,transcriber's ,note3 ,minor spelling and typographical errors have been corrected without note4 ,the oe ligature is shown as oe1 the ,greek letter pi is represented by pi1 and appears before a superscript character4 ,,the ,,seven ,,follies ,,of ,,science ,a ,,popular ,,account ,,of ,,the ,,most ,,famous ,,scientific ,,impossibilities ,,and ,,the ,,attempts ,,which ,,have ,,been ,,made ,,to ,,solve ,,them4 ,,to ,,which ,,is ,,added ,a ,,small ,,budget ,,of ,,interesting ,,paradoxes1 ,,illusions1 ,,and ,,marvels4 ,,with ,,numerous ,,illustrations ,,by ,,john ,,phin ,,author ,,of ,,how ,,to ,,use ,,the ,,microscope2 ,,the ,,workshop ,,companion2 ,,the ,,shakespeare ,,cyclopedia2 ,,editor ,,marquis ,,of ,,worcester',s1 ,,century ,,of ,,inventions2 ,,etc4 ,,second ,,edition ,device ,,new ,,york ,d4 ,,van ,,nostrand ,,company #bc ,,murray ,,and #bg ,,warren ,,sts4 #aijf ,,copyright1 #aijf1 ,,by ,d4 ,,van ,,nostrand ,,company4 ,,preface ,in the following pages ,i have endeavored to give a simple account of problems which have occupied the attention of the human mind ever since the dawn of civilization1 and which can never lose their interest until time shall be no more4 ,while to most persons these subjects will have but an historical interest1 yet even from this point of view they are of more value than the history of empires1 for they are the intellectual battlefields upon which much of our progress in science has been won4 ,to a few1 however1 some of them may be of actual practical importance1 for although the schoolmaster has been abroad for these many years1 it is an unfortunate fact that the circle-squarer and the perpetual-motion-seeker have not ceased out of the land4 ,in these days of almost miraculous progress it is difficult to realize that there may be such a thing as a scientific impossibility4 ,i have therefore endeavored to point out where the line must be drawn1 and by way of illustration ,i have added a few curious paradoxes and marvels1 some of which show apparent contradictions to known laws of nature1 but which are all simply and easily explained when we understand the fundamental principles which govern each case4 ,in presenting the various subjects which are here discussed1 ,i have endeavored to use the simplest language and to avoid entirely the use of mathematical formulae1 for ,i know by large experience that these are the bugbear of the ordinary reader1 for whom this volume is specially intended4 ,therefore ,i have endeavored to state everything in such a simple manner that any one with a mere common school education can understand it4 ,this1 ,i trust1 will explain the absence of everything which requires the use of anything higher than the simple rules of arithmetic and the most elementary propositions of geometry4 ,and even this ,i have found to be enough for many lawyers1 physicians1 and clergymen who1 in the ardent pursuit of their professions1 have forgotten much that they learned at college4 ,and as ,i hope to find many readers amongst intelligent mechanics1 ,i have in some cases suggested mechanical proofs which any expert handler of tools can easily carry out4 ,as a matter of course1 very little originality is claimed for anything in the book1--the only points that are new being a few illustrations of well-known principles1 some of which had already appeared in ,the ,young ,scientist and ,self-education for ,mechanics4 ,whenever the exact words of an author have been used1 credit has always been given2 but in regard to general statements and ideas1 ,i must rest content with naming the books from which ,i have derived the greatest assistance4 ,ozanam's ,recreations in ,science and ,natural ,philosophy1 in the editions of ,hutton 7#ahjc7 and ,riddle 7#ahed71 has been a storehouse of matter4 ,much has been gleaned from the ,budget of ,paradoxes by ,professor ,de ,morgan and also from ,professor ,w4 ,w4 ,r4 ,ball's ,mathematical ,recreations and ,problems4 ,those who wish to inform themselves in regard to what has been done by the perpetual-motion-mongers must consult ,mr4 ,dirck's two volumes entitled ,perpetuum ,mobile and ,i have made free use of his labors4 ,to these and one or two others ,i acknowledge unlimited credit4 ,some of the marvels which are here described1 although very old1 are not generally known1 and as they are easily put in practice they may afford a pleasant hour's amusement to the reader and his friends4 ,,john ,,phin ,paterson1 ,n4 ,j41 ,july1 #aije4 ,,contents ,preface ,,the ,,seven ,,follies ,,of ,,science ,,page ,introductory ,note #a ,i ,squaring the ,circle #i ,,ii ,the ,duplication of the ,cube #cj ,,iii ,the ,trisection of an ,angle #cc ,,iv ,perpetual ,motion #cf ,v ,the ,transmutation of ,metals--,alchemy #gi ,,vi ,the ,fixation of ,mercury #ib ,,vii ,the ,universal ,medicine and the ,elixir of ,life #ie ,,additional ,,follies ,perpetual or ,ever-burning ,lamps #ajj ,the ,alkahest or ,universal ,solvent #ajd ,palingenesy #ajf ,the ,powder of ,sympathy #aaa ,a ,,small ,,budget ,,of ,,paradoxes1 ,,illusions1 ,,and ,,marvels 7,,with ,,apologies ,,to ,,professor ,,de ,,morgan7 ,the ,fourth ,dimension #aag ,how a ,space may be apparently ,enlarged by merely changing its ,shape #abf ,can a ,man ,lift ,himself by the ,straps of his ,boots8 #abh ,how a ,spider ,lifted a ,snake #acj ,how the ,shadow may be made to move backward on the ,sun-dial #acc ,how a ,watch may be used as a ,compass #acd ,micrography or ,minute ,writing4 ,writing so fine that the whole ,bible1 if written in characters of the same size1 might be inscribed twenty-two times on a square inch #acf ,illusions of the ,senses #adi ,taste and ,smell #aej ,sense of ,heat #aej ,sense of ,hearing #aej ,sense of ,touch--,one ,thing ,appearing as ,two #aea ,how ,objects may be apparently ,seen through a ,hole in the ,hand #aef ,how to ,see 7apparently7 through a ,solid ,brick #aeh ,,curious ,,arithmetical ,,problems ,the ,chess-board ,problem #afc ,the ,nail ,problem #afd ,a ,question of ,population #afe ,how to ,become a ,millionaire #aff ,the ,actual ,cost and ,present ,value of the ,first ,folio ,shakespeare #afh ,arithmetical ,puzzles #agj ,archimedes and ,his ,fulcrum #aga ,,the ,,seven ,,follies ,,of ,,science ,the difficult1 the dangerous1 and the impossible have always had a strange fascination for the human mind4 ,we see this every day in the acts of boys who risk life and limb in the performance of useless but dangerous feats1 and amongst children of larger growth we find loop-the-loopers1 bridge-jumpers1 and all sorts of venture-seekers to whom much of the attraction of these performances is undoubtedly the mere risk that is involved1 although1 perhaps1 to some extent1 notoriety and money-making may contribute their share4 ,many of our readers will doubtless remember the words of ,james ,fitz-,james1 in ,the ,lady of the ,lake3 ,or1 if a path be dangerous known ,the danger's self is lure alone4 ,and in commenting on the old-time game laws of ,england1 ,froude1 the historian1 says3 ,although the old forest laws were terrible1 they served only to enhance the excitement by danger4 ,that which is true of physical dangers holds equally true in regard to intellectual difficulties4 ,professor ,de ,morgan tells us1 in his ,budget of ,paradoxes1 that he once gave a lecture on ,squaring the ,circle and that a gentleman who was introduced to it by what he said1 remarked loud enough to be heard by all around3 ,only prove to me that it is impossible and ,i will set about it this very evening4 ,therefore it is not to be wondered at that certain very difficult1 or perhaps impossible problems have in all ages had a powerful fascination for certain minds4 ,in that curious olla podrida of fact and fiction1 ,the ,curiosities of ,literature1 ,d',israeli gives a list of six of these problems1 which he calls ,the ,six ,follies of ,science4 ,i do not know whether the phrase ,follies of ,science originated with him or not1 but he enumerates the ,quadrature of the ,circle2 the ,duplication1 or1 as he calls it1 the ,multiplication of the ,cube2 the ,perpetual ,motion2 the ,philosophical ,stone2 ,magic1 and ,judicial ,astrology1 as those known to him4 ,this list1 however1 has no classical standing such as pertains to the ,seven ,wonders of the ,world1 the ,seven ,wise ,men of ,greece1 the ,seven ,champions of ,christendom1 and others4 ,there are some well-known follies that are omitted1 while some authorities would peremptorily reject ,magic and ,judicial ,astrology as being attempts at fraud rather than earnest efforts to discover and utilize the secrets of nature4 ,the generally accepted list is as follows3 #a4 ,the ,quadrature of the ,circle or1 as it is called in the vernacular1 ,squaring the ,circle4 #b4 ,the ,duplication of the ,cube4 #c4 ,the ,trisection of an ,angle4 #d4 ,perpetual ,motion4 #e4 ,the ,transmutation of the ,metals4 #f4 ,the ,fixation of ,mercury4 #g4 ,the ,elixir of ,life4 ,the ,transmutation of the ,metals1 the ,fixation of ,mercury1 and the ,elixir of ,life might perhaps be properly classed as one1 under the head of the ,philosopher's ,stone1 and then ,astrology and ,magic might come in to make up the mystic number ,seven4 ,the expression ,follies of ,science does not seem a very appropriate one4 ,real science has no follies4 ,neither can these vain attempts be called scientific follies because their very essence is that they are unscientific4 ,each one is really a veritable ,will-o'-the-,wisp for unscientific thinkers1 and there are many more of them than those that we have here named4 ,but the expression has been adopted in literature and it is just as well to accept it4 ,those on the list that we have given are the ones that have become famous in history and they still engage the attention of a certain class of minds4 ,it is only a few months since a man who claims to be a professional architect and technical writer put forth an alleged method of squaring the circle1 which he claims to be exact2 and the results of an attempt to make liquid air a pathway to perpetual motion are still in evidence1 as a minus quantity1 in the pockets of many who believed that all things are possible to modern science4 ,and indeed it is this false idea of the possibility of the impossible that leads astray the followers of these false lights4 ,inventive science has accomplished so much--many of her achievements being so astounding that they would certainly have seemed miracles to the most intelligent men of a few generations ago--that the ordinary mind cannot see the difference between unknown possibilities and those things which well-established science pronounces to be impossible1 because they contradict fundamental laws which are thoroughly established and well understood4 ,thus any one who would claim that he could make a plane triangle in which the three angles would measure more than two right angles1 would show by this very claim that he was entirely ignorant of the first principles of geometry4 ,the same would be true of the man who would claim that he could give1 in exact figures1 the diagonal of a square of which the side is exactly one foot or one yard1 and it is also true of the man who claims that he can give the exact area of a circle of which either the circumference or the diameter is known with precision4 ,that they cannot both be known exactly is very well understood by all who have studied the subject1 but that the area1 the circumference1 and the diameter of a circle may all be known with an exactitude which is far in excess of anything of which the human mind can form the least conception1 is quite true1 as we shall show when we come to consider the subject in its proper place4 ,these problems are not only interesting historically but they are valuable as illustrating the vagaries of the human mind and the difficulties with which the early investigators had to contend4 ,they also show us the barriers over which we cannot pass1 and they enforce the immutable character of the natural laws which govern the world around us4 ,we hear much of the progress of science and of the changes which this progress has brought about1 but these changes never affect the fundamental facts and principles upon which all true science is based4 ,theories and explanations and even practical applications change or pass away1 so that we know them no more1 but nature remains the same throughout the ages4 ,no new theory of electricity can ever take away from the voltaic battery its power1 or change it in any respect1 and no new discovery in regard to the constitution of matter can ever lessen the eagerness with which carbon and oxygen combine together4 ,every little while we hear of some discovery that is going to upset all our preconceived notions and entirely change those laws which long experience has proved to be invariable1 but in every case these alleged discoveries have turned out to be fallacies4 ,for example1 the wonderful properties of radium have led some enthusiasts to adopt the idea that many of our old notions about the conservation of energy must be abandoned1 but when all the facts are carefully examined it is found that there is no rational basis for such views4 ,upon this point ,sir ,oliver ,lodge says3 ,there is absolutely no ground for the popular and gratuitous surmise that radium emits energy without loss or waste of any kind1 and that it is competent to go on forever4 ,the idea1 at one time irresponsibly mooted1 that it contradicted the principle of the conservation of energy1 and was troubling physicists with the idea that they must overhaul their theories--a thing which they ought always to be delighted to do on good evidence--this idea was a gratuitous absurdity1 and never had the slightest foundation4 ,it is reasonable to suppose1 however1 that radium and the other like substances are drawing upon their own stores of internal atomic energy1 and thereby gradually disintegrating and falling into other and ultimately more stable forms of matter4 ,one would naturally suppose that the extensive diffusion of sound scientific knowledge which has taken place during the century just past1 would have placed these problems amongst the lumber of past ages2 but it seems that some of them1 particularly the squaring of the circle and perpetual motion1 still occupy considerable space in the attention of the world1 and even the futile chase after the ,elixir of ,life has not been entirely abandoned4 ,indeed certain professors who occupy prominent official positions1 assert that they have made great progress towards its attainment4 ,in view of such facts one is almost driven to accept the humorous explanation which ,de ,morgan has offered and which he bases on an old legend relating to the famous wizard1 ,michael ,scott4 ,the generally accepted tradition1 as related by ,sir ,walter ,scott in his notes to the ,lay of the ,last ,minstrel1 is as follows3 ,michael ,scott was1 once upon a time1 much embarrassed by a spirit for whom he was under the necessity of finding constant employment4 ,he commanded him to build a 'cauld1' or dam head across the ,tweed at ,kelso2 it was accomplished in one night1 and still does honor to the infernal architect4 ,michael next ordered that ,eildon ,hill1 which was then a uniform cone1 should be divided into three4 ,another night was sufficient to part its summit into the three picturesque peaks which it now bears4 ,at length the enchanter conquered this indefatigable demon1 by employing him in the hopeless task of making ropes out of sea-sand4 ,whereupon ,de ,morgan offers the following exceedingly interesting continuation of the legend3 ,the recorded story is that ,michael ,scott1 being bound by contract to procure perpetual employment for a number of young demons1 was worried out of his life in inventing jobs for them1 until at last he set them to make ropes out of sea-sand1 which they never could do4 ,we have obtained a very curious correspondence between the wizard ,michael and his demon slaves2 but we do not feel at liberty to say how it came into our hands4 ,we much regret that we did not receive it in time for the ,british ,association4 ,it appears that the story1 true as far as it goes1 was never finished4 ,the demons easily conquered the rope difficulty1 by the simple process of making the sand into glass1 and spinning the glass into thread which they twisted4 ,michael1 thoroughly disconcerted1 hit upon the plan of setting some to square the circle1 others to find the perpetual motion1 etc4 ,he commanded each of them to transmigrate from one human body into another1 until their tasks were done4 ,this explains the whole succession of cyclometers and all the heroes of the ,budget4 ,some of this correspondence is very recent2 it is much blotted1 and we are not quite sure of its meaning4 ,it is full of figurative allusions to driving something illegible down a steep into the sea4 ,it looks like a humble petition to be allowed some diversion in the intervals of transmigration2 and the answer is3 ',rumpat et serpens iter institutum' a line of ,horace1 which the demons interpret as a direction to come athwart the proceedings of the ,institute by a sly trick4 ,and really those who have followed carefully the history of the men who have claimed that they had solved these famous problems1 will be almost inclined to accept ,de ,morgan's ingenious explanation as something more than a mere skit4 ,the whole history of the philosopher's stone1 of machines and contrivances for obtaining perpetual motion1 and of circle-squaring1 is permeated with accounts of the most gross and obvious frauds4 ,that ignorance played an important part in the conduct of many who have put forth schemes based upon these pretended solutions is no doubt true1 but that a deliberate attempt at absolute fraud was the mainspring in many cases cannot be denied4 ,like ,dousterswivel in ,the ,antiquary1 many of the men who advocated these delusions may have had a sneaking suspicion that there might be some truth in the doctrines which they promulgated2 but most of them knew that their particular claims were groundless1 and that they were put forward for the purpose of deceiving some confiding patron from whom they expected either money or the credit and glory of having done that which had been hitherto considered impossible4 ,some of the questions here discussed have been called scientific impossibilities--an epithet which many have considered entirely inapplicable to any problem1 on the ground that all things are possible to science4 ,and in view of the wonderful things that have been