1 and ,dr4 ,rutherford#bje has verified #dda of these places4 ,but though #fjg looks large1 the general public will form but a hazy notion of the extent of accuracy acquired4 ,we have seen1 in ,charles ,knight's#bjf ,english ,cyclopaedia1 an account of the matter which may illustrate the unimaginable1 though rationally conceivable1 extent of accuracy obtained4 ,say that the blood-globule of one of our animalcules is a millionth of an inch in diameter4 ,fashion in thought a globe like our own1 but so much larger that our globe is but a blood-globule in one of its animalcules3 never mind the microscope which shows the creature being rather a bulky instrument4 ,call this the first globe above us4 ,let the first globe above us be but a blood-globule1 as to size1 in the animalcule of a still larger globe1 which call the second globe above us4 ,go on in this way to the twentieth globe above us4 ,now go down just as far on the other side4 ,let the blood-globule with which we started be a globe peopled with animals like ours1 but rather smaller3 #aaj and call this the first globe below us4 ,take a blood-globule out of this globe1 people it1 and call it the second globe below us3 and so on to the twentieth globe below us4 ,this is a fine stretch of progression both ways4 ,now give the giant of the twentieth globe above us the #fjg decimal places1 and1 when he has measured the diameter of his globe with accuracy worthy of his size1 let him calculate the circumference of his equator from the #fjg places4 ,bring the little philosopher from the twentieth globe below us with his very best microscope1 and set him to see the small error which the giant must make4 ,he will not succeed1 unless his microscopes be much better for his size than ours are for ours4 ,now it must be remembered by any one who would laugh at the closeness of the approximation1 that the mathematician generally goes nearer2 in fact his theorems have usually no error at all4 ,the very person who is bewildered by the preceding description may easily forget that if there were no error at all1 the ,lilliputian of the millionth globe below us could not find a flaw in the ,brobdingnagian of the millionth globe above4 ,the three angles of a triangle1 of perfect accuracy of form1 are absolutely equal to two right angles2 no stretch of progression will detect any error4 ,now think of ,mr4 ,lacomme's mathematical adviser 7ante1 ,vol4 ,i1 p4 #df7 making a difficulty of advising a stonemason about the quantity of pavement in a circular floor6 ,we will now1 for our non-calculating reader1 put the matter in another way4 ,we see that a circle-squarer can advance1 with the utmost confidence1 the assertion that when the diameter is #a1jjj1 the circumference is accurately #c1abe3 the mathematician declaring that it is a trifle more than #c1ada-a_/b4 ,if the squarer be right1 the mathematician has erred by about a #bjjth part of the whole3 or has not kept his accounts right by about #ajs4 in every #ajjl4 ,of course1 if he set out with such an error he will accumulate blunder upon blunder4 ,now1 if there be a process in which #aaa close knowledge of the circle is requisite1 it is in the prediction of the moon's place--say1 as to the time of passing the meridian at ,greenwich--on a given day4 ,we cannot give the least idea of the complication of details3 but common sense will tell us that if a mathematician cannot find his way round the circle without a relative error four times as big as a stockbroker's commission1 he must needs be dreadfully out in his attempt to predict the time of passage of the moon4 ,now1 what is the fact8 ,his error is less than a second of time1 and the moon takes #bg days odd to revolve4 ,that is to say1 setting out with #ajs4 in #ajjl4 of error in his circumference1 he gets within the fifth part of a farthing in #ajjl4 in predicting the moon's transit4 ,now we cannot think that the respect in which mathematical science is held is great enough--though we find it not small--to make this go down4 ,that respect is founded upon a notion that right ends are got by right means3 it will hardly be credited that the truth can be got to farthings out of data which are wrong by shillings4 ,even the celebrated ,hamilton#bjg of ,edinburgh1 who held that in mathematics there was no way of going wrong1 was fully impressed with the belief that this was because error was avoided from the beginning4 ,he never went so far as to say that a mathematician who begins wrong must end right somehow4 ,there is always a difficulty about the mode in which the thinking man of common life is to deal with subjects he has not studied to a professional extent4 ,he must form opinions on matters theological1 political1 legal1 medical1 and social4 ,if he can make up his mind to choose a guide1 there is1 of course1 no perplexity3 but on all the subjects mentioned the direction-posts point different ways4 ,now why should he not form his opinion upon an abstract mathematical question8 ,why not conclude that1 as to the circle1 it is possible ,mr4 ,james ,smith may be the man1 just #aab as ,adam ,smith#bjh was the man of things then to come1 or ,luther1 or ,galileo8 ,it is true that there is an unanimity among mathematicians which prevails in no other class3 but this makes the chance of their all being wrong only different in degree4 ,and more than this1 is it not generally thought among us that priests and physicians were never so much wrong as when there was most appearance of unanimity among them8 ,to the preceding questions we see no answer except this1 that the individual inquirer may as rationally decide a mathematical question for himself as a theological or a medical question1 so soon as he can put himself into a position in mathematics1 level with that in which he stands in theology or medicine4 ,the every-day thought and reading of common life have a certain resemblance to the thought and reading demanded by the learned faculties4 ,the research1 the balance of evidence1 the estimation of probabilities1 which are used in a question of medicine1 are closely akin in character1 however different the matter of application1 to those which serve a merchant to draw his conclusions about the markets4 ,but the mathematicians have methods of their own1 to which nothing in common life bears close analogy1 as to the nature of the results or the character of the conclusions4 ,the logic of mathematics is certainly that of common life3 but the data are of a different species2 they do not admit of doubt4 ,an expert arithmetician1 such as is ,mr4 ,j4 ,smith1 may fancy that calculation1 merely as such1 is mathematics3 but the value of his book1 and in this point of view it is not small1 is the full manner in which it shows that a practised arithmetician1 venturing into the field of mathematical demonstration1 may show himself utterly destitute of all that distinguishes the reasoning geometrical investigator from the calculator4 #aac ,and further1 it should be remembered that in mathematics the power of verifying results far exceeds that which is found in anything else3 and also the variety of distinct methods by which they can be attained4 ,it follows from all this that a person who desires to be as near the truth as he can will not judge the results of mathematical demonstration to be open to his criticism1 in the same degree as results of other kinds4 ,should he feel compelled to decide1 there is no harm done3 his circle may be #c-a_/h times its diameter1 if it please him4 ,but we must warn him that1 in order to get this circle1 he must1 as ,mr4 ,james ,smith has done1 make it at home3 the laws of space and thought beg leave respectfully to decline the order4 ,i will insert now at length1 from the ,athenaeum of ,june #h1 #ahfa1 the easy refutation given by my deceased friend1 with the remarks which precede4 ,mr4 ,james ,smith1 of whose performance in the way of squaring the circle we spoke some weeks ago in terms short of entire acquiescence1 has advertised himself in our columns1 as our readers will have seen4 ,he has also forwarded his letter to the ,liverpool ,albion1 with an additional statement1 which he did not make in our journal4 ,he denies that he has violated the decencies of private life1 since his correspondent revised the proofs of his own letters1 and his 'protest had respect only to making his name public4' ,this statement ,mr4 ,james ,smith precedes by saying that we have treated as true what we well knew to be false3 and he follows by saying that we have not read his work1 or we should have known the above facts to be true4 ,mr4 ,smith's pretext is as follows4 ,his correspondent ,e4 ,m4 says1 ',my letters were not intended for publication1 and ,i protest against their being published1' and he subjoins ',therefore ,i must desire that my name may not be used4' ,the obvious meaning is that ,e4 ,m4 protested against the publication altogether1 but1 judging that ,mr4 ,smith was #aad determined to publish1 desired that his name should not be used4 ,that he afterwards corrected the proofs merely means that he thought it wiser to let them pass under his own eyes than to leave them entirely to ,mr4 ,smith4 ,we have received from ,sir ,w4 ,rowan ,hamilton#bji a proof that the circumference is more than #c-a_/h diameters1 requiring nothing but a knowledge of four books of ,euclid4 ,we give it in brief as an exercise for our juvenile readers to fill up4 ,it reminds us of the old days when real geometers used to think it worth while seriously to demolish pretenders4 ,mr4 ,smith's fame is now assured3 ,sir ,w4 ,r4 ,hamilton's brief and easy exposure will procure him notice in connection with this celebrated problem4 ,it is to be shown that the perimeter of a regular polygon of #bj sides is greater than #c-a_/h diameters of the circle1 and still more1 of course1 is the circumference of the circle greater than #c-a_/h diameters4 #a4 ,it follows from the #dth ,book of ,euclid1 that the rectangle under the side of a regular decagon inscribed in a circle1 and that side increased by the radius1 is equal to the square of the radius4 ,but the product #gia 7#gia #abhj7 is less than #abhj x #abhj2 if then the radius be #abhj the side of the decagon is greater than #gia4 #b4 ,when a diameter bisects a chord1 the square of the chord is equal to the rectangle under the doubles of the segments of the diameter4 ,but the product #abe 7#d x #abhj - #abe7 is less than #gia x #gia4 ,if then the bisected chord be a side of the decagon1 and if the radius be still #abhj1 the double of the lesser segment exceeds #abe4 #c4 ,the rectangle under this doubled segment and the radius is equal to the square of the side of an inscribed regular polygon of #bj sides4 ,but the product #abe x #abhj is equal to #djj x #djj2 therefore1 the side of the last-mentioned polygon is greater than #djj1 if the radius be still #abhj4 ,in other words1 if the radius be represented by the new #aae member #af1 and therefore the diameter by #cb1 this side is greater than #e1 and the perimeter exceeds #ajj4 ,so that1 finally1 if the diameter be #h1 the perimeter of the inscribed regular polygon of #bj sides1 and still more the circumference of the circle1 is greater than #be3 that is1 the circumference is more than #c-a_/h diameters4 ,the last work in the list was thus noticed in the ,athenaeum1 ,may #bg1 #ahfe4 ,mr4 ,james ,smith appears to be tired of waiting for his place in the ,budget of ,paradoxes1 and accordingly publishes a long letter to ,professor ,de ,morgan1 with various prefaces and postscripts4 ,the letter opens by a hint that the ,budget appears at very long intervals1 and 'apparently without any sufficient reason for it4' ,as ,mr4 ,smith hints that he should like to see ,mr4 ,de ,morgan1 whom he calls an 'elephant of mathematics1' 'pumping his brains' 'behind the scenes'--an odd thing for an elephant to do1 and an odd place to do it in--to get an answer1 we think he may mean to hint that the ,budget is delayed until the pump has worked successfully4 ,mr4 ,smith is informed that we have had the whole manuscript of the ,budget1 excepting only a final summing-up1 in our hands since ,october1 #ahfc4 ,this does not refer to the ,supplement4 ,there has been no delay3 we knew from the beginning that a series of historical articles would be frequently interrupted by the things of the day4 ,mr4 ,james ,smith lets out that he has never been able to get a private line from ,mr4 ,de ,morgan in answer to his communications3 we should have guessed it4 ,he says1 ',the ,professor is an old bird and not to be easily caught1 and by no efforts of mine have ,i been able1 up to the present moment1 either to induce or twit him into a discussion4444' ,mr4 ,smith curtails the proverb3 old birds are not to be caught with chaff1 nor with twit1 which seems to be ,mr4 ,smith's word for his own chaff1 and1 so long as the first letter is sounded1 a very proper word4 ,why does he not try a little grain of sense8 ,mr4 ,smith evidently #aaf thinks that1 in his character as an elephant1 the ,professor has not pumped up brain enough to furnish forth a bird4 ,in serious earnest1 ,mr4 ,smith needs no answer4 ,in one thing he excites our curiosity3 what is meant by demonstrating 'geometrically and mathematically8' ,i now proceed to my original treatment of the case4 ,mr4 ,james ,smith will1 ,i have no doubt1 be the most uneclipsed circle-squarer of our day4 ,he will not owe this distinction to his being an influential and respected member of the commercial world of ,liverpool1 even though the power of publishing which his means give him should induce him to issue a whole library upon one paradox4 ,neither will he owe it to the pains taken with him by a mathematician who corresponded with him until the joint letters filled an octavo volume4 ,neither will he owe it to the notice taken of him by ,sir ,william ,hamilton1 of ,dublin1 who refuted him in a manner intelligible to an ordinary student of ,euclid1 which refutation he calls a remarkable paradox easily explainable1 but without explaining it4 ,what he will owe it to ,i proceed to show4 ,until the publication of the ,nut to ,crack ,mr4 ,james ,smith stood among circle-squarers in general4 ,i might have treated him with ridicule1 as ,i have done others3 and he says that he does not doubt he shall come in for his share at the tail end of my ,budget4 ,but ,i can make a better job of him than so1 as ,locke would have phrased it3 he is such a very striking example of something ,i have said on the use of logic that ,i prefer to make an example of his writings4 ,on one point indeed he well deserves the scutica1#baj if not the horribile flagellum4#baa ,he tells me that he will bring his solution to me in such a form as shall compel me to admit it as un fait accompli une faute accomplie8#bab #aag or leave myself open to the humiliating charge of mathematical ignorance and folly4 ,he has also honored me with some private letters4 ,in the first of these he gives me a piece of information1 after which he cannot imagine that ,i1 as an honest mathematician1 can possibly have the slightest hesitation in admitting his solution4 ,there is a tolerable reservoir of modest assurance in a man who writes to a perfect stranger with what he takes for an argument1 and gives an oblique threat of imputation of dishonesty in case the argument be not admitted without hesitation2 not to speak of the minor charges of ignorance and folly4 ,all this is blind self-confidence1 without mixture of malicious meaning2 and ,i rather like it3 it makes me understand how ,sam ,johnson came to say of his old friend ,mrs4 ,cobb1#bac--;,i love ,moll ,cobb for her impudence4 ,i have now done with my friend's suaviter in modo1#bad and proceed to his fortiter in re#bae3 ,i shall show that he has convicted himself of ignorance and folly1 with an honesty and candor worthy of a better value of pi4 ,mr4 ,smith's method of proving that every circle is #c-a_/h diameters is to assume that it is so1--if you dislike the term datum1 then1 by hypothesis1 let #h circumferences be exactly equal to #be diameters1--and then to show that every other supposition is thereby made absurd4 ,the right to this assumption is enforced in the ,nut by the following analogy3 ,i think you 767 will not dare 767 to dispute my right to this hypothesis1 when ,i can prove by means of it that every other value of pi will lead to the grossest absurdities2 unless indeed1 you are prepared to dispute the right of ,euclid to adopt a false line hypothetically for the purpose #aah of a 'reductio ad absurdum'#baf demonstration1 in pure geometry4 ,euclid assumes what he wants to disprove1 and shows that his assumption leads to absurdity1 and so upsets itself4 ,mr4 ,smith assumes what he wants to prove1 and shows that his assumption makes other propositions lead to absurdity4 ,this is enough for all who can reason4 ,mr4 ,james ,smith cannot be argued with2 he has the whip-hand of all the thinkers in the world4 ,montucla would have said of ,mr4 ,smith what he said of the gentleman who squared his circle by giving #ej and #di the same square root1 ,il a perdu le droit d'etre frappe de l'evidence4#bag ,it is ,mr4 ,smith's habit1 when he finds a conclusion agreeing with its own assumption1 to regard that agreement as proof of the assumption4 ,the following is the piece of information which will settle me1 if ,i be honest4 ,assuming pi to be #c-a_/h1 he finds out by working instance after instance that the mean proportional between one-fifth of the area and one-fifth of eight is the radius4 ,that is1 if pi #be_/h1 sqrt77pir#b7_/e 4 #h_/e7 r4 ,this remarkable general principle may fail to establish ,mr4 ,smith's quadrature1 even in an honest mind1 if that mind should happen to know that1 a and b being any two numbers whatever1 we need only assume-- pi a#b_/;b1 to get at sqrt77pir#b7_/;a 4 b_/a7 r4 ,we naturally ask what sort of glimmer can ,mr4 ,smith have of the subject which he professes to treat8 ,on this point he has given satisfactory information4 ,i had mentioned the old problem of finding two mean proportionals1 #aai as a preliminary to the duplication of the cube4 ,on this mention ,mr4 ,smith writes as follows4 ,i put a few words in capitals2 and ,i write rq#bah for the sign of the square root1 which embarrasses small type3 ,this establishes the following infallible rule1 for finding two mean proportionals ,,of ,,equal ,,value1 and is more than a preliminary1 to the famous old problem of ',squaring the circle4' ,let any finite number1 say #bj1 and its fourth part 7#a_/d77bj7 #e1 be given numbers4 ,then rq7#bj x #e7 rq #ajj #aj1 is their mean proportional4 ,let this be a given mean proportional ,,to ,,find ,,another ,,mean ,,proportional ,,of ,,equal ,,value4 ,then #bj x pi_/#d #bj x #c4abe_/d #bj x 4#ghabe #ae4fbe will be the first number2 as #be 3 #af 33 rq #bj 3 rq #h4aib3 and 7rq #h4aib7b x pi_/#d #h4aib x 4#ghabe #f4d will be the second number2 therefore rq7#ae4fbe x #f4d7 rq #ajj #aj1 is the required mean proportional4444 ,now1 my good ,sir1 however competent you may be to prove every man a fool not every man1 ,mr4 ,smith6 only some2 pray learn logical quantification who now thinks1 or in times gone by has thought1 the ',squaring of the ,circle' a possibility2 ,i doubt1 and1 on the evidence afforded by your ,budget1 ,i cannot help doubting1 whether you were ever before competent to find two mean proportionals by my unique method4--7,nut1 pp4 #dg1 #dh47 ,that ,i never was1 ,i solemnly declare6 ,all readers can be made to see the following exposure4 ,when #e and #bj are given1 x is a mean proportional when in #e1 x1 #bj1 #e is to x as x to #bj4 ,and x must be #aj4 ,but x and y are two mean proportionals when in #e1 x1 y1 #bj1 x #abj is a mean proportional between #e and y1 and y is a mean proportional between x and #bj4 ,and these means are x #e cuberoot#d1 y #e cuberoot#af4 ,but ,mr4 ,smith finds one mean1 finds it again in a roundabout way1 and produces #aj and #aj as the two 7equal67 means1 in solution of the famous old problem4 ,this is enough3 if more were wanted1 there is more where this came from4 ,let it not be forgotten that ,mr4 ,smith has found a translator abroad1 two1 perhaps three1 followers at home1 and--most surprising of all--a real mathematician to try to set him right4 ,and this mathematician did not discover the character of the subsoil of the land he was trying to cultivate until a goodly octavo volume of letters had passed and repassed4 ,i have noticed1 in more quarters than one1 an apparent want of perception of the full amount of ,mr4 ,smith's ignorance3 persons who have not been in contact with the non-geometrical circle-squarers have a kind of doubt as to whether anybody can carry things so far4 ,but ,i am an old bird as ,mr4 ,smith himself calls me2 a ,simorg1 an all-knowing ,bird of ,ages in matters of cyclometry4 ,the curious phenomena of thought here exhibited illustrate1 as above said1 a remark ,i have long ago made on the effect of proper study of logic4 ,most persons reason well enough on matter to which they are accustomed1 and in terms with which they are familiar4 ,but in unaccustomed matter1 and with use of strange terms1 few except those who are practised in the abstractions of pure logic can be tolerably sure to keep their feet4 ,and one of the reasons is easily stated3 terms which are not quite familiar partake of the vagueness of the ,x and ,y on which the student of logic learns to see the formal force of a proposition independently of its material elements4 ,i make the following quotation from my fourth paper on logic in the ,cambridge ,transactions3 ,the uncultivated reason proceeds by a process almost entirely material4 ,though the necessary law of thought #aba must determine the conclusion of the ploughboy as much as that of ,aristotle himself1 the ploughboy's conclusion will only be tolerably sure when the matter of it is such as comes within his usual cognizance4 ,he knows that geese being all birds does not make all birds geese1 but mainly because there are ducks1 chickens1 partridges1 etc4 ,a beginner in geometry1 when asked what follows from ',every ,a is ,b1' answers ',every ,b is ,a4' ,that is1 the necessary laws of thought1 except in minds which have examined their tools1 are not very sure to work correct conclusions except upon familiar matter4444 ,as the cultivation of the individual increases1 the laws of thought which are of most usual application are applied to familiar matter with tolerable safety4 ,but difficulty and risk of error make a new appearance with a new subject2 and this1 in most cases1 until new subjects are familiar things1 unusual matter common1 untried nomenclature habitual2 that is1 until it is a habit to be occupied upon a novelty4 ,it is observed that many persons reason well in some things and badly in others2 and this is attributed to the consequence of employing the mind too much upon one or another subject4 ,but those who know the truth of the preceding remarks will not have far to seek for what is often1 perhaps most often1 the true reason4444 ,i maintain that logic tends to make the power of reason over the unusual and unfamiliar more nearly equal to the power over the usual and familiar than it would otherwise be4 ,the second is increased2 but the first is almost created4 ,mr4 ,james ,smith1 by bringing ignorance1 folly1 dishonesty into contact with my name1 in the way of conditional insinuation1 has done me a good turn3 he has given me right to a freedom of personal remark which ,i might have declined to take in the case of a person who is useful and respected in matters which he understands4 ,tit for tat is logic all the world over4 ,by the way1 what has become of the rest of the maxim3 we never hear it #abb now4 ,when ,i was a boy1 in some parts of the country at least1 it ran thus3 ,tit for tat2 ,butter for fat3 ,if you kill my dog1 ,i'll kill your cat4 ,he is a glaring instance of the truth of the observations quoted above4 ,i will answer for it that1 at the ,mersey ,dock ,board1 he never dreams of proving that the balance at the banker's is larger than that in the book by assuming that the larger sum is there1 and then proving that the other supposition--the smaller balance--is upon that assumption1 an absurdity4 ,he never says to another director1 ,how can you dare to refuse me a right to assume the larger balance1 when you yourself1 the other day1 said1--,suppose1 for argument's sake1 we had #hj1jjjl4 at the banker's1 though you knew the book only showed #cj1jjjl48 ,this is the way in which he has supported his geometrical paradox by ,euclid's example3 and this is not the way he reasons at the board2 ,i know it by the character of him as a man of business which has reached my ears from several quarters4 ,but in geometry and rational arithmetic he is a smatterer1 though expert at computation2 at the board he is a trained man of business4 ,the language of geometry is so new to him that he does not know what is meant by two mean proportionals3 but all the phrases of commerce are rooted in his mind4 ,he is most unerasably booked in the history of the squaring of the circle1 as the speculator who took a right to assume a proposition for the destruction of other propositions1 on the express ground that ,euclid assumes a proposition to show that it destroys itself3 which is as if the curate should demand permission to throttle the squire because ,st4 ,patrick drove the vermin to suicide to save themselves from slaughter4 ,he is conspicuous as a speculator who1 more visibly than almost any other known to history1 reasoned in a circle by way of reasoning on a circle4 ,but #abc what ,i have chiefly to do with is the force of instance which he has lent to my assertion that men who have not had real training in pure logic are unsafe reasoners in matter which is not familiar4 ,it is hard to get first-rate examples of this1 because there are few who find the way to the printer until practice and reflection have given security against the grossest slips4 ,i cannot but think that his case will lead many to take what ,i have said into consideration1 among those who are competent to think of the great mental disciplines4 ,to this end ,i should desire him to continue his efforts1 to amplify and develop his great principle1 that of proving a proposition by assuming it and taking as confirmation every consequence that does not contradict the assumption4 ,since my ,budget commenced1 ,mr4 ,smith has written me notes3 the portion which ,i have preserved--,i suppose several have been mislaid--makes a hundred and seven pages of note-paper1 closely written4 ,to all this ,i have not answered one word3 but ,i think ,i cannot have read fewer than forty pages4 ,in the last letter the writer informs me that he will not write at greater length until ,i have given him an answer1 according to the rules of good society4 ,did ,i not know that for every inch ,i wrote back he would return an ell8 ,surely in vain the net is spread in the eyes of anything that hath a wing4 ,there were several good excuses for not writing to ,mr4 ,j4 ,smith3 ,i will mention five4 ,first1 ,i distinctly announced at the beginning of this ,budget that ,i would not communicate with squarers of the circle4 ,secondly1 any answer ,i might choose to give might with perfect propriety be reserved for this article2 had the imputation of incivility been made after the first note1 ,i should immediately have replied to this effect3 but ,i presumed it was quite understood4 ,thirdly1 ,mr4 ,smith1 by his publication of ,e4 ,m4's letters against the wish of the writer1 had put himself out of the pale of correspondence4 ,fourthly1 he had also gone beyond the rules of good society in sending #abd letter after letter to a person who had shown by his silence an intention to avoid correspondence4 ,fifthly1 these same rules of good society are contrived to be flexible or frangible in extreme cases3 otherwise there would be no living under them2 and good society would be bad4 ,father ,aldrovand has laid down the necessary distinction--,i tell thee1 thou foolish ,fleming1 the text speaketh but of promises made unto ,christians1 and there is in the rubric a special exemption of such as are made to ,welchmen4 ,there is also a rubric to the rules of good society2 and squarers of the circle are among those whom there is special permission not to answer3 they are the wild ,welchmen of geometry1 who are always assailing1 but never taking1 the ,garde ,douloureuse#bai of the circle4 ,at this commentary1 proceeds the story1 the ,fleming grinned so broadly as to show his whole case of broad strong white teeth4 ,i know not whether the ,welchman would have done the like1 but ,i hope ,mr4 ,james ,smith will3 and ,i hope he has as good a case to show as ,wilkin ,flammock4 ,for ,i wish him long life and long health1 and should be very glad to see so much energy employed in a productive way4 ,i hope he wishes me the same3 if not1 ,i will give him what all his judicious friends will think a good reason for doing so4 ,his pamphlets and letters are all tied up together1 and will form a curious lot when death or cessation of power to forage among book-shelves shall bring my little library to the hammer4 ,and this time may not be far off3 for ,i was ,x years old in ,a4,d4 ,x#b2 not #d in ,a4,d4 #af1 nor #e in ,a4,d4 #be1 but still in one case under that law4 ,and now ,i have made my own age a problem of quadrature1 and ,mr4 ,j4 ,smith may solve it4 ,but ,i protest against his method of assuming a result1 and making itself prove itself3 he might in this way1 as sure as eggs is eggs 7a corruption of ,x is ,x71 make me #a1hfd years old1 which is a great deal too much4 #abe ,april #e1 #ahfd4--,mr4 ,smith continues to write me long letters1 to which he hints that ,i am to answer4 ,in his last1 of #ca closely written sides of note-paper1 he informs me1 with reference to my obstinate silence1 that though ,i think myself and am thought by others to be a mathematical ,goliath1 ,i have resolved to play the mathematical snail1 and keep within my shell4 ,a mathematical snail6 ,this cannot be the thing so called which regulates the striking of a clock2 for it would mean that ,i am to make ,mr4 ,smith sound the true time of day1 which ,i would by no means undertake upon a clock that gains #ai seconds odd in every hour by false quadrature4 ,but he ventures to tell me that pebbles from the sling of simple truth and common sense will ultimately crack my shell1 and put me hors de combat4#bbj ,the confusion of images is amusing3 ,goliath turning himself into a snail to avoid pi #c-a_/h1 and ,james ,smith1 ,esq41 of the ,mersey ,dock ,board3 and put hors de combat--which should have been cache#bba--;by pebbles from a sling4 ,if ,goliath had crept into a snail-shell1 ,david would have cracked the ,philistine with his foot4 ,there is something like modesty in the implication that the crack-shell pebble has not yet taken effect2 it might have been thought that the slinger would by this time have been singing-- ,and thrice and one-eighth ,i routed all my foes1 ,and thrice and one-eighth ,i slew the slain4 ,but he promises to give the public his nut-cracker if ,i do not1 before the ,budget is concluded1 unravel the paradox1 which is the mathematico-geometrical nut he has given me to crack4 ,mr4 ,smith is a crack man3 he will crack his own nut2 he will crack my shell2 in the mean time he cracks himself up4 ,heaven send he do not crack himself into lateral contiguity with himself4 ,on ,june #bg ,i received a letter1 in the handwriting of ,mr4 ,james ,smith1 signed ,nauticus4 ,i have ascertained #abf that one of the letters to the ,athenaeum signed ,nauticus is in the same handwriting4 ,i make a few extracts3 444 ,the important question at issue has been treated by a brace of mathematical birds with too much levity4 ,it may be said1 however1 that sarcasm and ridicule sometimes succeed1 where reason fails4444 ,such a course is not well suited to a discussion4444 ,for this reason ,i shall for the future this implies there has been a past1 so that ,nauticus is not before me for the first time endeavor to confine myself to dry reasoning from incontrovertible premises4 444 ,it appears to me that so far as his theory is concerned he comes off unscathed4 ,you might have found a hole in ,smith's circle 7have you seen a pamphlet bearing this title8 ,i never heard of it until now71 but after all it is quite possible the hole may have been left by design1 for the purpose of entrapping the unwary4 ,on the publication of the above1 the author of the pamphlet obligingly forwarded a copy to me of ,a ,hole in ,smith's ,circle--by a ,cantab3 ,longman and ,co41 #ahei1 7pp4 #ae74 ,it is pity to lose any fun we can get out of the affair1 says my almamaternal brother3 to which ,i add that in such a case warning without joke is worse than none at all1 as giving a false idea of the nature of the danger4 ,the ,cantab takes some absurdities on which ,i have not dwelt3 but there are enough to afford a ,cantab from every college his own separate hunting ground4 ,does this hint that his mode of proof1 namely1 assuming the thing to be proved1 was a design to entrap the unwary8 if so1 it bangs ,banagher4 ,was his confounding two mean proportionals with one mean proportional found twice over a trick of the same intent8 if so1 it beats cockfighting4 ,that ,nauticus is ,mr4 ,smith appears from other internal evidence4 ,in #ahai1 ,mr4 ,j4 ,c4 ,hobhouse#bbb was sent to ,newgate for a #abg libel on the ,house of ,commons which was only intended for a libel on ,lord ,erskine4#bbc ,the ex-,chancellor had taken ,mr4 ,hobhouse to be thinking of him in a certain sentence2 this ,mr4 ,hobhouse denied1 adding1 ,there is but one man in the country who is always thinking of ,lord ,erskine4 ,i say that there is but one man of our day who would couple me and ,mr4 ,james ,smith as a brace of mathematical birds4 ,mr4 ,smith's theory is unscathed by me4 ,not a doubt about it3 but how does he himself come off8 ,i should never think of refuting a theory proved by assumption of itself4 ,i left ,mr4 ,smith's pi untouched3 or1 if ,i put in my thumb and pulled out a plum1 it was to give a notion of the cook1 not of the dish4 ,the important question at issue was not the circle3 it was1 wholly and solely1 whether the abbreviation of ,james might be spelled ,jimm4#bbd ,this is personal to the verge of scurrility3 but in literary controversy the challenger names the weapons1 and ,mr4 ,smith begins with charge of ignorance1 folly1 and dishonesty1 by conditional implication4 ,so that the question is1 not the personality of a word1 but its applicability to the person designated3 it is enough if1 as the ,latin grammar has it1 ,verbum personale concordat cum nominativo4#bbe ,i may plead precedent for taking a liberty with the orthography of ,jem4 ,an instructor of youth was scandalized at the abrupt and irregular--but very effective--opening of ,wordsworth's little piece3 #abh ,a simple child ,that lightly draws its breath1 ,and feels its life in every limb1 ,what should it know of death8 ,so he mended the matter by instructing his pupils to read the first line thus3 ,a simple child1 dear brother ----4 ,the brother1 we infer from sound1 was to be ,james1 and the blank must therefore be filled up with ,jimb4 ,i will notice one point of the letter1 to make a little more distinction between the two birds4 ,nauticus lays down--quite correctly--that the sine of an angle is less than its circular measure4 ,he then takes #c4adaf for #ahj deg41 and finds that #cf' is 4#jajdgb4 ,but this is exactly what he finds for the sine of #cf' in tables3 he concludes that either #c4adaf or the tables must be wrong4 ,he does not know that sines1 as well as pi1 are interminable decimals1 of which the tables1 to save printing1 only take in a finite number4 ,he is a six-figure man3 let us go thrice again to make up nine1 and we have as follows3 ,circular measure of #cf' 4#jajdgaige444 ,sine of #cf' 4#jajdgaghd444 ,excess of measure over sine 4#jjjjjjaia444 ,mr4 ,smith invites me to say which is wrong1 the quadrature1 or the tables3 ,i leave him to guess4 ,he says his assertions arise naturally and necessarily out of the arguments of a circle-squarer3 he might just as well lay down that all the pigs went to market because it is recorded that ,this pig went to market4 ,i must say for circle-squarers that very few bring their pigs to so poor a market4 ,i answer the above argument because it is1 of all which ,mr4 ,james ,smith has produced1 the only one which rises to the level of a schoolboy3 to meet him halfway ,i descend to that level4 ,mr4 ,smith asks me to solve a problem in the ,athenaeum3 #abi and ,i will do it1 because the question will illustrate what is below schoolboy level4 ,let x represent the circular measure of an angle of #ae deg41 and y half the sine of an angle of #cj deg4 area of the square on the radius of a circle of diameter unity 4#be4 ,if x - y xy1 firstly1 what is the arithmetical value of xy8 secondly1 what is the angle of which xy represents the circular measure8 ,if x represent #ae deg4 and y be #a_/d1 xy represents #c deg4 #de'1 whether x - y be xy or no4 ,but1 y being #a_/d1 x - y is not xy unless x be #a_/c1 that is1 unless #abx or pi be #d1 which ,mr4 ,smith would not admit4 ,how could a person who had just received such a lesson as ,i had given immediately pray for further exposure1 furnishing the stuff so liberally as this8 ,is it possible that ,mr4 ,smith1 because he signs himself ,nauticus1 means to deny his own very regular1 legible1 and peculiar hand8 ,it is enough to make the other members of the ,liverpool ,dock ,board cry1 ,mersey on the man6 ,mr4 ,smith says that for the future he will give up what he calls sarcasm1 and confine himself1 as far as possible1 to what he calls dry reasoning from incontrovertible premises4 ,if ,i have fairly taught him that his sarcasm will not succeed1 ,i hope he will find that his wit's end is his logic's beginning4 ,i now reply to a question ,i have been asked again and again since my last ,budget appeared3 ,why do you take so much trouble to expose such a reasoner as ,mr4 ,smith8 ,i answer as a deceased friend of mine used to answer on like occasions--,a man's capacity is no measure of his power to do mischief4 ,mr4 ,smith has untiring energy1 which does something2 self-evident honesty of conviction1 which does more2 and a long purse1 which does most of all4 ,he has made at least ten publications1 full of figures which few readers can criticize4 ,a great many people are staggered to this extent1 that they imagine there must be #acj the indefinite something in the mysterious all this4 ,they are brought to the point of suspicion that the mathematicians ought not to treat all this with such undisguised contempt1 at least4 ,now ,i have no fear for pi3 but ,i do think it possible that general opinion might in time demand that the crowd of circle-squarers1 etc4 should be admitted to the honors of opposition2 and this would be a time-tax of five per cent41 one man with another1 upon those who are better employed4 ,mr4 ,james ,smith may be made useful1 in hands which understand how to do it1 towards preventing such opinion from growing4 ,a speculator who expressly assumes what he wants to prove1 and argues that all which contradicts it is absurd1 because it cannot stand side by side with his assumption1 is a case which can be exposed to all4 ,and the best person to expose it is one who has lived in the past as well as the present1 who takes misthinking from points of view which none but a student of history can occupy1 and who has something of a turn for the business4 ,whether ,i have any motive but public good must be referred to those who can decide whether a missionary chooses his pursuit solely to convert the heathen4 ,i shall certainly be thought to have a little of the spirit of ,col4 ,quagg1 who delighted in strapping the ,grace-walking ,brethren4 ,i must quote this myself3 if ,i do not1 some one else will1 and then where am ,i8 ,the ,colonel's principle is described as follows3 ,i licks ye because ,i kin1 and because ,i like1 and because ye'se critters that licks is good for4 ,skins ye have on1 and skins ,i'll have off2 hard or soft1 wet or dry1 spring or fall4 ,walk in grace if ye like till pumpkins is peaches2 but licked ye must be till your toe-nails drop off and your noses bleed blue ink4 ,and--licked--they--were--accordingly4 ,i am reminded of this by the excessive confidence with which ,mr4 ,james ,smith predicted that he would treat me as ,zephaniah ,stockdolloger 7,sam ,slick calls it slockdollager7 treated ,goliah ,quagg4 ,he has announced his #aca intention of bringing me1 with a contrite heart1 and clean shaved1--#daeibfe444 razored down to #be1--to a camp-meeting of circle-squarers4 ,but there is this difference3 ,zephaniah only wanted to pass the ,colonel's smithy in peace2 ,mr4 ,james ,smith sought a fight with me4 ,as soon as this ,budget began to appear1 he oiled his own strap1 and attempted to treat me as the terrible ,colonel would have treated the inoffensive brother4 ,he is at liberty to try again4 ,,the ,,moon ,,hoax4 ,the ,moon-hoax2 or the discovery that the moon has a vast population of human beings4 ,by ,richard ,adams ,locke4#bbf ,new ,york1 #ahei1 #hvo4 ,this is a reprint of the hoax already mentioned4 ,i suppose ,r4 ,a4 ,locke is the name assumed by ,m4 ,nicollet4#bbg ,the publisher informs us that when the hoax first appeared day by day in a morning paper1 the circulation increased fivefold1 and the paper obtained a permanent footing4 ,besides this1 an edition of #fj1jjj was sold off in less than one month4 ,the discovery was also published under the name of ,a4 ,r4 ,grant4#bbh ,sohncke's#bbi ,bibliotheca ,mathematica confounds this ,grant with ,prof4 ,r4 ,grant#bcj of ,glasgow1 the author of the ,history of ,physical ,astronomy1 who is accordingly made to guarantee the discoveries in the moon4 ,i hope ,adams ,locke will not merge in ,j4 ,c4 ,adams1#bca the co-discoverer of ,neptune4 ,sohncke gives the titles of #acb three ,french translations of the ,moon hoax at ,paris1 of one at ,bordeaux1 and of ,italian translations at ,parma1 ,palermo1 and ,milan4 ,a ,correspondent1 who is evidently fully master of details1 which he has given at length1 informs me that the ,moon hoax appeared first in the ,new ,york ,sun1 of which ,r4 ,a4 ,locke was editor4 ,it so much resembled a story then recently published by ,edgar ,a4 ,poe1 in a ,southern paper1 ,adventures of ,hans ,pfaal1 that some ,new ,york journals published the two side by side4 ,mr4 ,locke1 when he left the ,new ,york ,sun1 started another paper1 and discovered the manuscript of ,mungo ,park2#bcb but this did not deceive4 ,the ,sun1 however1 continued its career1 and had a great success in an account of a balloon voyage from ,england to ,america1 in seventy-five hours1 by ,mr4 ,monck ,mason1#bcc ,mr4 ,harrison ,ainsworth1#bcd and others4 ,i have no doubt that ,m4 ,nicollet was the author of the ,moon hoax1#bce written in a way which marks the practised observatory astronomer beyond all doubt1 and by evidence seen in the most minute details4 ,nicollet had an eye to ,europe4 ,i suspect that he took ,poe's story1 and made it a basis for his own4 ,mr4 ,locke1 it would seem1 when he attempted a fabrication for himself1 did not succeed4 ,the ,earth we inhabit1 its past1 present1 and future4 ,by ,capt4 ,drayson4#bcf ,london1 #ahei1 #hvo4 ,the earth is growing2 absolutely growing larger3 its diameter increases three-quarters of an inch per mile every year4 ,the foundations of our buildings will give way in #acc time3 the telegraph cables break1 and no cause ever assigned except ships' anchors1 and such things4 ,the book is for those whose common sense is unwarped1 who can judge evidence as well as the ablest philosopher4 ,the prospect is not a bad one1 for population increases so fast that a larger earth will be wanted in time1 unless emigration to the ,moon can be managed1 a proposal of which it much surprises me that ,bishop ,wilkins has a monopoly4 ,,impalement ,,by ,,request4 ,athenaeum1 ,august1 #ai1 #ahfe4 ,notice to ,correspondents4 ,r4 ,w4--,if you will consult the opening chapter of the ,budget of ,paradoxes1 you will see that the author presents only works in his own library at a given date2 and this for a purpose explained4 ,for ourselves we have carefully avoided allowing any writers to present themselves in our columns on the ground that the ,budget has passed them over4 ,we gather that ,mr4 ,de ,morgan contemplates additions at a future time1 perhaps in a separate and augmented work2 if so1 those who complain that others of no greater claims than themselves have been ridiculed may find themselves where they wish to be4 ,we have done what we can for you by forwarding your letter to ,mr4 ,de ,morgan4 ,the author of ,an ,essay on the ,constitution of the ,earth1 published in #ahdd1 demanded of the ,athenaeum1 as an act of fairness1 that a letter from him should be published1 proving that he had as much right to be impaled as ,capt4 ,drayson4 ,he holds1 on speculative grounds1 what the other claims to have proved by measurement1 namely1 that the earth is growing2 and he believes that in time--a good long time1 not our time--the earth and other planets may grow into suns1 with systems of their own4 ,this gentleman sent me a copy of his work1 after the commencement of my ,budget2 but ,i have no recollection of having received it1 and ,i cannot find it on the 7nursery8 #acd quarantine87 shelves on which ,i keep my unestablished discoveries4 ,had ,i known of this work in time1 7see the ,introduction7 ,i should of course1 have impaled it 7heraldically7 with the other work2 but the two are very different4 ,capt4 ,drayson professes to prove his point by results of observation2 and ,i think he does not succeed4 ,the author before me only speculates2 and a speculator can get any conclusion into his premises1 if he will only build or hire them of shape and size to suit4 ,it reminds me of a statement ,i heard years ago1 that a score of persons1 or near it1 were to dine inside the skull of one of the aboriginal animals1 dear little creatures6 ,whereat ,i wondered vastly1 nothing doubting2 facts being stubborn and not easy drove1 as ,mrs4 ,gamp said4 ,but ,i soon learned that the skull was not a real one1 but artificially constructed by the methods--methods which have had striking verifications1 too--which enable zoologists to go the whole hog by help of a toe or a bit of tail4 ,this took off the edge of the wonder3 a hundred people can dine inside an inference1 if you draw it large enough4 ,the method might happen to fail for once3 for instance1 the toe-bone might have been abnormalized by therian or saurian malady2 and the possibility of such failure1 even when of small probability1 is of great alleviation4 ,the author before me is1 apparently1 the sole fabricator of his own premises4 ,with vital force in the earth and continual creation on the part of the original ,creator1 he expands our bit of a residence as desired4 ,but1 as the ,newtoness of ,cookery observed1 ,first catch your hare4 ,when this is done1 when you have a growing earth1 you shall dress it with all manner of proximate causes1 and serve it up with a growing ,moon for sauce1 a growing ,sun1 if it please you1 at the other end1 and growing planets for side-dishes4 ,hoping this amount of impalement will be satisfactory1 ,i go on to something else4 #ace ,,the ,,hailesean ,,system ,,of ,,astronomy4 ,the ,hailesean ,system of ,astronomy4 ,by ,john ,davey ,hailes#bcg 7two pages duodecimo1 #ahfj74 ,he offers to take #ajj1jjjl4 to #a1jjjl4 that he shows the sun to be less than seven millions of miles from the earth4 ,the earth in the center1 revolving eastward1 the sun revolving westward1 so that they meet at half the circle distance in the #bd hours4 ,the diameter of the circle being #ihcidehcjc1 the circumference is #cjiaaefiibj4 ,the following written challenge was forwarded to the ,council of the ,astronomical ,society3 it will show the general reader--and help him towards earning his name--what sort of things come every now and then to our scientific bodies4 ,i have added punctuation3 ,challenge4 #a1jjj to #cj1jjj4 ,leverrier's#bch name stand placed first4 ,do the worthy ,frenchman justice4 ,by awarding him the medal in a trice4 ,give ,adams#bci an extra--of which neck and neck the race4 ,now ,i challenge to meet them and the ,f4,r4,s4's all1 ,for good will and one thousand pounds to their thirty thousand withall1 ,that ,i produce a system1 which shall measure the time1 ,when the ,sun was vertical to ,gibeon1 afterward to ,syene4 ,to meet any time in ,london--name your own period1 ,to be decided by a majority of twelve persons--a ,president1 odd4 ,that mean1 if the twelve equally divide1 the ,president decide1 ,i should prefer the ,bishop of ,london1 over the meeting to preside4 ,,john ,,davy ,,hailes4 ,feb4 #ag1 #ahdg4 ,mr4 ,hailes still issues his flying sheets4 ,the last ,i have met with 7,october #g1 #ahfc7 informs us that the latitude of #acf ,england is slowly increasing1 which is the true cause of the alteration in the variation of the magnet4 ,mr4 ,hailes continues his researches4 ,witness his new ,hailesean system of ,astronomy1 displaying ,joshua's miracle-time1 origin of time from science1 with ,bible and ,egyptian history4 ,rewards offered for astronomical problems4 ,with magnetism1 etc4 etc4 ,astronomical challenge to all the world4 ,published at ,cambridge1 in #ahfe4 ,the author agrees with ,newton in one marked point4 ,errores quam minimi non sunt contemnendi1#bdj says ,isaac3 meaning in figures1 not in orthography4 ,mr4 ,hailes enters into the spirit1 both positive and negative1 of this dictum1 by giving the distance of ,sidius from the center of the earth at #afc1afb1jjh miles #aj feet #h inches #ag-bhths of an inch4 ,of course1 he is aware that the center of figure of the earth is #ag4aiih inches from the center of gravity4 ,which of the two is he speaking of8 ,the ,divine ,mystery of ,life4 ,london #ahfa1 #ahmo4 7pp4#cb74 ,the author has added one class to zoology1 which is printed in capitals1 as derived from zoe1 life1 not from zoon1 animal4 ,that class is of ,incorporealia1 order ,i41 ,infinitum1 of one genus without plurality1 ,deus3 order ,,ii41 ,finita1 angels good and evil4 ,the rest is all about a triune system1 with a diagram4 ,the author is not aware that ,greek3 zoon is not animal1 but living being4 ,aristotle had classed gods under ,greek3 zoa1 and has been called to account for it by moderns who have taken the word to mean animal4 ,a ,,chance ,,for ,,inventors4 ,explication du ,zodiaque de ,denderah1 des ,pyramides1 et de ,genese4 ,par le ,capitaine au longcours ,justin ,roblin4#bda ,caen1 #ahfa4 #hvo4 #acg ,capt4 ,roblin1 having discovered the sites of gold and diamond mines by help of the zodiac of ,denderah1 offered half to the shareholders of a company which he proposed to form4 ,one of our journals1 by help of the zodiac of ,esne1 offered1 at five francs a head1 to tell the shareholders the exact amount of gold and diamonds which each would get1 and to make up the amount predicted to those who got less4 ,there are moods of the market in ,england in which this company could have been formed3 so we must not laugh at our neighbors4 ,,johannes ,,von ,,gumpach4 ,a million's worth of property1 and five hundred lives annually lost at sea by the ,theory of ,gravitation4 ,a letter on the true figure of the earth1 addressed to the ,astronomer ,royal1 by ,johannes von ,gumpach4#bdb ,london1 #ahfa1 #hvo4 7pp4 #ed74 ,the true figure and dimensions of the earth1 in a letter addressed to the ,astronomer ,royal4 ,by ,joh4 von ,gumpach4 #bnd ed4 entirely recast4 ,london1 #ahfb1 #hvo4 7pp4 #bff74 ,two issues of a letter published with two different title-pages1 one addressed to the ,secretary of the ,royal ,society1 the other to the ,secretary of the ,royal ,astronomical ,society4 ,it would seem that the same letter is also issued with two other titles1 addressed to the ,british ,association and the ,royal ,geographical ,society4 ,by ,joh4 von ,gumpach4 ,london1 #ahfb1 #hvo4 ,baby-,worlds4 ,an essay on the nascent members of our solar household4 ,by ,joh4 von ,gumpach4 ,london1 #ahfc1 #hvo4 ,the earth1 it appears1 instead of being flattened1 is elongated at the poles3 by ignorance of which the loss above mentioned occurs yearly4 ,there is1 or is to be1 a substitute for attraction and an application hitherto neglected1 of a #ach recognized law of optics to the astronomical theory1 showing the true orbits of the heavenly bodies to be perfectly circular1 and their orbital motions to be perfectly uniform4 all irregularities being1 ,i suppose1 optical delusions4 ,mr4 ,von ,gumpach is a learned man2 what else1 time must show4 ,,slander ,,paradoxes4 ,perpetuum ,mobile3 or ,search for self-motive ,power4 ,by ,henry ,dircks4#bdc ,london1 #ahfa1 #hvo4 ,a useful collection on the history of the attempts at perpetual motion1 that is1 at obtaining the consequences of power without any power to produce them4 ,september #g1 #ahfc1 a correspondent of the ,times gave an anecdote of ,george ,stephenson1#bdd which he obtained from ,robert ,stephenson4#bde ,a perpetual motionist wanted to explain his method2 to which ,george replied--,sir6 ,i shall believe it when ,i see you take yourself up by the waistband1 and carry yourself about the room4 ,never was the problem better stated4 ,there is a paradox of which ,i ought to give a specimen1 ,i mean the slander-paradox2 the case of a person who takes it into his head1 upon evidence furnished entirely by the workings of his own thoughts1 that some other person has committed a foul act of which the world at large would no more suppose him guilty than they would suppose that the earth is a flat bordered by ice4 ,if ,i were to determine on giving cases in which the self-deluded person imagines #aci a conspiracy against himself1 there would be no end of choices4 ,many of the grosser cases are found at last to be accompanied by mental disorder1 and it is difficult to avoid referring the whole class to something different from simple misuse of the reasoning power4 ,the first instance is one which puts in a strong light the state of things in which we live1 brought about by our glorious freedom of thought1 speech1 and writing4 ,the ,government treated it with neglect1 the press with silent contempt1 and ,i will answer for it many of my readers now hear of it for the first time1 when it comes to be enrolled among circle-squarers and earth-stoppers1 where1 as the old philosopher said1 it will not gravitate1 being in proprio loco4#bdf #ahfb4 ,on new year's day1 #ahfb1 when the nation was in the full tide of sympathy with the ,queen1 and regret for its own loss1 a paper called the ,free ,press published a number devoted to the consideration of the causes of the death of the ,prince ,consort4 ,it is so rambling and inconsecutive that it takes more than one reading to understand it4 ,it is against the ,times newspaper4 ,first1 the following insinuation3 ,to the legal mind1 the part of the part taken by the ,times will present a prima facie case of the gravest nature1 in the evident fore-knowledge of the event1 and the preparation to turn it to account when it should have occurred4 ,the article printed on ,saturday must have been written on ,friday4 ,that article could not have appeared had the ,prince been intended to live4 ,next1 it is affirmed that the ,times intended to convey the idea that the ,prince had been poisoned4 ,up to this point we are merely dealing with words which the ,times publishes1 and these can leave not a shadow of doubt that there is an intention to promulgate the idea that ,prince ,albert had been poisoned4 ,the article then goes on with a strange olio of #adj insinuations to the effect that the ,prince was the obstacle to ,russian intrigue1 and that if he should have been poisoned1--which the writer strongly hints may have been the case1--some ,minister under the influence of ,russia must have done it4 ,enough for this record4 ,un sot trouve toujours un plus sot qui l'admire3#bdg who can he be in this case8 ,,the ,,neptune ,,controversy4 #ahdf4 ,at the end of this year arose the celebrated controversy relative to the discovery of ,neptune4 ,those who know it are well aware that ,mr4 ,adams's#bdh now undoubted right to rank with ,le ,verrier#bdi was made sure at the very outset by the manner in which ,mr4 ,airy1#bej the ,astronomer ,royal1 came forward to state what had taken place between himself and ,mr4 ,adams4 ,those who know all the story about ,mr4 ,airy being arrested in his progress by the neglect of ,mr4 ,adams to answer a letter1 with all the imputations which might have been thrown upon himself for laxity in the matter1 know also that ,mr4 ,airy's conduct exhibited moral courage1 honest feeling1 and willingness to sacrifice himself1 if need were1 to the attainment of the ends of private justice1 and the establishment of a national claim4 ,a writer in a magazine1 in a long and elaborate article1 argued the supposition--put in every way except downright assertion1 after the fashion of such things--that ,mr4 ,airy had communicated ,mr4 ,adams's results to ,m4 ,le ,verrier1 with intention that they should be used4 ,his presumption as to motive is that1 had ,mr4 ,adams been recognized1 then the discovery must have been indisputably an ,englishman's1 and that ,englishman not the ,astronomer ,royal4 ,mr4 ,adams's conclusions were retouched in ,france1 and sent #ada over the year after4 ,the proof given is that it cannot be imagined otherwise4 ,can it then be imagined that the ,astronomer ,royal received such results from ,mr4 ,adams1 supported as they were by ,professor ,challis's#bea valuable testimony as to their probable accuracy1 and did not bring the ,french astronomer acquainted with them1 especially as he was aware that his friend was engaged in matters bearing directly upon these results8 ,the whole argument the author styles evidence which ,i consider it difficult to refute4 ,he ends by calling upon certain persons1 of whom ,i am one1 to see ample justice done4 ,this is the duty of every one1 according to his opportunities4 ,so when the reputed author--the article being anonymous--was1 in #ahdi1 proposed as a ,fellow of the ,astronomical ,society1 ,i joined--if ,i remember right1 ,i originated--an opposition to his election1 until either the authorship should be denied1 or a proper retraction made4 ,the friends of the author neither denied the first1 nor produced the second3 and they judged it prudent to withdraw the proposal4 ,had ,i heard of any subsequent repentance1 ,i would have taken some other instance1 instead of this3 should ,i yet hear of such a thing1 ,i will take care to notice it in the continuation of this list1 which ,i confidently expect1 life and health permitting1 to be able to make in a few years4 ,this much may be said1 that the author1 in a lecture on the subject1 given in #ahdi1 and published with his name1 did not repeat the charge4 ,the libel was published in the ,mechanics' ,magazine1#beb 7vol4 for #ahdf1 pp4 #fjd-fae73 and the editor supported it as follows1 7vol4 for #ahdg1 p4 #dgf74 ,in answer to ,mr4 ,sheepshanks's charitable hope that he had been hoaxed1 #adb he says3 ,mr4 ,sheepshanks cannot certainly have read the article referred to4444 ,severe and inculpatory it is--unjust some may deem it 7though we ourselves are out of the number47444 ,a 'hoax' forsooth6 ,may we be often the dupes of such hoaxes6 ,he then goes on to describe the article as directed against the ,astronomer ,royal's alleged neglect to give ,mr4 ,adams that encouragement and protection which was his due1 and does not hint one word about the article containing the charge of having secretly and fraudulently transmitted news of ,mr4 ,adams's researches to ,france1 that an ,englishman might not have the honor of the discovery4 ,mr4 ,sheepshanks having called this a deliberate calumny1 without a particle of proof or probability to support it1 the editor says what the reverend gentleman means by this1 we are at a loss to understand4 ,he then proceeds not to remember4 ,i repeat here1 what ,i have said elsewhere1 that the management of the journal has changed hands2 but from #ahdf to #ahef1 it had the collar of ,s4,s4 7scientific slander74 ,the prayer for more such things was answered 7,see p4 #cdi74 ,,james ,,ivory4#bec ,i have said that those who are possessed with the idea of conspiracy against themselves are apt to imagine both conspirators and their bad motives and actions4 ,a person who should take up the idea of combination against himself without feeling ill-will and originating accusations would be indeed a paradox4 ,but such a paradox has existed4 ,it is very well known1 both in and beyond the scientific world1 that the late ,james ,ivory was subject to the #adc impression of which ,i am speaking2 and the diaries and other sources of anecdote of our day will certainly1 sooner or later1 make it a part of his biography4 ,the consequence will be that to his memory will be attached the unfavorable impression which the usual conduct of such persons creates2 unless it should happen that some one who knows the real state of the case puts the two sides of it properly together4 ,ivory was of that note in the scientific world which may be guessed from ,laplace's description of him as the first geometer in ,britain and one of the first in ,europe4 ,being in possession of accurate knowledge of his peculiarity in more cases than one2 and in one case under his own hand3 and having been able to make full inquiry about him1 especially from my friend the late ,thomas ,galloway#bed--who came after him at ,sandhurst--one of the few persons with whom he was intimate3--,i have decided1 after full deliberation1 to forestall the future biographies4 ,that ,ivory was haunted by the fear of which ,i have spoken1 to the fullest extent1 came to my own public and official knowledge1 as ,secretary of the ,astronomical ,society4 ,it was the duty of ,mr4 ,epps1#bee the ,assistant ,secretary1 at the time when ,francis ,baily#bef first announced his discovery of the ,flamsteed ,papers1 to report to me that ,mr4 ,ivory had called at the ,society's apartments to inquire into the contents of those papers1 and to express his hope that ,mr4 ,baily was not attacking living persons under the names of ,newton and ,flamsteed4#beg ,mr4 ,galloway1 to whom ,i communicated this1 immediately went to ,mr4 ,ivory1 and succeeded1 after some explanation1 in setting him right4 ,this is but one of many instances in which a man of thoroughly sound judgment in every other respect seemed to be under a complete chain of delusions about the conduct of #add others to himself4 ,but the paradox is this3--,i never could learn that ,ivory1 passing his life under the impression that secret and unprovoked enemies were at work upon his character1 ever originated a charge1 imputed a bad motive1 or allowed himself an uncourteous expression4 ,some letters of his1 now in my possession1 referring to a private matter1 are1 except in the main impression on which they proceed1 unobjectionable in every point3 they might have been written by a cautious friend1 whose object was1 if possible1 to prevent a difference from becoming a duel without compromising his principal's rights or character4 ,knowing that in some quarters the knowledge of ,ivory's peculiarity is more or less connected with a notion that the usual consequences followed1 ,i think the preceding statement due to his memory4 ,,three ,,classes ,,of ,,journals4 ,in such a record as the present1 which mixes up the grossest speculative absurdities with every degree of what is better1 an instance of another kind may find an appropriate place4 ,the faults of journalism1 when merely exposed by other journalism pass by and are no more regarded4 ,a distinct account of an undeniable meanness1 recorded in a work of amusement and reference both1 may have its use3 such a thing may act as a warning4 ,an editor who is going to indulge his private grudge may be prevented from counting upon oblivion as a matter of certainty4 ,there are three kinds of journals1 with reference to the mode of entrance of contributors4 ,first1 as a thing which has been1 but which now hardly exists1 there is the journal in which the editor receives a fixed sum to find the matter4 ,in such a journal1 every article which the editor can get a friend to give him is so much in his own pocket1 which has a great tendency to lower the character of the articles2 but ,i am not concerned with this point4 ,secondly1 there is the journal which is supported by voluntary contributions of #ade matter1 the editor selecting4 ,thirdly1 there is the journal in which the contributor is paid by the proprietors in a manner with which the literary editor has nothing to do4 ,the third class is the safe class1 as its editors know3 and1 as a usual rule1 they refuse unpaid contributions of the editorial cast4 ,it is said that when ,canning#beh declined a cheque forwarded for an article in the ,quarterly1 ,john ,murray#bei sent it back with a blunt threat that if he did not take his money he could never be admitted again4 ,the great publisher told him that if men like himself in position worked for nothing1 all the men like himself in talent who could not afford it would not work for the ,quarterly4 ,if the above did not happen between ,canning and ,murray1 it must have happened between some other two4 ,now journals of the second class--and of the first1 if such there be--have a fault to which they alone are very liable1 to say nothing of the editorial function 7see the paper at the beginning1 p4 #aa et seq471 being very much cramped1 a sort of gratitude towards effective contributors leads the journal to help their personal likes and dislikes1 and to sympathize with them4 ,moreover1 this sort of journal is more accessible than others to articles conveying personal imputation3 and when these provoke discussion1 the journal is apt to take the part of the assailant to whom it lent itself in the first instance4 ,,the ,,mechanics' ,,magazine4 ,among the journals which went all lengths with contributors whom they valued1 was the ,mechanics' ,magazine#bfj in the period #ahdf-ef4 ,i cannot say that matters have not mended in the last ten years3 and ,i draw some #adf presumption that they have mended from my not having heard1 since #ahef1 of anything resembling former proceedings4 ,and on actual inquiry1 made since the last sentence was written1 ,i find that the property has changed hands1 the editor is no longer the same1 and the management is of a different stamp4 ,this journal is chiefly supported by voluntary articles3 and it is the journal in which1 as above noted1 the ridiculous charge against the ,astronomer ,royal was made in #ahdi4 ,the following instance of attempt at revenge is so amusing that ,i select it as the instance of the defect which ,i intend to illustrate2 for its puerility brings out in better relief the points which are not so easily seen in more adult attempts4 ,the ,mechanics' ,magazine1 which by its connection with engineering1 etc41 had always taken somewhat of a mathematical character1 began1 a little before #ahdf1 to have more to do with abstract science4 ,observing this1 ,i began to send short communications1 which were always thankfully received1 inserted1 and well spoken of4 ,any one who looks for my name in that journal in #ahdf-di1 will see nothing but the most respectful and even laudatory mention4 ,in ,may #ahdi occurred the affair at the ,astronomical ,society1 and my share in forcing the withdrawal of the name of the alleged contributor to the journal4 ,in ,february #ahej occurred the opportunity of payment4 ,the ,companion to the ,almanac#bfa had to be noticed1 in which1 as then usual1 was an article signed with my name4 ,i shall give the review of this article entire1 as a sample of a certain style1 as well as an illustration of my point4 ,the reader will observe that my name is not mentioned4 ,this would not have done2 the readers of the ,magazine would have stared to see a name of not infrequent occurrence in previous years all of a sudden fallen from the heaven of respect into the pit of contempt1 like ,lucifer1 son of the morning4 ,but before #adg giving the review1 ,i shall observe that ,mr4 ,adams1 in whose favor the attack on the ,astronomer ,royal was made1 did not appreciate the favor2 and of course did not come forward to shield his champion4 ,this gave deadly offence1 as appear from the following passage1 7,february #af1 #ahej73 ,it was our intention to enter into a comparison of the contents of our ,nautical ,almanack with those of its rival1 the ,connaissance des ,temps2 but we shall defer it for the present4 ,the ,nautical ,almanack for #ahea will contain ,mr4 ,adams's paper ',on the ,perturbation of ,uranus'2 and when it comes1 in due course1 before the public1 we are quite sure that that gentleman will expect that we shall again enter upon the subject with peculiar delight4 ,whilst we have a thorough loathing for mean1 cowardly1 crawlers--we have an especial pleasure in maintaining the claims of men who are truly grateful as well as highly talented3 ,mr4 ,adams1 therefore1 will find that he cannot be disappointed--and the occasion will afford us an opportunity for making the comparison to which we have adverted4 ,this passage illustrates what ,i have said on the editorial function 7,vol4 ,i1 p4 #ae74 ,what precedes and follows has some criticism on the ,government1 the ,astronomer ,royal1 etc41 but reserved in allusion1 oblique in sarcasm1 and not fiercely uncourteous4 ,the coarseness of the passage ,i have quoted shows editorial insertion1 which is also shown by its blunder4 ,the inserter is waiting for the ,almanac of #ahea that he may review ,mr4 ,adams's paper1 which is to be contained in it4 ,his own contributor1 only two sentences before the insertion1 had said1 ,the ,nautical ,almanac1 we believe1 is published three or four years in advance4 ,in fact1 the ,almanac for #ahea--with ,mr4 ,adams's paper at the end--was published at the end of #ahdg or very beginning of #ahdh2 it had therefore been more than two years before the public when the passage quoted was written4 ,and probably every person in the country who was fit to review ,mr4 ,adams's #adh paper--and most of those who were fit to read it--knew that it had been widely circulated1 in revise1 at the end of #ahdf3 my copy has written on it1 #b;d revise1 ,december #bg1 #ahdf1 at noon1 in the handwriting of the ,superintendent of the ,almanac2 and ,i know that there was an extensive issue of these revises1 brought out by the ,le-,verrier-and-,adams discussion4 ,i now give the review of myself1 7,february #bc1 #ahej73 ,the ,british ,almanack and ,companion4 ,the ,companion to this ,almanack1 for some years after its first publication1 annually contained scientific articles by ,sir ,j4 ,lubbock#bfb and others of a high order and great interest2 we have now1 however1 closed the publication as a scientific one in remembrance of what it was1 and not in consequence of what it is4 ,its list of contributors on science1 has grown 'small by degrees and beautifully less1' until it has dwindled down to one--'a last rose of summer left withering alone4' ,the one contributor has contributed one paper ',on ,ancient and ,modern ,usage in ,reckoning4' ,the learned critic's chef d'oeuvre1 is considered1 by competent judges1 to be an ,essay on ,old ,almanacks printed a few years ago in this annual1 and supposed to be written with the view of surpassing a profound memoir on the same subject by ,james ,o4 ,halliwell1#bfc ,esq41 ,f4,r4 and ,a4,s4,s41 but the tremendous effort which the learned writer then made to excel many titled competitors for honors in the antique line appears to have had a sad effect upon his mental powers--at any rate1 his efforts have since yearly become duller and duller2 happily1 at last1 we should suppose1 'the ancient #adi and modern usage in reckoning' indicates the lowest point to which the vis inertia of the learned writer's peculiar genius can force him4 ,we will give a few extracts from the article4 ,the learned author says1 ',those who are accustomed to settle the meaning of ancient phrases by self-examination will find some strange conclusions arrived at by us4' ,the writer never wrote a more correct sentence--it admits of no kind of dispute4 ',language and counting1' says the learned author1 'both came before the logical discussion of either4 ,it is not allowable to argue that something is or was1 because it ought to be or ought to have been4 ,that two negatives make an affirmative1 ought to be2 if no man have done nothing1 the man who has done nothing does not exist1 and every man has done something4 ,but in ,greek1 and in uneducated ,english1 it is unquestionable that 'no man has done nothing' is only an emphatic way of saying that no man has done anything2 and it would be absurd to reason that it could not have been so1 because it should not4'--p4 #e4 ',but there is another difference between old and new times1 yet more remarkable1 for we have nothing of it now3 whereas in things indivisible we count with our fathers1 and should say in buying an acre of land1 that the result has no parts1 and that the purchaser1 till he owns all the ground1 owns none1 the change of possession being instantaneous4 ,this second difference lies in the habit of considering nothing1 nought1 zero1 cipher1 or whatever it may be called1 to be at the beginning of the scale of numbers4 ,count four days from ,monday3 we should now say ,tuesday1 ,wednesday1 ,thursday1 ,friday2 formerly1 it would have been ,monday1 ,tuesday1 ,wednesday1 ,thursday4 ,had we asked1 what at that rate is the first day from ,monday1 all would have stared at a phrase they had never heard4 ,those who were capable of extending language would have said1 ,why it must be ,monday itself3 the rest would have said1 there can #aej be no first day from ,monday1 for the day after is ,tuesday1 which must be the second day3 ,monday1 one2 ,tuesday1 two1'--p4 #aj4 ,we assure our readers that the whole article is equally lucid1 and its logic alike formal4 ,there are some exceedingly valuable footnotes2 we give one of the most interesting1 taken from the learned ,mr4 ,halliwell's profound book on ,nursery ,rhymes#bfd--;a celebrated production1 for which it is supposed the author was made ,f4,r4,s4 ',one's nine1 ,two's some1 ,three's a many1 ,four's a penny1 ,five's a little hundred4' ',the last line refers to five score1 the so-called hundred being more usually six score4 ,the first line1 looked at etymologically1 is one is not one1 and the change of thought by which nine1 the decimal of one1 aims to be associated with the decimal of plurality is curious3'--,very4 ,this valuable and profound essay will very probably be transferred to the next edition of the learned ,mr4 ,halliwell's rare work1 of kindred worth1 entitled ',,rara ,,mathematica1' it will then be deservedly handed down to posterity as a covering for cheap trunks--a most appropriate archive for such a treasure4 ,in ,december1 #ahdf1 the ,mechanics' ,magazine published a libel on ,airy in the matter of the discovery of ,neptune4 ,in ,may1 #ahdi1 one 99 99 99 was to have been brought forward for election at the ,astronomical ,society1 and was opposed by me and others1 on the ground that he was the probable author of this libel1 and that he would not1 perhaps could #aea not1 deny it4 ,n4,b4 ,i no more doubt that he was the author then ,i doubt that ,i am the author of this sentence4#bfe ,accordingly1 99 99 99 was withdrawn1 and a discussion took place1 for which see the ,athenaeum1 ,no4 #aabf1 ,may #bf1 #ahdi1 p4 #edd4 ,the ,mechanics' ,magazine was very sore1 but up to this day has never ventured beyond an attack on ,airy1 private whisperings against ,adams--7see ante1 p4 #adg71--;and the above against myself4 ,in due time1 ,i doubt not my name will appear as one of the ames damnees#bff of the ,mechanics' ,magazine4#bfg ,t4 ,s4 ,,davies ,,on ,,euclid4 ,first1 as to ,mr4 ,halliwell4 ,the late ,thomas ,stephens ,davies1#bfh excellent in geometry1 and most learned in its history1 was also a good hand at enmity1 though not implacable4 ,he and ,mr4 ,halliwell1 who had long before been very much one1 were1 at this date1 very much two4 ,i do not think ,t4 ,s4 ,davies wrote this article2 and ,i think that by giving my reasons ,i shall do service to his memory4 ,it must have been written at the beginning of ,february2 and within three days of that time ,t4 ,s4 ,davies was making over to me1 by his own free act1 to be kept until claimed by the relatives1 what all who knew even his writings knew that he considered as the most precious deposit he had ever had in his keeping--,horner's#bfi papers4 ,his letter announcing the transmission is dated ,february #b1 #ahej4 ,this is a strong point2 but there is another quite as strong4 ,euclid and #aeb his writings were matters on which ,t4 ,s4 ,davies knew neither fear nor favor3 he could not have written lightly about a man who stood high with him as a judge of ,euclid4 ,now in this very letter of ,feb4 #b1 there is a sentence which ,i highly value1 because1 as aforesaid1 it is on a point on which he would never have yielded anything1 to which he had paid life-long attention1 and on which he had the bias of having long stood alone4 ,in fact1 knowing--and what ,i shall quote confirms me1--that in the matter of ,euclid his hand was against every man1 ,i expected1 when ,i sent him a copy of my #bb-;column article1 ,eucleides in ,smith's ,dictionary1#bgj to have received back a criticism1 that would have blown me out of the water3 and ,i thought it not unlikely that a man so well up in the subject might have made me feel demolished on some points4 ,instead of this1 ,i got the following3 ,although on one or two minor points ,i do not quite accord with your views1 yet as a whole and without regard to any minor points1 ,i think you are the first who has succeeded in a delineation of ,euclid as a geometer4 ,all this duly considered1 it is utterly incredible that ,t4 ,s4 ,davies should have written the review in question4 ,and yet ,mr4 ,halliwell is treated just as ,t4 ,s4 ,davies would have treated him1 as to tone and spirit4 ,the inference in my mind is that we have here a marked instance of the joining of hatreds which takes place in journals supported by voluntary contributions of matter4 ,should anything ever have revived this article--and no one ever knows what might have been fished up from the forgotten mass of journals--the treatment of ,mr4 ,halliwell would certainly have thrown a suspicion on ,t4 ,s4 ,davies1 a large and regular contributor to the ,magazine4 ,it is good service to his memory to point out what makes it incredible that he should have written so unworthy an article4 ,the fault is this4 ,there are four extracts3 the first #aec three are perfectly well printed4 ,the printing of the ,mechanics' ,magazine was very good4 ,i was always exceedingly satisfied with the manner in which my articles appeared1 without my seeing proof4 ,most likely these extracts were printed from my printed paper2 if not the extractor was a good copier4 ,i know this by a test which has often served me4 ,i use the subjunctive--if no man have done nothing1 an ordinary transcriber1 narrating a quotation almost always lets his own habit write has4 ,the fourth extract has three alterations1 all tending to make me ridiculous4 ,none is altered1 in two places1 into nine1 denial into decimal1 and comes into aims2 so that none1 the denial of one1 comes to be associated with the denial of plurality1 reads as nine1 the decimal of one1 aims to be associated with the decimal of plurality4 ,this is intentional2 had it been a compositor's reading of bad handwriting1 these would not have been the only mistakes2 to say nothing of the corrector of the press4 ,and both the compositor and reader would have guessed1 from the first line being translated into one is not one1 that it must have been one's none1 not one's nine4 ,but it was not intended that the gem should be recovered from the unfathomed cave1 and set in a ,budget of ,paradoxes4 ,we have had plenty of slander-paradox4 ,i now give a halfpennyworth of bread to all this sack1 an instance of the paradox of benevolence1 in which an individual runs counter to all the ideas of his time1 and sees his way into the next century4 ,at ,amiens1 at the end of the last century1 an institution was endowed by a ,m4 de ,morgan1 to whom ,i hope ,i am of kin1 but ,i cannot trace it2 the name is common at ,amiens4 ,it was the first of the kind ,i ever heard of4 ,it is a ,salle d',asyle for children1 who are taught and washed and taken care of during the hours in which their parents must be at work4 ,the founder was a large wholesale grocer and colonial importer1 who was made a ,baron by ,napoleon ,i for his commercial success and his charities4 #aed ,,jas4 ,,smith ,,again4 #ahfb4 ,mr4 ,smith replies to me1 still signing himself ,nauticus3 ,i give an extract3 ,by hypothesis what1 again6 let #ad deg4 #bd' be the chord of an arc of #ae deg4 but ,i wont1 says #ad deg4 #bd'1 and consequently equal to a side of a regular polygon of #bd sides inscribed in the circle4 ,then #d times #ad deg4 #bd' #eg deg4 #cf' the radius of the circle 444 ,that is1 four times the chord of an arc is the chord of four times the arc3 and the sum of four sides of a certain pentagon is equal to the fifth4 ,this is the capital of the column1 the crown of the arch1 the apex of the pyramid1 the watershed of the elevation4 ,oh6 ,j4 ,s46 ,j4 ,s46 groans ,geometry--,summum ,j4 ,s4 summa injuria6#bga ,the other ,j4 ,s41 ,joseph ,scaliger1#bgb as already mentioned1 had his own way of denying that a straight line is always the shortest distance between two points4 ,a parallel might be instituted1 but not in half a column4 ,and ,j4 ,s4 the second has been so tightly handled that he may now be dismissed1 with an inscription for his circular shield1 obtained by changing ,lexica contexat into ,circus quadrandus in an epigram of ,j4 ,s4 the first3 ,si quem dura manet sententia judicis1 olim ,damnatum aerumnis suppliciisque caput1 ,hunc neque fabrili lassent ergastula massa1 ,nec rigidas vexent fossa metalla manus4 ,circus quadrandus3 nam--caetera quid moror8--omnes ,poenarum facies hic labor unus habet4#bgc #aee ,i had written as far as damnatum when in came the letter of ,nauticus as a printed slip1 with a request that ,i would consider the slip as a 'revised copy4' ,not a word of alteration in the part ,i have quoted6 ,and in the evening came a letter desiring that ,i would alter a gross error2 but not the one above3 this is revising without revision6 ,if there were cyclometers enough of this stamp1 they would1 as cultivation progresses--and really1 with ,john ,stuart ,mill in for ,westminster1 it seems on the move1 even though1 as ,i learn while correcting the proof1 ,gladstone be out from ,oxford2 for ,oxford is no worse than in #ahbi1 while ,westminster is far above what she ever has been3 election time excuses even such a parenthesis as this--be engaged to amuse those who can afford it with paralogism at their meals1 after the manner of the other jokers who wore the caps and bells4 ,the rich would then order their dinners with panem et ,circenses1--up with the victuals and the circle-games--as the poor did in the days of old4 ,mr4 ,smith is determined that half a column shall not do4 ,not a day without something from him3 letter1 printed proof1 pamphlet4 ,in what is the last at this moment of writing he tells me that part of the title of a work of his will be ,professor ,de ,morgan in the pillory without hope of escape4 ,and where will he be himself8 ,this ,i detected by an effort of reasoning which ,i never could have made except by following in his steps4 ,in all matters connected with pi the letters l and g are closely related3 this appears in the well-known formula for the time of oscillation pi sqrt7l 3 g74 ,hence g may be written for l1 but only once3 do it twice1 and you require the time to be pi sqrt7l#b 3 g#b74 ,this may be reinforced by observing that if as a datum1 or if you dislike that word1 by hypothesis1 the first l be a g1 it is absurd that it should be an l4 ,write g for the first l1 and we have un fait accompli4 ,i shall be in pillory2 and overhead1 in a cloud1 will sit ,mr4 ,james ,smith on one stick laid across two others1 under a nimbus of #c-a_/h diameters to #aef the circumference--in pi-glory4 ,oh for a drawing of this scene6 ,mr4 ,de ,morgan presents his compliments to ,mr4 ,james ,smith1 and requests the honor of an exchange of photographs4 ,july #bf4--;,another printed letter4--,mr4 ,james ,smith begs for a distinct answer to the following plain question3 ,have ,i not in this communication brought under your notice truths that were never before dreamed of in your geometrical and mathematical philosophy8 ,to which1 he having taken the precaution to print the word truths in italics1 ,i can conscientiously answer1 ,yes1 you have4 ,and now ,i shall take no more notice of these truths1 until ,i receive something which surpasses all that has yet been done4 ,a ,,few ,,small ,,paradoxers4 ,the ,circle secerned from the ,square2 and its area gauged in terms of a triangle common to both4 ,by ,wm4 ,houlston1#bgd ,esq4 ,london and ,jersey1 #ahfb1 #dto4 ,mr4 ,houlston squares at about four poetical quotations in a page1 and brings out pi #c4adbac4444 ,his frontispiece is a variegated diagram1 having parts designated ,inigo and ,outigo4 ,all which relieves the subject1 but does not remove the error4 ,considerations respecting the figure of the ,earth4444 ,by ,c4 ,f4 ,bakewell4#bge ,london1 #ahfb1 #hvo4 ,newton and others think that in a revolving sphere the #aeg loose surface matter will tend to the equator3 ,mr4 ,bakewell thinks it will tend to the poles4 ,on eccentric and centric force3 a new theory of projection4 ,by ,h4 ,f4 ,a4 ,pratt1 ,m4,d4#bgf ,london1 #ahfb1 #hvo4 ,dr4 ,pratt not only upsets ,newton1 but cuts away the very ground he stands on3 for he destroys the first law of motion1 and will not have the natural tendency of matter in motion to be rectilinear4 ,this1 as we have seen1 was ,john ,walsh's#bgg notion4 ,in a more recent work ,on ,orbital ,motion1 ,london1 #ahfc1 #hvo41 ,dr4 ,pratt insists on another of ,walsh's notions1 namely1 that the precession of the equinoxes is caused by the motion of the solar system round a distant central sun4 ,in this last work the author refers to a few notes1 which completely destroy the theory of gravitation in terms perfectly intelligible as well to the unlearned as to the learned3 to me they are quite unintelligible1 which rather tends to confirm a notion ,i have long had1 that ,i am neither one thing nor the other4 ,there is an ambiguity of phrase which delights a writer on logic1 always on the look-out for specimens of homonymia or aequivocatio4 ,the author1 as a physician1 is accustomed to appeal from mere formulae3 accordingly1 he sets at nought the whole of the mathematics1 which he does not understand4 ,this equivocation between the formula of the physician and that of the mathematician is as good1 though not so perceptible to the world at large1 as that made by ,mr4 ,briggs's friend in ,punch's picture1 which ,i cut out to paste into my ,logic4 ,mr4 ,briggs wrote for a couple of bruisers1 meaning to prepare oats for his horses3 his friend sent him the ,whitechapel ,chicken and the ,bayswater ,slasher1 with the gloves1 all ready4 #aeh ,on matter and ether1 and the secret laws of physical change4 ,by ,t4 ,r4 ,birks1 ,m4,a4#bgh ,cambridge1 #ahfb1 #hvo4 ,bold efforts are made at molecular theories1 and the one before me is ably aimed4 ,when the ,newton of this subject shall be seated in his place1 books like the present will be sharply looked into1 to see what amount of anticipation they have made4 ,,dr4 ,,thorn ,,and ,,mr4 ,,biden4 ,the history of the 'thorn tree and bush' from the earliest to the present time3 in which is clearly and plainly shown the descent of her most gracious ,majesty and her ,anglo-,saxon people from the half tribe of ,ephraim1 and possibly from the half tribe of ,manasseh2 and consequently her right and title to possess1 at the present moment1 for herself and for them1 a share or shares of the desolate cities and places in the land of their forefathers6 ,by ,theta1 ,m4,d4#bgi 7,private circulation47 ,london1 #ahfb1 #hvo4 ,this is much about ,thorn1 and its connected words1 ,thor1 ,thoth1 ,theta1 etc4 ,it is a very mysterious vagary4 ,the author of it is the person whom ,i have described elsewhere as having for his device the round man in the three-cornered hole1 the writer of the little heap of satirical anonymous letters about the ,beast and #fff4 ,by accident ,i discovered the writer3 so that if there be any more thorns to crackle under the pot1 they need not be anonymous4 ,nor will they be anonymous4 ,since ,i wrote the above1 ,i have received onymous letters1 as ominous as the rest4 ,the writer1 ,william ,thorn1 ,m4,d41 is obliged to reveal #aei himself1 since it is his object to prove that he himself is one #fff4 ,by using ,w for double ,vau 7or #ab7 he cooks the number out of his own name4 ,but he says it is the number not of a beast but of a man1 and adds1 ,thereby hangs a tale6 which sounds like contradiction4 ,he informs me that he will talk the matter over with me3 but ,i shall certainly have nothing to say to a gentleman of his number2 it is best to keep on the safe side4 ,in one letter ,i am informed that not a line should ,i have had1 but for my sneer at #fff1 which1 therefore1 ,i am well pleased to have given4 ,i am also told that my name means the 'garden of death1' that place in which the tree of knowledge was plucked1 and so you are like your name 'dead' to the fact that you are an ,israelite1 like those in ,ezekiel #cg ch4 ,some hints are given that ,i shall not fare well in the next world1 which any one who reads the chapter in ,ezekiel will see is quite against his comparison4 ,the reader must not imagine that my prognosticator means ,morgan to be a corruption of ,mortjardin2 he proves his point by ,hebrew3 but any philologist would tell him the true derivation of the name1 and how ,glamorgan came to get it4 ,it will be of much comfort to those young men who have not got through to know that the tree of knowledge itself was once in the same case4 ,and so good bye to #fff for the present1 and the assumption that the enigma is to be solved by the united numeral forces of the letters of a word4 ,it is worthy of note that1 as soon as my ,budget commenced1 two guardian spirits started up1 fellow men as to the flesh1 both totally unknown to me3 they have stuck to me from first to last4 ,james ,smith1 ,esq41 finally ,nauticus1 watches over my character in this world1 and would fain preserve me from ignorance1 folly1 and dishonesty1 by inclosing me in a magic circle of #c-a_/h diameters in circumference4 ,the round man in the three-cornered hole1 finally ,william ,thorn1 ,m4,d41 takes charge of my future destiny1 #afj and tries to bring me to the truth by unfolding a score of meanings--all right--of #fff4 ,he hints that ,i1 and my wife1 are servants of ,satan3 at least he desires us both to remember that we cannot serve ,god and ,satan2 and he can hardly mean that we are serving the first1 and that he would have us serve the second4 ,as becomes an interpreter of the ,apocalypse1 he uses seven different seals2 but not more than one to one letter4 ,if his seals be all signet-rings1 he must be what ,aristophanes calls a sphragidonychargocometical fellow4 ,but--and many thanks to him for the same--though an ,m4,d41 he has not sent me a single vial4 ,and so much for my tree of secular knowledge and my tree of spiritual life3 ,i dismiss them with thanks from myself and thanks from my reader4 ,the dual of the ,pythagorean system was ,isis and ,diana2 of the ,jewish law1 ,moses and ,aaron2 and of the ,city of ,london1 ,gog and ,magog2 of the ,paradoxiad1 ,james ,smith1 ,esq41 and ,william ,thorn1 ,m4,d4 ,september1 #ahff4 ,mr4 ,james ,biden#bhj has favored me with some of his publications4 ,he is a rival of ,dr4 ,thorn2 a prophet by name-right and crest-right4 ,he is of royal descent through the ,de ,biduns4 ,he is the watchman of ,ezekiel3 ,god has told him so4 ,he is the author of ,the ,true ,church1 a phrase which seems to have a book-meaning and a mission-meaning4 ,he shall speak for himself3 ,a crest of the ,bidens has significance4 ,it is a lion rampant between wings--wings in ,scripture denote the flight of time4 ,thus the beasts or living creatures of the ,revelations have each six wings1 intimating a condition of mankind up to and towards the close of six thousand years of ,bible teaching4 ,the two wings of the crest would thus intimate power towards the expiration of #bjjj years1 as time is marked in the history of ,great ,britain4 #afa ,in a recent publication1 ,the ,pestilence1 ,why ,inflicted1 are given many reasons why the writer thinks himself to be the appointed watchman foretold by ,ezekiel1 chapters iii4 and xxxiii4 ,among the reasons are many prophecies fulfilled in him4 ,of these it is now needful to note two as bearing especially on the subject of the reign of ,darius4 #a4--;,in ,daniel it is said1 ',darius the ,median took the kingdom1 being about threescore and two years old4'--,daniel v4 #ca4 ,when ',belshazzar' the king of the ,chaldeans is found wanting1 ,darius takes the kingdom4 ,it is not given him by the popular voice2 he asserts his right1 and this is not denied4 ,he takes it when about sixty-two years of age4 ,the language of ,daniel is prophetic1 and ,darius has in another an antitype4 ,the writer was born ,july #ahth1 #ahjc2 and the claim was asserted at the close of #ahfe1 when he was about sixty-two years of age4 ,the claims which have been asserted demand a settled faith1 and which could only be reached through a long course of divine teaching4 ,when ,i was a little boy at school1 one of my school-fellows took it into his head to set up a lottery of marbles3 the thing took1 and he made a stony profit4 ,soon1 one after another1 every boy had his lottery1 and it was1 ,i won't put into yours unless you put into mine4 ,this knocked up the scheme4 ,it will be the same with the prophets4 ,dr4 ,thorn1 ,mr4 ,biden1 ,mrs4 ,cottle1#bha etc4 will grow imitators1 until we are all pointed out in the ,bible3 but ,a will not admit ,b's claim unless ,b admits his4 ,for myself1 as elsewhere shown1 ,i am the first ,beast in the ,revelations4 ,every contraband prophet gets a few followers3 it is a great point to make these sequacious people into ,buridan's asses1 which they will become when prophets are so numerous that there is no choosing4 #afb ,,sir ,g4 ,c4 ,,lewis4 ,an historical survey of the ,astronomy of the ,ancients4 ,by the ,rt4 ,hon4 ,sir ,g4 ,c4 ,lewis4#bhb #hvo4 #ahfb4 ,there are few men of our day whom ,i admire more than the late ,sir ,g4 ,lewis3 he was honest1 earnest1 sagacious1 learned1 and industrious4 ,he probably sacrificed his life to his conjunction of literature and politics3 and he stood high as a minister of state in addition to his character as a man of letters4 ,the work above named is of great value1 and will be read for its intrinsic merit1 consulted for its crowd of valuable references1 quoted for its aid to one side of many a discussion1 and opposed for its force against the other4 ,its author was also a wit and a satirist4 ,i know of three classical satires of our day which are inimitable imitations3 ,mr4 ,malden's#bhc ,pragmatized ,legends1 ,mr4 ,mansel's#bhd ,phrontisterion1 and ,sir ,g4 ,cornewall ,lewis's ,inscriptio ,antiqua4 ,in this last1 ,,heydiddlediddlethecatandthefiddle etc4 is treated as an ,oscan inscription1 and rendered into ,latin by approved methods4 ,as few readers have seen it1 ,i give the result3 ,hejus dedit libenter1 dedit libenter4 ,deus propitius est1 deus donatori libenter favet4 ,deus in viarum #afc junctura ovorum dape colitur1 deus mundi4 ,deus in litatione voluit1 benigno animo1 haedum1 taurum intra fines loci sacri portandos4 ,deus1 bis lustratus1 beat fossam sacrae libationis4#bhe ,how then comes the history of astronomy among the paradoxes8 ,simply because the author1 so admirably when writing about what he knew1 did not know what he did not know1 and blundered like a circle-squarer4 ,and why should the faults of so good a writer be recorded in such a list as the present8 ,for three reasons3 ,first1 and foremost1 because if the exposure be not made by some one1 the errors will gradually ooze out1 and the work will get the character of inaccurate4 ,nothing hurts a book of which few can fathom the depths so much as a plain blunder or two on the surface4 ,secondly1 because the reviews either passed over these errors or treated them too gently1 rather implying their existence than exposing them4 ,thirdly1 because they strongly illustrate the melancholy truth1 that no one knows enough to write about what he does not know4 ,the distinctness of the errors is a merit2 it proceeds from the clear-headedness of the author4 ,the suppression in the journals may be due partly to admiration of the talent and energy which lived two difficult lives at once1 partly to respect for high position in public affairs1 partly to some of the critics being themselves men of learning only1 unable to detect the errors4 ,but we know that action and reaction are equal and contrary4 ,if our generation take no notice of defects1 and allow them to go down undetected among merits1 the next generation will discover them1 will perhaps believe us incapable of detecting them1 at least will pronounce our judgment good for nothing1 and will form an #afd opinion in which the merits will be underrated3 so it has been1 is1 and will be4 ,the best thing that can be done for the memory of the author is to remove the unsound part that the remainder may thrive4 ,the errors do not affect the work2 they occur in passages which might very well have been omitted3 and ,i consider that1 in making them conspicuous1 ,i am but cutting away a deleterious fungus from a noble tree4 7,p4 #aed74 ,the periodic times of the five planets were stated by ,eudoxus1#bhf as we learn from ,simplicius2#bhg the following is his statement1 to which the true times are subjoined1 for the sake of comparison3 ,,statement ,,of ,,eudoxus ,,true ,,time ,mercury #a year -- #hg;d4 #bc;h4 ,venus #a -- #bbd;d4 #af;h4 ,mars #b #ay4 #cba;d4 #bc;h4 ,jupiter #ab #aay4 #cae;d4 #ad;h4 ,saturn #cj #biy4 #agd;d4 #a;h4 ,upon this determination two remarks may be made4 ,first1 the error with respect to ,mercury and ,venus is considerable2 with respect to ,mercury1 it is1 in round numbers1 #cfe instead of #hh days1 more than four times too much4 ,aristotle remarks that ,eudoxus distinguishes ,mercury and ,venus from the other three planets by giving them one sphere each1 with the poles in common4 ,the proximity of ,mercury to the sun would render its course difficult to observe and to measure1 but the cause of the large error with respect to ,venus 7#acj days7 is not apparent4 #afe ,sir ,g4 ,lewis takes ,eudoxus as making the planets move round the sun2 he has accordingly compared the geocentric periods of ,eudoxus with our heliocentric periods4 ,what greater blunder can be made by a writer on ancient astronomy than giving ,eudoxus the ,copernican system8 ,if ,mercury were a black spot in the middle of the sun it would of course move round the earth in a year1 or appear to do so3 let it swing a little on one side and the other of the sun1 and the average period is still a year1 with slight departures both ways4 ,the same for ,venus1 with larger departures4 ,say that a person not much accustomed to the distinction might for once write down the mistake2 how are we to explain its remaining in the mind in a permanent form1 and being made a ground for such speculation as that of the difficulty of observing ,mercury leading to a period four times what it ought to be1 corrected in proof and published by an industrious and thoughtful person8 ,only in one way3 the writer was quite out of his depth4 ,this one case is conclusive2 be it said with all respect for the real staple of the work and of the author4 ,he knew well the difference of the systems1 but not the effect of the difference3 he is another instance of what ,i have had to illustrate by help of a very different person1 that it is difficult to reason well upon matter which is not familiar4 7,p4 #bed74 ,copernicus1 in fact1 supposed the axis of the earth to be always turned towards the ,sun47#afi7 7#afi74 ,see ,delambre1 ,hist4 ,astr4 ,mod41 ,vol4 ,i1 p4 #if4 ,it was reserved to ,kepler to propound the hypothesis of the constant parallelism of the earth's axis to itself4 ,if there be one thing more prominent than another in the work of ,copernicus himself1 in the popular explanations of it1 and in the page of ,delambre#bhh cited1 it is that the parallelism of the earth's axis is a glaring part of the #aff theory of ,copernicus4 ,what ,kepler#bhi did was to throw away1 as unnecessary1 the method by which ,copernicus1 per fas et nefas1#bij secured it4 ,copernicus1 thinking of the earth's orbital revolution as those would think who were accustomed to the solid orbs--and much as the stoppers of the moon's rotation do now3 why do they not strengthen themselves with ,copernicus8--thought that the earth's axis would always incline the same end towards the sun1 unless measures were taken to prevent it4 ,he did take measures3 he invented a compensating conical motion of the axis to preserve the parallelism2 and1 which is one of the most remarkable points of his system1 he obtained the precession of the equinoxes by giving the necessary trifle more than compensation4 ,what stares us in the face at the beginning of the paragraph to which the author refers8 ,c'est donc pour arriver a ce parallelisme1 ou pour le conserver1 que ,copernic a cru devoir recourir a ce mouvement egal et oppose qui detruit l'effet qu'il attribue si gratuitement au premier1 de deranger le parallelisme4#bia ,parallelism at any price1 is the motto of ,copernicus3 you need not pay so dear1 is the remark of ,kepler4 ,the opinions given by ,sir ,g4 ,lewis about the effects of modern astronomy1 which he does not understand and singularly undervalues1 will now be seen to be of no authority4 ,he fancies that--to give an instance--for the determination of a ship's place1 the invention of chronometers has been far more important than any improvement in astronomical theory 7p4 #bed74 ,not to speak of latitude1--though the omission is not without importance1--he ought to have known that longitude is found by the difference between what o'clock it is at ,greenwich and at the ship's place1 at #afg one absolute moment of time4 ,now if a chronometer were quite perfect--which no chronometer is1 be it said--and would truly tell ,greenwich mean time all over the world1 it ought to have been clear that just as good a watch is wanted for the time at the place of observation1 before the longitude of that place with respect to ,greenwich can be found4 ,there is no such watch1 except the starry heaven itself3 and that watch can only be read by astronomical observation1 aided by the best knowledge of the heavenly motions4 ,i think ,i have done ,sir ,g4 ,lewis's very excellent book more good than all the reviewers put together4 ,i will give an old instance in which literature got into confusion about astronomy4 ,theophrastus1#bib who is either the culprit or his historian1 attributes to ,meton1#bic the contriver of the lunar calendar of nineteen years1 which lasts to this day1 that his solstices were determined for him by a certain ,phaeinus of ,elis on ,mount ,lycabettus4 ,nobody else mentions this astronomer3 though it is pretty certain that ,meton himself made more than one appointment with him for the purpose of observing solstices2 and we may be sure that if either were behind his time1 it was ,meton4 ,for ,phaeinus ,helius is the shining sun himself2 and in the astronomical poet ,aratus#bid we read about the nineteen years of the shining sun3 ,greek3 ,enneakaideka kukla phaeinou eelioio4#bie ,some man of letters must have turned ,apollo into ,phaeinus of ,elis2 and there he is in the histories of astronomy to #afh this day4 ,salmasius#bif will have ,aratus to have meant him1 and proposes to read ,greek3 eleioio3 he did not observe that ,phaeinus is a very common adjective of ,aratus1 and that1 if his conjecture were right1 this ,phaeinus would be the only non-mythical man in the poems of ,aratus4 ,when ,i read ,sir ,george ,lewis's book1 the points which ,i have criticized struck me as not to be wondered at1 but ,i did not remember why at the time4 ,a ,chancellor of the ,exchequer and a writer on ancient astronomy are birds of such different trees that the second did not recall the first4 ,in #ahee ,i was one of a deputation of about twenty persons who waited on ,sir ,g4 ,lewis1 as ,chancellor of the ,exchequer1 on the subject of a decimal coinage4 ,the deputation was one of much force3 ,mr4 ,airy1 with myself and others1 represented mathematics2 ,william ,brown1#big whose dealings with the ,united ,states were reckoned by yearly millions1 counted duodecimally in ,england and decimally in ,america1 was the best1 but not the only1 representative of commerce4 ,there were bullionists1 accountants1 retailers1 etc4 ,sir ,g4 ,l4 walked into the room1 took his seat1 and without waiting one moment1 began to read the deputation a smart lecture on the evils of a decimal coinage2 it would require alteration of all the tables1 it would impede calculation1 etc4 etc4 ,of those arguments against it which weighed with many of better knowledge than his1 he obviously knew nothing4 ,the members of the deputation began to make their statements1 and met with curious denials4 ,he interrupted me with ,surely there is no doubt that the calculations of our books of arithmetic are easier #afi than those in the ,french books4 ,he was not aware that the universally admitted superiority of decimal calculation made many of those who prefer our system for the market and the counter cast a longing and lingering look towards decimals4 ,my answer and the smiles which he saw around1 made him give a queer puzzled look1 which seemed to say1 ,i may be out of my depth here6 ,his manner changed1 and he listened4 ,i saw both the slap-dash mode in which he dealt with subjects on which he had not thought1 and the temperament which admitted suspicion when the means of knowledge came in his way4 ,having seen his two phases1 ,i wonder neither at his more than usual exhibition of shallowness when shallow1 nor at the intensity of the contrast when he had greater depth4 ,,decimal ,,coinage4 ,among the paradoxers are the political paradoxers who care not how far they go in debate1 their only object being to carry the ,house with them for the current evening4 ,what ,i have said of editors ,i repeat of them4 ,the preservation of a very marked instance1 the association of political recklessness with cyclometrical and ,apocalyptic absurdity1 may have a tendency to warn1 not indeed any hardened public-man and sinner1 but some young minds which have yearnings towards politics1 and are in formation of habits4 ,in the debate on decimal coinage of ,july #ab1 #ahee1 ,mr4 ,lowe1#bih then member for ,kidderminster1 an effective speaker and a smart man1 exhibited himself in a speech on which ,i wrote a comment for the ,decimal ,association4 ,i have seldom seen a more wretched attempt to distort the points of a public question than the whole of this speech4 ,looking at the intelligence shown by the speaker on other occasions1 #agj it is clear that if charity1 instead of believing all things1 believed only all things but one1 he might tremble for his political character2 for the honesty of his intention on this occasion might be the incredible exception4 ,i give a few paragraphs with comments3 ,in commenting on the humorous1 but still argumentative speech of ,mr4 ,lowe1 the member for ,kidderminster1 we may observe1 in general1 that it consists of points which have been several times set forth1 and several times answered4 ,mr4 ,lowe has seen these answers1 but does not allude to them1 far less attempt to meet them4 ,there are1 no doubt1 individuals1 who show in their public speaking the outward and visible signs of a greater degree of acuteness than they can summon to guide their private thinking4 ,if ,mr4 ,lowe be not one of these1 if the power of his mind in the closet be at all comparable to the power of his tongue in the ,house1 it may be suspected that his reserve with respect to what has been put forward by the very parties against whom he was contending1 arises from one or both of two things--a high opinion of the arguments which he ignored--a low opinion of the generality of the persons whom he addressed4 ,both1 ,i doubt not4 ,did they calculate in florins ,in the name of common sense1 8 how can it be objected to a system that people do not use it before it is introduced8 ,let the decimal system be completed1 and calculation shall be made in florins2 that is1 florins shall take their proper place4 ,if florins were introduced now1 there must be a column for the odd shilling4 ,he was glad that some hon4 ,if the hon4 gentleman make gentleman had derived benefit this assertion of himself1 it from the issue of florins4 ,his is not for us to gainsay it4 only experience of their ,it only proves that he is one convenience was1 that when he of that class of #aga men who ought to have received are described in the old song1 half-a-crown1 he had generally of which one couplet runs received a florin1 and when he thus3 ought to have paid a florin1 he had generally paid ,i sold my cow to buy me a half-a-crown4 7,hear1 hear1 calf2 and laughter47 ,i never make a bargain but ,i lose half1 ,with a etc4 etc4 etc4 ,but he cannot mean that ,englishmen in general are so easily managed4 ,and as to ,jonathan1 who is but ,john lengthened out a little1 he would see creation whittled into chips before he would even split what may henceforth be called the ,kidderminster difference4 ,the ,house1 not unmoved--for it laughed--with sly humor decided that the introduction of the florin had been eminently successful and satisfactory4 ,the truth is that ,mr4 ,lowe here attacks nothing except the coexistence of the florin and half-crown4 ,we are endeavoring to abolish the half-crown4 ,let ,mr4 ,lowe join us2 and he will1 if we succeed1 be relieved from the pressure on his pocket which must arise from having the turn of the market always against him4 ,from a florin they get to #b ,note the sophism of expressing #b-eths of a penny1 but who our coin in terms of the ever bought anything1 who ever penny1 which we abandon1 reckoned or wished to reckon instead of the florin1 which in such a coin as that8 we retain4 ,remember that this 7,hear1 hear47 #b #b-eths is the hundredth part of the pound1 which is called1 as yet1 a cent4 ,nobody buys anything at a cent1 because the cent is not yet introduced4 ,nobody reckons in cents for the same reason4 ,everybody wishes to reckon in cents1 who wishes to combine the advantage of decimal reckoning with the preservation of the pound as #agb the highest unit of account2 amongst others1 a majority of the ,house of ,commons1 the ,bank of ,england1 the majority of ,london bankers1 the ,chambers of ,commerce in various places1 etc4 etc4 etc4 ,such a coin could never come ,does #b-a_/b;d4 never pass from into general circulation hand to hand8 ,and is #b-a_/b;d4 because it represents nothing so precisely the modulus of which corresponds with any of popular wants1 that an the wants of the people4 alteration of #d per cent4 would make it useless8 ,of all the values which #b-a_/b;d4 measures1 from three pounds of potatoes down to certain arguments used in the ,house of ,commons1 there is not one for which a cent would not do just as well4 ,mr4 ,lowe has fallen into the misconception of the person who admired the dispensation of ,providence by which large rivers are made to run through cities so great and towns so many4 ,if the cent were to be introduced to-morrow1 straightway the buns and cakes1 the soda-water bottles1 the short omnibus fares1 the bunches of radishes1 etc4 etc4 etc41 would adapt themselves to the coin4 ,if the proposed system were ,the confusion of ideas here adopted1 they would all be exhibited is most instructive4 compelled to live in decimals ,the speaker is under the for ever2 if a man dined at a impression that we are public house he would have to introducing fractions3 the pay for his dinner in decimal truth is1 that we only want to fractions4 7,hear1 hear47 ,he abandon the more difficult objected to that1 for he fractions which we have got1 thought that a man ought to be and to introduce easier able to pay for his dinner in fractions4 ,does he deny this8 integers4 7,hear1 hear1 and a ,let us trace his denial to its laugh47 legitimate consequences4 ,a man ought to pay for his dinner in integers4 #agc ,now1 if ,mr4 ,lowe insists on it that our integer is the pound1 he is bound to admit that the present integer is the pound1 of which a shilling1 etc41 are fractions4 ,the next time he has a chop and a pint of stout in the city1 the waiter should say--,a pound1 sir1 to you1 and should add1 ,please to remember the waiter in integers4 ,mr4 ,lowe fancies that when he pays one and sixpence1 he pays in integers1 and so he does1 if his integer be a penny or a sixpence4 ,let him bring his mind to contemplate a mil as the integer1 the lowest integer1 and the seven cents five mils which he would pay under the new system would be payment in integers also4 ,but1 as it happens with some others1 he looks up the present system1 with ,cocker1#bii and ,walkingame1#cjj and always looks down the proposed system4 ,the word decimal is obstinately associated with fractions1 for which there is no need4 ,hence it becomes so much of a bugbear1 that1 to parody the lines of ,pope1 which probably suggested one of ,mr4 ,lowe's phrases-- ,dinner he finds too painful an endeavor1 ,condemned to pay in decimals for ever4 ,the present system1 however1 ,a pleasant sum even for an had not yet been changed into accomplished mathematician4 decimal system4 ,that change ,what does divided by the might appear very easy to decimal of a pound mean8 accomplished mathematicians ,perhaps it means reduced to and men of science1 but it was the decimal of a pound6 ,mr4 one which it would be very ,lowe supposes1 as many others difficult to carry out4 7,hear1 do1 that1 after the change1 hear74 ,what would have to be all calculations will be done8 ,every sum would have to proposed in old money1 and be reduced into a vulgar then converted into new4 ,he fraction of a pound1 and then cannot hit the #agd idea that divided by the decimal of a the new coins will take the pound--a pleasant sum for an place of the old4 ,this lack of old applewoman to work out6 apprehension will presently 7,hear1 hear1 and laughter47 appear further4 ,it would not be an agreeable ,let the members be assured task1 even for some members of that nine half-pence will be1 that ,house1 to reduce #d-a_/b;d41 for every practical purpose1 or nine half-pence1 to mils4 #ah mils4 ,but now to the fact 7,hear1 hear47 asserted4 ,davies ,gilbert#cja used to maintain that during the long period he sat in the ,house1 he never knew more than three men in it1 at one time1 who had a tolerable notion of fractions4 ,i heard him give the names of three at the time when he spoke3 they were ,warburton1#cjb ,pollock1#cjc and ,hume4#cjd ,he himself was then out of ,parliament4 ,joseph ,hume affirmed that he had never met with more than ten members who were arithmeticians4 ,but both these gentlemen had a high standard4 ,mr4 ,lowe has given a much more damaging opinion4 ,he evidently means that the general run of members could not do his question4 ,it is done as follows3 ,since farthings gain on mils1 at the rate of a whole mil in #bd farthings 7#bd farthings being #be mils71 it is clear that #ah farthings being three-quarters of #bd farthings1 will gain three-quarters of a mil2 that is1 #ah farthings are eighteen #age mils and three-quarters of a mil4 ,any number of farthings is as many mils and as many twenty-fourths of a mil4 ,to a certain extent1 we feel able to protest against the manner in which ,kidderminster has treated the other constituencies4 ,we do not hold it impossible to give the ,members of the ,house in general a sufficient knowledge of the meaning and consequences of the decimal succession of units1 tens1 hundreds1 thousands1 etc42 and we believe that there are in the ,house itself competent men1 in number enough to teach all the rest4 ,all that is wanted is the power of starting from the known to arrive at the unknown4 ,now there is one kind of decimals with which every member is acquainted--the ,chiltern ,hundreds4 ,if public opinion would enable the competent minority to start from this in their teaching1 not as a basis1 but as an alternative1 in three weeks the fundamentals would be acquired1 and members in general would be as fit to turn #d-a_/b;d4 into mils1 as any boys on the lower forms of a commercial school4 ,for a long period of years1 allusion to the general ignorance of arithmetic1 has been a standing mode of argument1 and has always been well received3 whenever one member describes others as knownothings1 those others cry ,hear to the country in a transport of delight4 ,in the meanwhile the country is gradually arriving at the conclusion that a true joke is no joke4 ,the main objection was1 if ,fine words1 wrongly used4 ,the they went below #f;d41 that the new coins are commensurable new scale of coins would not with1 and in a finite ratio be commensurate in any finite to1 the old ones4 ,the farthing ratio with anything in this is to the mil as #be to #bd4 ,the new currency of mils4 speaker has something here in the bud1 which we shall presently meet with in the flower2 and fallacies are more easily nipped in flower than in bud4 #agf ,no less than five of our ,this dreadful change of value present coins must be called consists in sixpence farthing in1 or else--which would be going to the half-shilling worse--new values must be instead of sixpence4 ,whether given to them4 the new farthings be called mils or not is of no consequence4 ,if a poor man put a penny in ,mr4 ,lowe1 who cannot pass a his pocket1 it would come out half-crown for more than a a coin of different value1 florin1 or get in a florin at which he would not understand4 less than half-a-crown1 has ,suppose he owed another man a such a high faith in the penny1 how was he to pay him 8 sterner stuff of his fellow ,was he to pay him in mils8 countrymen1 that he believes ,four mils would be too little1 any two of them would go to and five mils would be too fisty cuffs for the #beth part much4 ,the hon4 gentlemen said of a farthing4 ,he reasons there would be only a mil thus3 ,he has often heard in between them4 ,that was exactly the streets1 ,i'd fight you it4 ,he believed there would be for the fiftieth part of a a 'mill' between them4 7,much farden3 and having 7that is1 laughter47 for a ,member7 a notion both of fractions and logic1 he infers that those who would fight for the #ejth of a farthing would1 a fortiori1 fight for a #beth4 ,his mistake arises from his not knowing that when a person offers to fight another for #a_/bjj;d41 he really means to fight for love2 and that the stake is merely a matter of form1 a feigned issue1 a pro forma report of progress4 ,do the ,members of the ,house think they have all the forms to themselves8 ,what would be the present ,we should hardly believe all expression for four-pence8 this to be uttered in earnest1 ,why1 #j4aff 7a laugh72 for if we had not known #agg that threepence8 4#jabe2 for a several persons who have not penny8 4#jjdaff1 and so on ad ,mr4 ,lowe's humor1 nevertheless infinitum 7a laugh72 for a have his impressions on this half-penny8 4#jjbjhc ad point4 ,it must therefore be infinitum4 7,a laugh74 ,what answered2 but how is this to would be the present be done seriously8 expression for a farthing8 ,why1 4#jjajdaf ad infinitum4 ,dialogue between a member of 7,a laugh74 ,and this was the ,parliament and an orange-boy1 system which was to cause such three days after the a saving in figures1 and these introduction of the complete were the quantities into which decimal system4 ,the member1 the poor would have to reduce going down to the ,house1 wants the current coin of the realm4 oranges to sustain his voice 7,cheers74 ,with every respect in a two hours' speech on for decimal fractions1 of moving that #ajjjjjl4 be placed which he boasted no profound at the disposal of ,her knowledge1 he doubted whether ,majesty1 to supply the poor the poor were equal to mental with ready-reckoners4 arithmetic of this kind1 7hear1 hear7 and he hoped the ,boy4 ,fine oranges6 two a adoption of the system would penny6 two a penny6 #agh be deferred until there were some proof that they would be ,member4 ,here boy1 two6 ,now1 able to understand it2 for1 how am ,i to pay you8 after all1 this was the question of the poor1 and the ,boy4 ,give you change1 your whole weight of the change honor4 would fall upon them4 ,let the rich by all means have ,member4 ,ah6 but how8 ,where's permission to perplex your ready-reckoner8 themselves by any division of a pound they pleased2 but do ,boy4 ,i sells a better sort not let them1 by any nor them4 ,mine's real ,cheyny4 experiment like this1 impose difficulties upon the poor and ,member4 ,but you see a compel men to carry farthing is now 4#jjadafffff ready-reckoners in their ad infinitum1 and if we pocket to give them all these multiply this by #d---- fractional quantities4 7,hear1 hear47 ,boy4 ,hold hard1 ,guv'ner2 ,i sees what you're arter4 ,now what'll you stand if ,i puts you up to it8 which ,bill ,smith he put me up in two minutes1 cause he goes to the ,ragged ,school4 ,member4 ,you don't mean that you do without a book6 ,boy4 ,book be blowed4 ,come now1 old un1 here's summut for both on us4 ,i got a florin1 you gives me a half-a-crown for it1 and ,i larns you the new money1 gives you your oranges1 and calls you a brick into the bargain4 ,member 7to himself74 ,never had such a chance of getting off half-a-crown for value since that ---- fellow ,bowring carried his crochet4 7,aloud47 ,well1 boy1 it's a bargain4 ,now6 ,boy4 ,why1 look 'e here1 my trump1 its a farden more to the tizzy--that's what it is4 ,member4 ,what's that8 ,boy4 ,why1 you knows a sixpence when you sees it4 7,aside74 ,blest if ,i think he does6 ,well1 its six browns and a farden now4 ,a lady buys two oranges1 and forks #agi out a sixpence2 well in coorse1 ,i hands over fippence farden astead of fippence4 ,i always gives a farden more change1 and takes according4 ,member 7in utter surprise1 lets his oranges tumble into the gutter74 ,never mind6 ,they won't be wanted now4 7,walks off one way4 ,boy makes a pass of naso-digital mesmerism1 and walks off the other way74 ,to the poor1 who keep no books1 the whole secret is ,sixpence farthing to the half shilling1 twelve pence halfpenny to the shilling4 ,the new twopence halfpenny1 or cent1 will be at once five to the shilling4 ,in conclusion1 we remark that three very common misconceptions run through the hon4 ,member's argument2 and1 combined in different proportions1 give variety to his patterns4 ,first1 he will have it that we design to bring the uneducated into contact with decimal fractions4 ,if it be so1 it will only be as ,m4 ,jourdain was brought into contact with prose4 ,in fact1 ,quoi6 quand je dis1 ,nicole1 apportez-moi mes pantoufles1 c'est de la prose8#cje may be rendered3 ,what6 do you mean that ten to the florin is a cent a piece must be called decimal reckoning8 ,if we had to comfort a poor man1 horror-struck by the threat of decimals1 we should tell him what manner of fractions had been inflicted upon him hitherto2 nothing less awful than quarto-duodecimo-vicesimals1 we should assure him4 ,secondly1 he assumes that the penny1 such as it now is1 will remain1 as a coin of estimation1 after it has ceased to be a coin of exchange2 and that the mass of the people will continue to think of prices in old pence1 and to calculate them in new ones1 or else in new mils4 ,no answer is required to this1 beyond the mere statement of the nature of the assumption and denial4 #ahj ,thirdly1 he attributes to the uneducated community a want of perception and of operative power which really does not belong to them4 ,the evidence offered to the ,committee of the ,house shows that no fear is entertained on this point by those who come most in contact with farthing purchasers4 ,and this would seem to be a rule1--that is1 fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them1 no fear at all in the minds of those who are4 ,a remarkable instance of this distinction happened five-and-twenty years ago4 ,the ,admiralty requested the ,astronomical ,society to report on the alterations which should be made in the ,nautical ,almanac1 the seaman's guide-book over the ocean4 ,the greatest alteration proposed was the description of celestial phenomena in mean 7or clock time71 instead of apparent 7or sundial7 time1 till then always employed4 ,this change would require that in a great many operations the seaman should let alone what he formerly altered by addition or subtraction1 and alter by addition or subtraction what he formerly let alone2 provided always that what he formerly altered by addition he should1 when he altered at all1 alter by subtraction1 and vice versa4 ,this was a tolerably difficult change for uneducated skippers1 working by rules they had only learned by rote4 ,the ,astronomical ,society appointed a ,committee of forty1 of whom nine were naval officers or merchant seamen ,i was on this ,committee4 ,some men of science were much afraid of the change4 ,they could not trust an ignorant skipper or mate to make those alterations in their routine1 on the correctness of which the ship might depend4 ,had the ,committee consisted of men of science only1 the change might never have been ventured on4 ,but the naval men laughed1 and said there was nothing to fear2 and on their authority the alteration was made4 ,the upshot was1 that1 after the new almanacs appeared1 not a word of complaint was ever heard on the matter4 ,had the ,house of ,commons had to #aha decide this question1 with ,mr4 ,lowe to quote the description given by ,basil ,hall#cjf 7who1 by the way1 was one of the ,committee7 of an observation on which the safety of the ship depended1 worked out by the light of a lantern in a gale of wind off a lee shore1 this simple and useful change might at this moment have been in the hands of its tenth ,government ,commission4 ,aug4 #ad1 #ahff4 ,the ,committee was appointed in the spring of #ahcj3 it consisted of forty members4 ,death1 of course1 has been busy2 there are now left ,lord ,shaftesbury1#cjg ,mr4 ,babbage1#cjh ,sir ,john ,herschel1#cji ,sir ,thomas ,maclear#caj 7,astronomer ,royal at the ,cape of ,good ,hope71 ,dr4 ,robinson#caa 7of ,armagh71 ,sir ,james ,south1#cab ,lord ,wrottesley1#cac and myself4 #ahb ,,the ,,tonal ,,system4 ,project of a new system of arithmetic1 weight1 measure1 and coins1 proposed to be called the tonal system1 with sixteen to the base4 ,by ,j4 ,w4 ,mystrom4#cad ,philadelphia1 #ahfb1 #hvo4 ,that is to say1 sixteen is to take the place of ten1 and to be written #aj4 ,the whole language is to be changed2 every man of us is to be sixteen-stringed ,jack and every woman sixteen-stringed ,jill4 ,our old one1 two1 three1 up to sixteen1 are to be 7,noll going for nothing1 which will please those who dislike the memory of ,old ,noll7 replaced by ,an1 ,de1 ,ti1 ,go1 ,su1 ,by1 ,ra1 ,me1 ,ni1 ,ko1 ,hu1 ,vy1 ,la1 ,po1 ,fy1 ,ton2 and then ,ton-an1 ,ton-de1 etc4 for #ag1 #ah1 etc4 ,the number which in the system has the symbol #bh7ac7e7aa7g7ad7j7ae7 7using our present compounds instead of new types7 is to be pronounced ,detam-memill-lasan-suton-hubong-ramill- posanfy4 ,the year is to have sixteen months1 and here they are3 ,anuary1 ,debrian1 ,timander1 ,gostus1 ,suvenary1 ,bylian1 ,ratamber1 ,mesudius1 ,nictoary1 ,kolumbian1 ,husamber1 ,vyctorius1 ,lamboary1 ,polian1 ,fylander1 ,tonborius4 ,surely ,an-month1 ,de-month1 etc4 would do as well4 ,probably the wants of poetry were considered4 ,but what are we to do with our old poets8 ,for example-- ,it was a night of lovely ,june1 ,high rose in cloudless blue the moon4 ,let us translate-- ,it was a night of lovely ,nictoary1 ,high rose in cloudless blue the 7what1 in the name of all that is absurd874 ,and again1 ,fylander thrown into our ,december6 ,what is #ahc to become of those lines of ,praed1 which ,i remember coming out when ,i was at ,cambridge1-- ,oh6 now's the time of all the year for flowers and fun1 the ,maydays2 ,to trim your whiskers1 curl your hair1 and sinivate the ladies4 ,if ,i were asked which ,i preferred1 this system or that of ,baron ,ferrari#cae already mentioned1 proceeding by twelves1 ,i should reply1 with ,candide1 when he had the option given of running the gauntlet or being shot3 ,les volontes sont libres1 et je ne veux ni l'un ni l'autre4#caf ,we can imagine a speculator providing such a system for ,utopia as it would be in the mind of a ,laputan3 but to explain how an engineer who has surveyed mankind from ,philadelphia to ,rostof on the ,don should for a moment entertain the idea of such a system being actually adopted1 would beat a jury of solar-system-makers1 though they were shut up from the beginning of ,anuary to the end of ,tonborius4 ,when ,i see such a scheme as this imagined to be practicable1 ,i admire the wisdom of ,providence in providing the quadrature of the circle1 etc41 to open a harmless sphere of action to the possessors of the kind of ingenuity which it displays4 ,those who cultivate mathematics have a right to speak strongly on such efforts of arithmetic as this3 for1 to my knowledge1 persons who have no knowledge are frequently disposed to imagine that their makers are true brothers of the craft1 a little more intelligible than the rest4 ,,some ,,small ,,paradoxers4 ,vis inertiae victa1#cag or ,fallacies affecting science4 ,by ,james ,reddie4#cah ,london1 #ahfb1 #hvo4 #ahd ,an attack on the ,newtonian mechanics2 revolution by gravitation demonstrably impossible2 much to be said for the earth being the immovable center4 ,a good analysis of contents at the beginning1 a thing seldom found4 ,the author has followed up his attack in a paper submitted to the ,british ,association1 but which it appears the ,association declined to consider4 ,it is entitled-- ,victoria ,toto ,coelo2 or1 ,modern ,astronomy recast4 ,london1 #ahfc1 #hvo4 ,at the end is a criticism of ,sir ,g4 ,lewis's ,history of ,ancient ,astronomy4 ,on the definition and nature of the ,science of ,political ,economy4 ,by ,h4 ,dunning ,macleod1#cai ,esq4 ,cambridge1 #ahfb1 #hvo4 ,a paper read--but1 according to the report1 not understood--at the ,british ,association4 ,there is a notion that political economy is entirely mathematical2 and its negative quantity is strongly recommended for study3 it contains the whole of the ,funds1 ,credit1 #cb parts out of #cc of the value of ,land4444 ,the mathematics are described as consisting of--first1 number1 or ,arithmetic2 secondly1 the theory of dependent quantities1 subdivided into dependence by cause and effect1 and dependence by simultaneous variations2 thirdly1 independent quantities or unconnected events1 which is the theory of probabilities4 ,i am not ashamed1 having the ,british ,association as a co-non-intelligent1 to say ,i do not understand this3 there is a paradox in it1 and the author should give further explanation1 especially of his negative quantity4 ,mr4 ,macleod has gained #ahe praise from great names for his political economy2 but this1 ,i suspect1 must have been for other parts of his system4 ,on the principles and practice of just ,intonation1 with a view to the abolition of temperament4444 ,by ,general ,perronet ,thompson4#cbj ,sixth ,edition4 ,london1 #ahfb1 #hvo4 ,here is ,general ,thompson again1 with another paradox3 but always master of the subject1 always well up in what his predecessors have done1 and always aiming at a useful end4 ,he desires to abolish temperament by additional keys1 and has constructed an enharmonic organ with forty sounds in the octave4 ,if this can be introduced1 ,i1 for one1 shall delight to hear it3 but there are very great difficulties in the way1 greater than stood even in the way of the repeal of the bread-tax4 ,in a paper on the beats of organ-pipes and on temperament published some years ago1 ,i said that equal temperament appeared to me insipid1 and not so agreeable as the effect of the instrument when in progress towards being what is called out of tune1 before it becomes offensively wrong4 ,there is throughout that period unequal temperament1 determined by accident4 ,general ,thompson1 taking me one way1 says ,i have launched a declaration which is likely to make an epoch in musical practice2 a public musical critic1 taking me another way1 quizzes me for preferring music out of tune4 ,i do not think ,i deserve either one remark or the other4 ,my opponent critic1 ,i suspect1 takes equally tempered and in tune to be phrases of one meaning4 ,but by equal temperament is meant equal distribution among all the keys of the error which an instrument must have1 which1 with twelve sounds only in the octave1 professes to be fit for all the keys4 ,i am reminded of the equal temperament which was once applied to the postmen's jackets4 ,the coats were all made for the average man3 the #ahf consequence was that all the tall men had their tails too short2 all the short men had them too long4 ,some one innocently asked why the tall men did not change coats with the short ones4 ,a diagram illustrating a discovery in the relation of circles to right-lined geometrical figures4 ,london1 #ahfc1 #abmo4 ,the circle is divided into equal sectors1 which are joined head and tail3 but a property is supposed which is not true4 ,an attempt to assign the square roots of negative powers2 or what is sqrt -#a8 ,by ,f4,h4 ,laing4#cba ,london1 #ahfc1 #hvo4 ,if ,i understand the author1 -a and a are the square roots of -a#b1 as proved by multiplying them together4 ,the author seems quite unaware of what has been done in the last fifty years4 ,,byrne',s ,,dual ,,arithmetic4 ,dual ,arithmetic4 ,a new art4 ,by ,oliver ,byrne4#cbb ,london1 #ahfc1 #hvo4 ,the plan is to throw numbers into the form a7#a4a7;b 7#a4ja7;c 7#a4jja7;d444 and to operate with this form4 ,this is an ingenious and elaborate speculation2 and ,i have no doubt the author has practised his method until he could surprise any one else by his use of it4 ,but ,i doubt if he will persuade others to use it4 ,as asked of ,wilkins's universal language1 ,where is the second man to come from8 ,an effective predecessor in the same line of invention #ahg was the late ,mr4 ,thomas ,weddle1#cbc in his ,new1 simple1 and general method of solving numeric equations of all orders1 #dto1 #ahdb4 ,the ,royal ,society1 to which this paper was offered1 declined to print it3 they ought to have printed an organized method1 which1 without subsidiary tables1 showed them1 in six quarto pages1 the solution 7x#h4cfgigedca7 of the equation #acgi4ffd x#fbb #bfhfjcd x #ajdcb x#aeb - #agbijbbd x #ajeah x#fj #bebdaef x #ajegd #j4 ,the method proceeds by successive factors of the form1 a being the first approximation1 a x #a4;b x #a4j;c x #a4jj;d4444 ,in my copy ,i find a few corrections made by me at the time in ,mr4 ,weddle's announcement4 ,it was read before that learned body the ,r4 ,s4 and they were pleased but to transmit their thanks to the author4 ,the endiscouragement which he received induces obliges him to lay the result of his enquiries in this important branch of mathematics before the public 1 at his own expense2 he being an usher in a school at ,newcastle4 ,which is most satirical1 ,mr4 ,weddle or myself8 ,the ,society1 in the account which it gave of this paper1 described it as a new and remarkably simple method possessing several important advantages4 ,mr4 ,rutherford's#cbd extended value of pi was read at the very next meeting1 and was printed in the ,transactions2 and very properly3 ,mr4 ,weddle's paper was excluded1 and very very improperly4 ,,horner',s ,,method4 ,i think it may be admited that the indisposition to look at and encourage improvements of calculation which once #ahh marked the ,royal ,society is no longer in existence4 ,but not without severe lessons4 ,they had the luck to accept ,horner's#cbe now celebrated paper1 containing the method which is far on the way to become universal3 but they refused the paper in which ,horner developed his views of this and other subjects3 it was printed by ,t4 ,s4 ,davies#cbf after ,horner's death4 ,i make myself responsible for the statement that the ,society could not reject this paper1 yet felt unwilling to print it1 and suggested that it should be withdrawn2 which was done4 ,but the severest lesson was the loss of ,barrett's ,method1#cbg now the universal instrument of the actuary in his highest calculations4 ,it was presented to the ,royal ,society1 and refused admission into the ,transactions3 ,francis ,baily#cbh printed it4 ,the ,society is now better informed3 live and learn1 meaning must live1 so better learn1 ought to be the especial motto of a corporation1 and is generally acted on1 more or less4 ,horner's method begins to be introduced at ,cambridge3 it was published in #ahbj4 ,i remember that when ,i first went to ,cambridge 7in #ahbc7 ,i heard my tutor say1 in conversation1 there is no doubt that the true method of solving equations is the one which was published a few years ago in the ,philosophical ,transactions4 ,i wondered it was not taught1 but presumed that it belonged to the higher mathematics4 ,this ,horner himself had in his head3 and in a sense it is true2 for all lower branches belong to the higher3 but he would have stared to have been told that he1 ,horner1 #ahi was without a ,european predecessor1 and in the distinctive part of his discovery was heir-at-law to the nameless ,brahmin--,tartar--,antenoachian--what you please--who concocted the extraction of the square root4 ,it was somewhat more than twenty years after ,i had thus heard a ,cambridge tutor show sense of the true place of ,horner's method1 that a pupil of mine who had passed on to ,cambridge was desired by his college tutor to solve a certain cubic equation--one of an integer root of two figures4 ,in a minute the work and answer were presented1 by ,horner's method4 ,how6 said the tutor1 this can't be1 you know4 ,there is the answer1 ,sir6 said my pupil1 greatly amused1 for my pupils learnt1 not only ,horner's method1 but the estimation it held at ,cambridge4 ,yes6 said the tutor1 there is the answer certainly2 but it stands to reason that a cubic equation cannot be solved in this space4 ,he then sat down1 went through a process about ten times as long1 and then said with triumph3 ,there6 that is the way to solve a cubic equation6 ,i think the tutor in this case was never matched1 except by the country organist4 ,a master of the instrument went into the organ-loft during service1 and asked the organist to let him play the congregation out2 consent was given4 ,the stranger1 when the time came1 began a voluntary which made the people open their ears1 and wonder who had got into the loft3 they kept their places to enjoy the treat4 ,when the organist saw this1 he pushed the interloper off the stool1 with ,you'll never play 'em out this side ,christmas4 ,he then began his own drone1 and the congregation began to move quietly away4 ,there1 said he1 that's the way to play 'em out6 ,i have not scrupled to bear hard on my own university1 on the ,royal ,society1 and on other respectable existences3 being very much the friend of all4 ,i will now clear the ,royal ,society from a very small and obscure slander1 simply because ,i know how4 ,this dissertation began with #aij the work of ,mr4 ,oliver ,byrne1 the dual arithmetician1 etc4 ,this writer published1 in #ahdi1 a method of calculating logarithms4#cbi ,first1 a long list of instances in which1 as he alleges1 foreign discoverers have been pillaged by ,englishmen1 or turned into ,englishmen3 for example1 ,o',neill1#ccj so called by ,mr4 ,byrne1 the rectifier of the semi-cubical parabola claimed by the ,saxons under the name of ,neal3 the grandfather of this mathematician was conspicuous enough as ,neal2 he was archbishop of ,york4 ,this list1 says the writer1 might be continued without end2 but he has mercy1 and finishes with his own case1 as follows3--,about twenty years ago1 ,i discovered this method of directly calculating logarithms4 ,i could generally find the logarithm of any number in a minute or two without the use of books or tables4 ,the importance of the discovery subjected me to all sorts of prying4 ,some asserted that ,i committed a table of logarithms to memory2 others attributed it to a peculiar mental property2 and when ,societies and individuals failed to extract my secret1 they never failed to traduce the inventor and the invention4 ,among the learned ,societies1 the ,royal ,society of ,london played a very base part4 ,when ,i have more space and time at my disposal1 ,i will revert to this subject again4 ,such a trumpery story as this remains unnoticed at the time2 but when all are gone1 a stray copy from a stall falls into hands which1 not knowing what to make of it1 make history of it4 ,it is a very curious distortion4 ,the reader may take it on my authority1 that the ,royal ,society played no part1 good or bad1 nor had the option of playing a part4 #aia ,but ,i myself pars magna fui3#cca and when the author has space and time at his disposal1 he must not take all of them2 ,i shall want a little of both4 ,,are ,,atoms ,,worlds8 ,the mystery of being2 or are ultimate atoms inhabited worlds8 ,by ,nicholas ,odgers4#ccb ,redruth and ,london1 #ahfc1 #hvo4 ,this book1 as a paradox1 beats quadrature1 duplication1 trisection1 philosopher's stone1 perpetual motion1 magic1 astrology1 mesmerism1 clairvoyance1 spiritualism1 homoeopathy1 hydropathy1 kinesipathy1 ,essays and ,reviews1 and ,bishop ,colenso1#ccc all put together4 ,of all the suppositions ,i have given as actually argued1 this is the one which is hardest to deny1 and hardest to admit4 ,reserving the question--as beyond human discussion--whether our particles of carbon1 etc4 are