accomplished in the past1 some of my readers may well ask3 ,who shall decide when doctors disagree8 ,perhaps the best answer to this question is that given by ,ozanam1 the old historian of these and many other scientific puzzles4 ,he claimed that it was the business of the ,doctors of the ,sorbonne to discuss1 of the ,pope to decide1 and of a mathematician to go straight to heaven in a perpendicular line6 ,in this connection the words of ,de ,morgan have a deep significance4 ,alluding to the difficulty of preventing men of no authority from setting up false pretensions and the impossibility of destroying the assertions of fancy speculation1 he says3 ,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-conceit2 learning can annihilate learning2 but learning cannot annihilate ignorance4 ,a sword may cut through an iron bar1 and the severed ends will not reunite2 let it go through the air1 and the yielding substance is whole again in a moment4 ,i4 ,,squaring ,,the ,,circle ,undoubtedly one of the reasons why this problem has received so much attention from those whose minds certainly have no special leaning towards mathematics1 lies in the fact that there is a general impression abroad that the governments of ,great ,britain and ,france have offered large rewards for its solution4 ,de ,morgan tells of a ,jesuit who came all the way from ,south ,america1 bringing with him a quadrature of the circle and a newspaper cutting announcing that a reward was ready for the discovery in ,england4 ,as a matter of fact his method of solving the problem was worthless1 and even if it had been valuable1 there would have been no reward4 ,another case was that of an agricultural laborer who spent his hard-earned savings on a journey to ,london1 carrying with him an alleged solution of the problem1 and who demanded from the ,lord ,chancellor the sum of one hundred thousand pounds1 which he claimed to be the amount of the reward offered and which he desired should be handed over forthwith4 ,when he failed to get the money he and his friends were highly indignant and insisted that the influence of the clergy had deprived the poor man of his just deserts6 ,and it is related that in the year #aghh1 one of these deluded individuals1 a ,m4 de ,vausenville1 actually brought an action against the ,french ,academy of ,sciences to recover a reward to which he felt himself entitled4 ,it ought to be needless to say that there never was a reward offered for the solution of this or any other of the problems which are discussed in this volume4 ,upon this point ,de ,morgan has the following remarks3 ,montucla says1 speaking of ,france1 that he finds three notions prevalent among the cyclometers or circle-squarers3 #a4 ,that there is a large reward offered for success2 #b4 ,that the longitude problem depends on that success2 #c4 ,that the solution is the great end and object of geometry4 ,the same three notions are equally prevalent among the same class in ,england4 ,no reward has ever been offered by the government of either country4 ,the longitude problem in no way depends upon perfect solution2 existing approximations are sufficient to a point of accuracy far beyond what can be wanted4 ,and geometry1 content with what exists1 has long pressed on to other matters4 ,sometimes a cyclometer persuades a skipper1 who has made land in the wrong place1 that the astronomers are in fault for using a wrong measure of the circle2 and the skipper thinks it a very comfortable solution6 ,and this is the utmost that the problem ever has to do with longitude4 ,in the year #agge the ,royal ,academy of ,sciences of ,paris passed a resolution not to entertain communications which claimed to give solutions of any of the following problems3 ,the duplication of the cube1 the trisection of an angle1 the quadrature of a circle1 or any machine announced as showing perpetual motion4 ,and we have heard that the ,royal ,society of ,london passed similar resolutions1 but of course in the case of neither society did these resolutions exclude legitimate mathematical investigations--the famous computations of ,mr4 ,shanks1 to which we shall have occasion to refer hereafter1 were submitted to the ,royal ,society of ,london and published in their ,transactions4 ,attempts to square the circle1 when made intelligently1 were not only commendable but have been productive of the most valuable results4 ,at the same time there is no problem1 with the possible exception of that of perpetual motion1 that has caused more waste of time and effort on the part of those who have attempted its solution1 and who have in almost all cases been ignorant both of the nature of the problem and of the results which have been already attained4 ,from ,archimedes down to the present time some of the ablest mathematicians have occupied themselves with the quadrature1 or1 as it is called in common language1 the squaring of the circle2 but these men are not to be placed in the same class with those to whom the term circle-squarers is generally applied4 ,as already noted1 the great difficulty with most circle-squarers is that they are ignorant both of the nature of the problem to be solved and of the results which have been already attained4 ,sometimes we see it explained as the drawing of a square inside a circle and at other times as the drawing of a square around a circle1 but both these problems are amongst the very simplest in practical geometry1 the solutions being given in the sixth and seventh propositions of the ,fourth ,book of ,euclid4 ,other definitions have been given1 some of them quite absurd4 ,thus in ,france1 in #agec1 ,m4 de ,causans1 of the ,guards1 cut a circular piece of turf1 squared it1 and from the result deduced original sin and the ,trinity4 ,he found out that the circle was equal to the square in which it is inscribed1 and he offered a reward for the detection of any error1 and actually deposited #aj1jjj francs as earnest of #cjj1jjj4 ,but the courts would not allow any one to recover4 ,in the last number of the ,athenaeum for #ahee a correspondent says the thing is no longer a problem but an axiom4 ,he makes the square equal to a circle by making each side equal to a quarter of the circumference4 ,as ,de ,morgan says1 he does not know that the area of the circle is greater than that of any other figure of the same circuit4 ,such ideas are evidently akin to the poetic notion of the quadrature4 ,aristophanes1 in the ,birds1 introduces a geometer1 who announces his intention to make a square circle4 ,and ,pope in the ,dunciad delivers himself as follows3 ,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 ,as stated by all recognized authorities1 the problem is this3 ,to describe a square which shall be exactly equal in area to a given circle4 ,the solution of this problem may be given in two ways3 7#a7 the arithmetical method1 by which the area of a circle is found and expressed numerically in square measure1 and 7#b7 the geometrical quadrature1 by which a square1 equal in area to a given circle1 is described by means of rule and compasses alone4 ,of course1 if we know the area of the circle1 it is easy to find the side of a square of equal area2 this can be done by simply extracting the square root of the area1 provided the number is one of which it is possible to extract the square root4 ,thus1 if we have a circle which contains #ajj square feet1 a square with sides of #aj feet would be exactly equal to it4 ,but the ascertaining of the area of the circle is the very point where the difficulty comes in2 the dimensions of circles are usually stated in the lengths of the diameters1 and when this is the case1 the problem resolves itself into another1 which is3 ,to find the area of a circle when the diameter is given4 ,now ,archimedes proved that the area of any circle is equal to that of a triangle whose base has the same length as the circumference and whose altitude or height is equal to the radius4 ,therefore if we can find the length of the circumference when the diameter is given1 we are in possession of all the points needed to enable us to square the circle4 ,in this form the problem is known to mathematicians as that of the rectification of the curve4 ,in a practical form this problem must have presented itself to intelligent workmen at a very early stage in the progress of operative mechanics4 ,architects1 builders1 blacksmiths1 and the makers of chariot wheels and vessels of various kinds must have had occasion to compare the diameters and circumferences of round articles4 ,thus in ,i ,kings1 vii1 #bc1 it is said of ,hiram of ,tyre that he made a molten sea1 ten cubits from the one brim to the other2 it was round all about 99 99 99 and a line of thirty cubits did compass it round about1 from which it has been inferred that among the ,jews1 at that time1 the accepted ratio was #c to #a1 and perhaps1 with the crude measuring instruments of that age1 this was as near as could be expected4 ,and this ratio seems to have been accepted by the ,babylonians1 the ,chinese1 and probably also by the ,greeks1 in the earliest times4 ,at the same time we must not forget that these statements in regard to the ratio come to us through historians and prophets1 and may not have been the figures used by trained mechanics4 ,an error of one foot in a hoop made to go round a tub or cistern of seven feet in diameter1 would hardly be tolerated even in an apprentice4 ,the ,egyptians seem to have reached a closer approximation1 for from a calculation in the ,rhind papyrus1 the ratio of #c4af to #a seems to have been at one time in use4 ,it is probable1 however1 that in these early times the ratio accepted by mechanics in general was determined by actual measurement1 and this1 as we shall see hereafter1 is quite capable of giving results accurate to the second fractional place1 even with very common apparatus4 ,to ,archimedes1 however1 is generally accorded the credit of the first attempt to solve the problem in a scientific manner2 he took the circumference of the circle as intermediate between the perimeters of the inscribed and the circumscribed polygons1 and reached the conclusion that the ratio lay between #c-a_/g and #c-aj_/ga1 or between #c4adbh and #c4adjh4 ,this ratio1 in its more accurate form of #c4adaeib44 is now known by the ,greek letter pi 7pronounced like the common word pie71 a symbol which was introduced by ,euler1 between #agcg and #agdh1 and which is now adopted all over the world4 ,i have1 however1 used the term ratio1 or value of the ratio instead1 throughout this chapter1 as probably being more familiar to my readers4 ,professor ,muir justly says of this achievement of ,archimedes1 that it is a most notable piece of work2 the immature condition of arithmetic1 at the time1 was the only real obstacle preventing the evaluation of the ratio to any degree of accuracy whatever4 ,and when we remember that neither the numerals now in use nor the ,arabic numerals1 as they are usually called1 nor any system equivalent to our decimal system1 was known to these early mathematicians1 such a calculation as that made by ,archimedes was a wonderful feat4 ,if any of my readers1 who are familiar with the ,hebrew or ,greek numbers1 and the mode of representing them by letters1 will try to do any of those more elaborate sums which1 when worked out by modern methods1 are mere child's play in the hands of any of the bright scholars in our common schools1 they will fully appreciate the difficulties under which ,archimedes labored4 ,or1 if ignorant of ,greek and ,hebrew1 let them try it with the ,roman numerals1 and multiply ,,xcviii by ,,mdlvii1 without using ,arabic or common numerals4 ,professor ,mc,arthur1 in his article on ,arithmetic in the ,encyclopaedia ,britannica1 makes the following statement on this point3 ,the methods that preceded the adoption of the ,arabic numerals were all comparatively unwieldy1 and very simple processes involved great labor4 ,the notation of the ,romans1 in particular1 could adapt itself so ill to arithmetical operations1 that nearly all their calculations had to be made by the abacus4 ,one of the best and most manageable of the ancient systems is the ,greek1 though that1 too1 is very clumsy4 ,after ,archimedes1 the most notable result was that given by ,ptolemy1 in the ,great ,syntaxis4 ,he made the ratio #c4adaeeb1 which was a very close approximation4 ,for several centuries there was little progress towards a more accurate determination of the ratio4 ,among the ,hindoos1 as early as the sixth century1 the now well-known value1 #c4adaf1 had been obtained by ,arya-,bhata1 and a little later another of their mathematicians came to the conclusion that the square root of #aj was the true value of the ratio4 ,he was led to this by calculating the perimeters of the successive inscribed polygons of #ab1 #bd1 #dh1 and #if sides1 and finding that the greater the number of sides the nearer the perimeter of the polygon approached the square root of #aj4 ,he therefore thought that the perimeter or circumference of the circle itself would be the square root of exactly #aj4 ,it is too great1 however1 being #c4afbb instead of #c4adaei444 ,the same idea is attributed to ,bovillus1 by ,montucla4 ,by calculating the perimeters of the inscribed and circumscribed polygons1 ,vieta 7#aegi7 carried his approximation to ten fractional places1 and in #aehe ,peter ,metius1 the father of ,adrian1 by a lucky step reached the now famous fraction #cee_/aac1 or #c4adaeibib1 which is correct to the sixth fractional place4 ,the error does not exceed one part in thirteen millions4 ,at the beginning of the seventeenth century1 ,ludolph ,van ,ceulen reached #ce places4 ,this result1 which in his life he found by much labor1 was engraved upon his tombstone in ,st4 ,peter's ,church1 ,leyden4 ,the monument has now unfortunately disappeared4 ,from this time on1 various mathematicians succeeded1 by improved methods1 in increasing the approximation4 ,thus in #agje1 ,abraham ,sharp carried it to #gb places2 ,machin 7#agjf7 to #ajj places2 ,rutherford 7#ahda7 to #bjh places1 and ,mr4 ,shanks in #ahec1 to #fjg places4 ,the same computer in #ahgc reached the enormous number of #gjg places4 ,printed in type of the same size as that used on this page1 these figures would form a line nearly six feet long4 ,as a matter of interest ,i give here the value of the ratio of the circumference to the diameter1 to #abg places3 #c4adaei #bfece #higic #bchdf #bfdcc #hcbgi #ejbhh #daiga #ficii #cgeaj #ehbji #gdidd #eibcj #ghafd #jfbhf #bjhii #hfbhj #cdhbe #cdbaa #gjfgi #hbadh #jhfea #cbgbc #jffdg #jichd #df ,the degree of accuracy which may be attained by using a ratio carried to only ten fractional places1 far exceeds anything that can be required in even the finest work1 and indeed it is beyond anything attainable by means of our present tools and instruments4 ,for example3 ,if the length of a curve of #ajj feet radius were determined by a value of ten fractional places1 the result would not err by the one-millionth part of an inch1 a quantity which is quite invisible under the best microscopes of the present day4 ,this shows us that in any calculations relating to the dimensions of the earth1 such as longitude1 etc41 we have at our command1 in the #abg places of figures given above1 an exactness which for all practical purposes may be regarded as absolute4 ,this will be best appreciated by a consideration of the fact that if the earth were a perfect sphere and if we knew its exact diameter1 we could calculate so exactly the length of an iron hoop which would go round it1 that the difference produced by a change of temperature equal to the millionth of a millionth part of a degree ,fahrenheit1 would far exceed the error arising from the difference between the true ratio and the result thus reached4 ,such minute quantities are far beyond the powers of conception of even the most thoroughly trained human mind1 but when we come to use six and seven hundred places the results are simply astounding4 ,professor ,de ,morgan1 in his ,budget of ,paradoxes1 gives the following illustration of the extreme accuracy which might be attained by the use of #fjg fractional places1 the highest number which had been reached when he wrote3 ,say that the blood-globule of one of our animalcules is a millionth of an inch in diameter4#a ,fashion in thought a globe like our own1 but so much larger that our globe is but a blood-globule in one of its animalcules2 never mind the microscope which shows the creature being rather a bulky instrument4 ,call this the first globule 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 ,now1 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 smaller1 and call this the first globe below us4 ,this is a fine stretch of progression both ways4 ,now1 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 ,it would of course be impossible for any human mind to grasp the range of such an illustration as that just given4 ,at the same time these illustrations do serve in some measure to give us an impression1 if not an idea1 of the vastness on the one hand and the minuteness on the other of the measurements with which we are dealing4 ,i therefore offer no apology for giving another example of the nearness to absolute accuracy with which the circle has been squared4 ,it is common knowledge that light travels with a velocity of about #ahe1jjj miles per second4 ,in other words1 light would go completely round the earth in a little more than one-eighth of a second1 or1 as ,herschel puts it1 in less time than it would take a swift runner to make a single stride4 ,taking this distance of #ahe1jjj miles per second as our unit of measurement1 let us apply it as follows3 ,it is generally believed that our solar system is but an individual unit in a stellar system which may include hundreds of thousands of suns like our own1 with all their attendant planets and moons4 ,this stellar system again may be to some higher system what our solar system is to our own stellar system1 and there may be several such gradations of systems1 all going to form one complete whole which1 for want of a better name1 ,i shall call a universe4 ,now this universe1 complete in itself1 may be finite and separated from all other systems of a similar kind by an empty space1 across which even gravitation cannot exert its influence4 ,let us suppose that the imaginary boundary of this great universe is a perfect circle1 the extent of which is such that light1 traveling at the rate we have named 7#ahe1jjj miles per