clusters of worlds1 the author produces his reasons for thinking that they are at least single worlds4 ,of course--though not mentioned--the possibility is to be added of the same thing being true of the particles which make up our particles1 and so down1 for ever3 and1 on the other hand1 of our planets and stars as being particles in some larger universe1 and so up1 for ever4 ,great fleas have little fleas upon their backs to bite 'em1 ,and little fleas have lesser fleas1 and so ad infinitum4 ,and the great fleas themselves1 in turn1 have greater fleas to go on2 ,while these again have greater still1 and greater still1 and so on4#ccd ,i have often had the notion that all the nebulae we see1 including our own1 which we call the ,milky ,way1 may be particles of snuff in the box of a giant of a proportionately #aib larger universe4 ,of course the minim of time--a million of years or whatever the geologists make it#cce--which our little affair has lasted1 is but a very small fraction of a second to the great creature in whose nose we shall all be in a few tens of thousands of millions of millions of millions of years4 ,all this is quite possible1 and the probabilities for and against are quite out of reach4 ,perhaps also all the worlds1 both above and below us1 are fac-similes of our own4 ,if so1 away goes free will for good and all2 unless1 indeed1 we underpin our system with the hypothesis that all the fac-simile bodies of different sizes are actuated by a common soul4 ,these acute supplementary notions of mine go far to get rid of the difficulty which some have found in the common theory that the soul inhabits the body3 it has been stated that there is1 somewhere or another1 a world of souls which communicate with their bodies by wondrous filaments of a nature neither mental nor material1 but of a tertium quid fit to be a go-between2 as it were a corporispiritual copper encased in a spiritucorporeal gutta-percha4 ,my theory is that every soul is everywhere in posse1 as the schoolmen said1 but not anywhere in actu1 except where it finds one of its bodies4 ,these a priori difficulties being thus removed1 the system of particle-worlds is reduced to a dry question of fact1 and remitted to the decision of the microscope4 ,and a grand field may thus be opened1 as optical science progresses6 ,for the worlds are not fac-similes of ours in time3 there is not a moment of our past1 and not a moment of our future1 but is the present of one or more of the particles4 ,a will write the death of ,caesar1 and ,b the building of the ,pyramids1 by actual observation of the processes with a power of a thousand millions2 ,c will discover the commencement of the ,millennium1 and ,d the #aic termination of ,ersch and ,gruber's ,lexicon1#ccf as mere physical phenomena4 ,against this glorious future there is a sad omen3 the initials of the forerunner of this discovery are--,,no6 ,,the ,,supernatural4 ,the ,history of the ,supernatural in all ages and nations1 and in all ,churches1 ,christian and ,pagan3 demonstrating a universal faith4 ,by ,wm4 ,howitt4#ccg ,london1 #b vols4 #hvo4 #ahfc4 ,mr4 ,howitt is a preacher of spiritualism4 ,he cements an enormous collection of alleged facts with a vivid outpouring of exhortation1 and an unsparing flow of sarcasm against the scorners of all classes4 ,he and the ,rev4 ,j4 ,smith#cch 7ante1 #ahed7 are the most thoroughgoing universalists of all the writers ,i know on spiritualism4 ,if either can insert the small end of the wedge1 he will not let you off one fraction of the conclusion that all countries1 in all ages1 have been the theaters of one vast spiritual display4 ,and ,i suspect that this consequence cannot be avoided1 if any part of the system be of truly spiritual origin4 ,mr4 ,howitt treats the philosophers either as ignorant babies1 or as conscious spirit-fearers3 and seems much inclined to accuse the world at large of dreading1 lest by the actual presence of the other world their ,christianity should imbibe a spiritual element which would unfit it for the purposes of their lives4 #aid ,,from ,,matter ,,to ,,spirit4 ,from ,matter to ,spirit4 ,by ,c4 ,d4 ,with a preface by ,a4 ,b4#cci ,london1 #ahfc1 #hvo4 ,this is a work on ,spiritual ,manifestations4 ,the author upholds the facts for spiritual phenomena3 the prefator suspends his opinion as to the cause1 though he upholds the facts4 ,the work begins systematically with the lower class of phenomena1 proceeds to the higher class1 and offers a theory1 suggested by the facts1 of the connection of the present and future life4 ,i agree in the main with ,a4 ,b42 but can1 of course1 make none but horrescent reference to his treatment of the smaller philosophers4 ,this is always the way with your paradoxers3 they behave towards orthodoxy as the thresher fish behaves towards the whale4 ,but if true1 as is said1 that the drubbing clears the great fish of parasites which he could not otherwise get rid of1 he ought to bear no malice4 ,this preface retorts a little of that contempt which the philosophical world has bestowed with heaped measure upon those who have believed their senses1 and have drawn natural1 even if hasty1 inferences4 ,there is philosophercraft as well as priestcraft1 both from one source1 both of one spirit4 ,in ,english cities and towns1 the minister of religion has been tamed3 so many weapons are bared against him when he obtrudes his office in a dictatory manner1 that1 as a rule1 there is no more quiet and modest member of society than the urban clergyman4 ,domination over religious belief is reserved for the exclusive use of those who admit the right3 the rare exception to this mode of behavior is laughed at as a bigot1 or shunned as a nuisance4 ,but the overbearing minister of nature1 who snaps you with unphilosophical as the clergyman once frightened you with infidel1 is still a recognized member of society1 wants taming1 and will get it4 ,he wears the priest's cast-off #aie clothes1 dyed to escape detection3 the better sort of philosophers would gladly set him to square the circle4 ,the book just named appeared about the same time as this ,budget began in the ,athenaeum4 ,it was commonly attributed1 the book to my wife1 the preface to myself4 ,some time after1 our names were actually announced by the publisher1 who ought to know4 ,it will be held to confirm this statement that ,i announce our having in our possession some twenty reviews of different lengths1 and of all characters3 who ever collects a number of reviews of a book1 except the author8 ,a great many of these reviews settle the matter a priori4 ,if there had been spirits in the matter1 they would have done this1 and they would not have done that4 ,jean ,meslier#cdj said there could be no ,god over all1 for1 if there had been one1 ,he would have established a universal religion4 ,if ,j4 ,m4 knew that1 ,j4 ,m4 was right3 but if ,j4 ,m4 did not know that1 then ,j4 ,m4 was on the high priori road1 and may be left to his course4 ,the same to all who know what spirits would do and would not do4 ,a4 ,b4 very distinctly said that he knew some of the asserted facts1 believed others on testimony1 but did not pretend to know whether they were caused by spirits1 or had some unknown and unimagined origin4 ,this he said as clearly as ,i could have said it myself4 ,but a great many persons cannot understand such a frame of mind3 their own apparatus is a kind of spirit-level1 and their conclusion on any subject is the little bubble1 which is always at one end or the other4 ,many of the reviewers declare that ,a4 ,b4 is a secret believer in the spirit-hypothesis3 and one of them wishes that he had endorsed his opinion more boldly4 ,according to this reviewer1 any one who writes ,i boldly #aif say ,i am unable to choose1 contradicts himself4 ,in truth1 a person who does say it has a good deal of courage1 for each side believes that he secretly favors the other2 and both look upon him as a coward4 ,in spite of all this1 ,a4 ,b4 boldly repeats that he feels assured of many of the facts of spiritualism1 and that he cannot pretend to affirm or deny anything about their cause4 ,the great bulk of the illogical part of the educated community--whether majority or minority ,i know not2 perhaps six of one and half-a-dozen of the other--have not power to make a distinction1 cannot be made to take a distinction1 and of course1 never attempt to shake a distinction4 ,with them all such things are evasions1 subterfuges1 come-offs1 loopholes1 etc4 ,they would hang a man for horse-stealing under a statute against sheep-stealing2 and would laugh at you if you quibbled about the distinction between a horse and a sheep4 ,i divide the illogical--,i mean people who have not that amount of natural use of sound inference which is really not uncommon--into three classes3--,first class1 three varieties3 the ,niddy1 the ,noddy1 and the ,noodle4 ,second class1 three varieties3 the ,niddy-,noddy1 the ,niddy-,noodle1 and the ,noddy-,noodle4 ,third class1 undivided3 the ,niddy-,noddy-,noodle4 ,no person has a right to be angry with me for more than one of these subdivisions4 ,the want of distinction was illustrated to me1 when a boy1 about #ahbj1 by the report of a trial which ,i shall never forget3 boys read newspapers more keenly than men4 ,every now and then a bench of country magistrates rather astonishes the town populations1 accustomed to rub their brains#cda against one another4 ,such a story as the following would1 #aig in our day1 bring down grave remarks from above3 but ,i write of the olden 7or ,eldon#cdb7 time1 when nothing but conviction in a court of record would displace a magistrate4 ,in that day the third-class amalgamator of distinct things was often on the bench of quarter-sessions4 ,an attorney was charged with having been out at night poaching4 ,a clear alibi was established2 and perjury had certainly been committed4 ,the whole gave reason to suspect that some ill-willers thought the bench disliked the attorney so much that any conviction was certain on any evidence4 ,the bench did dislike the attorney3 but not to the extent of thinking he could snare any partridges in the fields while he was asleep in bed1 except the dream-partridges which are not always protected by the dream-laws4 ,so the chairman said1 ,mr4 ----1 you are discharged2 but you should consider this one of the most fortunate days of your life4 ,the attorney indignantly remonstrated1 but the magistrate was right2 for he said1 ,mr4 ----1 you have frequently been employed to defend poachers3 have you been careful to impress upon them the enormity of their practices8 ,it appeared in a wrangling conversation that the magistrates saw little moral difference between poaching and being a poacher's professional defender without lecturing him on his wickedness3 but they admitted with reluctance1 that there was a legal distinction2 and the brain of ,n#c could no further go4 ,this is nearly fifty years ago2 and ,westernism was not quite extinct4 ,if the present lords of the hills and the valleys want to shine1 let them publish a true history of their own order4 ,i am just old enough to remember some of the last of the squires and parsons who protested against teaching the poor to read and write4 ,they now write books for the working classes1 give them lectures1 and the like4 ,there is now no class1 as a class1 more highly educated1 broadly educated1 and deeply educated1 #aih than those who were1 in old times1 best described as partridge-popping squireens4 ,i have myself1 when a boy1 heard ,old ,booby speaking with pride of ,young ,booby as having too high a spirit to be confined to books3 and ,i suspected that his dislike to teaching the poor arose in fact from a feeling that they would1 if taught a little1 pass his heir4 ,a4 ,b4 recommended the spirit-theory as an hypothesis on which to ground inquiry2 that is1 as the means of suggestion for the direction of inquiry4 ,every person who knows anything of the progress of physics understands what is meant2 but not the reviewers ,i speak of4 ,many of them consider ,a4 ,b4 as adopting the spirit-hypothesis4 ,the whole book was written1 as both the authors point out1 to suggest inquiry to those who are curious2 ,c4 ,d4 firmly believing1 ,a4 ,b4 as above4 ,neither ,c4 ,d4 nor ,a4 ,b4 make any other pretence4 ,both dwell upon the absence of authentications and the suppression of names as utterly preventive of anything like proof4 ,and ,a4 ,b4 says that his reader will give him credit1 if not himself a goose1 for seeing that the tender of an anonymous cheque would be of equal effect1 whether drawn on the ,bank of ,england or on ,aldgate ,pump4 ,by this test a number of the reviewers are found to be geese3 for they take the authors as offering proof1 and insist1 against the authors1 on the very point on which the authors had themselves insisted beforehand4 ,leaving aside imperceptions of this kind1 ,i proceed to notice a clerical and medical review4 ,i have lived much in the middle ages1 especially since the invention of printing2 and from thence ,i have brought away a high respect for and grateful recollection of--the priest in everything but theology1 and the physician in everything but medicine4 ,the professional harness was unfavorable to all progress1 except on a beaten road2 the professional blinkers prevented all but the beaten road from being seen3 the professional reins were pulled at the slightest attempt to quicken pace1 even on the permitted path2 and the #aii professional whip was heavily laid on at the slightest attempt to diverge4 ,but when the intelligent man of either class turned his attention out of his ordinary work1 he had1 in most cases1 the freshness and vigor of a boy at play1 and like the boy1 he felt his freedom all the more from the contrast of school-restraint4 ,in the case of medicine1 and physics generally1 the learned were1 in some essential points1 more rational than many of their present impugners4 ,they pass for having put a priori obstacles in the way of progress3 they might rather be reproved for too much belief in progress obtained by a priori means4 ,they would have shouted with laughter at a dunce who--in a review ,i read1 but without making a note--declared that he would not believe his senses except when what they showed him was capable of explanation upon some known principle4 ,i have seen such stuff as this attributed to the schoolmen2 but only by those who knew nothing about them4 ,the following1 which ,i wrote some years ago1 will give a notion of a distinction worth remembering4 ,it is addressed to the authorities of the ,college of ,physicians4 ,the ignominy of the word empiric dates from the ages in which scholastic philosophy deduced physical consequences a priori2--the ages in which1 because a lion is strong1 rubbing with lion's fat would have been held an infallible tonic4 ,in those happy days1 if a physician had given decoction of a certain bark1 only because in numberless instances that decoction had been found to strengthen the patient1 he would have been a miserable empiric4 ,not that the colleges would have passed over his returns because they were empirical3 they knew better4 ,they were as skilful in finding causes for facts1 as facts for causes4 ,the president and the elects of that day would have walked out into the forest with a rope1 and would have pulled heartily at the tree which yielded the bark3 nor would they ever have left it until they had pulled out a legitimate #bjj reason4 ,if the tree had resisted all their efforts1 they would have said1 ',ah6 no wonder now2 the bark of a strong tree makes a strong man4' ,but if they had managed to serve the tree as you would like to serve homoeopathy1 then it would have been ',we might have guessed it2 all the virtus roborativa has settled in the bark4' ,they admitted1 as we know from ,moliere1 the virtus dormitiva#cdc of opium1 for no other reason than that opium facit dormire4#cdd ,had the medicine not been previously known1 they would1 strange as it may seem to modern pharmacopoeists1 have accorded a virtus dormitiva to the new facit dormire4 ,on this point they have been misapprehended4 ,they were prone to infer facit from a virtus imagined a priori2 and they were ready in supplying facit in favor of an orthodox virtus4 ,they might have gone so far1 for example1 under pre-notional impressions1 as the alliterative allopath1 who1 when maintenance of truth was busy opposing the progress of science called vaccination1 declared that some of its patients coughed like cows1 and bellowed like bulls2 but they never refused to find virtus when facit came upon them1 no matter whence4 ,they would rather have accepted ,tenterden steeple than have rejected the ,goodwin ,sands4 ,they would have laughed their modern imitators to scorn3 but as they are not here1 we do it for them4 ,the man of our day--the a priori philosopher--tries the question whether opium can cause sleep by finding out in the recesses of his own noddle whether the drug can have a dormitive power3 ,well6 but did not the schoolman do the same8 ,he did2 but mark the distinction4 ,the schoolman had recourse to first principles1 when there was no opium to try it by3 our man settles the point in the same way with a lump of opium before him4 ,the schoolman shifted his principles with his facts3 the man of our drawing-rooms will fight facts with his principles1 just as an old #bja physician would have done in actual practice1 with the rod of his ,church at his back4 ,the story about ,galileo--which seems to have been either a joke made against him1 or by him--illustrates this4 ,nature abhors a vacuum was the explanation of the water rising in a pump3 but they found that the water would not rise more than #cb feet4 ,they asked for explanation3 what does the satirist make the schoolmen say8 ,that the stoppage is not a fact1 because nature abhors a vacuum8 ,no6 but that the principle should be that nature abhors a vacuum as far as #cb feet4 ,and this is what would have been done4 ,there are still among us both priests and physicians who would have belonged1 had they lived three or four centuries ago1 to the glorious band of whom ,i have spoken1 the majority of the intelligent1 working well for mankind out of the professional pursuit4 ,but we have a great many who have helped to abase their classes4 ,go where we may1 we find specimens of the lower orders of the ministry of religion and the ministry of health showing themselves smaller than the small of other pursuits4 ,and how is this8 ,first1 because each profession is entered upon a mere working smack of its knowledge1 without any depth of education1 general or professional4 ,not that this is the whole explanation1 nor in itself objectionable3 the great mass of the world must be tended1 soul and body1 by those who are neither ,hookers#cde nor ,harveys#cdf3 let such persons not venture ultra crepidam1 and they are useful and respectable4 ,but1 secondly1 there is a vast upheaving of thought from the depths of commonplace learning4 ,i am a clergyman6 ,sir6 ,i am a medical man6 ,sir6 and forthwith the nature of things is picked to pieces1 and there is a race1 with the last the winner1 between ,philosophy mounted on ,folly's donkey1 and ,folly mounted on ,philosophy's donkey4 ,how fortunate #bjb it is for ,law that her battles are fought by politicians in the ,houses of ,parliament4 ,not that it is better done3 but then politics bears the blame4 ,i now come to the medical review4 ,after a quantity of remark which has been already disposed of1 the writer shows ,greek learning1 a field in which the old physician would have had a little knowledge4 ,a4 ,b41 for the joke's sake1 had left untranslated1 as being too deep1 a remarkably easy sentence of ,aristotle1 to the effect that what has happened was possible1 for if impossible it would not have happened4 ,the reviewer1 in simple astonishment1--it was simple--at the pretended incapacity--,i was told by ,a4 ,b4 that the joke was intended to draw out a reviewer--translates3--,he says that this sentence is ,a4 ,b4's summing up of the evidence of ,spiritualism4 ,now1 being a sort of alter ego#cdg of ,a4 ,b41 ,i do declare that he is not such a fool as to rest the evidence of ,spiritualism--the spirit explanation--upon the occurrence of certain facts proving the possibility of those very facts4 ,in truth1 ,a4 ,b4 refuses to receive spiritualism1 while he receives the facts3 this is the gist of his whole preface1 which simply admits spiritualism among the qualified candidates1 and does not know what others there may be4 ,the reviewer speaks of ,aristotle as that clear thinker and concise writer4 ,i strongly suspect that his knowledge of ,aristotle was limited to the single sentence which he had translated or got translated4 ,aristotle is concise in phrase1 not in book1 and is powerful and profound in thought3 but no one who knows that his writing1 all we have of him1 is the very opposite of clear1 will pretend to decide that he thought clearly4 ,as his writing1 so probably was his thought2 and his books are1 if not anything but clear1 at least anything good but clear4 ,nobody thinks them clear except a person who always clears difficulties3 which ,i have no doubt was the reviewer's habit2 that is1 if he ever took the field #bjc at all4 ,the gentleman who read ,euclid1 all except the ,as and ,bs and the pictures of scratches and scrawls1 is the type of a numerous class4 ,the reviewer finds that the word amosgepotically1 used by ,a4 ,b41 is utterly mysterious and incomprehensible4 ,he hopes his translation of the bit of ,greek will shield him from imputation of ignorance3 and thinks the word may be referred to the obscure dialect out of which sprung aneroid1 kalos geusis sauce1 and ,anaxyridian trousers4 ,to lump the first two phrases with the third smacks of ignorance in a ,greek critic2 for ,greek3 anaxuridia1 breeches1 would have turned up in the lexicon2 and kalos geusis1 though absurd1 is not obscure4 ,and ,greek3 amosgepos1 somehow or other1 is as easily found as ,greek3 anaxuridia4 ,the word aneroid1 ,i admit1 has puzzled better scholars than the critic3 but never one who knows the unscholarlike way in which words ending in ,greek3 eides have been rendered4 ,the aneroid barometer does not use a column of air in the same way as the old instrument4 ,now ,greek3 aeroeides--properly like the atmosphere--is by scientific non-scholarship rendered having to do with the atmosphere2 and ,greek3 anaeroeides--say anaeroid--denies having to do with the atmosphere2 a nice thing to say of an instrument which is to measure the weight of the atmosphere4 ,one more absurdity1 and we have aneroid1 and there you are4 ,the critic ends with a declaration that nothing in the book shakes his faith in a ,quarterly reviewer who said that suspension of opinion1 until further evidence arrives1 is justifiable3 a strange summing up for an article which insists upon utter rejection being unavoidable4#cdh ,the expressed aim of both ,a4 ,b4 and ,c4 ,d4 was to excite inquiry1 and get further evidence3 until this is done1 neither asks for a verdict4 ,oh where6 and oh where6 is old ,medicine's learning gone6 ,there was some in the days of yore1 when ,popery #bjd was on6 ,and it's oh6 for some ,greek1 just to find a word upon6 ,the reviewer who1 lexicon in hand1 can neither make out anaxyridical1 amosgepotical1 kalos geusis1 nor distinguish them from aneroid1 cannot be trusted when he says he has translated a sentence of ,aristotle4 ,he may have done it2 but1 as he says of spiritualism1 we must suspend our opinion until further evidence shall arrive4 ,we now come to the theological review4 ,i have before alluded to the faults of logic which are ,protestant necessities3 but ,i never said that ,protestant argument had nothing but paralogism4 ,the writer before me attains this completeness3 from beginning to end he is of that confusion and perversion which1 as applied to interpretation of the ,new ,testament1 is so common as to pass unnoticed by sermon-hearers2 but which1 when applied out of church1 is exposed with laughter in all subjects except theology4 ,i shall take one instance1 putting some words in italics4 ,a4 ,b4 ,theological ,critic4 ,my state of mind1 which refers 444 he proceeds to argue that the whole either to unseen he himself is outside its intelligence1 or something sacred pale because he refers which man has never had any all these strange phenomena to conception of1 proves me to unseen spiritual be out of the pale of the intelligence4 ,royal ,society4 ,the possibility of a yet unimagined cause is insisted on in several places4 ,on this ground it is argued by ,a4 ,b4 that spiritualists are incautious for giving in at once to the spirit doctrine4 ,but1 it is said1 they may be justified by the philosophers1 who make the flint axes1 as they call them1 to be the works of men1 because no one can see what else they can be4 ,this kind of adoption1 condemned as a conclusion1 is approved as a provisional theory1 suggestive of direction of inquiry3 experience having shown that #bje inquiry directed by a wrong theory has led to more good than inquiry without any theory at all4 ,all this ,a4 ,b4 has fully set forth1 in several pages4 ,on it the reviewer remarks that with infinite satisfaction he tries to justify his view of the case by urging that there is no other way of accounting for it2 after the fashion of the philosophers of our own day1 who conclude that certain flints found in the drift are the work of men1 because the geologist does not see what else they can be4 ,after this twist of meaning1 the reviewer proceeds to say1 and ,a4 ,b4 would certainly join him1 ,there is no need to combat any such mode of reasoning as this1 because it would apply with equal force and justice to any theory whatever1 however fantastic1 profane1 or silly4 ,and so1 having shown how the reviewer has hung himself1 ,i leave him funipendulous4 ,one instance more1 and ,i have done4 ,a reviewer1 not theological1 speaking of the common argument that things which are derided are not therefore to be rejected1 writes as follows3--,it might as well be said that they who laughed at ,jenner#cdi and vaccination were1 in a certain but very unsatisfactory way1 witnesses to the possible excellence of the system of ,st4 ,john ,long4#cej ,of course it might3 and of course it is said by all people of common sense4 ,in introducing the word possible1 the reviewer has hit the point3 ,i suspect that this word was introduced during revision1 to put the sentence into fighting order2 hurry preventing it being seen that the sentence was thus made to fight on the wrong side4 ,jenner1 who was laughed at1 was right2 therefore1 it is not impossible--that is1 it is possible--that a derided system may be right4 ,mark the three gradations3 in medio tutissimus ibis4#cea #bjf ,reviewer4--,if a system be derided1 it is no ground of suspense that derided systems have turned out true3 if it were1 you would suspend your opinion about ,st4 ,john ,long on account of ,jenner4--,ans4 ,you ought to do so1 as to possibility2 and before examination2 not with the notion that ,j4 proves ,st4 ,j4 probable2 only possible4 ,common ,sense4--,the past emergence of truths out of derided systems proves that there is a practical certainty of like occurrence to come4 ,but1 inasmuch as a hundred speculative fooleries are started for one truth1 the mind is permitted to approach the examination of any one given novelty with a bias against it of a hundred to one3 and this permission is given because so it will be1 leave or no leave4 ,every one has licence not to jump over the moon4 ,paradoxer4--,great men have been derided1 and ,i am derided3 which proves that my system ought to be adopted4 ,this is a summary of all the degrees in which paradoxers contend for the former derision of truths now established1 giving their systems probability4 ,i annex a paragraph which ,d e c4 inserted in the ,athenaeum of ,october #bc1 #ahdg4 ,discoverers and ,discoveries4 ,aristotle once sent his servant to the cellar to fetch wine3--and the fellow brought him back small beer4 ,the ,stagirite 7who knew the difference7 called him a blockhead4 ',sir1' said the man1 'all ,i can say is1 that ,i found it in the cellar4' ,the philosopher muttered to himself that an affirmative conclusion could not be proved in the second figure1--and ,mrs4 ,aristotle1 who was by1 was not less effective in her remark1 that small beer was not wine because it was in the same cellar4 ,both were right enough3 and our philosophers might take a lesson from either--for they insinuate an affirmative conclusion in the second figure4 ,great discoverers have been little valued by established #bjg schools1--and they are little valued4 ,the results of true science are strange at first1--and so are their's4 ,many great men have opposed existing notions1--and so do they4 ,all great men were obscure at first1--and they are obscure4 ,thinking men doubt1--and they doubt4 ,their small beer1 ,i grant1 has come out of the same cellar as the wine2 but this is not enough4 ,if they had let it stand awhile in the old wine-casks1 it might have imbibed a little of the flavor4 ,there are better reviews than ,i have noticed2 which1 though entirely dissenting1 are unassailable on their own principles4 ,what ,i have given represents five-sixths of the whole4 ,but it must be confessed that the fraction of fairness and moderation and suspended opinion which the doctrine of ,spirit ,manifestations has met with--even in the lower reviews--is strikingly large compared to what would have been the case fifty years ago4 ,it is to be hoped that our popular and periodical literatures are giving us one thinker created for twenty geese double-feathered3 if this hope be realized1 we shall do6 ,seeing all that ,i see1 ,i am not prepared to go the length of a friend of mine who1 after reading a good specimen of the lower reviewing1 exclaimed--,oh6 if all the fools in the world could be rolled up into one fool1 what a reviewer he would make6 ,calendrier ,universel et ,perpetuel2 par le ,commandeur ,p4 ,j4 ,arson4#ceb ,publie par ses ,enfans 7,oeuvre posthume74 ,nice1 #ahfc1 #dto4 ,i shall not give any account of this curious calendar1 with all its changes and symbols4 ,but there is one proposal1 which1 could we alter the general notions of time--a thing of very dubious possibility--would be convenient4 ,the week is made to wax and wane1 culminating on the ,sunday1 #bjh which comes in the middle4 ,thursday1 ,friday1 ,saturday1 are ascending or waxing days2 ,monday1 ,tuesday1 ,wednesday1 are descending or waning days4 ,our six days1 lumped together after the great distinguishing day1 ,sunday1 are too many to be distinctly thought of together3 a division of three preceding and three following the day of most note would be much more easily used4 ,but all this comes too late4 ,it may be1 nevertheless1 that some individuals may be able to adjust their affairs with advantage by referring ,thursday1 ,friday1 ,saturday1 to the following ,sunday1 and ,monday1 ,tuesday1 ,wednesday1 to the preceding ,sunday4 ,but ,m4 ,arson's proposal to alter the names of the days is no more necessary than it is practicable4 ,,cyclometry4 ,i am not to enter anything ,i do not possess4 ,the reader therefore will not learn from me the feats of many a man-at-arms in these subjects4 ,he must be content1 unless he will bestir himself for himself1 not to know how ,mr4 ,patrick ,cody trisects the angle at ,mullinavat1 or ,professor ,recalcati squares the circle at ,milan4 ,but this last is to be done by subscription1 at five francs a head3 a banker is named who guarantees restitution if the solution be not perfectly rigorous2 the banker himself1 ,i suppose1 is the judge4 ,i have heard of a man of business who settled the circle in this way3 if it can be reduced to a debtor and creditor account1 it can certainly be done2 if not1 it is not worth doing4 ,montucla will give the accounts of the lawsuits which wagers on the problem have produced in ,france4 ,neither will ,i enter at length upon the success of the new squarer who advertises 7,nov4 #ahfc7 in a country paper that1 having read that the circular ratio was undetermined1 ,i thought it very strange that so many great scholars in all ages should have failed in finding the true ratio1 and have been determined to try myself4444 ,i am about to secure the #bji benefit of the discovery1 so until then the public cannot know my new and true ratio4 ,i have been informed that this trial makes the diameter to the circumference as #fd to #bja1 giving pi #c4adjfbe exactly4 ,the result was obtained by the discoverer in three weeks after he first heard of the existence of the difficulty4 ,this quadrator has since published a little slip1 and entered it at ,stationers' ,hall4 ,he says he has done it by actual measurement2 and ,i hear from a private source that he uses a disk of #ab inches diameter1 which he rolls upon a straight rail4 ,mr4 ,james ,smith did the same at one time2 as did also his partisan at ,bordeaux4 ,we have1 then1 both #c4abe and #c4adjfbe1 by actual measurement4 ,the second result is more than the first by about one part in #bjj4 ,the second rolling is a very creditable one2 it is about as much below the mark as ,archimedes was above it4 ,its performer is a joiner1 who evidently knows well what he is about when he measures2 he is not wrong by #a in #c1jjj4 ,the reader will smile at the quiet self-sufficiency with which ,i have been determined to try myself follows the information that so many great scholars in all ages have failed4 ,it is an admirable spirit1 when accompanied by common sense and uncommon self-knowledge4 ,when ,i was an undergraduate there was a little attendant in the library who gave me the following1--,as to cleaning this library1 ,sir1 if ,i have spoken to the ,master once about it1 ,i have spoken fifty times3 but it is of no use2 he will not employ littery men2 and so ,i am obliged to look after it myself4 ,i do not think ,i have mentioned the bright form of quadrature in which a square is made equal to a circle by making each side equal to a quarter of the circumference4 ,the last squarer of this kind whom ,i have seen figures in the last number of the ,athenaeum for #ahee3 he says the thing is no longer a problem1 but an axiom4 ,he does not know that the area of the circle is greater than that of any other figure of the same circuit4 ,this any one might see without #baj mathematics4 ,how is it possible that the figure of greatest area should have any one length in its circuit unlike in form to any other part of the same length8 ,the feeling which tempts persons to this problem is that which1 in romance1 made it impossible for a knight to pass a castle which belonged to a giant or an enchanter4 ,i once gave a lecture on the subject3 a gentleman who was introduced to it by what ,i said remarked1 loud enough to be heard by all around1 ,only prove to me that it is impossible1 and ,i will set about it this very evening4 ,this rinderpest of geometry cannot be cured1 when once it has seated itself in the system3 all that can be done is to apply what the learned call prophylactics to those who are yet sound4 ,when once the virus gets into the brain1 the victim goes round the flame like a moth2 first one way and then the other1 beginning where he ended1 and ending where he begun3 thus verifying the old line ,in girum imus nocte1 ecce6 et consumimur igni4#cec ,every mathematician knows that scores of methods1 differing altogether from each other in process1 all end in this mysterious #c4adaei4441 which insists on calling itself the circumference to a unit of diameter4 ,a reader who is competent to follow processes of arithmetic may be easily satisfied that such methods do actually exist4 ,i will give a sketch1 carried out to a few figures1 of three3 the first two ,i never met with in my reading2 the third is the old method of ,vieta4#ced ,i find that both the first and second methods are contained in a theorem of ,euler4 ,what ,mr4 ,james ,smith says of these methods is worth noting4 ,he says ,i have given three fancy proofs of the value of pi3 he evidently takes me to be offering demonstration4 ,he proceeds thus3-- ,his first proof is traceable to the diameter of a circle #baa of radius #a4 ,his second1 to the side of any inscribed equilateral triangle to a circle of radius #a4 ,his third1 to a radius of a circle of diameter #a4 ,now1 it may be frankly admitted that we can arrive at the same result by many other modes of arithmetical calculation1 all of which may be shown to have some sort of relation to a circle2 but1 after all1 these results are mere exhibitions of the properties of numbers1 and have no more to do with the ratio of diameter to circumference in a circle than the price of sugar with the mean height of spring tides4 7,corr4 ,oct4 #ba1 #ahfe74 ,i quote this because it is one of the few cases--other than absolute assumption of the conclusion--in which ,mr4 ,smith's conclusions would be true if his premise were true4 ,had ,i given what follows as proof1 it would have been properly remarked1 that ,i had only exhibited properties of numbers4 ,but ,i took care to tell my reader that ,i was only going to show him methods which end in #c4adaei4444 ,the proofs that these methods establish the value of pi are for those who will read and can understand4 #bjjjjjjjj #cadae #cgii #fffffffg #bhag #bffffffg #acfc #aadbhega #ffa #ejgicfe #cba #bcjhhjb #aef #ajfefja #gf #digbha #cg #bcdjad #ah #aajhdi #i #ebghe #e #bebde #b #abaah #a #ehcd -------- -------- ------- #cadaecgii #cadae #ibfe #bab #a4 ,take any diameter1 double it1 take #a-c;d of that double1 #b-eths of the last1 #c-gths of the last1 #d-iths of the last1 #e-aaths of the last1 and so on4 ,the sum of all is the circumference of that diameter4 ,the preceding is the process when the diameter is a hundred millions3 the errors arising from rejection of fractions being lessened by proceeding on a thousand millions1 and striking off one figure4 ,here #bjj etc4 is double of the diameter2 #fff etc4 is #a-crd of #bjj etc42 #bff etc4 is #b-eths of #fff etc42 #aad etc4 is #c-gths of #bff etc42 #ejg etc4 is #d-iths of #aad etc42 and so on4 #b4 ,to the square root of #c add its half4 ,take half the third part of this2 half #b-eths of the last2 half #c-gths of the last2 and so on4 ,the sum is the circumference to a unit of diameter4 ,square root of #c4444 #a4gcbjejha 4#hffjbedj ------------ #b4eihjgfba 4#dccjabgj 4#jhffjbed #aheegfh #dabcic #icgbf #bafbi #ejdg #aahh #bha #fg #af #d #a ------------ #c4adaeibfe #c4 ,take the square root of #a_/b2 the square root of half of one more than this2 the square root of half of one more #bac than the last2 and so on1 until we come as near to unity as the number of figures chosen will permit4 ,multiply all the results together1 and divide #b by the product3 the quotient is an approximation to the circumference when the diameter is unity4 ,taking aim at four figures1 that is1 working to five figures to secure accuracy in the fourth1 we have 4#gjgab for the square root of #a_/b2 4#ibcij for the square root of half one more than 4#gjgab2 and so on1 through 4#ihjhj1 4#iiebj1 4#iihhj1 4#iiigj1 4#iiiib1 4#iiiih4 ,the product of the eight results is 4#fcffg2 divide #b by this1 and the quotient is #c4adac4441 of which four figures are correct4 ,had the product been 4#fcfcfc444 instead of 4#fcffg4441 the famous result of ,archimedes1 #bb-gths1 would have been accurately true4 ,it is singular that no cyclometer maintains that ,archimedes hit it exactly4 ,a literary journal could hardly admit as much as the preceding1 if it stood alone4 ,but in my present undertaking it passes as the halfpennyworth of bread to many gallons of sack4 ,many more methods might be given1 all ending in the same result1 let that result mean what it may4 ,now since dozens of methods1 to which dozens more might be added at pleasure1 concur in giving one and the same result2 and since these methods are declared by all who have shown knowledge of mathematics to be demonstrated3 it is not asking too much of a person who has just a little knowledge of the first elements that he should learn more1 and put his hand upon the error1 before he intrudes his assertion of the existence of error upon those who have given more time and attention to it than himself1 and who are in possession1 over and above many demonstrations1 of many consequences verifying each other1 of which he can know nothing4 ,this is all that is required4 ,let any one square the circle1 and persuade his friends1 if he and they please3 let him print1 and let all read who choose4 ,but let him abstain from intruding himself upon those who have been satisfied by existing demonstration1 until he is prepared #bad to lay his finger on the point in which existing demonstration is wrong4 ,let him also say what this mysterious #c4adaei444 really is1 which comes in at every door and window1 and down every chimney1 calling itself the circumference to a unit of diameter4 ,this most impudent and successful impostor holds false title-deeds in his hands1 and invites examination3 surely those who can find out the rightful owner are equally able to detect the forgery4 ,all the quadrators are agreed that1 be the right what it may1 #c4adaei444 is wrong4 ,it would be well if they would put their heads together1 and say what this wrong result really means4 ,the mathematicians of all ages have tried all manner of processes1 with one object in view1 and by methods which are admitted to yield demonstration in countless cases4 ,they have all arrived at one result4 ,a large number of opponents unite in declaring this result wrong1 and all agree in two points3 first1 in differing among themselves2 secondly1 in declining to point out what that curious result really is which the mathematical methods all agree in giving4 ,most of the quadrators are not aware that it has been fully demonstrated that no two numbers whatsoever can represent the ratio of the diameter to the circumference with perfect accuracy4 ,when therefore we are told that either #h to #be or #fd to #bja is the true ratio1 we know that it is no such thing1 without the necessity of examination4 ,the point that is left open1 as not fully demonstrated to be impossible1 is the geometrical quadrature1 the determination of the circumference by the straight line and circle1 used as in ,euclid4 ,the general run of circle-squarers1 hearing that the quadrature is not pronounced to be demonstratively impossible1 imagine that the arithmetical quadrature is open to their ingenuity4 ,before attempting the arithmetical problem1 they ought to acquire knowledge enough to read ,lambert's#cee demonstration 7last given in ,brewster's#cef translation #bae of ,legendre's#ceg ,geometry7 and1 if they can1 to refute it4 ,it will be given in an ,appendix4 ,probably some have begun this way1 and have caught a ,tartar who has refused to let them go3 ,i have never heard of any one who1 in producing his own demonstration1 has laid his finger on the faulty part of ,lambert's investigation4 ,this is the answer to those who think that the mathematicians treat the arithmetical squarers too lightly1 and that as some person may succeed at last1 all attempts should be examined4 ,those who have so thought1 not knowing that there is demonstration on the point1 will probably admit that a person who contradicts a theorem of which the demonstration has been acknowledged for a century by all who have alluded to it as read by themselves1 may reasonably be required to point out the error before he demands attention to his own result4 ,apopempsis of the ,tutelaries4--,again and again ,i am told that ,i spend too much time and trouble upon my two tutelaries3 but when ,i come to my summing-up ,i shall make it appear that ,i have a purpose4 ,some say ,i am too hard upon them3 but this is quite a mistake4 ,both of them beat little ,oliver himself in the art and science of asking for more2 but without ,oliver's excuse1 for ,i had given good allowance4 ,both began with me1 not ,i with them3 and both knew what they had to expect when they applied for a second helping4 ,on ,july #ca1 the ,monday after the publication of my remarks on my #fff correspondent1 ,i found three notes in separate envelopes1 addressed to me at #g;,a1 ,university ,college4 ,when ,i saw the three new digits ,i was taken rhythmopoetic1 as follows-- ,here's the ,doctor again with his figs1 and by ,heavens6 ,he was always at sixes1 and now he's at sevens4 ,to understand this fully the reader must know that the greater part of ,apocalyptic interpretation has long been condensed1 in my mind1 into the ,turkish street-cry--,in the #baf name of the ,prophet6 figs6 ,i make a few extracts4 ,the reader will observe that ,dr4 ,thorn grumbles at his private letters being publicly ridiculed4 ,a man was summoned for a glutolactic assault2 he complained of the publication of his proceeding3 ,i kicked etc4 in confidence1 he said4 ,after reading your last1 which tries in every way to hold me up to public ridicule for daring to write you privately 'that you would be d----d1' omitted by accident one would say1 ,why have anything to do with such a testy person8 ,wrong word2 no testy person can manage cool and consecutive ridicule4 ,quaere1 what is this word8 ,is it anything but a corruption of the obsolete word tetchy of the same meaning8 ,some think touchy is our modern form of tetchy1 which ,i greatly doubt4 ,my answer is1 the poor man is lamentably ignorant2 he is not only so1 but 'out of the way' quite true2 my readers know me by this time for an out-of-the-way person4 ,what other could tackle my squad of paradoxers8 ,what other would undertake the job8 ,can he be brought back and form one of those who in ,ezekiel #cg ch4 have the ,spirit breathed into them and live4444 ,have ,i any other feeling towards you except that of peace and goodwill8 ,not to your distinct knowledge2 but in all those who send people to 'the other place' for contempt of their interpretations1 there is a lurking wish which is father to the thought2 'you will be d----d' and 'you be d--d' are ,siamese twins4 ,of course your sneer at #fff brought plain words2 but when men meddle with what they do not understand 7not having the double ,vahu7 they must be dealt with faithfully by those who do4444 ,they must2 which justifies the ,budget of ,paradoxes3 but no occasion to send them anywhere2 no preachee and floggee too1 as the negro said4 ,many will find the text ,prov4 i4 #bf fully realized4 ,all this contains distinct assumption of a right 'of course' to declare accursed those who do not respect the writer's vagary4444 ,if ,i could but get the ,hebrew3 ,a1 the ,ox-head1 which in ,old ,hebrew was just the ,latin ,digamma1 ,f1 out #bag of your name1 and could then ,thau you with the ,thau of ,ezekiel ix1 #d1 the chi1 then you would bear the number of a man6 ,but this is too hard for me1 although not so for the ,lord6 ,jer4 xxxii4 #ag4444 ,and now a word3 is ridicule the right thing in so solemn a matter as the discussion of ,holy ,writ8 ,is food for ridicule the right thing8 ,did ,i discuss ,holy ,writ8 ,i did not3 ,i concussed profane scribble4 ,even the ,doctor did not discuss2 he only enunciated and denunciated out of the mass of inferences which a mystical head has found premises for in the ,bible4 ,m #dj ,o #gj ,r #ajj ,g #f ,n #ej ---- #bff ,hebrew3 tchi #djj ,that ill opinions are near relations of ill wishes1 will be detected by those who are on the look out4 ,the following was taken down in a ,scotch ,church by ,mr4 ,cobden1#ceh who handed it to a ,roman friend of mine1 for his delectation 7in #ahee73 ,lord1 we thank thee that thou hast brought the ,pope into trouble2 and we pray that thou wouldst be mercifully pleased to increase the same4 ,here is a martyr who quarrels with his crown2 a missionary who reviles his persecutor3 send him to ,new ,zealand1 and he would disagree with the ,maoris who ate him4 ,man of unilateral reciprocity6 have you1 who write to a stranger with hints that that stranger and his wife are children of perdition1 the bad taste to complain of a facer in return8 ,as ,james ,smith#cei--the ,attorney-wit1 not the ,dock-cyclometer--said1 or nearly said1 ,a pretty thing1 forsooth6 ,is he to burn1 all scalding hot1 ,me and my wife1 and am ,i not ,to job him out a tooth8 #bah ,those who think parody vulgar will be pleased to substitute for the above a quotation from ,butler#cfj3-- ,there's nothing so absurd or vain ,or barbarous or inhumane1 ,but if it lay the least pretence ,to piety and godliness1 ,or tender-hearted conscience1 ,and zeal for gospel truths profess1-- ,does sacred instantly commence1 ,and all that dare but question it are straight ,pronounced th' uncircumcised and reprobate1 ,as malefactors that escape and fly ,into a sanctuary for defence1 ,must not be brought to justice thence1 ,although their crimes be ne'er so great and high4 ,and he that dares presume to do't ,is sentenced and delivered up ,to ,satan that engaged him to't4 ,,the ,,number ,,of ,,the ,,beast4 ,of all the drolleries of controversy none is more amusing than the manner in which those who provoke a combat expect to lay down the laws of retaliation4 ,you must not strike this way6 you must not parry that way6 ,if you don't take care1 we shall never meddle with you again6 ,we were not prepared for such as this6 ,why did we have anything to do with such a testy person8 ,m4 ,jourdain must needs show ,nicole1 his servant-maid1 how good a thing it was to be sure of fighting without being killed1 by care and tierce4#cfa ,et cela n'est il pas beau d'etre assure de son fait quand on se bat contre quelqu'un8 ,la1 pousse moi un peu1 pour voir4 ,,nicole4 ,eh bien6 quoi8 ,m4 ,,jourdain4 ,tout beau4 ,hola6 #bai ,ho6 doucement4 ,diantre soit la coquine6 ,,nicole4 ,vous me dites de pousser4 ,m4 ,,jourdain4 ,oui2 mais tu me pousses en tierce1 avant que de pousser en quarte1 et tu n'as pas la patience que je pare4 ,his colleague1 my secular tutelary1 who also made an anachronistic onset1 with his repartees and his retorts1 before there was anything to fire at1 takes what ,i give by way of subsequent provocation with a good humor which would make a convert of me if he could afford 4#jafeibfe 444 of a grain of logic4 ,he instantly sent me his photograph for the asking1 and another letter in proof4 ,the ,thor-hammerer does nothing but grumble1 except when he tells a good story1 which he says he had from ,dr4 ,abernethy4#cfb ,a ,mr4 ,james ,dunlop was popping at the ,papists with a #fff-rifled gun1 when ,dr4 ,chalmers#cfc quietly said1 ,why1 ,dunlop1 you bear it yourself1 and handed him a paper on which the numerals in ,i ,a ,c ,o ,b ,v ,s ,d ,v ,n ,l ,o ,p ,v ,s #a #ajj #e #ejj #e #ej #e were added up4 ,this is almost as good as the ,filii ,dei ,vicarius1 the numerical letters of which also make #fff4 ,no more of these crazy--,i first wrote puerile1 but why should young cricketers be libelled8--attempts to extract religious use from numerical vagaries1 and to make ,god over all a proposer of salvation conundrums3 and no more of the trumpery hints about future destiny which is too great a compliment to call blasphemous4 ,if the ,doctor will cipher upon the letter in ,greek3 en hoi metroi metreite metrethesetai humin#cfd with double ,vahu cubic measure1 he will perhaps learn to leave off trying to frighten me into gathering grapes from thorns4 ,mystical hermeneutics may be put to good use by out-of-the-way people4 ,they may be made to call the attention #bbj of the many to a distinction well known among the learned4 ,the books of the ,new ,testament have been for #a1ejj years divided into two classes3 the acknowledged 7,greek3 homologoumena71 which it has always been paradox not to receive2 and the controverted 7,greek3 antilegomena71 about which there has always been that difference of opinion which no scholar overlooks1 however he may decide for himself after balance of evidence4 ,eusebius1#cfe who first 7l4 #c1 c4 #be7 recorded the distinction--which was much insisted on by the early ,protestants--states the books which are questioned as doubtful1 but which yet are approved and acknowledged by many--or the many1 it is not easy to say which he means--to be the ,epistles of ,james and ,jude1 the second of ,peter and the second and third of ,john4 ,in other places he speaks doubtingly of the ,epistle to the ,hebrews4 ,the ,apocalypse he does not even admit into this class1 for he proceeds as follows--,i use the second edition of the ,english folio translation 7#agji71 to avert suspicion of bias from myself3-- ,among the spurious ,greek3 nothoi let there be ranked both the work entitled the ,acts of ,paul1 and the book called ,pastor1 and the ,revelation of ,peter3 and moreover1 that which is called the ,epistle of ,barnabas1 and that named the ,doctrines of the ,apostles3 and moreover1 as ,i said1 the ,revelation of ,john 7if you think good71 which some1 as ,i have said1 do reject1 but others allow of1 and admit among those books which are received as unquestionable and undoubted4 ,eusebius1 though he will not admit the ,apocalypse even into the controverted list1 but gives permission to call it spurious1 yet qualifies his permission in a manner which almost annihilates the distinctive force of ,greek3 nothos1 and gives the book a claim to rank 7if you think good1 again7 in the controverted list4 ,and this is the impression received by #bba the mind of ,lardner1 who gives ,eusebius fully and fairly1 but when he sums up1 considers his author as admitting the ,apocalypse into the second list4 ,a stick may easily be found to beat the father of ecclesiastical history4 ,there are whole faggots in writers as opposite as ,baronius and ,gibbon1 who are perhaps his two most celebrated sons4 ,but we can hardly imagine him totally misrepresenting the state of opinion of those for whom and among whom he wrote4 ,the usual plan1 that of making an author take the views of his readers1 is more easy in his case than in that of any other writer3 for1 as the riddle says1 he is ,you-see-by-us2 and to this reading of his name he has often been subjected4 ,dr4 ,nathaniel ,lardner1#cff who1 though heterodox in doctrine1 tries hard to be orthodox as to the ,canon1 is sometimes apt to think that the list should be collected and divided as in ,eusebius4 ,he would have no one of the controverted books to be allowed1 by itself1 to establish any doctrine4 ,even without going so far1 a due use of early opinion and long continued discussion would perhaps prevent rational people from being induced by those who have the double ,vahu to place the ,apocalypse above the ,gospels1 which all the ,bivahuites do in effect1 and some are said to have done in express words4 ,but my especial purpose is to point out that an easy way of getting rid of #ffe out of #fff of the mystics is to require them to establish the ,apocalypse before they begin4 ,see if they even know so much as that there is a crowd of testimonies for and against1 running through the first four centuries1 which makes this book the most difficult of the whole ,canon4 ,try this method1 and you will escape beautiful1 as the ,french say4 ,dean ,alford1#cfg in ,vol4 ,,iv1 p4 #h1 of his ,new ,testament1 gives an elaborate handling of this question4 ,he concludes by saying that he cannot #bbb venture to refuse his consent to the tradition that the ,apostle is the author4 ,this modified adherence1 or non-nonadherence1 pretty well represents the feeling of orthodox ,protestants1 when learning and common sense come together4 ,i have often1 in former days1 had the attempt made to place the ,apocalypse on my neck as containing prophecies yet unfulfilled4 ,the preceding method prevents success2 and so does the following4 ,it may almost be taken for granted that theological system-fighters do not read the ,new ,testament3 they hunt it for detached texts2 they listen to it in church in that state of quiescent nonentity which is called reverent attention3 but they never read it4 ,when it is brought forward1 you must pretend to find it necessary to turn to the book itself3 you must read ,the revelation 444 to show unto his servants things which must shortly come to pass4444 ,blessed is he that readeth 444 for the time is at hand4 ,you must then ask your mystic whether things deferred for #ahjj years were shortly to come to pass1 etc48 ,you must tell him that the ,greek ,greek3 en tachei1 rendered shortly1 is as strong a phrase as the language has to signify soon4 ,the interpreter will probably look as if he had never read this opening3 the chances are that he takes up the book to see whether you have been committing a fraud4 ,he will then give you some exquisite evasion3 ,i have heard it pleaded that the above was a mere preamble4 ,this word mere is all-sufficient3 it turns anything into nothing4 ,perhaps he will say that the argument is that of the ,papists3 if so1 tell him that there is no ,christian sect but bears true witness against some one or more absurdities in other sects4 ,an anonyme suggests that ,greek3 en tachei may not be soon1 it may be quickly1 without reference to time when3 he continues thus1 ,may not time be 'at hand' when it is ready to come1 no matter how long delayed8 ,i now understand what 999999 and 999999 meant when they borrowed my books and promised to return them quickly1 it was without #bbc reference to time when4 ,as to time at hand--provided you make a long arm--,i admire the quirk1 but cannot receive it3 the word is ,greek3 engus1 which is a word of closeness in time1 in place1 in reckoning1 in kindred1 etc4 ,another gentleman is not surprised that ,apocalyptic reading leads to a doubt of the canonicity of the book3 it ought not to rest on church testimony1 but on visible miracle4 ,he offers me1 or any reader of the ,athenaeum1 the sight of a miracle to that effect1 and within forty-eight hours' journey 7fare paid74 ,i seldom travel1 and my first thought was whether my carpet-bag would be found without a regular hunt3 but1 on reading further1 ,i found that it was only a concordance that would be wanted4 ,forty hours' collection and numerical calculation of ,greek nouns would make it--should ,i happen to agree with the writer--many hundred millions to one that ,revelation xiii is superhuman4 ,there is but one verse 7the fifth7 which the writer does not see verified4 ,i looked at this verse1 and was much startled4 ,the ,budget began in ,october #ahfc3 should it last until ,march #ahfg--;it is now ,august #ahff--;it is clear that ,i am the first ,beast1 and my paradoxers are the saints whom ,i persecute4 ,the ,budget did terminate in ,march #ahfg3 ,i hope the gentleman will be satisfied with the resulting interpretation4 ,the same opponent is surprised that ,i should suppose a thing which comes to pass must be completed1 and cannot contain what is to happen #ahjj years after4 ,all who have any knowledge of ,english idiom know that a thing comes to pass when it happens1 and came to pass afterwards4 ,but as the original is ,greek1 we must look at the ,greek3 it is ,greek3 dei genesthai for must come to pass1 and we know that ,greek3 egeneto is what is usually translated came to pass4 ,no word of more finished completion exists in ,greek4 ,and now for a last round of biter-bit with the ,thor-hammerer1 of whom1 as in the other case1 ,i shall take no #bbd more notice until he can contrive to surpass himself1 which ,i doubt his being able to do4 ,he informs me that by changing ,a into ,hebrew3 t in my name he can make a #fff of me2 adding1 ,this is too hard for me1 although not so for the ,lord6 ,sheer nonsense6 ,he could just as easily have directed to ,prof4 ,de ,morg,hebrew3 tn as have assigned me apartment #g;,a in ,university ,college4 ,it would have been seen for whom it was intended3 and if not1 it would still have reached me1 for my colleagues have for many a year handed all out-of-the-way things over to me4 ,there is no #g;,a3 but #g is the ,museum of ,materia ,medica4 ,i took the only hint which the address gave3 ,i inquired for hellebore1 but they told me it was not now recognized1 that the old notion of its value was quite obsolete1 and that they had nothing which was considered a specific in senary or septenary cases4 ,the great platitude is the reference of such a difficulty as writing ,hebrew3 t for ,a to the ,almighty6 ,not childish1 but fatuous3 real childishness is delightful4 ,i knew an infant to whom1 before he could speak plain1 his parents had attempted to give notions of the ,divine attributes3 a wise plan1 many think4 ,his father had dandled him up-side-down1 ending with1 ,there now6 ,papa could not dance on his head6 ,the mannikin made a solemn face1 and said1 ,but ,dod tood6 ,i think the ,doctor has rather mistaken the way of becoming as a little child1 intended in ,matt4 xviii4 #c3 let us hope the will may be taken for the deed4 ,two poets have given images of transition from infancy to manhood3 ,dryden1--for the ,hind is ,dryden himself on all fours6 and ,wordsworth1 in his own character of broad-nailed1 featherless biped3 ,the priest continues what the nurse began1 ,and thus the child imposes on the man4 ,the child's the father of the man1 ,and ,i could wish my days to be ,bound each to each by natural piety4 #bbe ,in ,wordsworth's aspiration it is meant that sense and piety should grow together3 in ,dryden's description a combination of ,mysticism ,and ,bigotry 7can this be the double ,vahu871 personified as the priest1--who always catches it on this score1 though the same spirit is found in all associations1--succeeds the boguey-teaching of the nurse4 ,never was the contrast of smile and scowl1 of light and darkness1 better seen than in the two pictures4 ,but an acrostic distinction may be drawn4 ,when mysticism predominates over bigotry1 we have the grotesque picturesque1 and the natural order of words gives us ,mab1 an appropriate suggestion4 ,but when bigotry has the upper hand1 we see ,bam1 which is just as appropriate2 for bigotry nearly always deals with facts and logic so as to require the application of at least one of the minor words by which dishonesty is signified4 ,i think that ,m is the ,doctor's initial1 and that ,queen ,mab tickles him in his sleep with the sharp end of a #f4 7,monday1 ,august #ba47 ,three weeks having elapsed without notice from me of the ,doctor1 ,i receive a reminder of his existence1 in which ,i find that as ,i am the ,daniel who judges the ,magi of ,babylon1 it is to be pointed out that ,daniel bore a certain number1 that of a man 7beloved71 ,daniel1 ch4 #aj4 v4 #aa1 and which you certainly do not4 ,then1 by ,greek power1 ,belteshazzar is made #fff4 ,here is another awkward imitation of the way of a baby child4 ,when you have sported with the tiny creature until it runs away offended1 by the time you have got into conversation again you will find the game is to be renewed3 a little head peeps out from a hiding-place with ,i don't love you4 ,the proper rejoinder is1 ,very well6 then ,i'll have pussy4 ,but in the case before me there is a rule of three sums to do2 as baby 3 ,pussy ,dr4 33 #fff 3 the answer required4 ,i will work it out1 if ,i can4 ,the squaring of the circle and the discovery of the ,beast are the two goals--and goals also--of many unbalanced intellects1 and of a few instances of the better kind4 #bbf ,i might have said more of #fff1 but ,i am not deep in its bibliography4 ,a work has come into my hands which contains a large number of noted cases3 to some of my readers it will be a treat to see the collection2 and the sight will perhaps be of some use to those who have read controversy on the few celebrated cases which are of general notoriety4 ,it is written by a learned decipherer1 a man who really knew the history of the subject1 the ,rev4 ,david ,thom1#cfh of ,bold ,street ,chapel1 ,liverpool1 who died1 ,i am told1 a few years ago4 ,anybody who reads his book will be inclined to parody a criticism which was once made on ,paley's#cfi ,evidences--,well6 if there be anything in ,christianity1 this man is no fool4 ,and1 if he should chance to remember it1 he will be strongly reminded of a sentence in my opening chapter1--,the manner in which a paradoxer will show himself1 as to sense or nonsense1 will not depend upon what he maintains1 but upon whether he has or has not made a sufficient knowledge of what has been done by others1 especially as to the mode of doing it1 a preliminary to inventing knowledge for himself4 ,and this is reinforced by the fact that ,mr4 ,thom1 though a scholar1 was not conspicuous for learning1 except in this his great pursuit4 ,he was a paradoxer on other points4 ,he reconciled ,calvinism and eternal reprobation with ,universalism and final salvation2 showing these two doctrines to be all one4 ,this gentleman must not be confounded with the ,rev4 ,john ,hamilton ,thom#cgj 7no relation71 at or near the same #bbg time and until recently1 of ,renshaw ,street ,chapel1 ,liverpool who was one of the minority in the ,liverpool controversy when1 nearly thirty years ago1 three heretical ,unitarian schooners exchanged shotted sermons with thirteen ,orthodox ships of the line1 and put up their challengers' dander--an ,american corruption of d--d anger--to such an extent1 by quiet and respectful argument1 that those opponents actually addressed a printed intercession to the ,almighty for the ,unitarian triad1 as for ,jews1 ,turks1 ,infidels1 and ,heretics4 ,so much for the distinction1 which both gentlemen would thank me for making very clear3 ,i take it quite for granted that a guesser at #fff would feel horrified at being taken for a ,unitarian1 and that a ,unitarian would feel queerified at being taken for a guesser at #fff4 ,mr4 ,david ,thom's book is ,the ,number and ,names of the ,apocalyptic ,beasts1 ,part ,i1 #ahdh1 #hvo43 ,i think the second part was never published4 ,i give the ,greek and ,latin solutions1 omitting the ,hebrew3 as usual1 all the ,greek letters are numeral1 but only ,m ,d ,c ,l ,x ,v ,i of the ,latin4 ,i do not give either the decipherers or their reasons3 ,i have not room for this2 nor would ,i1 if ,i could1 bias my reader for one rather than another4 ,d4 ,f4 ,julianus ,caesar ,atheus 7or ,aug4#cga72 ,diocles ,augustus2 ,ludovicus2 ,silvester ,secundus2 ,linus ,secundus2 #bbh ,vicarius ,filii ,dei2 ,doctor et ,rex ,latinus2 ,paulo ,v4 ,vice-,deo2 ,vicarius ,generalis ,dei in ,terris2 ,ipse ,catholicae ,ecclesiae ,visibile ,caput2 ,dux ,cleri2 ,una1 ,vera1 ,catholica1 ,infallibilis ,ecclesia2 ,auctoritas politica ecclesiasticaque ,papalis 7,latina will also do72 ,lutherus ,ductor ,gregis2 ,calvinus tristis fidei interpres2 ,dic ,lux 2 ,ludvvic2 ,will4 ,laud2 ,greek3 ,lateinos2#cgb ,greek3 he latine basileia2 ,greek3 ekklesia italika2 ,greek3 euanthas2 ,greek3 teitan2 ,greek3 arnoume2 ,greek3 lampetis2 ,greek3 ho niketes2 ,greek3 kakos hodegos2 ,greek3 alethes blaberos2 ,greek3 palai baskanos2 ,greek3 amnos adikos2 ,greek3 antemos2 ,greek3 genserikos2 ,greek3 euinas2 ,greek3 ,benediktos2 ,greek3 ,bonibazios g4 papa x4 e4 e4 e4 a41 meaning ,boniface ,,iii4 ,pope #fhth1 bishop of bishops the first6 ,greek3 oulpios2 ,greek3 dios eimi he heras2 ,greek3 he missa he papike2 ,greek3 loutherana2 ,greek3 saxoneios2 ,greek3 ,bezza antitheos 7,beza72 ,greek3 he alazoneia biou2 ,greek3 ,maometis2 ,greek3 ,maometes b42 ,greek3 theos eimi epi gaies2 ,greek3 iapetos2 ,greek3 papeiskos2 ,greek3 dioklasianos2 ,greek3 cheina2 ,greek3 braski2 ,greek3 ,ion ,paune2 ,greek3 koupoks2 7cowpox1 ,greek3 s being the vau2 certainly the #bbi vaccinated have the mark of the ,beast72 ,greek3 ,bonneparte2 ,greek3 ,n4 ,boneparte2 ,greek3 euporia2 ,greek3 paradosis2 ,greek3 to megatherion4 ,all sects fasten this number on their opponents4 ,it is found in ,martin ,lauter1 affirmed to be the true way of writing the name1 by carrying numbers through the ,roman ,alphabet4 ,some ,jews1 according to ,mr4 ,thorn1 found it in ,hebrew3 ,,jshw ,,ntsrj ,jesus of ,nazareth4 ,i find on inquiry that this satire was actually put forth by some medieval rabbis1 but that it is not idiomatic3 it represents quite fairly ,jesus ,nazarene1 but the ,hebrew wants an article quite as much as the ,english wants the4 ,mr4 ,david ,thom's own solution hits hard at all sides3 he finds a #fff for both beasts2 ,greek3 he phren 7the mind7 for the first1 and ,greek3 ekklesiai sarkikai 7fleshly churches7 for the second4 ,a solution which embodies all mental philosophy in one beast and all dogmatic theology in the other1 is very tempting3 for in these are the two great supports of ,antichrist4 ,it will not1 however1 mislead me1 who have known the true explanation a long time4 ,the three sixes indicate that any two of the three subdivisions1 ,roman1 ,greek1 and ,protestant1 are1 in corruption of ,christianity1 six of one and half a dozen of the other3 the distinctions of units1 tens1 hundreds1 are nothing but the old way 7#a ,samuel xviii4 #g1 and ,concordance at ten1 hundred1 thousand7 of symbolizing differences of number in the subdivisions4 ,it may be good to know that1 even in speculations on #fff1 there are different degrees of unreason4 ,all the diviners1 when they get a colleague or an opponent1 at once proceed to reckon him up3 but some do it in play and some in earnest4 ,mr4 ,david ,thom found a young gentleman of the name ,st4 ,claire busy at the ,beast number3 he forthwith added the letters in ,greek3 st klaire and found #fff3 this was good fun4 ,but my spiritual tutelary1 when he found that he could not make a beast of me1 except by changing ,hebrew3 ,a into ,hebrew3 ,t1 solemnly referred the difficulty to the ,almighty3 this was poor earnest4 #bcj ,i am glad ,i did not notice1 in time to insert it in the ,athenaeum1 a very remarkable paradoxer brought forward by ,mr4 ,thom1 his friend ,mr4 ,wapshare#cgc3 it is a little too strong for the general public4 ,in the ,athenaeum they would have seen and read it3 but this book will be avoided by the weaker brethren4 ,it is as follows3 ,god1 the ,elohim1 was six days in creating all things1 and having made ,,man he entered into his rest4 ,he is no more seen as a ,creator1 as ,elohim1 but as ,jehovah1 the ,lord of the ,sabbath1 and the ,spirit of life in ,,man1 which ,spirit worketh sin in the flesh2 for the ,spirit of ,love1 in all flesh1 is ,lust1 or the spirit of a beast1 ,so ,rom4 vii4 ,and which ,spirit is crucified in the flesh4 ,he then1 as ,jehovah--as the power of the ,law1 in and over all flesh1 ,john viii4 #dd--;increases that which he has made as the ,elohim1 and his power shall last for #f days1 or #f periods of time1 computed at a millennium of years2 and at the end of which six days1 he who is the ,spirit of all flesh shall manifest himself as the ,holy ,spirit of ,almighty ,love1 and of all truth2 and so shall the ,church have her ,sabbath of ,rest--all contention being at an end4 ,this is1 as well as ,i may now express it1 my solution of the mystery in ,hebrew1 and in ,greek1 and also in ,latin1 ,,ihs4 ,for he that was lifted up is ,king of the ,jews1 and is the ,lord of all ,life1 working in us1 both to will and to do2 as is manifest in the ,jews--they slaying him that his blood might be good for the healing of the nations1 of all people and tongues4 ,as the ,father of all natural flesh1 he is the ,spirit of ,lust1 as in all beasts2 as the ,father1 or ,king of the ,jews1 he is the ,devil1 as he himself witnesseth in ,john viii41 already referred to4 ,as lifted up1 he is transformed into the ,spirit of ,love1 a light to the ,gentiles1 and the glory of his people ,israel4444 ,for there is but ,,one ,god1 ,,one ,lord1 ,,one ,spirit1 ,,one body1 etc4 and he who was ,satan1 the ,spirit of life in that body1 is1 in #bca ,christ crucified1 seen in the ,spirit that is in all1 and through all and over all1 ,god blessed for ever4 ,all this seems well meant1 and ,mr4 ,thom prints it as convinced of its piety1 and pronounces no opinion4 ,mystics of all sorts6 see what you may come to1 or what may come to you6 ,i have inserted the above for your good4 ,there is nothing in this world so steady as some of the paradoxers4 ,they are like the spiders who go on spinning after they have web enough to catch all the flies in the neighborhood1 if the flies would but come4 ,they are like the wild bees who go on making honey which they never can eat1 proving sic vos non vobis to be a physical necessity of their own contriving4 ,but nobody robs their hives3 no1 unlike the bees1 they go about offering their ware to any who will take it as a gift4 ,i had just written the last sentence 7,oct4 #cj1 #ahff1 #h4de ,a4,m47 when in comes the second note received this morning from ,dr4 ,thorn3 at #a4cj ,p4,m4 came in a third4 ,these arise out of the above account of the ,rev4 ,d4 ,thom1 published ,oct4 #bg3 three notes had arrived before4 ,for curiosity ,i give one day's allowance1 supposing these to be all3 more may arrive before night4 #bith ,oct4 #ahff4 ,dear ,sir1-- ,in re swastika4#cgd ,so that ',zaphnath ,paaneah' may be after all the revealer of the ',northern ,tau' ,greek3 ,phaneroo--,to make manifest1 shew1 or explain2 and this may satisfy the ,house of ,joseph in ,amos #e;c4 ,while ,belteshazzar #fff may be also satisfactory to the ,house of ,david1 and so we may have ,zech4 #aj;c4 #fv4 in operation when ,ezekiel #cg;c4 #afv4 has been realised2--but there1 what is the use of writing1 it is all ,coptic #bcb to a man who has not swastika1 ,the ,thau of the ,north1 the double ,vahu ,hebrew3 ,wqamats,w4 ,look at ,jeremiah #c;c4 #hv4 and then to ,psalm #hc for 'hidden ones' ,hebrew3 ,,tssheva,,pwdagesh,nsegol,y ,ysheva,,hwqamats,h--,the ,zephoni ,jehovah1 and say whether they have any connection with the ,zephon ,thau4 ,the ,hammer of ,thor of ,jeremiah #bc;c4 #biv4 as ,i gave you in ,no4 #c of my present edition4 ,yours truly ,,le ,,chevalier ,,au ,,cin4 ,by ,greek ,power4 ,c #bj ,h #h ,e #e ,v #f ,a #a ,l #cj ,i #aj ,e #e ,r #ajj ,a #a ,u #djj ,c #bj ,i #aj ,n #ej ---- #fff ,there will be thousands of ,morgans who will be among the wise and prudent of ,hosea #ad;c4 #iv4 when the ,seventh ,angel sounds1 let me number that ,one by ,greek1 ,rev4 #ag;c4 #av3 #bcc ,s #bjj ,e #e x ,v #f ,e #e ,n #ej ,t #cjj ,h #h ,a #a ,n #ej x ,g #f ,e #e ,l #cj ---- #fff ,v and ,g #ab ought to be equal to one ,gammadion or #cswastika#c x #d #ab1 what say you8 ,london1 ,october #bi1 #ahff4 ,dear ,sir1-- ,in re swastika versus maltese cross4 ,however pretentious the ,x or maltese cross may be1 and it is peculiarly so just now in this land2 after all it is only made of two ,roman ,v's--and so is only one inverted7#aj7--;and therefore is not the perfect number #ab of ,reveln1 but is the mark of the goddess ,decima6 ,yours truly ,,wm4 ,,thorn4 ,had the one who sent forth a pastoral 7,romish7 the other day1 remained amongst the faithful expectants1 see how he would have numbered1 whereas he sold himself for the privilege of signing maltese cross ,,henry ,e4 ,,manning4#cge #bcd ,by ,english ,key4 ,h #h ,e #e ,n #dj ,r #hj ,y #adj ,e #e ,d #d ,w #abj ,a #a ,r #hj ,d #d ,m #cj ,a #a ,n #dj ,n #dj ,i #i ,n #dj ,g #g swastika #ab ---- #fff ,can you now understand the difference between swastika and maltese cross or ,x8 ,look to my challenge4 ,cutting from newspaper3-- ,,italy4 ,rome 7via ,marseilles71 ,october ,mr4 ,gladstone has paid a visit to the ,pope4 ,by ,greek ,power4 ,g #f ,l #cj ,a #a ,d #d ,s #bjj ,t #cjj ,o #gj ,n #ej ,e #e ---- #fff ,and what then swastika8 #bce ,in other letters ,john ,stuart ,mill is #fff if the a be left out2 ,chasuble is perfect4 ,john ,brighte#cgf is a fait accompli2 and ,i am asked whether intellect can account for the final e4 ,very easily3 this ,beast is not the ,m4 ,p41 but another person who spells his name differently4 ,but if ,john ,sturt ,mill and ,john ,brighte choose so to write themselves1 they may4 ,a curious collection2 a mystical phantasmagoria6 ,there are those who will try to find meaning3 there are those who will try to find purpose4 ,and some they said--,what are you at8 ,and some--,what are you arter8 ,my account of ,mr4 ,thom and his #fff appeared on ,october #bg3 and on the #bith ,i received from the editor a copy of ,mr4 ,thom's sermons published in #ahfc 7he died ,feb4 #bg1 #ahfb7 with best wishes for my health and happiness4 ,the editor does not name himself in the book2 but he signed his name in my copy3 and may my circumference never be more than #c-a_/h of my diameter if the signature1 name and writing both1 were not that of my circle square ing friend ,mr4 ,james ,smith6 ,and so ,i have come in contact with him on #fff as well as on pi6 ,i should have nothing left to live for1 had ,i not happened to hear that he has a perpetual motion on hand4 ,i returned thanks and kind regards3 and ,miss ,miggs's words--,here's forgivenesses of injuries6 here's amicablenesses6--rang in my ears4 ,but ,i was made slightly uncomfortable3 how could the war go on after this armistice8 ,could ,i ever make it understood that the truce only extended to the double ,vahu and things thereunto relating8 ,it was once held by seafaring men that there was no peace with ,spaniards beyond the line3 ,i was determined that there must be no concord with ,j4 ,s4 inside the circle2 that this must be a special exception1 like ,father ,huddleston #bcf and old ,grouse in the gun-room4 ,i was not long in anxiety2 twenty-four hours after the book of sermons there came a copy of the threatened exposure--,the ,british ,association in ,jeopardy1 and ,professor ,de ,morgan in the ,pillory without hope of escape4 ,by ,james ,smith1 ,esq4 ,london and ,liverpool1 #hvo41 #ahff 7pp4 #id74 ,this exposure consists of reprints from the ,athenaeum and ,correspondent3 of things new there is but one4 ,in a short preface ,mr4 ,j4 ,s4 particularly recommends to read to the end4 ,at the end is an appendix of two pages1 in type as large as the work2 a very prominent peroration4 ,it is an article from the ,athenaeum1 left out of its place4 ,in the last sentence ,mr4 ,j4 ,smith1 who had asked whether his character as an honest ,geometer and ,mathematician was not at stake1 is warned against the fallacia plurium interrogationum4#cgg ,he is told that there is not a more honest what's-his-name in the world3 but that as to the counter which he calls his character as a mathematician1 he is assured that it has been staked years ago1 and lost4 ,and thus truth has the last word4 ,there is no occasion to say much about reprints4 ,one of them is a letter that given above of ,august #be1 #ahfe1 written by ,mr4 ,j4 ,s4 to the ,correspondent4 ,it is one of his quadratures2 and the joke is that ,i am made to be the writer3 it appears as what ,mr4 ,j4 ,s4 hopes ,i shall have the sense to write in the ,athenaeum and forestall him4 ,when ,i saw myself thus quoted--yes6 quoted6 double commas1 first person--,i felt as ,i suppose did ,wm4 ,wilberforce#cgh when he set eyes on the affectionate benediction of the potato which waggish comrades had imposed on a raw ,irish reporter as part of his speech4 ,i felt as ,martin#cgi of #bcg ,galway--kind friend of the poor dumb creatures6--when he was told that the newspapers had put him in ,italics4 ,i appeal to you1 ,mr4 ,speaker6 ,i appeal to the ,house6 ,did ,i speak in ,italics8 ,do ,i ever speak in ,italics8 ,i appeal to editor and readers1 whether ,i ever squared the circle until a week or two ago1 when ,i gave my charitable mode of reconciling the discrepant cyclometers4 ,the absurdity of the imitation of symbolic reasoning is so lusciously rich1 that ,i shall insert it when ,i make up my final book4 ,somebody mastered ,spanish merely to read ,don ,quixote3 it would be worth while to learn a little algebra merely to enjoy this a b-istical attack on the windmills4 ,the principle is1 ,prove something in as roundabout a way as possible1 mention the circle once or twice irrelevantly in the course of your proof1 and then make an act of ,q4 ,e4 ,d4 in words at length4 ,the following is hardly caricature3-- ,to prove that #b and #b make #e4 ,let a #b1 b #e3 let c #feh1 the number of the ,house3 let d #fff1 the number of the ,beast4 ,then of necessity d a b c #a2 so that #a is a harmonious and logical quantification of the number of which we are to take care4 ,now1 b1 the middle of our digital system1 is1 by mathematical and geometrical combination1 a mean between #e #a and #b #b4 ,let #a be removed to be taken care of1 a thing no real mathematician can refuse without serious injury to his mathematical and geometrical reputation4 ,it follows of necessity that #b #b #e1 quod erat demonstrumhorrendum4 ,if ,simpkin ,marshall have not1 after my notice1 to account for a gross of copies more than would have gone off without me1 the world is not worthy of its ,james ,smith6 ,the only fault of the above is1 that there is more #bch connection than in the process of ,faber ,cyclometricus3 so much1 in fact1 that the blunders are visible4 ,the utter irrelevance of premises to conclusion cannot be exhibited with the requisite obscurity by any one who is able to follow reasoning3 it is high art displayed in a certain toning down of the aegri somnia1 which brings them to a certain look of reproach to reasoning which ,i can only burlesque4 ,mr4 ,j4 ,s4 produces something which resembles argument much as a chimpanzee in dolor1 because balked of his dinner1 resembles a thinking man at his studies4 ,my humble attempt at imitation of him is more like a monkey hanging by his tail from a tree and trying to crack a cocoa-nut by his chatter4 ,i could forgive ,mr4 ,j4 ,s4 anything1 properly headed4 ,i would allow him to prove--for himself--that the ,quadrature of the ,circle is the child of a private marriage between the ,bull ,unigenitus and the ,pragmatic ,sanction1 claiming tithe of onions for repeal of the ,mortmain ,act1 before the ,bishops in ,committee under the kitchen table3 his mode of imitating reason would do this with ease4 ,but when he puts his imitation into my mouth1 to make me what he calls a real mathematician1 my soul rises in epigram against him4 ,i say with the doll's dressmaker--such a job makes me feel like a puppet's tailor myself--,he ought to have a little pepper8 just a few grains8 ,i think the young man's tricks and manners make a claim upon his friends for a little pepper8 ,de ,faure#chj and ,joseph ,scaliger#cha come into my head3 my reader may look back for them4 ,three circlesquarers to the manner born1 ,switzerland1 ,france1 and ,england did adorn1 ,de ,faure in equations did surpass1 ,joseph at contradictions was an ass4 ,groaned ,folly1 ,i'm used up6 ,what shall ,i do ,to make ,james ,smith8 ,grinned ,momus1 ,join the two6 #bci ,as to my locus poenitentiae1#chb the reader who is fit to enjoy the letter ,i have already alluded to will see that ,i have a soft and easy position2 that the thing is really a pillowry2 and that ,i am1 like ,perrette's pot of milk1 ,bien pose sur un coussinet4#chc ,joanna ,southcott#chd never had a follower who believed in her with more humble piety than ,mr4 ,james ,smith believes in himself4 ,after all that has happened to him1 he asks me with high confidence to favor the writer with a proof that ,i still continue of opinion that the best of the argument is in my jokes1 and the best of the joke is in his arguments4 ,i will not so favor him4 ,at the very outset ,i told him in plain ,english that he has the whiphand of all the reasoners in the world1 and in plain ,french that il a perdu le droit d'etre frappe de l'evidence#che2 ,i might have said pendu4#chf ,to which ,i now add1 in plain ,latin1 ,sapienti pauca1 indocto nihil4#chg ,the law of ,chancery says that he who will have equity must do equity3 the law of reasoning says that he who will have proof must see proof4 ,the introduction of things quite irrelevant1 by way of reproach1 is an argument in universal request3 and it often happens that the argument so produced really tells against the producer4 ,so common is it that we forget how boyish it is2 but we are strikingly reminded when it actually comes from a boy4 ,in a certain police court1 certain small boys were arraigned for conspiring to hoot an obnoxious individual on his way from one of their school exhibitions4 ,this proceeding was necessary1 because there seemed to be a permanent conspiracy to annoy the gentleman2 and the #bdj masters did not feel able to interfere in what took place outside the school4 ,so the boys were arraigned2 and their friends1 as silly in their way as themselves1 allowed one of them to make the defence1 instead of employing counsel2 and did not even give them any useful hints4 ,the defence was as follows2 and any one who does not see how richly it sets off the defences of bigger boys in bigger matters has much to learn4 ,the innocent conviction that there was answer in the latter part is delightful4 ,of course fine and recognizance followed4 ,a---- said the boys had received great provocation from ,b----4 ,he was constantly threatening them with a horsewhip which he carried in his hand the boy did not say what had passed to induce him to take such a weapon1 and he had repeatedly insulted the master1 which the boys could not stand4 ,b---- had in his own drawing-room told him 7,a----7 that he had drawn his sword against the master and thrown away the scabbard4 ,b---- knew well that if he came to the college he would catch it1 and then he went off through a side door--which was no sign of pluck2 and then he brought ,mrs4 ,b---- with him1 thinking that her presence would protect him4 ,my readers may expect a word on ,mr4 ,thom's sermons1 after my account of his queer doings about #fff4 ,he is evidently an honest and devout man1 much wanting in discrimination4 ,he has a sermon about private judgment1 in which he halts between the logical and legal meanings of the word4 ,he loathes those who apply their private judgment to the word of ,god3 here he means those who decide what it ought to be4 ,he seems in other places aware that the theological phrase means taking right to determine what it is4 ,he uses his own private judgment very freely1 and is strong in the conclusion that others ought not to use theirs except as he tells them how2 he leaves all the rest of mankind free to think with him4 ,in this he is not original3 his fame must rest on his senary tripod4 #bda ,,james ,,smith ,,once ,,more4 ,mr4 ,james ,smith's procedures are not caricature of reasoning2 they are caricature of blundering4 ,the old way of proving that #b #a is solemn earnest compared with his demonstrations4 ,as follows3#chh ,let x #a ,then x#b x ,and x#b - #a x - #a ,divide both sides by x - #a2 then x #a #a2 but x #a1 whence #b #a4 ,when a man is regularly snubbed1 bullied1 blown up1 walked into1 and put down1 there is usually some reaction in his favor1 a kind of deostracism1 which cannot bear to hear him always called the blunderer4 ,i hope it will be so in this case4 ,there is nothing ,i more desire than to see sects of paradoxers4 ,there are fully five thousand adults in ,england who ought to be the followers of some one false quadrature4 ,and ,i have most hope of #c-a_/h1 because ,i think ,mr4 ,james ,smith better fitted to be the leader of an organized infatuation than any one ,i know of4 ,he wants no pity1 and will get none4 ,he has energy1 means1 good humor1 strong conviction1 character1 and popularity in his own circle4 ,and1 most indispensable point of all1 he sticks at nothing2 ,in coelum jusseris1 ibit4#chi ,when my instructor found ,i did not print an acceptance of what ,i have quoted1 he addressed me as follows 7,corr41 ,sept #bc73-- ,in this life1 however1 we must do our duty1 and1 when #bdb necessary1 use the rod1 not in a spirit of revenge1 but for the benefit of the culprit and the good of society4 ,now1 ,sir1 the opportunity has been thrown in your way of slipping out of the pillory without risk of serious injury2 but1 like an obstinate urchin1 you have chosen to quarrel with your opportunity and remain there1 and thus you compel me to deal with you as schoolmasters used to do with stupid boys in bygone days--that is to say1 you force me to the use of the critic's rod1 compel me to put you where little ,jack ,horner sat1 and1 as a warning to other naughty boys1 to ornament you with a dunce's cap4 ,the task ,i set you was a very simple one1 as ,i shall make manifest at the proper time4 ,in one or more places1 as well as this1 ,mr4 ,smith shows that he does not know the legend of little ,jack ,horner1 whom he imagines to be put in the corner as a bad boy4 ,this is curious2 for there had been many allusions to the story in the journal he was writing in1 and the ,christmas pie had become altered into the ,seaforth pi4 ,mr4 ,smith is satisfied at last that--what between argument and punishment he has convinced me4 ,he says 7,corr41 ,jan4 #bg1 #ahff73 ,i tell him without hesitation that he knows the true ratio of diameter to circumference as well as ,i do1 and if he be wise he will admit it4 ,i should hope ,i do1 and better2 but there is no occasion to admit what everybody knows4 ,i have often wished that we could have a slight glimpse of the reception which was given to some of the old cyclometers3 but we have nothing1 except the grave disapprobation of historians4 ,i am resolved to give the ,new ,zealander a chance of knowing a little more than this about one of them at least2 and1 by the fortunate entrance into life of the ,correspondent1 ,i am able to do it4 ,i omit sober mathematical answers1 of which there were several4 ,the following letter is grave earnest3 ,sir1--,i have watched ,mr4 ,james ,smith's writings on this subject from the first1 and ,i did hope that1 as the more #bdc he departs from truth the more easy it must be to refute him1 this by no means always true some of your correspondents would by this time have done so4 ,i own that ,i am unable to detect the fallacy of his argument2 and ,i am quite certain that ',pi' is wrong1 in ,no4 #bc1 where he declares that ,mr4 ,smith is 'ignorant of the very elements of mathematical truth4' ,i have observed an immense amount of geometrical reasoning on his part1 and ,i cannot see that it is either fair or honest to deny this1 which may be regarded as the 'elements' of mathematical truth4 ,would it not be better for ',pi' to answer ,mr4 ,smith1 to refute his arguments1 to point out their fallacies1 and to save learners from error1 than to plunge into gross insult and unmanly abuse8 ,would it not be well1 also1 that ,professor ,de ,morgan should favour us with a little reasoning8 ,i have hitherto seen no attempt to overthrow ,mr4 ,smith's arguments2 ,i trust that this will not continue1 since the subject is one of immense importance to science in general1 especially to nautical science1 and all that thereto belongs4 ,yours1 etc41 ,a ,,captain1 ,r4,n4 ,on looking at this homoeopathic treatment of the #c-a_/h quadrature--remember1 homoeopathic1 similia similibus1#cij not infinitesimal--and at the imputation thrown upon it1 ,i asked myself1 what is vulgarity8 ,no two agree1 except in this1 that every one sees vulgarity in what is directed against himself4 ,mark the world1 and see if anything be so common as the description of the other side's remarks as vulgar attempt at wit4 ,i suppose you think that very witty3 the answer is ,no my friend6 your remark shows that you feel it as wit1 so that the purpose is answered2 ,i keep my razor for something else than cutting blocks2 ,i am inclined to think that out of place is a necessary attribute of true vulgarity4 ,and further1 it is to be noticed that nothing is #bdd unproducible--salvo pudore#cia--which has classical authority1 modern or ancient1 in its favor4 ,he is a vulgar fellow2 ,i asked him what he was upon1 and what do you think he answered1 ,my legs6--,well1 and has he not justification8 what do you find in ,terence8 ,quid agitur8 ,statur4#cib ,i do not even blench from my principle where ,i find that it brings what is called taking a sight within permissible forms of expression3 ,rabelais not only establishes its antiquity1 but makes it ,english4 ,our old translation#cic has it thus 7book #b4 ch4 #ai73 ,then made the ,englishman this sign4 ,his left hand1 all open1 he lifted up into the air1 then instantly shut into his fist the four fingers thereof2 and his thumb extended at length he placed upon the tip of his nose4 ,presently after he lifted up his right hand all open and abased and bent it downwards1 putting the thumb thereof in the very place where the little finger of the left hand did close in the fist1 and the four right hand fingers he softly moved in the air4 ,then contrarily he did with the right hand what he had done with the left1 and with the left what he had done with the right4 ,an impressive sight6 ,the making of a fist of the left hand is a great addition of power1 and should be followed in modern practice4 ,the gentle sullation of the front fingers1 with the clenched fist behind them1 says as plainly as possible1 ,put suaviter in modo in the van1 but don't forget to have fortiter in re#cid in the rear4 #bde ,my ,budget was announced 7,march #bc1 #ahfg7 for completion on the #cjth4 ,mr4 ,james ,smith wrote five letters1 one before the completion1 four after it2 the five contained #fh pages of quarto letter paper4 ,mr4 ,j4 ,s4 had picked up a clerical correspondent1 with whom he was in the heat of battle4 ,march #bg4--;,dear ,sir4 ,very truly yours4 ,duty2 for my own sake2 just time left to retrieve my errors2 sends copy of letter to clergyman2 new proof never before thought of2 merest tyro would laugh if ,i were to stifle it1 whether by rhodomontade or silent contempt2 keep your temper4 ,i shall be convinced2 and if world be right in supposing me incapable of a foul act1 ,i shall proclaim glorious discovery in the ,athenaeum4 ,april #ae4--,sir1444 ,my dear ,sir1 ,your sincere tutelary4 ,copy of another letter to clergyman2 discovery tested by logarithms2 reasons such as none but a knave or a sinner can resist4 ,let me advise you to take counsel before it is too late6 ,keep your temper4 ,let not your pride get the better of your discretion6 ,screw up your courage1 my good friend1 and resolve to show the world that you are an honest man4444 ,april #bj4--,sir 444 ,your very sincere and favorite tutelary4 ,i have long played the cur1 snapping and snarling4442 suddenly lost my power1 and became half-starved dog without spirit to bark2 try if air cannot restore me2 calls himself the thistle in allusion to my other tutelary1 the thorn2 ,would ,i prefer his next work to be1 ',a whip for the ,mathematical ,cur1 ,prof4 ,de ,m4' ,in some previous letter which ,i have mislaid1 he told me his next would be 'a muzzle for the ,mathematical ,bull dog1 ,prof4 ,de ,m4' ,april #bc4--,sir4 ,very sincerely yours4 ,more letters to clergyman2 you may as well knock your head against a stone wall to improve your intellect as attempt to controvert my proofs4 ,i thought so too2 and tried neither4 #bdf ,may #f4--,my dear ,sir4 ,very sincerely yours4 ,all to myself1 and nothing to note4 ,july #b4--,no more in this interval4 ,all that precedes is a desperate attempt to induce me to continue my descriptions3 notoriety at any price4 ,i dare say the matter is finished3 the record of so marked an instance of self-delusion will be useful4 ,i append to the foregoing a letter from ,dr4 ,whewell#cie to ,mr4 ,james ,smith4 ,the ,master of ,trinity was conspicuous as a rough customer1 an intellectual bully1 an overbearing disputant3 the character was as well established as that of ,sam ,johnson4 ,but there was a marked difference4 ,it was said of ,johnson that if his pistol missed fire1 he would knock you down with the butt end of it3 but ,whewell1 in like case1 always acknowledged the miss1 and loaded again or not1 as the case might be4 ,he reminded me of ,dennis ,brulgruddery1 who says to ,dan1 ,pacify me with a good reason1 and you'll find me a dutiful master4 ,i knew him from the time when he was my teacher at ,cambridge1 more than forty years4 ,as a teacher1 he was anything but dictatorial1 and he was perfectly accessible to proposal of objections4 ,he came in contact with me in his slashing way twice in our after joint lives1 and on both occasions he acknowledged himself overcome1 by that change of manner1 and apologetic mode of continuance1 which ,i had seen him employ towards others under like circumstances4 ,i had expressed my wish to have a thermometer of probability1 with impossibility at one end1 as #b and #b make #e1 and necessity at the other1 as #b and #b make #d1 and a graduated rise of examples between them4 ,down came a blow3 ,what6 put necessary and contingent propositions together6 ,it's absurd6 ,i pointed out that the two kinds of necessity are but such extremes of probability as #j and infinity are of number1 and illustrated by an urn with #a white and n black #bdg balls1 n increasing without limit4 ,it was frankly seen1 and the point yielded2 a large company was present4 ,again1 in a large party1 after dinner1 and politics being the subject1 ,i was proceeding1 in discussion with ,mr4 ,whewell1 with ,i think444--,ugh6 you think6 was the answer4 ,i repeated my phrase1 and gave as a reason the words which ,lord ,grey#cif had used in the ,house of ,lords the night before 7the celebrated advice to the ,bishops to set their houses in order74 ,he had not heard of this1 and his manner changed in an instant3 he was the rational discutient all the rest of the evening1 having previously been nothing but a disputant with all the distinctions strongly marked4 ,i have said that ,whewell was gentle with his pupils2 it was the same with all who wanted teaching3 it was only on an armed enemy that he drew his weapon4 ,the letter which he wrote to ,mr4 ,j4 ,smith is an instance3 and as it applies with perfect fidelity to the efforts of unreasoning above described1 ,i give it here4 ,mr4 ,james ,smith is skilfully exposed1 and felt it2 as is proved by putting the writer in the stocks4 ,the ,lodge1 ,cambridge1 ,september #adth1 #ahfb4 ,sir1--,i have received your explanation of your proposition that the circumference of the circle is to its diameter as #be to #h4 ,i am afraid ,i shall disappoint you by saying that ,i see no force in your proof3 and ,i should hope that you will see that there is no force in it if you consider this3 ,in the whole course of the proof1 though the word cycle occurs1 there is no property of the circle employed4 ,you may do this3 you may put the word hexagon or dodecagon1 or any other word describing a polygon in the place of ,circle in your proof1 and the proof would be just as good as before4 ,does not this satisfy you that you cannot have proved a property of that special figure--a circle8 #bdh ,or you may do this3 calculate the side of a polygon of #bd sides inscribed in a circle4 ,i think you are a ,mathematician enough to do this4 ,you will find that if the radius of the circle be one1 the side of this polygon is 4#bfd etc4 ,now1 the arc which this side subtends is according to your proposition #c4abe_/ab 4#bfjd1 and therefore the chord is greater than its arc1 which you will allow is impossible4 ,i shall be glad if these arguments satisfy you1 and ,i am1 ,sir1 your obedient ,servant1 ,w4 ,,whewell4 ,,an ,m4,p4',s ,,arithmetic4 ,in the debate of ,may1 #ahff1 on ,electoral ,qualifications1 a question arose about arithmetical capability4 ,mr4 ,gladstone asked how many members of the ,house could divide #accjl4 #gs4 #f;d4 by #bl4 #acs4 #h;d4 ,six hundred and fifty-eight1 answered one member2 the thing cannot be done1 answered another4 ,there is an old paradox to which this relates3 it arises out of the ignorance of the distinction between abstract and concrete arithmetic4 ,magnitude may be divided by magnitude2 and the answer is number3 how often does #ab;d4 contain #d;d42 answer three times4 ,magnitude may be divided by number1 and the answer is magnitude3 #ab;d4 is divided in four equal parts1 what is each part8 ,answer three pence4 ,the honorable objector1 whose name ,i suppress1 trusting that he has mended his ways1 gave the following utterance3 ,with regard to the division sum1 it was quite possible to divide by a sum1 but not by money4 ,how could any one divide money by #bl4 #afs4 #h;d48 7,laughter47 ,the question might be asked1 ',how many times #bs4 will go into #al48' but that was not dividing by money2 it was simply dividing #bj by #b4 ,he might be asked1 ',how many times will #fs4 #h;d4 go into a pound8' but it was only required to divide #bdj by #hj4 ,if the right hon4 gentleman were to ask the hon4 #bdi member for ,brighton 7,professor ,fawcett71#cig or any other authority1 he would receive the same answer--viz41 that it was possible to divide by a sum1 but not by money4 7,hear47 ,i shall leave all comment for the second edition1 if ,i publish one4#cih ,i shall be sure to have something to laugh at4 ,anything said from a respectable quarter1 or supposed to be said1 is sure to find defenders4 ,sam ,johnson1 a sound arithmetician1 comparing himself1 and what he alone had done in three years1 with forty ,french ,academicians and their forty years1 said it proved that an ,englishman is to a ,frenchman as #dj x #dj to #c1 or as #afjj to #c4 ,boswell1 who was no great hand at arithmetic1 made him say that an ,englishman is to a ,frenchman as #c to #afjj4 ,when ,i pointed this out1 the supposed ,johnson was defended through thick and thin in ,notes and ,queries4 ,i am now curious to see whether the following will find a palliator4 ,it is from ,tristram ,shandy1 book ,v4 chapter #c4 ,there are two curious idioms1 for for and half in half2 but these have nothing to do with my point3 ,a blessing which tied up my father's tongue1 and a misfortune which set it loose with a good grace1 were pretty equal3 sometimes1 indeed1 the misfortune was the better of the two2 for1 for instance1 where the pleasure of harangue was as ten1 and the pain of the misfortune but as five1 my father gained half in half2 and consequently was as well again off as if it had never befallen him4 ,this is a jolly confusion of ideas2 and wants nothing but a defender to make it perfect4 ,a person who invests five #bej with a return of ten1 and one who loses five with one hand and gains ten with the other1 both leave off five richer than they began1 no doubt4 ,the first gains half in half1 more properly half on half1 that is1 of the return1 #aj1 the second #e is gain upon the first #e invested4 ,half in half is a queer way of saying cent4 per cent4 ,if the #el4 invested be all the man had in the world1 he comes out1 after the gain1 twice as well off as he began1 with reference to his whole fortune4 ,but it is very odd to say that balance of #el4 gain is twice as good as if nothing had befallen1 either loss or gain4 ,a mathematician thinks #e an infinite number of times as great as #j4 ,the whole confusion is not so apparent when money is in question3 for money is money whether gained or lost4 ,but though pleasure and pain stand to one another in the same algebraical relation as money gained and lost1 yet there is more than algebra can take account of in the difference4 ,next1 ,ri4 ,milward#cii 7,richard1 no doubt1 but it cannot be proved7 who published ,selden's#djj ,table ,talk1 which he had collected while serving as amanuensis1 makes ,selden say1 ,a subsidy was counted the fifth part of a man's estate2 and so fifty subsidies is five and forty times more than a man is worth4 ,for times read subsidies1 which seems part of the confusion1 and there remains the making all the subsidies equal to the first1 though the whole of which they are to be the fifths is perpetually diminished4 ,thirdly1 there is the confusion of the great misomath #bea of our own day1 who discovered two quantities which he avers to be identically the same1 but the greater the one the less the other4 ,he had a truth in his mind1 which his notions of quantity were inadequate to clothe in language4 ,this erroneous phraseology has not found a defender2 and ,i am almost inclined to say1 with ,falstaff1 ,the poor abuses of the time want countenance4 ,,erroneous ,,arithmetical ,,notions4 ,shallow numerists1 as ,cocker#dja is made to call them1 have long been at work upon the question how to multiply money by money4 ,it is1 ,i have observed1 a very common way of amusing the tedium of a sea voyage3 ,i have had more than one bet referred to me4 ,because an oblong of five inches by four inches contains #e x #d or #bj square inches1 people say that five inches multiplied by four inches is twenty square inches3 and1 thinking that they have multiplied length by length1 they stare when they are told that money cannot be multiplied by money4 ,one of my betters made it an argument for the thing being impossible1 that there is no square money3 what could ,i do but suggest that postage-stamps should be made legal tender4 ,multiplication must be repetition3 the repeating process must be indicated by number of times4 ,i once had difficulty in persuading another of my betters that if you repeat five shillings as often as there are hairs in a horse's tail1 you do not multiply five shillings by a horsetail4#djb ,i am very sorry to say that these wrong notions have found support--,i think they do so no longer--in the ,university of ,cambridge4 ,in #ahef or #aheg1 an examiner was displaced by a vote of the ,senate4 ,the pretext was that he was too severe an examiner3 but it was well known that #beb great dissatisfaction had been expressed1 far and wide through the ,colleges1 at an absurd question which he had given4 ,he actually proposed such a fraction as #fs4 #c;d4 --------4 #ags4 #d;d4 ,as common sense gained a hearing very soon1 there is no occasion to say more4 ,in #aheh1 it was proposed at a college examination1 to divide #bbeeg days1 #bj hours1 #bj minutes1 #dh seconds1 by #eg minutes1 #ab seconds1 and also to explain the fraction #cbl4 #ahs4 #h;d4 -------------4 #fbl4 #abs4 #i;d4 ,all paradoxy1 in matters of demonstration1 arises out of muddle about first principles4 ,who can say how much of it is to be laid at the door of the ,university of ,cambridge1 for not taking care of the elements of arithmetical thought8 ,,on ,,literary ,,bargains4 ,the phenomena of the two ends of society1 when brought together1 give interesting comparisons3 ,i mean the early beginnings of thought and literature1 and our own high and finished state1 as we think it4 ,there is one very remarkable point4 ,in the early day1 the letter was matter of the closest adherence1 and implied meanings were not admitted4 ,the blessing of ,isaac meant for ,esau1 went to false ,jacob1 in spite of the imposition2 and the writer of ,genesis seems to intend to give the notion that ,isaac had no power to pronounce it null and void4 ,and ,jacob's policy1 whereby he became rich--as the chapter-heading puts it--in speckled and spotted stock1 is not considered as a violation of the agreement1 which contemplated natural proportions4 ,in #bec the story of ,lycurgus the lawgiver is held to have behaved fairly when he bound the ,spartans to obey his laws until he returned--intimating a short absence--he intending never to return4 ,and ,vishnoo1 when he asked the usurper for three steps of territory as a dwarf1 and then enlarged himself until he could bring heaven and earth under the bargain1 was thought clever1 certainly1 but quite fair4 ,there is nothing of this kind recognized in our day3 so far good4 ,but there is a bad contrary3 the age is apt1 in interpretation1 to upset the letter in favor of the view--very often the after thought--of one side only4 ,the case of ,john ,palmer1#djc the improver of the mail coach system1 is smothered4 ,he was to have an office and a salary1 and #b-a_/b per cent for life on the increased revenue of the ,post-,office4 ,his rights turned out so large1 that ,government would not pay them4 ,for misconduct1 real or pretended1 they turned him out of his office3 but his bargain as to the percentage had nothing to do with his future conduct2 it was payment for his plan4 ,i know nothing1 except from the debates of #ahjh in the two ,houses3 if any one can redeem the credit of the nation1 the field is open4 ,when ,i was young1 the old stagers spoke of this transaction sparingly1 and dismissed it speedily4 ,the government did not choose to remember what private persons must remember1 and are made to remember1 if needful4 ,when ,dr4 ,lardner#djd made his bargain with the #bed publishers for the ,cabinet ,cyclopaedia he proposed that he1 as editor1 should have a certain sum for every hundred sold above a certain number3 the publishers1 who did not think there was any chance of reaching the turning sale of this stipulation1 readily consented4 ,but it turned out that ,dr4 ,lardner saw further than they3 the returns under this stipulation gave him a very handsome addition to his other receipts4 ,the publishers stared2 but they paid4 ,they had no idea of standing out that the amount was too much for an editor2 they knew that1 though the editor had a percentage1 they had all the rest2 and they would not have felt aggrieved if he had received ten times as much4 ,but governments1 which cannot be brought to book before a sworn jury1 are ruled only by public opinion4 ,john ,palmer's day was also the day of ,thomas ,fyshe ,palmer1#dje and the governments1 in their prosecutions for sedition1 knew that these would have a reflex action upon the minds of all who wrote about public affairs4 ,,declaration ,,of ,,belief #ahfd-fe4--;,it often happens that persons combine to maintain and enforce an opinion2 but it is1 in our state of society1 a paradox to unite for the sole purpose of blaming the opposite side4 ,to invite educated men to do this1 and above all1 men of learning or science1 is the next paradoxical thing of all4 ,but this was done by a small combination in #ahfd4 ,they got together and drew up a declaration1 to be signed by students of the natural sciences1 who were to express their sincere regret that researches into #bee scientific truth are perverted by some in our own times into occasion for casting doubt upon the truth and authenticity of the ,holy ,scriptures4 ,in words of ambiguous sophistry1 they proceeded to request1 in effect1 that people would be pleased to adopt the views of churches as to the complete inspiration of all the canonical books4 ,the great question whether the ,word of ,god is in the ,bible1 or whether the ,word of ,god is all the ,bible1 was quietly taken for granted in favor of the second view2 to the end that men of science might be induced to blame those who took the first view4 ,the first public attention was drawn to the subject by ,sir ,john ,herschel1#djf who in refusing to sign the writ sent to him1 administered a rebuke in the ,athenaeum1 which would have opened most eyes to see that the case was hopeless4 ,the words of a man whose suaviter in modo makes his fortiter in re#djg cut blocks with a razor are worth preserving3 ,i consider the act of calling upon me publicly to avow or disavow1 to approve or disapprove1 in writing1 any religious doctrine or statement1 however carefully or cautiously drawn up 7in other words1 to append my name to a religious manifesto7 to be an infringement of that social forbearance which guards the freedom of religious opinion in this country with especial sanctity4444 ,i consider this movement simply mischievous1 having a direct tendency 7by putting forward a new ,shibboleth1 a new verbal test of religious partisanship7 to add a fresh element of discord to the already too discordant relations of the ,christian world4444 ,but no nicety of wording1 no artifice of human language1 will suffice to discriminate the hundredth part of the shades of meaning in which the most world-wide differences of thought on such subjects may be involved2 or prevent the most gentle worded and apparently justifiable expression of regret1 so embodied1 from grating on the #bef feelings of thousands of estimable and well-intentioned men with all the harshness of controversial hostility4 ,other doses were administered by ,sir ,j4 ,bowring1#djh ,sir ,w4 ,rowan ,hamilton1#dji and myself4 ,the signed declaration was promised for ,christmas1 #ahfd3 but nothing presentable was then ready2 and it was near ,midsummer1 #ahfe1 before it was published4 ,persons often incautiously put their names without seeing the character of a document1 because they coincide in its opinions4 ,in this way1 probably1 fifteen respectable names were procured before printing2 and these1 when committed1 were hawked as part of an application to solicit the favor of other signatures4 ,it is likely enough no one of the fifteen saw that the declaration was1 not maintenance of their own opinion1 but regret 7a civil word for blame7 that others should think differently4 ,when the list appeared1 there were no fewer than #gaf names6 ,but analysis showed that this roll was not a specimen of the mature science of the country4 ,the collection was very miscellaneous3 #ch were designated as students of the ,college of ,chemistry1 meaning young men who attended lectures in that college4 ,but as all the ,royal ,society had been applied to1 a test results as follows4 ,of ,fellows of the ,royal ,society1 #fjj in number1 #fb gave their signatures2 of writers in the ,philosophical ,transactions1 #aff in number1 #ai gave their signatures4 ,roughly speaking1 then1 only one out of ten could be got to express disapprobation of the free comparison of the results of science with the statements of the canonical books4 ,and ,i am satisfied that many of these thought they were signing only a declaration of difference of opinion1 not of blame for that difference4 ,the number of persons is not small who1 when it comes to signing printed documents1 would put their names to a declaration that the coffee-pot ought to be taken down-stairs1 meaning that the teapot ought to be brought #beg up-stairs4 ,and many of them would defend it4 ,some would say that the two things are not contradictory2 which1 with a snort or two of contempt1 would be very effective4 ,others would1 in the candid and quiet tone1 point out that it is all one1 because coffee is usually taken before tea1 and it keeps the table clear to send away the coffee-pot before the teapot is brought up4 ,the original signatures were decently interred in the ,bodleian ,library3 and the advocates of scattering indefinite blame for indefinite sins of opinion among indefinite persons are1 ,i understand1 divided in opinion about the time at which the next attempt shall be made upon men of scientific studies3 some are for the ,greek ,calends1 and others for the ,roman ,olympiads4 ,but1 with their usual love of indefiniteness1 they have determined that the choice shall be argued upon the basis that which comes first cannot be settled1 and is of no consequence4 ,i give the declaration entire1 as a curiosity3 and parallel with it ,i give a substitute which was proposed in the ,athenaeum1 as worthy to be signed both by students of theology1 and by students of science1 especially in past time4 ,when a new attempt is made1 it will be worth while to look at both3 ,declaration4 ,proposed ,substitute4 ,we1 the undersigned ,students ,we1 the undersigned ,students of the ,natural ,sciences1 of ,theology and of ,nature1 desire to express our sincere desire to express our sincere regret1 that researches into regret1 that common notions of scientific truth are perverted religious truth are perverted by some in our own times into by some in our own times into occasion for casting doubt occasion for casting reproach upon the ,truth and upon the advocates of ,authenticity of the ,holy demonstrated or highly ,scriptures4 probable scientific theories4 #beh ,we conceive that it is ,we conceive that it is impossible for the ,word of impossible for the ,word of ,god1 as written in the book of ,god1 as correctly read in the nature1 and ,god's ,word written ,book of ,nature1 and the ,word in ,holy ,scripture1 to of ,god1 as truly interpreted contradict one another1 out of the ,holy ,scripture1 to however much they may appear contradict one another1 to differ4 however much they may appear to differ4 ,we are not forgetful that ,we are not forgetful that ,physical ,science is not neither theological complete1 but is only in a interpretation nor physical condition of progress1 and knowledge is yet complete1 but that at present our finite that both are in a condition reason enables us only to see of progress2 and that at as through a glass darkly1 present our finite reason enables us only to see both one and the other as through a glass darkly the writers of the original declaration have distinctively applied to physical science the phrase by which ,st4 ,paul denotes the imperfections of theological vision1 which they tacitly assume to be quite perfect1 and we confidently believe1 and we confidently believe1 that a time will come when the that a time will come when the two records will be seen to two records will be seen to agree in every particular4 ,we agree in every particular4 ,we cannot but deplore that cannot but deplore that ,natural ,science should be ,religion should be looked upon looked upon with suspicion by with suspicion by some and many who do not make a study ,science by others1 of the of it1 merely on account of students of either who do not the unadvised manner in which make a study of the #bei some are placing it in other1 merely on account of opposition to ,holy ,writ4 the unadvised manner in which some are placing ,religion in opposition to ,science1 and some are placing ,science in opposition to ,religion4 ,we believe that it is the duty ,we believe that it is the duty of every ,scientific ,student to of every theological student investigate nature simply for to investigate the ,scripture1 the purpose of elucidating and of every scientific truth1 student to investigate ,nature1 simply for the purpose of elucidating truth4 and that if he finds that some ,and if either should find that of his results appear to be in some of his results appear to contradiction to the ,written be in contradiction1 whether ,word1 or rather to his own to ,scripture or to ,nature1 or interpretations of it1 which rather to his own may be erroneous1 he should interpretation of one or the not presumptuously affirm that other1 which may be erroneous1 his own conclusions must be he should not affirm as with right1 and the statements of certainty that his own ,scripture wrong2 conclusion must be right1 and the other interpretation wrong3 rather1 leave the two side by but should leave the two side side till it shall please ,god by side for further inquiry to allow us to see the manner into both1 until it shall in which they may be please ,god to allow us to reconciled2 arrive at the manner in which they may be reconciled4 and1 instead of insisting upon ,in the mean while1 instead of the seeming differences insisting1 and least of all between ,science and the with acrimony or injurious ,scriptures1 it would be as #bfj statements about others1 well to rest in faith upon the upon the seeming differences points in which they agree4 between ,science and the ,scriptures1 it would be a thousand times better to rest in faith as to our future state1 in hope as to our coming knowledge1 and in charity as to our present differences4 ,the distinctness of the fallacies is creditable to the composers1 and shows that scientific habits tend to clearness1 even to sophistry4 ,nowhere does it so plainly stand out that the ,written ,word means the sense in which the accuser takes it1 while the sense of the other side is their interpretation4 ,the infallible church on one side1 arrayed against heretical pravity on the other1 is seen in all subjects in which men differ4 ,at school there were various games in which one or another advantage was the right of those who first called for it4 ,in adult argument the same thing is often attempted3 we often hear--,i cried ,church first6 ,i end with the answer which ,i myself gave to the application3 its revival may possibly save me from a repetition of the like4 ,if there be anything ,i hate more than another it is the proposal to place any persons1 especially those who allow freedom to me1 under any abridgment of their liberty to think1 to infer1 and to publish4 ,if they break the law1 take the law2 but do not make the law3 ,greek3 agoraioi agontai enkaleitosan allelois4#daj ,i would rather be asked to take shares in an argyrosteretic company 7with limited liability7 for breaking into houses by night on fork and spoon errands4 ,i should put aside this proposal with nothing but laughter4 ,it was a joke against ,sam ,rogers#daa that his appearance was very like that of a corpse4 ,the ,john ,bull #bfa newspaper--suppose we now say ,theodore ,hook#dab--;averred that when he hailed a coach one night in ,st4 ,paul's ,churchyard1 the jarvey said1 ,ho6 ho6 my man2 ,i'm not going to be taken in that way3 go back to your grave6 ,this is the answer ,i shall make for the future to any relics of a former time who shall want to call me off the stand for their own purposes4 ,what obligation have ,i to admit that they belong to our world8 ,,scripture ,,and ,,science4 ,the ,writ ,de ,haeretico ,commiserando4#dac ,nov4 #ad1 #ahfd4 ,this document was sent to me four days ago4 ,it 'solicits the favor'--,i thought at first it was a grocer's supplication for tea and sugar patronage--of my signature to expression of 'sincere regret' that some persons unnamed--general warrants are illegal--differ from what ,i am supposed--by persons whom it does not concern--to hold about ,scripture and ,science in their real or alleged discrepancies4 ,no such favor from me3 for three reasons4 ,first1 ,i agree with ,sir4 ,j4 ,herschel that the solicitation is an intrusion to be publicly repelled4 ,secondly1 ,i do not regret that others should differ from me1 think what ,i may3 those others are as good as ,i1 and as well able to think1 and as much entitled to their conclusions4 ,thirdly1 even if ,i did regret1 ,i should be ashamed to put my name to bad chemistry made to do duty for good reasoning4 ,the declaration is an awkward attempt to saturate sophism with truism2 but the sophism is left largely in excess4 #bfb ,i owe the inquisitors a grudge for taking down my conceit of myself4 ,for two months ,i have crowed in my own mind over my friend ,sir ,j4 ,herschel1 fancying that the promoters instinctively knew better than to bring their fallacies before a writer on logic4 ,ah6 my dear ,sir ,john6 thought ,i1 if you had shown yourself to be well up in ,barbara ,celarent1#dad and had ever and anon astonished the natives with the distinction between simpliciter and secundum quid1 no autograph-hunters would have baited a trap with non sequitur#dae to catch your signature4 ,what can ,i say now8 ,i hide my diminished head1 diminished by the horns which ,i have been compelled to draw in4 ,those who make personal solicitation for support to an opinion about religion are bound to know their men4 ,the king had a right to ,brother ,neale's money1 because ,brother ,neale offered it4 ,had he put his hand into purse after purse by way of finding out all who were of ,brother ,neale's mind1 he would have been justly met by a rap on the knuckles whenever he missed his mark4 ,the kind of test before me is the utmost our time will allow of that inquisition into opinion which has been the curse of ,christianity ever since the ,state took ,providence under its protection4 ,the writ de haeretico commiserando is little more than the smell of the empty cask3 and those who issue it may represent the old woman with her ,o suavis anima1 quale in te dicam bonum ,antehac fuisse2 tales cum sint reliquiae4#daf ,it is no excuse that the illegitimate bantling is a very little one4 ,its parents may think themselves hardly treated when they are called lineal successors of ,tony ,fire-the-faggot3 #bfc but1 degenerate though they be1 such is their ancestry4 ,let every allowance be made for them3 but their unholy fire must be trodden out2 so long as a spark is left1 nothing but fuel is wanted to make a blaze4 ,if this cannot be done1 let the flame be confined to theology1 though even there it burns with diminished vigor3 and let charity1 candor1 sense1 and ridicule1 be ready to play upon it whenever there is any chance of its extending to literature and science4 ,what would be the consequence if this test-signing absurdity were to grow8 ,deep would call unto deep2 counter-declaration would answer declaration1 each stronger than the one before4 ,the moves would go on like the dispute of two ,german students1 of whom each is bound to a sharper retort on a graduated scale1 until at last comes dummer ,junge6#dag--;and then they must fight4 ,there is a gentleman in the upper fifteen of the signers of the writ--the hawking of whose names appears to me very bad taste--whom ,i met in cordial cooperation for many a year at a scientific board4 ,all ,i knew about his religion was that he1 as a clergyman1 must in some sense or other receive the #ci ,articles3--all that he could know about mine was that ,i was some kind of heretic1 or so reputed4 ,if we had come to signing opposite manifestoes1 turn-about1 we might have found ourselves in the lowest depths of party discussion at our very council-table4 ,i trust the list of subscribers to the declaration1 when it comes to be published1 will show that the bulk of those who have really added to our knowledge have seen the thing in its true light4 ,the promoters--,i say nothing about the subscribers--of the movement will1 ,i trust1 not feel aggrieved at the course ,i have taken or the remarks ,i have made4 ,walter ,scott says that before we judge ,napoleon by the temptation to which he yielded1 we ought to remember how much he may have resisted3 ,i invite them to apply this rule to myself2 they can have no idea of the feeling with which ,i #bfd contemplate all attempts to repress freedom of inquiry1 nor of the loathing with which ,i recoil from the proposal to be art and part4 ,they have asked me to give a public opinion upon a certain point4 ,it is true that they have had the kindness to tender both the opinion they wish me to form1 and the shape in which they would have it appear3 ,i will let them draw me out1 but ,i will not let them take me in4 ,if they will put an asterisk to my name1 and this letter to the asterisk1 they are welcome to my signature4 ,as ,i do not expect them to relish this proposal1 ,i will not solicit the favor of its adoption4 ,but they have given a right to think1 for they have asked me to think2 to publish1 for they have asked me to allow them to publish2 to blame them1 for they have asked me to blame their betters4 ,should they venture to find fault because my direction of disapproval1 publicly given1 is half a revolution different from theirs1 they will be known as having presented a loaded document at the head of a traveler in the highway of discussion1 with--,your signature or your silence6 ,,the ,,fly-,,leaf ,,paradox4 ,the paradox being the proposition of something which runs counter to what would generally be thought likely1 may present itself in many ways4 ,there is a fly-leaf paradox1 which puzzled me for many years1 until ,i found a probable solution4 ,i frequently saw1 in the blank leaves of old books1 learned books1 ,bibles of a time when a ,bible was very costly1 etc41 the name of an owner who1 by the handwriting and spelling1 must have been an illiterate person or a child1 followed by the date of the book itself4 ,accordingly1 this uneducated person or young child seemed to be the first owner1 which in many cases was not credible4 ,looking one day at a ,barker's#dah ,bible of #aeii1 ,i saw an #bfe inscription in a child's writing1 which certainly belonged to a much later date4 ,it was ,martha ,taylor1 her book1 giuen me by ,granny ,scott to keep for her sake4 ,with this the usual verses1 followed by #aeii1 the date of the book4 ,but it so chanced that the blank page opposite the title1 on which the above was written1 was a verso of the last leaf of a prayer book1 which had been bound before the ,bible2 and on the recto of this leaf was a colophon1 with the date #afcb4 ,it struck me immediately that uneducated persons and children1 having seen dates written under names1 and not being quite up in chronology1 did frequently finish off with the date of the book1 which stared them in the face4 ,always write in your books4 ,you may be a silly person--for though your reading my book is rather a contrary presumption1 yet it is not conclusive--and your observations may be silly or irrelevant1 but you cannot tell what use they may be of long after you are gone where ,budgeteers cease from troubling4 ,i picked up the following book1 printed by ,j4 ,franklin#dai at ,boston1 during the period in which his younger brother ,benjamin was his apprentice4 ,and as ,benjamin was apprenticed very early1 and is recorded as having learned the mechanical art very rapidly1 there is some presumption that part of it may be his work1 though he was but thirteen at the time4 ,as this set of editions of ,hodder#dbj 7by #bff ,mose#dba7 is not mentioned1 to my knowledge1 ,i give the title in full3 ,hodder's ,arithmetick3 or that necessary art made most easy3 ,being explained in a way familiar to the capacity of any that desire to learn it in a little time4 ,by ,james ,hodder1 ,writing-master4 ,the ,five and twentieth edition1 revised1 augmented1 and above a thousand faults amended1 by ,henry ,mose1 late servant and successor to the author4 ,boston3 printed by ,j4 ,franklin1 for ,s4 ,phillips1 ,n4 ,buttolph1 ,b4 ,elliot1 ,d4 ,henchman1 ,g4 ,phillips1 ,j4 ,elliot1 and ,e4 ,negus1 booksellers in ,boston1 and sold at their shops4 #agai4 ,the book is a very small octavo1 the type and execution are creditable1 the woodcut at the beginning is clumsy4 ,it is a perfect copy1 page for page1 of the ,english editions of ,mose's ,hodder1 of which the one called seventeenth is of ,london1 #afij4 ,there is not a syllable to show that the edition above described might not be of ,boston in ,england4 ,presumptions1 but not very strong ones1 might be derived from the name of ,franklin1 and from the large number of booksellers who combined in the undertaking4 ,it chanced1 however1 that a former owner had made the following note in my copy3 ,wednessday1 ,july ye #ad1 #agif1 att ten in ye forenoon we saild from ,boston1 came too twice1 once in ,king ,rode1 and once in ye ,narrows4 ,saild by ye lighthouse in ye eveng4 #bfg ,no ordinary map would decide these points3 so ,i had to apply to my friend ,sir ,francis ,beaufort1#dbb and the charts at the ,admiralty decided immediately for ,massachusetts4 ,,paradoxes ,,of ,,orthography ,,and ,,computation4 ,the ,french are able paradoxers in their spelling of foreign names4 ,the ,abbe ,sabatier de ,castres1#dbc in #aggb1 gives an account of an imaginary dialogue between ,swif1 ,adisson1 ,otwai1 and ,bolingbrocke4 ,i had hoped that this was a thing of former days1 like the literal roasting of heretics2 but the charity which hopeth all things must hope for disappointments4 ,looking at a recent work on the history of the popes1 ,i found referred to1 in the matter of ,urban ,,viii#dbd and ,galileo1 references to the works of two ,englishmen1 the ,rev4 ,win ,worewel and the ,rev4 ,raden ,powen4 ,wm4 ,whewell and ,baden ,powell4#dbe ,i must not forget the moderate computation paradox4 ,this is the way by which large figures are usually obtained4 ,anything surprisingly great is got by the lowest computation1 anything as surprisingly small by the utmost computation2 and these are the two great subdivisions of moderate computation4 ,in this way we learn that #gj1jjj persons were executed in one reign1 and #aej1jjj persons #bfh burned for witchcraft in one century4 ,sometimes this computation is very close4 ,by a card before me it appears that all the ,christians1 including those dispersed in heathen countries1 those of ,great ,britain and ,ireland excepted1 are #aih1gbh1jjj people1 and pay their clergy #h1heb1jjjl4 ,but #f1djj1jjj people pay the clergy of the ,anglo-,irish ,establishment #h1hif1jjjl42 and #ad1fjj1jjj of other denominations pay #a1jbd1jjjl4 ,when ,i read moderate computations1 ,i always think of ,voltaire and the memoires du fameux eveque de ,chiapa1 par lesquels il parait qu'il avait egorge1 ou brule1 ou noye dix millions d'infideles en ,amerique pour les convertir4 ,je crus que cet eveque exaggerait2 mais quand on reduisait ces sacrifices a cinq millions de victimes1 cela serait encore admirable4#dbf ,,centrifugal ,,force4 ,my ,budget has been arranged by authors4 ,this is the only plan1 for much of the remark is personal3 the peculiarities of the paradoxer are a large part of the interest of the paradox4 ,as to subject-matter1 there are points which stand strongly out2 the quadrature of the circle1 for instance4 ,but there are others which cannot be drawn out so as to be conspicuous in a review of writers3 as one instance1 ,i may take the centrifugal force4 ,when ,i was about nine years old ,i was taken to hear a course of lectures1 given by an itinerant lecturer in a country town1 to get as much as ,i could of the second half of a good1 sound1 philosophical omniscience4 ,the first half 7and sometimes more7 comes by nature4 ,to this end ,i smelt chemicals1 learned that they were different kinds of gin1 saw young wags try to kiss the girls under the excuse of what was called laughing gas--which ,i was sure #bfi was not to blame for more than five per cent of the requisite assurance--and so forth4 ,this was all well so far as it went2 but there was also the excessive notion of creative power exhibited in the millions of miles of the solar system1 of which power ,i wondered they did not give a still grander idea by expressing the distances in inches4 ,but even this was nothing to the ingenious contrivance of the centrifugal force4 ,you have heard what ,i have said of the wonderful centripetal force1 by which ,divine ,wisdom has retained the planets in their orbits round the ,sun4 ,but1 ladies and gentlemen1 it must be clear to you that if there were no other force in action1 this centripetal force would draw our earth and the other planets into the ,sun1 and universal ruin would ensue4 ,to prevent such a catastrophe1 the same wisdom has implanted a centrifugal force of the same amount1 and directly opposite1 etc4 ,i had never heard of ,alfonso ,x of ,castile1#dbg but ,i ventured to think that if ,divine ,wisdom had just let the planets alone it would come to the same thing1 with equal and opposite troubles saved4 ,the paradoxers deal largely in speculation conducted upon the above explanation4 ,they provide external agents for what they call the centrifugal force4 ,some make the sun's rays keep the planets off1 without a thought about what would become of our poor eyes if the push of the light which falls on the earth were a counterpoise to all its gravitation4 ,the true explanation cannot be given here1 for want of room4 ,,cambridge ,,poets4 ,sometimes a person who has a point to carry will assert a singular fact or prediction for the sake of his point2 and #bgj this paradox has almost obtained the sole use of the name4 ,persons who have reputation to care for should beware how they adopt this plan1 which now and then eventuates a spanker1 as the ,american editor said4 ,lord ,byron1 in ,english ,bards1 etc4 7#ahji71 ridiculing ,cambridge poetry1 wrote as follows3 ,but where fair ,isis rolls her purer wave1 ,the partial muse delighted loves to lave2 ,on her green banks a greener wreath she wove1 ,to crown the bards that haunt her classic grove2 ,where ,richards#dbh wakes a genuine poet's fires1 ,and modern ,britons glory in their sires4#dbi ,there is some account of the ,rev4 ,geo4 ,richards1 ,fellow of ,oriel and ,vicar of ,bampton1 7,m4,a4 in #agia7 in the ,living ,authors by ,watkins#dcj and ,shoberl#dca 7#ahaf74 ,in ,rivers's ,living ,authors1 of #agih1 which is best fitted for citation1 as being published before ,lord ,byron wrote1 he is spoken of in high terms4 ,the ,aboriginal ,britons was an ,oxford 7special7 prize poem1 of #agia4 ,charles ,lamb mentions ,richards as his school-fellow at ,christ's ,hospital1 author of the ,aboriginal ,britons1 the most spirited of the ,oxford ,prize ,poems3 a pale1 studious ,grecian4 ,as ,i never heard of ,richards as a poet1#dcb ,i conclude that his fame is defunct1 except in what may prove to be a very ambiguous kind of immortality1 conferred by ,lord ,byron4 ,the awkwardness of a case which time has broken down #bga is increased by the eulogist himself adding so powerful a name to the list of ,cambridge poets1 that his college has placed his statue in the library1 more conspicuously than that of ,newton in the chapel2 and this although the greatness of poetic fame had some serious drawbacks in the moral character of some of his writings4 ,and it will be found on inquiry that ,byron1 to get his instance against ,cambridge1 had to go back eighteen years1 passing over seven intermediate productions1 of which he had either never heard1 or which he would not cite as waking a genuine poet's fires4 ,the conclusion seems to be that the ,aboriginal ,britons is a remarkable youthful production1 not equalled by subsequent efforts4 ,to enhance the position in which the satirist placed himself1 two things should be remembered4 ,first1 the glowing and justifiable terms in which ,byron had spoken1--a hundred and odd lines before he found it convenient to say no ,cambridge poet could compare with ,richards1--of a ,cambridge poet who died only three years before ,byron wrote1 and produced greatly admired works while actually studying in the ,university4 ,the fame of ,kirke ,white#dcc still lives2 and future literary critics may perhaps compare his writings and those of ,richards1 simply by reason of the curious relation in which they are here placed alongside of each other4 ,and it is much to ,byron's credit that1 in speaking of the deceased ,cambridge poet1 he forgot his own argument and its exigencies1 and proved himself only a paradoxer pro re nata4 ,secondly1 ,byron was very unfortunate in another passage of the same poem3 #bgb ,what varied wonders tempt us as they pass6 ,the cow-pox1 tractors1 galvanism1 and gas4 ,in turns appear1 to make the vulgar stare1 ,till the swoln bubble bursts--and all is air6 ,three of the bubbles have burst to mighty ends4 ,the metallic tractors are disused2 but the force which1 if anything1 they put in action1 is at this day1 under the name of mesmerism1 used1 prohibited1 respected1 scorned1 assailed1 defended1 asserted1 denied1 declared utterly obscure1 and universally known4 ,it was hard lines to select for candidates for oblivion not one of whom got in4 ,i shall myself1 ,i am assured1 be some day cited for laughing at the great discovery of ----3 the blank is left for my reader to fill up in his own way2 but ,i think ,i shall not be so unlucky in four different ways4 ,,falsified ,,prediction4 ,the narration before the fact1 as prophecy has been called1 sometimes quite as true as the narration after the fact1 is very ridiculous when it is wrong4 ,why1 the pre-narrator could not know2 the post-narrator might have known4 ,a good collection of unlucky predictions might be made3 ,i hardly know one so fit to go with ,byron's as that of the ,rev4 ,daniel ,rivers1 already quoted1 about ,johnson's biographers4 ,peter ,pindar#dcd may be excused1 as personal satire was his object1 for addressing ,boswell and ,mrs4 ,piozzi#dce as follows3 ,instead of adding splendor to his name1 ,your books are downright gibbets to his fame2 ,you never with posterity can thrive1 ',tis by the ,rambler's death alone you live4 ,but ,rivers1 in prose narrative1 was not so excusable4 ,he says3 #bgc ,as admirers of the learning and moral excellence of their hero1 we glow at almost every page with indignation that his weaknesses and his failings should be disclosed to public view4444 ,johnson1 after the luster he had reflected on the name of ,thrale 444 was to have his memory tortured and abused by her detested itch for scribbling4 ,more injury1 we will venture to affirm1 has been done to the fame of ,johnson by this ,lady and her late biographical helpmate1 than his most avowed enemies have been able to effect3 and if his character becomes unpopular with some of his successors1 it is to those gossiping friends he is indebted for the favor4 ,poor dear old ,sam6 the best known dead man alive6 clever1 good-hearted1 logical1 ugly bear6 ,where would he have been if it had not been for ,boswell and ,thrale1 and their imitators8 ,what would biography have been if ,boswell had not shown how to write a life8 ,rivers is to be commended for not throwing a single ,stone at ,mrs4 ,thrale's second marriage4 ,this poor lady begins to receive a little justice4 ,the literary world seems to have found out that a blue-stocking dame who keeps open house for a set among them has a right1 if it so please her1 to marry again without taking measures to carry on the cake-shop4 ,i was before my age in this respect3 as a boy-reader of ,boswell1 and a few other things that fell in my way1 ,i came to a clearness that the conduct of society towards ,mrs4 ,piozzi was blackguard4 ,she wanted nothing but what was in that day a woman's only efficient protection1 a male relation with a brace of pistols1 and a competent notion of using them4 ,,byron ,,and ,,wordsworth4 ,byron's mistake about ,hallam in the ,pindar story may be worth placing among absurdities4 ,for elucidation1 suppose that some poet were now to speak-- #bgd ,of man's first disobedience1 and the fruit ,eve gave to ,adam in his birthday suit-- and some critic were to call it nonsense1 would that critic be laughing at ,milton8 ,payne ,knight1#dcf in his ,taste1 translated part of ,gray's ,bard into ,greek4 ,some of his lines are ,greek3 therma d' ho tengon dakrua stonachais ,greek3 oulon melos phoberai ,greek3 eeide phonai4 ,literally thus3 ,wetting warm tears with groans1 ,continuous chant with fearful ,voice he sang4 ,on which ,hallam remarks3 ,the twelfth line our first is nonsense4 ,and so it is1 a poet can no more wet his tears with his groans than wet his ale with his whistle4 ,now this first line is from ,pindar1 but is only part of the sense2 in full it is3 ,greek3 therma de tengon dakrua stonachais ,greek3 horthion phonase4 ,pindar's ,greek3 tengon must be ,englished by shedding1 and he stands alone in this use4 ,he says1 shedding warm tears1 he cried out loud1 with groans4 ,byron speaks of ,classic ,hallam1 much renowned for ,greek3 and represents him as criticising the ,greek of all ,payne's lines1 and not discovering that the lines were ,pindar's #bge until after publication4 ,byron was too much of a scholar to make this blunder himself3 he either accepted