second71 would take millions of millions of years to pass across it1 and let us further suppose that we know the diameter of this mighty space with perfect accuracy2 then1 using ,mr4 ,shanks' #gjg places of decimal fractions1 we could calculate the circumference to such a degree of accuracy that the error would not be visible under any microscope now made4 ,an illustration which may impress some minds even more forcibly than either of those which we have just given1 is as follows3 ,let us suppose that in some titanic iron-works a steel armor-plate had been forged1 perfectly circular in shape and having a diameter of exactly #ahe1jjj1jjj miles1 or very nearly that of the orbit of the earth1 and a thickness of #hjjj miles1 or about that of the diameter of the earth4 ,let us further assume that1 owing to the attraction of some immense stellar body1 this huge mass has what we would call a weight corresponding to that which a plate of the same material would have at the surface of the earth1 and let it be required to calculate the length of the side of a square plate of the same material and thickness and which shall be exactly equal to the circular plate4 ,using the #gjg places of figures of ,mr4 ,shanks1 the length of the required side could be calculated so accurately that the difference in weight between the two plates 7the circle and the square7 would not be sufficient to turn the scale of the most delicate chemical balance ever constructed4 ,of course in assuming the necessary conditions1 we are obliged to leave out of consideration all those more refined details which would embarrass us in similar calculations on the small scale and confine ourselves to the purely mathematical aspect of the case2 but the stretch of imagination required is not greater than that demanded by many illustrations of the kind4 ,so much1 then1 for what is claimed by the mathematicians2 and the certainty that their results are correct1 as far as they go1 is shown by the predictions made by astronomers in regard to the moon's place in the heavens at any given time4 ,the error is less than a second of time in twenty-seven days1 and upon this the sailor depends for a knowledge of his position upon the trackless deep4 ,this is a practical test upon which merchants are willing to stake1 and do stake1 billions of dollars every day4 ,it is now well established that1 like the diagonal and side of a square1 the diameter and circumference of any circle are incommensurable quantities4 ,but1 as ,de ,morgan says1 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 circumference1 with perfect accuracy4 ,when1 therefore1 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 ,but since ,de ,morgan wrote1 it has been shown that a ,euclidean construction is actually impossible4 ,those who desire to examine the question more fully1 will find a very clear discussion of the subject in ,klein's ,famous ,problems in ,elementary ,geometry4 7,boston1 ,ginn ,co47 ,there are various geometrical constructions which give approximate results that are sufficiently accurate for most practical purposes4 ,one of the oldest of these makes the ratio #c-a_/g to #a4 ,using this ratio we can ascertain the circumference of a circle of which the diameter is given by the following method3 ,divide the diameter into #g equal parts by the usual method4 ,then1 having drawn a straight line1 set off on it three times the diameter and one of the sevenths2 the result will give the circumference with an error of less than the one twenty-five-hundredth part or one twenty-fifth of one per cent4 ,if the circumference had been given1 the diameter might have been found by dividing the circumference into twenty-two parts and setting off seven of them4 ,this would give the diameter4 ,a more accurate method is as follows3 ,given a circle1 of which it is desired to find the length of the circumference3 ,inscribe in the given circle a square1 and to three times the diameter of the circle add a fifth of the side of the square2 the result will differ from the circumference of the circle by less than one-seventeen-thousandth part of it4 ,another method which gives a result accurate to the one-seventeen-thousandth part is as follows3 ,illustration3 ,fig4 #a4 ,let ,,ad1 ,fig4 #a1 be the diameter of the circle1 ,c the center1 and ,,cb the radius perpendicular to ,,ad4 ,continue ,,ad and make ,,de equal to the radius2 then draw ,,be1 and in ,,ae1 continued1 make ,,ef equal to it2 if to this line ,,ef1 its fifth part ,,fg be added1 the whole line ,,ag will be equal to the circumference described with the radius ,,ca1 within one-seventeen-thousandth part4 ,the following construction gives even still closer results3 ,given the semi-circle ,,abc1 ,fig4 #b2 from the extremities ,a and ,c of its diameter raise two perpendiculars1 one of them ,,ce1 equal to the tangent of #cj deg41 and the other ,,af1 equal to three times the radius4 ,if the line ,,fe be then drawn1 it will be equal to the semi-circumference of the circle1 within one-hundred-thousandth part nearly4 ,this is an error of one-thousandth of one per cent1 an accuracy far greater than any mechanic can attain with the tools now in use4 ,illustration3 ,fig4 #b4 ,when we have the length of the circumference and the length of the diameter1 we can describe a square which shall be equal to the area of the circle4 ,the following is the method3 ,draw a line ,,acb1 ,fig4 #c1 equal to half the circumference and half the diameter together4 ,bisect this line in ,o1 and with ,o as a center and ,,ao as radius1 describe the semi-circle ,,adb4 ,erect a perpendicular ,,cd1 at ,c1 cutting the arc in ,d2 ,,cd is the side of the required square which can then be constructed in the usual manner4 ,the explanation of this is that ,,cd is a mean proportional between ,,ac and ,,cb4 ,illustration3 ,fig4 #c4 ,de ,morgan says3 ,the following method of finding the circumference of a circle 7taken from a paper by ,mr4 ,s4 ,drach in the ',philosophical ,magazine1' ,january1 #ahfc1 ,suppl471 is as accurate as the use of eight fractional places3 ,from three diameters deduct eight-thousandths and seven-millionths of a diameter2 to the result1 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 ,for obtaining the side of a square which shall be equal in area to a given circle1 the empirical method1 given by ,ahmes in the ,rhind papyrus #djjj years ago1 is very simple and sufficiently accurate for many practical purposes4 ,the rule is3 ,cut off one-ninth of the diameter and construct a square upon the remainder4 ,this makes the ratio #c4af44 and the error does not exceed one-third of one per cent4 ,there are various mechanical methods of measuring and comparing the diameter and the circumference of a circle1 and some of them give tolerably accurate results4 ,the most obvious device and that which was probably the oldest1 is the use of a cord or ribbon for the curved surface and the usual measuring rule for the diameter4 ,with an accurately divided rule and a thin metallic ribbon which does not stretch1 it is possible to determine the ratio to the second fractional place1 and with a little care and skill the third place may be determined quite closely4 ,an improvement which was no doubt introduced at a very early day is the measuring wheel or circumferentor4 ,this is used extensively at the present day by country wheelwrights for measuring tires4 ,it consists of a wheel fixed in a frame so that it may be rolled along or over any surface of which the measurement is desired4 ,this may of course be used for measuring the circumference of any circle and comparing it with the diameter4 ,de ,morgan gives the following instance of its use3 ,a squarer1 having read that the circular ratio was undetermined1 advertised in a country paper as follows3 ,i thought it very strange that so many great scholars in all ages should have failed in finding the true ratio and have been determined to try myself4 ,he kept his method secret1 expecting to secure the benefit of the discovery1 but it leaked out that he did it by rolling a twelve-inch disk along a straight rail1 and his ratio was #fd to #bja or #c4adjfbe exactly4 ,as ,de ,morgan says1 this is a very creditable piece of work2 it is not wrong by #a in #cjjj4 ,skilful machinists are able to measure to the one-five-thousandth of an inch2 this1 on a two-inch cylinder1 would give the ratio correct to five places1 provided we could measure the curved line as accurately as we can the straight diameter1 but it is difficult to do this by the usual methods4 ,perhaps the most accurate plan would be to use a fine wire and wrap it round the cylinder a number of times1 after which its length could be measured4 ,the result would of course require correction for the angle which the wire would necessarily make if the ends did not meet squarely and also for the diameter of the wire4 ,very accurate results have been obtained by this method in measuring the diameters of small rods4 ,a somewhat original way of finding the area of a circle was adopted by one squarer4 ,he took a carefully turned metal cylinder and having measured its length with great accuracy he adopted the ,archimedean method of finding its cubical contents1 that is to say1 he immersed it in water and found out how much it displaced4 ,he then had all the data required to enable him to calculate the area of the circle upon which the cylinder stood4 ,since the straight diameter is easily measured with great accuracy1 when he had the area he could readily have found the circumference by working backward the rule announced by ,archimedes1 viz43 that the area of a circle is equal to that of a triangle whose base has the same length as the circumference and whose altitude is equal to the radius4 ,one would almost fancy that amongst circle-squarers there prevails an idea that some kind of ban or magical prohibition has been laid upon this problem2 that like the hidden treasures of the pirates of old it is protected from the attacks of ordinary mortals by some spirit or demoniac influence1 which paralyses the mind of the would-be solver and frustrates his efforts4 ,it is only on such an hypothesis that we can account for the wild attempts of so many men1 and the persistence with which they cling to obviously erroneous results in the face not only of mathematical demonstration1 but of practical mechanical measurements4 ,for even when working in wood it is easy to measure to the half or even the one-fourth of the hundredth of an inch1 and on a ten-inch circle this will bring the circumference to #c4adaf inches1 which is a corroboration of the orthodox ratio 7#c4adaei7 sufficient to show that any value which is greater than #c4adb or less than #c4ada cannot possibly be correct4 ,and in regard to the area the proof is quite as simple4 ,it is easy to cut out of sheet metal a circle #aj inches in diameter1 and a square of #g4he on the side1 or even one-thousandth of an inch closer to the standard #g4hed4 ,now if the work be done with anything like the accuracy with which good machinists work1 it will be found that the circle and the square will exactly balance each other in weight1 thus proving in another way the correctness of the accepted ratio4 ,but although even as early as before the end of the eighteenth century1 the value of the ratio had been accurately determined to #aeb places of decimals1 the nineteenth century abounded in circle-squarers who brought forward the most absurd arguments in favor of other values4 ,in #ahcf1 a ,french well-sinker named ,lacomme1 applied to a professor of mathematics for information in regard to the amount of stone required to pave the circular bottom of a well1 and was told that it was impossible to give a correct answer1 because the exact ratio of the diameter of a circle to its circumference had never been determined6 ,this absolutely true but very unpractical statement by the professor1 set the well-sinker to thinking2 he studied mathematics after a fashion1 and announced that he had discovered that the circumference was exactly #c-a_/h times the length of the diameter6 ,for this discovery 787 he was honored by several medals of the first class1 bestowed by ,parisian societies4 ,even as late as the year #ahfj1 a ,mr4 ,james ,smith of ,liverpool1 took up this ratio #c-a_/h to #a1 and published several books and pamphlets in which he tried to argue for its accuracy4 ,he even sought to bring it before the ,british ,association for the ,advancement of ,science4 ,professors ,de ,morgan and ,whewell1 and even the famous mathematician1 ,sir ,william ,rowan ,hamilton1 tried to convince him of his error1 but without success4 ,professor ,whewell's demonstration is so neat and so simple that ,i make no apology for giving it here4 ,it is in the form of a letter to ,mr4 ,smith3 ,you may do this3 calculate the side of a polygon of #bd sides inscribed in a circle4 ,i think you are mathematician enough to do this4 ,you will find that if the radius of the circle be one1 the side of the polygon is 4#bfd1 etc4 ,now the arc which this side subtends is1 according to your proposition1 #c4abe_/ab 4#bfjd1 and1 therefore1 the chord is greater than its arc1 which1 you will allow1 is impossible4 ,this must seem1 even to a school-boy1 to be unanswerable1 but it did not faze ,mr4 ,smith1 and ,i doubt if even the method which ,i have suggested previously1 viz41 that of cutting a circle and a square out of the same piece of sheet metal and weighing them1 would have done so4 ,and yet by this method even a common pair of grocer's scales will show to any common-sense person the error of ,mr4 ,smith's value and the correctness of the accepted ratio4 ,even a still later instance is found in a writer who1 in #ahib1 contended in the ,new ,york ,tribune for #c4b instead of #c4adaf1 as the value of the ratio4 ,he announces it as the re-discovery of a long lost secret1 which consists in the knowledge of a certain line called the ,nicomedean line4 ,this announcement gave rise to considerable discussion1 and even towards the dawn of the twentieth century #c4b had its advocates as against the accepted ratio #c4adaf4 ,verily the slaves of the mighty wizard1 ,michael ,scott1 have not yet ceased from their labors6 ,,footnotes3 #a ,what follows is an exceedingly forcible illustration of an important mathematical truth1 but at the same time it may be worth noting that the size of the blood-globules or corpuscles has no relation to the size of the animal from which they are taken4 ,the blood corpuscle of the tiny mouse is larger than that of the huge ox4 ,the smallest blood corpuscle known is that of a species of small deer1 and the largest is that of a lizard like reptile found in our southern waters--the amphiuma4 ,these facts do not at all affect the force or value of ,de ,morgan's mathematical illustration1 but ,i have thought it well to call the attention of the reader to this point1 lest he should receive an erroneous physiological idea4 ,,ii ,,the ,,duplication ,,of ,,the ,,cube ,this problem became famous because of the halo of mythological romance with which it was surrounded4 ,the story is as follows3 ,about the year #dcj ,b4,c4 the ,athenians were afflicted by a terrible plague1 and as no ordinary means seemed to assuage its virulence1 they sent a deputation of the citizens to consult the oracle of ,apollo at ,delos1 in the hope that the god might show them how to get rid of it4 ,the answer was that the plague would cease when they had doubled the size of the altar of ,apollo in the temple at ,athens4 ,this seemed quite an easy task2 the altar was a cube1 and they placed beside it another cube of exactly the same size4 ,but this did not satisfy the conditions prescribed by the oracle1 and the people were told that the altar must consist of one cube1 the size of which must be exactly twice the size of the original altar4 ,they then constructed a cubic altar of which the side or edge was twice that of the original1 but they were told that the new altar was eight times and not twice the size of the original1 and the god was so enraged that the plague became worse than before4 ,according to another legend1 the reason given for the affliction was that the people had devoted themselves to pleasure and to sensual enjoyments and pursuits1 and had neglected the study of philosophy1 of which geometry is one of the higher departments--certainly a very sound reason1 whatever we may think of the details of the story4 ,the people then applied to the mathematicians1 and it is supposed that their solution was sufficiently near the truth to satisfy ,apollo1 who relented1 and the plague disappeared4 ,in other words1 the leading citizens probably applied themselves to the study of sewerage and hygienic conditions1 and ,apollo 7the ,sun7 instead of causing disease by the festering corruption of the usual filth of cities1 especially in the ,east1 dried up the superfluous moisture1 and promoted the health of the inhabitants4 ,it is well known that the relation of the area and the cubical contents of any figure to the linear dimensions of that figure are not so generally understood as we should expect in these days when the schoolmaster is supposed to be abroad in the land4 ,at an examination of candidates for the position of fireman in one of our cities1 several of the applicants made the mistake of supposing that a two-inch pipe and a five-inch pipe were equal to a seven-inch pipe1 whereas the combined capacities of the two small pipes are to the capacity of the large one as #bi to #di4 ,this reminds us of a story which ,sir ,frederick ,bramwell1 the engineer1 used to tell of a water company using water from a stream flowing through a pipe of a certain diameter4 ,the company required more water1 and after certain negotiations with the owner of the stream1 offered double the sum if they were allowed a supply through a pipe of double the diameter of the one then in use4 ,this was accepted by the owner1 who evidently was not aware of the fact that a pipe of double the diameter would carry four times the supply4 ,a square whose side is twice the length of another1 and a circle whose diameter is twice that of another will each have an area four times that of the original4 ,and in the case of solids3 ,a ball of twice the diameter will weigh eight times as much as the original1 and a ball of three times the diameter will weigh twenty-seven times as much as the original4 ,in attempting to calculate the side of a cube which shall have twice the volume of a given cube1 we meet the old difficulty of incommensurability1 and the solution cannot be effected geometrically1 as it requires the construction of two mean proportionals between two given lines4 ,,iii ,,the ,,trisection ,,of ,,an ,,angle ,this problem is not so generally known as that of squaring the circle1 and consequently it has not received so much attention from amateur mathematicians1 though even within little more than a year a small book1 in which an attempted solution is given1 has been published4 ,when it is first presented to an uneducated reader1 whose mind has a mathematical turn1 and especially to a skilful mechanic1 who has not studied theoretical geometry1 it is apt to create a smile1 because at first sight most persons are impressed with an idea of its simplicity1 and the ease with which it may be solved4 ,and this is true1 even of many persons who have had a fair general education4 ,those who have studied only what is known as practical geometry think at once of the ease and accuracy with which a right angle1 for example1 may be divided into three equal parts4 ,thus taking the right angle ,,acb1 ,fig4 #d1 which may be set off more easily and accurately than any other angle except1 perhaps1 that of #fj deg41 and knowing that it contains #ij deg41 describe an arc ,,adeb1 with ,c for the center and any convenient radius4 ,now every school-boy who has played with a pair of compasses knows that the radius of a circle will step round the circumference exactly six times2 it will therefore divide the #cfj deg4 into six equal parts of #fj deg4 each4 ,this being the case1 with the radius ,,cb1 and ,b for a center1 describe a short arc crossing the arc ,,adeb in ,d1 and join ,,cd4 ,the angle ,,dcb will be #fj deg41 and as the angle ,,acb is #ij deg41 the angle ,,acd must be #cj deg41 or one-third part of the whole4 ,in the same way lay off the angle ,,ace of #fj deg41 and ,,ecb must be #cj deg41 and the remainder ,,dce must also be #cj deg44 ,the angle ,,acb is therefore easily divided into three equal parts1 or in other words1 it is trisected4 ,and with a slight modification of the method1 the same may be done with an angle of #de deg41 and with some others4 ,these however are only special cases1 and the very essence of a geometrical solution of any problem is that it shall be applicable to all cases so that we require a method by which any angle may be divided into three equal parts by a pure ,euclidean construction4 ,the ablest mathematicians declare that the problem cannot be solved by such means1 and ,de ,morgan gives the following reasons for this conclusion3 ,the trisector of an angle1 if he demand attention from any mathematician1 is bound to produce 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 the 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 it 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 ,illustration3 ,fig4 #d4 ,de ,morgan gives an account of a terrific construction by a friend of ,dr4 ,wallich1 which he says is so nearly true1 that unless the angle be very obtuse1 common drawing1 applied to the construction1 will not detect the error4 ,but geometry requires absolute accuracy1 not a mere approximation4 ,,iv ,,perpetual ,,motion ,it is probable that more time1 effort1 and money have been wasted in the search for a perpetual-motion machine than have been devoted to attempts to square the circle or even to find the philosopher's stone4 ,and while it has been claimed in favor of this delusion that the pursuit of it has given rise to valuable discoveries in mechanics and physics1 some even going so far as to urge that we owe the discovery of the great law of the conservation of energy to the suggestions made by the perpetual-motion seekers1 we certainly have no evidence to show anything of the kind4 ,perpetual motion was declared to be an impossibility upon purely mechanical and mathematical grounds long before the law of the conservation of energy was thought of1 and it is very certain that this delusion had no place in the thoughts of ,rumford1 ,black1 ,davy1 ,young1 ,joule1 ,grove1 and others when they devoted their attention to the laws governing the transformation of energy4 ,those who pursued such a will-o'-the-wisp1 were not the men to point the way to any scientific discovery4 ,the search for a perpetual-motion machine seems to be of comparatively modern origin2 we have no record of the labors of ancient inventors in this direction1 but this may be as much because the records have been lost1 as because attempts were never made4 ,the works of a mechanical inventor rarely attracted much attention in ancient times1 while the mathematical problems were regarded as amongst the highest branches of philosophy1 and the search for the philosopher's stone and the elixir of life appealed alike to priest and layman4 ,we have records of attempts made #djjj years ago to square the circle1 and the history of the philosopher's stone is lost in the mists of antiquity2 but it is not until the eleventh or twelfth century that we find any reference to perpetual motion1 and it was not until the close of the sixteenth and the beginning of the seventeenth century that this problem found a prominent place in the writings of the day4 ,by perpetual motion is meant a machine which1 without assistance from any external source except gravity1 shall continue to go on moving until the parts of which it is made are worn out4 ,some insist that in order to be properly entitled to the name of a perpetual-motion machine1 it must evolve more power than that which is merely required to run it1 and it is true that almost all those who have attempted to solve this problem have avowed this to be their object1 many going so far as to claim for their contrivances the ability to supply unlimited power at no cost whatever1 except the interest on a small investment1 and the trifling amount of oil required for lubrication4 ,but it is evident that a machine which would of itself maintain a regular and constant motion would be of great value1 even if it did nothing more than move itself4 ,and this seems to have been the idea upon which those men worked1 who had in view the supposed reward offered for such an invention as a means for finding the longitude4 ,and it is well known that it was the hope of attaining such a reward that spurred on very many of those who devoted their time and substance to the subject4 ,there are several legitimate and successful methods of obtaining a practically perpetual motion1 provided we are allowed to call to our aid some one of the various natural sources of power4 ,for example1 there are numerous mountain streams which have never been known to fail1 and which by means of the simplest kind of a water-wheel would give constant motion to any light machinery4 ,even the wind1 the emblem of fickleness and inconstancy1 may be harnessed so that it will furnish power1 and it does not require very much mechanical ingenuity to provide means whereby the surplus power of a strong gale may be stored up and kept in reserve for a time of calm4 ,indeed this has frequently been done by the raising of weights1 the winding up of springs1 the pumping of water into storage reservoirs and other simple contrivances4 ,the variations which are constantly occurring in the temperature and the pressure of the atmosphere have also been forced into this service4 ,a clock which required no winding was exhibited in ,london towards the latter part of the eighteenth century4 ,it was called a perpetual motion1 and the working power was derived from variations in the quantity1 and consequently in the weight of the mercury1 which was forced up into a glass tube closed at the upper end and having the lower end immersed in a cistern of mercury after the manner of a barometer4 ,it was fully described by ,james ,ferguson1 whose lectures on ,mechanics and ,natural ,philosophy were edited by ,sir ,david ,brewster4 ,it ran for years without requiring winding1 and is said to have kept very good time4 ,a similar contrivance was employed in a clock which was possessed by the ,academy of ,painting at ,paris4 ,it is described in ,ozanam's work1 ,vol4 ,,ii1 page #aje1 of the edition of #ahjc4 ,the changes which are constantly taking place in the temperature of all bodies1 and the expansion and contraction which these variations produce1 afford a very efficient power for clocks and small machines4 ,professor ,w4 ,w4 ,r4 ,ball tells us that there was at ,paris in the latter half of last century a clock which was an ingenious illustration of such perpetual motion4 ,the energy1 which was stored up in it to maintain the motion of the pendulum1 was provided by the expansion of a silver rod4 ,this expansion was caused by the daily rise of temperature1 and by means of a train of levers it wound up the clock4 ,there was a disconnecting apparatus1 so that the contraction due to a fall of temperature produced no effect1 and there was a similar arrangement to prevent overwinding4 ,i believe that a rise of eight or nine degrees ,fahrenheit was sufficient to wind up the clock for twenty-four hours4 ,another indirect method of winding a watch is thus described by ,professor ,ball3 ,i have in my possession a watch1 known as the ,lohr patent1 which produces the same effect by somewhat different means4 ,inside the case is a steel weight1 and if the watch is carried in a pocket this weight rises and falls at every step one takes1 somewhat after the manner of a pedometer4 ,the weight is moved up by the action of the person who has it in his pocket1 and in falling the weight winds up the spring of the watch4 ,on the face is a small dial showing the number of hours for which the watch is wound up4 ,as soon as the hand of this dial points to fifty-six hours1 the train of levers which wind up the watch disconnects automatically1 so as to prevent overwinding the spring1 and it reconnects again as soon as the watch has run down eight hours4 ,the watch is an excellent time-keeper1 and a walk of about a couple of miles is sufficient to wind it up for twenty-four hours4 ,dr4 ,hooper1 in his ,rational ,recreations1 has described a method of driving a clock by the motion of the tides1 and it would not be difficult to contrive a very simple arrangement which would obtain from that source much more power than is required for that purpose4 ,indeed the probability is that many persons now living will see the time when all our railroads1 factories1 and lighting plants will be operated by the tides of the ocean4 ,it is only a question of return for capital1 and it is well known that that has been falling steadily for years4 ,when the interest on investments falls to a point sufficiently low1 the tides will be harnessed and the greater part of the heat1 light1 and power that we require will be obtained from the immense amount of energy that now goes to waste along our coasts4 ,another contrivance by which a seemingly perpetual motion may be obtained is the dry pile or column of ,de ,luc4 ,the pile consists of a series of disks of gilt and silvered paper placed back to back and alternating1 all the gilt sides facing one way and all the silver sides the other4 ,the so-called gilding is really ,dutch metal or copper1 and the silver is tin or zinc1 so that the two actually form a voltaic couple4 ,sometimes the paper is slightly moistened with a weak solution of molasses to insure a certain degree of dampness2 this increases the action1 for if the paper be artificially dried and kept in a perfectly dry atmosphere1 the apparatus will not work4 ,a pair of these piles1 each containing two or three thousand disks the size of a quarter of a dollar1 may be arranged side by side1 vertically1 and two or three inches apart4 ,at the lower ends they are connected by a brass plate1 and the upper ends are each surmounted by a small metal bell and between these bells a gilt ball1 suspended by a silk thread1 keeps vibrating perpetually4 ,many years ago ,i made a pair of these columns which kept a ball in motion for nearly two years1 and ,professor ,silliman tells us that a set of these bells rang in ,yale ,college laboratory for six or eight years unceasingly4 ,how much longer the columns would have continued to furnish energy sufficient to cause the balls to vibrate1 it might be difficult to determine4 ,the amount of energy required is exceedingly small1 but since the columns are really nothing but a voltaic pile1 it is very evident that after a time they would become exhausted4 ,such a pair of columns1 covered with a tall glass shade1 form a very interesting piece of bric-a-brac1 especially if the bells have a sweet tone1 but the contrivance is of no practical use except as embodied in ,bohnenberger's electroscope4 ,inventions of this kind might be multiplied indefinitely1 but none of these devices can be called a perpetual motion because they all depend for their action upon energy derived from external sources other than gravity4 ,but the authors of these inventions are not to be classed with the regular perpetual-motion-mongers4 ,the purposes for which these arrangements were invented were legitimate1 and the contrivances answered fully the ends for which they were intended4 ,the real perpetual-motion-seekers are men of a different stamp1 and their schemes readily fall into one of these three classes3 #a4 ,,absurdities1 #b4 ,,fallacies1 #c4 ,,frauds4 ,the following is a description of the most characteristic machines and apparatus of which accounts have been published4 #a4 ,,absurdities ,in this class may be included those inventions which have been made or suggested by honest but ignorant persons in direct violation of the fundamental principles of mechanics and physics4 ,such inventions if presented to any expert mechanic or student of science1 would be at once condemned as impracticable1 but as a general rule1 the inventors of these absurd contrivances have been so confident of success1 that they have published descriptions and sketches of them1 and even gone so far as to take out patents before they have tested their inventions by constructing a working machine4 ,it is said1 that at one time the ,united ,states ,patent ,office issued a circular refusal to all applicants for patents of this kind1 but at present instead of sending such a circular1 the applicant is quietly requested to furnish a working model of his invention and that usually ends the matter4 ,while ,i have no direct information on the subject1 ,i suspect that the circular was withdrawn because of the amount of useless correspondence1 in the shape of foolish replies and arguments1 which it drew forth4 ,to require a working model is a reasonable request and one for which the law duly provides1 and when a successful model is forthcoming1 a patent will no doubt be granted2 but until that is presented the officials of the ,patent ,office can have no positive information in regard to the practicability of the invention4 ,the earliest mechanical device intended to produce perpetual motion is that known as the overbalancing wheel4 ,this is described in a sketch book of the thirteenth century by ,wilars de ,honecourt1 an architect of the period1 and since then it has been re-invented hundreds of times4 ,in its simplest forms it is thus described and figured by ,ozanam3 ,fig4 #e represents a large wheel1 the circumference of which is furnished1 at equal distances1 with levers1 each bearing at its extremity a weight1 and movable on a hinge so that in one direction they can rest upon the circumference1 while on the opposite side1 being carried away by the weight at the extremity1 they are obliged to arrange themselves in the direction of the radius continued4 ,this being supposed1 it is evident that when the wheel turns in the direction ,,abc1 the weights ,a1 ,b1 and ,c will recede from the center2 consequently1 as they act with more force1 they will carry the wheel towards that side2 and as a new lever will be thrown out1 in proportion as the wheel revolves1 it thence follows1 say they1 that the wheel will continue to move in the same direction4 ,but notwithstanding the specious appearance of this reasoning1 experience has proved that the machine will not go2 and it may indeed be demonstrated that there is a certain position in which the center of gravity of all these weights is in the vertical plane passing through the point of suspension1 and that therefore it must stop4 ,illustration3 ,fig4 #e4 ,illustration3 ,fig4 #f4 ,another invention of a similar kind is thus described by the same author3 ,in a cylindric drum1 in perfect equilibrium on its axis1 are formed channels as seen in ,fig4 #f1 which contain balls of lead or a certain quantity of quicksilver4 ,in consequence of this disposition1 the balls or quicksilver must1 on the one side1 ascend by approaching the center1 and on the other must roll towards the circumference4 ,the machine ought1 therefore1 to turn incessantly towards that side4 ,in his ,course of ,lectures on ,natural ,philosophy1 ,dr4 ,thomas ,young speaks of these contrivances as follows3 ,one of the most common fallacies1 by which the superficial projectors of machines for obtaining perpetual motion have been deluded1 has arisen from imagining that any number of weights ascending by a certain path1 on one side of the center of motion and descending on the other at a greater distance1 must cause a constant preponderance on the side of the descent3 for this purpose the weights have either been fixed on hinges1 which allow them to fall over at a certain point1 so as to become more distant from the center1 or made to slide or roll along grooves or planes which lead them to a more remote part of the wheel1 from whence they return as they ascend2 but it will appear on the inspection of such a machine1 that although some of the weights are more distant from the center than others1 yet there is always a proportionately smaller number of them on that side on which they have the greatest power1 so that these circumstances precisely counterbalance each other4 ,illustration3 ,fig4 #g4 ,he then gives the illustration 7,fig4 #g71 shown on the preceding page1 of a wheel supposed to be capable of producing a perpetual motion2 the descending balls acting at a greater distance from the center1 but being fewer in number than the ascending4 ,in the model1 the balls may be kept in their places by a plate of glass covering the wheel4 ,illustration3 ,fig4 #h4 ,a more elaborate arrangement embodying the same idea is figured and described by ,ozanam4 ,the machine1 which is shown in ,fig4 #h1 consists of a kind of wheel formed of six