the facts from report1 or else took satirical licence4 ,and why not8 ,if you want to laugh at a person1 and he will not give occasion1 whose fault is it that you are obliged to make it8 ,hallam did criticise some of ,payne ,knight's ,greek2 but with the caution of his character1 he remarked that possibly some of these queer phrases might be critic-traps justified by some one use of some one author4 ,i remember well having a ,latin essay to write at ,cambridge1 in which ,i took care to insert a few monstrous and unusual idioms from ,cicero3 a person with a ,nizolius1#dcg and without scruples may get scores of them4 ,so when my tutor raised his voice against these oddities1 ,i was up to him1 for ,i came down upon him with ,cicero1 chapter and verse1 and got round him4 ,and so my own solecisms1 many of them1 passed unchallenged4 ,byron had more good in his nature than he was fond of letting out3 whether he was a soured misanthrope1 or whether his vein lay that way in poetry1 and he felt it necessary to fit his demeanor to it1 are matters far beyond me4 ,mr4 ,crabb ,robinson#dch told me the following story more than once4 ,he was at ,charles ,lamb's chambers in the ,temple when ,wordsworth came in1 with the new ,edinburgh ,review in his hand1 and fume on his countenance4 ,these reviewers1 said he1 put me out of patience6 ,here is a young man--they say he is a lord--who has written a volume of poetry2 and these fellows1 just because he is a lord1 set upon him1 laugh at him1 and sneer at his writing4 ,the young man will do something1 if he goes on as he has begun4 ,but these reviewers seem to think #bgf that nobody may write poetry1 unless he lives in a garret4 ,crabb ,robinson told this long after to ,lady ,byron1 who said1 ,ah6 if ,byron had known that1 he would never have attacked ,wordsworth4 ,he went one day to meet ,wordsworth at dinner2 when he came home ,i said1 ',well1 how did the young poet get on with the old one8' ',why1 to tell you the truth1' said he1 ',i had but one feeling from the beginning of the visit to the end1 and that was--reverence6' ,lady ,byron told my wife that her husband had a very great respect for ,wordsworth4 ,i suppose he would have said--as the ,archangel said to his ,satan--,our difference is poli etical4 ,i suspect that ,fielding would1 if all were known1 be ranked among the unlucky railers at supposed paradox4 ,in his ,miscellanies 7#agdb1 #hvo7 he wrote a satire on the ,chrysippus or ,guinea1 an animal which multiplies itself by division1 like the polypus4 ,this he supposes to have been drawn up by ,petrus ,gualterus1 meaning the famous usurer1 ,peter ,walter4 ,he calls it a paper proper to be read before the ,r----l ,society3 and next year1 #agdc1 a quarto reprint was made to resemble a paper in the ,philosophical ,transactions4 ,so far as ,i can make out1 one object is ridicule of what the zoologists said about the polypus3 a reprint in the form of the ,transactions was certainly satire on the ,society1 not on ,peter ,walter and his knack of multiplying guineas4 ,old poets have recognized the quadrature of the circle as a well-known difficulty4 ,dante compares himself1 when bewildered1 to a geometer who cannot find the principle on which the circle is to be measured3 ,quale e 'l geometra che tutto s' affige ,per misurar lo cerchio1 e non ritruova1 ,pensando qual principio ond' egli indige4#dci #bgg ,and ,quarles#ddj speaks as follows of the summum bonum3 ,or is't a tart idea1 to procure ,an edge1 and keep the practic soul in ure1 ,like that dear chymic dust1 or puzzling quadrature8 ,the poetic notion of the quadrature must not be forgotten4 ,aristophanes1 in the ,birds1 introduces a geometer who announces his intention to make a square circle4 ,pope1 in the ,dunciad1 delivers himself as follows1 with a ,greek pronunciation rather strange in a translator of ,homer4 ,probably ,pope recognized1 as a general rule1 the very common practice of throwing back the accent in defiance of quantity1 seen in o'rator1 au'ditor1 se'nator1 ca'tenary1 etc4 ,mad ,mathesis alone was unconfined1 ,too mad for mere material chains to bind1-- ,now to pure space lifts her ecstatic stare1 ,now1 running round the circle1 finds it square4 ,the author's note explains that this regards the wild and fruitless attempts of squaring the circle4 ,the poetic idea seems to be that the geometers try to make a square circle4 ,disraeli quotes it as finds its square1 but the originals do not support this reading4 ,,de ,,becourt4 ,i have come in the way of a work1 entitled ,the ,grave of ,human ,philosophies 7#ahbg71 translated from the ,french of ,r4 de ,becourt#dda by ,a4 ,dalmas4 ,it supports1 but ,i suspect not very accurately1 the views of the old ,hindu books4 #bgh ,that the sun is only #dej miles from us1 and only #dj miles in diameter1 may be passed over2 my affair is with the state of mind into which persons of ,m4 ,becourt's temperament are brought by a fancy4 ,he fully grants1 as certain1 four millions of years as the duration of the ,hindu race1 and #aief as that of the universe4 ,it must be admitted he is not wholly wrong in saying that our errors about the universe proceed from our ignorance of its origin1 antiquity1 organization1 laws1 and final destination4 ,living in an age of light1 he avails himself of that opportunity to remove this veil of darkness1 etc4 ,the system of the ,brahmins is the only true one3 he adds that it has never before been attempted1 as it could not be obtained except by him4 ,the author requests us first1 to lay aside prejudice2 next1 to read all he says in the order in which he says it3 we may then pronounce judgment upon a work which begins by taking the ,brahmins for granted4 ,all the paradoxers make the same requests4 ,they do not see that compliance would bring thousands of systems before the world every year3 we have scores as it is4 ,how is a poor candid inquirer to choose4 ,fortunately1 the mind has its grand jury as well as its little one3 and it will not put a book upon its trial without a prima facie case in its favor4 ,and with most of those who really search for themselves1 that case is never made out without evidence of knowledge1 standing out clear and strong1 in the book to be examined4 ,,bequest ,,of ,a ,,quadrature4 ,there is much private history which will never come to light1 caret quia vate sacro1#ddb because no ,budgeteer comes across it4 ,many years ago a man of business1 whose life was passed in banking1 amused his leisure with quadrature1 was successful of course1 and bequeathed the result in a sealed book1 which the legatee was enjoined not to sell #bgi under a thousand pounds4 ,the true ratio was #c4adaf3 ,i have the anecdote from the legatee's executor1 who opened the book4 ,that a banker should square the circle is very credible3 but how could a ,city man come by the notion that a thousand pounds could be got for it8 ,a friend of mine1 one of the twins of my zodiac1 will spend a thousand pounds1 if he have not done it already1 in black and white cyclometry3 but ,i will answer for it that he1 a man of sound business notions1 never entertained the idea of pi recouping him1 as they now say4 ,i speak of individual success3 of course if a company were formed1 especially if it were of unlimited lie-ability1 the shares would be taken4 ,no offence2 there is nothing but what a pun will either sanctify1 justify1 or nullify3 ,it comes o'er the soul like the sweet ,south ,that breathes upon a bank of vile hits4 ,the shares would be at a premium of #c-a_/h on the day after issue4 ,if they presented me with the number of shares ,i deserve1 for suggestion and advertisement1 ,i should stand up for the ,archpriest of ,st4 ,vitus#ddc and #c-a_/e1 with a view to a little more gold on the bridge4 ,i now insert a couple of reviews1 one about ,cyclopaedias1 one about epistolary collections4 ,should any reader wish for explanation of this insertion1 ,i ask him to reflect a moment1 and imagine me set to justify all the additions now before him6 ,in truth these reviews are the repositories of many odds and ends3 they were not made to the books2 the materials were in my notes1 and the books came as to a ready-made clothes shop1 and found what would fit them4 ,many remember ,curll's#ddd bequest of some very good titles #bhj which only wanted treatises written to them4 ,well6 here were some tolerable reviews--as times go--which only wanted books fitted to them4 ,accordingly1 some tags were made to join on the books2 and then as the reader sees4 ,i should find it hard to explain why the insertion is made in this place rather than another4 ,but again1 suppose ,i were put to make such an explanation throughout the volume4 ,the improver who laid out grounds and always studied what he called unexpectedness1 was asked what name he gave it for those who walked over his grounds a second time4 ,he was silenced2 but ,i have an answer3 ,it is that which is given by the very procedure of taking up my book a second time4 ,,review ,,of ,,cyclopaedias4 ,october #ai1 #ahfa4 ,the ,english ,cyclopaedia4 ,conducted by ,charles ,knight4#dde #bb vols43 viz41 ,geography1 #d vols42 ,biography1 #f vols42 ,natural ,history1 #d vols42 ,arts and ,sciences1 #h vols4 7,bradbury ,evans47 ,the ,encyclopaedia ,britannica3 a ,dictionary of ,arts1 ,sciences1 and ,general ,literature4 ,eighth ,edition4 #ba vols4 and ,index4 7,black47 ,the two editions above described are completed at the same time3 and they stand at the head of the two great branches into which pantological undertakings are divided1 as at once the largest and the best of their classes4 ,when the works are brought together1 the first thing that strikes the eye is the syllable of difference in the names4 ,the word ,cyclopaedia is a bit of modern purism4 ,though ,greek3 enkuklopaideia#ddf is not absolutely ,greek of ,greece1 we learn from both ,pliny#ddg and ,quintilian#ddh that the circle #bha of the sciences was so called by the ,greeks1 and ,vitruvius#ddi has thence naturalized encyclium in ,latin4 ,nevertheless we admit that the initial en would have euphonized but badly with the word ,penny3 and the ,english ,cyclopaedia is the augmented1 revised1 and distributed edition of the ,penny ,cyclopaedia4 ,it has indeed been said that ,cyclopaedia should mean the education of a circle1 just as ,cyropaedia is the education of ,cyrus4 ,but this is easily upset by ,aristotle's word ,greek3 kuklophoria1#dej motion in a circle1 and by many other cases1 for which see the lexicon4 ,the earliest printed ,encyclopaedia of this kind was perhaps the famous myrrour of the worlde1 which ,caxton#dea translated from the ,french and printed in #adhj4 ,the original ,latin is of the thirteenth century1 or earlier4 ,this is a collection of very short treatises4 ,in or shortly after #adif appeared the ,margarita ,philosophica of ,gregory ,reisch1#deb the same we must suppose1 who was confessor to the ,emperor ,maximilian4#dec ,this is again a collection of treatises1 of much more pretension3 and the estimation formed of it is proved by the number of editions it went through4 ,in #aeca appeared the little collection of works of ,ringelberg1#ded which is truly called an ,encyclopaedia by #bhb ,morhof1 though the thumbs and fingers of the two hands will meet over the length of its one volume4 ,there are more small collections2 but we pass on to the first work to which the name of ,encyclopaedia is given4 ,this is a ponderous ,scientiarum ,omnium ,encyclopaedia of ,alsted1#dee in four folio volumes1 commonly bound in two3 published in #afbi and again in #afdi2 the true parent of all the ,encyclopaedias1 or collections of treatises1 or works in which that character predominates4 ,the first great dictionary may perhaps be taken to be ,hofman's ,lexicon ,universale#def 7#afgg72 but ,chambers's#deg 7so called7 ,dictionary 7#agbh7 has a better claim4 ,and we support our proposed nomenclature by observing that ,alsted accidentally called his work ,encyclopaedia1 and ,chambers simply ,cyclopaedia4 ,we shall make one little extract from the myrrour1 and one from ,ringelberg4 ,caxton's author makes a singular remark for his time2 and one well worthy of attention4 ,the grammar rules of a language1 he says1 must have been invented by foreigners3 ,and whan any suche tonge was perfytely had and usyd amonge any people1 than other people not used to the same tonge caused rulys to be made wherby they myght lerne the same tonge 444 and suche rulys be called the gramer of that tonge4 ,ringelberg says that if the right nostril bleed1 the little finger of the right hand should be crooked1 and squeezed with great force2 and the same for the left4 #bhc ,we pass on to the ,encyclopedie1#deh commenced in #agea2 the work which has1 in many minds1 connected the word encyclopaedist with that of infidel4 ,readers of our day are surprised when they look into this work1 and wonder what has become of all the irreligion4 ,the truth is1 that the work--though denounced ab ovo#dei on account of the character of its supporters--was neither adapted1 nor intended1 to excite any particular remark on the subject3 no work of which ,d',alembert#dfj was co-editor would have been started on any such plan4 ,for1 first1 he was a real sceptic3 that is1 doubtful1 with a mind not made up4 ,next1 he valued his quiet more than anything2 and would as soon have gone to sleep over an hornet's nest as have contemplated a systematic attack upon either religion or government4 ,as to ,diderot#dfa--of whose varied career of thought it is difficult to fix the character of any one moment1 but who is very frequently taken among us for a pure atheist--we will quote one sentence from the article ,encyclopedie1 which he wrote himself3--,dans le moral1 il n'y a que ,dieu qui doit servir de modele a #a';homme2 dans les art1 que la nature4#dfb ,a great many readers in our country have but a very hazy idea of the difference between the political ,encyclopaedia1 as we may call it1 and the ,encyclopedie ,methodique1#dfc which we always take to be meant--whether rightly or not we cannot tell--when we hear of the great ,french ,encyclopaedia4 ,this work1 which takes much from its #bhd predecessor1 professing to correct it1 was begun in #agib1 and finished in #ahcb4 ,there are #aff volumes of text1 and #fdci plates1 which are sometimes incorporated with the text1 sometimes make about #dj more volumes4 ,this is still the monster production of the kind2 though probably the ,german ,cyclopaedia of ,ersch and ,gruber1#dfd which was begun in #ahah1 and is still in progress1 will beat it in size4 ,the great ,french work is a collection of dictionaries2 it consists of ,cyclopaedias of all the separate branches of knowledge4 ,it is not a work1 but a collection of works1 one or another department is to be bought from time to time2 but we never heard of a complete set for sale in one lot4 ,as ships grow longer and longer1 the question arises what limit there is to the length4 ,one answer is1 that it will never do to try such a length that the stern will be rotten before the prow is finished4 ,this wholesome rule has not been attended to in the matter before us2 the earlier parts of the great ,french work were antiquated before the whole were completed3 something of the kind will happen to that of ,ersch and ,gruber4 ,the production of a great dictionary of either of the kinds is far from an easy task4 ,there is one way of managing the ,encyclopaedia which has been largely resorted to2 indeed1 we may say that no such work has been free from it4 ,this plan is to throw all the attention upon the great treatises1 and to resort to paste and scissors1 or some process of equally easy character1 for the smaller articles4 ,however it may be done1 it has been the rule that the ,encyclopaedia of treatises should have its supplemental ,dictionary of a very incomplete character4 ,it is true that the treatises are intended to do a good deal2 and that the ,index1 if it be good1 knits the treatises and the dictionary into one whole of reference4 ,still there are two stools1 and between them a great deal will fall to the ground4 ,the dictionary portion of the ,britannica is not to be compared with its #bhe treatises2 the part called ,miscellaneous and ,lexicographical in the ,metropolitana#dfe is a great failure4 ,the defect is incompleteness4 ,the biographical portion1 for example1 of the ,britannica is very defective3 of many names of note in literature and science1 which become known to the reader from the treatises1 there is no account whatever in the dictionary4 ,so that the reader who has learnt the results of a life in astronomy1 for example1 must go to some other work to know when that life began and ended4 ,this defect has run through all the editions2 it is in the casting of the work4 ,the reader must learn to take the results at their true value1 which is not small4 ,he must accustom himself to regard the ,britannica as a splendid body of treatises on all that can be called heads of knowledge1 both greater and smaller2 with help from the accompanying dictionary1 but not of the most complete character4 ,practically1 we believe1 this defect cannot be avoided3 two plans of essentially different structure cannot be associated on the condition of each or either being allowed to abbreviate the other4 ,the defect of all others which it is most difficult to avoid is inequality of performance4 ,take any dictionary you please1 of any kind which requires the association of a number of contributors1 and this defect must result4 ,we do not merely mean that some will do their work better than others2 this of course3 we mean that there will be structural differences of execution1 affecting the relative extent of the different parts of the whole1 as well as every other point by which a work can be judged4 ,a wise editor will not attempt any strong measures of correction3 he will remember that if some portions be below the rest1 which is a disadvantage1 it follows that some portions must be above the rest1 which is an advantage4 ,the only practical level1 if #bhf level there must be1 is that of mediocrity1 if not of absolute worthlessness3 any attempt to secure equality of strength will result in equality of weakness4 ,efficient development may be cut down into meager brevity1 and in this way only can apparent equality of plan be secured throughout4 ,it is far preferable to count upon differences of execution1 and to proceed upon the acknowledged expectation that the prominent merits of the work will be settled by the accidental character of the contributors2 it being held impossible that any editorial efforts can secure a uniform standard of goodness4 ,wherever the greatest power is found1 it should be suffered to produce its natural effect4 ,there are1 indeed1 critics who think that the merit of a book1 like the strength of a chain1 is that of its weakest part3 but there are others who know that the parallel does not hold1 and who will remember that the union of many writers must show exaggeration of the inequalities which almost always exist in the production of one person4 ,the true plan is to foster all the good that can be got1 and to give development in the directions in which most resources are found3 a ,cyclopaedia1 like a plant1 should grow towards the light4 ,the ,penny ,cyclopaedia had its share of this kind of defect or excellence1 according to the way in which the measure is taken4 ,the circumstance is not so much noticed as might be expected1 and this because many a person is in the habit of using such a dictionary chiefly with relation to one subject1 his own2 and more still want it for the pure dictionary purpose1 which does not go much beyond the meaning of the word4 ,but the person of full and varied reference feels the differences2 and criticism makes capital of them4 ,the ,useful ,knowledge ,society was always odious to the organs of religious bigotry2 and one of them1 adverting to the fact that geography was treated with great ability1 and most unusual fullness1 in the ,penny ,cyclopaedia1 announced it by making it the sole merit of #bhg the work that1 with sufficient addition1 it would make a tolerably good gazetteer4 ,some of our readers may still have hanging about them the feelings derived from this old repugnance of a class to all that did not associate direct doctrinal teaching of religion with every attempt to communicate knowledge4 ,i will take one more instance1 by way of pointing out the extent to which stupidity can go4 ,if there be an astronomical fact of the telescopic character which1 next after ,saturn's ring and ,jupiter's satellites1 was known to all the world1 it was the existence of multitudes of double stars1 treble stars1 etc4 ,a respectable quarterly of the theological cast1 which in mercy we refrain from naming1 was ignorant of this common knowledge1--imagined that the mention of such systems was a blunder of one of the writers in the ,penny ,cyclopaedia1 and lashed the presumed ignorance of the statement in the following words1 delivered in ,april1 #ahcg3 ,we have forgotten the name of that ,sidrophel who lately discovered that the fixed stars were not single stars1 but appear in the heavens like soles at ,billingsgate1 in pairs2 while a second astronomer1 under the influence of that competition in trade which the political economists tell us is so advantageous to the public1 professes to show us1 through his superior telescope1 that the apparently single stars are really three4 ,before such wondrous mandarins of science1 how continually must homunculi like ourselves keep in the background1 lest we come between the wind and their nobility4 ,certainly these little men ought to have kept in the background2 but they did not3 and the growing reputation of the work which they assailed has chronicled them in literary history2 grubs in amber4 ,this important matter of inequality1 which has led us so far1 is one to which the ,encyclopaedia is as subject as the ,cyclopaedia2 but it is not so easily recognized as a fault4 #bhh ,we receive the first book as mainly a collection of treatises3 we know their authors1 and we treat them as individuals4 ,we see1 for instance1 the names of two leading writers on ,optics1 ,brewster#dff and ,herschel4#dfg ,it would not at all surprise us if either of these writers should be found criticising the other by name1 even though the very view opposed should be contained in the same ,encyclopaedia with the criticism4 ,and in like manner1 we should hold it no wonder if we found some third writer not comparable to either of those we have named4 ,it is not so in the ,cyclopaedia3 here we do not know the author1 except by inference from a list of which we never think while consulting the work4 ,we do not dissent from this or that author3 we blame the book4 ,the ,encyclopaedia ,britannica is an old friend4 ,though it holds a proud place in our present literature1 yet the time was when it stood by itself1 more complete and more clear than anything which was to be found elsewhere4 ,there must be studious men alive in plenty who remember when they were studious boys1 what a literary luxury it was to pass a few days in the house of a friend who had a copy of this work4 ,the present edition is a worthy successor of those which went before4 ,the last three editions1 terminating in #ahbd1 #ahdb1 and #ahfa1 seem to show that a lunar cycle cannot pass without an amended and augmented edition4 ,detailed criticism is out of the question2 but we may notice the effective continuance of the plan of giving general historical dissertations on the progress of knowledge4 ,of some of these dissertations we have had to take separate notice2 and all will be referred to in our ordinary treatment of current literature4#dfh ,the literary excellence of these two extensive undertakings is of the same high character4 ,to many this will #bhi need justification3 they will not easily concede to the cheap and recent work a right to stand on the same shelf with the old and tried magazine1 newly replenished with the best of everything4 ,those who are cognizant by use of the kind of material which fills the ,penny ,cyclopaedia will need no further evidence3 to others we shall quote a very remarkable and certainly very complete testimony4 ,the ,cyclopaedia of the ,physical ,sciences1 published by ,dr4 ,nichol#dfi in #aheg 7noticed by us1 ,april #d71 is one of the most original of our special dictionaries4 ,the following is an extract from the editor's preface3 ,when ,i assented to ,mr4 ,griffin's proposal that ,i should edit such a ,cyclopaedia1 ,i had it in my mind that ,i might make the scissors eminently effective4 ,alas6 on narrowly examining our best ,cyclopaedias1 ,i found that the scissors had become blunted through too frequent and vigorous use4 ,one great exception exists3 viz41 the ,penny ,cyclopaedia of ,charles ,knight4#dgj ,the cheapest and the least pretending1 it is really the most philosophical of our scientific dictionaries4 ,it is not made up of a series of treatises1 some good and many indifferent1 but is a thorough ,dictionary1 well proportioned and generally written by the best men of the time4 ,the more closely it is examined1 the more deeply will our obligation be felt to the intelligence and conscientiousness of its projector and editor4 ,after ,dr4 ,nichol's candid and amusing announcement of his scissorial purpose1 it is but fair to state that nothing of the kind was ultimately carried into effect1 even upon the work in which he found so much to praise4 ,i quote this testimony because it is of a peculiar kind4 #bij ,the success of the ,penny ,magazine led ,mr4 ,charles ,knight in #ahcb to propose to the ,useful ,knowledge ,society a ,cyclopaedia in weekly penny numbers4 ,these two works stamp the name of the projector on the literature of our day in very legible characters4 ,eight volumes of #dhj pages each were contemplated2 and ,mr4 ,long#dga and ,mr4 ,knight were to take the joint management4 ,the plan embraced a popular account of ,art and ,science1 with very brief biographical and geographical information4 ,the early numbers of the work had some of the ,penny ,magazine character3 no one can look at the pictures of the ,abbot and ,abbess in their robes without seeing this4 ,by the time the second volume was completed1 it was clearly seen that the plan was working out its own extension3 a great development of design was submitted to1 and ,mr4 ,long became sole editor4 ,contributors could not be found to make articles of the requisite power in the assigned space4 ,one of them told us that when he heard of the eight volumes1 happening to want a shelf to be near at hand for containing the work as it went on1 he ordered it to be made to hold twenty-five volumes easily4 ,but the inexorable logic of facts beat him after all3 for the complete work contained twenty-six volumes and two thick volumes of ,supplement4 ,the penny issue was brought to an end by the state of the law1 which required1 in #ahcc1 that the first and last page of everything sold separately should contain the name and address of the printer4 ,the penny numbers contained this imprint on the fold of the outer leaf3 and qui tam#dgb informations were laid against the agents in various towns4 #bia ,it became necessary to call in the stock2 and the penny issue was abandoned4 ,monthly parts were substituted1 which varied in bulk1 as the demands of the plan became more urgent1 and in price from one sixpence to three4 ,the second volume of ,supplement appeared in #ahdf1 and during the fourteen years of issue no one monthly part was ever behind its time4 ,this result is mainly due to the peculiar qualities of ,mr4 ,long1 who unites the talents of the scholar and the editor in a degree which is altogether unusual4 ,if any one should imagine that a mixed mass of contributors is a punctual piece of machinery1 let him take to editing upon that hypothesis1 and he shall see what he shall see and learn what he shall learn4 ,the ,english contains about ten per cent more matter than the ,penny ,cyclopaedia and its supplements2 including the third supplementary volume of #ahdh1 which we now mention for the first time4 ,the literary work of the two editions cost within #ejjl4 and #ej1jjjl43 that of the two editions of the ,britannica cost #da1jjjl4 ,but then it is to be remembered that the ,britannica had matter to begin upon1 which had been paid for in the former editions4 ,roughly speaking1 it is probable that the authorship of a page of the same size would have cost nearly the same in one as in the other4 ,the longest articles in the ,penny ,cyclopaedia were ,rome in #ih columns and ,yorkshire in #hf columns4 ,the only article which can be called a treatise is the ,astronomer ,royal's ,gravitation1 founded on the method of ,newton in the eleventh section1 but carried to a much greater extent4 ,in the ,english ,cyclopaedia1 the longest article of geography is ,asia1 in #de columns4 ,in natural history the antelopes demand #cf columns4 ,in biography1 ,wellington uses up #db columns1 and his great military opponent #da columns4 ,in the division of ,arts and ,sciences1 which includes much of a social and commercial character1 the length of articles often depends upon the state of the #bib times with regard to the subject4 ,our readers would not hit the longest article of this department in twenty guesses3 it is ,deaf and ,dumb in #fj columns4 ,as other specimens1 we may cite ,astronomy1 #ai2 ,banking1 #cf2 ,blind1 #bd2 ,british ,museum1 #ce2 ,cotton1 #bg2 ,drama1 #bf2 ,gravitation1 #ej2 ,libraries1 #ej2 ,painting1 #cd2 ,railways1 #ah2 ,sculpture1 #cf2 ,steam1 etc41 #cg2 ,table1 #dj2 ,telegraph1 #cj2 ,welsh language and literature1 #ci2 ,wool1 #ba4 ,these are the long articles of special subdivisions3 the words under which the ,encyclopaedia gives treatises are not so prominent4 ,as in ,algebra1 #aj2 ,chemistry1 #ab2 ,geometry1 #h2 ,logic1 #ad2 ,mathematics1 #e2 ,music1 #i4 ,but the difference between the collection of treatises and the dictionary may be illustrated thus3 though ,mathematics have only five columns1 ,mathematics1 recent terminology of1 has eight3 and this article we believe to be by ,mr4 ,cayley1#dgc who certainly ought to know his subject1 being himself a large manufacturer of the new terms which he explains4 ,again1 though ,music in genere1 as the schoolmen said1 has only nine columns1 ,temperament and ,tuning1 has eight1 and ,chord alone has two4 ,and so on4 ,in a dictionary of this kind it is difficult to make a total clearance of personality3 by which we mean that exhibition of peculiar opinion which is offensive to taste when it is shifted from the individual on the corporate book4 ,the treatise of the known author may1 as we have said1 carry that author's controversies on its own shoulders3 and even his crotchets1 if we may use such a word4 ,but #bic the dictionary should not put itself into antagonism with general feeling1 nor even with the feelings of classes4 ,we refer particularly to the ordinary and editorial teaching of the article4 ,if1 indeed1 the writer1 being at issue with mankind1 should confess the difference1 and give abstract of his full grounds1 the case is altered3 the editor then1 as it were1 admits a correspondent to a statement of his own individual views4 ,the dictionary portion of the ,britannica is quite clear of any lapses on this point1 so far as we know3 the treatises and dissertations rest upon their authors4 ,the ,penny ,cyclopaedia was all but clear3 and great need was there that it should have been so4 ,the ,useful ,knowledge ,society1 starting on the principle of perfect neutrality in politics and religion1 was obliged to keep strict watch against the entrance of all attempt even to look over the hedge4 ,there were two--we believe only two--instances of what we have called personality4 ,the first was in the article ,bunyan4 ,it is worth while to extract all that is said--in an article of thirty lines--about a writer who is all but universally held to be the greatest master of allegory that ever wrote3 ,his works were collected in two volumes1 folio1 #agcf-g3 among them ',the ,pilgrim's ,progress' has attained the greatest notoriety4 ,if a judgment is to be formed of the merits of a book by the number of times it has been reprinted1 and the many languages into which it has been translated1 no production in ,english literature is superior to this coarse allegory4 ,on a composition which has been extolled by ,dr4 ,johnson1 and which in our own times has received a very high critical opinion in its favor probably ,southey1 it is hazardous to venture a disapproval1 and we1 perhaps1 speak the opinion of a small minority when we confess that to us it appears to be mean1 jejune and wearisome4 --,if the unfortunate critic who thus individualized himself had been a sedulous reader of ,bunyan1 his power over #bid ,english would not have been so jejune as to have needed that fearful word4 ,this little bit of criticism excited much amusement at the time of its publication3 but it was so thoroughly exceptional and individual that it was seldom or never charged on the book4 ,the second instance occurred in the article ,socinians4 ,it had been arranged that the head-words of ,christian sects should be intrusted to members of the sects themselves1 on the understanding that the articles should simply set forth the accounts which the sects themselves give of their own doctrines4 ,thus the article on the ,roman ,church was written by ,dr4 ,wiseman4#dgd ,but the ,unitarians were not allowed to come within the rule3 as in other quarters1 they were treated as the gypsies of ,christianity4 ,under the head ,socinians--a name repudiated by themselves--an opponent was allowed not merely to state their alleged doctrines in his own way1 but to apply strong terms1 such as audacious unfairness1 to some of their doings4 ,the protests which were made against this invasion of the understanding produced1 in due time1 the article ,unitarians1 written by one of that persuasion4 ,we need not say that these errors have been amended in the ,english ,cyclopaedia3 and our chief purpose in mentioning them is to remark1 that this is all we can find on the points in question against twenty-eight large volumes produced by an editor whose task was monthly1 and whose issue was never delayed a single hour4 ,how much was arrested before publication none but himself can say4 ,we have not alluded to one or two remonstrances on questions of absolute fact1 which are beside the present purpose4 ,both kinds of encyclopaedic works have been fashioned upon predecessors1 from the very earliest which had a predecessor to be founded upon2 and the undertakings before us will be themselves the ancestors of a line of successors4 ,those who write in such collections should be #bie careful what they say1 for no one can tell how long a mis-statement may live4 ,on this point we will give the history of a pair of epithets4 ,when the historian ,de ,thou#dge died1 and left the splendid library which was catalogued by ,bouillaud#dgf and the brothers ,dupuis#dgg 7,bullialdus and ,puteanus71 there was a manuscript of ,de ,thou's friend ,vieta1#dgh the ,harmonicon ,coeleste1 of which it is on record1 under ,bouillaud's hand1 that he himself lent it to ,cosmo de' ,medici1#dgi to which must be added that ,m4 ,libri#dhj found it in the ,magliabecchi ,library at ,florence in our own day4 ,bouillaud1 it seems1 entirely forgot what he had done4 ,something1 probably1 that ,peter ,dupuis said to ,bouillaud1 while they were at work on the catalogue1 remained on his memory1 and was published by him in #afde1 long after2 to the effect that ,dupuis lent the manuscript to ,mersenne1#dha from whom it was procured by some intending plagiarist1 who would not give it back4 ,this was repeated by ,sherburne1#dhb in #afge1 who speaks of the work1 which being communicated to ,mersennus was1 by some perfidious acquaintance of that honest-minded person1 surreptitiously taken from him1 and irrecoverably lost or suppressed1 to the unspeakable detriment of the lettered world4 ,now let the #bif reader look through the dictionaries of the last century and the present1 scientific or general1 at the article1 ,vieta1 and he will be amused with the constant recurrence of honest-minded ,mersenne1 and his surreptitious acquaintance4 ,we cannot have seen less than thirty copies of these epithets4 ,,review ,,of ,,macclesfield ,,letters4 ,october #ah1 #ahfb4 ,correspondence of ,scientific ,men of the ,seventeenth ,century1 in the ,collection of the ,earl of ,macclesfield4#dhc #b vols4 7,oxford1 ,university ,press47 ,though the title-page of this collection bears the date #ahda1 it is only just completed by the publication of its ,table of ,contents and ,index4 ,without these1 a work of the kind is useless for consultation1 and cannot make its way4 ,the reason of the delay will appear3 its effect is well known to us4 ,we have found inquirers into the history of science singularly ignorant of things which this collection might have taught them4 ,in the same year1 #ahda1 the ,historical ,society of ,science1 which had but a brief existence1 published a collection of letters1 eighty-three in number1 edited by ,mr4 ,halliwell1#dhd of ,english men of science1 which dovetails with the one before us1 and is for the most part of a prior date4 ,the two should be bound up together4 ,the smaller collection runs from #aefb to #afhb2 the larger1 from #afjf to past #agjj4 ,we shall speak of the two as the ,museum collection and the ,macclesfield collection4 ,and near them should be placed1 in every scientific library1 the valuable collection published1 by ,mr4 ,edleston1#dhe for ,trinity ,college1 in #ahej4 #big ,the history of these letters runs back to famous ,john ,collins1 the attorney-general of the mathematics1 as he has been called1 who wrote to everybody1 heard from everybody1 and sent copies of everybody's letter to everybody else4 ,he was in ,england what ,mersenne#dhf was in ,france3 as early as #afga1 ,e4 ,bernard#dhg addresses him as the very ,mersennus and intelligence of this age4 ,john ,collins#dhh was never more than accountant to the ,excise ,office1 to which he was promoted from teaching writing and ciphering1 at the ,restoration3 he died in #afhb4 ,we have had a man of the same office in our own day1 the late ,prof4 ,schumacher1#dhi who made the little ,danish ,observatory of ,altona the junction of all the lines by which astronomical information was conveyed from one country to another4 ,when the collision took place between ,denmark and the ,duchies1 the ,english ,government1 moved by the ,astronomical ,society1 instructed its diplomatic agents to represent strongly to the ,danish ,government1 when occasion should arise1 the great importance of the ,observatory of ,altona to the astronomical communications of the whole world4 ,but ,schumacher had his own celebrated journal1 the ,astronomische ,nachrichten1 by which to work out part of his plan2 private correspondence was his supplementary assistant4 ,collins had only correspondence to rely on4 ,nothing is better known than that it was ,collins's collection which furnished the materials put forward by the ,committee of the ,royal ,society in #agab1 as a defence of ,newton against the partisans of ,leibnitz4 ,the noted ,commercium ,epistolicum is but the abbreviation of a title which runs on with ,d4 ,johannis ,collins et aliorum 444 ,the whole of this collection passed into the hands of #bih ,william ,jones1#dij the father of the ,indian ,judge of the same name1 who died in #agdi4 ,jones was originally a teacher1 but was presented with a valuable sinecure by the interest of ,george1 second ,earl of ,macclesfield1 the mover of the bill for the change of style in ,britain1 who died ,president of the ,royal ,society4 ,this change of style may perhaps be traced to the union of energies which were brought into concert by the accident of a common teacher3 ,lord ,macclesfield and ,lord ,chesterfield1#dia the mover and the seconder1 and ,daval1#dib who drew the bill1 were pupils of ,de ,moivre4#dic ,jones1 who was a respectable mathematician though not an inventor1 collected the largest mathematical library of his day1 and became possessor of the papers of ,collins1 which contained those of ,oughtred#did and others4 ,some of these papers passed into the custody of the ,royal ,society3 but the bulk was either bequeathed to1 or purchased by1 ,lord ,macclesfield2 and thus they found their way to ,shirburn ,castle1 where they still remain4 ,a little before #ahcf1 this collection attracted the attention of a searching inquirer into points of mathematical history1 the late ,professor ,rigaud1#die who died in #ahci4 ,he examined the whole collection of letters1 obtained ,lord ,macclesfield's consent to their publication1 and induced the ,oxford ,press to bear the expense4 ,it must be particularly remembered that there still remains at ,shirburn ,castle a #bii valuable mass of non-epistolary manuscripts4 ,so far as we can see1 the best chance of a further examination and publication lies in public encouragement of the collection now before us3 the ,oxford ,press might be induced to extend its operations if it were found that the results were really of interest to the literary and scientific world4 ,rigaud died before the work was completed1 and the publication was actually made by one of his sons1 ,s4 ,jordan ,rigaud1#dif who died ,bishop of ,antigua4 ,but this publication was little noticed1 for the reasons given4 ,the completion now published consists of a sufficient table of contents1 of the briefest kind1 by ,professor ,de ,morgan1 and an excellent index by the ,rev4 ,john ,rigaud4#dig ,the work is now fairly started on its career4 ,if we were charged to write a volume with the title ,small things in their connection with great1 we could not do better than choose the small part of this collection of letters as our basis4 ,the names1 as well as the contents1 are both great and small3 the great names1 those which are known to every mathematician who has any infusion of the history of his pursuit1 are ,briggs1#dih ,oughtred1 ,charles ,cavendish1#dii ,gascoigne1#ejj ,seth ,ward1#eja ,wallis1#ejb #cjj ,huygens1#ejc ,collins1#ejd ,william ,petty1#eje ,hooke1#ejf ,boyle1#ejg ,pell1#ejh ,oldenburg1#eji ,brancker1#eaj ,slusius1#eaa ,bertit1#eab ,bernard1#eac ,borelli1#ead ,mouton1#eae ,pardies1#eaf ,fermat1#eag ,towneley1#eah ,auzout1#eai #cja ,d4 ,gregory1#ebj ,halley1#eba ,machin1#ebb ,montmort1#ebc ,cotes1#ebd ,jones1#ebe ,saunderson1#ebf ,reyneau1#ebg ,brook ,taylor1#ebh ,maupertuis1#ebi ,bouguer1#ecj ,la ,condamine1#eca ,folkes1#ecb ,macclesfield1#ecc #cjb ,baker1#ecd ,barrow1#ece ,flamsteed1#ecf ,lord ,brounker1#ecg ,j4 ,gregory1#ech ,newton#eci and ,keill4#edj ,to these the ,museum collection adds the names of ,thomas ,digges1#eda ,dee1#edb ,tycho ,brahe1#edc ,harriot1#edd ,lydyat1#ede ,briggs1#edf ,warner1#edg ,tarporley1 ,pell1#edh ,lilly1#edi ,oldenburg1#eej ,collins1#eea ,morland4#eeb #cjc ,the first who appears on the scene is the celebrated ,oughtred1 who is related to have died of joy at the ,restoration3 but it should be added1 by way of excuse1 that he was eighty-six years old4 ,he is an animal of extinct race1 an ,eton mathematician4 ,few ,eton men1 even of the minority which knows what a sliding rule is1 are aware that the inventor was of their own school and college3 but they may be excused1 for ,dr4 ,hutton1#eec so far as his ,dictionary bears witness1 seems not to have known it any more than they4 ,a glance at one of his letters reminds us of a letter from the ,astronomer ,royal on the discovery of ,neptune1 which we printed ,march #bj1 #ahdg4 ,mr4 ,airy#eed there contends1 and proves it both by ,leverrier#eee and by ,adams1#eef that the limited publication of a private letter is more efficient than the more general publication of a printed memoir4 ,the same may be true of a dead letter1 as opposed to a dead book4 ,our eye was caught by a letter of ,oughtred 7#afbi71 containing systematic use of contractions for the words sine1 cosine1 etc41 prefixed to the symbol of the angle4 ,this is so very important a step1 simple as it is1 that ,euler#eeg is justly held to have greatly advanced trigonometry by its introduction4 ,nobody that we know of has noticed that ,oughtred was master of the improvement1 and willing to have taught it1 if people would have learnt4 ,after looking at his dead letter1 we naturally turned to his dead book on trigonometry1 and there we found the abbreviations s1 sco1 t1 tco1 se1 seco1 regularly established as part of the system of the work4 ,but not one of those who have investigated the contending claims of ,euler and ,thomas #cjd ,simpson#eeh has chanced to know of ,oughtred's ,trigonometrie3 and the present revival is due to his letter1 not to his book4 ,a casual reader1 turning over the pages1 would imagine that almost all the letters had been printed1 either in the ,general ,dictionary1 or in ,birch1#eei etc43 so often does the supplementary remark begin with this letter has been printed in ----4 ,for ourselves we thought1 until we counted1 that a large majority of the letters had been given1 either in whole or in part4 ,but the positive strikes the mind more forcibly than the negative3 we find that all of which any portion has been in type makes up very little more than a quarter2 the cases in which the whole letter is given being a minority of this quarter4 ,the person who has been best ransacked is ,flamsteed3 of #cf letters from him1 #cd had been previously given in whole or in part4 ,of #ei letters to and from ,newton1 only #ag have been culled4 ,the letters have been modernized in spelling1 and1 to some extent1 in algebraical notation2 it also seems that conjectural methods of introducing interpolations into the text have been necessary4 ,for all this we are sorry3 the scientific value of the collection is little altered1 but its literary value is somewhat lowered4 ,but it could not be helped3 the printers could not work from the originals1 and ,professor ,rigaud had to copy everything himself4 ,a fac-simile must have been the work of more time than he had to give3 had he attempted it1 his death would have cut short the whole undertaking1 instead of allowing him to prepare everything but a preface1 and to superintend the printing of one of the volumes4 ,we may also add1 that we believe we have notices of all the letters in the ,macclesfield collection4 ,we judge this because several which are too trivial to print are numbered and described2 and those would certainly not have been noticed if any omissions had #cje been made4 ,and we know that every letter was removed from ,shirburn ,castle to ,oxford4 ,two persons emerge from oblivion in this series of letters4 ,the first is ,michael ,dary1#efj an obscure mathematician1 who was in correspondence with ,newton and other stars4 ,he was a gauger at ,bristol1 by the interest of ,collins2 afterwards a candidate for the mathematical school at ,christ's ,hospital1 with a certificate from ,newton3 he was then a gunner in the ,tower1 and is lastly described by ,wallis as ,mr4 ,dary1 the tobacco-cutter1 a knowing man in algebra4 ,in #afgd1 ,dary writes to ,newton at ,cambridge1 as follows3--,although ,i sent you three papers yesterday1 ,i cannot refrain from sending you this4 ,i have had fresh thoughts this morning4 ,two months afterwards poor ,newton writes to ,collins1 ,mr4 ,dary is very solicitous about mathematics3 but in spite of the persecution1 he subscribes himself to ,dary your loving friend4 ,dary's problem is that of finding the rate of interest of an annuity of which the value and term are given4 ,dary's theorem1 which he seems to have invented specially for the solution of his problem1 though it is of wide range1 can be exhibited to mathematical readers even in our columns4 ,in modern language1 it is that the limit of phinx1 when n increases without limit1 is a solution of phix x4 ,we have mentioned the ,i4 ,newton to whom ,dary looked up2 we add a word about the one on whom he looked down4 ,dr4 ,john ,newton1#efa a sedulous publisher of logarithms1 tables of interest1 etc41 who began his career before ,isaac ,newton1 sometimes puzzles those who do not know him1 when described as ,i4 ,newton4 ,the scientific world was of opinion that all that was valuable in one of his works was taken from ,dary's private communications4 #cjf ,the second character above alluded to is one who carried mathematical researches a far greater length than ,newton himself3 the assistance which he rendered in this respect1 even to ,newton1 has never been acknowledged in modern times3 though the work before us shows that his contemporaries were fully aware of it1 and never thought of concealing it4 ,in his theory of gravitation1 in which1 so far as he went1 we have every reason to believe he was prior to ,newton1 he did not extend his calculations to the distance of the moon2 his views in this matter were purely terrestrial1 and led him to charge according to weight4 ,he was ,john ,stiles1 the ,london and ,cambridge carrier3 his name is a household word in the ,macclesfield ,letters1 and is even enshrined in the depths of ,birch's quartos4 ,dary informs ,newton--let us do his memory this justice--that he had paid ,john ,stiles for the carriage4 ,at the time when the railroad to ,cambridge was opened1 a correspondent recommended the directors1 in our columns1 to call an engine by the name of ,john ,stiles1 and never to let that name go off the road4 ,we do not know whether the advice was followed3 if not1 we repeat it4 ,little points of life and manners come out occasionally4 ,baker1 the author of a work on algebra much esteemed at the time1 wrote to ,collins that their circumstances are alike1 having a just and equal number of chargeable olive-branches1 and being in the same predicament and blessed condemnation with you1 not more preaching than unpaid1 and preaching the art of contentment to others1 am forced to practise it4 ,but the last sentence of his letter runs as follows3 ,i have sent by the bearer 444 twenty shillings1 as a token to you2 desiring you to accept of it1 as a small taste from ,yours1 ,thos4 ,baker4 ,in our day1 men of a station to pay parish taxes do not offer their friends hard money to buy liquor4 ,but ,flamsteed#efb writes to ,collins as follows3 ,last week he sent us down the counterpart1 which #cjg my father has scaled1 and ,i return up to you by the carrier1 with #el4 to be paid to ,mr4 ,leneve for the writing1 ,i have added #bs4 #f;d4 over1 which will pay the expenses and serve to drink1 with him4 ,this would seem as odd to us as it would have seemed thirty years ago that half-a-crown should pay carriage for a deed from ,derby to ,london1 and leave margin for a bottle of wine3 in our day1 the ,post-office and the ,french treaty would just manage it between them4 ,but ,flamsteed does not limit his friend to one bottle2 he adds1 ,if you expend more than the half-crown1 ,i will make it good after ,whitsuntide4 ,collins does not remember exactly where he had met ,james ,gregory1 and mentions two equally likely places thus3 ,sir1 it was once my good hap to meet with you in an alehouse or in ,sion ,college4 ,there is a little proof how universally the dinner-hour was twelve o'clock4 ,astronomers well know the method of finding time by equal altitudes of the sun before and after noon3 ,huyghens calls it le moyen de deux egales hauteurs du soleil devant et apres diner4#efc ,there is one mention of ,mr4 ,cocker1#efd our famous ,english graver and writer1 now a schoolmaster at ,northampton4 ,this is the true ,cocker3 his genuine works are specimens of writing1 such as engraved copy-books1 including some on arithmetic1 with copper-plate questions and space for the working2 also a book of forms for law-stationers1 with specimens of legal handwriting4 ,it is recorded somewhere that ,cocker and another1 whose name we forget1 competed with the ,italians in the beauty of their flourishes4 ,this was his real fame3 and in these matters he was great4 ,the eighth edition of his book of law forms 7#afge71 published shortly after ,cocker's death1 has a preface signed ,j4 ,h4 ,this was ,john ,hawkins1 who became possessed of ,cocker's papers--at least he said so--and #cjh subsequently forged the famous ,arithmetic1#efe a second work on ,decimal ,arithmetic1 and an ,english dictionary1 all attributed to ,cocker4 ,the proofs of this are set out in ,de ,morgan's ,arithmetical ,books4 ,among many other corroborative circumstances1 the clumsy forger1 after declaring that ,cocker to his dying day resisted strong solicitation to publish his ,arithmetic1 makes him write in the preface ,ille ego qui quondam#eff of this kind3 ,i have been instrumental to the benefit of many1 by virtue of those useful arts1 writing and engraving2 and do now1 with the same wonted alacrity1 cast this my arithmetical mite into the public treasury4 ,the book itself is not comparable in merit to at least half-a-dozen others4 ,how then comes ,cocker to be the impersonation of ,arithmetic8 ,unless some one can show proof1 which we have never found1 that he was so before #agef1 the matter is to be accounted for thus4 ,arthur ,murphy1#efg the dramatist1 was by taste a man of letters1 and ended by being the translator of ,tacitus2 though many do not know that the two are one4 ,his friends had tried to make him a man of business2 and no doubt he had been well plied with commercial arithmetic4 ,his first dramatic performance1 the farce of ,the ,apprentice1 produced in #agef1 is about an idle young man who must needs turn actor4 ,two of the best known books of the day in arithmetic were those of ,cocker and ,wingate4#efh ,murphy chooses ,wingate to be the name of an old merchant who #cji delights in vulgar fractions1 and ,cocker to be his arithmetical catchword--,you read ,shakespeare6 get ,cocker's ,arithmetic6 you may buy it for a shilling on any stall2 best book that ever was wrote6 and so on4 ,the farce became very popular1 and1 as we believe1 was the means of elevating ,cocker to his present pedestal1 where ,wingate would have been1 if his name had had the droller sound of the two to ,english ears4 ,a notoriety of an older day turns up1 ,major-,general ,lambert4#efi ,the common story is that he was banished to ,guernsey1 where he passed thirty years in confinement1 rearing and painting flowers4 ,but ,baker1 in #afgh1 represents him as a prisoner at ,plymouth1 sending equations for solution as a challenge3 probably his place of confinement was varied1 and his occupation also4 ,general ,lambert was removed to ,plymouth1 probably about #affh4 ,his daughter captured the son of the ,governor of ,guernsey1 who therefore probably was reckoned an unsafe custodier thenceforward2 though he assured the king that he had turned the young couple out of doors1 and had never given them a penny4 ,great importance was attached to ,lambert's safe detention3 probably the remaining republicans looked upon him as to be their next ,cromwell1 if such a thing were to be4 ,there were standing orders to shoot him at once on the first appearance of any enemy before the island4 ,see ,notes and ,queries1 #c;d ,s4 iv4 #hi4 ,collins informs ,james ,gregory that some of the ,royal ,academy wrote over to ,mr4 ,oldenburg1 who was desired to impart the same to the ,council of the ,royal ,society1 that the ,french ,king was willing to allow pensions to one or two learned ,englishmen1 but they never made any answer #caj to such a proposal4 ,this was written in #afga1 and the thing probably happened several years before4 ,mr4 ,de ,morgan communicated the account of the proposal to ,lord ,macaulay1 who replied that he did not think that any ,englishman received a literary pension from ,louis2 but that there is a curious letter1 about #affd1 from the ,french ,ambassador1 in which he says that he has1 by his master's orders1 been making inquiries as to the state of learning in ,england1 and that he is sorry to find that the best writer is the infamous ,miltonus4 ,on two such independent testimonies it may be held proved that the ,french ,king had attempted to buy a little adherence from ,english literature and science2 and the silent contempt of the ,royal ,society is an honorable fact in their history4 ,another little bit of politics is as follows4 ,oughtred is informed that ,mr4 ,foster1#egj our ,lecturer on ,astronomy at ,gresham ,college1 is put out because he will not kneel down at the communion-table4 ,a ,scotsman ,mungo ,murray1 one that is verbi bis minister1#ega is now lecturer in ,mr4 ,foster's place4 ,ward in his work on the ,gresham ,professors1#egb suppresses the reason1 and the suppression lowers the character of his book4 ,foster was expelled in #afcf1 and re-elected on a vacancy in #afda1 when ,puritanism had gained strength4 ,the correspondence of ,newton would require deeper sifting than could be given in such an article as the present4 ,the first of the letters 7#affi7 is curious1 as presenting the #caa appearance of forms belonging to the great calculus which1 in this paragraph1 we ought to call that of fluxions4 ,we find1 of the date ,february #ah1 #affi-gj1 what we believe is the earliest manifestation of that morbid part of ,newton's temperament which has been so variously represented4 ,he had solved a problem--being that which we have called ,dary's--on which he writes as follows3 ,the solution of the annuity problem1 if it will be of any use1 you have my leave to insert into the ,philosophical ,transactions1 so it be without my name to it4 ,for ,i see not what there is desirable in public esteem1 were ,i able to acquire and maintain it4 ,it would perhaps increase my acquaintance1 the thing which ,i chiefly study to decline4 ,three letters touch upon the experiment of glass rubbed to cause various motions in bits of paper underneath3 they are supplements to the account given by ,newton to the ,royal ,society1 and printed by ,birch4 ,it was ,newton1 so far as appears1 who added glass to the substances known to be electric4 ,soon afterwards we come to a little bit of the history of the appointment to the ,mint4 ,it has appeared from the researches of late years that ,newton was long an aspirant for public employment3 the only coolness which is known to have taken place between him and ,charles ,montague#egc ,halifax arose out of his imagining that his friend was not in earnest about getting him into the public service4 ,march #ad1 #afif1 ,newton writes thus to ,halley3 ,and if the rumour of preferment for me in the ,mint should hereafter1 upon the death of ,mr4 ,hoar the comptroller1 or any other occasion1 be revived1 ,i pray that you would #cab endeavour to obviate it by acquainting your friends that ,i neither put in for any place in the ,mint1 nor would meddle with ,mr4 ,hoar's place1 were it offered to me4 ,this means that ,mr4 ,hoar's place had been suggested1 which ,newton seems to have declined4 ,five days afterwards1 ,montague writes to ,newton that he is to have the ,wardenship4 ,it is fair to ,newton to say that in all probability this was not--or only in a smaller degree--a question of personal dignity1 or of salary4 ,it must by this time have been clear to him that the minister1 though long bound to make him an object of patronage1 was actually seeking him for the ,mint1 because he wanted both ,newton's name and his talents for business--which he knew to be great--in the weighty and dangerous operation of restoring the coinage4 ,it may have been1 and probably was1 the case that ,newton had a tolerably accurate notion of what he would have to do1 and of what degree of power would be necessary to enable him to do it in his own way4 ,we have said that the non-epistolary manuscripts are still unexamined4 ,there is a chance that one of them may answer a question of two centuries' standing1 which is worth answering1 because it has been so often asked4 ,about #afdj1 ,warner1#egd afterwards assisted by ,pell1#ege commenced a table of antilogarithms1 of the kind which ,dodson#egf afterwards constructed anew and published4 ,in the ,museum collection there is inquiry after inquiry from ,charles ,cavendish1#egg first1 as to when the ,analogics1 as he called them1 would be finished2 next1 when they would be printed4 ,pell answers1 in #afdd1 that ,warner left his papers to a kinsman1 who had become bankrupt1 and proceeds thus3 ,i am not a little afraid that all ,mr4 ,warner's papers1 #cac and no small share of my labours therein1 are seazed upon1 and most unmathematically divided between the sequestrators and creditors1 who 7not being able to ballance the account where there appeare so many numbers1 and much troubled at the sight of so many crosses and circles in the superstitious ,algebra and that black art of ,geometry7 will1 no doubt1 determine once in their lives to become figure-casters1 and so vote them all to be throwen into the fire1 if some good body doe not reprieve them for pye-bottoms1 for which purposes you know analogicall numbers are incomparably apt1 if they be accurately calculated4 ,pell afterwards told ,wallis#egh that the papers had fallen into the hands of ,dr4 ,busby1#egi and ,collins#ehj writes that they were left in the hands of ,dr4 ,thorndike1#eha a prebendary of ,westminster2 whence ,rigaud#ehb seems to say that ,thorndike had left them to ,dr4 ,busby4 ,birch#ehc says that he procured for the ,royal ,society four boxes from ,busby's trustees1 containing papers of ,warner and ,pell3 but there is no other tradition of such things in the ,society4 ,but in the ,birch manuscripts at the ,british ,museum1 there turns up1 as printed in what we call the ,museum collection1 a list of ,warner's papers1 with ,collins's receipt to ,dr4 ,thorndike at the bottom1 and engagement to restore them on demand4 ,the date is ,december #ad1 #affg2 ,wallis's statement being in #afic4 ,it is possible that ,busby may be a mistake altogether3 he was very unlikely to have had charge of any mathematical papers3 there may have been a confusion between the ,prebendary of ,westminster and the ,head ,master of ,westminster ,school4 ,if so1 in all probability ,thorndike handed #cad the cumbrous lot over to the notorious collector of mathematical papers1 blessing himself that he got rid of them in a manner which would insure their return if he were called upon by the owners to restore them4 ,it is much against this hypothesis that ,dodson1 who certainly recalculated1 can say nothing more about ,warner than a repetition of ,wallis's story3 though1 had ,collins kept the papers1 they would probably have been in ,jones's possession at the very time when ,dodson1 who was a friend of ,jones and a user of his library1 was engaged on his own computations4 ,but even books1 and still more manuscripts1 are often singularly overlooked2 and it remains not very improbable that ,warner's table is now at ,shirburn ,castle1 among the unexamined manuscripts4 ,,cyclometry ,,and ,,steel ,,pens4 ,redit labor actus in orbem4#ehd ,among the matters which have come to me since the ,budget opened1 there is a pamphlet of quadrature of two pages and a half from ,professor ,recalcati1#ehe already mentioned4 ,it ends with ,quelque objection qu'on fasse touchant les raisonnements ci-dessus on tombera toujours dans l'absurde4#ehf ,a civil engineer--so he says--has made the quadrature no longer a problem1 but an axiom4 ,as follows3 ,take the quadrant of a circle whose circumference is given1 square the quadrant which gives the true square of the circle4 ,because #cj _/ #d #g4e x #g4e #ef4be the positive square of a circle whose circumference is #cj4 ,brevity1 the soul of wit1 is the wings of mighty-winds to quadrature1 and sends it flying all abroad4 ,a surbodhicary--something like ,m4,a4 or ,,ll4,d41 ,i understand--at ,calcutta1 published in #ahfc the division of an #cae angle into any odd number of parts1 demonstration and all in--when the diagram is omitted--one page1 good-sized1 well-leaded type1 small duodecimo4 ,but in the ,preface he acknowledges sheer inability to execute his task4 ,mr4 ,william ,dean1 of ,todmorden1 in #ahfc1 announced #c-i_/fd as proved both practically and geometrically3 he has been already mentioned anonymously4 ,next ,i have the tract of ,don ,juan ,larriva1 published at ,leiria in #ahef1 and dedicated to ,queen ,victoria4 ,mr4 ,w4 ,peters1#ehg already mentioned1 who has for some months been circulating diagrams on a card1 publishes 7,august1 #ahfe7 ,the ,circle ,squared4 ,he agrees with the ,archpriest of ,st4 ,vitus4 ,he hints that a larger publication will depend partly on the support he receives1 and partly on the castigation1 for which last1 of course1 he looks to me4 ,cyclometers have their several styles of wit2 so have anticyclometers too1 for that matter4 ,mr4 ,peters will not allow me any extra-journal being3 ,i am essentially a quotation from the ,athenaeum2 ,a4 ,de ,morgan et praeterea nihil4#ehh ,if he had to pay for keeping me set up1 he would find out his mistake1 and would be glad to compound handsomely for a stereotype4 ,next comes a magnificent sheet of pasteboard1 printed on both sides4 ,having glanced at it and detected quadrature1 ,i began methodically at the beginning--,by ,royal ,command1 with the lion and unicorn1 and all that comes between4 ,mercy on us6 thought ,i to myself3 has ,her ,majesty referred the question to the ,judicial ,committee of the ,privy ,council1 where all the great difficulties go now-a-days1 and is this proclamation the result8 ,on reading further ,i was relieved by finding that the first side is entirely an advertisement of ,joseph ,gillott's#ehi steel pens1 with engraving of his #caf premises1 and notice of novel application of his unrivalled machinery4 ,the second side begins with the circle rectified by ,w4 ,e4 ,walker1#eij who finds pi #c4adaeidghifbdaee4444 ,this is an off-shoot from an accurate geometrical rectification1 on which is to be presumed ,mr4 ,gillott's new machinery is founded4 ,i have no doubt that ,mr4 ,walker's error1 which is only in the sixth place of decimals1 will not hurt the pens1 unless it be by the slightest possible increase of the tendency to open at the points4 ,this arises from ,mr4 ,walker having rectified above proof by 4#jjjjjbacfjcdcfb4444 ,lastly1 ,i1 even ,i myself1 who have long felt that ,i was a quadrature below par1 have solved the problem by means which1 in the present state of the law of libel1 ,i dare not divulge4 ,but the result is permitted2 and it goes far to explain all the discordances4 ,the ratio of the circumference to the diameter is not always the same6 ,not that it varies with the radius2 the geometers are right enough on that point3 but it varies with the time1 in a manner depending upon the difference of the true longitudes of the ,sun and ,moon4 ,a friend of mine--at least until he misbehaved--insisted on the mean right ascensions3 but ,i served him as ,abraham served his guest in ,franklin's parable4 ,the true formula is1 ,a and a being the ,sun's and ,moon's longitudes1 pi #c-ac_/hj #c_/hj cos7,a - a74 ,mr4 ,james ,smith obtained his quadrature at full moon2 the ,archpriest of ,st4 ,vitus and some others at new moon4 ,until ,i can venture to publish the demonstration1 ,i recommend the reader to do as ,i do1 which is to adopt #c4adaei4441 and to think of the matter only at the two points of the lunar month at which it is correct4 ,the ,nautical ,almanac will no doubt give these points in a short time3 ,i am in correspondence with the ,admiralty1 with nothing #cag to get over except what ,i must call a perverse notion on the part of the ,superintendent of the ,almanac1 who suspects one correction depending on the ,moon's latitude2 and the ,astronomer ,royal leans towards another depending on the date of the ,queen's accession4 ,i have no patience with these men3 what can the ,moon's node of the ,queen's reign possibly have to do with the ratio in question8 ,but this is the way with all the regular men of science2 ,newton is to them etc4 etc4 etc4 etc4 ,the following method of finding the circumference of a circle 7taken from a paper by ,mr4 ,s4 ,drach#eia in the ,phil4 ,mag41 ,jan4 #ahfc1 ,suppl47 is as accurate as the use of #c4adaeibfe4 ,from three diameters deduct #h-thousandths and #g-millionths of a diameter2 to the result add five per cent4 ,we have then not quite enough2 but the shortcoming is at the rate of about an inch and a sixtieth of an inch in #ad1jjj miles4 ,,jacob ,,behmen4 ,though ,i have met with nothing but a little tract from the school of ,jacob ,behmen#eib 7or ,boehme2 ,i keep to the old ,english version of his name71 yet there has been more1 and of a more recent date4 ,i am told of an ,introduction to ,theosophy ,theo private1 ,i suppose1 as in theological2 or1 the ,science of the ,mystery of ,christ1 published in #ahed1 mostly from the writings of ,william ,law#eic3 and also of a volume of #fhh pages1 of the same year1 printed for private circulation1 containing notes for a biography of ,william ,law4 ,the editor of the first work wishes to grow a #cah generation of perfect ,christians by founding a ,theosophic ,college1 for which he requests the public to raise a hundred thousand pounds4 ,there is a good account of ,jacob ,behmen in the ,penny ,cyclopaedia4 ,the author mentions inaccurate accounts1 one of which he quotes1 as follows3 ,he derived all his mystical and rapturous doctrine from ,wood's#eid ,athenae ,oxonienses1 ,vol4 ,i1 p4 #faj1 and ,hist4 et ,antiq4 ,acad4 ,oxon41 ,vol4 ,,ii1 p4 #cjh4 ,on which the author remarks that ,wood was born after ,behmen's death4 ,there must have been a few words which slipped out3 what is meant is that ,behmen derived his doctrine from ,robert ,fludd1#eie for whom see ,wood's etc4 etc4 ,even this is absurd enough3 for ,behmen began to publish in #afaj1 and ,fludd in #afaf4 ,fludd was a ,rosicrucian1 and a mystic of a different type from ,behmen4 ,i have some of his works1 and could produce out of them paradoxes enough1 according to our ways of thinking1 to fit out a host4 ,but the ,rosicrucian system was a recognized school of its day1 and ,fludd1 a man of great learning1 had abettors enough in all which he advanced1 and predecessors in most of it4 ,a ,correspondent has recently sent a short summary of the claims of ,jacob ,behmen to rank higher than ,i have placed him4 ,i shall gladly insert this summary in the book ,i contemplate1 as a statement of what is said of ,behmen far less liable to suspicion of exaggeration than anything ,i could write4 ,i shall add a few extracts from ,behmen himself1 in support of his right to be in my list4 ,jacob ,behmen4--,that ,prof4 ,de ,morgan classes ,jacob ,behmen among paradoxers can only be attributed to the fact of his being avowedly unacquainted with the writings #cai of that author4 ,perhaps you may think a few words from one who knows them well of sufficient interest to the learned ,professor1 and your readers in general1 to be worthy of space in your columns4 ,the metaphysical system of ,behmen--the most perfect and only true one--still awaits a qualified commentator4 ,behmen's countryman1 ,dionysius ,andreas ,freher1#eif who spent the greater part of his life in this country1 and whose exposition of ,behmen exists only in ,,ms41 filling many volumes1 written in ,english1 with the exception of two1 written in ,german1 with numerous beautiful1 highly ingenious1 and elaborate illustrations1--copies of some of which are in the ,british ,museum1 but all the originals of which are in the possession of the gentleman who is the editor of the two works alluded to by ,professor ,de ,morgan1--this ,freher was the first to philosophically expound ,behmen's system1 which was afterwards1 with the help of these ,,mss41 as it were1 popularized by ,william ,law2 but both ,freher and ,law confined themselves chiefly to its theological aspect4 ,in ,behmen1 however1 is to be found1 not only the true ground of all theology1 but also that of all physical science4 ,he demonstrated with a fullness1 accuracy1 completeness and certainty that leave nothing to be desired1 the innermost ground of ,deity and ,nature2 and1 confining myself to the latter1 ,i can from my own knowledge assert1 that in ,behmen's writings is to be found the true and clear demonstration of every physical fact that has been discovered since his day4 ,thus1 the science of electricity1 which was not yet in existence when he wrote1 is there anticipated2 and not only does ,behmen describe all the now known phenomena of that force1 but he even gives us the origin1 generation and birth of electricity itself4 ,again1 positive evidence can be adduced that ,newton derived all his knowledge of gravitation and its #cbj laws from ,behmen1 with whom gravitation or attraction is1 and very properly so1 as he shows us1 the first of the seven properties of ,nature4 ,the theory defended by ,mr4 ,grove1#eig at the ,nottingham meeting of last year1 that all the apparently distinct causes of moral and physical phenomena are but so many manifestations of one central force1 and that ,continuity is the law of nature1 is clearly laid down1 and its truth demonstrated1 by ,behmen1 as well as the distinction between spirit and matter1 and that the moral and material world is pervaded by a sublime unity4 ,and though all this was not admitted in ,behmen's days1 because science was not then sufficiently advanced to understand the deep sense of our author1 many of his passages1 then unintelligible1 or apparently absurd1 read by the light of the present age1 are found to contain the positive enunciation of principles at whose discovery and establishment science has only just arrived by wearisome and painful investigations4 ,every new scientific discovery goes to prove his profound and intuitive insight into the most secret workings of nature2 and if scientific men1 instead of sharing the prejudice arising from ignorance of ,behmen's system1 would place themselves on the vantage ground it affords1 they would at once find themselves on an eminence whence they could behold all the arcana of nature4 ,behmen's system1 in fact1 shows us the inside of things1 while modern physical science is content with looking at the outside4 ,behmen traces back every outward manifestation or development to its one central root1--to that one central energy which1 as yet1 is only suspected2 every link in the chain of his demonstration is perfect1 and there is not one link wanting4 ,he carries us from the out-births of the circumference1 along the radius to the center1 #cba or point1 and beyond that even to the zero1 demonstrating the constitution of the zero1 or nothing1 with mathematical precision4 ,c4 ,w4 ,h4 ,and so ,behmen is no subject for the ,budget6 ,i waited until ,i should chance to light on one of his volumes1 knowing that any volume would do1 and almost any page4 ,my first hap was on the second volume of the edition of #affd 7#dto1 published by ,m4 ,richardson7 and opening near the beginning1 a turn or two brought me to page #ac1 where ,i saw about sulphur and mercurius as follows3 ,thus ,,sul is the soul1 in an herb it is the oil1 and in man also1 according to the spirit of this world in the third principle1 which is continually generated out of the anguish of the will in the mind1 and the ,brimstone-worm is the ,spirit1 which hath the fire and burneth3 ,,phur is the sour wheel in itself which causeth that4 ,mercurius comprehendeth all the four forms1 even as the life springeth up1 and yet hath not its dark beginning in the ,center as the ,,phur hath1 but after the flash of fire1 when the sour dark form is terrified1 where the hardness is turned into pliant sharpness1 and where the second will 7viz4 the will of nature1 which is called the ,anguish7 ariseth1 there ,mercurius hath its original4 ,for ,,mer is the shivering wheel1 very horrible1 sharp1 venomous1 and hostile2 which assimulateth it thus in the sourness in the flash of fire1 where the sour wrathful life ariseth4 ,the syllable ,,cu is the pressing out1 of the ,anxious will of the mind1 from ,nature3 which is climbing up1 and willeth to be out aloft4 ,,ri is the comprehension of the flash of fire1 which in ,,mer giveth a clear sound and tune4 ,for the flash maketh the tune1 and it is the ,salt-,spirit which soundeth1 and its form 7or quality7 is gritty like sand1 and herein arise noises1 sounds and voices1 and thus ,,cu comprehendeth the flash1 and so the pressure is as a wind which thrusteth1 and giveth a spirit to the flash1 so that it liveth and burneth4 ,thus the #cbb syllable ,,us is called the burning fire1 which with the spirit continually driveth itself forth3 and the syllable ,,cu presseth continually upon the flash4 ,shades of ,tauler#eih and ,paracelsus1#eii how strangely you do mix6 ,well may ,hallam call ,germany the native soil of ,mysticism4 ,had ,behmen been the least of a scholar1 he would not have divided sulph-ur and merc-ur-i-us as he has done3 and the inflexion us1 that boy of all work1 would have been rejected4 ,i think it will be held that a writer from whom hundreds of pages like the above could be brought together1 is fit for the ,budget4 ,if ,sampson ,arnold ,mackay#fjj had tied his etymologies to a mystical ,christology1 instead of a mystical infidelity1 he might have had a school of followers4 ,the nonsense about ,newton borrowing gravitation from ,behmen passes only with those who know neither what ,newton did1 nor what was done before him4 ,the above reminds me of a class of paradoxers whom ,i wonder that ,i forgot2 they are without exception the greatest bores of all1 because they can put the small end of their paradox into any literary conversation whatever4 ,i mean the people who have heard the local pronunciation of celebrated names1 and attempt not only to imitate it1 but to impose on others their broken ,german or ,arabic1 or what not4 ,they also learn the vernacular names of those who are generally spoken of in their ,latin forms2 at least1 they learn a few cases1 and hawk them as evidences of erudition4 ,they are miserably mistaken3 scholarship1 as a rule1 #cbc always accepts the vernacular form of a name which has vernacular celebrity4 ,hallam writes ,behmen3 his index-maker1 rather superfluously1 gives ,behmen or ,boehm4 ,and he retains ,melanchthon1#fja the name given by ,reuchlin#fjb to his little kinsman ,schwartzerd1 because the world has adopted it3 but he will none of ,capnio1 the name which ,reuchlin fitted on to himself1 because the world has not adopted it4 ,he calls the old forms pedantry3 but he sees that the rejection of well-established results of pedantry would be greater pedantry still4 ,the paradoxers assume the question that it is more correct to sound a man by lame imitation of his own countrymen than as usual in the country in which the sound is to be made4 ,against them are1 first1 the world at large2 next1 an overpowering majority of those who know something about surnames and their history4 ,some thirty years ago--a fact--there appeared at the police-office a complainant who found his own law4 ,in the course of his argument1 he asked1 ,what does ,kitty say8--,who's ,kitty8 said the magistrate1 your wife1 or your nurse8--,sir6 ,i mean ,kitty1 the celebrated lawyer4--,oh6 said the magistrate1 ,i suspect you mean ,mr4 ,chitty1#fjc the author of the great work on pleading4--,i do sir6 ,but ,chitty is an ,italian name1 and ought to be pronounced ,kitty4 ,this man was a full-blown flower3 but there is many a modest bud2 and all ought either to blush when seen or to waste their pronunciation on the desert air4 #cbd ,a ,,plea ,,for ,,king ,,custom4 ,i stand up for ,king ,custom1 or ,usus1 as ,horace called him1 with whom is arbitrium the decision1 and jus the right1 and norma the way of deciding1 simply because he has potestas the power4 ,he may admit one and another principle to advise3 but ,custom is not a constitutional king2 he may listen to his cabinet1 but he decides for himself3 and if the ministry should resign1 he blesses his stars and does without them4 ,we have a glorious liberty in ,england of owning neither dictionary1 grammar1 nor spelling-book3 as many as choose write by either of the three1 and decide all disputed points their own way1 those following them who please4 ,throughout this book ,i have called people by the names which denote them in their books1 or by our vernacular names4 ,this is the intelligible way of proceeding4 ,i might1 for instance 7,vol4 ,i1 p4 #dd71 have spoken of ,charles de ,bovelles1#fjd of ,lefevre d',etaples1#fje of ,pelerin1#fjf and of ,etienne4#fjg ,but ,i prefer the old plan4 ,those who like another plan better1 are welcome to substitute with a pen1 when they know what to write2 when they do not1 it is clear that they would not have understood me if ,i had given modern names4 ,the principal advisers of ,king ,custom are as follows4 ,first1 there is ,etymology1 the chiffonnier1 or general rag-merchant1 who has made such a fortune of late years in his own business that he begins to be considered highly respectable4 ,he gives advice which is more thought of than followed1 partly on account of the fearful extremes into which he runs4 ,he lately asked some boys of sixteen1 at a matriculation examination in ,english1 to what branch of #cbe the ,indo-,germanic family they felt inclined to refer the ,pushto language1 and what changes in the force of the letters took place in passing from ,greek into ,moeso-,gothic4 ,because all syllables were once words1 he is a little inclined to insist that they shall be so still4 ,he would gladly rule ,english with a ,saxon rod1 which might be permitted with a certain discretion which he has never attained3 and when opposed1 he defends himself with analogies of the ,aryan family until those who hear him long for the discovery of an ,athanasyus4 ,he will transport a word beyond seas--he is recorder of ,rhematopolis--on circumstantial evidence which looks like mystery gone mad2 but1 strange to say1 something very often comes to light after sentence is passed which proves the soundness of the conviction4 ,the next adviser is ,logic1 a swearing old justice of peace1 quorum1 and rotulorum1 whose excesses brought on such a fit of the gout that for many years he was unable to move4 ,he is now mending1 and his friends say he has sown his wild oats4 ,he has some influence with the educated subjects of ,custom1 and will have more1 if he can learn the line at which interference ought to stop3 with them he has succeeded in making an affirmative of two negatives2 but the vulgar won't never have nothing to say to him4 ,he has always railed at ,milton for writing that ,eve was the fairest of her daughters2 but has never satisfactorily shown what ,milton ought to have said instead4 ,the third adviser has more influence with the mass of the subjects of ,king ,custom than the other two put together2 his name is ,fiddlefaddle1 the toy-shop keeper2 and the other two put him forward to do their worst work4 ,in return1 he often uses their names without authority4 ,he took ,etymology to witness that means to an end must be plural3 and he would have any one method to be a mean4 ,but ,etymology proved him wrong1 ,king ,custom referred him to his ,catechism1 in which is a means whereby we receive the same1 and ,analogy--a subordinate of #cbf ,etymology--asked whether he thought it a great new to hear that he was wrong4 ,it was either this ,fiddlefaddle1 or ,lindley ,murray#fjh his traveler1 who persuaded the ,miss ,slipslops1 of the ,ladies ,seminary1 to put ,the ,misses ,slipslop over the gate4 ,sixty years ago1 this bagman called at all the girls' schools1 and got many of the teachers to insist on the pupils saying ,is it not and ,can ,i not for ,isn't it and ,can't ,i3 of which it came that the poor girls were dreadfully laughed at by their irreverent brothers when they went home for the holidays4 ,had this bad adviser not been severely checked1 he might by this time have proposed our saying ,the ,queen's of ,england son1 declaring1 in the name of ,logic1 that the prince was the ,queen's son1 not ,england's4 ,lastly1 there is ,typography the metallurgist1 an executive officer who is always at work in secret1 and whose lawless mode of advising is often done by carrying his notions into effect without leave given4 ,he it is who never ceases suggesting that the same word is not to occur in a second place within sight of the first4 ,when the ,authorized ,version was first printed1 he began this trick at the passage1 ,let there be light1 and there was light2 he drew a line on the proof under the second light1 and wrote luminosity8 opposite4 ,he is strongest in the punctuations and other signs2 he has a pepper-box full of commas always by his side4 ,he puts everything under marks of quotation which he has ever heard before4 ,an earnest preacher1 in a very moving sermon1 used the phrase ,alas6 and alack a day6 ,typography stuck up the inverted commas because he had read the old ,anglo-,indian toast1 ,a lass and a lac a day6 ,if any one should have the sense to leave out of his ,greek #cbg the unmeaning scratches which they call accents1 he goes to a lexicon and puts them in4 ,he is powerful in routine2 but when two routines interlace or overlap1 he frequently takes the wrong one4 ,subject to bad advice1 and sometimes misled for a season1 ,king ,custom goes on his quiet way and is sure to be right at last4 ,treason does never prosper3 what's the reason8 ,why1 when it prospers1 none dare call it treason4 ,language is in constant fermentation1 and all that is thrown in1 so far as it is not fit to assimilate1 is thrown off2 and this without any obvious struggle4 ,in the meanwhile every one who has read good authors1 from ,shakspeare downward1 knows what is and what is not ,english2 and knows1 also1 that our language is not one and indivisible4 ,two very different turns of phrase may both be equally good1 and as good as can be3 we may be relieved of the consequences of contempt of one court by habeas corpus issuing out of another4 ,,test ,,of ,,language4 ,hallam remarks that the ,authorized ,version of the ,bible is not in the language of the time of ,james the ,first3 that it is not the ,english of ,raleigh or of ,bacon4 ,here arises the question whether ,raleigh and ,bacon are the true expositors of the language of their time2 and whether they were not rather the incipient promoters of a change which was successfully resisted by--among other things--the ,authorized ,version of the ,testaments4 ,i am not prepared to concede that ,i should have given to the ,english which would have been fashioned upon that of ,bacon by imitators1 such as they usually are1 the admiration which is forced from me by ,bacon's ,english from ,bacon's pen4 ,on this point we have a notable parallel4 ,samuel ,johnson #cbh commands our admiration1 at least in his matured style3 but we nauseate his followers4 ,it is an opinion of mine that the works of the leading writers of an age are seldom the proper specimens of the language of their day1 when that language is in its state of progression4 ,i judge of a language by the colloquial idiom of educated men3 that is1 ,i take this to be the best medium between the extreme cases of one who is ignorant of grammar and one who is perched upon a style4 ,dialogue is what ,i want to judge by1 and plain dialogue3 so ,i choose ,robert ,recorde#fji and his pupil in the ,castle of ,knowledge1 written before #aeef4 ,when ,dr4 ,robert gets into his altitudes of instruction1 he differs from his own common phraseology as much as probably did ,bacon when he wrote morals and philosophy4 ,but every now and then ,i come to a little plain talk about a common thing1 of which ,i propose to show a specimen4 ,anything can be made to look old by such changes as makes into maketh1 with a little old spelling4 ,i shall invert these changes1 using the newer form of inflexion1 and the modern spelling3 with no other variation whatever4 ,scholar4 ,yet the reason of that is easy enough to be conceived1 for when the day is at the longest the ,sun must needs shine the more time1 and so must it needs shine the less time when the day is at the shortest3 this reason ,i have heard many men declare4 ,master4 ,that may be called a crabbed reason1 for it #cbi goes backward like a crab4 ,the day makes not the ,sun to shine1 but the ,sun shining makes the day4 ,and so the length of the day makes not the ,sun to shine long1 neither the shortness of the day causes not sic the ,sun to shine the lesser time1 but contrariwise the long shining of the ,sun makes the long day1 and the short shining of the ,sun makes the lesser day3 else answer me what makes the days long or short8 ,scholar4 ,i have heard wise men say that ,summer makes the long days1 and ,winter makes the long nights4 ,master4 ,they might have said more wisely1 that long days make summer and short days make winter4 ,scholar4 ,why1 all that seems one thing to me4 ,master4 ,is it all one to say1 ,god made the earth1 and the earth made ,god8 ,covetousness overcomes all men1 and all men overcome covetousness8 ,scholar4 ,no1 not so2 for here the effect is turned to be the cause1 and the agent is made the patient4 ,master4 ,so is it to say ,summer makes long days1 when you should say3 ,long days make summer4 ,scholar4 ,i perceive it now3 but ,i was so blinded with the vulgar error1 that if you had demanded of me further what did make the summer1 ,i had been like to have answered that green leaves do make summer2 and the sooner by remembrance of an old saying that a year should come in which the summer should not be known but by the green leaves4 ,master4 ,yet this saying does not import that green leaves do make summer1 but that they betoken summer2 so are they the sign and not the cause of summer4 ,i have taken a whole page of our author1 without omission1 that the reader may see that ,i do not pick out sentences convenient for my purpose4 ,i have done nothing but alter the third person of the verb and the spelling3 but great is the effect thereof4 ,we say the ,sun shining makes the day2 ,recorde1 the ,sonne shynynge maketh the daye4 #ccj ,these points apart1 we see a resemblance between our ,english and that of three hundred years ago1 in the common talk of educated persons1 which will allow us to affirm that the language of the authorized ,bible must have been very close to that of its time4 ,for ,i cannot admit that much change can have taken place in fifty years3 and the language of the version represents both our common ,english and that of ,recorde with very close approximation4 ,take sentences from ,bacon and ,raleigh1 and it will be apparent that these writers will be held to differ from all three1 ,recorde1 the version1 and ourselves1 by differences of the same character4 ,but we speak of ,recorde's conversation1 and of our own4 ,we conclude that it is the plain and almost colloquial character of the ,authorized ,version which distinguishes it from the ,english of ,bacon and ,raleigh1 by approximating it to the common idiom of the time4 ,if any one will cast an eye upon the letters of instruction written by ,cecil#faj and the ,bishop of ,london to the translators themselves1 or to the general directions sent to them in the ,king's name1 he will find that these plain business compositions differ from the ,english of ,bacon and ,raleigh by the same sort of differences which distinguish the version itself4 ,,pronunciation4 ,the foreign word1 or the word of a district1 or class of people1 passes into the general vernacular2 but it is long before the specially learned will acknowledge the right of those with whom they come in contact to follow general usage4 ,the rule is simple3 so long as a word is technical or local1 those who know its technical or local pronunciation may reasonably employ it4 ,but when the word has become general1 the specialist is not very wise if he refuse to follow #cca the mass1 and perfectly foolish if he insist on others following him4 ,there have been a few who demanded that ,euler should be pronounced in the ,german fashion3#faa ,euler has long been the property of the world at large2 what does it matter how his own countrymen pronounce the letters8 ,shall we insist on the ,french pronouncing ,newton without that final tong which they never fail to give him8 ,they would be wise enough to laugh at us if we did4 ,we remember that a pedant who was insisting on all the pronunciations being retained1 was met by a maxim in contradiction1 invented at the moment1 and fathered upon ,kaen-foo-tzee1#fab an authority which he was challenged to dispute4 ,whom did you speak of8 said the bewildered man of accuracy4 ,learn your own system1 was the answer1 before you impose it on others2 ,confucius says that too4#fac ,the old ,english has fote1 fode1 loke1 coke1 roke1 etc41 for foot1 etc4 ,and above rhymes in ,chaucer to remove4 ,suspecting that the broader sounds are the older1 we may surmise that remove and food have retained their old sounds1 and that cook1 once coke1 would have rhymed to our ,luke1 the vowel being brought a little nearer1 perhaps1 to the o in our present coke1 the fuel1 probably so called as used by cooks4 ,if this be so1 the ,chief ,justice ,cook#fad of our lawyers1 and the ,coke 7pronounced like the fuel7 of the greater part of the world1 are equally wrong4 ,the lawyer has no right whatever to fasten his pronunciation upon us3 even leaving aside the general custom1 he cannot prove himself right1 and is probably wrong4 ,those who #ccb know the village of ,rokeby 7pronounced ,rookby7 despise the world for not knowing how to name ,walter ,scott's poem3 that same world never asked a question about the matter1 and the reception of the parody of ,jokeby1 which soon appeared1 was a sufficient indication of their notion4 ,those who would fasten the hodiernal sound upon us may be reminded that the question is1 not what they call it now1 but what it was called in ,cromwell's time4 ,throw away general usage as a lawgiver1 and this is the point which emerges4 ,probably ,ruke-by would be right1 with a little turning of the ,italian u towards o of modern ,english4 ,some of the above is from an old review4 ,i do not always notice such insertions3 ,i take nothing but my own writings4 ,a friend once said to me1 ,ah6 you got that out of the ,athenaeum6 ,excuse me1 said ,i4 the ,athenaeum got that out of me6 ,,apologies ,,to ,,cluvier4 ,it is part of my function to do justice to any cyclometers whose methods have been wrongly described by any orthodox sneerers 7myself included74 ,in this character ,i must notice ,dethlevus ,cluverius1#fae as the ,leipzig ,acts call him 7probably ,dethleu ,cluvier71 grandson of the celebrated geographer1 ,philip ,cluvier4 ,the grandson was a ,fellow of the ,royal ,society1 elected on the same day as ,halley1#faf ,november #cj1 #afgh3 ,i suppose he lived in ,england4 ,this #ccc man is quizzed in the ,leipzig ,acts for #afhf2 and1 if ,montucla insinuate rightly1 by ,leibnitz1 who is further suspected of wanting to embroil ,cluvier with his own opponent ,nieuwentiit1#fag on the matter of infinitesimals4 ,so far good3 ,i have nothing against ,leibnitz1 who though he was ironical1 told us what he laughed at4 ,but ,montucla has behaved very unfairly3 he represents ,cluvier as placing the essence of his method in the solution of the problem construere mundum divinae menti analogum1 to construct a world corresponding to the divine mind4 ,nothing to begin with3 no way of proceeding4 ,now1 it ought to have been ex data linea construere1#fah etc43 there is a given line1 which is something to go on4 ,further1 there is a way of proceeding3 it is to find the product of #a1 #b1 #c1 #d1 etc4 for ever4 ,moreover1 ,montucla charges ,cluvier with unsquaring the parabola1 which ,archimedes had squared as tight as a glove4 ,but he never mentions how very nearly ,cluvier agrees with the ,greek3 they only differ by #a divided by #cn#b1 where n is the infinite number of parts of which a parabola is composed4 ,this must have been the conceit that tickled ,leibnitz1 and made him wish that ,cluvier and ,nieuwentiit should fight it out4 ,cluvier1 was admitted1 on terms of irony1 into the ,leipzig ,acts3 he appeared on a more serious footing in ,london4 ,it is very rare for one cyclometer to refute another3 les corsaires ne se battent pas4#fai ,the only instance ,i recall is that of ,m4 ,cluvier1 who 7,phil4 ,trans41 #afhf1 ,no4 #ahe7 refuted ,m4 ,mallemont de ,messange1#fbj who #ccd published at ,paris in #afhf4 ,he does it in a very serious style1 and shows himself a mathematician4 ,and yet in the year in which1 in the ,phil4 ,trans41 he was a geometer1 and one who rebukes his squarer for quoting ,matthew xi4 #be1 in that very year he was the visionary who1 in the ,leipzig ,acts1 professed to build a world resembling the divine mind by multiplying together #a1 #b1 #c1 #d1 etc4 up to infinity4 ,,the ,,rainbow ,,paradox4 ,there is a very pretty opening for a paradox which has never found its paradoxer in print4 ,the philosophers teach that the rainbow is not material3 it comes from rain-drops1 but those rain-drops do not take color4 ,they only give it1 as lenses and mirrors2 and each one drop gives all the colors1 but throws them in different directions4 ,accordingly1 the same drop which furnishes red light to one spectator will furnish violet to another1 properly placed4 ,enter the paradoxer whom ,i have to invent4 ,the philosopher has gulled you nicely4 ,look into the water1 and you will see the reflected rainbow3 take a looking-glass held sideways1 and you see another reflection4 ,how could this be1 if there were nothing colored to reflect8 ,the paradoxer's facts are true3 and what are called the reflected rainbows are other rainbows1 caused by those other drops which are placed so as to give the colors to the eye after reflection1 at the water or the looking-glass4 ,a few years ago an artist exhibited a picture with a rainbow and its apparent reflection3 he simply copied what he had seen4 ,when his picture was examined1 some started the idea that there could be no reflection of a rainbow2 they were right3 they inferred that the artist had made a mistake2 they were wrong4 ,when it was explained1 some agreed and some dissented4 ,wanted1 #cce immediately1 an able paradoxer3 testimonials to be forwarded to either end of the rainbow1 ,no4 #a4 ,no circle-squarer need apply1 ,his ,variegatedness having been pleased to adopt #c4adaei444 from ,noah downwards4 ,,tycho ,,brahe ,,revived4 ,the system of ,tycho ,brahe1#fba with some alteration and addition1 has been revived and contended for in our own day by a ,dane1 ,w4 ,zytphen1#fbb who has published ,the ,motion of the ,sun in the ,universe1 7second edition7 ,copenhagen1 #ahfe1 #hvo1 and ,le ,mouvement ,sideral1 #ahfe1 #hvo4 ,i make an extract4 ,how can one explain ,copernically that the velocity of the ,moon must be added to the velocity of the ,earth on the one place in the ,earth's orbit1 to learn how far the ,moon has advanced from one fixed star to another2 but in another place in the orbit these velocities must be subtracted 7the movements taking place in opposite directions7 to attain the same result8 ,in the ,copernican and other systems1 it is well known that the ,moon1 abstracting from the insignificant excentricity of the orbit1 always in twenty-four hours performs an equally long distance4 ,why has ,copernicus never been denominated ,fundamentus or ,fundator8 ,because he has never convinced anybody so thoroughly that this otherwise so natural epithet has occurred to the mind4 ,really the second question is more effective against ,newton than against ,copernicus2 for it upsets gravity3 the first is of great depth4 #ccf ,,james ,,smith ,,will ,,not ,,down4 ,the ,correspondent journal makes a little episode in the history of my ,budget 7born ,may1 #ahfe1 died ,april1 #ahff74 ,it consisted entirely of letters written by correspondents4 ,in ,august1 a correspondent who signed ,fair ,play--and who ,i was afterwards told was a lady--thought it would be a good joke to bring in the ,cyclometers4 ,accordingly a letter was written1 complaining that though ,mr4 ,sylvester's#fbc demonstration of ,newton's theorem--then attracting public attention--was duly lauded1 the possibly greater discovery of the quadrature seemed to be blushing unseen1 and wasting etc4 ,it went on as follows3 ,prof4 ,de ,morgan1 who1 from his position in the scientific world1 might fairly afford to look favourably on less practised efforts than his own1 seems to delight in ridiculing the discoverer4 ,science is1 of course1 a very respectable person when he comes out and makes himself useful in the world it must have been a lady2 each sex gives science to the other3 but when1 like a monk of the ,middle ,ages1 he shuts himself up it must have been a lady2 they always snub the bachelors in his cloistered cell1 repeating his mumpsimus from day to day1 and despising the labourers on the outside1 we begin to think of ,galileo1#fbd ,jenner1#fbe ,harvey1#fbf and other glorious trios1 who have been contemned 444 ,the writer then called upon ,mr4 ,james ,smith#fbg to come #ccg forward4 ,the irony was not seen2 and that day fortnight appeared the first of more than thirty letters from his pen4 ,mr4 ,smith was followed by ,mr4 ,reddie1#fbh ,zadkiel1#fbi and others1 on their several subjects4 ,to some of the letters ,i have referred2 to others ,i shall come4 ,the ,correspondent was to become a first-class scientific journal2 the time had arrived at which truth had an organ3 and ,i received formal notice that ,i could not stifle it by silence1 nor convert it into falsehood by ridicule4 ,when my reader sees my extracts1 he will readily believe my declaration that ,i should have been the last to stifle a publication which was every week what ,james ,mill#fcj would call a dose of capital for my ,budget4 ,a few anti-paradoxers brought in common sense3 but to the mass of the readers of the journal it all seemed to be the difference between ,tweedledum and ,tweedledee4 ,some said that the influx of scientific paradoxes killed the journal3 but my belief is that they made it last longer than it otherwise would have done4 ,twenty years ago ,i recommended the paradoxers to combine and publish their views in a common journal3 with a catholic editor1 who had no pet theory1 but a stern determination not to exclude anything merely for absurdity4 ,i suspect it would answer very well4 ,a strong title1 or motto1 would be wanted3 not so coarse as was roared out in a ,cambridge mob when ,i was an undergraduate--,no ,king6 ,no ,church6 ,no ,house of ,lords6 ,no nothing1 blast me6--but something on that principle4 ,at the end of #ahfg ,i addressed the following letter to the ,athenaeum3 ,,pseudomath1 ,,philomath1 ,,and ,,graphomath4 ,december #ca1 #ahfg ,many thanks for the present of ,mr4 ,james ,smith's letters #cch of ,sept4 #bh and of ,oct4 #aj and #ab4 ,he asks where you will be if you read and digest his letters3 you probably will be somewhere first4 ,he afterwards asks what the ,,we of the ,athenaeum will be if1 finding it impossible to controvert1 it should refuse to print4 ,i answer for you1 that ,we-,we of the ,athenaeum1 not being ,wa-,wa the wild goose1 so conspicuous in ,hiawatha1 will leave what controverts itself to print itself1 if it please4 ,philomath is a good old word1 easier to write and speak than mathematician4 ,it wants the words between which ,i have placed it4 ,they are not well formed3 pseudomathete and graphomathete would be better3 but they will do4 ,i give an instance of each4 ,the pseudomath is a person who handles mathematics as the monkey handled the razor4 ,the creature tried to shave himself as he had seen his master do2 but1 not having any notion of the angle at which the razor was to be held1 he cut his own throat4 ,he never tried a second time1 poor animal6 but the pseudomath keeps on at his work1 proclaims himself clean-shaved1 and all the rest of the world hairy4 ,so great is the difference between moral and physical phenomena6 ,mr4 ,james ,smith is1 beyond doubt1 the great pseudomath of our time4 ,his #c-a_/h is the least of a wonderful chain of discoveries4 ,his books1 like ,whitbread's barrels1 will one day reach from ,simpkin ,marshall's to ,kew1 placed upright1 or to ,windsor laid length-ways4 ,the ,queen will run away on their near approach1 as ,bishop ,hatto did from the rats3 but ,mr4 ,james ,smith will follow her were it to ,john o' ,groats4 ,the philomath1 for my present purpose1 must be exhibited as giving a lesson to presumption4 ,the following anecdote is found in ,thiebault's#fca ,souvenirs de vingt ans de sejours a ,berlin1 published in #ahjd4 ,the book itself got a high character for truth4 ,in #ahjg ,marshal ,mollendorff#fcb #cci answered an inquiry of the ,duc de ,bassano1#fcc by saying that it was the most veracious of books1 written by the most honest of men4 ,thiebault does not claim personal knowledge of the anecdote1 but he vouches for its being received as true all over the north of ,europe4#fcd ,diderot#fce paid a visit to ,russia at the invitation of ,catherine the ,second4 ,at that time he was an atheist1 or at least talked atheism3 it would be easy to prove him either one thing or the other from his writings4 ,his lively sallies on this subject much amused the ,empress1 and all the younger part of her ,court4 ,but some of the older courtiers suggested that it was hardly prudent to allow such unreserved exhibitions4 ,the ,empress thought so too1 but did not like to muzzle her guest by an express prohibition3 so a plot was contrived4 ,the scorner was informed that an eminent mathematician had an algebraical proof of the existence of ,god1 which he would communicate before the whole ,court1 if agreeable4 ,diderot gladly consented4 ,the mathematician1 who is not named1 was ,euler4#fcf ,he came to ,diderot with the gravest air1 and in a tone of perfect conviction said1 ,monsieur6 7a bn7_/n x donc ,dieu existe2 repondez6#fcg ,diderot1 to whom algebra was ,hebrew1 though this is expressed in a very roundabout way by ,thiebault--and whom we may suppose to have expected some verbal argument of alleged algebraical closeness1 was disconcerted2 while peals of laughter sounded on all sides4 ,next day he asked permission to return to ,france1 which was granted4 ,an algebraist would have #cdj turned the tables completely1 by saying1 ,monsieur6 vous savez bien que votre raisonnement demande le developpement de x suivant les puissances entieres de n4#fch ,goldsmith could not have seen the anecdote1 or he might have been supposed to have drawn from it a hint as to the way in which the ,squire demolished poor ,moses4 ,the graphomath is a person who1 having no mathematics1 attempts to describe a mathematician4 ,novelists perform in this way3 even ,walter ,scott now and then burns his fingers4 ,his dreaming calculator1 ,davy ,ramsay1 swears by the bones of the immortal ,napier4 ,scott thought that the the philomaths worshiped relics3 so they do1 in one sense4 ,look into ,hutton's#fci ,dictionary for ,napier's ,bones1 and you shall learn all about the little knick-knacks by which he did multiplication and division4 ,but never a bone of his own did he contribute2 he preferred elephants' tusks4 ,the author of ,headlong ,hall#fdj makes a grand error1 which is quite high science3 he says that ,laplace proved the precession of the equinoxes to be a periodical inequality4 ,he should have said the variation of the obliquity4 ,but the finest instance is the following3 ,mr4 ,warren1#fda in his well-wrought tale of the martyr-philosopher1 was incautious enough to invent the symbols by which his savant satisfied himself ,laplace#fdb was right on a doubtful point4 ,and this is what he put together-- sqrt-#c;a#b1 rectangley#b _/ z#b #i - n #i1 n x log e4 ,now1 to ,diderot and the mass of mankind this might be ,laplace all over3 and1 in a forged note of ,pascal1 would #cda prove him quite up to gravitation4 ,but ,i know of nothing like it1 except in the lately received story of the ,american orator1 who was called on for some ,latin1 and perorated thus3 ,committing the destiny of the country to your hands1 ,gentlemen1 ,i may without fear declare1 in the language of the noble ,roman poet1 ,e pluribus unum1 ,multum in parvo1 ,ultima ,thule1 ,sine qua non4#fdc ,but the ,american got nearer to ,horace than the martyr-philosopher to ,laplace4 ,for all the words are in ,horace1 except ,thule1 which might have been there4 ,but rectangle is not a symbol wanted by ,laplace2 nor can we see how it could have been2 in fact1 it is not recognized in algebra4 ,as to the junctions1 etc41 ,laplace and ,horace are about equally well imitated4 ,further thanks for ,mr4 ,smith's letters to you of ,oct4 #ae1 #ah1 #ai1 #bh1 and ,nov4 #d1 #ae4 ,the last of these letters has two curious discoveries4 ,first1 ,mr4 ,smith declares that he has seen the editor of the ,athenaeum3 in several previous letters he mentions a name4 ,if he knew a little of journalism he would be aware that editors are a peculiar race1 obtained by natural selection4 ,they are never seen1 even by their officials2 only heard down a pipe4 ,secondly1 an ellipse or oval is composed of four arcs of circles4 ,mr4 ,smith has got hold of the construction ,i was taught1 when a boy1 for a pretty four-arc oval4 ,but my teachers knew better than to call it an ellipse3 ,mr4 ,smith does not2 but he produces from it such confirmation of #c-a_/h as would convince any honest editor4 ,surely the cyclometer is a ,darwinite development of a spider1 who is always at circles1 and always begins again when his web is brushed away4 ,he informs you that he #cdb has been privileged to discover truths unknown to the scientific world4 ,this we know2 but he proceeds to show that he is equally fortunate in art4 ,he goes on to say that he will make use of you to bring those truths to light1 just as an artist makes use of a dummy for the purpose of arranging his drapery4 ,the painter's lay-figure is for flowing robes2 the hairdresser's dummy is for curly locks4 ,mr4 ,james ,smith should read ,sam ,weller's pathetic story of the four wax dummies4 ,as to his use of a dummy1 it is quite correct4 ,when ,i was at ,university ,college1 ,i walked one day into a room in which my ,latin colleague was examining4 ,one of the questions was1 ,give the lives and fates of ,sp4 ,maelius1#fdd and ,sp4 ,cassius4#fde ,umph6 said ,i1 surely all know that ,spurius ,maelius was whipped for adulterating flour1 and that ,spurius ,cassius was hanged for passing bad money4 ,now1 a robe arranged on a dummy would look just like the toga of ,cassius on the gallows4 ,accordingly1 ,mr4 ,smith is right in the drapery-hanger which he has chosen3 he has been detected in the attempt to pass bad circles4 ,he complains bitterly that his geometry1 instead of being read and understood by you1 is handed over to me to be treated after my scurrilous fashion4 ,it is clear enough that he would rather be handled in this way than not handled at all1 or why does he go on writing8 ,he must know by this time that it is a part of the institution that his untruthful and absurd trash shall be distilled into mine at the rate of about #c-a_/h pages of the first to one column of the second4 ,your readers will never know how much they gain by the process1 until ,mr4 ,james ,smith publishes it all in a big book1 or until they get hold of what he has already published4 ,i have six pounds avoirdupois of pamphlets and letters2 and there is more than half a pound of letters #cdc written to you in the last two months4 ,your compositor must feel aggrieved by the rejection of these clearly written documents1 without erasures1 and on one side only4 ,your correspondent has all the makings of a good contributor1 except the knowledge of his subject and the sense to get it4 ,he is1 in fact1 only a mask3 of whom the fox ,o quanta species1 inquit1 cerebrum non habet4#fdf ,i do not despair of ,mr4 ,smith on any question which does not involve that unfortunate two-stick wicket at which he persists in bowling4 ,he has published many papers2 he has forwarded them to mathematicians3 and he cannot get answers2 perhaps not even readers4 ,does he think that he would get more notice if you were to print him in your journal8 ,who would study his columns8 ,not the mathematician1 we know2 and he knows4 ,would others8 ,his balls are aimed too wide to be blocked by any one who is near the wicket4 ,he has long ceased to be worth the answer which a new invader may get4 ,rowan ,hamilton1#fdg years ago1 completely knocked him over2 and he has never attempted to point out any error in the short and easy method by which that powerful investigator condescended to show that1 be right who may1 he must be wrong4 ,there are some persons who feel inclined to think that ,mr4 ,smith should be argued with3 let those persons understand that he has been argued with1 refuted1 and has never attempted to stick a pen into the refutation4 ,he stated that it was a remarkable paradox1 easily explicable2 and that is all4 ,after this evasion1 ,mr4 ,james ,smith is below the necessity of being told that he is unworthy of answer4 ,his friends complain that ,i do nothing but chaff him4 ,absurd6 ,i winnow him2 and if nothing but chaff results1 whose fault is that8 ,i am usefully employed3 for he is the type of a class which ought to be known1 and which ,i have done much to make known4 #cdd ,nothing came of this until ,july #ahfi1 when ,i received a reprint of the above letter1 with a comment1 described as ,appendix ,d of a work in course of publication on the geometry of the circle4 ,the ,athenaeum journal received the same3 but the ,editor1 in his private capacity1 received the whole work1 being ,the ,geometry of the ,circle and ,mathematics as applied to ,geometry by ,mathematicians1 shown to be a mockery1 delusion1 and a snare1 ,liverpool1 #hvo1 #ahfi4 ,mr4 ,j4 ,s4 here appears in deep fight with ,professor ,whitworth1#fdh and ,mr4 ,wilson1#fdi the author of the alleged amendment of ,euclid4 ,how these accomplished mathematicians could be inveigled into continued discussion is inexplicable4 ,mr4 ,whitworth began by complaining of ,mr4 ,smith's attacks upon mathematicians1 continued to correspond after he was convinced that ,j4 ,s4 proved an arc and its chord to be equal1 and only retreated when ,j4 ,s4 charged him with believing in #c-a_/h1 and refusing acknowledgment4 ,mr4 ,wilson was introduced to ,j4 ,s4 by a volunteer defense of his geometry from the assaults of the ,athenaeum4 ,this the editor would not publish2 so ,j4 ,s4 sent a copy to ,mr4 ,wilson himself4 ,some correspondence ensued1 but ,mr4 ,wilson soon found out his man1 and withdrew4 ,there is a little derision of the ,athenaeum and a merited punishment for that unscrupulous critic and contemptible mathematical twaddler1 ,de ,morgan4 ,,mr4 ,,reddie',s ,,astronomy4 ,at p4 #ahc ,i mentioned ,mr4 ,reddie1#fej the author of ,vis ,inertiae ,victa and of ,victoria toto coelo1#fea which last is not #cde an address to the whole heaven1 either from a ,roman ,goddess or a ,british ,queen1 whatever a scholar may suppose4 ,between these ,mr4 ,reddie has published ,the ,mechanics of the ,heavens1 #hvo1 #ahfb3 this ,i never saw until he sent it to me1 with an invitation to notice it1 he very well knowing that it would catch4 ,his speculations do battle with common notions of mathematics and of mechanics1 which1 to use a feminine idiom1 he blasphemes so you can't think6 and ,i suspect that if you do not blaspheme them too1 you can't think4 ,he appeals to the truly scientific1 and would be glad to have readers who have read what he controverts1 i4e41 ,newton's ,principia3 ,i wish he may get them2 ,i mean ,i hope he may obtain them4 ,to none but these would an account of his speculations be intelligible3 ,i accordingly disposed of him in a very short paragraph of description4 ,now many paradoxers desire notice1 even though it be disparaging4 ,i have letters from more than one--besides what have been sent to the ,editor of the ,athenaeum--complaining that they are not laughed at2 although they deserve it1 they tell me1 as much as some whom ,i have inserted4 ,mr4 ,reddie informs me that ,i have not said a single word against his books1 though ,i have given nearly a column to sixteen-string arithmetic1 and as much to animalcule universes4 ,what need to say anything to readers of ,newton against a book from which ,i quoted that revolution by gravitation is demonstrably impossible8 ,it would be as useless as evidence against a man who has pleaded guilty4 ,mr4 ,reddie derisively thanks me for small mercies2 he wrote me private letters2 he published them1 and more1 in the ,correspondent4 ,he gave me1 pro viribus suis1#feb such a dressing you can't think1 both for my ,budget non-notice1 and for reviews which he assumed me to have written4 ,he outlawed himself by declaring 7,correspondent1 ,nov4 #aa1 #ahef7 that ,i--in a review--had made a quotation which was garbled1 evidently on purpose #cdf to make it appear that he was advocating solely a geocentric hypothesis1 which is not true4 ,in fact1 he did his best to get larger mercy4 ,and he shall have it2 and at a length which shall content him1 unless his mecometer be an insatiable apparatus4 ,but ,i fear that in other respects ,i shall no more satisfy him than the ,irish drummer satisfied the poor culprit when1 after several times changing the direction of the stroke at earnest entreaty1 he was at last provoked to call out1 ,bad cess to ye1 ye spalpeen6 strike where one will1 there's no plasing ye6 ,mr4 ,reddie attaches much force to ,berkeley's#fec old arguments against the doctrine of fluxions1 and advances objections to ,newton's second section1 which he takes to be new4 ,to me they appear such as have been often made1 to copy a description given in a review3 though ,i have no doubt ,mr4 ,reddie got them out of himself4 ,but the whole matter comes to this3 ,mr4 ,reddie challenged answer1 especially from the ,british ,association1 and got none4 ,he presumes that this is because he is right1 and cannot be answered3 the ,association is willing to risk itself upon the counter-notion that he is wrong1 and need not be answered2 because so wrong that none who could understand an answer would be likely to want one4 ,mr4 ,reddie demands my attention to a point which had already particularly struck me1 as giving the means of showing to all readers the kind of confusion into which paradoxers are apt to fall1 in spite of the clearest instruction4 ,it is a very honest blunder1 and requires notice3 it may otherwise mislead some1 who may suppose that no one able to read could be mistaken about so simple a matter1 #cdg let him be ever so wrong about ,newton4 ,according to his own mis-statement1 in less than five months he made the ,astronomer ,royal abandon the theory of the solar motion in space4 ,the announcement is made in ,august1 #ahfe1 as follows3 the italics are not mine3 ,the third 7,victoria 44471 although only published in ,september1 #ahfc1 has already had its triumph4 ,it is the book that forced the ,astronomer ,royal of ,england1 after publicly teaching the contrary for years1 to come to the conclusion1 strange as it may appear1 that the whole question of solar motion in space is at the present time in doubt and abeyance4 ,this admission is made in the ,annual ,report of the ,council of the ,royal ,astronomical ,society1 published in the ,society's ,monthly ,notices for ,february1 #ahfd4 ,it is added that solar motion is full of self-contradiction1 which the astronomers simply overlooked1 but which they dare not now deny after being once pointed out4 ,the following is another of his accounts of the matter1 given in the ,correspondent1 ,no4 #ah1 #ahfe3 444 ,you ought1 when you came to put me in the ',budget1' to have been aware of the ,report of the ,council of the ,royal ,astronomical ,society1 where it appears that ,professor ,airy1#fed with a better appreciation of my demonstrations1 had admitted--'strange1' say the ,council1 'as it may appear1'--that 'the whole question of solar motion in space and here ,mr4 ,reddie omits some words is now in doubt and abeyance4' ,you were culpable as a public teacher of no little pretensions1 if you were 'unaware' of this4 ,if aware of it1 you ought not to have suppressed such an important testimony to my really having been 'very successful' in drawing the teeth of the pegtops1 though you thought them so firmly fixed4 ,and if you still suppress #cdh it1 in your ,appendix1 or when you reprint your ',budget1' you will then be guilty of a suppressio veri1 also of further injury to me1 who have never injured you4444 ,mr4 ,reddie must have been very well satisfied in his own mind before he ventured such a challenge1 with an answer from me looming in the distance4 ,the following is the passage of the ,report of the ,council1 etc41 from which he quotes3 ,and yet1 strange to say1 notwithstanding the near coincidence of all the results of the before-mentioned independent methods of investigation1 the inevitable logical inference deduced by ,mr4 ,airy is1 that the whole question of solar motion in space1 so far at least as accounting for the proper motion of the stars is concerned1 ,i have put in italics the words omitted by ,mr4 ,reddie appears to remain at this moment in doubt and abeyance4 ,mr4 ,reddie has forked me1 as he thinks1 on a dilemma3 if unaware1 culpable ignorance2 if aware1 suppressive intention4 ,but the thing is a trilemma1 and the third horn1 on which ,i elect to be placed1 is surmounted by a doubly-stuffed seat4 ,first1 ,mr4 ,airy has not changed his opinion about the fact of solar motion in space1 but only suspends it as to the sufficiency of present means to give the amount and direction of the motion4 ,secondly1 all that is alluded to in the ,astronomical ,report was said and printed before the ,victoria proclamation appeared4 ,so that the author1 instead of drawing the tooth of the ,astronomer ,royal's pegtop1 has burnt his own doll's nose4 ,william ,herschel1#fee and after him about six other astronomers1 had aimed at determining1 by the proper motions of the stars1 the point of the heavens towards which the solar system is moving3 their results were tolerably accordant4 ,mr4 ,airy1 in #ahei1 proposed an improved method1 and1 applying it to stars of large proper motion1 produced #cdi much the same result as ,herschel4 ,mr4 ,e4 ,dunkin1#fef one of ,mr4 ,airy's staff at ,greenwich1 applied ,mr4 ,airy's method to a very large number of stars1 and produced1 again1 nearly the same result as before4 ,this paper was read to the ,astronomical ,society in ,march1 #ahfc1 was printed in abstract in the ,notice of that month1 was printed in full in the volume then current1 and was referred to in the ,annual ,report of the ,council in ,february1 #ahfd1 under the name of the ,astronomer ,royal's elaborate investigation1 as exhibited by ,mr4 ,dunkin4 ,both ,mr4 ,airy and ,mr4 ,dunkin express grave doubts as to the sufficiency of the data3 and1 regarding the coincidence of all the results as highly curious1 feel it necessary to wait for calculations made on better data4 ,the report of the ,council states these doubts4 ,mr4 ,reddie1 who only published in ,september1 #ahfc1 happened to see the ,report of ,february1 #ahfd1 assumes that the doubts were then first expressed1 and declares that his book of ,september had the triumph of forcing the ,astronomer ,royal to abandon the fact of motion of the solar system by the ,february following4 ,had ,mr4 ,reddie1 when he saw that the ,council were avowedly describing a memoir presented some time before1 taken the precaution to find out when that memoir was presented1 he would perhaps have seen that doubts of the results obtained1 expressed by one astronomer in ,march1 #ahfc1 and by another in #ahei1 could not have been due to his publication of ,september1 #ahfc4 ,and any one else would have learnt that neither astronomer doubts the solar motion1 though both doubt the sufficiency of present means to determine its amount and direction4 ,this is implied in the omitted words1 which ,mr4 ,reddie--whose omission would have been dishonest if he had seen their meaning--no doubt took for pleonasm1 superfluity1 overmuchness4 ,the rashness which pushed him headlong #cej into the quillet that his thunderbolt had stopped the chariot of the ,sun and knocked the ,greenwich ,phaeton off the box1 is the same which betrayed him into yet grander error--which deserves the full word1 quidlibet--about the ,principia of ,newton4 ,there has been no change of opinion at all4 ,when a person undertakes a long investigation1 his opinion is that1 at a certain date1 there is prima facie ground for thinking a sound result may be obtained4 ,should it happen that the investigation ends in doubt upon the sufficiency of the grounds1 the investigator is not put in the wrong4 ,he knew beforehand that there was an alternative3 and he takes the horn of the alternative indicated by his calculations4 ,the two sides of this case present an instructive contrast4 ,eight astronomers produce nearly the same result1 and yet the last two doubt the sufficiency of their means3 compare them with the what's-his-name who rushes in where thing-em-bobs fear to tread4 ,i was not aware1 until ,i had written what precedes1 that ,mr4 ,airy had given a sufficient answer on the point4 ,mr4 ,reddie says 7,correspondent1 ,jan4 #bj1 #ahff73 ,i claim to have forced ,professor ,airy to give up the notion of 'solar motion in space' altogether1 for he admits it to be 'at present in doubt and abeyance4' ,i first made that claim in a letter addressed to the ,astronomer ,royal himself in ,june1 #ahfd1 and in replying1 very courteously1 to other portions of my letter1 he did not gainsay that part of it4 ,mr4 ,reddie is not ready at reading satire1 or he never would have so missed the meaning of the courteous reply on one point1 and the total silence upon another4 ,mr4 ,airy must be one of those peculiar persons who1 when they do not think an assertion worth notice1 let it alone1 without noticing it by a notification of non-notice4 ,he would never commit the bull of ,sir6 ,i will not say a word on that subject4 ,he would put it thus1 ,sir6 ,i will only say ten words on that subject1--and1 having thus said them1 would #cea proceed to something else4 ,he assumed1 as a matter of form1 that ,mr4 ,reddie would draw the proper inference from his silence3 and this because he did not care whether or no the assumption was correct4 ,the ,mechanics of the ,heavens1 which ,mr4 ,reddie sends to be noticed1 shall be noticed1 so far as an extract goes3 ,my connection with this subject is1 indeed1 very simply explained4 ,in endeavoring to understand the laws of physical astronomy as generally taught1 ,i happened to entertain some doubt whether gravitating bodies could revolve1 and having afterwards imbibed some vague idea that the laws of the universe were chemical and physical rather than mechanical1 and somehow connected with electricity and magnetism as opposing correlative forces--most probably suggested to my mind1 as to many others1 by the transcendent discoveries made in electro-magnetism by ,professor ,faraday#feg--my former doubts about gravitation were revived1 and ,i was led very naturally to try and discover whether a gravitating body really could revolve2 and ,i became convinced it could not1 before ,i had ever presumed to look into the demonstrations of the ,principia4 ,this is enough against the book1 without a word from me3 ,i insert it only to show those who know the subject what manner of writer ,mr4 ,reddie is4 ,it is clear that presumed is a slip of the pen2 it should have been condescended4 ,mr4 ,reddie represents me as dreaming over paltry paradoxes4 ,he is right2 many of my paradoxes are paltry3 he is wrong2 ,i am wide awake to them4 ,a single moth1 beetle1 or butterfly1 may be a paltry thing2 but when a cabinet is arranged by genus and species1 we then begin to admire the #ceb infinite variety of a system constructed on a wonderful sameness of leading characteristics4 ,and why should paradoxes be denied that collective importance1 paltry as many of them may individually be1 which is accorded to moths1 beetles1 or butterflies8 ,mr4 ,reddie himself sees that there is a method in my mode of dealing with paradoxes4 ,i hope ,i have atoned for the scantiness of my former article1 and put the demonstrated impossibility of gravitation on that level with ,hubongramillposanfy arithmetic and inhabited atoms which the demonstrator--not quite without reason--claims for it4 ,in the ,introduction to a collected edition of the three works1 ,mr4 ,reddie describes his ,mechanism of the ,heavens1 from which ,i have just quoted1 as-- a public challenge offered to the ,british ,association and the mathematicians at ,cambridge1 in ,august1 #ahfb1 calling upon them to point to a single demonstration in the ,principia or elsewhere1 which even attempts to prove that ,universal ,gravitation is possible1 or to show that a gravitating body could possibly revolve about a center of attraction4 ,the challenge was not accepted1 and never will be4 ,no such demonstration exists4 ,and the public must judge for themselves as to the character of a so-called certain science1 which thus shrinks from rigid examination1 and dares not defend itself when publicly attacked3 also of the character of its teachers1 who can be content to remain dumb under such circumstances4 ,,on ,,paradoxers ,,in ,,general4 ,the above is the commonplace talk of the class1 of which ,i proceed to speak without more application to this paradoxer than to that4 ,it reminds one of the funny young rascals who used1 in times not yet quite forgotten1 to abuse the passengers1 as long as they could keep up with the #cec stage coach2 dropping off at last with ,why don't you get down and thrash us8 ,you're afraid1 you're afraid6 ,they will allow the public to judge for themselves1 but with somewhat of the feeling of the worthy uncle in ,tom ,jones1 who1 though he would let young people choose for themselves1 would have them choose wisely4 ,they try to be so awfully moral and so ghastly satirical that they must be answered3 and they are best answered in their own division4 ,we have all heard of the way in which sailors cat's-pawed the monkeys3 they taunted the dwellers in the trees with stones1 and the monkeys taunted them with cocoa-nuts in return4 ,but these were silly dendrobats3 had they belonged to the ,british ,association they would have said--,no6 ,no6 dear friends2 it is not in the itinerary3 if you want nuts1 you must climb1 as we do4 ,the public has referred the question to ,time3 the procedure of this great king ,i venture to describe1 from precedents1 by an adaptation of some smart anapaestic tetrameters--your anapaest is the foot for satire to halt on1 both in ,greek and ,english--which ,i read about twenty years ago1 and with the point of which ,i was much tickled4 ,poetasters were laughed at2 but ,mr4 ,slum1 whom ,i employed--,mr4 ,charles ,dickens obliged me with his address--converted the idea into that of a hit at mathematicasters1 as easily as he turned the ,warren acrostic into ,jarley4 ,as he observed1 when ,i settled his little account1 it is cheaper than any prose1 though the broom was not stolen quite ready made3 ,forty stripes save one for the smaller ,paradoxers4 ,hark to the wisdom the sages preach ,who never have learnt what they try to teach4 ,we are the lights of the age1 they say6 ,we are the men1 and the thinkers we6 ,so we build up guess-work the livelong day1 ,in a topsy-turvy sort of way1 ,some with and some wanting a plus b4 ,let the ,british ,association fuss2 ,what are theirs to the feats to be wrought by us8 #ced ,shall the earth stand still8 ,will the round come square8 ,must ,isaac's book be the nest of a mare8 ,ought the moon to be taught by the laws of space ,to turn half round without right-about-face8 ,our whimsey crotchets will manage it all2 ,deep6 ,deep6 posterity will them call6 ,though the world1 for the present1 lets them fall ,down6 ,down6 to the twopenny box of the stall6 ,thus they--,but the marplot ,time stands by1 ,with a knowing wink in his funny old eye4 ,he grasps by the top an immense fool's cap1 ,which he calls a philosophaster-trap3 ,and rightly enough1 for while these little men ,croak loud as a concert of frogs in a fen1 ,he first singles out one1 and then another1 ,down goes the cap--lo6 a moment's pother1 ,a spirit like that which a rushlight utters ,as just at the last it kicks and gutters3 ,when the cruel smotherer is raised again ,only snuff1 and but little of that1 will remain4 ,but though uno avulso thus comes every day ,non deficit alter is also in play3 ,for the vacant parts are1 one and all1 ,soon taken by puppets just as small2 ,who chirp1 chirp1 chirp1 with a grasshopper's glee1 ,we're the lamps of the ,universe1 ,we6 ,we6 ,we6 ,but ,time1 whose speech is never long1-- ,he hasn't time for it--stops the song ,and says--,lilliput lamps6 leave the twopenny boxes1 ,and shine in the ,budget of ,paradoxes6 ,when a paradoxer parades capital letters and diagrams which are as good as ,newton's to all who know nothing about it1 some persons wonder why science does not rise and triturate the whole thing4 ,this is why3 all who are fit to read the refutation are satisfied already1 and can1 if they please1 detect the paradoxer for themselves4 ,those who are not fit to do this would not know the difference between the true answer and the new capitals and diagrams on which the delighted paradoxer would declare #cee that he had crumbled the philosophers1 and not they him4 ,trust him for having the last word3 and what matters it whether he crow the unanswerable sooner or later8 ,there are but two courses to take4 ,one is to wait until he has committed himself in something which all can understand1 as ,mr4 ,reddie has done in his fancy about the ,astronomer ,royal's change of opinion3 he can then be put in his true place4 ,the other is to construct a ,budget of ,paradoxes1 that the world may see how the thing is always going on1 and that the picture ,i have concocted by cribbing and spoiling a bit of poetry is drawn from life4 ,he who wonders at there being no answer has seen one or two3 he does not know that there are always fifty with equal claims1 each of whom regards his being ranked with the rest as forty-nine distinct and several slanders upon himself1 the great ,mully ,ully ,gue4 ,and the fifty would soon be five hundred if any notice were taken of them4 ,they call mankind to witness that science will not defend itself1 though publicly attacked in terms which might sting a pickpocket into standing up for his character3 science1 in return1 allows mankind to witness or not1 at pleasure1 that it does not defend itself1 and yet receives no injury from centuries of assault4 ,demonstrative reason never raises the cry of ,church in ,danger6 and it cannot have any ,dictionary of ,heresies except a ,budget of ,paradoxes4 ,mistaken claimants are left to ,time and his extinguisher1 with the approbation of all thinking non-claimants3 there is no need of a succession of exposures4 ,time gets through the job in his own workmanlike manner as already described4 ,on looking back more than twenty years1 ,i find among my cuttings the following passage1 relating to a person who had signalized himself by an effort to teach comets to the conductor of the ,nautical ,almanac3 ,our brethren of the literary class have not the least idea of the small amount of appearance of knowledge #cef which sets up the scientific charlatan4 ,their world is large1 and there are many who have that moderate knowledge1 and perception of what is knowledge1 before which extreme ignorance is detected in its first prank4 ,there is a public of moderate cultivation1 for the most part sound in its judgment1 always ready in its decisions4 ,accordingly1 all their successful pretenders have some pretension4 ,it is not so in science4 ,those who have a right to judge are fewer and farther between4 ,the consequence is1 that many scientific pretenders have nothing but pretension4 ,this is nearly as applicable now as then4 ,it is impossible to make those who have not studied for themselves fully aware of the truth of what ,i have quoted4 ,the best chance is collection of cases2 in fact1 a ,budget of ,paradoxes4 ,those who have no knowledge of the subject can thus argue from the seen to the unseen4 ,all can feel the impracticability of the ,hubongramillposanfy numeration1 and the absurdity of the equality of contour of a regular pentagon and hexagon in one and the same circle4 ,many may accordingly be satisfied1 on the assurance of those who have studied1 that there is as much of impracticability1 or as much of absurdity1 in things which are hidden under ,sines1 tangents1 secants1 radius1 cosines ,subtangents1 segments and all those signs2 ,enough to prove that he who read 'em ,was just as mad as he who made 'em4 ,not that ,i mean to be disrespectful to mathematical terms3 they are short and easily explained1 and compete favorably with those of most other subjects3 for instance1 with ,horse-pleas1 traverses1 demurrers1 ,jeofails1 imparlances1 and errors1 ,averments1 bars1 and protestandos1 ,and puis d'arreign continuandos4 #ceg ,from which it appears that1 taking the selections made by satirists for our samples1 there are1 one with another1 four letters more in a law term than in one of mathematics4 ,but pleading has been simplified of late years4 ,all paradoxers can publish2 and any one who likes may read4 ,but this is not enough2 they find that they cannot publish1 or those who can find they are not read1 and they lay their plans athwart the noses of those who1 they think1 ought to read4 ,to recommend them to be content with publication1 like other authors1 is an affront3 of this ,i will give the reader an amusing instance4 ,my good nature1 of which ,i keep a stock1 though ,i do not use it all up in this ,budget1 prompts me to conceal the name4 ,i received the following letter1 accompanied by a prospectus of a work on metaphysics1 physics1 astronomy1 etc4 ,the author is evidently one whom ,i should delight to honor3 ,sir1--,a friend of mine has mentioned your name in terms of panigeric sic1 as being of high standing in mathematics1 and of greatly original thought4 ,i send you the enclosed without comment2 and1 assuming that the bent of your mind is in free inquiry1 shall feel a pleasure in showing you my portfolio1 which1 as a mathematician1 you will acknowledge to be deeply interesting1 even in an educational point of view4 ,the work is complete1 and the system so far perfected as to place it above criticism2 and1 so far as regards astronomy1 as will ,ptolemy beyond rivalry sic3 no doubt some words omitted4 ,believe me to be1 ,sir1 with the profoundest respect1 etc4 ,the work is the result of thirty-five years' travel and observation1 labor1 expense1 and self-abnegation4 ,i replied to the effect that my time was fully occupied1 and that ,i was obliged to decline discussion with many persons who have views of their own2 that the proper way is to publish1 so that those who choose may read when they can find leisure4 ,i added that ,i should advise a precursor in the shape of a small pamphlet1 as two octavo volumes #ceh would be too much for most persons4 ,this was sound advice2 but it is not the first1 second1 or third time that it has proved very unpalatable4 ,i received the following answer1 to which ,i take the liberty of prefixing a bit of leonine wisdom3 ,si doceas stultum1 laetum non dat tibi vultum2 ,odit te multum2 vellet te scire sepultum4#feh ,sir1--,i pray you pardon the error ,i unintentionally have fallen into2 deceived by the ,f4,r4,s4 ,i am not ,f4,r4,s4 ,i took you to be a man of science omnis homo est animal1 ,sortes est homo1 ergo ,sortes est animal#fei instead of the mere mathematician1 or human calculating-machine4 ,believe me1 ,sir1 you also have mistaken your mission1 as ,i have mine4 ,i wrote to you as ,i would to any other man well up in mathematics1 with the intent to call your attention to a singular fact of omission by ,euclid1 and other great mathematicians3 and1 in selecting you1 ,i did you an honor which1 from what ,i have just now heard1 was entirely out of place4 ,i think1 considering the nature of the work set forth in the prospectus1 you are guilty of both folly and presumption1 in assuming the character of a patron2 for your own sense ought to have assured you that was such my object ,i should not have sought him in a ,de ,morgan1 who exists only by patronage of others4 ,on the other hand1 ,i deem it to be an unpardonable piece of presumption in offering your advice upon a subject the magnitude1 importance1 and real utility of which you know nothing about3 by doing so you have offered me a direct insult4 ,the system is a manual of ,philosophy1 a one inseparable whole of metaphysics and physic2 embracing points the most interesting1 laws the most important1 #cei doctrines the most essential to advance man in accordance with the spirit of the times4 ,i may not live to see it in print2 for1 at ----1 life at best is uncertain3 but1 live or die1 be assured ,sir1 it is not my intention to debase the work by seeking patronage1 or pandering to the public taste4 ,your advice was the less needed1 seeing ,i am an old-established ----4 ,i remain1 etc4--,p4,s4 ,you will oblige me by returning the prospectus of my work4 ,my reader will1 ,i am sure1 not take this transition from the profoundest respect to the loftiest insolence for an apocraphical correspondence1 to use a word ,i find in the ,prospectus3 on my honor it is genuine4 ,he will be better employed in discovering whether ,i exist by patronizing others1 or by being patronized by them4 ,i make any one who can find it out a fair offer3 ,i will give him my patronage if ,i turn out to be ,bufo1 on condition he gives me his1 if ,i turn out to be ,bavius4#ffj ,i need hardly say that ,i considered the last letter to be one of those to which no answer is so good as no answer4 ,these letters remind me in one respect of the correspondents of the newspapers4 ,my other party wrote because a friend had pointed me out3 but he would not have written if he had known what another friend told him just in time for the second letter4 ,the man who sends his complaint to the newspaper very often says1 in effect1 ,don't imagine1 ,sir1 that ,i read your columns2 but a friend who sometimes does has told me 444 ,it is worded thus3 ,my attention #cfj has been directed to an article in your paper of 444 ,many thanks to my friend's friends for not mentioning the ,budget3 had my friend's attention been directed to it ,i might have lost a striking example of the paradoxer in search of a patron4 ,that my ,friend was on this scent in the first