or eight arms1 proceeding from a center where the axis of motion is placed4 ,each of these arms is furnished with a receptacle in the form of a pair of bellows3 but those on the opposite arms stand in contrary directions1 as seen in the figure4 ,the movable top of each receptacle has affixed to it a weight1 which shuts it in one situation and opens it in the other4 ,in the last place1 the bellows of the opposite arms have a communication by means of a canal1 and one of them is filled with quicksilver4 ,these things being supposed1 it is visible that the bellows on the one side must open1 and those on the other must shut2 consequently1 the mercury will pass from the latter into the former1 while the contrary will be the case on the opposite side4 ,ozanam naively adds3 ,it might be difficult to point out the deficiency of this reasoning2 but those acquainted with the true principles of mechanics will not hesitate to bet a hundred to one1 that the machine1 when constructed1 will not answer the intended purpose4 ,that this bet would have been a perfectly safe one must be quite evident to any person who has the slightest knowledge of practical mechanics1 and yet the fundamental idea which is embodied in this and the other examples which we have just given1 forms the basis of almost all the attempts which have been made to produce a perpetual motion by purely mechanical means4 ,the hydrostatic paradox by which a few ounces of liquid may apparently balance many pounds1 or even tons1 has frequently suggested a form of apparatus designed to secure a perpetual motion4 ,dr4 ,arnott1 in his ,elements of ,physics1 relates the following anecdote3 ,a projector thought that the vessel of his contrivance1 represented here 7,fig4 #i71 was to solve the renowned problem of the perpetual motion4 ,it was goblet-shaped1 lessening gradually towards the bottom until it became a tube1 bent upwards at c and pointing with an open extremity into the goblet again4 ,he reasoned thus3 ,a pint of water in the goblet a must more than counterbalance an ounce which the tube b will contain1 and must1 therefore1 be constantly pushing the ounce forward into the vessel again at a1 and keeping up a stream or circulation1 which will cease only when the water dries up4 ,he was confounded when a trial showed him the same level in a and in b4 ,illustration3 ,fig4 #i4 ,this suggestion has been adopted over and over again by sanguine inventors4 ,dircks1 in his ,perpetuum ,mobile1 tells us that a contrivance1 on precisely the same principle1 was proposed by the ,abbe de la ,roque1 in ,le ,journal des ,scavans1 ,paris1 #afhf4 ,the instrument was a ,u tube1 one leg longer than the other and bent over1 so that any liquid might drop into the top end of the short leg1 which he proposed to be made of wax1 and the long one of iron4 ,presuming the liquid to be more condensed in the metal than the wax tube1 it would flow from the end into the wax tube and so continue4 ,this is a typical case4 ,a man of learning and of high position is so confident that his theory is right that he does not think it worth while to test it experimentally1 but rushes into print and immortalizes himself as the author of a blunder4 ,it is safe to say that this absurd invention will do more to perpetuate his name than all his learning and real achievements4 ,and there are others in the same predicament--circle-squarers who1 a quarter of a century hence1 will be remembered for their errors when all else connected with them will be forgotten4 ,to every miller whose mill ceased working for want of water1 the idea has no doubt occurred that if he could only pump the water back again and use it a second or a third time he might be independent of dry or wet seasons4 ,of course no practical miller was ever so far deluded as to attempt to put such a suggestion into practice1 but innumerable machines of this kind1 and of the most crude arrangement1 have been sketched and described in magazines and papers4 ,figures of wheels driving an ordinary pump1 which returns to an elevated reservoir the water which has driven the wheel1 are so common that it is not worth while to reproduce any of them4 ,in the following attempt1 however1 which is copied from ,bishop ,wilkins' famous book1 ,mathematical ,magic 7#afdh71 the well-known ,archimedean screw is employed instead of a pump1 and the naivete of the good bishop's description and conclusion are well worth the space they will occupy4 ,after an elaborate description of the screw1 he says3 ,these things1 considered together1 it will hence appear how a perpetual motion may seem easily contrivable4 ,for1 if there were but such a water-wheel made on this instrument1 upon which the stream that is carried up may fall in its descent1 it would turn the screw round1 and by that means convey as much water up as is required to move it2 so that the motion must needs be continual since the same weight which in its fall does turn the wheel1 is1 by the turning of the wheel1 carried up again4 ,or1 if the water1 falling upon one wheel1 would not be forcible enough for this effect1 why then there might be two1 or three1 or more1 according as the length and elevation of the instrument will admit2 by which means the weight of it may be so multiplied in the fall that it shall be equivalent to twice or thrice that quantity of water which ascends2 as may be more plainly discerned by the following diagram 7,fig4 #aj73 ,where the figure ,,lm at the bottom does represent a wooden cylinder with helical cavities cut in it1 which at ,,ab is supposed to be covered over with tin plates1 and three waterwheels1 upon it1 ,,hik2 the lower cistern1 which contains the water1 being ,,cd4 ,now1 this cylinder being turned round1 all the water which from the cistern ascends through it1 will fall into the vessel at ,e1 and from that vessel being conveyed upon the water-wheel ,h1 shall consequently give a circular motion to the whole screw4 ,or1 if this alone should be too weak for the turning of it1 then the same water which falls from the wheel ,h1 being received into the other vessel ,f1 may from thence again descend on the wheel ,i1 by which means the force of it will be doubled4 ,and if this be yet insufficient1 then may the water1 which falls on the second wheel ,i1 be received into the other vessel ,g1 and from thence again descend on the third wheel at ,k2 and so for as many other wheels as the instrument is capable of4 ,so that besides the greater distance of these three streams from the center or axis by which they are made so much heavier2 and besides that the fall of this outward water is forcible and violent1 whereas the ascent of that within is natural--besides all this1 there is twice as much water to turn the screw as is carried up by it4 ,illustration3 ,fig4 #aj4 ,but1 on the other side1 if all the water falling upon one wheel would be able to turn it round1 then half of it would serve with two wheels1 and the rest may be so disposed of in the fall as to serve unto some other useful1 delightful ends4 ,when ,i first thought of this invention1 ,i could scarce forbear1 with ,archimedes1 to cry out ',eureka6 ,eureka6' it seeming so infallible a way for the effecting of a perpetual motion that nothing could be so much as probably objected against it2 but1 upon trial and experience1 ,i find it altogether insufficient for any such purpose1 and that for these two reasons3 #a4 ,the water that ascends will not make any considerable stream in the fall4 #b4 ,this stream1 though multiplied1 will not be of force enough to turn about the screw4 ,how well it would have been for many of those inventors1 who supposed that they had discovered a successful perpetual motion1 if they had only given their contrivances a fair and unprejudiced test as did the good old bishop6 ,a modification of this device1 in which mercury is used instead of water1 is thus described by a correspondent of ,the ,mechanic's ,magazine4 7,london47 ,in ,fig4 #aa1 ,a is the screw turning on its two pivots ,,gg2 ,b is a cistern to be filled above the level of the lower aperture of the screw with mercury1 which ,i conceive to be preferable to water on many accounts1 and principally because it does not adhere or evaporate like water2 ,c is a reservoir1 which1 when the screw is turned round1 receives the mercury which falls from the top2 there is a pipe1 which1 by the force of gravity1 conveys the mercury from the reservoir ,c on to 7what for want of a better term may be called7 the float-board ,e1 fixed at right angles to the center axis of the screw1 and furnished at its circumference with ridges or floats to intercept the mercury1 the moment and weight of which will cause the float-board and screw to revolve1 until1 by the proper inclination of the floats1 the mercury falls into the receiver ,f1 from whence it again falls by its spout into the cistern ,g1 where the constant revolution of the screw takes it up again as before4 ,he then suggests some difficulties which the ball1 seen just under the letter ,e1 is intended to overcome1 but he confesses that he has never tried it1 and to any practical mechanic it is very obvious that the machine will not work4 ,but we give the description in the language of the inventor1 as a fair type of this class of perpetual-motion machines4 ,illustration3 ,fig4 #aa4 ,in the year #agij a ,doctor ,schweirs took out a patent for a machine in which small metal balls were used instead of a liquid1 and they were raised by a sort of chain pump which delivered them upon the circumference of a large wheel1 which was thus caused to revolve4 ,it was claimed for this invention that it kept going for some months1 but any mechanic who will examine the ,doctor's drawing must see that it could not have continued in motion after the initial impulse had been expended4 ,that property of liquids known as capillary attraction has been frequently called to the aid of perpetual-motion seekers1 and the fact that although water will1 in capillary tubes and sponges1 rise several inches above the general level1 it will not overflow1 has been a startling surprise to the would-be inventors4 ,perhaps the most notable instance of a mistake of this kind occurred in the case of the famous ,sir ,william ,congreve1 the inventor of the military rockets that bore his name1 and the author of certain improvements in matches which were called after him4 ,it was thus described and figured in an article which appeared in the ,atlas 7,london7 and was copied into ,the ,mechanic's ,magazine 7,london7 for #ahbg3 ,the celebrated ,boyle entertained an idea that perpetual motion might be obtained by means of capillary attraction2 and1 indeed1 there seems but little doubt that nature has employed this force in many instances to produce this effect4 ,there are many situations in which there is every reason to believe that the sources of springs on the tops and sides of mountains depend on the accumulation of water created at certain elevations by the operation of capillary attraction1 acting in large masses of porous material1 or through laminated substances4 ,these masses being saturated1 in process of time become the sources of springs and the heads of rivers2 and thus by an endless round of ascending and descending waters1 form1 on the great scale of nature1 an incessant cause of perpetual motion1 in the purest acceptance of the term1 and precisely on the principle that was contemplated by ,boyle4 ,it is probable1 however1 that any imitation of this process on the limited scale practicable by human art would not be of sufficient magnitude to be effective4 ,nature1 by the immensity of her operations1 is able to allow for a slowness of process which would baffle the attempts of man in any direct and simple imitation of her works4 ,working1 therefore1 upon the same causes1 he finds himself obliged to take a more complicated mode to produce the same effect4 ,to amuse the hours of a long confinement from illness1 ,sir ,william ,congreve has recently contrived a scheme of perpetual motion1 founded on this principle of capillary attraction1 which1 it is apprehended1 will not be subject to the general refutation applicable to those plans in which the power is supposed to be derived from gravity only4 ,sir ,william's perpetual motion is as follows3 ,illustration3 ,fig4 #ab4 ,let ,,abc1 ,fig4 #ab1 be three horizontal rollers fixed in a frame2 aaa1 etc41 is an endless band of sponge1 running round these rollers2 and bbb1 etc41 is an endless chain of weights1 surrounding the band of sponge1 and attached to it1 so that they must move together2 every part of this band and chain being so accurately uniform in weight that the perpendicular side ,,ab will1 in all positions of the band and chain1 be in equilibrium with the hypothenuse ,,ac1 on the principle of the inclined plane4 ,now1 if the frame in which these rollers are fixed be placed in a cistern of water1 having its lower part immersed therein1 so that the water's edge cuts the upper part of the rollers ,,bc1 then1 if the weight and quantity of the endless chain be duly proportioned to the thickness and breadth of the band of sponge1 the band and chain will1 on the water in the cistern being brought to the proper level1 begin to move round the rollers in the direction ,,ab1 by the force of capillary attraction1 and will continue so to move4 ,the process is as follows3 ,on the side ,,ab of the triangle1 the weights bbb1 etc41 hanging perpendicularly alongside the band of sponge1 the band is not compressed by them1 and its pores being left open1 the water at the point x1 at which the band meets its surface1 will rise to a certain height y1 above its level1 and thereby create a load1 which load will not exist on the ascending side ,,ca1 because on this side the chain of weights compresses the band at the water's edge1 and squeezes out any water that may have previously accumulated in it2 so that the band rises in a dry state1 the weight of the chain having been so proportioned to the breadth and thickness of the band as to be sufficient to produce this effect4 ,the load1 therefore1 on the descending side ,,ab1 not being opposed by any similar load on the ascending side1 and the equilibrium of the other parts not being disturbed by the alternate expansion and compression of the sponge1 the band will begin to move in the direction ,,ab2 and as it moves downwards1 the accumulation of water will continue to rise1 and thereby carry on a constant motion1 provided the load at xy be sufficient to overcome the friction on the rollers ,,abc4 ,now to ascertain the quantity of this load in any particular machine1 it must be stated that it is found by experiment that the water will rise in a fine sponge about an inch above its level2 if1 therefore1 the band and sponge be one foot thick and six feet broad1 the area of its horizontal section in contact with the water would be #hfd square inches1 and the weight of the accumulation of water raised by the capillary attraction being one inch rise upon #hfd square inches1 would be #cj lb41 which1 it is conceived1 would be much more than equivalent to the friction of the rollers4 ,the article1 inspired no doubt by ,sir ,william1 then goes on to give elaborate reasons for the success of the device1 but all these are met by the damning fact that the machine never worked4 ,some time afterwards ,sir ,william1 at considerable expense1 published a pamphlet in which he explained and defended his views4 ,if he had only had a working model made and the thing had continued in motion for a few hours1 he would have silenced all objectors far more quickly and forcibly than he ever could have done by any amount of argument4 ,and in his case there could have been no excuse for his not making a small machine after the plans that he published and even patented4 ,he was wealthy and could have commanded the services of the best mechanics in ,london1 but no working model was ever made4 ,many inventors of perpetual-motion machines offer their poverty as an excuse for not making a model or working machine4 ,thus ,dircks1 in his ,perpetuum ,mobile gives an account of a mechanic1 a model maker1 who had a neat brass model of a time-piece1 in which were two steel balls ,a and ,b2--,b to fall into a semicircular gallery ,c1 and be carried to the end ,d of a straight trough ,,de2 while ,a in its turn rolls to ,e1 and so on continuously2 only the gallery ,c not being screwed in its place1 we are desired to take the will for the deed1 until twenty shillings be raised to complete this part of the work6 ,and ,mr4 ,dircks also quotes from the ,builder of ,june1 #ahdg3 ,this vain delusion1 if not still in force1 is at least as standing a fallacy as ever4 ,joseph ,hutt1 a frame-work knitter1 in the neighborhood of the enlightened town of ,hinckley1 professes to have discovered it perpetual motion and only wants twenty pounds1 as usual1 to set it agoing4 ,the following rather curious arrangement was described in ,the ,mechanic's ,magazine for #ahbe4 ,i beg leave to offer the prefixed device4 ,the point at which1 like all the rest1 it fails1 ,i confess ,i did not 7as ,i do now7 plainly perceive at once1 although it is certainly very obvious4 ,the original idea was this--to enable a body which would float in a heavy medium and sink in a lighter one1 to pass successively through the one to the other1 the continuation of which would be the end in view4 ,to say that valves cannot be made to act as proposed will not be to show the rationale 7if ,i may so say7 upon which the idea is fallacious4 ,the figure is supposed to be tubular1 and made of glass1 for the purpose of seeing the action of the balls inside1 which float or fall as they travel from air through water and from water through air4 ,the foot is supposed to be placed in water1 but it would answer the same purpose if the bottom were closed4 ,,description ,,of ,,the ,,engraving1 ,,fig4 #ac4 ,no4 #a1 the left leg1 filled with water from ,b to ,a4 #b and #c1 valves1 having in their centers very small projecting valves2 they all open upwards4 #d1 the right leg1 containing air from ,a to ,f4 #e and #f1 valves1 having very small ones in their centers2 they all open downwards4 ,the whole apparatus is supposed to be air and water-tight4 ,the round figures represent hollow balls1 which will sink one-fourth of their bulk in water 7of course will fall in air72 the weight therefore of three balls resting upon one ball in water1 as at ,e1 will just bring its top even with the water's edge2 the weight of four balls will sink it under the surface until the ball immediately over it is one-fourth its bulk in water1 when the under ball will escape round the corner at ,c1 and begin to ascend4 ,the machine is supposed 7in the figure7 to be in action1 and ,no4 #h 7one of the balls7 to have just escaped round the corner at ,c1 and to be1 by its buoyancy1 rising up to valve ,no4 #c1 striking first the small projecting valve in the center1 which when opened1 the large one will be raised by the buoyancy of the ball2 because the moment the small valve in the center is opened 7although only the size of a pin's head71 ,no4 #b valve will have taken upon itself to sustain the whole column of water from ,a to ,b4 ,the said ball 7,no4 #h7 having passed through the valve ,no4 #c1 will1 by appropriate weights or springs1 close2 the ball will proceed upwards to the next valve 7,no4 #b71 and perform the same operation there4 ,having arrived at ,a1 it will float upon the surface three-fourths of its bulk out of water4 ,upon another ball in due course arriving under it1 it will be lifted quite out of the water1 and fall over the point ,d1 pass into the right leg 7containing air71 and fall to valve ,no4 #e1 strike and open the small valve in its center1 then open the large one1 and pass through2 this valve will then1 by appropriate weights or springs1 close2 the ball will roll on through the bent tube 7which is made in that form to gain time as well as to exhibit motion7 to the next valve 7,no4 #f71 where it will perform the same operation1 and then1 falling upon the four balls at ,e1 force the bottom one round the corner at ,c4 ,this ball will proceed as did ,no4 #h1 and the rest in the same manner successively4 ,illustration3 ,fig4 #ac4 ,that an ordinary amateur mechanic should be misled by such arguments is perhaps not so surprising1 when we remember that the famous ,john ,bernoulli claimed to have invented a perpetual motion based on the difference between the specific gravities of two liquids4 ,a translation of the original ,latin may be found in the ,encyclopaedia ,britannica1 ,vol4 ,,xviii1 page #eee4 ,some of the premises on which he depends are1 however1 impossibilities1 and ,professor ,chrystal concludes his notice of the invention thus3 ,one really is at a loss with ,bernoulli's wonderful theory1 whether to admire most the conscientious statement of the hypothesis1 the prim logic of the demonstration--so carefully cut according to the pattern of the ancients--or the weighty superstructure built on so frail a foundation4 ,most of our perpetual motions were clearly the result of too little learning2 surely this one was the product of too much4 ,a more simple device was suggested recently by a correspondent of ,power4 ,he describes it thus3 ,the ,j-shaped tube ,a1 ,fig4 #ad1 is open at both ends1 but tapers at the lower end1 as shown4 ,a well-greased cotton rope ,c passes over the wheel ,b and through the small opening of the tube with practically little or no friction1 and also without leakage4 ,the tube is then filled with water4 ,the rope above the line ,,wx balances over the pulley1 and so does that below the line ,,yz4 ,the rope in the tube between these lines is lifted by the water1 while the rope on the other side of the pulley between these lines is pulled downward by gravity4 ,illustration3 ,fig4 #ad4 ,the inventor offers the above suggestion rather as a kind of puzzle than as a sober attempt to solve the famous problem1 and he concludes by asking why it will not work8 ,in addition to the usual resistance or friction offered by the air to all motion1 there are four drawbacks3 #a4 ,the friction in its bearings of the axle of the wheel ,b4 #b4 ,the power required to bend and unbend the rope4 #c4 ,the friction of the rope in passing through the water from z to x and its tendency to raise a portion of the water above the level of the water at x4 #d4 ,the friction at the point y1 this last being the most serious of all4 ,an opening of the tube with practically little or no friction1 and also without leakage is a mechanical impossibility4 ,in order to have the joint water-tight1 the tube must hug the rope very tightly and this would make friction enough to prevent any motion4 ,and the longer the column of water xz1 the greater will be the tendency to leak1 and consequently the tighter must be the joint and the greater the friction thereby created4 ,a favorite idea with perpetual-motion seekers is the utilization of the force of magnetism4 ,some time prior to the year #aegi1 ,joannes ,taisnierus wrote a book which is now in the ,british ,museum and in which considerable space is devoted to ,continual ,motions and to the solving of this problem by magnetism4 ,bishop ,wilkins in his ,mathematical ,magick describes one of the many devices which have been invented with this end in view4 ,he says3 ,but amongst all these kinds of invention1 that is most likely1 wherein a loadstone is so disposed that it shall draw unto it on a reclined plane a bullet of steel1 which steel as it ascends near to the loadstone1 may be contrived to fall down through some hole in the plane1 and so to return unto the place from whence at first it began to move2 and1 being there1 the loadstone will again attract it upwards till coming to this hole1 it will fall down again2 and so the motion shall be perpetual1 as may be more easily conceivable by this figure 7,fig4 #ae73 ,suppose the loadstone to be represented at ,,ab1 which1 though it have not strength enough to attract the bullet ,c directly from the ground1 yet may do it by the help of the plane ,,ef4 ,now1 when the bullet is come to the top of this plane1 its own gravity 7which is supposed to exceed the strength of the loadstone7 will make it fall into that hole at ,e2 and the force it receives in this fall will carry it with such a violence unto the other end of this arch1 that it will open the passage which is there made for it1 and by its return will again shut it3 so that the bullet 7as at the first7 is in the same place whence it was attracted1 and1 consequently must move perpetually4 ,illustration3 ,fig4 #ae4 ,notwithstanding the positiveness of the must at the close of his description1 it is very obvious to any practical mechanic that the machine will not move at all1 far less move perpetually1 and the bishop himself1 after carefully and conscientiously discussing the objections1 comes to the same conclusion4 ,he ends by saying3 ,so that none of all these magnetical experiments1 which have been as yet discovered1 are sufficient for the effecting of a perpetual motion1 though these kind of qualities seem most conducible unto it1 and perhaps hereafter it may be contrived from them4 ,it has occurred to several would-be inventors of perpetual motion that if some substance could be found which would prevent the passage of the magnetic force1 then by interposing a plate of this material at the proper moment1 between the magnet and the piece of iron to be attracted1 a perpetual motion might be obtained4 ,several inventors have claimed that they had discovered such a non-conducting substance1 but it is needless to say that their claims had no foundation in fact1 and if they had discovered anything of the kind1 it would have required just as much force to interpose it as would have been gained by the interposition4 ,it has been fully proved that in every case where a machine was made to work apparently by the interposition of such a material1 a fraud was perpetrated and the machine was really made to move by means of some concealed springs or weights4 ,a correspondent of the ,mechanic's ,magazine 7,vol4 xii1 ,london1 #ahbi71 gives the following curious design for a ,self-moving ,railway ,carriage4 ,he describes it as a machine which1 were it possible to make its parts hold together unimpaired by rotation or the ravages of time1 and to give it a path encircling the earth1 would assuredly continue to roll along in one undeviating course until time shall be no more4 ,a series of inclined planes are to be erected in such a manner that a cone will ascend one 7its sides forming an acute angle71 and being raised to the summit1 descend on the next 7having parallel sides71 at the foot of which it must rise on a third and fall on a fourth1 and so continue to do alternately throughout4 ,the diagram1 ,fig4 #af1 is the section of a carriage ,a1 with broad conical wheels a1 a1 resting on the inclined plane b4 ,the entrance to the carriage is from above1 and there are ample accommodations for goods and passengers4 ,the most singular property of this contrivance is1 that its speed increases the more it is laden2 and when checked on any part of the road1 it will1 when the cause of stoppage is removed1 proceed on its journey by mere power of gravity4 ,its path may be a circular road formed of the inclined planes4 ,but to avoid a circuitous route1 a double road ought to be made4 ,the carriage not having a retrograde motion on the inclined planes1 a road to set out upon1 and another to return by1 are indispensable4 ,illustration3 ,fig4 #af4 ,how any one could ever imagine that such a contrivance would ever continue in motion for even a short time1 except1 perhaps1 on the famous descensus averni1 must be a puzzle to every sane mechanic4 ,i therefore give it as a climax to the absurdities which have been proposed in sober earnest4 ,as a fitting close1 however1 to this chapter of human folly1 ,i give the following joke from the ,penny ,magazine1 published by the ,society for the ,diffusion of ,useful ,knowledge4 ',father1 ,i have invented a perpetual motion6' said a little fellow of eight years old4 ',it is thus3 ,i would make a great wheel1 and fix it up like a water-wheel2 at the top ,i would hang a great weight1 and at the bottom ,i would hang a number of little weights2 then the great weight would turn the wheel half round and sink to the bottom1 because it is so heavy3 and when the little weights reach the top they would sink down1 because they are so many2 and thus the wheel would turn round for ever4' ,the child's fallacy is a type of all the blunders which are made on this subject4 ,follow a projector in his description1 and if it be not perfectly unintelligible1 which it often is1 it always proves that he expects to find certain of his movements alternately strong and weak--not according to the laws of nature--but according to the wants of his mechanism4 #b4 ,,fallacies ,fallacies are distinguished from absurdities on the one hand and from frauds on the other1 by the fact that without any intentionally fraudulent contrivances on the part of the inventor1 they seem to produce results which have a tendency to afford to certain enthusiasts a basis of hope in the direction of perpetual motion1 although usually not under that name1 for that is always explicitly disclaimed by the promoters4 ,the most notable instance of this class in recent times was the application of liquid air as a source of power1 the claim having been actually made by some of the advocates of this fallacy that a steamship starting from ,new ,york with #ajjj gallons of liquid air1 could not only cross the ,atlantic at full speed but could reach the other side with more than #ajjj gallons of liquid air on board--the power required to drive the vessel and to liquefy the surplus air being all obtained during the passage by utilizing the original quantity of liquid air that had been furnished in the first place4 ,that this was equivalent to perpetual motion1 pure and simple1 was obvious even to those who were least familiar with such subjects1 though the idea of calling it perpetual motion was sternly repudiated by all concerned--the term perpetual motion having become thoroughly offensive to the ears of common-sense people1 and consequently tending to cast doubt over any enterprise to which it might be applied4 ,that liquid air is a real and wonderful discovery1 and that for a certain small range of purposes it will prove highly useful1 cannot be doubted by those who have seen and handled it and are familiar with its properties1 but that it will ever be successfully used as an economical source of mechanical power is1 to say the least1 very improbable4 ,that a small quantity of the liquid is capable of doing an enormous amount of work1 and that under some conditions there is apparently more power developed than was originally required to liquefy the air1 is undoubtedly true1 but when a careful quantitative examination is made of the outgo and the income of energy1 it will be found in this1 as in every similar case1 that instead of a gain there is a very decided and serious loss4 ,the correct explanation of the fallacy was published in the ,scientific ,american1 by the late ,dr4 ,henry ,morton1 president of the ,stevens ,institute1 and the same explanation and exposure were made by the writer1 nearly fifty years ago1 in the case of a very similar enterprise4 ,the form of the fallacy in both cases is so similar and so interesting that ,i shall make no apology for giving the details4 ,about the year #ahec or #ahed1 two ingenious mechanics of ,rochester1 ,n4 ,y41 conceived the idea that by using some liquid more volatile than water1 a great saving might be effected in the cost of running an engine4 ,at that time gasolene and benzine were unknown in commerce1 and the same was true in regard to bisulphide of carbon1 but as the process of manufacturing the latter was simple and the sources of supply were cheap and apparently unlimited1 they adopted that liquid4 ,the name of one of these inventors was ,hughes and that of the other was ,hill1 and it would seem that each had made the invention independently of the other4 ,they had a fierce conflict over the patent1 but this does not concern us except to this extent1 that the records of the case may therefore be found in the archives of the ,patent ,office at ,washington1 ,d4,c4 ,hughes was backed by the wealth of a well-known lawyer of ,rochester1 whose son subsequently occupied a high office in the state of ,new ,york1 and he constructed a beautiful little steam-engine and boiler1 made of the very finest materials and with such skill and accuracy that it gave out a very considerable amount of power in proportion to its size4 ,the source of heat was a series of lamps1 fed1 ,i think1 with lard oil 7this was before the days of kerosene71 and the exhibition test consisted in first filling the boiler with water1 and noting the time that it took to get up a certain steam pressure as shown by the gage4 ,after this test1 bisulphide of carbon was added to the water1 and the time and pressure were noted4 ,the difference was of course remarkable1 and altogether in favor of the new liquid4 ,the exhaust was carried into a vessel of cold water and as bisulphide of carbon is very easily condensed and very heavy1 almost the entire quantity used was recovered and used over and over again4 ,but to the uninstructed onlooker1 the most remarkable part of the exhibition was when the steam pressure was so far lowered that the engine revolved very slowly1 and then1 on a little bisulphide being injected into the boiler1 the pressure would at once rise1 and the engine would work with great rapidity4 ,this seemed almost like magic4 ,the same experiment was tried on an engine of twelve horse-power1 and with a like result4 ,when the steam pressure had fallen so far that the engine began to move quite slowly1 a quantity of the bisulphide would be injected into the boiler and the pressure would at once rise1 the engine would move with renewed vigor1 and the fly-wheel would revolve with startling velocity4 ,all this was seen over and over again by myself and others4 ,at that time the writer1 then quite a young man1 had just recovered from a very severe illness and was making a living by teaching mechanical drawing and making drawings for inventors and others1 and in the course of business he was brought into contact with some parties who thought of investing in the new and apparently wonderful invention4 ,they employed him to examine it and give an opinion as to its value4 ,after careful consideration and as thorough a calculation as the data then at command would allow1 he showed his clients that the tests which had been exhibited to them proved nothing1 and that if a clear proof of the value of the invention was to be given1 it must be after a run of many hours and not of a few minutes1 and against a properly adjusted load1 the amount of which had been carefully ascertained4 ,this test was never made1 or if made the results were not communicated to the prospective purchasers2 the negotiations fell through1 and the invention which was to have revolutionized our mechanical industries fell into innocuous desuetude4 ,that the inventors were honest ,i have no doubt4 ,they were themselves deceived when they saw the engine start off with tremendous velocity as soon as a little bisulphide of carbon was injected into the boiler1 and they failed to see that this spurt1 if ,i may use the expression1 was simply due to a draft upon capital previously stored up4 ,the capacity of bisulphide of carbon for heat is quite low1 when compared with that of water2 its vaporizing point is also much lower and consequently1 an ordinary boiler full of hot water contains enough heat to vaporize a considerable quantity of bisulphide of carbon at a pretty high pressure4 ,in even a still greater measure the same is true of liquid air1 and this was the underlying fallacy in the case of the tests made with liquid-air motors4 #c4 ,,frauds ,but while the inventors of these schemes may have been honest1 there is another class who deliberately set out to perpetrate a fraud4 ,their machines work1 and work well1 but there is always some concealed source of power1 which causes them to move4 ,as a general rule1 such inventors form a company or corporation of unlimited lie-ability1 as ,de ,morgan phrases it1 and then they proceed by means of flaring prospectuses and liberal advertising1 to gather in the dupes who are attracted by their seductive promises of enormous returns for a very small outlay4 ,perhaps the most widely known of these fraudulent schemes of recent years was the notorious ,keeley motor1 the originator of which managed to hoodwink a respectable old lady1 and to draw from her enormous supplies of cash4 ,at his death1 however1 the absolutely fraudulent nature of his contrivances was fully disclosed1 and nothing more has been heard of his alleged discovery4 ,but1 while he lived and was able to put forward claims based upon some apparent results1 he found plenty of fools