letter is revealed in the second4 ,language was given to man to conceal his thoughts2 but it is not every one who can do it4 ,among the most valuable information which my readers will get from me is comparison of the reactions of paradoxers1 when not admitted to argument1 or when laughed at4 ,of course1 they are misrepresented2 and at this they are angry1 or which is the same thing1 take great pains to assure the reader that they are not4 ,so far natural1 and so far good2 anything short of concession of a case which must be seriously met by counter-reasons is sure to be misrepresentation4 ,my friend ,mr4 ,james ,smith and my friend ,mr4 ,reddie are both terribly misrepresented3 they resent it by some insinuations in which it is not easy to detect whether ,i am a conscious smotherer of truth1 or only muddle-headed and ignorant4 ,this was written before ,i received my last communication from ,mr4 ,james ,smith4 ,he tells me that ,i am wrong in saying that his work in which ,i stand in the pillory is all reprint3 ,i have no doubt ,i confounded some of it with some of the manuscript or slips which ,i had received from my much not-agreed-with correspondent4 ,he adds that my mistake was intentional1 and that my reason is obvious to the reader4 ,this is information1 as the sea-serpent said when he read in the newspaper that he had a mane and tusks4 ,,the ,,double ,,vahu ,,process4 ,my friend ,dr4 ,thorn#ffa sees deeper into my mystery4 ,by the way1 he still sends an occasional touch at the old #cfa subject2 and he wants me particularly to tell my readers that the ,latin numeral letters1 if ,m be left out1 give #fff4 ,and so they do3 witness ,,dclxvi4 ,a person who thinks of the origin of symbols will soon see that #fff is our number because we have five fingers on each hand3 had we had but four1 our mystic number would have been expressed by #eee1 and would have stood for our present #cfe4 ,had n been the number on each hand1 the great number would have been 7n #a7 7#dn#b #bn #a7 ,with no finger on each hand1 the number would have been #a3 with one finger less than none at all on each hand1 it would have been #j4 ,but what does this mean8 ,here is a question for an algebraical paradoxer6 ,so soon as we have found out how many fingers the inhabitants of any one planet have on each hand1 we have the means of knowing their number of the ,beast1 and thence all about them4 ,very much struck with this hint of discovery1 ,i turned my attention to the means of developing it4 ,the first point was to clear my vision of all the old cataracts4 ,i propose the following experiment1 subject of course to the consent of parties4 ,let ,dr4 ,thorn ,double-,vahu ,mr4 ,james ,smith1 and ,thau ,mr4 ,reddie3 if either be deparadoxed by the treatment1 ,i will consent to undergo it myself4 ,provided always that the temperature required be not so high as the ,doctor hints at3 if the ,turkish ,baths will do for this world1 ,i am content4 ,the three paradoxers last named and myself have a pentasyllable convention1 under which1 though we go far beyond civility1 we keep within civilization4 ,though ,mr4 ,james ,smith pronounced that ,i must be dishonest if ,i did not see his argument1 which he knew ,i should not do to say nothing of recent accusation2 though ,dr4 ,thorn declared me a competitor for fire and brimstone--and my wife1 too1 which doubles the joke3 though ,mr4 ,reddie #cfb was certain ,i had garbled him1 evidently on purpose to make falsehood appear truth2 yet all three profess respect for me as to everything but power to see truth1 or candor to admit it4 ,and on the other hand1 though these were the modes of opening communication with me1 and though ,i have no doubt that all three are proper persons of whom to inquire whether ,i should go up-stairs or down-stairs1 etc41 yet ,i am satisfied they are thoroughly respectable men1 as to everything but reasoning4 ,and ,i dare say our several professions are far more true in extent than in many which are made under more parliamentary form4 ,we find excuses for each other3 they make allowances for my being hoodwinked by ,aristotle1 by ,newton1 by the ,devil2 and ,i permit them to feel1 for ,i know they cannot get on without it1 that their reasons are such as none but a knave or a sinner can resist4 ,but they are content with cutting a slice each out of my character3 neither of them is more than an uncle1 a ,bone-a-part2 ,i now come to a dreadful nephew1 ,bone-the-whole4 ,i will not give the name of the poor fellow who has fallen so far below both the honestum and the utile1 to say nothing of the decorum or the dulce4#ffb ,he is the fourth who has taken elaborate notice of me2 and my advice to him would be1 ,nec quarta loqui persona laboret4#ffc ,according to him1 ,i scorn humanity1 scandalize learning1 and disgrace the press2 it admits of no manner of doubt that my object is to mislead the public and silence truth1 at the expense of the interests of science1 the wealth of the nation1 and the lives of my fellow men4 ,the only thing left to be settled is1 whether this is due to ignorance1 natural distaste for truth1 personal malice1 a wish to curry favor with the ,astronomer ,royal1 or mere toadyism4 ,the only accusation which has truth in it is1 that ,i have made myself a public scavenger of science3 the assertion1 which is the #cfc most false of all is1 that the results of my broom and spade are shot right in between the columns of the ,athenaeum4 ,i declare ,i never in my life inserted a word between the columns of the ,athenaeum3 ,i feel huffed and miffed at the very supposition4 ,i have made myself a public scavenger2 and why not8 ,is the mud never to be collected into a heap8 ,i look down upon the other scavengers1 of whom there have been a few--mere historical drudges2 ,montucla1 ,hutton1 etc4--as not fit to compete with me4 ,i say of them what one crossing-sweeper said of the rest3 ,they are well enough for the common thing2 but put them to a bit of fancy-work1 such as sweeping round a post1 and see what a mess they make of it6 ,who can touch me at sweeping round a paradoxer8 ,if ,i complete my design of publishing a separate work1 an old copy will be fished up from a stall two hundred years hence by the coming man1 and will be described in an article which will end by his comparing our century with his own1 and sighing out in the best ,new ,zealand pronunciation-- ,dans ces tems-la ,c'etait deja comme ca6#ffd ,,orthodox ,,paradoxers4 ,and pray1 ,sir6 ,i have been asked by more than one--do your orthodox never fall into mistake1 nor rise into absurdity8 ,they not only do both1 but they admit it of each other very freely2 individually1 they are convinced of sin1 but not of any particular sin4 ,there is not a syndoxer among them all but draws his line in such a way as to include among paradoxers a great many whom ,i should exclude altogether from this work4 ,my worst specimens are but exaggerations of what may be found1 occasionally1 in the thoughts of sagacious investigators4 ,at the end of the #cfd glorious dream1 we learn that there is a way to ,hell from the gates of ,heaven1 as well as from the ,city of ,destruction3 and that this is true of other things besides ,christian pilgrimage is affirmed at the end of the ,budget of ,paradoxes4 ,if ,d',alembert#ffe had produced enough of a quality to match his celebrated mistake on the chance of throwing head in two throws1 he would have been in my list4 ,if ,newton had produced enough to match his reception of the story that ,nausicaa1 ,homer's ,phaeacian princess1 invented the celestial sphere1 followed by his serious surmise that she got it from the ,argonauts1--then ,newton himself would have had an appearance entered for him1 in spite of the ,principia4 ,in illustration1 ,i may cite a few words from ,tristram ,shandy3 ',a soldier1' cried my uncle ,toby1 interrupting the ,corporal1 'is no more exempt from saying a foolish thing1 ,trim1 than a man of letters4'--',but not so often1 an' please your honor1' replied the ,corporal4 ,my uncle ,toby gave a nod4 ,i now proceed to die out4 ,some prefatory remarks will follow in time4#fff ,i shall have occasion to insist that all is not barren3 ,i think ,i shall find1 on casting up1 that two out of five of my paradoxers are not to be utterly condemned4 ,among the better lot will be found all gradations of merit2 at the same time1 as was remarked on quite a different subject1 there may be little to choose between the last of the saved and the first of the lost4 ,the higher and better class is worthy of blame2 the lower and worse class is worthy of praise4 ,the higher men are to be reproved for not taking up things in which they could do some good3 the lower men are to be commended for taking up things in which they can do no great harm4 ,the circle problem is like ,peter ,peebles's lawsuit3 #cfe ',but1 ,sir1 ,i should really spoil any cause thrust on me so hastily4'--',ye cannot spoil it1 ,alan1' said my father1 'that is the very cream of the business1 man1--444 the case is come to that pass that ,stair or ,arniston could not mend it1 and ,i don't think even you1 ,alan1 can do it much harm4' ,i am strongly reminded of the monks in the darker part of the ,middle ,ages4 ,to a certain proportion of them1 perhaps two out of five1 we are indebted for the preservation of literature1 and their contemporaries for good teaching and mitigation of socials evils4 ,but the remaining three were the fleas and flies and thistles and briars with whom the satirist lumps them1 about a century before the ,reformation3 ,flen1 flyys1 and freris1 populum domini male caedunt2 ,thystlis and breris crescentia gramina laedunt4 ,christe nolens guerras qui cuncta pace tueris1 ,destrue per terras breris1 flen1 flyys1 and freris4 ,flen1 flyys1 and freris1 foul falle hem thys fyften yeris1 ,for non that her is lovit flen1 flyys ne freris4#ffg ,i should not be quite so savage with my second class4 ,taken together1 they may be made to give useful warning to those who are engaged in learning under better auspices3 aye1 even useful hints2 for bad things are very often only good things spoiled or misused4 ,my plan is that of a predecessor in the time of ,edward the ,second3 ,meum est propositum genti imperitae ,artes frugi reddere melioris vitae4#ffh ,to this end ,i have spoken with freedom of books as books1 of opinions as opinions1 of ignorance as ignorance1 of #cff presumption as presumption2 and of writers as ,i judge may be fairly inferred from what they have written4 ,some--to whom ,i am therefore under great obligation--have permitted me to enlarge my plan by assaults to which ,i have alluded2 assaults which allow a privilege of retort1 of which ,i have often availed myself2 assaults which give my readers a right of partnership in the amusement which ,i myself have received4 ,for the present ,i cut and run3 a ,catiline1 pursued by a chorus of ,ciceros1 with ,quousque tandem8 ,quamdiu nos8 ,nihil ne te8#ffi ending with1 ,in te conferri pestem istam jam pridem oportebat1 quam tu in nos omnes jamdiu machinaris6 ,i carry with me the reflection that ,i have furnished to those who need it such a magazine of warnings as they will not find elsewhere2 a signatis cavetote3#fgj and ,i throw back at my pursuers--,valete1 doctores sine doctrina2 facite ut proxima congressu vos salvos corporibus et sanos mentibus videamus4#fga ,here ends the ,budget of ,paradoxes4 #cfg 99 99 99 99 99 ,,appendix4 ,i think it right to give the proof that the ratio of the circumference to the diameter is incommensurable4 ,this method of proof was given by ,lambert1#fgb in the ,berlin ,memoirs for #agfa1 and has been also given in the notes to ,legendre's#fgc ,geometry1 and to the ,english translation of the same4 ,though not elementary algebra1 it is within the reach of a student of ordinary books4#fgd ,let a continued fraction1 such as a ----- b c ----- d e - f etc41 be abbreviated into a_/b c_/d e_/f etc43 each fraction being understood as falling down to the side of the preceding sign 4 ,in every such fraction we may suppose b1 d1 f1 etc4 #cfh positive2 a1 c1 e1 c4 being as required3 and all are supposed integers4 ,if this succession be continued ad infinitum1 and if a_/b1 c_/d1 e_/f1 etc4 all lie between -#a and #a1 exclusive1 the limit of the fraction must be incommensurable with unity2 that is1 cannot be ,a_/,b1 where ,a and ,b are integers4 ,first1 whatever this limit may be1 it lies between -#a and #a4 ,this is obviously the case with any fraction p_/7q omega71 where omega is between -#a3 for1 p_/q1 being #a1 and p and q integer1 cannot be brought up to #a1 by the value of omega4 ,hence1 if we take any of the fractions a_/b1 a_/b c_/d1 a_/b c_/d e_/f1 etc4 say a_/b c_/d e_/f g_/h we have1 g_/h being between -#a1 so is e_/f g_/h1 so therefore is c_/d e_/f g_/h2 and so therefore is a_/b c_/d e_/f g_/h4 ,now1 if possible1 let a_/b c_/d etc4 be ,a_/,b at the limit2 ,a and ,b being integers4 ,let ,p ,a c_/d e_/f etc41 ,q ,p e_/f g_/h etc41 ,r ,q g_/h i_/k etc4 ,p1 ,q1 ,r1 etc4 being integer or fractional1 as may be4 ,it is easily shown that all must be integer3 for #cfi ,a_/,b a_/b ,p_/,a1 or1 ,p a,b - b,a ,p_/,a c_/d ,q_/,p1 or1 ,q c,a - d,p ,q_/,p e_/f ,r_/,q1 or1 ,r e,p - f,q etc41 etc4 ,now1 since a1 ,b1 b1 ,a1 are integers1 so also is ,p2 and thence ,q2 and thence ,r1 etc4 ,but since ,a_/,b1 ,p_/,a1 ,q_/,p1 ,r_/,q1 etc4 are all between -#a and #a1 it follows that the unlimited succession of integers ,p1 ,q1 ,r1 are each less in numerical value than the preceding4 ,now there can be no such unlimited succession of descending integers3 consequently1 it is impossible that a_/b c_/d1 etc4 can have a commensurable limit4 ,it easily follows that the continued fraction is incommensurable if a_/b1 c_/d1 etc41 being at first greater than unity1 become and continue less than unity after some one point4 ,say that i_/k1 l_/m1444 are all less than unity4 ,then the fraction i_/k l_/m 444 is incommensurable1 as proved3 let it be kappa4 ,then g_/7h kappa7 is incommensurable1 say lambda2 e_/7f lambda7 is the same1 say mu2 also c_/7d mu71 say nu1 and a_/7b nu71 say rho4 ,but rho is the fraction a_/b c_/d 444 itself2 which is therefore incommensurable4 ,let phiz represent a a#b a#c #a - ------- -------------- 4444 z #bz7z#a7 #b4c4z7z#a77z#b7 #cgj ,let z be positive3 this series is convergent for all values of a1 and approaches without limit to unity as z increases without limit4 ,change z into z #a1 and form phiz - phi7z#a73 the following equation will result-- a phiz-phi7z#a7 ------7phi7z#b77 z7z#a7 a phi7z#a7 a phi7z#a7 a phi7z#b7 or a - ---------- 4 z - ---------- 4 --- ---------- z phiz z phiz z#a phi7z#a7 a psiz7zpsi7z#a77 psiz being 7a_/z77phi7z#a7_/phiz72 of which observe that it diminishes without limit as z increases without limit4 ,accordingly1 we have psiz a_/z psi7z#a7 a_/z a_/7z#a7 psi7z#b7 a_/z a_/7z#a7 a_/7z#b7 psi7z#c71 etc4 ,and1 psi7z n7 diminishing without limit1 we have a_/z 4 phi7z#a7_/phiz 7a_/z7 7a_/7z#a77 7a_/7z#b77 7a_/77z#c7 44477 ,let z #a_/b2 and let #d;a -x#b4 ,then 7a_/z7phi7z#a7 is -7x#b_/b7 7 #a - x#b_/7b4c7 x#d_/7b4c4d4e44477 or -7x_/#b7 sin x4 ,again phiz is #a - x#b_/b x#d_/7b4c4d7 or cos x3 and the continued fraction is 7#a_/d7x#b_/7a_/b7 7#a_/d7x#b_/7c_/b7 7#a_/d7x#b_/7e_/b7 444 or -x_/#b x_/#a -x#b_/c -x#b_/e 444 #cga whence tan x x_/#a -x#b_/c -x#b_/e -x#b_/g 444 ,or1 as written in the usual way1 tan x x ------- #a - x#b ------- #c - x#b ------- #e - x#b ------- #g - 444 ,this result may be proved in various ways3 it may also be verified by calculation4 ,to do this1 remember that if a#a_/;b#a a#b_/;b#b a#c_/;b#c 444 an_/bn ,pn_/,qn2 then ,p#a;a#a1 ,p#b;b#b ,p#a1 ,p#c;b#c ,p#b;a#c ,p#a1 ,p#d;b#d ,p#c;a#d ,p#b1 etc4 ,q#a;b#a1 ,q#b;b#b ,q#a;a#b1 ,q#c;b#c ,q#b;a#c ,q#a1 ,q#d;b#d ,q#c;a#d ,q#b1 etc4 in the case before us we have a#ax1 a#b-x#b1 a#c-x#b1 a#d-x#b1 a#e-x#b1 etc4 b#aa1 b#bc1 b#ce1 b#dg1 b#ei1 etc4 ,p#ax ,q#aa ,p#bcx ,q#bc-x#b ,p#caex-x#c ,q#cae-fx#b ,p#dajex-#ajx#c ,q#daje-dex#bx#d ,p#eidex-#ajex#cx#e ,q#eide-dbjx#baex#d ,p#fajciex-#abfjx#cbax#e ,q#fajcie-dgbex#bbajx#d-x#f ,we can use this algebraically1 or arithmetically4 ,if we divide ,pn by ,qn1 we shall find a series agreeing with the known series for tan x1 as far as n terms4 ,that series is x x#c_/c #bx#e_/ae #agx#g_/cae #fbx#i_/bhce 444 #cgb ,take ,p#e1 and divide it by ,q#e in the common way1 and the first five terms will be as here written4 ,now take x 4#a1 which means that the angle is to be one tenth of the actual unit1 or1 in degrees #e deg44#gbiegh4 ,we find that when x 4#a1 ,p#f #ajch4bdjba1 ,q#f #ajcdg4ggjiii2 whence ,p#f divided by ,q#f gives 4#ajjccdfgaa4 ,now #e deg44#gbiegh is #e deg4#dc'df-a_/b2 and from the old tables of ,rheticus#fge--no modern tables carry the tangents so far--the tangent of this angle is 4#ajjccdgfgj4 ,now let x 7#a_/d7pi2 in which case tan x #a4 ,if 7#a_/d7pi be commensurable with the unit1 let it be 7m_/n71 m and n being integers3 we know that 7#a_/d7pi #a4 ,we have then #a7m_/n7_/#a- 7m#b_/n#b7_/c- 7m#b_/n#b7_/e- 444 m_/n- m#b_/cn- m#b_/en- m#b_/gn- 444 ,now it is clear that m#b_/cn1 m#b_/en1 m#b_/gn1 etc4 must at last become and continue severally less than unity4 ,the continued fraction is therefore incommensurable1 and cannot be unity4 ,consequently pi#b cannot be commensurable3 that is1 pi is an incommensurable quantity1 and so also is pi#b4 ,i thought ,i should end with a grave bit of appendix1 deeply mathematical3 but paradox follows me wherever ,i go4 ,the foregoing is--in my own language--from ,dr4 7now ,sir ,david7 ,brewster's#fgf ,english edition of ,legendre's ,geometry1 7,edinburgh1 #ahbd1 #hvo47 translated by some one who is not named4 ,i picked up a notion1 which others had at ,cambridge in #ahbe1 that the translator was the late ,mr4 ,galbraith1#fgg then known at ,edinburgh as a writer and teacher4 #cgc ,but it turns out that it was by a very different person1 and one destined to shine in quite another walk2 it was a young man named ,thomas ,carlyle4#fgh ,he prefixed1 from his own pen1 a thoughtful and ingenious essay on ,proportion1 as good a substitute for the fifth ,book of ,euclid as could have been given in the space2 and quite enough to show that he would have been a distinguished teacher and thinker on first principles4 ,but he left the field immediately4 99 99 99 99 99 7,the following is the passage referred to at ,vol4 ,,ii1 page #ed47 ,michael ,stifelius#fgi edited1 in #aeed1 a second edition of the ,algebra 7,die ,coss471 of ,christopher ,rudolff4#fhj ,this is one of the earliest works in which and - are used4 ,stifelius was a queer man4 ,he has introduced into this very work of ,rudolff his own interpretation of the number of the ,beast4 ,he determined to fix the character of ,pope ,leo3 so he picked the numeral letters from ,,leodecimvs1 and by taking in ,x from ,,leo ,x4 and striking out ,m as standing for mysterium1 he hit the number exactly4 ,this discovery completed his conversion to ,luther1 and his determination to throw off his monastic vows4 ,luther dealt with him as straight-forwardly as with ,melanchthon about his astrology3 he accepted the conclusions1 but told him to clear his mind of all the premises about the ,beast4 ,stifelius #cgd did not take the advice1 and proceeded to settle the end of the world out of the prophet ,daniel3 he fixed on ,october1 #aecc4 ,the parishioners of some cure which he held1 having full faith1 began to spend their savings in all kinds of good eating and drinking2 we may charitably hope this was not the way of preparing for the event which their pastor pointed out4 ,they succeeded in making themselves as fit for ,heaven as ,lazarus1 so far as beggary went3 but when the time came1 and the world lasted on1 they wanted to kill their deceiver1 and would have done so but for the interference of ,luther4 #cge 99 99 99 99 99 ,,index4 ,pages denoted by numerals of this kind 7#bhg7 refer to biographical notes1 chiefly by the editor4 ,numerals like #dbf refer to books discussed by ,de ,morgan1 or to leading topics in the text4 ,numerals like #abf indicate minor references4 ,abbott1 ,justice1 ,i1 #aha4 ,abernethy1 ,j41 ,,ii1 #bai4 ,aboriginal ,britons1 a poem1 ,,ii1 #bgj4 ,academy of ,sciences1 ,french1 ,i1 #afc4 ,adair1 ,j41 ,i1 #bbc4 ,adam1 ,m41 ,i1 #fe4 ,adams1 ,j4 ,c41 ,i1 #dc1 #hb1 #che1 #chh2 ,,ii1 #aca1 #ace1 #adj1 #cjc4 ,ady1 ,joseph1 ,,ii1 #db1 #db4 ,agnew1 ,h4 ,c41 ,i1 #cbh4 ,agricola1 ,j41 ,i1 #cid4 ,agricultural ,laborer's letter1 ,,ii1 #af4 ,agrippa1 ,h4 ,c41 ,i1 #dh1 #dh4 ,ainsworth1 ,w4 ,h41 ,,ii1 #acb4 ,airy1 ,i1 #he1 #hh1 #aeb1 #bdb2 ,,ii1 #he1 #adj1 #aej1 #cjc1 #cdg4 ,alchemy1 ,i1 #abe4 ,alfonso ,x 7,el ,sabio71 ,,ii1 #bfi4 ,alford1 ,h41 ,,ii1 #bba4 ,alfred1 ,king1 ,ballad of1 ,,ii1 #bb4 ,algebra1 ,i1 #aba4 ,algebraic symbols1 ,i1 #aba4 ,almanac1 ,i1 #cjj2 ,,ii1 #adg1 #adh1 #bjg4 7,see ,easter47 ,aloysius ,lilius1 ,i1 #cfb4 ,alsted1 ,j4 ,h41 ,,ii1 #bhb4 ,ameen ,bey1 ,,ii1 #ae4 ,amicable ,society1 ,i1 #cdg4 ,ampere1 ,i1 #hf4 ,amphisbaena serpent1 ,i1 #ca4 ,anagrams1 ,de ,morgan1 ,i1 #ach4 ,anaxagoras1 ,,ii1 #ei4 ,anghera1 ,,ii1 #fj1 #fj1 #fa1 #bgi4 ,annuities1 ,fallacies of1 ,i1 #aeg4 ,antichrist1 ,i1 #acj4 ,antimony1 ,i1 #abe4 ,antinewtonism1 ,i1 #afb4 ,antinomians1 ,i1 #cid4 ,antiphon1 ,,ii1 #ei4 ,antonie1 ,f41 ,i1 #abf1 #abf4 ,apollonius1 ,i1 #da1 #ajg4 ,apparitions1 ,,ii1 #dg4 ,arago1 ,i1 #bdc1 #cij4 ,aratus1 ,,ii1 #afg4 ,arbuthnot1 ,i1 #acc1 #acd4 ,archer1 ,h41 ,,ii1 #ij4 ,archimedes1 ,i1 #e1 #aa1 #db1 #hc1 #ajg4 ,archytas1 ,i1 #ec4 ,argoli1 ,i1 #ajd4 ,aristocrat1 as a scientist1 ,i1 #aca4 ,aristotle1 ,i1 #e1 #cca4 ,arnobius1 ,,ii1 #gc4 ,arson1 ,p4 ,j41 ,,ii1 #bjg4 ,ashton1 ,r41 ,,ii1 #ii4 ,astrology1 ,i1 #aah1 #abg1 #abh1 #cej2 ,,ii1 #dc4 ,astronomer's ,drinking ,song1 ,i1 #chj4 ,astronomical ,aphorisms1 ,i1 #cih4 ,paradox1 ,i1 #cid4 ,police ,report1 ,i1 #cij4 ,society4 7,see ,royal ,astronomical ,society47 ,astronomy1 ,bailly's exaggerated view of1 ,i1 #aff4 ,astunica1 ,didacas1 ,i1 #ij4 ,athanasian ,creed1 ,i1 #cga4 ,atheists1 ,philosophical1 ,i1 #a4 ,atoms1 ,,ii1 #aia4 #cgf ,attraction1 ,i1 #acf1 #aea1 #aee4 ,augustine1 ,st41 ,,ii1 #bc4 ,aurora borealis1 ,i1 #acd4 ,austen1 ,jane1 ,i1 #aia4 ,auzout1 ,a41 ,,ii1 #cjj4 ,aviation1 ,early ideas of1 ,,ii1 #h4 ,babbage1 ,c41 ,i1 #bjg1 #bij1 #bia2 ,,ii1 #aha4 ,bachet1 de ,meziriac1 ,i1 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,j4 ,h41 ,,ii1 #bbf4 ,thompson1 ,p41 ,i1 #g4 ,thompson1 ,t4 ,p41 ,i1 #beb1 #bhg1 #cdd2 ,,ii1 #hc1 #ahe4 ,thomson1 ,dr41 ,i1 #ba4 ,thomson1 ,w41 ,i1 #cbe4 ,thorn1 ,w41 ,,ii1 #aeh1 #aeh1 #cfj4 ,thorndike1 ,h41 ,,ii1 #cac4 ,thrale1 ,mrs41 ,i1 #bce4 ,thurlow1 ,baron1 ,i1 #bbb4 ,thyraeus1 ,i1 #ej4 ,tides1 ,new theory of1 ,i1 #cic4 ,tombstones of mathematicians1 ,i1 #ajf4 ,tonal ,system1 ,,ii1 #ahb4 ,tooke1 ,h41 ,i1 #agh4 ,torriano1 ,e41 ,i1 #bej4 ,towneley1 ,,ii1 #cjj4 ,townley1 ,c41 ,,ii1 #cjj4 ,trisection problem1 ,i1 #aah2 ,,ii1 #aj1 #ab1 #ac1 #ae4 ,troughton1 ,i1 #aeb4 ,turnor1 ,e41 ,i1 #acg4 ,tycho ,brahe1 ,i1 #e1 #gf1 #cha2 ,,ii1 #cjb1 #cce4 ,upton1 ,w41 ,,ii1 #ab1 #ab1 #ae4 ,ursus1 ,i1 #eb4 ,valentine1 ,b41 ,i1 #abe1 #abe4 ,van ,ceulen1 ,i1 #eb1 #gj1 #ajj4 ,van de ,weyer1 ,i1 #cac4 ,van ,etten1 ,i1 #afa4 ,van ,helmont1 ,i1 #abe1 #abe4 ,van ,roomen1 ,i1 #aaj4 ,van ,schooten1 ,,ii1 #ei4 ,vaughan1 ,t41 ,i1 #bee4 ,victorinus1 ,i1 #cei4 ,viete1 ,i1 #ea2 ,,ii1 #baj1 #bie4 ,virgil1 ,st41 ,i1 #cb1 #cc1 #cd1 #ii4 #chg ,virginia1 ,university of1 ,i1 #bcc4 ,viscellinus1 ,,ii1 #cdb4 ,vitruvius1 ,,ii1 #bha4 ,vivian1 ,t41 ,i1 #agb1 #agb4 ,vogel1 ,a4 ,f41 ,i1 #cgc4 ,voltaire1 ,i1 #ajc1 #afe1 #aff1 #afg1 #afh1 #bdh2 ,,ii1 #bfh4 ,von ,gumpach1 ,,ii1 #acg1 #acg4 ,von ,hutten1 ,i1 #cah4 ,von ,wolzogen4 7,see ,wolzogen47 ,vyse1 ,r4 ,w4 ,h41 ,i1 #cbh4 ,walker1 ,w4 ,e41 ,,ii1 #caf4 ,walkingame1 ,f41 ,,ii1 #agc4 ,wallich1 ,n41 ,,ii1 #ad4 ,wallis1 ,j41 ,i1 #ajg1 #aji1 #aaj2 ,,ii1 #bii1 #cac4 ,walpole1 ,i1 #bc1 #aca4 ,walsh1 ,john1 ,i1 #bfj1 #bfj2 ,,ii1 #aeg4 ,wapshare1 ,j41 ,,ii1 #bcj4 ,warburton1 ,h41 ,i1 #cdi4 ,warburton1 ,wm41 ,i1 #ee1 #aab2 ,,ii1 #agd4 ,ward1 ,s41 ,,ii1 #bii4 ,waring1 ,e41 ,i1 #bjc1 #bbb4 ,warner1 ,w41 ,,ii1 #cjb1 #cab4 ,warren1 ,s41 ,,ii1 #cdj4 ,watkins1 ,j41 ,,ii1 #bgj4 ,watson1 ,bp41 ,i1 #bbc4 ,watt1 ,r41 ,i1 #ajb1 #djb4 ,watts1 ,i41 ,,ii1 #ah4 ,weddle1 ,t41 ,,ii1 #ahg4 ,wentworth1 ,thos41 ,i1 #bdj4 ,wharton1 ,i1 #aae4 ,whately1 ,r41 ,i1 #bdf1 #bdf1 #cbd4 ,whately's ,paradox1 ,i1 #bdf4 ,whewell1 ,i1 #aja1 #aja1 #bgc1 #cad1 #chj2 ,,ii1 #ajd1 #bdf1 #bdg4 ,whigs1 ,,ii1 #bb4 ,whiston1 ,j41 ,i1 #adg4 ,whiston1 ,w41 ,i1 #acc1 #acc1 #adf1 #aef1 #caa4 ,white1 ,h4 ,k41 ,,ii1 #bga4 ,white1 ,j4 ,b41 ,i1 #bdh4 ,white1 ,r41 ,i1 #aa4 ,whitford1 ,i1 #aje4 ,whitworth1 ,w4 ,a41 ,,ii1 #cdd4 ,whizgig1 ,on the1 ,i1 #bed4 ,wightman1 ,i1 #ei4 ,wilberforce1 ,w41 ,,ii1 #bcf4 ,wilkins1 ,j41 ,i1 #if1 #ajj1 #aaf1 #bbf4 ,williams1 ,j4 ,b41 ,i1 #cgh4 ,williams1 ,t41 ,i1 #aga1 #aga4 ,wilson1 ,sir ,j41 ,i1 #bba4 ,wilson1 ,j4 ,m41 ,,ii1 #cdd4 ,wilson1 ,r41 ,,ii1 #g1 #g4 ,wilson's ,theorem1 ,i1 #bbb4 ,wingate1 ,e41 ,,ii1 #cjh4 ,winter1 ,i1 #df4 ,wirgman1 ,t41 ,i1 #beh1 #beh4 ,wiseman1 ,n4 ,p4 ,s41 ,,ii1 #bf1 #fa1 #bid4 ,wolcot1 ,j4 7,peter ,pindar71 ,,ii1 #bgb4 ,wollstonecraft1 ,i1 #agc1 #agc4 ,wolzogen1 ,i1 #ajf4 ,wood1 ,a41 ,i1 #ih4 ,wood1 ,john1 ,i1 #bcc4 ,wood1 ,wm41 ,i1 #bdf1 #bdf4 ,woodley1 ,w41 ,i1 #cjg1 #cjg4 ,wordsworth1 ,,ii1 #bgc4 ,wright1 ,e41 ,i1 #hd4 ,wright1 ,t41 ,i1 #aea1 #aea1 #aeb1 #aec4 ,wright1 ,w41 ,,ii1 #i4 ,wronski1 ,i1 #bdi1 #bej4 ,wrottesley1 ,j4 7,baron71 ,,ii1 #aha4 ,young1 ,b41 ,,ii1 #fi4 ,young1 ,j4 ,w4 ,a41 ,,ii1 #cfg4 ,young1 ,t41 ,i1 #bd1 #cj1 #bej4 ,youthful ,prodigies1 ,i1 #bai4 ,yvon1 ,i1 #big4 ,zach1 von1 ,,ii1 #de1 #aif4 ,zachary1 ,pope1 ,i1 #cb1 #cd4 ,zadkiel1 ,i1 #cba2 ,,ii1 #dc4 ,zetetic ,astronomy1 ,,ii1 #hh4 ,zodiac1 ,,ii1 #acf4 ,zytphen1 ,,ii1 #cce4 99 99 99 99 99 ,notes ,transcriber's note3 ,references to ,notes in ,volume ,i are shown as in the printed book1 with the resequenced footnote numbers in the ,project ,gutenberg ,edition 7,e,text-,no4 #bcajj7 added thus #abc4 #a ,see ,vol4 ,i1 page #bee1 note #f #ehd4 #b ,i have no need for this hypothesis4 #c ,ah1 it is a beautiful hypothesis2 it explains many things4 #d ,what we know is very slight2 what we don't know is immense4 #e ,brewster relates 7,life of ,sir ,isaac ,newton1 ,vol4 ,,ii1 p4 #djg7 that1 a short time before his death1 ,newton remarked3 ,i do not know what ,i may appear to the world1 but to myself ,i seem to have been only like a boy playing on the seashore1 and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary1 whilst the great ocean of truth lay all undiscovered before me4 #f ,see ,vol4 ,i1 p4 #bib1 note #a #fcb4 #g ,what is all that6 #h ,i have some good news to tell you3 at the ,bureau of ,longitudes they have just received a letter from ,germany announcing that ,m4 ,bessel has verified by observation your theoretical discoveries on the satellites of ,jupiter4 #i ,man follows only phantoms4 #aj ,see ,vol4 ,i1 page #chb1 note #ac #ghf4 #aa ,dieudonne ,thiebault 7#agcc-ahjg7 was a ,jesuit in his early life1 but he left the order and took up the study of law4 ,in #agfe he went to ,prussia and became a favorite of ,frederick the ,great4 ,he returned to ,france in #aghe and became head of the ,lycee at ,versailles4 #ab ,memories of ,twenty ,years of ,residence in ,berlin4 ,there was a second ,french and an ,english edition in #ahje4 #ac ,richard ,joachim ,heinrich von ,mollendorff 7#agbd-ahaf7 began his career as a page of ,frederick the ,great 7#agdj7 and became field marshal 7#agic7 and commander of the ,prussian army on the ,rhine 7#agid74 #ad ,hugues ,bernard ,maret 7#agfc-ahci7 was not ,duc de ,bassano in #ahjg1 this title not being conferred upon him until #ahji4 ,he was ambassador to ,england in #agib and to ,naples in #agic4 ,napoleon made him head of the cabinet and his special confidant4 ,the ,bourbons exiled him in #ahaf4 #ae ,denis ,diderot 7#agac-aghd71 whose ,lettre sur les aveugles 7#agdi7 introduced him to the world as a philosopher1 and whose work on the ,encyclopedie is so well known4 #af ,sir1 7a bn7 _/ n x1 whence ,god exists2 answer6 #ag ,this was one ,james ,laurie of ,musselburgh4 #ah ,jelinger ,cookson ,symons 7#ahji-ahfj7 was an office-holder with a decided leaning towards the improvement of education and social conditions4 ,he wrote ,a ,plea for ,schools 7#ahdg71 ,the ,industrial ,capacities of ,south ,wales 7#ahee71 and ,lunar ,motion 7#ahef71 to which last work the critic probably refers4 #ai ,protimalethes followed this by another work along the same line the following year1 ,the ,independence of the ,testimony of ,st4 ,matthew and ,st4 ,john tested and vindicated by the theory of chances4 #bj ,wilson had already taken up the lance against science in his ,strictures on ,geology and ,astronomy1 in reference to a supposed want of harmony between these sciences and some parts of ,divine ,revelation1 ,glasgow1 #ahdc4 ,he had also ventured upon poetry in his ,pleasures of ,piety1 ,glasgow1 #ahcg4 #ba ,mrs4 ,borron was ,elizabeth ,willesford ,mills before her marriage4 ,she made an attempt at literature in her ,sibyl's ,leaves1 ,london 7printed at ,devonport71 #ahbf4 #bb ,see ,vol4 ,i1 page #chf1 note #aj #hja4 #bc ,see ,vol4 ,i1 page #dc1 notes #g #cb and #h #cc4 #bd ,his flying machine1 designed in #ahdc1 was one of the earliest attempts at aviation on any extensive scale4 #be ,erasmus ,darwin 7#agca-ahjb7 was the grandfather of ,charles ,darwin4 ,the work here mentioned had great influence1 being translated into ,french1 ,portuguese1 and ,italian4 ,canning parodied it in his ,loves of the ,triangles4 #bf ,see ,vol4 ,i1 page #adg1 note #a #cab4 #bg ,the notes on this page were written on the day of the funeral of ,wilbur ,wright1 ,june #a1 #aiab1 the man who realized all of these prophecies1 and then died a victim of municipal crime1--of typhoid fever4 #bh ,john ,charles1 third ,earl ,spencer 7#aghb-ahde71 to whose efforts the ,reform ,bill was greatly indebted for its final success4 #bi ,this was published in ,london in #ahea instead of #ahdh4 #cj ,this appeared in #ahdf4 #ca ,this was done in ,the ,circle ,squared1 published at ,brighton in #ahfe4 #cb ,it first appeared in #ahdg1 under the title1 ,the ,scriptural ,calendar and ,chronological ,reformer1 #ahdh4 ,including a review of tracts by ,dr4 ,wardlaw and others on the ,sabbath question4 ,by ,w4 ,h4 ,black4 ,the one above mentioned1 for #ahdi1 was printed in #ahdh1 and was also by ,black 7#ahjh-ahgb74 ,he was pastor of the ,seventh ,day ,baptists and was interested in archeology and in books4 ,he catalogued the manuscripts of the ,ashmolean ,museum at ,oxford4 #cc ,william ,upton1 a ,trinity ,college man1 ,dublin4 ,he also wrote ,upton's ,physioglyphics1 ,london1 #ahdd2 ,pars prima4 ,geometria vindicata2 antiquorumque ,problematum1 ad hoc tempus desperatorum1 ,trisectionis ,anguli1 ,circulique ,quadraturae1 ,solutio1 per ,eucliden effecta1 ,london 7printed at ,southampton71 #ahdg2 ,the ,uptonian ,trisection1 ,london1 #ahff2 and ,the ,circle ,squared1 ,london1 #ahgb4 #cd ,for example1 if theta #ij deg4 we should have #c cos #cj deg4 #a root7#d - sin#b #ij deg471 or #c4 #a_/b root#c #a root#c1 or #a_/b root#c #a4 #ce ,nathaniel ,wallich 7#aghf-ahed7 was surgeon at the ,danish settlement at ,serampore when the ,east ,india ,company took over the control in #ahjg4 ,he entered the ,british medical service and was invalided to ,england in #ahbh4 ,his ,plantae ,asiaticae ,rariores 7#c vols41 ,london1 #ahcj-ahcb7 was recognized as a standard4 ,he became vice-president of the ,linnean ,society1 ,f4 ,r4 ,s41 and fellow of the ,royal ,asiatic ,society4 #cf ,but if theta #ij deg4 this asserts that cos #cj deg4 7sin #bgj deg4 4 cos #bbe deg4 sin#b #ij deg4 4 sin #bbe deg47 _/ root7sin#b #bgj deg4 4 cos#b #bbe deg4 sin#d #ij deg4 sin #bgj deg4 4 sin #dej deg4 4 sin#b #ij deg471 or that #a_/b root#c 7-#a 4 7-#a _/root#b7 #a 4 7-#a_/root#b7 _/ root#a 4 #a_/b #a - #a 4 #a 4 #a7 #j _/ root7#a_/b71 so that ,de ,morgan must have made some error in copying4 #cg ,john ,bonnycastle 7died in #ahba7 was professor of mathematics at ,woolwich4 ,his edition of ,bossut's ,history of ,mathematics 7#ahjc71 and his works on elementary mathematics were well known4 #ch ,the bibliographies give ,husain ,rifki as the translator1 a practical geometry as the work1 and #ahjb as the date4 #ci ,see ,vol4 ,i1 page #cji1 note #b #fgj4 #dj ,probably in ,the ,improvement of the ,mind which ,isaac ,watts 7#afgd-agdh7 published in #agda4 ,his ,horae ,lyricae appeared in #agjf1 and the ,hymns1 by which he is still well known1 in #agjg4 #da ,spencer ,joshua ,alwyne ,compton1 second ,marquis of ,northampton 7#agij-ahea71 was a poet1 a scientist1 and a statesman4 ,he was president of the ,royal ,society from #ahch to #ahdi4 #db ,besides the writings here mentioned ,perigal published a work on ,geometric ,maps 7,london1 #ahec71 and ,graphic ,demonstrations of ,geometric ,problems 7#ahia74 #dc ,see ,vol4 ,,ii1 page #e1 note #ah4 #dd ,james ,ferguson 7#agaj-aggf7 was a portrait painter1 an astronomer1 and a popular writer and lecturer on various subjects4 #de ,in the old ballad of ,king ,alfred and the ,shepherd1 when the latter is tempting the disguised king into his service1 he says3 ,of whig and whey we have good store1 ,and keep good pease-straw fire4 ,whig is then a preparation of milk4 ,but another commonly cited derivation may be suspected from the word whiggamor being used before whig1 as applied to the political party2 whig may be a contraction4 ,perhaps both derivations conspired3 the word whiggamor1 said to be a word of command to the horses1 might contract into whig1 and the contraction might be welcomed for its own native meaning4--,a4 ,de ,m4 #df ,this was p4 #adg in the first edition4 #dg ,st4 ,augustine 7#ced-dcj7 was bishop of ,hippo4 ,his ,confessiones1 in #ac books1 was written in #cig1 and his ,de ,civitate ,dei in #dbf4 #dh ,he was wont to indulge in certain ,punic subtleties lest he should weary the reader by much speaking4 #di ,john ,milner 7#agea-ahbf71 bishop of ,castabala1 a well-known antiquarian4 #ej ,it will be said that when the final happiness is spoken of in sure and certain hope1 it is the ,resurrection1 generally2 but when afterwards application is made to the individual1 simple hope is all that is predicated which merely means wish8 ,i know it3 but just before the general declaration1 it is declared that it has pleased ,god of his great mercy to take unto ,himself1 the soul of our dear brother3 and between the hopes hearty thanks are given that it has pleased ,god to deliver our dear brother out of the miseries of this wicked world1 with an additional prayer that the number of the elect may shortly be accomplished4 ,all which means1 that our dear brother is declared to be taken to ,god1 to be in a place not so miserable as this world--a description which excludes the wicked place--and to be of the elect4 ,yes1 but it will be said again6 do you not know that when this ,liturgy was framed1 all who were not in the road to ,heaven were excommunicated burial service read over them4 ,supposing the fact to have been true in old time1 which is a very spicy supposition1 how does that excuse the present practice8 ,have you a right always to say what you believe cannot always be true1 because you think it was once always true8 ,yes1 but1 choose whom you please1 you cannot be certain ,he is not gone to ,heaven4 ,true1 and choose which ,bishop you please1 you cannot be demonstratively certain1 he is not a concealed unbeliever3 may ,i therefore say of the whole bench1 singulatim et seriatim1 that they are unbelievers8 ,no6 ,no6 ,the voice of common sense1 of which common logic is a part1 is slowly opening the eyes of the multitude to the unprincipled reasoning of theologians4 ,remember #ahai4 ,what chance had ,parliamentary ,reform when the ,house of ,commons thanked the ,manchester sabre-men8 ,if you do not reform your ,liturgy1 it will be reformed for you1 and sooner than you think6 ,the dishonest interpretations1 by defence of which even the minds of children are corrupted1 and which throw their shoots into literature and commerce1 will be sent to the place whence they came3 and over the door of the established organization for teaching religion will be posted the following notice3 ,shift and ,subterfuge1 ,shuffle and ,dodge1 ,no longer here allowed to lodge6 ,all this ought to be written by some one who belongs to the ,establishment3 in him1 it would be quite prudent and proper2 in me1 it is kind and charitable4--,a4 ,de ,m4 #ea ,but few do have access to it1 for the work is not at all common1 and this ,piscator is rarely mentioned4 #eb ,this derivation has been omitted4--,s4 ,e4 ,de ,m4 #ec ,a blow for a blow4 ,roland and ,oliver were two of the paladins of ,charlemagne whose exploits were so alike that each was constantly receiving credit for what the other did4 ,finally they met and fought for five days on an island in the ,rhine1 but even at the end of that period it was merely a drawn battle4 #ed ,in the name of the church4 #ee ,from the chair1 officially4 #ef ,nicholas ,patrick ,stephen ,wiseman 7#ahjb-ahfe71 whose elevation to the archbishopric of ,westminster and the cardinalate 7#ahej7 led to the act prohibiting ,roman ,catholics from assuming episcopal titles in ,england1 a law that was never enforced4 #eg ,he was born in #ahab and was converted to ,catholicism in #ahci4 ,he founded the ,tablet in ,london in #ahdj1 removing its office to ,dublin in #ahdi4 ,he became ,m4 ,p4 in #aheb1 and at the time of his death 7#ahee7 he was preparing a memorial to the ,pope asking him to annul the proclamation of an ,irish bishop prohibiting his priests from taking part in politics4 #eh ,john ,guillim 7#aefe-afba7 was the first to systematize and illustrate the whole science of heraldry4 ,he published ,a display of ,heraldrie3 manifesting a more easie accesse to the knowledge thereof in #afaj4 #ei ,faith4 #fj ,faithful4 #fa ,for the faith vindicated4 #fb ,the words are of the same root1 and hence our word fiddle4 ,some suppose this root means a rope1 which1 as that to which you trust1 becomes1 in one divergence1 confidence itself--just as a rock1 and other words1 come to mean reliance--and in another1 a little string4--,a4 ,de ,m4 #fc ,the ,greek lexicographer1 a ,christian1 living after #ajjj ,a4 ,d4 ,his lexicon was first printed at ,milan in #adii4 #fd ,skindapsos4 #fe ,this was ,john ,william ,burgon 7#ahac-ahhh71 ,gresham professor of theology 7#ahfg7 and dean of ,chichester4 ,he was an ultra-conservative1 opposing the revised version of the ,new ,testament1 and saying of the admission of women to the university examinations that it was a thing inexpedient and immodest4 #ff ,ekklesia1 or ecclesia4 #fg ,ennomos ekklesia4 #fh ,without doubt ,i shall perish forever4 #fi ,every man is an animal4 ,sortes is a man4 ,sortes is an animal4 #gj ,for a special purpose4 #ga ,heraclitus of ,ephesus1 the weeping philosopher1 #fth century ,b4 ,c4 #gb ,democritus1 the laughing philosopher1 founder of the atomistic theory1 #eth century ,b4 ,c4 #gc ,ends to which4 #gd ,ends from which4 #ge ,in just as many syllables1 ,with just as many letters1 ,in just as many words4 #gf ,i shall make a way1 ,i shall find a way4 #gg ,the notion that the ,evil ,spirit is a functionary liable to be dismissed for not attending to his duty1 is1 so far as my reading goes1 utterly unknown in theology4 ,my first wrinkle on the subject was the remark of the ,somersetshire farmer upon ,palmer the poisoner-- ,well6 if the ,devil don't take he1 he didn't ought to be allowed to be devil no longer4--,a4 ,de ,m4 ,william ,palmer 7#ahbd-ahef7 was a member of the ,royal ,college of ,surgeons and practised medicine at ,london4 ,he was hanged in #ahef for having poisoned a friend and was also suspected of having poisoned his wife and brother for their insurance money1 besides being guilty of numerous other murders4 ,his trial was very much in the public attention at the time4 #gh ,advantages and dangers4 #gi ,the old priory of ,st4 ,mary of ,bethlehem in ,london1 was used as an asylum for the insane4 ,the name was corrupted to ,bedlam4 #hj ,referring to the common ,english pronunciation of ,st4 ,john1 almost ,sinjin4 ,john ,st4 ,john ,long 7#agih-ahcd71 an ,irishman by birth1 practised medicine in ,london4 ,he claimed to have found a specific for rheumatism and tuberculosis1 but upon the death of one of his patients in #ahcj he was tried for manslaughter4 ,he died of tuberculosis four years later1 refusing to take his own treatment4 #ha ,william of ,occam 7d4 #acdi71 so called from his birthplace1 ,ockham1 in ,surrey4 ,he was a ,franciscan1 and lectured on philosophy in the ,sorbonne4 #hb ,he signs himself ,james ,hopkins1 schoolmaster1 and this seems to have been his only published effort4 #hc ,joseph ,ady 7#aggj-aheb7 was a famous swindler4 ,one of his best-known schemes was to send out letters informing the recipients that they would learn something to their advantage on payment of a certain sum4 ,he spent some time in prison4 #hd ,sir ,peter ,laurie 7c4 #aggi-ahfa7 was worth referring to1 for he was prominent as a magistrate and was honored because of his interest in all social reforms4 ,he made a fortune as a contractor1 became sheriff of ,london in #ahbc1 and was knighted in the following year4 ,he became ,lord ,mayor of ,london in #ahcb4 #he ,see ,vol4 ,i1 page #cba1 note #b #fia4 ,the ,astronomy in a nutshell appeared in #ahfj4 ,the ,herald of ,astrology was first published in ,london in #ahca1 by ,zadkiel the ,seer4 ,it was continued as ,the ,astrological ,almanac 7,london1 #ahcd71 as ,zadkiel's ,almanac and ,herald of ,astrology 7ibid41 #ahce1 edited by ,r4 ,j4 ,morrison1 and subsequently by ,a4 ,j4 ,pearce71 and as ,raphael's ,prophetic ,almanac 7#ahdj-ahee74 #hf ,see ,vol4 ,i1 page #agb1 note #c #chb4 #hg ,see ,vol4 ,i1 page #hg1 note #d #acc4 #hh ,franz ,xaver1 ,freiherr von ,zach 7#aged-ahcb7 was director of the observatory at ,seeberge near ,gotha4 ,he wrote the ,tabulae speciales aberrationis et mutationis 7#ahjf-g71 ,novae et correctae tabulae solis 7#agib71 and ,l'attraction des montagnes et ses effets sur le fil a plomb 7#ahad74 #hi ,jean ,louis ,pons 7#agfa-ahca7 was connected with the observatory at ,marseilles for thirty years 7#aghi-ahai74 ,he later became director of the observatory at ,marlia1 near ,lucca1 and subsequently filled the same office at ,florence4 ,he was an indefatigable searcher for comets1 discovering #cg between #ahja and #ahbg1 among them being the one that bears ,encke's name4 #ij ,this hypothesis has now become an established fact4 #ia ,john ,chetwode ,eustace 7c4 #agfb-ahae7 was born in ,ireland4 ,although a ,roman ,catholic priest he lived for a time at ,cambridge where he did some tutoring4 ,his ,classical ,tour appeared in #ahac and went through several editions4 #ib ,crimes should be exposed when they are punished1 but disgraceful acts should be hidden4 #ic ,henri ,hureau de ,senarmont 7#ahjh-ahfb7 was professor of mineralogy at the ,ecole des mines and examiner at the ,ecole polytechnique at ,paris4 #id ,augustin ,jean ,fresnel 7#aghh-ahbg71 ,ingenieur des ponts et chaussees1 gave the first experimental proofs of the wave theory of light4 ,he studied the questions of interference and polarization1 and determined the approximate velocity of light4 #ie ,as is my custom4 #if ,francis ,heywood 7#agif-aheh7 made the first ,english translation of ,kant's ,critick of ,pure ,reason 7#ahch1 reprinted in #ahdh74 ,the ,analysis came out1 as here stated1 in #ahdd4 #ig ,louise ,renee de ,keroualle1 ,duchess of ,portsmouth and ,aubigny 7#afdi-agcd71 was a favorite of ,charles ,,ii4 ,she used her influence to keep him under the control of ,louis ,,xiv4 #ih ,william ,chiffinch 7c4 #afjb-afhh7 was page of the king's bed-chamber and keeper of the private closet to ,charles ,,ii4 ,he was one of the king's intimates and was an unscrupulous henchman4 #ii ,well devised4 #ajj ,john ,bellingham ,inglis4 ,his ,philobiblion translated from the first edition 7of ,ricardus d',aungervile1 ,bishop of ,durham71 #adgc1 appeared at ,london in #ahcb4 ,it was republished in ,america 7,albany1 ,n4 ,y47 in #ahfd4 #aja ,what are you laughing at8 #ajb ,see ,vol4 ,i1 page #cad1 note #d #fha4 #ajc ,see ,vol4 ,i1 page #aab1 note #g #baa4 #ajd ,referring to ,hamilton's edition of the ,collected ,works of ,dugald ,stewart1 #aj volumes1 ,edinburgh1 #ahed-eh4 ,it is not commonly remembered that ,stewart 7#agec-ahbh7 taught mathematics at the ,university of ,edinburgh before he took up philosophy4 #aje ,this was ,hamilton's edition of the ,works of ,thomas ,reid 7#b vols41 ,edinburgh1 #ahdf-ahfc74 ,reid 7#agaj-agif7 included mathematics in his work in philosophy at ,aberdeen4 ,in #agfd he succeeded ,adam ,smith at ,glasgow4 #ajf ,edward ,irving 7#agib-ahcd71 the famous preacher4 ,at first he assisted ,dr4 ,chalmers at ,glasgow1 but in #ahbb he went to ,london where he met with great success4 ,a few years later he became mentally unbalanced and was finally expelled from his church 7#ahcb7 for heresy4 ,he was a great friend of ,carlyle4 #ajg ,he also wrote a number of other paradoxes1 including ,an ,essay towards a ,science of ,consciousness 7#ahch71 ,instinctive ,natural ,religion 7#aheh71 ,popular ,treatise on the structure1 diseases1 and treatment of the human teeth 7#ahcg71 and ,on ,headache 7#ahei74 #ajh ,james ,smith 7#ahja-aheg71 known as ,shepherd ,smith1 was a socialist and a mystic1 with a philosophy that was wittily described as ,oriental pantheism translated into ,scotch4 ,he was editor of several journals4 #aji ,joanna ,southcott 7#agej-ahad7 was known for her rhyming prophecies in which she announced herself as the woman spoken of in ,revelations xii4 ,she had at one time as many as #ajj1jjj disciples1 and she established a sect that long survived her4 #aaj ,thales1 c4 #fdj-edh ,b4 ,c4 #aaa ,pythagoras1 #ehj-eja ,b4 ,c4 #aab ,anaxagoras1 #dii-dbh ,b4 ,c41 the last of the ,ionian school1 teacher of ,euripides and ,pericles4 ,plutarch speaks of him as having squared the circle4 #aac ,oinopides of ,chios1 contemporary of ,anaxagoras4 ,proclus tells us that ,oinopides was the first to show how to let fall a perpendicular to a line from an external point4 #aad ,bryson and ,antiphon1 contemporaries of ,socrates1 invented the so-called method of exhaustions1 one of the forerunners of the calculus4 #aae ,he wrote1 c4 #ddj ,b4 ,c41 the first elementary textbook on mathematics in the ,greek language4 ,the lunes of ,hippocrates are well known in geometry4 #aaf ,jabir ben ,aflah4 ,he lived c4 #ajhe1 at ,seville1 and wrote on astronomy and spherical trigonometry4 ,the ,gebri filii ,affla ,hispalensis de astronomia libri ,,ix was published at ,nuremberg in #aecc4 #aag ,hieronymus ,cardanus1 or ,girolamo ,cardano 7#aeja-aegf71 the great algebraist4 ,his ,artis magnae sive de regulis ,algebrae was published at ,nuremberg in #aede4 #aah ,nicolo ,tartaglia 7c4 #aejj-aeeg71 the great rival of ,cardan4 #aai ,see note #e #ih1 ,vol4 ,i1 page #fi4 #abj ,see note #aj #abd1 ,vol4 ,i41 page #hc4 #aba ,see note #i #abc1 ,vol4 ,i1 page #hc4 #abb ,pierre ,herigone lived in ,paris the first half of the #agth century4 ,his ,cours mathematique 7#f vols41 #afcd-afdd7 had some standing but was not at all original4 #abc ,franciscus van ,schooten 7died in #affa7 was professor of mathematics at ,leyden4 ,he edited ,descartes's ,la ,geometrie4 #abd ,florimond de ,beaune 7#afja-afeb7 was the first ,frenchman to write a commentary on ,descartes's ,la ,geometrie4 ,he did some noteworthy work in the theory of curves4 #abe ,see note #c #bc1 ,vol4 ,i1 page #da4 #abf ,olivier de ,serres 7b4 in #aeci7 was a writer on agriculture4 ,montucla speaks of him in his ,quadrature du cercle 7page #bbg7 as having asserted that the circle is twice the inscribed equilateral triangle1 although1 as ,de ,morgan points out1 this did not fairly interpret his position4 #abg ,anghera wrote not only the three works here mentioned1 but also the ,problemi del piu alto interesse scientifico1 geometricamente risoluti e dimostrati1 ,naples1 #ahfa4 ,his quadrature was defended by ,giovanni ,motti in a work entitled ,matematica ,vera4 ,falsita del sistema ciclometrico d',archimede1 quadratura del cerchio d',anghera1 ricerca algebraica dei lati di qualunque poligono regolare inscritto in un circolo1 ,voghera1 #ahgg4 ,the ,problemi of #ahfa contains ,anghera's portrait1 and states that he lived at ,malta from #ahdi to #ahfa4 ,it further states that the ,malta publications are in part reproduced in this work4 #abh ,this was his friend ,paolo ,pullicino whose ,elogio was pronounced by ,l4 ,farrugia at ,malta in #ahij4 ,he wrote a work ,la ,santa ,effegie della ,blata ,vergine ,maria1 published at ,valetta in #ahfh4 #abi ,st4 ,vitus1 ,st4 ,modestus1 and ,st4 ,crescentia were all martyred the same day1 being torn limb from limb after lions and molten lead had proved of no avail4 ,at least so the story runs4 #acj ,the reference is to ,cardinal ,wiseman4 ,see ,vol4 ,,ii1 page #bf1 note #ef4 #aca ,worthy of esteem4 #acb ,pedro de ,ribadeneira 7,ribadeneyra1 ,rivadeneira71 was born at ,toledo in #aebf and died in #afaa4 ,he held high position in the ,jesuit order4 ,the work referred to is the ,flos ,sanctorum o libro de las vidas de los santos1 of which there was an edition at ,barcelona in #afdc4 ,his life of ,loyola 7#aegb7 and ,historia ecclesiastica del ,cisma del reino de ,inglaterra were well known4 #acc ,caesar ,baronius 7#aech-afjg7 was made a cardinal in #aeie and became librarian at the ,vatican in #aeig4 ,the work referred to appeared at ,rome in #aehi4 #acd ,mrs4 ,jameson's 7#agid-ahfj7 works were very popular half a century ago1 and still have some circulation among art lovers4 ,the first edition of the work mentioned appeared in #ahdh4 #ace ,the barnyard cock4 #acf ,shanks did nothing but computing4 ,the title should1 of course1 read to #fjg ,places of ,decimals4 ,he later carried the computation to #gjg decimal places4 7,proc4 ,roy4 ,society1 ,,xxi1 p4 #cai47 ,he also prepared a table of prime numbers up to #fj1jjj4 7,proc4 ,roy4 ,society1 ,,xxii1 p4 #bjj47 #acg ,see ,vol4 ,i1 page #db1 note #d #bd4 #ach ,see ,vol4 ,i1 page #fd1 note #a #gh4 #aci ,see ,vol4 ,i1 page #cbh1 note #a #gjd4 #adj ,george ,suffield published ,synthetic ,division in ,arithmetic1 to which reference is made1 in #ahfc4 #ada ,john ,robert ,lunn wrote chiefly on ,church matters1 although he published a work on motion in #ahei4 #adb ,jean ,baptiste ,joseph1 ,baron ,fourier 7#agfh-ahcj71 sometime professor in the ,military ,school at ,paris1 and later at the ,ecole polytechnique4 ,he is best known by his ,theorie analytique de la chaleur 7,paris1 #ahbb71 in which the ,fourier series is used4 ,the work here referred to is the ,analyse des equations determinees 7,paris1 #ahca74 #adc ,william ,george ,horner 7#aghf-ahcg7 acquired a name for himself in mathematics in a curious manner4 ,he was not a university man nor was he a mathematician of any standing4 ,he taught school near ,bristol and at ,bath1 and seems to have stumbled upon his ingenious method for finding the approximate roots of numerical higher equations1 including as a special case the extracting of the various roots of numbers4 ,davies ,gilbert presented the method to the ,royal ,society in #ahai1 and it was reprinted in the ,ladies' ,diary for #ahch1 and in the ,mathematician in #ahdc4 ,the method was original as far as ,horner was concerned1 but it is practically identical with the one used by the ,chinese algebraist ,ch'in ,chiu-shang1 in his ,su-shu ,chiu-chang of #abdg4 ,but even ,ch'in ,chiu-shang can hardly be called the discoverer of the method since it is merely the extension of a process for root extracting that appeared in the ,chiu-chang ,suan-shu of the second century ,b4 ,c4 #add ,he afterwards edited ,loftus's ,inland ,revenue ,officers' ,manual 7,london1 #ahfe74 ,the two equations mentioned were x#c - #bx #e and y#c - #ijy#b #bejjy - #af1jjj #j1 in which y #cj - #ajx4 ,hence each place of y is the complement of the following place of x with respect to #i4 #ade ,probably the ,john ,power ,hicks who wrote a memoir on ,t4 ,h4 ,key1 ,london1 #ahic4 #adf ,possibly the one who wrote on the quadrature of the circle in #ahha4 #adg ,as it is4 ,but what a pity that we have not #ab fingers1 with duodecimal fractions instead of decimals6 ,we should then have #j4f for #a_/b1 #j4d for #a_/c1 #j4h for #b_/c1 #j4c for #a_/d1 #j4i for #c_/d1 and #j4af for #a_/h1 instead of #j4e1 #j4ccc1 #j4fff1 #j4be1 #j4ge1 and #j4abe as we now have with our decimal system4 ,in other words1 the most frequently used fractions in business would be much more easily represented on the duodecimal scale than on the decimal scale that we now use4 #adh ,he wrote ,hints for an ,essay on ,anemology and ,ombrology 7,london1 #ahci-dj7 and ,the ,music of the ,eye 7,london1 #ahca74 #adi ,brigham ,young 7#ahja-ahgg7 was born at ,whitingham1 ,vermont1 and entered the ,mormon church in #ahcb4 ,in #ahdj he was sent as a missionary to ,england4 ,after the death of ,joseph ,smith he became president of the ,mormons 7#ahdg71 leading the church to ,salt ,lake ,city 7#ahdh74 #aej ,joseph ,smith 7#ahje-ahdd7 was also born in ,vermont1 and was four years the junior of ,brigham ,young4 ,the ,book of ,mormon appeared in #ahbg1 and the church was founded in #ahcj4 ,he was murdered in #ahdd4 #aea ,orson ,pratt 7#ahaa-ahha7 was one of the twelve apostles of the ,mormon ,church 7#ahce71 and made several missionary journeys to ,england4 ,he was professor of mathematics in the ,university of ,deseret 7the ,mormon name for ,utah74 ,besides the paper mentioned ,pratt wrote the ,divine ,authenticity of the ,book of ,mormon 7#ahdi71 ,cubic and ,biquadratic ,equations 7#ahff71 and a ,key to the ,universe 7#ahff74 #aeb ,it does not follow4 #aec ,dryden 7#afca-agjj7 published his ,religio ,laici in #afhb4 ,the use of the word proportion in the sense of ratio was common before his time1 but he uses it in the sense of having four terms2 that is1 that price is to price as offence is to offence4 #aed ,olinthus ,gilbert ,gregory 7#aggd-ahda7 succeeded ,hutton as professor of mathematics at ,woolwich4 ,he was1 with ,de ,morgan1 much interested in founding the ,university of ,london4 ,he wrote on astronomy 7#agic71 mechanics 7#ahjf71 practical mathematics 7#ahbe71 and ,christian evidences 7#ahaa74 #aee ,see ,vol4 ,i1 page #bbj1 note #f #dhb4 ,the ,pensees appeared posthumously in #afgj4 #aef ,the right thing to do is not to wager at all4 ,yes1 but you ought to wager2 you have started out2 and not to wager at all that ,god exists is to wager that he does not exist4 #aeg ,he lived about #cjj ,a4,d41 in ,africa1 and wrote ,libri septem adversus ,gentes4 ,this was printed at ,rome in #aedb-c4 #aeh ,pierre ,bayle 7#afdg-agjf7 was professor of philosophy at the ,prostestant ,university at ,sedan from #afge until its dissolution in #afha4 ,he then became professor at ,rotterdam 7#afha-afic74 ,in #afhd he began the publication of his journal of literary criticism ,nouvelles de la ,republique des ,lettres4 ,he is best known for his erudite ,dictionnaire historique et critique 7#afig74 #aei ,but ,christ himself does not prove what he promises4 ,it is true4 ,for1 as ,i have said1 there cannot be any absolute proof of future events4 ,therefore since it is a condition of future events that they cannot be grasped or comprehended by any efforts of anticipation1 is it not more reasonable1 out of two alternatives that are uncertain and that are hanging in doubtful expectation1 to give credence to the one that gives some hope rather than to the one that offers none at all8 ,for in the former case there is no danger if1 as is said to threaten1 it becomes empty and void2 while in the latter case the danger is greatest1 that is1 the loss of salvation1 if when the time comes it is found that it was not a falsehood4 #afj ,gregg wrote several other paradoxes1 including the following3 ,the ,authentic ,report of the extraordinary case of ,tresham ,dames ,gregg 444 his committal to ,bridewell for refusing to give his recognizance 7,dublin1 #ahda71 ,an ,appeal to ,public ,opinion upon a ,case of ,injury and ,wrong 444 in the case of a question of prerogative that arose between ,r4 ,whately 444 ,archbishop of ,dublin and the author 7,london1 #ahfa71 ,the ,cosmology of ,sir ,isaac ,newton proved to be in accordance with the ,bible 7,london1 #ahga71 ,the ,steam ,locomotive as revealed in the ,bible 7,london #ahfc7 and ,on the ,sacred ,law of #ahff1 conferring perpetual life with immunity from decay and disease4 ,a cento of decisive scriptural oracles strangely discovered 7,london and ,dublin1 #ahge74 ,these titles will help the reader to understand the man whom ,de ,morgan so pleasantly satirizes4 #afa ,see ,vol4 ,i1 page #bfa1 note #b #eib4 #afb ,they have found it4 #afc ,the late ,greeks used the letters of their alphabet as numerals1 adding three early alphabetic characters4 ,the letter chi represented #fjj1 xi represented #fj1 and digamma stood for #f4 ,this gives #fff1 the number of the ,beast given in the ,revelation4 #afd ,allowing for necessary exceptions4 #afe ,mr4 ,gregg is not alone in his efforts to use the calculus in original lines1 as any one who has read ,herbart's application of the subject to psychology will recall4 #aff ,see ,vol4 ,i1 page #aje1 note #d #ahh2 page #aji1 note #a #aig4 #afg ,the full title shows the plan1--,the ,decimal ,system as a whole1 in its relation to time1 measure1 weight1 capacity1 and money1 in unison with each other4 ,but why is this so much worse than the ,french plan of which we have only the metric system and the decimal division of the angle left8 #afh ,one of the brothers of ,sir ,isaac ,pitman 7#ahac-ahig71 the inventor of modern stenography4 ,of these brothers1 ,benjamin taught the art in ,america1 ,jacob in ,australia1 and ,joseph1 ,henry1 and ,frederick in ,england4 #afi ,for example1 ,the ,phonographic ,lecturer 7,london1 #ahga etc471 ,the ,phonographic ,student 7#ahfg1 etc471 and ,the ,shorthand ,magazine 7#ahff1 etc474 #agj ,see ,vol4 ,,ii1 page #fh1 note #adh4 #aga ,it involves the theory of non-,euclidean geometry1 ,euclid's postulate of parallels being used in proving this theorem4 #agb ,referring to the fact that none of the works of ,thales is extant4 #agc ,the author was one ,b4 ,bulstrode4 ,parts #d and #e were printed at ,calcutta4 #agd ,see ,vol4 ,,ii1 page #e1 note #ah4 #age ,see ,vol4 ,i1 page #he1 note #b #abi4 #agf ,alexander ,vasilievich ,suvaroff 7#agbi-ahjj71 a ,russian general who fought against the ,turks1 in the ,polish wars1 and in the early ,napoleonic campaigns4 ,when he took ,ismail in #agij he sent this couplet to ,empress ,catherine4 #agg ,newton hath determined rightly1 ,newton hath not determined rightly4 #agh ,see ,vol4 ,i1 page #bhh1 note #c #fba4 #agi ,see ,vol4 ,i1 page #cbf1 note #a #gjj4 #ahj ,with great honor4 #aha ,apparently unknown to biographers4 ,he seems to have written nothing else4 #ahb ,captain ,marryat 7#agib-ahdh7 published ,snarley-yow1 or the ,dog ,fiend in #ahcg4 #ahc ,he is not known to biographers1 and published nothing else under this name4 #ahd ,see ,vol4 ,i1 page #hj1 note #e #aai4 #ahe ,he published a ,family and ,commercial ,illustrated ,almanack and ,year ,book 444 for #ahfa 7,bath1 #ahfj74 #ahf ,louis ,dutens 7#agcj-ahab7 was born at ,tours1 but went to ,england as a young man4 ,he made the first collection of the works of ,leibnitz1 against the advice of ,voltaire1 who wrote to him3 ,les ecrits de ,leibnitz sont epars comme les feuilles de la ,sybille1 et aussi obscurs que les ecrits de cette vieille4 ,the work appeared at ,geneva1 in six volumes1 in #agfi4 #ahg ,mungo ,park 7#agga-ahjf71 the first ,european to explore the ,niger 7#agie-f74 ,his ,travels in the ,interior of ,africa appeared in #agii4 ,he died in ,africa4 #ahh ,gerhard ,mercator 7#aeab-aeid7 the well-known map maker of ,louvain4 ,the ,mercator's ,projection was probably made as early as #aeej1 but the principle of its construction was first set forth by ,edward ,wright 7,london1 #aeii74 #ahi ,quirico ,barilli ,filopanti wrote a number of works and monographs4 ,he succeeded in getting his ,cesare al ,rubicone and ,degli usi idraulici della ,tela in the ,memoria letta 444 all' ,accademia delle ,scienze in ,bologna 7#ahdg1 #ahff74 ,he also wrote ,dio esiste 7#ahha71 ,dio ,liberale 7#ahhj71 and ,sunto della memoria sulle geuranie ossia di alcune singolari relazioni cosmiche della terra e del cielo 7#ahfb74 #aij ,the periods of disembodiment may be interesting4 ,they will be seen from the following dates3 ,descartes 7#aeif-afej71 ,william ,,iii 7#afej-agjb72 ,roger ,bacon 7#abad to c4 #abid71 ,boccaccio 7#acac-acge74 ,charles ,,ix was born in #aeej and died in #aegd4 #aia ,his real name was ,frederick ,parker1 and he wrote several works on the ,greek language and on religion4 ,among these were a translation of the ,new ,testament from the ,vatican ,,ms4 7#ahfd71 ,the ,revealed ,history of ,man 7#ahed71 ,an ,enquiry respecting the ,punctuation of ,ancient ,greek 7#ahda71 and ,rules for ,ascertaining the sense conveyed in ,ancient ,greek ,manuscripts 7#ahdh1 the seventh edition appearing in #ahfb74 #aib ,see ,vol4 ,i1 page #ceb1 second note #a #gcf4 ,the literature on the subject of the ,great ,pyramid1 considered from the standpoint of metrology1 is extensive4 #aic ,see ,vol4 ,i1 page #hj1 note #e #aai4 #aid ,sir ,philip ,francis 7#agdj-ahah7 was a ,whig politician4 ,the evidence that he was the author of the ,letters of ,junius 7#agfi-aggb7 is purely circumstantial4 ,he was clerk in the war office at the time of their publication4 ,in #aggd he was made a member of the ,supreme ,council of ,bengal1 and was a vigorous opponent of ,warren ,hastings1 the two fighting a duel in #aghj4 ,he entered parliament in #aghd and was among the leaders in the agitation for parliamentary reform4 #aie ,mrs4 ,cottle published a number of letters that attracted attention at the time4 ,among these were letters to the emperor of ,france and king of ,sardinia 7#ahei7 relating to the prophecies of the war between ,france and ,austria2 to ,g4 ,c4 ,lavis and ,her ,majesty's ,ministers 7#ahei7 relating to her claims as a prophetess2 and to the ,crowned ,heads at ,st4 ,james1 the ,king of ,prussia1 and others 7#ahfj71 relating to certain passages of ,scripture4 ,she also wrote ,the ,lamb's ,book of ,life for the ,new ,jerusalem ,church and ,kingdom1 interpreted for all nations 7#ahfa74 #aif ,see ,vol4 ,i1 page #cae1 note #b #fhe1 and ,vol4 ,,ii1 page #eh1 note #aji4 #aig ,a ,congregational minister1 who published a number of sermons1 chiefly obituaries1 between #ahjd and #ahea4 ,his ,frailty of ,human ,life1 two sermons delivered on the occasion of the death of ,princess ,charlotte1 went through at least three editions4 #aih ,he was secretary of the ,congregational ,board and editor of the ,congregational ,year ,book 7from #ahdf7 and the ,congregational ,manual4 #aii ,frederick ,denison ,maurice 7#ahje-ahgb7 began his preaching as a ,unitarian but entered the ,established ,church in #ahca1 being ordained in #ahcd4 ,he was professor of ,english and ,history at ,king's ,college1 ,london1 from #ahdj to #ahec4 ,he was one of the founders of ,queen's ,college for women1 and was the first principal of the ,working ,men's ,college1 ,london4 ,the subject referred to by ,de ,morgan is his expression of opinion in his ,theological ,essays 7#ahec7 that future punishment is not eternal4 ,as a result of this expression he lost his professorship at ,king's ,college4 ,in #ahff he was made ,knightbridge ,professor of ,casuistry1 ,moral ,theology1 and ,moral ,philosophy at ,cambridge4 #bjj ,see ,vol4 ,i1 page #df1 note #a #db4 ,besides the books mentioned in this list he wrote ,the ,ratio between ,diameter and ,circumference demonstrated by angles1 and ,euclid's ,theorem1 ,proposition #cb1 ,book ,i1 proved to be fallacious 7,liverpool1 #ahgj74 ,this is the theorem which asserts that the exterior angle of a triangle is equal to the sum of the two opposite interior angles1 and that the sum of the interior angles equals two right angles4 ,he also published his ,curiosities of ,mathematics in #ahgj1 a work containing an extensive correspondence with every one who would pay any attention to him4 ,de ,morgan was then too feeble to show any interest in the final effort of the subject of some of his keenest satire4 #bja ,see ,vol4 ,i1 page #ccb1 note #d #gji4 #bjb ,see ,vol4 ,i1 page #aja1 note #d #agd4 #bjc ,the circle-squaring disease2 literally1 the circle-measuring disease4 #bjd ,see ,vol4 ,,ii1 page #fc1 note #acf4 #bje ,william ,rutherford 7c4 #agih-ahga71 teacher of mathematics at ,woolwich1 secretary of the ,royal ,astronomical ,society1 editor of ,the ,mathematician1 and author of various textbooks4 ,the ,extension of pi to #ddj places1 appeared in the ,proceedings of the ,royal ,society in #ahec 7p4 #bgd74 #bjf ,charles ,knight 7#agia-ahgc7 was associated with ,de ,morgan for many years4 ,after #ahbh he superintended the publications of the ,society for the ,diffusion of ,useful ,knowledge1 to which ,de ,morgan contributed1 and he edited the ,penny ,cyclopedia 7#ahcc-ahdd7 for which ,de ,morgan wrote the articles on mathematics4 #bjg ,sir ,william ,hamilton4 ,see ,vol4 ,i1 page #aab1 note #g #baa4 #bjh ,adam ,smith 7#agbc-agij7 was not only known for his ,wealth of ,nations 7#aggf71 but for his ,theory of ,moral ,sentiments 7#agei71 published while he was professor of moral philosophy at ,glasgow 7#ageb-agfd74 ,he was ,lord ,rector of the university in #aghg4 #bji ,see ,vol4 ,i1 page #ccb1 note #d #gji4 #baj ,whip4 #baa ,terrible lash4 #bab ,an accomplished fact an accomplished fault4 #bac ,see ,extracts from the ,diary and ,letters of ,mrs4 ,mary ,cobb1 ,london1 #ahje4 #bad ,gentle in manner4 #bae ,brave in action4 ,the motto of ,earl ,newborough was ,suaviter in modo1 fortiter in re4 #baf ,reduction to an absurdity1 a method of proof occasionally used in geometry and in logic4 #bag ,he has lost the right of being moved 7struck7 by evidence4 #bah ,for radix quadratus4 ,the usual root sign is supposed to be derived from r 7for radix71 and at one time q was commonly used for square1 as in ,viete's style of writing ,aq for ,a#b4 #bai ,the ,garde ,douloureuse was a castle in the marches of ,wales and received its name because of its exposure to attacks by the ,welsh4 #bbj ,out of the fight4 #bba ,hidden4 #bbb ,john ,cam ,hobhouse 7#aghf-ahfi71 ,baron ,broughton1 was committed to ,newgate for two months in #ahai for his anonymous pamphlet1 ,a ,trifling ,mistake4 ,this was a great advertisement for him1 and upon his release he was at once elected to parliament for ,westminster4 ,he was a strong supporter of all reform measures1 and was ,secretary for ,war in #ahcb4 ,he was created ,baron ,broughton de ,gyfford in #ahea4 #bbc ,thomas ,erskine 7#agej-ahbc71 the famous orator4 ,he became ,lord ,chancellor in #ahjf1 but sat in the ,house of ,commons most of his life4 #bbd ,the above is explained in the ,,ms4 by a paragraph referring to some anagrams1 in one of which1 by help of the orthography suggested1 a designation for this cyclometer was obtained from the letters of his name4--,s4 ,e4 ,de ,m4 #bbe ,a personal verb agrees with its subject4 #bbf ,see ,vol4 ,i1 page #cbf1 note #a #gjj4 #bbg ,see ,vol4 ,i1 page #cbf1 note #b #gja4 #bbh ,apparently unknown to biographers4 #bbi ,the ,bibliotheca ,mathematica of ,ludwig ,adolph ,sohncke 7#ahjg-ahec71 professor of mathematics at ,koenigsberg and ,halle1 covered the period from #ahcj to #ahed1 being completed by ,w4 ,engelmann4 ,it appeared in #ahed4 #bcj ,see ,vol4 ,i1 page #cib1 note #b #hje4 #bca ,see ,vol4 ,i1 page #dc1 note #g #cb4 #bcb ,see ,vol4 ,,ii1 page #ia1 note #ahg4 #bcc ,mason made a notable balloon trip from ,london to ,weilburg1 in the ,duchy of ,nassau1 in ,november1 #ahcf1 covering #ejj miles in #ah hours4 ,he published an account of this trip in #ahcg1 and a work entitled ,aeronautica in #ahch4 #bcd ,william ,harrison ,ainsworth 7#ahje-ahhe7 the novelist4 #bce ,on this question see ,vol4 ,i1 page #cbf1 note #b #gja4 #bcf ,major ,general ,alfred ,wilks ,drayson1 author of various works on geology1 astronomy1 military surveying1 and adventure4 #bcg ,hailes also wrote several other paradoxes on astronomy and circle squaring during the period #ahdc-ahgb4 #bch ,see ,vol4 ,i1 page #dc1 note #h #cc4 #bci ,see ,vol4 ,i1 page #dc1 note #g #cb4 #bdj ,very small errors are not to be condemned4 #bda ,he seems to have written nothing else4 #bdb ,besides the paradoxes here mentioned by ,de ,morgan he wrote several other works1 including the following3 ,abriss der ,babylonisch-,assyrischen ,geschichte 7,mannheim1 #ahed71 ,a ,popular ,inquiry into the ,moon's rotation on her axis 7,london1 #ahef71 ,practical ,tables for the reduction of the ,mahometan dates to the ,christian kalendar 7,london1 #ahef71 ,grundzuege einer neuen ,weltlehre 7,munich1 #ahfj71 and ,on the historical ,antiquity of the ,people of ,egypt 7,london1 #ahfc74 #bdc ,dircks 7#ahjf-ahgc7 was a civil engineer of prominence1 and a member of the ,british ,association and the ,royal ,society of ,edinburgh4 ,he wrote 7#ahfc7 on ,pepper's ,ghost1 an ingenious optical illusion invented by him4 ,there was a second edition of the ,perpetuum ,mobile in #ahgj4 #bdd ,george ,stephenson 7#agha-ahdh71 the inventor of the first successful steam locomotive4 ,his first engine was tried in #ahad4 #bde ,robert ,stephenson 7#ahjc-ahei71 the only son of ,george4 ,most of the early improvements in locomotive manufacture were due to him4 ,he was also well known for his construction of great bridges4 #bdf ,in its proper place4 #bdg ,a fool always finds a bigger fool to admire him4 #bdh ,see ,vol4 ,i1 page #dc1 note #g #cb4 #bdi ,see ,vol4 ,i1 page #dc1 note #h #cc4 #bej ,see ,vol4 ,i1 page #he1 note #b #abi4 #bea ,see ,vol4 ,i1 page #cij1 note #a #cij4 #beb ,from #ahbc to #aheb it was edited by ,i4 ,c4 ,robertson2 from #aheb to #aheg by ,r4 ,a4 ,brooman2 and from #aheg to #ahfc by ,brooman and ,e4 ,j4 ,reed4 #bec ,sir ,james ,ivory 7#agfe-ahdb7 was1 as a young man1 manager of a flax mill in ,scotland4 ,in #ahjd he was made professor of mathematics at the ,royal ,military ,college1 then at ,marlow and later at ,sandhurst4 ,he was deeply interested in mathematical physics1 and there is a theorem on the attraction of ellipsoids that bears his name4 ,he was awarded three medals of the ,royal ,society1 and was knighted together with ,herschel and ,brewster1 in #ahca4 #bed ,see ,vol4 ,i1 page #ef1 note #a #fd4 #bee ,see ,vol4 ,i1 page #aec1 note #e #cch4 #bef ,see ,vol4 ,i1 page #cji1 note #b #fgj4 #beg ,see ,vol4 ,i1 page #hg1 note #d #acc4 #beh ,george ,canning 7#aggj-aheg71 the ,tory statesman and friend of ,scott1 was much interested in founding the ,quarterly ,review 7#ahjh7 and was a contributor to its pages4 #bei ,see ,vol4 ,i1 page #ahf1 note #ad #dah4 #bfj ,see ,vol4 ,,ii1 page #ada1 note #beb4 #bfa ,de ,morgan had a number of excellent articles in this publication4 #bfb ,see ,vol4 ,i1 page #bgi1 note #a #faa4 #bfc ,james ,orchard ,halliwell 7#ahbj-ahhi71 afterwards ,halliwell-,phillips1 came into prominence as a writer at an early age4 ,when he was seventeen he wrote a series of lives of mathematicians for the ,parthenon4 ,his ,rara ,mathematica appeared when he was but nineteen4 ,he was a great bibliophile and an enthusiastic