who accepted the idea that there is nothing impossible to science4 ,it is true that the ,keeley motor was examined by several committees and some very respectable gentlemen acted in such a way as to give a seeming endorsement of the scheme1 but it must not be supposed for an instant that any well-educated engineers and scientific men were deceived by ,mr4 ,keeley's nonsense4 ,the very fact that he refused to allow a complete examination of his machine by intelligent practical men1 ought to have been enough to condemn his scheme1 for if he had really made the discovery which he claimed there would have been no difficulty in proving it practically and thoroughly1 and then he might have formed company after company that would have rewarded him with wealth beyond the dreams of avarice4 ,the ,keeley motor was not put forward as a perpetual motion2 in these days none of these schemes is admitted to be a perpetual motion1 for that term has now become exceedingly offensive and would condemn any invention2 but the result is the same in the end1 and the whole history of perpetual motion is permeated with frauds of this kind1 some of them having been so simple that they were obvious to even the most unskilled observer1 while others were exceedingly complicated and most ingeniously concealed4 ,many years ago a number of these fraudulent perpetual-motion machines were manufactured in ,america and sent over to ,great ,britain for exhibition1 and quite a lucrative business was done by showing them in various towns4 ,but the fraud was soon detected and the ,british police then made it too warm for these swindlers4 ,mr4 ,dircks1 in his ,perpetuum ,mobile1 has given accounts of quite a number of these impostures4 ,the following are some of the most notable3 ,m4 ,poppe of ,tuebingen tells of a clock made by ,m4 ,geiser1 which was an admirable piece of mechanism and seemed to have solved this great problem in an ingenious and simple manner1 but it deceived only for a time4 ,when thoroughly examined inwardly and outwardly1 some time after his death1 it was found that the center props supporting its cylinders contained cleverly constructed1 hidden clock-work1 wound up by inserting a key in a small hole under the second-hand4 ,another case was that of a man named ,adams who exhibited1 for eight or nine days1 his pretended perpetual motion in a town in ,england and took in the natives for fifty or sixty pounds4 ,accident1 however1 led to a discovery of the imposture4 ,a gentleman1 viewing the machine took hold of the wheel or trundle and lifted it up a little1 which probably disengaged the wheels that connected the hidden machinery in the plinth1 and immediately he heard a sound similar to that of a watch when the spring is running down4 ,the owner was in great anger and directly put the wheel into its proper position1 and the machine again went around as before4 ,the circumstance was mentioned to an intelligent person who determined to find out and expose the imposture4 ,he took with him a friend to view the machine and they seated themselves one on each side of the table upon which the machine was placed4 ,they then took hold of the wheel and trundle and lifted them up1 there being some play in the pivots4 ,immediately the hidden spring began to run down and they continued to hold the machine in spite of the endeavors of the owner to prevent them4 ,when the spring had run down1 they placed the machine again on the table and offered the owner fifty pounds if it could then set itself going1 but notwithstanding his fingering and pushing1 it remained motionless4 ,a constable was sent for1 the impostor went before a magistrate and there signed a paper confessing his perpetual motion to be a cheat4 ,in the ,mechanic's ,magazine1 ,vol4 #df1 is an account of a perpetual motion1 constructed by one ,redhoeffer of ,pennsylvania1 which obtained sufficient notoriety to induce the ,legislature to appoint a committee to enquire into its merits4 ,the attention of ,mr4 ,lukens was turned to the subject1 and although the actual moving cause was not discovered1 yet the deception was so ingeniously imitated in a machine of similar appearance made by him and moved by a spring so well concealed1 that the deceiver himself was deceived and ,redhoeffer was induced to believe that ,mr4 ,lukens had been successful in obtaining a moving power in some way in which he himself had failed1 when he had produced a machine so plausible in appearance as to deceive the public4 ,instances of a similar kind might be multiplied indefinitely4 ,the experienced mechanic who reads the descriptions here given of the various devices which have been proposed for the construction of a perpetual-motion machine must be struck with the childish simplicity of the plans which have been offered2 and those who will search the pages of the mechanical journals of the last century or who will examine the two closely printed volumes in which ,mr4 ,dircks has collected almost everything of the kind1 will be astonished at the sameness which prevails amongst the offerings of these would-be inventors4 ,amongst the hundreds1 or1 perhaps1 thousands1 of contrivances which have been described1 there is probably not more than a dozen kinds which differ radically from each other2 the same arrangement having been invented and re-invented over and over again4 ,and one of the strange features of the case is that successive inventors seem to take no note of the failure of those predecessors who have brought forward precisely the same combination of parts under a very slightly different form4 ,it is true that we occasionally find a very elaborate and apparently complicated machine1 but in such cases it will be found1 on close examination1 to owe its apparent complexity to a mere multiplication of parts2 no real inventive ingenuity is exhibited in any case4 ,another singular characteristic of almost all those who have devoted themselves to the search for a perpetual motion is their absolute confidence in the success of the plans which they have brought forth4 ,so confident are they in the soundness of their views and so sure of the success of their schemes that they do not even take the trouble to test their plans but announce them as accomplished facts1 and publish their sketches and descriptions as if the machine was already working without a hitch4 ,indeed1 so far was one inventor carried away with this feeling of confidence in the success of his machine that he no longer allowed himself to be troubled with any doubts as to the machine's going but was greatly puzzled as to what means he should take to stop it after it had been set in motion6 ,these facts1 which are well known to all who have been brought into contact with this class of minds1 explain many otherwise puzzling circumstances and enable us to place a proper value on assertions which1 if not made so positively and by such apparently good authority1 would be at once condemned as deliberate falsehoods4 ,that falsehood1 pure and simple1 has formed the basis of a good many claims of this kind1 there can be no doubt1 but at the same time1 it is probable that some of the claimants really deceived themselves and attributed to causes other than radical errors of theory1 the fact that their machines would not continue to move4 ,while many have claimed the actual invention of a perpetual motion it is very certain that not one has ever succeeded4 ,how1 then1 are we to explain the statements which have been made in regard to ,orffyreus and the claims of the ,marquis of ,worcester8 ,for both of these men it is claimed that they constructed wheels which were capable of moving perpetually and apparently strong testimony is offered in support of these assertions4 ,in the famous ,century of ,inventions1 published by the ,marquis in #affc1 four years before his death1 the celebrated #efth article reads as follows 7verbatim et literatim73 ,to provide and make that all the ,weights of the descending side of a ,wheel shall be perpetually further from the ,centre1 then those of the mounting side1 and yet equal in number and heft to the one side as the other4 ,a most incredible thing1 if not seen1 but tried before the late king 7of blessed memory7 in the ,tower1 by my directions1 two ,extraordinary ,embassadors accompanying ,his ,majesty1 and the ,duke of ,richmond and ,duke ,hamilton1 with most of the ,court1 attending ,him4 ,the ,wheel was #ad4 ,foot over1 and #dj4 ,weights of #ej4 pounds apiece4 ,sir ,william ,balfore1 then ,lieutenant of the ,tower1 can justifie it1 with several others4 ,they all saw1 that no sooner these great ,weights passed the ,diameter-line of the lower side1 but they hung a foot further from the ,centre1 nor no sooner passed the ,diameter-line of the upper side1 but they hung a foot nearer4 ,be pleased to judge the consequence4 ,such is the account given by the ,marquis himself1 and that he exhibited such a wheel at the time and place which he names1 ,i have not the least doubt4 ,and that some of the weights on one side hung a foot further from the center than did weights on the other side is also no doubt true1 but1 as the judging of the consequence is left to ourselves we know that after the first impulse given to it had been expended1 the wheel would simply stand still unless kept in motion by some external force4 ,illustration3 ,fig4 #ag4 ,mr4 ,dircks in his ,life1 ,times and ,scientific ,labours of the ,second ,marquis of ,worcester1 gives an engraving of a wheel which complies with all the conditions laid down by the ,marquis and which is thus described3 ,let the annexed diagram1 ,fig4 #ag1 represent a wheel of #ad feet in diameter1 having #dj spokes1 seven feet each1 and with an inner rim coinciding with the periphery1 at one foot distance all round4 ,next provide #dj balls or weights1 hanging in the center of cords or chains two feet long4 ,now1 fasten one end of this cord at the top of the center spoke ,c1 and the other end of the cord to the next right-hand spoke one foot below the upper end1 or on the inner ring2 proceed in like manner with every other spoke in succession2 and it will be found that1 at ,a1 the cord will have the position shown outside the wheel2 while at ,b1 ,c1 and ,d1 it will also take the respective positions1 as shown on the outside4 ,the result in this case will be1 that all the weights on the side ,a1 ,c1 ,d1 hang to the great or outer circle1 while on the side ,b1 ,c1 ,d1 all the weights are suspended from the lesser or inner circle4 ,and if we reverse the motion of the wheel1 turning it from the right to the left hand1 we shall reverse these positions also 7the lower end of the cord sliding in a groove towards a left-hand spoke71 but without the wheel having any tendency to move of itself4 ,but it is quite as likely that the wheel constructed by the ,marquis was like one of the overbalancing wheels described at the beginning of this article4 ,it is upon this scantling that has been based the claim that the ,marquis really invented a perpetual motion1 but to those who have seen much of inventors of this kind1 the discrepancy between the suggested claim made by the ,marquis and what we know must have been the actual results1 is easily explained4 ,the ,marquis felt sure that the thing ought to work1 and the excuse for its not doing so was probably the imperfect manner in which the wheel was made4 ,only put a little better work on it1 says the inventor1 and it will go4 ,caspar ,kaltoff1 mechanician to the ,marquis1 probably got the wheel up in a hurry so as to exhibit it on the occasion of the king's visit to the tower4 ,if he only had had a little more time he would have made a machine that would have worked4 787 ,i have heard the same excuse under almost the same circumstances1 scores of times4 ,the case of ,orffyreus was very different4 ,the real name of this inventor was ,jean ,ernest ,elie-,bessler1 and he is said to have manufactured the name ,orffyreus by placing his own name between two lines of letters1 and picking out alternate letters above and below4 ,he was educated for the church1 but turned his attention to mechanics and became an expert clock maker4 ,his character1 as given by his contemporaries was fickle1 tricky1 and irascible4 ,having devised a scheme for perpetual motion he constructed several wheels which he claimed to be self-moving4 ,the last one which he made was #ab feet in diameter and #ad inches deep1 the material being light pine boards1 covered with waxed cloth to conceal the mechanism4 ,the axle was #h inches thick1 thus affording abundant space for concealed machinery4 ,this wheel was submitted to the ,landgrave of ,hesse who had it placed in a room which was then locked1 and the lock secured with the ,landgrave's own seal4 ,at the end of forty days it was found to be still running4 ,professor ,gravesande having been employed by the ,landgrave to make an examination and pronounce upon its merits1 he endeavored to perform his work thoroughly2 this so irritated ,orffyreus that the latter broke the machine in pieces1 and left on the wall a writing stating that he had been driven to do this by the impertinent curiosity of the ,professor6 ,i have no doubt that this was a clear case of fraud1 and that the wheel was driven by some mechanism concealed in the huge axle4 ,as already stated1 ,orffyreus was at one time a clock maker2 now clocks have been made to go for a whole year without having to be rewound1 so that forty days was not a very long time for the apparatus to keep in motion4 ,professor ,gravesande seems to have had some faith in the invention1 but then we must remember that it would not have been very difficult to deceive an honest old professor whose confidence in humanity was probably unbounded4 ,the crowning argument against the genuineness of the motion was the fact that the inventor refused to allow a thorough examination1 although a wealthy patron stood ready with a large reward if the machine could be proved to be what was claimed4 ,and now comes up the question which has arisen in regard to other problems1 and will recur again and again to the end of the chapter3 ,is a perpetual motion machine one of the scientific impossibilities8 ,the answer to this question lies in the fact that there is no principle more thoroughly established than that no combination of machinery can create energy4 ,so far as our present knowledge of nature goes we might as well try to create matter as to create energy1 and the creation of energy is essential to the successful working of a perpetual-motion machine because some power must always be lost through friction and other resistances and must be supplied from some source if the machine is to keep on moving4 ,and since the law of the conservation of energy makes it positive that no more power can be given out by a machine than was originally supplied to it1 it seems as certain as anything can be that the construction of a perpetual-motion machine is one of the impossibilities4 ,v ,,transmutation ,,of ,,the ,,metals ,the accursed thirst for gold has existed from the earliest ages and1 as the apostle says1 is the root of all evil4 ,those who have a greed for power1 a craving for luxury1 or a fever for lust1 all think that their wildest dreams might be realized if they could only command sufficient gold4 ,never was there a more lurid picture of a mind inflamed with all these evil passions than that set forth by ,ben ,jonson in the ,second ,act of ,the ,alchemist1 and who can doubt but that such desires and dreams spurred on many1 either to engage in an actual search for the philosopher's stone1 or to become the dupes of what ,van ,helmont calls a diabolical crew of gold and silver sucking flies and leeches4 ,as we might naturally expect1 the early history of alchemy is shrouded in myths and fables4 ,zosimos the ,panopolite tells us that the art of ,alchemy was first taught to mankind by demons1 who fell in love with the daughters of men1 and1 as a reward for their favors1 taught them all the works and mysteries of nature4 ,on this ,boerhaave remarks3 ,this ancient fiction took its rise from a mistaken interpretation of the words of ,moses1 ',that the sons of ,god saw the daughters of men that they were fair1 and they took them wives of all which they chose4'#b ,from whence it was inferred that the sons of ,god were daemons1 consisting of a soul1 and a visible but impalpable body1 like the image in a looking-glass 7to which notion we find several allusions in the evangelists72 that they know all things1 appeared to men and conversed with them1 fell in love with women1 had intrigues with them and revealed secrets4 ,from the same fable probably arose that of the ,sibyl1 who is said to have obtained of ,apollo the gift of prophecy1 and revealing the will of heaven in return for a like favor4 ,so prone is the roving mind of man to figments1 which it can at first idly amuse itself with1 and at length fall down and worship4 ,this idea of the supernatural origin of the arts permeates the ancient mythology which everywhere teaches that men were taught the sacred arts of medicine and chemistry by gods and demigods4 ,modern science discards all these mythological accounts4 ,whatever knowledge the ancients acquired of medicine and chemistry was1 no doubt1 reached along two lines--pharmacy and metallurgy4 ,that the pharmacist or apothecary exercised his calling at a very early period we have positive knowledge2 thus in the ,book of ,ecclesiastes we are told that dead flies cause the ointment of the apothecary to send forth a stinking savor1 and that men at a very early day found out the means of working iron1 copper1 gold1 silver1 etc41 is evident from the accounts given of ,vulcan and ,tubalcain1 as well as from the remains of old tools and weapons4 ,and that ,alchemy1 as it is generally understood1 is a comparatively modern outgrowth of these two arts1 is pretty certain4 ,no mention of the art of converting the baser metals into gold1 and no account of a universal medicine or elixir of life is to be found in any of the authentic writings of the ancients4 ,homer1 ,aristotle1 and even ,pliny are all silent on the subject1 and those writings which treat of the art1 and which claim an ancient origin1 such as the books of ,hermes ,trismegistus1 are now regarded by the best authorities as spurious--the evidence that they were the work of a far later age being irrefragable4 ,several writers have taken the ground that the alchemical treatises which have come down to us from the early writers on the subject1 are purely