student of ,shakespeare4 #bfd ,this was written at the age of twenty-two4 #bfe ,the subject of this criticism is of long past date1 and as it has only been introduced by the author as an instance of faulty editorship1 ,i have omitted the name of the writer of the libel1 and a few lines of further detail4--,s4 ,e4 ,de ,m4 #bff ,condemned souls4 #bfg ,the editor of the ,mechanics' ,magazine died soon after the above was written4--,s4 ,e4 ,de ,m4 #bfh ,thomas ,stephens ,davies 7#agie-ahea7 was mathematical master at ,woolwich and ,f4 ,r4 ,s4 ,he contributed a series of ,geometrical ,notes to the ,mechanics' ,magazine and edited the ,mathematician4 ,he also published a number of text-books4 #bfi ,see ,vol4 ,,ii1 page #ff1 note #adc4 #bgj ,the ,dictionary of ,greek and ,roman ,biography 7#ahdi71 edited by ,sir ,william ,smith 7#ahac-ahic71 whose other dictionaries on classical and biblical matters are well known4 #bga ,o ,j4 ,s46 ,this is the worst6 the greatest possible injury6 #bgb ,see ,vol4 ,i1 page #dd1 note #i #cd and page #aaj1 note #e #bja4 #bgc ,if there's a man whom the judge's pitiless sentence awaiteth1 ,his head condemned to penalties and tribulations1 ,let neither penitentiaries tire him with laborer's burdens ,nor let his stiffened hands be harrassed by work in the mines4 ,he must square the circle6 ,for what else do ,i care8--all ,known punishments this one task hath surely included4 #bgd ,houlston was in the customs service4 ,he also published ,inklings of ,areal ,autometry1 ,london1 #ahgd4 #bge ,this is ,frederick ,c4 ,bakewell4 ,he had already published ,natural ,evidence of a ,future ,life 7,london1 #ahce71 ,philosophical ,conversations 7,london1 #ahcc1 with other editions71 and ,electric ,science 7,london1 #ahec1 with other editions74 #bgf ,henry ,f4 ,a4 ,pratt had already published ,a ,dissertation on the power of the intercepted pressure of the ,atmosphere 7,london1 #ahdd7 and ,the ,genealogy of ,creation 7#ahfa74 ,later he published a work ,on ,orbital ,motion 7#ahfc71 and ,astronomical ,investigations 7#ahfe74 #bgg ,see ,vol4 ,i1 page #bfj1 note #a #eia4 #bgh ,thomas ,rawson ,birks 7#ahaj-ahhc71 a theologian and controversialist1 fellow of ,trinity ,college1 ,cambridge1 and 7#ahgb7 professor of moral philosophy in that university4 ,he wrote ,modern ,rationalism 7#ahec71 ,the ,bible and ,modern ,thought 7#ahfa71 ,the ,first ,principles of ,moral ,science 7#ahgc71 and ,modern ,physical ,fatalism and the ,doctrine of ,evolution 7#ahgf71 the last being an attack on ,herbert ,spencer's ,first ,principles4 #bgi ,pseudonym for ,william ,thorn4 ,in the following year 7#ahfc7 he published a second work1 ,the ,thorn-,tree3 being a ,history of ,thorn ,worship1 a reply to ,bishop ,colenso's work entitled ,the ,pentateuch and the ,book of ,joshua critically examined4 #bhj ,besides ,the ,pestilence 7#ahff7 he published ,the ,true ,church 7#ahea71 ,the ,church and her destinies 7#ahee71 ,religious reformation imperatively demanded 7#ahfd71 and ,the ,bible plan unfolded 7second edition1 #ahgb74 #bha ,see ,vol4 ,,ii1 page #ig1 note #aie4 #bhb ,sir ,george ,cornewall ,lewis 7#ahjf-ahfc7 also wrote an ,essay on the ,origin and ,formation of the ,romance ,languages 7#ahce71 an ,essay on the ,government of ,dependencies 7#ahda71 and an ,essay on ,foreign ,jurisdiction and the ,extradition of ,criminals 7#ahei74 ,he was ,chancellor of the ,exchequer in #ahee and ,home ,secretary in #ahei4 #bhc ,henry ,malden 7#ahjj-ahgf71 a classical scholar1 fellow of ,trinity ,college1 ,cambridge1 and professor of ,greek at ,university ,college 7#ahca-ahgf71 then 7#ahca7 the ,university of ,london4 ,he wrote a ,history of ,rome to #cij ,b4 ,c4 7#ahcj71 and ,on the ,origin of ,universities and ,academical ,degrees 7#ahce74 #bhd ,henry ,longueville ,mansel 7#ahbj-ahga71 theologian and metaphysician1 reader in theology at ,magdalen ,college1 ,oxford 7#ahee71 and professor of ecclesiastical history and ,dean of ,st4 ,paul's 7#ahff74 ,he wrote on metaphysics1 and his ,bampton ,lectures 7#aheh7 were reprinted several times4 #bhe ,hejus gave freely1 gave freely4 ,god is propitious1 ,god is favorable to him who gives freely4 ,god is honored with a banquet of eggs at the cross roads1 the god of the world4 ,god1 with benignant spirit1 desired in sacrifice a goat1 a bull to be carried within the precincts of the holy place4 ,god1 twice propitiated1 blesses the pit of the sacred libation4 #bhf ,eudoxus of ,cnidus 7#djh-cee ,b4 ,c47 had much to do with the early scientific astronomy of the ,greeks4 ,the fifth book of ,euclid is generally attributed to him4 ,his astronomical works are known chiefly through the poetical version of ,aratus mentioned in note #ac1 page #afg4 #bhg ,simplicius1 a native of ,cilicia1 lived in the #fth century of our era4 ,he was driven from ,athens by ,justinian and went to ,persia 7#eca71 but he returned later and had some fame as a teacher4 #bhh ,see ,vol4 ,i1 page #afj1 note #c #cdh4 #bhi ,see ,vol4 ,i1 page #gf1 note #c #aab4 #bij ,through right and wrong4 #bia ,it is therefore to arrive at this parallelism1 or to preserve it1 that ,copernicus feared to be obliged to have recourse to this equal and opposite movement which destroys the effect which he attributed so freely to the first1 of deranging the parallelism4 #bib ,a contemporary of ,plato and a disciple of ,aristotle4 #bic ,meton's solstice1 the beginning of the ,metonic cycles1 has been placed at #dcb ,b4 ,c4 ,ptolemy states that he made the length of the year #cfe-a_/d #a_/gb days4 #bid ,aratus lived about #bgj ,b4 ,c41 at the court of ,antigonus of ,macedonia1 and probably practiced medicine there4 ,he was the author of two astronomical poems1 the ,greek3 ,phainomena1 apparently based on the lost work of ,eudoxus1 and the ,greek3 ,dioseeia based on ,aristotle's ,meteorologica and ,de ,signis ,ventorum of ,theophrastus4 #bie ,the nineteen 7-year7 cycle of the shining sun4 #bif ,claudius ,salmasius 7#aehh-afec71 or ,claude ,saumaise1 was a distinguished classicist1 and professor at the ,university of ,leyden4 ,the word ,greek3 eleioio means ,elian1 thus making the phrase refer to the brilliant one of ,elis4 #big ,sir ,william ,brown 7#aghd-ahfd74 ,in #ahjj the family moved to ,baltimore1 and there the father1 ,alexander ,brown1 became prominent in the linen trade4 ,william went to ,liverpool where he acquired great wealth as a merchant and banker4 ,he was made a baronet in #ahfc4 #bih ,robert ,lowe 7#ahaa-ahib71 viscount ,sherbrooke1 was a fellow of ,magdalen ,college1 ,oxford 7#ahce74 ,he went to ,australia in #ahdb and was very successful at the bar4 ,he returned to ,england in #ahej and became leader writer on the ,times4 ,he was many years in parliament1 and in #ahhj was raised to the peerage4 #bii ,see ,vol4 ,i1 page #db1 note #d #bd4 #cjj ,francis ,walkingame 7fl4 about #agea-aghe71 whose ,tutor's ,assistant went through many editions from #agea-ahed4 #cja ,davies ,gilbert 7#agfg-ahci74 ,his family name was ,giddy1 but he assumed his wife's name4 ,he sat in parliament from #ahjf to #ahcb4 ,in #ahai he secured the establishment of the ,cape of ,good ,hope observatory4 ,he was ,treasurer 7#ahbj-ahbg7 and ,president 7#ahbg-ahcj7 of the ,royal ,society4 #cjb ,see ,vol4 ,i1 page #ee1 note #b #fc4 #cjc ,sir ,jonathan ,frederick ,pollock 7#aghc-ahgj7 entered parliament in #ahca and was knighted in #ahcd4 #cjd ,joseph ,hume 7#aggg-ahee7 entered parliament in #ahab and for thirty years was leader of the ,radical party4 #cje ,what6 when ,i say1 ',nicole1 bring me my slippers1' is that prose8 #cjf ,captain ,basil ,hall 7#aghh-ahdd71 a naval officer1 carried on a series of pendulum observations in #ahbj-ahbb1 while on a cruise of the west coast of ,north ,america4 ,the results were published in #ahbc in the ,philosophical ,transactions4 ,he also wrote two popular works on travel that went through numerous editions4 #cjg ,anthony ,ashley ,cooper 7#ahja-ahhe71 ,earl of ,shaftesbury4 ,his name is connected with philanthropic work and factory legislation4 #cjh ,see ,vol4 ,i1 page #bjg1 note #ab #dfi4 #cji ,see ,vol4 ,i1 page #hj1 note #e #aai4 #caj ,sir ,thomas ,maclear 7#agid-ahgi71 an ,irishman by birth1 became ,astronomer ,royal at the ,cape of ,good ,hope in #ahcc4 ,he was an indefatigable observer4 ,he was knighted in #ahfj4 #caa ,thomas ,romney ,robinson 7#agib-ahhb71 another ,irish astronomer of prominence4 ,he was a deputy professor at ,trinity ,college1 ,dublin1 but took charge of the ,armagh observatory in #ahbc and remained there until his death4 #cab ,sir ,james ,south 7#aghe-ahfg7 was in early life a surgeon1 but gave up his practice in #ahaf and fitted up a private observatory4 ,he contributed to the science of astronomy1 particularly with respect to the study of double stars4 #cac ,sir ,john ,wrottesley 7#agih-ahfg71 second ,baron ,wrottesley4 ,like ,sir ,james ,south1 he took up the study of astronomy after a professional career1--in his case in law4 ,he built a private observatory in #ahbi and made a long series of observations1 publishing three star catalogues4 ,he was president of the ,astronomical ,society from #ahda to #ahdc1 and of the ,royal ,society from #ahed to #aheg4 #cad ,he seems to have written nothing else4 #cae ,see ,vol4 ,,ii1 page #fh1 note #adg4 #caf ,the wills are free1 and ,i wish neither the one nor the other4 #cag ,the force of inertia conquered4 #cah ,reddie also wrote ,the ,mechanics of the ,heavens1 referred to later in this work4 ,he must not be confused with ,judge ,james ,reddie 7#aggc-aheb71 of ,glasgow1 who wrote on international law1 although this is done in the printed edition of the ,british ,museum catalogue1 for he is mentioned by ,de ,morgan somewhat later as alive in #ahfb4 #cai ,henry ,dunning ,macleod 7#ahba-aijb71 a lawyer and writer on political economy1 was a ,scotchman by birth4 ,he wrote on economical questions1 and lectured on banking at ,cambridge 7#ahgg7 and at ,king's ,college1 ,london 7#ahgh74 ,he was a free lance in his field1 and was not considered orthodox by the majority of economists of his time4 ,he was an unsuccessful candidate for the chairs of political economy at ,cambridge 7#ahfc71 ,edinburgh 7#ahga71 and ,oxford 7#ahhh74 #cbj ,see ,vol4 ,i1 page #beb1 note #b #egf4 #cba ,francis ,henry ,laing 7#ahaf-ahhi7 was a graduate of ,queen's ,college1 ,cambridge1 and a clergyman in the ,church of ,england until #ahdf1 when he entered the ,church of ,rome4 ,he taught in various ,jesuit colleges until #ahfb1 when his eccentricity was too marked to warrant the ,church in allowing him to continue4 ,he published various controversial writings during his later years4 ,of course if he had known the works of ,wessel1 ,gaus1 ,buee1 ,argand1 and others1 he would not have made such a sorry exhibition of his ignorance of mathematics4 #cbb ,see ,vol4 ,i1 page #cbi1 note #a #gje4 ,the book went into a second edition in #ahfd4 #cbc ,thomas ,weddle 7#ahag-ahec7 was1 at the time of publishing this paper1 a teacher in a private school4 ,in #ahea he became professor of mathematics at ,sandhurst4 ,he contributed several papers to the ,cambridge and ,dublin ,mathematical ,journal1 chiefly on geometry4 #cbd ,see ,vol4 ,,ii1 page #aji1 note #bje4 #cbe ,see ,vol4 ,,ii1 page #ff1 note #adc4 #cbf ,see ,vol4 ,,ii1 page #aea1 note #bfh4 #cbg ,george ,barrett 7#ageb-ahba7 worked from #aghf to #ahaa on a set of life insurance and annuity tables4 ,he invented a plan known as the columnar method for the construction of such tables1 and as ,de ,morgan states1 this was published by ,francis ,baily1 appearing in the appendix to his work on annuities1 in the edition of #ahac4 ,some of his tables were used in ,babbage's ,comparative ,view of the various ,institutions for the ,assurance of ,lives 7#ahbf74 #cbh ,see ,vol4 ,i1 page #cji1 note #b #fgj4 #cbi ,this was his ,practical short and direct ,method of ,calculating the ,logarithm of any given ,number1 and the ,number corresponding to any given ,logarithm 7#ahdi74 #ccj ,this is ,william ,neile 7#afcg-afgj71 grandson of ,richard ,neile 7not ,neal71 ,archbishop of ,york4 ,at the age of #ai1 in #afeg1 he gave the first rectification of the semicubical parabola4 ,although he communicated it to ,brouncker1 ,wren1 and others1 it was not published until #afci1 when it appeared in ,john ,wallis's ,de ,cycloide4 #cca ,i myself was a considerable part4 #ccb ,he also wrote ,a ,glance at the ,universe 7#b;d thousand in #ahfb71 and ,the ,resurrection ,body 7#ahfi74 #ccc ,see ,vol4 ,i1 page #fc1 note #a #gd4 #ccd ,as ,swift gave it in his ,poetry4 ,a ,rhapsody1 it is as follows3 ,so1 naturalists observe1 a flea ,has smaller fleas that on him prey2 ,and these have smaller still to bite 'em4 ,and so proceed ad infinitum4 #cce ,perhaps #a1fjj1jjj1jjj years1 if ,boltwood's recent computations based on radium disintegration stand the test4 ,this would mean1 according to ,mac,curdy's estimate1 #fj1jjj1jjj years since life first appeared on the earth4 #ccf ,de ,morgan wrote better than he knew1 for this work1 the ,allgemeine ,encyclopaedie der ,wissenschaften und ,kuenste1 begun at ,leipsic in #ahah1 is still 7#aiac7 unfinished4 ,section ,i1 ,a-,g1 consists of #ii parts in #ef volumes2 ,section ,,ii1 ,h-,n1 consists of #dc volumes and is not yet completed2 and ,section ,,iii1 ,o-,z1 consists of #be volumes thus far1 with most of the work still to be done4 ,johann ,samuel ,ersch 7#agff-ahbh71 the founder1 was head librarian at ,halle4 ,johann ,gottfried ,gruber 7#aggd-ahea71 his associate1 was professor of philosophy at the same university4 #ccg ,william ,howitt 7#agib-ahgi7 was a poet1 a spiritualist1 and a miscellaneous writer4 ,he and his wife became spiritualists about #ahej4 ,he wrote numerous popular works on travel1 nature and history4 #cch ,see ,vol4 ,,ii1 page #ee1 note #ajh4 #cci ,as will be inferred from the text1 ,c4 ,d4 was ,mrs4 ,de ,morgan1 and ,a4 ,b4 was ,de ,morgan4 #cdj ,jean ,meslier 7#afgh-agcc71 cure of ,estrepigny1 in ,champagne1 was a skeptic1 but preached only strict orthodoxy to his people4 ,it was only in his manuscript1 ,mon ,testament1 that was published after his death1 and that caused a great sensation in ,france1 that his antagonism to ,christianity became known4 #cda ,baron ,zach relates that a friend of his1 in a writing intended for publication1 said ,un esprit doit se frotter contre un autre4 ,the censors struck it out4 ,the ,austrian police have a keen eye for consequences4--,a4 ,de ,m4 ,one mind must rub against another4 ,on ,baron ,zach1 see ,vol4 ,,ii1 page #de1 note #d4 #cdb ,referring to the first ,lord ,eldon 7#agea-ahch71 who was ,lord ,chancellor from #agii to #ahbg1 with the exception of one year4 #cdc ,sleeping power4 #cdd ,causes sleep4 #cde ,richard ,hooker 7c4 #aeed-afjj71 a theologian1 the ablest living advocate of the ,church of ,england as by law established4 #cdf ,see ,vol4 ,i1 page #gf1 note #c #aab4 #cdg ,other ,i1--other self4 #cdh ,this utter rejection has been repeated 7#ahgb7 by the same writer4--,s4 ,e4 ,de ,m4 #cdi ,edward ,jenner 7#agdi-ahbc7 was a physician and biologist4 ,his first experiments in vaccination were made in #agif1 and his discovery was published in #agih4 #cej ,see ,vol4 ,,ii1 page #ch1 note #hj4 #cea ,you will go most safely in the middle 7way74 #ceb ,pierre ,joseph ,arson was known early in the #aith century for his controversy with ,hoene ,wronski the mathematician1 whom he attacked in his ,document pour l'histoire des grands fourbes qui ont figure sur la terre 7#ahag-ahah74 #cec ,we enter the course by night and are consumed by fire4 #ced ,see ,vol4 ,i1 page #ea1 note #c #ea4 #cee ,see ,vol4 ,i1 page #ccf1 note #h #gac4 #cef ,see ,vol4 ,i1 page #acg1 note #h #bhf4 #ceg ,see ,vol4 ,i1 page #bbi1 note #b #eae4 #ceh ,richard ,cobden 7#ahjd-ahfe71 the cotton manufacturer and statesman who was prominent in his advocacy of the repeal of the ,corn ,laws4 #cei ,james ,smith 7#agge-ahci71 solicitor to the ,board of ,ordnance4 ,with his brother ,horatio he wrote numerous satires4 ,his ,horace in ,london 7#ahac7 imitated the ,roman poet4 ,his works were collected and published in #ahdj4 #cfj ,samuel ,butler 7#afab-afhj71 the poet and satirist1 author of ,hudibras 7#affc-afgh74 #cfa ,is it not fine to be sure of one's action when entering in a combat with another8 ,there1 push me a little in order to see4 ,,nicole4 ,well6 what's the matter8 ,m4 ,,jourdain4 ,slowly4 ,ho there6 ,ho6 gently4 ,deuce take the rascal6 ,,nicole4 ,you told me to push4 ,m4 ,,jourdain4 ,yes1 but you pushed me en tierce1 before you pushed en quarte1 and you did not give me time to parry4 #cfb ,john ,abernethy 7#agfd-ahca71 the famous physician and surgeon4 #cfc ,see ,vol4 ,i1 page #ajb1 note #e #age4 #cfd ,with what measure ye mete1 it shall be measured to you again4 #cfe ,eusebius of ,caesarea 7c4 #bfj-cdj71 leader of the moderate party at the ,council of ,nicaea1 and author of a ,history of the ,christian ,church in ten books 7c4 #cbd ,a4 ,d474 #cff ,nathaniel ,lardner 7#afhd-agfh71 a non-conformist minister and one of the first to advocate the scientific study of early ,christian literature4 #cfg ,henry ,alford 7#ahaj-ahga7 ,dean of ,canterbury 7#aheg-ahga7 and editor of the ,greek ,testament 7#ahdi-ahfa74 #cfh ,the work was ,the ,number and ,names of the ,apocalyptic ,beasts3 with an explanation and application4 ,part ,i4 ,london1 #ahdh1 as mentioned below4 ,thom also wrote ,the ,assurance of ,faith1 or ,calvinism identified with ,universalism 7,london1 #ahcc71 and various other religious works4 #cfi ,see ,vol4 ,i1 page #bbb1 note #ad #dij4 #cgj ,john ,hamilton ,thom 7#ahjh-ahid7 was converted to ,unitarianism and was long a minister in that church1 preaching in the ,renshaw ,street ,chapel from #ahca to #ahff4 ,de ,morgan refers to the ,liverpool ,unitarian controversy conducted by ,james ,martineau and ,henry ,giles in response to a challenge by thirteen ,anglican ,clergy4 ,in #ahci ,thom contributed four lectures and a letter to this controversy4 ,among his religious works were a ,life of ,blanco ,white 7#ahde7 and ,hymns1 ,chants1 and ,anthems 7#ahed74 #cga ,the spelling of these names is occasionally changed to meet the condition that the numerical value of the letters shall be #fff1 the number of the beast of ,revelations4 ,the names include ,julius ,caesar2 ,valerius ,jovius ,diocletianus 7#bdi-cac71 emperor from #bhg to #cje1 persecutor of the ,christians2 ,louis1 presumably ,louis ,,xiv2 ,gerbert 7#idj-ajjc71 who reigned as ,pope ,sylvester ,,ii from #iii to #ajjc1 known to mathematicians for his abacus and his interest in geometry1 and accused by his opponents as being in league with the devil2 ,linus1 the second ,bishop of ,rome1 the successor of ,peter2 ,camillo ,borghese 7#aeeb-afba71 who reigned as ,pope ,paul ,v from #afje to #afba1 and who excommunicated all ,venice in #afjf for its claim to try ecclesiastics before lay tribunals1 thus taking a position which he was forced to abandon2 ,luther1 ,calvin2 ,laud 7see ,vol4 ,i1 page #ade1 note #g #cjg72 ,genseric 7c4 #djf-dgg71 king of the ,vandals1 who sacked ,rome in #dee and persecuted the orthodox ,christians in ,africa2 ,boniface ,,iii1 who was pope for nine months in #fjf2 ,beza 7see ,vol4 ,i1 page #ff1 note #f #hc72 ,mohammed2 ,greek3 braski1 who was ,giovanni ,angelo ,braschi 7#agag-agii71 and who reigned as ,pope ,pius ,,vi from #agge to #agii1 dying in captivity because he declined to resign his temporal power to ,napoleon2 ,bonaparte2 and1 under ,greek3 ,ion ,paune1 possibly ,pope ,john ,,xiv1 who reigned in #ihc and #ihd during the absence of ,boniface ,,vii in ,constantinople4 #cgb ,the ,greek words and names are also occasionally misspelled so as to fit them to the number #fff4 ,they are ,greek3 ,lateinos 7,latin71 ,greek3 he latine basileia 7the ,latin kingdom71 ,greek3 ekklesia italika 7the ,italian ,church71 ,greek3 euanthas 7blooming71 ,greek3 teitan 7,titan71 ,greek3 arnoume 7renounce71 ,greek3 lampetis 7the lustrous71 ,greek3 ho niketes 7conqueror71 ,greek3 kakos hodegos 7bad guide71 ,greek3 alethes blaberos 7truthful harmful one71 ,greek3 palai baskanos 7a slanderer of old71 ,greek3 amnos adikos 7unmanageable lamb71 ,greek3 antemos 7,antemos71 ,greek3 genserikos 7,genseric71 ,greek3 euinas 7with stout fibers71 ,greek3 ,benediktos 7,benedict71 ,greek3 ,bonibazios g4 papa x4 e4 e4 e4 a4 7,boniface ,,iii1 pope #fh1 bishop of bishops ,i71 ,greek3 oulpios 7baneful71 ,greek3 dios eimi he heras 7,i1 a god1 am the71 ,greek3 he missa he papike 7the papal brief71 ,greek3 loutherana 7,lutheran71 ,greek3 saxoneios 7,saxon71 ,greek3 ,bezza antitheos 7,beza antigod71 ,greek3 he alazoneia biou 7the illusion of life71 ,greek3 ,maometis 7,mahomet72 ,greek3 ,maometes b4 7,mahomet ,,ii71 ,greek3 theos eimi epi gaies 7,i am lord over the earth71 ,greek3 iapetos 7,iapetos1 father of ,atlas71 ,greek3 papeiskos 7,papeiskos71 ,greek3 dioklasianos 7,diocletian71 ,greek3 cheina 7,cheina ,cain8 ,china871 ,greek3 braski 7,braschi1 as explained in note #aj71 ,greek3 ,ion ,paune 7,paunian violet1 but see note #aj71 ,greek3 koupoks 7cowpox71 ,greek3 ,bonneparte 7,bonneparte71 ,greek3 ,n4 ,boneparte 7,n4 ,boneparte71 ,greek3 euporia 7facility71 ,greek3 paradosis 7surrender71 ,greek3 to megatherion 7the megathereum1 the beast74 #cgc ,james ,wapshare1 whose ,harmony of the ,word of ,god in ,spirit and in ,truth appeared in #ahdi4 #cgd ,the literature relating to the ,swastika is too extended to permit of any adequate summary in these notes4 #cge ,henry ,edward ,manning 7#ahjh-ahib71 at first an ,anglican clergyman1 he became a ,roman ,catholic priest in #ahea1 and became ,cardinal in #ahge4 ,he succeeded ,cardinal ,wiseman as ,archbishop of ,westminster in #ahfe4 ,he wrote a number of religious works4 #cgf ,john ,bright 7#ahaa-ahhi71 ,quaker1 cotton manufacturer1 and statesman4 ,he worked with ,cobden for free trade1 peace1 and reform of the electorate4 #cgg ,the fallacy of many questions4 #cgh ,william ,wilberforce 7#agei-ahcc71 best known for his long fight for the abolition of the slave trade4 #cgi ,richard ,martin 7#aged-ahcd71 high sheriff of ,county ,galway and owner of a large estate in ,connemara4 ,curiously enough1 he was known both for his readiness in duelling and for his love for animals4 ,he was known as ,humanity ,martin1 and in #ahbb secured the passage of an act to prevent the cruel and improper treatment of cattle4 ,he was one of the founders 7#ahbd7 of the ,royal ,society for the ,prevention of ,cruelty to ,animals4 ,he is usually considered the original of ,godfrey ,o',malley in ,lever's novel1 ,charles ,o',malley4 #chj ,see ,vol4 ,i1 page #adi1 note #a #cbc1 also text on same page4 #cha ,see ,vol4 ,i1 page #dd1 note #i #cd1 also text1 ,vol4 ,i1 page #aaj4 #chb ,penitential seat4 #chc ,well placed upon the cushion4 #chd ,see ,vol4 ,,ii1 page #eh1 note #aji4 #che ,he has lost the right of being influenced by evidence4 #chf ,hung up4 #chg ,a few things to the wise1 nothing to the unlettered4 #chh ,the fallacy results from dividing both members of an equation by #j1 x - #a being the same as #a - #a1 and calling the quotients finite4 #chi ,if you order him to the sky he will go4 #cij ,similia similibus curanter1 ,like cures like1 the homeopathic motto4 #cia ,without harm to the proprieties4 #cib ,what are you doing8 ,i am standing here4 #cic ,lors feist l',anglois tel signe4 ,la main gausche toute ouverte il leva hault en l'aer1 puis ferma au poing les quatres doigtz d'icelle et le poulce estendu assit sus la pinne du nez4 ,soubdain apres leva la dextre toute ouverte1 et toute ouverte la baissa1 joignant la poulce au lieu que fermait le petit doigt de la gausche1 et les quatre doigtz d'icelle mouvoit lentement en l'aer4 ,puis au rebours feit de la dextre ce qu'il avoit faict de la gausche1 et de la gausche ce que avoit faict de la dextre4--,a4 ,de ,m4 #cid ,suaviter in modo1 fortiter in re1 ,gentle in manners1 firm in action4 #cie ,see ,vol4 ,i1 page #aja1 note #d #agd4 #cif ,see ,vol4 ,i1 page #cae1 note #c #fhf4 #cig ,henry ,fawcett 7#ahcc-ahhd7 became totally blind in #aheh1 but in spite of this handicap he became professor of political economy at ,cambridge and sat in parliament for a number of years4 ,he championed the cause of reform and in particular he was prominent in the protection of the native interests of ,india4 ,the establishing of the parcels post 7#ahhb7 took place while he was postmaster general 7#ahhj-ahhd74 #cih ,of course the whole thing depends upon what definition of division is taken4 ,we can multiply #b ft4 by #c ft4 if we define multiplication so as to allow it1 or #b ft4 by #c lb1 getting foot-pounds1 as is done in physics4 #cii ,richard ,milward 7#afji-afhj71 for so the name is usually given1 was rector of ,great ,braxted 7,essex7 and canon of ,windsor4 ,he was long the amanuensis of ,john ,selden1 and the ,table ,talk was published nine years after ,milward's death1 from notes that he left4 ,some doubt has been cast upon the authenticity of the work owing to many of the opinions that it ascribes to ,selden4 #djj ,john ,selden 7#aehd-afed7 was a jurist1 legal antiquary1 and ,oriental scholar4 ,he sat in the ,long ,parliament1 and while an advocate of reform he was not an extremist4 ,he was sent to the ,tower for his support of the resolution against tonnage and poundage1 in #afbi4 ,his ,history of ,tythes 7#afah7 was suppressed at the demand of the bishops4 ,his ,de ,diis ,syriis 7#afag7 is still esteemed a classic on ,semitic mythology4 #dja ,see ,vol4 ,i1 page #db1 note #d #bd4 #djb ,see ,vol4 ,,ii1 page #bdi1 note #cih4 #djc ,john ,palmer 7#agdb-ahah7 was a theatrical manager4 ,in #aghb he set forth a plan for forwarding the mails by stage coaches instead of by postmen4 ,pitt adopted the plan in #aghd4 ,palmer was made comptroller-general of the post office in #aghf and was dismissed six years later for arbitrarily suspending a deputy4 ,he had been verbally promised #b-a_/b on the increased revenue1 but ,pitt gave him only a pension of ,l#cjjj4 ,in #ahac he was awarded ,l#ej1jjj in addition to his pension4 #djd ,dionysius ,lardner 7#agic-ahei71 professor of natural philosophy in ,london ,university 7now ,university ,college74 ,his ,cabinet ,cyclopaedia 7#ahbi-ahdi7 contained #acc volumes4 ,de ,morgan wrote on probabilities1 and ,lardner on various branches of mathematics1 and there were many other well-known contributors4 ,lardner is said to have made #bjj1jjj on a lecture tour in ,america4 #dje ,thomas ,fysche ,palmer 7#agdg-ahjb7 joined the ,unitarians in #aghc1 and in #aghe took a charge in ,dundee4 ,he was arrested for sedition because of an address that it was falsely alleged that he gave before a society known as the ,friends of ,liberty4 ,as a matter of fact the address was given by an uneducated weaver1 and ,palmer was merely asked to revise it1 declining to do even this4 ,nevertheless he was sentenced to ,botany ,bay 7#agid7 for seven years4 ,the trial aroused great indignation4 #djf ,see ,vol4 ,i1 page #hj1 note #e #aai4 #djg ,see ,vol4 ,,ii1 page #bdd1 note #cid4 #djh ,see ,vol4 ,i1 page #ceb1 note #a #gca4 #dji ,see ,vol4 ,i1 page #ccb1 note #d #gji4 #daj ,the lawyers are brought into court2 let them accuse each other4 #daa ,samuel ,rogers 7#agfc-ahee71 the poet and art connoisseur4 ,he declined the laureateship on the death of ,wordsworth 7#ahej74 ,byron1 his pretended friend1 wrote a lampoon 7#ahah7 ridiculing his cadaverous appearance4 #dab ,theodore ,edward ,hook 7#aghh-ahda71 the well-known wit4 ,he is satirized as ,mr4 ,wagg in ,vanity ,fair4 ,the ,john ,bull was founded in #ahbj and ,hook was made editor4 #dac ,on pitying the heretic4 #dad ,a term of medieval logic4 ,barbara3 ,all ,m is ,p1 all ,s is ,m1 hence all ,s is ,p4 ,celarent3 ,no ,m is ,p1 all ,s is ,m1 hence no ,s is ,p4 #dae ,simply1 ,according to which1 ,it does not follow4 #daf ,o sweet soul1 what good shall ,i declare ,that heretofore was thine1 since such are thy remains6 #dag ,stupid fellow6 #dah ,christopher ,barker 7c4 #aebi-aeii71 also called ,barkar1 was the ,queen's printer4 ,he began to publish books in #aefi1 but did no actual printing until #aegf4 ,in #aege the ,geneva ,bible was first printed in ,england1 the work being done for ,barker4 ,he published #ch partial or complete editions of the ,bible from #aege to #aehh1 and #cd were published by his deputies 7#aehh-aeii74 #dai ,james ,franklin 7#afig-agce7 was born in ,boston1 ,mass41 and was sent to ,london to learn the printer's trade4 ,he returned in #agag and started a printing house4 ,benjamin1 his brother1 was apprenticed to him but ran away 7#agbc74 ,james published the ,new ,england ,courant 7#agba-agbg71 and ,benjamin is said to have begun his literary career by writing for it4 #dbj ,james ,hodder was a writing master in ,tokenhouse ,yard1 ,lothbury1 in #affa1 and later kept a boarding school in ,bromley-by-,bow4 ,his famous arithmetic appeared at ,london in #affa and went through many editions4 ,it was the basis of ,cocker's work4 7,see ,vol4 ,i1 page #db1 note #d #bd47 ,it was long thought to have been the first arithmetic published in ,america1 and it was the first ,english one4 ,there was1 however1 an arithmetic published much earlier than this1 in ,mexico1 the ,sumario compendioso 444 con algunas reglas tocantes al ,aritmetica1 by ,juan ,diaz ,freyle1 in #aeef4 #dba ,henry ,mose1 ,hodder's successor1 kept a school in ,sherborne ,lane1 ,london4 #dbb ,rear ,admiral ,sir ,francis ,beaufort 7#aggd-aheg71 ,f4,r4,s41 was hydrographer to the ,navy from #ahbi to #ahee4 ,he prepared an atlas that was printed by the ,society for the ,diffusion of ,useful ,knowledge4 #dbc ,antoine ,sabatier 7#agdb-ahag71 born at ,castres1 was known as the ,abbe but was really nothing more than a clerc tonsure4 ,he lived at ,court and was pensioned to write against the philosophers of the ,voltaire group4 ,he posed as the defender of morality1 a commodity of which he seems to have possessed not the slightest trace4 #dbd ,maffeo ,barberini was pope1 as ,urban ,,viii1 from #afbc to #afdd4 ,it was during his ambitious reign that ,galileo was summoned to ,rome to make his recantation 7#afcc71 the exact nature of which is still a matter of dispute4 #dbe ,this ,baden ,powell 7#agif-ahfj7 was the ,savilian professor of geometry 7#ahbg-ahfj7 at ,oxford4 #dbf ,memoirs of the famous bishop of ,chiapa1 by which it appears that he had butchered or burned or drowned ten million infidels in ,america in order to convert them4 ,i believe that this bishop exaggerated2 but if we should reduce these sacrifices to five million victims1 this would still be admirable4 #dbg ,alfonso ,x 7#abba-abhd71 known as ,el ,sabio 7the ,wise71 was interested in astronomy and caused the ,alphonsine ,tables to be prepared4 ,these table were used by astronomers for a long time4 ,it is said that when the ,ptolemaic system of the universe was explained to him he remarked that if he had been present at the ,creation he could have shown how to arrange things in a much simpler fashion4 #dbh ,george ,richards 7c4 #agfg-ahcg71 fellow of ,oriel 7#agij-agif71 ,bampton lecturer 7#ahjj71 ,vicar of ,st4 ,martin's-in-the-,fields1 ,westminster 7#ahbd71 and a poet of no mean ability4 #dbi ,the ,aboriginal ,britons1 an excellent poem1 by ,richards4 7,note by ,byron47--,a4 ,de ,m4 #dcj ,john ,watkins 7d4 after #ahca71 a teacher and miscellaneous writer4 #dca ,frederic ,shoberl 7#agge-ahec71 a miscellaneous writer4 #dcb ,he wrote1 besides the ,aboriginal ,britons1 ,songs of the ,aboriginal ,bards 7#agib71 ,modern ,france3 a ,poem 7#agic71 ,odin1 a drama 7#ahjd71 ,emma1 a drama on the model of the ,greek theatre 7#ahjd71 ,poems 7#b volumes1 #ahjd71 and a ,monody on the ,death of ,lord ,nelson 7#ahjf74 #dcc ,henry ,kirke ,white 7#aghe-ahjf71 published his first volume of poems at the age of #ah4 ,southey and ,william ,wilberforce became interested in him and procured for him a sizarship at ,st4 ,john's ,college1 ,cambridge4 ,he at once showed great brilliancy1 but he died of tuberculosis at the age of #ba4 #dcd ,john ,wolcot1 known as ,peter ,pindar 7#agch-ahai71 was a ,london physician4 ,he wrote numerous satirical poems4 ,his ,bozzy and ,piozzi1 or the ,british ,biographers1 appeared in #aghf1 and reached the #ith edition in #aghh4 #dce ,see ,vol4 ,i1 page #bce1 note #h #ecb4 #dcf ,richard ,payne ,knight 7#agej-ahbd7 was a collector of bronzes1 gems1 and coins1 many of his pieces being now in the ,british ,museum4 ,he sat in parliament for twenty-six years 7#aghj-ahjf71 but took no active part in legislation4 ,he opposed the acquisition of the ,elgin ,marbles1 holding them to be of little importance4 ,his ,analytical ,inquiry into the ,principles of ,taste appeared in #ahjh4 #dcg ,mario ,nizzoli 7#adih-aeff71 a well-known student of ,cicero1 was for a time professor at the ,university of ,parma4 ,his ,observationes in ,m4 ,tullium ,ciceronem appeared at ,pratalboino in #aece4 ,it was revised by his nephew under the title ,thesaurus ,ciceronianus 7,venice1 #aegj74 #dch ,see ,vol4 ,i1 page #cad1 note #d #fha4 #dci ,like the geometer1 who bends all his powers ,to measure the circle1 and does not succeed1 ,thinking what principle he needs4 #ddj ,francis ,quarles 7#aeib-afdd71 a religious poet4 ,he wrote paraphrases of the ,bible and numerous elegies4 ,in the early days of the revolutionary struggle he sided with the ,royalists4 ,one of his most popular works was the ,emblems 7#afce71 with illustrations by ,william ,marshall4 #dda ,regnault de ,becourt wrote ,la ,creation du monde1 ou ,systeme d'organisation primitive suivi de l'interpretation des principaux phenomenes et accidents que se sont operes dans la nature depuis l'origine de univers jusqu'a nos jours 7#ahaf74 ,this may be the work translated by ,dalmas4 #ddb ,because it lacks a holy prophet4 #ddc ,anghera4 ,see ,vol4 ,,ii1 page #fj1 note #abg4 #ddd ,edmund ,curll 7#afge-agdg71 a well-known bookseller1 publisher1 and pamphleteer4 ,he was for a time at ,the ,peacock without ,temple ,bar1 and later at ,the ,dial and ,bible against ,st4 ,dunstan's ,church4 ,he was fined repeatedly for publishing immoral works1 and once stood in the pillory for it4 ,he is ridiculed in the ,dunciad for having been tossed in a blanket by the boys of ,westminster ,school because of an oration that displeased them4 #dde ,see ,vol4 ,,ii1 page #aji1 note #bjf4 #ddf ,encyclopaedia4 #ddg ,author of the ,historia ,naturalis 7#gg ,a4,d47 #ddh ,author of the ,de ,institutione ,oratorio ,libri ,,xii 7c4 #ia ,a4,d47 #ddi ,his ,de ,architectures ,libri ,x was not merely a work on architecture and building1 but on the education of the architect4 #dej ,cyclophoria4 #dea ,william ,caxton 7c4 #adbb-;c4#adib71 sometime ,governor of the ,company of ,merchant ,adventurers in ,bruges 7between #addi and #adgj74 ,he learned the art of printing either at ,bruges or ,cologne1 and between #adga and #adgg set up a press at ,westminster4 ,tradition says that the first book printed in ,england was his ,game and ,playe of ,chesse 7#adgd74 ,the ,myrrour of the ,worlde and th'ymage of the same appeared in #adhj4 ,it contains a brief statement on arithmetic1 the first mathematics to appear in print in ,england4 #deb ,see ,vol4 ,i1 page #de1 note #f #dj4 ,de ,morgan is wrong as to the date of the ,margarita ,philosophica4 ,the first edition appeared at ,freiburg in #aejc4 #dec ,reisch was confessor to ,maximilian ,i 7#adei-aeai71 ,king of the ,romans 7#adhf7 and ,emperor 7#adic-aeai74 #ded ,joachim ,sterck ,ringelbergh 7c4 #adii-;c4 #aecf71 teacher of philosophy and mathematics in various cities of ,france and ,germany4 ,his ,institutionum astronomicarum libri ,,iii appeared at ,basel in #aebh1 his ,cosmographia at ,paris in #aebi1 and his ,opera at ,leyden in #aeca4 #dee ,johannes ,heinrich ,alsted 7#aehh-afch7 was professor of philosophy and theology at his birthplace1 ,herborn1 in ,nassau1 and later at ,weissenberg4 ,he published several works1 including the ,elementale mathematicum 7#afaa71 ,systema physicae harmonicae 7#afab71 ,methodus admirandorum mathematicorum 7#afac71 ,encyclopaedia septem tomis distincta 7#afcj71 and the work mentioned above4 #def ,johann ,jakob ,hoffmann 7#afce-agjf71 professor of ,greek and history at his birthplace1 ,basel4 ,he also wrote the ,epitome metrica historiae universalis civilis et sacrae ab orbe condito 7#afhf74 #deg ,ephraim ,chambers 7c4 #afhj-agdj71 a crotchety1 penurious1 but kind-hearted freethinker4 ,his ,cyclopaedia1 or an ,universal ,dictionary was translated into ,french and is said to have suggested the great ,encyclopedie4 #deh ,encyclopedie1 ou ,dictionnaire raisonne des sciences1 des arts et des metiers1 par un societe de gens de lettres4 ,mis en ordre et publie par ,m4 ,diderot1 et quant a la partie mathematique1 par ,m4 d',alembert4 ,paris1 #agea-aghj1 #ce volumes4 #dei ,from the egg 7state74 #dfj ,see ,vol4 ,i1 page #chb1 note #ab #ghe4 #dfa ,see ,vol4 ,,ii1 page #d1 note #ae4 #dfb ,in morals nothing should serve man as a model but ,god2 in the arts1 nothing but nature4 #dfc ,encyclopedie ,methodique1 ou par ordre de matieres4 ,paris1 #aghb-ahcb1 #aff-a_/b volumes4 #dfd ,see ,vol4 ,,ii1 page #aic1 note #ccf4 #dfe ,encyclopaedia ,metropolitana2 or1 ,universal ,dictionary of ,knowledge4 ,london1 #ahde1 #bi volumes4 ,a second edition came out in #ahdh-aheh in #dj volumes4 #dff ,see ,vol4 ,i1 page #acg1 note #h #bhf4 #dfg ,see ,vol4 ,i1 page #hj1 note #e #aai4 #dfh ,de ,morgan should be alive to satirize some of the statements on the history of mathematics in the eleventh edition4 #dfi ,john ,pringle ,nichol 7#ahjd-ahei71 ,regius professor of astronomy at ,glasgow and a popular lecturer on the subject4 ,he lectured in the ,united ,states in #ahdh-ahdi4 ,his ,views of the ,architecture of the ,heavens 7#ahch7 was a very popular work1 and his ,planetary ,system 7#ahdh1 #ahej7 contains the first suggestion for the study of sun spots by the aid of photography4 #dgj ,see ,vol4 ,,ii1 page #aji1 note #bjf4 #dga ,george ,long 7#ahjj-ahgi71 a native of ,poulton1 in ,lancashire1 was called to the ,university of ,virginia when he was only twenty-four years old as professor of ancient languages4 ,he returned to ,england in #ahbh to become professor of ,greek at ,london ,university4 ,from #ahcc to #ahdi he edited the twenty-nine volumes of the ,penny ,cyclopaedia4 ,he was an authority on ,roman law4 #dgb ,a legal phrase1 ,qui tam pro domina regina1 quam pro se ipso sequitur1--,who sues as much on the ,queen's account as on his own4 #dgc ,arthur ,cayley 7#ahba-ahie7 was a fellow of ,trinity ,college1 ,cambridge 7#ahdb-ahdf7 and was afterwards a lawyer 7#ahdi-ahfc74 ,during his fourteen years at the bar he published some two hundred mathematical papers4 ,in #ahfc he became professor of mathematics at ,cambridge1 and so remained until his death4 ,his collected papers1 nine hundred in number1 were published by the ,cambridge ,press in #ac volumes 7#ahhi-ahih74 ,he contributed extensively to the theory of invariants and covariants4 ,de ,morgan's reference to his coining of new names is justified1 although his contemporary1 ,professor ,sylvester1 so far surpassed him in this respect as to have been dubbed the mathematical ,adam4 #dgd ,see ,vol4 ,,ii1 page #bf1 note #ef4 #dge ,see ,vol4 ,i1 page #aaa1 note #c #bjg4 #dgf ,see ,vol4 ,i1 page #hg1 note #f #ace4 #dgg ,pierre ,dupuy 7#aehb-afea7 was a friend and relative of ,de ,thou4 ,with the collaboration of his brother and ,nicolas ,rigault he published the #afbj and #afbf editions of ,de ,thou's ,history4 ,he also wrote on law and history4 ,his younger brother1 ,jacques 7died in #afef71 edited his works4 ,the two had a valuable collection of books and manuscripts which they bequeathed to the ,royal ,library at ,paris4 #dgh ,see ,vol4 ,i1 page #ea1 note #c #ea4 #dgi ,it was ,cosmo de' ,medici 7#aeij-afba7 who was the patron of ,galileo4 #dhj ,see ,vol4 ,i1 page #dj1 note #d #bj4 #dha ,see ,vol4 ,i1 page #ajf1 note #d #ahh4 #dhb ,sir ,edward ,sherburne 7#afah-agjb71 a scholar of considerable reputation4 ,the reference by ,de ,morgan is to ,the ,sphere of ,marcus ,manilius1 in the appendix to which is a ,catalogue of ,astronomers1 ancient and modern4 #dhc ,george ,parker1 second ,earl of ,macclesfield 7#afig-agfd74 ,he erected an observatory at ,shirburn ,castle1 ,oxfordshire1 in #agci1 and fitted it out with the best equipment then available4 ,he was ,president of the ,royal ,society in #ageb4 #dhd ,see ,vol4 ,,ii1 page #adh1 note #bfc4 #dhe ,see ,vol4 ,i1 page #adj1 note #g #bif4 #dhf ,see ,vol4 ,i1 page #ajf1 note #d #ahh4 #dhg ,edward ,bernard 7#afch-afif71 although ,savilian professor of astronomy at ,oxford1 was chiefly interested in archeology4 #dhh ,see ,vol4 ,i1 page #ajg1 note #a #aij4 #dhi ,see ,vol4 ,i1 page #ajg1 note #a #aij4 #dij ,see ,vol4 ,i1 page #ace1 note #c #bha4 #dia ,philip ,dormer ,stanhope1 fourth ,earl of ,chesterfield 7#afid-aggc71 well known for the letters written to his son which were published posthumously 7#aggd74 #dib ,peter ,daval 7died in #agfc71 ,vice-,president of the ,royal ,society1 and an astronomer of some ability4 #dic ,see ,vol4 ,i1 page #cgf1 note #a #gff4 #did ,william ,oughtred 7c4 #aegc-affj71 a fellow of ,king's ,college1 ,cambridge1 and afterwards vicar of ,aldbury1 ,surrey1 wrote the best-known arithmetic and trigonometry of his time4 ,his ,arithmeticae in ,numero ,speciebus ,institutio 444 quasi ,clavis ,mathematicae est 7#afca7 went through many editions and appeared in ,english as ,the ,key to the ,mathematicks new forged and filed in #afdg4 #die ,see ,vol4 ,i1 page #adj1 note #e #bid4 #dif ,stephen ,jordan ,rigaud 7#ahaf-ahei7 was senior assistant master of ,westminster ,school 7#ahdf7 and head master of ,queen ,elizabeth's ,school at ,ipswich 7#ahej74 ,he was made ,bishop of ,antigua in #aheh and died of yellow fever the following year4 #dig ,he also wrote a memoir of his father1 privately printed at ,oxford in #ahhc4 #dih ,see ,vol4 ,i1 page #fi1 note #c #if4 #dii ,see ,vol4 ,i1 page #ajf1 note #d #ahh4 #ejj ,william ,gascoigne was born at ,middleton before #afab and was killed in the battle of ,marston ,moor in #afdd4 ,he was an astronomer and invented the micrometer with movable threads 7before #afci74 #eja ,seth ,ward 7#afag-afhi7 was deprived of his fellowship at ,cambridge for refusing to sign the covenant4 ,he became professor of astronomy at ,oxford 7#afdi71 ,bishop of ,exeter 7#affb71 ,bishop of ,salisbury 7#affg71 and ,chancellor of the ,garter 7#afga74 ,he is best known for his solution of ,kepler's problem to approximate a planet's orbit1 which appeared in his ,astronomia geometrica in #afef4 #ejb ,see ,vol4 ,i1 page #aaj1 note #b #aih4 #ejc ,see ,vol4 ,i1 page #ajj1 note #b #agb4 #ejd ,see ,vol4 ,i1 page #ajg1 note #a #aij4 #eje ,see ,vol4 ,i page #aad1 note #f #bbj4 #ejf ,see ,vol4 ,i1 page #gg1 note #d #aah4 #ejg ,see ,vol4 ,i1 page #abe1 note #c #bec4 #ejh ,see ,vol4 ,i1 page #aje1 note #b #ahf4 #eji ,heinrich ,oldenburgh 7#afbf-afgh7 was consul in ,england for the ,city of ,bremen1 his birthplace1 and afterwards became a private teacher in ,london4 ,he became secretary of the ,royal ,society and contributed on physics and astronomy to the ,philosophical ,transactions4 #eaj ,thomas ,brancker1 or ,branker 7#afcf-afgf7 wrote the ,doctrinae sphaericae adumbratio et usus globorum artificialium 7#affb7 and translated the algebra of ,rhonius with the help of ,pell4 ,the latter work appeared under the title of ,an ,introduction to ,algebra 7#affh71 and is noteworthy as having brought before ,english mathematicians the symbol _/ for division4 ,the symbol never had any standing on the ,continent for this purpose1 but thereafter became so popular in ,england that it is still used in all the ,english-speaking world4 #eaa ,see ,vol4 ,i1 page #aah1 note #a #bcj4 #eab ,pierre ,bertius 7#aefe-afbi7 was a native of ,flanders and was educated at ,london and ,leyden4 ,he became a professor at ,leyden1 and later held the chair of mathematics at the ,college de ,france4 ,he wrote chiefly on geography4 #eac ,see ,vol4 ,,ii1 page #big1 note #dhg4 #ead ,giovanni ,alphonso ,borelli 7#afjh-afgi7 was professor of mathematics at ,messina 7#afdf-afef7 and at ,pisa 7#afef-afeg71 after which he taught in ,rome at the ,convent of ,st4 ,panteleon4 ,he wrote several works on geometry1 astronomy1 and physics4 #eae ,see ,vol4 ,i1 page #agb1 note #b #cha4 #eaf ,ignace ,gaston ,pardies 7c4 #afcf-afgc71 a ,jesuit1 professor of ancient languages and later of mathematics and physics at the ,college of ,pau1 and afterwards professor of rhetoric at the ,college ,louis-le-,grand at ,paris4 ,he wrote on geometry1 astronomy and physics4 #eag ,pierre ,fermat was born in #afjh 7or possibly in #aeie7 near ,toulouse1 and died in #affe4 ,although connected with the parliament of ,toulouse1 his significant work was in mathematics4 ,he was one of the world's geniuses in the theory of numbers1 and was one of the founders of the theory of probabilities and of analytic geometry4 ,after his death his son published his edition of ,diophantus 7#afgj7 and his ,varia opera mathematica 7#afgi74 #eah ,this may be ,christopher ,townley 7#afjc-afgd7 the antiquary1 or his nephew1 ,richard1 who improved the micrometer already invented by ,gascoigne4 #eai ,adrien ,auzout a native of ,rouen1 who died at ,rome in #afia4 ,he invented a screw micrometer with movable threads 7#afff7 and made many improvements in astronomical instruments4 #ebj ,see ,vol4 ,i1 page #ff1 note #i #hf4 #eba ,see ,vol4 ,i1 page #abd1 note #g #bdh4 #ebb ,john ,machin 7d4 #agea7 was professor of astronomy at ,gresham ,college 7#agac-agea7 and secretary of the ,royal ,society4 ,he translated ,newton's ,principia into ,english4 ,his computation of pi to #ajj places is given in ,william ,jones's ,synopsis palmariorum matheseos 7#agjf74 #ebc ,pierre ,remond de ,montmort 7#afgh-agai7 was canon of ,notre ,dame until his marriage4 ,he was a gentleman of leisure and devoted himself to the study of mathematics1 especially of probabilities4 #ebd ,roger ,cotes 7#afhb-agaf71 first ,plumian professor of astronomy and physics at ,cambridge1 and editor of the second edition of ,newton's ,principia4 ,his posthumous ,harmonia ,mensurarum 7#agbb7 contains ,cotes's ,theorem on the binomial equation4 ,newton said of him1 ,if ,mr4 ,cotes had lived we had known something4 #ebe ,see ,vol4 ,i1 page #ace1 note #c #bha4 #ebf ,see ,vol4 ,i1 page #cgg1 note #d #gfi4 #ebg ,charles ,rene ,reyneau 7#afef-agbh7 was professor of mathematics at ,angers4 ,his ,analyse demontree1 ou ,maniere de resoudre les problemes de mathematiques 7#agjh7 was a successful attempt to popularize the theories of men like ,descartes1 ,newton1 ,leibnitz1 and the ,bernoullis4 #ebh ,brook ,taylor 7#afhe-agca71 secretary of the ,royal ,society1 and student of mathematics and physics4 ,his ,methodus incrementorum directa et inversa 7#agae7 was the first treatise on the calculus of finite differences4 ,it contained the well-known theorem that bears his name4 #ebi ,pierre ,louis ,moreau de ,maupertuis 7#afih-agei7 was sent with ,clairaut 7#agce7 to measure an arc of a meridian in ,lapland4 ,he was head of the physics department in the ,berlin ,academy from #agde until #agec4 ,he wrote ,sur la figure de la terre 7#agch7 and on geography and astronomy4 #ecj ,pierre ,bouguer 7#afih-ageh7 was professor of hydrography at ,paris1 and was one of those sent by the ,academy of ,sciences to measure an arc of a meridian in ,peru 7#agce74 ,the object of this and the work of ,maupertuis was to determine the shape of the earth and see if ,newton's theory was supported4 #eca ,charles ,marie de la ,condamine 7#agja-aggd7 was a member of the ,paris ,academy of ,sciences and was sent with ,bouguer to ,peru1 for the purpose mentioned in the preceding note4 ,he wrote on the figure of the earth1 but was not a scientist of high rank4 #ecb ,see ,vol4 ,i1 page #acf1 note #e #bhc4 #ecc ,see ,vol4 ,,ii1 page #bif1 note #dhc4 #ecd ,thomas ,baker 7c4 #afbe-afhi7 gave a geometric solution of the biquadratic in his ,geometrical ,key1 or ,gate of ,equations unlocked 7#afhd74 #ece ,see ,vol4 ,i1 page #afj1 note #e #cej4 #ecf ,see ,vol4 ,i1 page #hg1 note #d #acc4 #ecg ,see ,vol4 ,i1 page #acb1 note #b #bgb4 #ech ,see ,vol4 ,i1 page #aah1 second note #a #bca4 #eci ,the name of ,newton is so well known that no note seems necessary4 ,he was born at ,woolsthorpe1 ,lincolnshire1 in #afdb1 and died at ,kensington in #agbg4 #edj ,john ,keill 7#afga-agba71 professor of astronomy at ,oxford from #agaj1 is said to have been the first to teach the ,newtonian physics by direct experiment1 the apparatus being invented by him for the purpose4 ,he wrote on astronomy and physics4 ,his ,epistola de legibus virium centripetarum1 in the ,philosophical ,transactions for #agjh1 accused ,leibnitz of having obtained his ideas of the calculus from ,newton1 thus starting the priority controversy4 #eda ,thomas ,digges 7d4 in #aeie7 wrote ,an ,arithmeticall ,militare ,treatise1 named ,stratioticos 7#aegi71 and completed ,a geometrical practise1 named ,pantometria 7#aega7 that had been begun by his father1 ,leonard ,digges4 #edb ,john ,dee 7#aebg-afjh71 the most famous astrologer of his day1 and something of a mathematician1 wrote a preface to ,billingsley's translation of ,euclid into ,english 7#aegj74 #edc ,see ,vol4 ,i1 page #gf1 note #c #aab4 #edd ,thomas ,harriot 7#aefj-afba7 was tutor in mathematics to ,sir ,walter ,raleigh1 who sent him to survey ,virginia 7#aehe74 ,he was one of the best ,english algebraists of his time1 but his ,artis ,analyticae ,praxis ad ,aequationes ,algebraicas resolvendas 7#afca7 did not appear until ten years after his death4 #ede ,thomas ,lydiat 7#aegb-afbf71 rector of ,alkerton1 devoted his life chiefly to the study of chronology1 writing upon the subject and taking issue with ,scaliger 7#afja74 #edf ,see ,vol4 ,i1 page #fi1 note #c #if4 #edg ,walter ,warner edited ,harriot's ,artis ,analyticae ,praxis 7#afca74 ,tarporley is not known in mathematics4 #edh ,see ,vol4 ,i1 page #aje1 note #b #ahf4 #edi ,see ,vol4 ,i1 page #aae1 note #c #bbd4 #eej ,see ,vol4 ,,ii1 page #cjj1 note #eji4 #eea ,see ,vol4 ,i1 page #ajg1 note #a #aij4 #eeb ,sir ,samuel ,morland 7#afbe-afie7 was a diplomat and inventor4 ,for some years he was assistant to ,john ,pell1 then ambassador to ,switzerland4 ,he wrote on arithmetical instruments invented by him 7#afgc71 on hydrostatics 7#afig7 and on church history 7#afeh74 #eec ,see ,vol4 ,i1 page #aec1 note #d #ccg4 #eed ,see ,vol4 ,i1 page #he1 note #b #abi4 #eee ,see ,vol4 ,i1 page #dc1 note #h #cc4 #eef ,see ,vol4 ,i1 page #dc1 note #g #cb4 #eeg ,see ,vol4 ,i1 page #chb1 note #ac #ghf4 ,the history of the subject may be followed in ,braunmuehl's ,geschichte der ,trigonometrie4 #eeh ,see ,vol4 ,i1 page #cgg1 note #c #gfh4 #eei ,see ,vol4 ,i1 page #ajh1 note #b #aib4 #efj ,michael ,dary wrote ,dary's ,miscellanies 7#affi71 ,gauging epitomised 7#affi71 and ,the general ,doctrine of ,equation 7#affd74 #efa ,john ,newton 7#afbb-afgh71 canon of ,hereford 7#afgc71 educational reformer1 and writer on elementary mathematics and astronomy4 #efb ,see ,vol4 ,i1 page #hg1 note #d #acc4 #efc ,the average of the two equal altitudes of the sun before and after dinner4 #efd ,see ,vol4 ,i1 page #db1 note #d #bd4 #efe ,london1 #afgh4 ,it went though many editions4 #eff ,this ,i who once 444 #efg ,arthur ,murphy 7#agbg-ahje7 worked in a banking house until #aged4 ,he then went on the stage and met with some success at ,covent ,garden4 ,his first comedy1 ,the ,apprentice 7#agef7 was so successful that he left the stage and took to play writing4 ,his translation of ,tacitus appeared in #agic1 in four volumes4 #efh ,edmund ,wingate 7#aeif-afef7 went to ,paris in #afbd as tutor to ,princess ,henrietta ,maria and remained there several years4 ,he wrote ,l'usage de la regle de proportion 7,paris1 #afbd1 with an ,english translation in #afbf71 ,arithmetique ,logarithmetique 7,paris1 #afbf1 with an ,english translation in #afce71 and ,of ,natural and ,artificial ,arithmetick 7,london1 #afcj1 revised in #afej-afeb71 part ,i of which was one of the most popular textbooks ever produced in ,england4 #efi ,john ,lambert 7#afai-afid7 was ,major-,general during the ,revolution and helped to draw up the request for ,cromwell to assume the protectorate4 ,he was imprisoned in the ,tower by the ,rump ,parliament4 ,he was confined in ,guernsey until the clandestine marriage of his daughter ,mary to ,charles ,hatton1 son of the governor1 after which he was removed 7#affg7 to ,st4 ,nicholas in ,plymouth ,sound4 #egj ,samuel ,foster 7d4 in #afeb7 was made professor of astronomy at ,gresham ,college in ,march1 #afcf1 but resigned in ,november of that year1 being succeeded by ,mungo ,murray4 ,murray vacated his chair by marriage in #afda and ,foster succeeded him4 ,he wrote on dialling and made a number of improvements in geometric instruments4 #ega ,twice of the word a minister1 that is1 twice a minister of the ,gospel4 #egb ,this is ,the ,lives of the ,professors of ,gresham ,college to which is prefixed the ,life of the ,founder1 ,sir ,thomas ,gresham1 ,london1 #agdj4 ,it was written by ,john ,ward 7c4 #afgi-ageh71 professor of rhetoric 7#agbj7 at ,gresham ,college and vice-president 7#ageb7 of the ,royal ,society4 #egc ,charles ,montagu 7#affa-agae71 first ,earl of ,halifax1 was ,lord of the ,treasury in #afib1 and was created ,baron ,halifax in #agjj and ,viscount ,sunbury and ,earl of ,halifax in #agad4 ,he introduced the bill establishing the ,bank of ,england1 the bill becoming a law in #afid4 ,he had troubles of his own1 without considering ,newton1 for he was impeached in #agja1 and was the subject of a damaging resolution of censure as auditor of the exchequer in #agjc4 ,although nothing came of either of these attacks1 he was out of office during much of ,queen ,anne's reign4 #egd ,see ,vol4 ,,ii1 page #cjb1 note #edg4 #ege ,see ,vol4 ,i1 page #aje1 note #b #ahf4 #egf ,james ,dodson 7d4 #ageg7 was master of the ,royal ,mathematical ,school1 ,christ's ,hospital4 ,he was ,de ,morgan's great-grandfather4 ,the ,anti-,logarithmic ,canon was published in #agdb4 #egg ,see ,vol4 ,i1 page #ajf1 note #d #ahh4 #egh ,see ,vol4 ,i1 page #aaj1 note #b #aih4 #egi ,richard ,busby1 7#afjf-afie71 master of ,westminster ,school 7#afdj7 had among his pupils ,dryden and ,locke4 #ehj ,see ,vol4 ,i1 page #ajg1 note #a #aij4 #eha ,herbert ,thorndike 7#aeih-afgb71 fellow of ,trinity ,college1 ,cambridge 7#afbj-afdf71 and ,prebend of ,westminster 7#affa71 was a well-known theological writer of the time4 #ehb ,see ,vol4 ,i1 page #adj1 note #e #bid4 #ehc ,see ,vol4 ,i1 page #ajh1 note #b #aib4 #ehd ,labor performed returns in a circle4 #ehe ,see ,vol4 ,,ii1 page #bjh4 #ehf ,whatever objections one may make to the above arguments1 one always falls into an absurdity4 #ehg ,see ,vol4 ,,ii4 page #aa1 note #bi4 ,the ,circle ,squared2 and the solution of the problem adapted to explain the difference between square and superficial measurement appeared at ,brighton in #ahfe4 #ehh ,and beyond that nothing4 #ehi ,gillott 7#agei-ahgc7 was the pioneer maker of steel pens by machinery1 reducing the price from #as4 each to #d;d4 a gross4 ,he was a great collector of paintings and old violins4 #eij ,william ,edward ,walker wrote five works on circle squaring 7#ahec1 #ahed1 #aheg1 #ahfb1 #ahfd71 mostly and perhaps all published at ,birmingham4 #eia ,solomon ,m4 ,drach wrote ,an easy ,rule for formulizing all ,epicyclical ,curves 7,london1 #ahdi71 ,on the ,circle area and ,heptagon-chord 7,london1 #ahfd71 ,an easy general ,rule for filling up all ,magic ,squares 7,london1 #ahgc71 and ,hebrew ,almanack-,signs 7,london1 #ahgg71 besides numerous articles in journals4 #eib ,see ,vol4 ,i1 page #afh1 note #c #cga4 #eic ,see ,vol4 ,i1 page #bed1 note #b #ehj4 #eid ,see ,vol4 ,i1 page #ih1 note #f #afc4 #eie ,robert ,fludd or ,flud 7#aegd-afcg7 was a physician with a large ,london practice4 ,he denied the diurnal rotation of the earth1 and was attacked by ,kepler and ,mersenne1 and accused of magic by ,gassendi4 ,his ,apologia ,compendiania1 ,fraternitatem de ,rosea ,cruce suspicionis 444 maculis aspersam1 veritatis quasi ,fluctibus abluens 7,leyden1 #afaf7 is one of a large number of works of the mystic type4 #eif ,consult ,to the ,christianity of the ,age4 ,notes 444 comprising an elucidation of the scope and contents of the writings 444 of ,dionysius ,andreas ,freher 7#ahed74 #eig ,sir ,william ,robert ,grove 7#ahaa-ahif71 although called to the bar 7#ahce7 and to the bench 7#ahec71 is best known for his work as a physicist4 ,he was professor of experimental philosophy 7#ahdj-ahdg7 at the ,london ,institution1 and invented a battery 7#ahci7 known by his name4 ,his ,correlation of ,physical ,forces 7#ahdf7 went through six editions and was translated into ,french4 #eih ,johann ,tauler 7c4 #acjj-acfa71 a ,dominican monk of ,strassburg1 a mystic1 closely in touch with the ,gottesfreunde of ,basel4 ,his ,sermons first appeared in print at ,leipsic in #adih4 #eii ,paracelsus 7c4 #adij-aeda74 ,his real name was ,theophrastes ,bombast von ,hohenheim1 and he took the name by which he is generally known because he held himself superior to ,celsus4 ,he was a famous physician and pharmacist1 but was also a mystic and neo-,platonist4 ,he lectured in ,german on medicine at ,basel1 but lost his position through the opposition of the orthodox physicians and apothecaries4 #fjj ,see ,vol4 ,i1 page #bef1 note #b #ehh4 #fja ,philip ,schwarzerd 7#adig-aefj7 was professor of ,greek at ,wittenberg4 ,he helped ,luther with his translation of the ,bible4 #fjb ,johann ,reuchlin 7#adee-aebb71 the first great ,german humanist1 was very influential in establishing the study of ,greek and ,hebrew in ,germany4 ,his lectures were mostly delivered privately in ,heidelberg and ,stuttgart4 ,unlike ,melanchthon1 he remained in the ,catholic ,church4 #fjc ,joseph ,chitty 7#aggf-ahda7 published his ,precedents of ,pleading in #ahjh and his ,reports of ,cases on ,practice and ,pleading in #ahbj-bc 7#b volumes74 #fjd ,see ,vol4 ,i1 page #dd1 note #a #ce4 #fje ,see ,vol4 ,i1 page #dd1 note #d #ch4 #fjf ,jean ,pelerin1 also known as ,viator1 who wrote on perspective4 ,his work appeared in #aeje1 with editions in #aeji and #aeba4 #fjg ,henry ,stephens4 ,see ,vol4 ,i1 page #dd1 note #c #cg4 #fjh ,the well-known grammarian 7#agde-ahbf74 ,he was born at ,swatara1 in ,pennsylvania1 and practised law in ,new ,york until #aghd1 after which he resided in ,england4 ,his grammar 7#agie7 went through #ej editions1 and the abridgment 7#ahah7 through #abj editions4 ,murray's friend ,dalton1 the chemist1 said that of all the contrivances invented by human ingenuity for puzzling the brains of the young1 ,lindley ,murray's grammar was the worst4 #fji ,robert ,recorde 7c4 #aeaj-aeeh7 read and probably taught mathematics and medicine at ,cambridge up to #aede4 ,after that he taught mathematics at ,oxford and practised medicine in ,london4 ,his ,grounde of ,artes1 published about #aedj1 was the first arithmetic published in ,english that had any influence4 ,it went through many editions4 ,the ,castle of ,knowledge appeared in #aeea4 ,it was a textbook on astronomy and the first to set forth the ,copernican theory in ,england4 ,like ,recorde's other works it was written on the catechism plan4 ,his ,whetstone of ,witte 444 containying thextraction of ,rootes3 ,the ,cosike practise1 with the rule of ,equation3 and the woorkes of ,surde ,nombres appeared in #aeeg1 and it is in this work that the modern sign of equality first appears in print4 ,the word ,cosike is an adjective that was used for a long time in ,germany as equivalent to algebraic1 being derived from the ,italian cosa1 which stood for the unknown quantity4 #faj ,robert ,cecil 7c4 #aefc-afab71 first ,earl of ,salisbury1 ,secretary of ,state under ,elizabeth 7#aeif-afjc7 and under ,james ,i 7#afjc-afab74 #faa ,in ,america the ,german pronunciation is at present universal among mathematicians1 as in the case of most other ,german names4 ,this is due1 no doubt1 to the great influence that ,germany has had on ,american education in the last fifty years4 #fab ,the latest transliteration is substantially ,k'ung-fu-tzvu4 #fac ,the tendency seems to be1 however1 to adopt the forms used of individuals or places as rapidly as the mass of people comes to be prepared for it4 ,thus the spelling ,leipzig1 instead of ,leipsic1 is coming to be very common in ,america4 #fad ,sir ,edward ,coke 7#aeeb-afcd71 the celebrated jurist4 #fae ,dethlef ,cluvier or ,cluever 7d4 #agjh at ,hamburg7 was a nephew1 not a grandson1 of ,philippe ,cluvier1 or ,philipp ,cluever 7#aehj-;c4 #afbc74 ,dethlef traveled in ,france and ,italy and then taught mathematics in ,london4 ,he wrote on astronomy and philosophy and also published in the ,acta ,eruditorum 7#afhf7 his ,schediasma geometricum de nova infinitorum scientia4 ,quadratura circuli infinitis modis demonstrata1 and his ,monitum ad geometras 7#afhg74 ,philippe was geographer of the ,academy of ,leyden4 ,his ,introductionis in universam geographiam tam veterem quam novam libri sex appeared at ,leyden in #afbd1 about the time of his death4 #faf ,see ,vol4 ,i1 page #abd1 note #g #bdh4 #fag ,bernard ,nieuwentijt 7#afed-agah71 a physician and burgomaster at ,purmerend4 ,his ,considerationes circa ,analyseos ad quantitates infinite parvas applicatae ,principia et ,calculi ,differentialis usum 7,amsterdam1 #afid7 was attacked by ,leibnitz4 ,he replied in his ,considerationes secundae 7#afid71 and also wrote the ,analysis ,infinitorum1 seu ,curvilineorum ,proprietates ex ,polygonorum ,natura deductae 7#afie74 ,his most famous work was on the existence of ,god1 ,het ,regt ,gebruik der ,werelt ,beschouwingen 7#agah74 #fah ,from a given line to construct etc4 #fai ,pirates do not fight one another4 #fbj ,claude ,mallemens 7,mallement7 de ,messanges 7#afec-agbc7 was professor of philosophy at the ,college du ,plessis1 in ,paris1 for #cd years4 ,the work to which ,de ,morgan refers is probably the ,fameux ,probleme de la quadrature du cercle1 resolu geometriquement par le cercle et a ligne droite that appeared in #afhc4 #fba ,on ,tycho ,brahe see ,vol4 ,i1 page #gf1 note #c #aab4 #fbb ,wilhelm ,frederik von ,zytphen also published the ,tidens ,stroem1 a chronological table1 in #ahdj4 ,the work to which ,de ,morgan refers1 the ,solens ,bevaegelse i ,verdensrummet1 appeared first in #ahfa4 ,de ,morgan seems to have missed his ,nogl ,ord om ,cirkelens ,quadratur which appeared in #ahfe1 at ,copenhagen4 #fbc ,james ,joseph ,sylvester 7#ahad-ahig71 professor of natural philosophy at ,university ,college1 ,london 7#ahcg-ahda71 professor of mathematics at the ,university of ,virginia 7#ahda-ahde71 actuary in ,london 7#ahde-ahee71 professor of mathematics at ,woolwich 7#ahgg-ahhd7 and at ,johns ,hopkins ,university1 ,baltimore 7#ahgg-ahhd71 and ,savilian professor of geometry at ,oxford 7#ahhd-ahid74 #fbd ,see ,vol4 ,i1 page #gf1 note #c #aab4 #fbe ,see ,vol4 ,,ii1 page #bje1 note #cdi4 #fbf ,see ,vol4 ,i1 page #gf1 note #c #aab4 #fbg ,see ,vol4 ,i1 page #df1 note #a #db4 #fbh ,see ,vol4 ,,ii1 page #ahc1 note #cah4 #fbi ,see ,vol4 ,i1 page #cba1 note #b #fia4 #fcj ,james ,mill1 born #aggc1 died #ahcf4 #fca ,see ,vol4 ,,ii1 page #c1 note #aa4 #fcb ,see ,vol4 ,,ii1 page #c1 note #ac4 #fcc ,see ,vol4 ,,ii1 page #c1 note #ad4 #fcd ,this anecdote is printed at page #d 7,vol4 ,,ii72 but as it is used in illustration here1 and is given more in detail1 ,i have not omitted it4--,s4,e4 ,de ,m4 #fce ,see ,vol4 ,,ii1 page #d1 note #ae4 #fcf ,see ,vol4 ,i1 page #chb1 note #ac #ghf4 #fcg ,monsieur1 7a bn7_/n x1 whence ,god exists2 answer that6 #fch ,monsieur1 you know very well that your argument requires the development of x according to integral powers of n4 #fci ,see ,vol4 ,i1 page #aec1 note #d #ccg4 #fdj ,thomas ,love ,peacock 7#aghe-ahff7 an ,english novelist and poet4 #fda ,perhaps ,dr4 ,samuel ,warren 7#ahjg-ahgg71 the author of ,ten ,thousand a ,year 7serially in ,blackwood's in #ahci2 ,london1 #ahda74 #fdb ,see ,vol4 ,i1 page #bee1 note #f #ehd4 #fdc ,from many1 one2 much in little2 ,ultima ,thule 7the most remote region72 without which not4 #fdd ,spurius ,maelius 7fl4 #ddj ,b4 ,c471 who distributed corn freely among the poor in the famine of #ddj ,b4 ,c4 and was assassinated by the patricians4 #fde ,spurius ,cassius ,viscellinus1 ,roman consul in #ejb1 #dic1 and #dhf ,b4 ,c4 ,put to death in #dhe4 #fdf ,o what a fine bearing1 he said1 that has no brain4 #fdg ,sir ,william ,rowan ,hamilton4 ,see ,vol4 ,i1 page #ccb1 note #d #gji4 #fdh ,william ,allen ,whitworth1 the author of the well-known ,choice and ,chance 7,cambridge1 #ahfg71 and other works4 #fdi ,james ,maurice ,wilson1 whose ,elementary ,geometry appeared in #ahfh and went through several editions4 #fej ,see ,vol4 ,,ii1 page #ahc1 note #cae4 #fea ,force of inertia conquered1 and ,victory in the whole heavens4 #feb ,with all his might4 #fec ,george ,berkeley 7#afhe-agec71 ,bishop of ,cloyne1 the idealistic philosopher and author of the ,principles of ,human ,knowledge 7#agaj71 ,the ,analyst1 or a ,discourse addressed to an ,infidel ,mathematician 7#agcd71 and ,a ,defense of ,freethinking in ,mathematics 7#agce74 ,he asserted that space involves the idea of movement without the sensation of resistance4 ,space sensation less than the minima sensibilia is1 therefore1 impossible4 ,from this he argues that infinitesimals are impossible concepts4 #fed ,see ,vol4 ,i1 page #he1 note #b #abi4 #fee ,see ,vol4 ,i1 page #ha1 note #f #abj4 #fef ,edwin ,dunkin revised ,lardner's ,handbook of ,astronomy 7#ahfi7 and ,milner's ,the ,heavens and the ,earth 7#ahgc7 and wrote ,the ,midnight ,sky 7#ahfi74 #feg ,michael ,faraday 7#agia-ahfg7 the celebrated physicist and chemist4 ,he was an assistant to ,sir ,humphrey ,davy 7#ahac7 and became professor of chemistry at the ,royal ,institution1 ,london1 in #ahbg4 #feh ,if you teach a fool he shows no joyous countenance2 he cordially hates you2 he wishes you buried4 #fei ,every man is an animal1 ,sortes is a man1 therefore ,sortes is an animal4 #ffj ,may some choice patron bless each grey goose quill2 ,may every ,bavius have his ,bufo still4--,,pope1 ,prologue to the ,satires4 ,bavius has become proverbial as a bad poet from the lines in ,vergil's ,eclogues 7,,iii1 #ij73 ,qui ,bavium non odit1 amet tua carmina1 ,maevi1 ,atque idem jungat vulpes1 et mulgeat hircos4 ,he who does not hate ,bavius shall love thy verses1 ,o ,maevius2 and the same shall yoke foxes and shall milk he-goats4 ,bavius and ,maevius were the worst of ,latin poets1 condemned by ,horace as well as ,vergil4 #ffa ,see ,vol4 ,,ii1 page #aeh1 note #bgi4 #ffb ,honest1 useful1 handsome1 sweet4 #ffc ,let not the fourth man attempt to speak4 #ffd ,in those old times1--ah ',twas just like this1 ah6 #ffe ,see ,vol4 ,i1 page #chb1 note #ab #ghe4 #fff ,these remarks were never written4--,s4 ,e4 ,de ,m4 #ffg ,fleas1 flies1 and friars1 are masters who sadly the people abuse1 ,and thistles and briars are sure growing grains to abuse4 ,o ,christ1 who hatest strife and slayst all things in peace1 ,destroy where'er are rife1 briars1 friars1 flies and fleas4 ,fleas1 flies1 and friars foul fall them these fifteen years ,for none that there is loveth fleas1 flies1 nor freres4 #ffh ,it is my plan to restore to an unskilled race the worthy arts of a better life4 #ffi ,the first sentences of the first oration of ,cicero against ,catiline3 ,quo usque tandem abutere1 ,catilina1 patientia nostra8 7,how long1 ,o ,catiline1 will you abuse our patience87 ,quamdiu etiam furor iste tuus nos eludet8 7,how long will this your madness baffle us87 ,nihilne te nocturnum praesidium ,palati1 444 nihil horum ora voltusque moverunt8 7,does the night watch of the ,palatium1 444 do the faces and expressions of all these men fail to move you87 ,in te conferri 444 7,this plague should have been inflicted upon you long ago1 which you have plotted against us so long47 #fgj ,beware of the things that are marked4 #fga ,farewell1 ye teachers without learning6 ,see to it that at our next meeting we may find you strong in body and sound in mind4 #fgb ,see ,vol4 ,i1 page #ccf1 note #h #gac4 #fgc ,see ,vol4 ,i1 page #bbi1 note #b #eae4 #fgd ,this proof1 although capable of improvement1 is left as in the original4 ,those who may be interested in the mathematics of the question1 may consult ,f4 ,enriques1 ,fragen der ,elementargeometrie 7,german by ,fleischer71 ,leipsic1 #aijg1 ,part ,,ii1 p4 #bfg2 ,f4 ,rudio1 ,archimedes1 ,huygens1 ,lambert1 ,legendre4 ,vier ,abhandlungen ueber die ,kreismessung1 ,leipsic1 #ahib2 ,f4 ,klein1 ,famous ,problems of ,elementary ,geometry 7,english by ,beman and ,smith71 ,boston1 #ahie2 ,j4 ,w4 ,a4 ,young1 ,monographs on ,modern ,mathematics1 ,new ,york1 #aiaa1 ,chap4 ,,ix 7by the editor of the present edition of ,de ,morgan47 #fge ,see ,vol4 ,i1 page #fi1 note #b #ie4 #fgf ,see ,vol4 ,i1 page #acg1 note #h #bhf4 #fgg ,joseph ,allen ,galbraith who1 with ,samuel ,haughton1 wrote the ,galbraith and ,haughton's ,scientific ,manuals4 7,euclid1 #ahef2 ,algebra1 #ahfj2 ,trigonometry1 #ahed2 ,optics1 #ahed1 and others47 #fgh ,this note on ,carlyle 7#agie-ahha7 is interesting4 ,the translation of ,legendre appeared in the same year 7#ahbd7 as his translation of ,goethe's ,wilhelm ,meister4 #fgi ,michael ,stifel 7#adhg-aefg71 also known as ,stiefel1 ,styfel1 and ,stifelius1 was an ,augustine monk but became a convert to ,lutheranism4 ,he was professor of mathematics at ,jena 7#aeei-aefg74 ,his edition of the ,coss appeared at ,koenigsberg in #aeec1 the first edition having been published in #aebe4 ,the and - signs first appeared in print in ,widman's arithmetic of #adhi1 but for purposes of algebra this book was one of the first to make them known4 #fhj ,christoff ,rudolff was born about #aejj and died between #aedj and #aeeb4 ,die ,coss appeared in #aebe and his arithmetic in #aebf4 99 99 99 99 99 ,corrections made to printed original4 ,page #i1 long-fostered prejudice3 'perjudice' in original4 ,page #gc1 ,pensees1 ch4 #g3 ',pansees' in original4 ,page #abg1 and pulled out a plum3 'und' in original4 ,page #adg1 did not come forward3 'forword' in original4 ,page #agb1 come into general circulation3 'circulalation' in original4 ,ibid41 the more difficult fractions which we have got3 'he have got' in original4 ,page #aib1 it has been stated3 'started' in original4 ,page #baf1 the obsolete word tetch of the same meaning3 'meaing' in original4 ,page #bbh1 ,greek3 dioklasianos3 'dioklalasianos' in original4 ,page #bcc4 ,after ,henry ,e4 ,manning' were printed two paragraphs ,shilling versus ,franc4' and ,teutonic ,long ,hundred #abj versus #ajj or the ,decimal question4' ,these appear to have been set in error1 there is no applicable context4 ,page #caf1 in a manner depending upon the difference3 'maner' in original4 ,page #cbb1 neither what ,newton did1 nor what was done before him43 'not' 7for 'nor'7 in original4 ,page #cdd1 ,victoria toto coelo3 'tolo' in original4 ,page #cfh1 cannot be brought up to #a3 'up to -' in original4 ,page #cga1 ,q#b;b#b ,q#a;a#b3 ',q#b;b#b ,q#a-;a#b' in original4 ,note #ej1 all who were not in the road to ,heaven were excommunicated3 'excomunicated' in original4 ,note #cgb1 ,greek3 he alazoneia biou3 'alaxoneia' in original4 ,ibid41 ,iapetos3 ',ispetos' in original4 ,ibid41 ,papeiskos3 ',paspeisoks' in original4 ,ibid41 ,greek3 dioklasianos3 'dioklalasianos' in original4