allegorical and do not relate to material things1 but to the principles of a higher religion which1 in those days1 it was dangerous to expound in plain language4 ,one or two elaborate works and several articles supporting this view have been published1 but the common-sense reader who will glance through the immense collection of alchemical tracts gathered together by ,mangetus in two folio volumes of a thousand pages each1 will rise from such examination1 very thoroughly convinced that it was the actual metal gold1 and the fabled universal medicine that these writers had in view4 ,there can be little doubt that ,geber1 ,roger ,bacon1 ,albertus ,magnus1 ,raymond ,lully1 ,helvetius1 ,van ,helmont1 ,basil ,valentine1 and others1 describe very substantial things with a minuteness of detail which leaves no room for doubt as to their materiality though we cannot always be sure of their identity4 ,some confusion of thought has been caused by the difference which has been made between the terms alchemy and chemistry and their applications4 ,the word alchemy is simply the word chemistry with the ,arabic word al1 which signifies the1 prefixed1 and the history of alchemy is really the history of chemistry--wild and erratic in its beginnings1 and giving rise to strange hopes and still stranger theories1 but ever working along the line of discovery and progress4 ,and1 although many of the professional chemists or alchemists of the middle ages were undoubted charlatans and quacks1 yet did we not have many of the same kind in the nineteenth century8 ,we may use the word alchemist as a term of reproach1 and apply it to these early workers because their theories appear to us to be absurd1 but how do we know that the chemists of the twenty-second century will not regard us in a similar light1 and set at naught the theories we so fondly cherish8 ,only seven out of the large number of metals now catalogued by us were known to the ancients2 these were gold1 silver1 mercury1 copper1 tin1 lead1 and iron4 ,and as it happened that the list of so-called planets also numbered exactly seven1 it was thought that there must be a connection between the two1 and1 consequently1 in the alchemical writings1 each metal was called by the name of that one of the heavenly bodies which was supposed to be connected with it in influence and quality4 ,in the astronomy of the ancients1 as is generally known1 the earth occupied the center of the universe1 and the list of planets included the sun and moon4 ,after them came ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn4 ,to the metal gold was given the name of ,sol1 or the sun1 on account of its brightness and its power of resisting corroding agents2 hence the compounds of gold were known as solar compounds and solar medicines4 ,as might have been expected1 silver was assigned to ,luna or the moon1 and in the modern pharmacopoeia such terms as lunar caustic and lunar salts still have a place4 ,mercury was1 of course1 appropriated to the planet of that name4 ,copper was named after ,venus1 and cupreous salts were known as venereal salts4 ,iron1 probably from its being the metal chiefly used for making arms and armor1 was dedicated to ,mars1 and we still speak of martial salts4 ,tin was named after ,jupiter from his brilliancy1 the compounds of tin being called jovial salts4 ,the dull1 leaden color of ,saturn1 with his apparently heavy and slow motion1 seemed to fit him for association with lead1 and we still have the saturnine ointment as a reminder of old alchemical times4 ,of these metals gold was supposed to be the only one that was perfect1 and the belief was general that if the others could be purified and perfected they would be changed to gold4 ,many of the old chemists worked faithfully and honestly to accomplish this1 but the path to wealth seemed so direct and the means for deception were so ready and simple1 that large numbers of quacks and charlatans entered the field and held out the most alluring inducements to dupes who furnished them liberally with money and other necessaries in the hope that when the discovery was made they would be put in possession of unbounded wealth4 ,these dupes were easily deceived and led astray by simple frauds1 which scarcely rose to the level of amateur legerdemain4 ,in the ,memoirs of the ,academy of ,sciences for #aggb1 ,m4 ,geoffroy gives an account of the various modes in which the frauds of these swindlers were carried on4 ,the following are a few of their tricks3 ,instead of the mineral substances which they pretended to transmute they put a salt of gold or silver at the bottom of the crucible1 the mixture being covered with some powdered crucible and gum water or wax so that it might look like the bottom of the crucible4 ,another method was to bore a hole in a piece of charcoal1 fill the hole with fine filings of gold or silver1 stopping it with powered charcoal1 mixed with some agglutinant so that the whole might look natural4 ,then when the charcoal burned away1 the silver or gold was found in the bottom of the crucible4 ,or they soaked charcoal in a solution of these metals and threw the charcoal1 when powdered1 upon the material to be transmuted4 ,sometimes they whitened gold with mercury and made it pass for silver or tin1 and the gold when melted was exhibited as the result of transmutation4 ,a common exhibition was to dip nails in a liquid and to take them out apparently half converted into gold2 these nails consisted of one-half iron neatly soldered to the other half1 which was gold1 and covered with something to conceal the color4 ,the paint or covering was removed by the liquid4 ,a very common trick was the use of a hollow1 iron stirring rod2 the hollow was filled with gold or silver filings1 and neatly stopped with wax4 ,when used to stir the contents of the crucible the wax melted and allowed the gold or silver to fall out4 ,these frauds were rendered all the more easy because of certain statements which were current in regard to successful attempts to convert lead and other metals into gold4 ,these accounts were vouched for by well-known chemists and others of high standing4 ,perhaps the most famous of these is that given by ,helvetius in his ,brief of the ,golden ,calf2 ,discovering the ,rarest ,miracle in ,nature2 how by the smallest portion of the ,philosopher's ,stone1 a great piece of common lead was totally transmuted into the purest transplendent gold1 at the ,hague in #afff4 ,the following is ,brande's abridgment of this singular account4 ,the #bgth day of ,december1 #afff1 in the afternoon1 came a stranger to my house at the ,hague1 in a plebeick habit1 of honest gravity and serious authority1 of a mean stature and a little long face1 black hair not at all curled1 a beardless chin1 and about forty-four years 7as ,i guess7 of age and born in ,north ,holland4 ,after salutation1 he beseeched me with great reverence to pardon his rude accesses1 for he was a lover of the ,pyrotechnian art1 and having read my treatise against the sympathetic powder of ,sir ,kenelm ,digby1 and observed my doubt about the philosophic mystery1 induced him to ask me if ,i really was a disbeliever as to the existence of an universal medicine which would cure all diseases1 unless the principal parts were perished1 or the predestinated time of death come4 ,i replied1 ,i never met with an adept1 or saw such a medicine1 though ,i had fervently prayed for it4 ,then ,i said1 ',surely you are a learned physician4' ',no1' said he1 ',i am a brass-founder1 and a lover of chemistry4' ,he then took from his bosom-pouch a neat ivory box1 and out of it three ponderous lumps of stone1 each about the bigness of a walnut4 ,i greedily saw and handled for a quarter of an hour this most noble substance1 the value of which might be somewhere about twenty tons of gold2 and having drawn from the owner many rare secrets of its admirable effects1 ,i returned him this treasure of treasures with a most sorrowful mind1 humbly beseeching him to bestow a fragment of it upon me in perpetual memory of him1 though but the size of a coriander seed4 ',no1 no1' said he1 'that is not lawful1 though thou wouldest give me as many golden ducats as would fill this room2 for it would have particular consequences1 and if fire could be burned of fire1 ,i would at this instant rather cast it all into the fiercest flames4' ,he then asked if ,i had a private chamber whose prospect was from the public street2 so ,i presently conducted him to my best furnished room backwards1 which he entered1 says ,helvetius 7in the true spirit of ,dutch cleanliness71 without wiping his shoes1 which were full of snow and dirt4 ,i now expected he would bestow some great secret upon me2 but in vain4 ,he asked for a piece of gold1 and opening his doublet showed me five pieces of that precious metal which he wore upon a green riband1 and which very much excelled mine in flexibility and color1 each being the size of a small trencher4 ,i now earnestly again craved a crumb of the stone1 and at last1 out of his philosophical commiseration1 he gave me a morsel as large as a rapeseed2 but ,i said1 ',this scanty portion will scarcely transmute four grains of lead4' ',then1' said he1 ',deliver it me back3' which ,i did1 in hopes of a greater parcel2 but he1 cutting off half with his nail1 said3 ',even this is sufficient for thee4' ',sir1' said ,i1 with a dejected countenance1 'what means this8' ,and he said1 ',even that will transmute half an ounce of lead4' ,so ,i gave him great thanks1 and said ,i would try it1 and reveal it to no one4 ,he then took his leave1 and said he would call again next morning at nine4 ,i then confessed1 that while the mass of his medicine was in my hand the day before1 ,i had secretly scraped off a bit with my nail1 which ,i projected on lead1 but it caused no transmutation1 for the whole flew away in fumes4 ',friend1' said he1 'thou art more dexterous in committing theft than in applying medicine2 hadst thou wrapt up thy stolen prey in yellow wax1 it would have penetrated and transmuted the lead into gold4' ,i then asked if the philosophic work cost much or required long time1 for philosophers say that nine or ten months are required for it4 ,he answered1 ',their writings are only to be understood by the adepts1 without whom no student can prepare this magistery4 ,fling not away1 therefore1 thy money and goods in hunting out this art1 for thou shalt never find it4' ,to which ,i replied1 ',as thy master showed it thee so mayest thou perchance discover something thereof to me who know the rudiments1 and therefore1 it may be easier to add to a foundation than begin anew4' ',in this art1' said he1 'it is quite otherwise1 for unless thou knowest the thing from head to heel1 thou canst not break open the glassy seal of ,hermes4 ,but enough2 tomorrow at the ninth hour ,i will show thee the manner of projection4' ,but ,elias never came again2 so my wife1 who was curious in the art whereof the worthy man had discoursed1 teazed me to make the experiment with the little spark of bounty the artist had left me2 so ,i melted half an ounce of lead1 upon which my wife put in the said medicine2 it hissed and bubbled1 and in a quarter of an hour the mass of lead was transmuted into fine gold1 at which we were exceedingly amazed4 ,i took it to the goldsmith1 who judged it most excellent1 and willingly offered fifty florins for each ounce4 ,such is the celebrated history of ,elias the artist and ,dr4 ,helvetius4 ,helvetius stood very high as a man and chemist1 but in connection with this and some other narratives of the same kind1 it may be well to remember that something over a hundred years before that time the celebrated ,paracelsus had introduced laudanum4 ,the following is another history of transmutation1 given by ,mangetus1 on the authority of ,m4 ,gros1 a clergyman of ,geneva1 of the most unexceptionable character1 and at the same time a skilful physician and expert chemist4 ,about the year #afej an unknown ,italian came to ,geneva and took lodgings at the sign of the ,green ,cross4 ,after remaining there a day or two1 he requested ,de ,luc1 the landlord1 to procure him a man acquainted with ,italian1 to accompany him through the town and point out those things which deserved to be examined4 ,de ,luc was acquainted with ,m4 ,gros1 at that time about twenty years of age1 and a student in ,geneva1 and knowing his proficiency in the ,italian language1 requested him to accompany the stranger4 ,to this proposition he willingly acceded1 and attended the ,italian everywhere for the space of a fortnight4 ,the stranger now began to complain of want of money1 which alarmed ,m4 ,gros not a little1 for at that time he was very poor1 and he became apprehensive1 from the tenor of the stranger's conversation1 that he intended to ask the loan of money from him4 ,but instead of this1 the ,italian asked him if he was acquainted with any goldsmith1 whose bellows and other utensils they might be permitted to use1 and who would not refuse to supply them with the different articles requisite for a particular process which he wanted to perform4 ,m4 ,gros named a ,m4 ,bureau1 to whom the ,italian immediately repaired4 ,he readily furnished crucibles1 pure tin1 quicksilver1 and the other things required by the ,italian4 ,the goldsmith left his workshop1 that the ,italian might be under the less restraint1 leaving ,m4 ,gros1 with one of his own workmen as an attendant4 ,the ,italian put a quantity of tin into one crucible1 and a quantity of quicksilver into another4 ,the tin was melted in the fire and the mercury heated4 ,it was then poured into the melted tin1 and at the same time a red powder enclosed in wax was projected into the amalgam4 ,an agitation took place and a great deal of smoke was exhaled from the crucible2 but this speedily subsided1 and the whole being poured out1 formed six heavy ingots1 having the color of gold4 ,the goldsmith was called in by the ,italian and requested to make a rigid examination of the smallest of these ingots4 ,the goldsmith not content with the touch-stone and the application of aquafortis1 exposed the metal on the cupel with lead and fused it with antimony1 but it sustained no loss4 ,he found it possessed of the ductility and specific gravity of gold2 and full of admiration1 he exclaimed that he had never worked before upon gold so perfectly pure4 ,the ,italian made him a present of the smallest ingot as a recompense and then1 accompanied by ,m4 ,gros1 he repaired to the mint1 where he received from ,m4 ,bacuet1 the mint-master1 a quantity of ,spanish gold coin1 equal in weight to the ingots which he had brought4 ,to ,m4 ,gros he made a present of twenty pieces on account of the attention that he had paid to him and after paying his bill at the inn1 he added fifteen pieces more1 to serve to entertain ,m4 ,gros and ,m4 ,bureau for some days1 and in the meantime he ordered a supper1 that he might1 on his return1 have the pleasure of supping with these two gentlemen4 ,he went out1 but never returned1 leaving behind him the greatest regret and admiration4 ,it is needless to add that ,m4 ,gros and ,m4 ,bureau continued to enjoy themselves at the inn till the fifteen pieces which the stranger had left1 were exhausted4 ,narratives such as these led even ,bergman1 a very able chemist of the period1 to take the ground that although most of these relations are deceptive and many uncertain1 some bear such character and testimony that1 unless we reject all historical evidence1 we must allow them entitled to confidence4 ,a much more probable explanation is that the relators were either dreaming or deceived by clever legerdemain4 ,of the possibility or impossibility of converting the more common metals into gold or silver1 it would be rash to give a positive opinion4 ,to say that gold1 silver1 lead1 copper1 etc41 are elements and cannot be changed1 is merely to say that we have not been able to decompose them4 ,water1 potash1 soda1 and other substances1 were at one time considered elements1 and resisted all the efforts of the older chemists to resolve them into their components1 but with the advent of more powerful means of analysis they were shown to be compounds1 and it is not impossible that the so-called elements into which they were resolved may themselves be found to be compounds4 ,this has happened in regard to some substances which were at one time announced as elements1 and it is not impossible that it may happen in regard to others4 ,the ablest chemists of the present day recognize this fully and are prepared for radical changes in our knowledge of the nature and constitution of matter4 ,amongst the new views is the hypothesis of ,rutherford and ,soddy1 which1 as given by ,sir ,william ,ramsay1 in a recent article contributed by him to ,harper's ,magazine1 is that1 atoms of elements of high atomic weight1 such as radium1 uranium1 thorium1 and the suspected elements polonium and actinium1 are unstable2 that they undergo spontaneous change into other forms of matter1 themselves radioactive and themselves unstable2 and that finally elements are produced1 which1 on account of their non-radioactivity1 are as a rule1 impossible to recognize1 for their minute amount precludes the application of any ordinary test with success4 ,the recognition of helium however1 which is comparatively easy of detection1 lends great support to this hypothesis4 ,at the same time we must not lose sight of the fact that the substances which we now recognize as elements have not only resisted the most powerful analytical agencies and dissociating forces1 but have maintained their elemental character in spectrum analysis1 and shown their presence as distinct elements in the sun and other heavenly bodies where they must have been subjected to the action of the most energetic decomposing forces4 ,so that in the present state of our knowledge the near prospect of successful transmutation does not seem to be very bright1 although we cannot regard it as impossible4 ,in the article from which we have already quoted1 ,sir ,william ,ramsay1 after discussing the bearing of certain experiments in regard to the parting with and absorbing of energy by certain elements1 says3 ,if these hypotheses are just1 then the transmutation of the elements no longer appears an idle dream4 ,the philosopher's stone will have been discovered1 and it is not beyond the bounds of possibility that it may lead to that other goal of the philosophers of the dark ages--the elixir vitae4 ,for the action of living cells is also dependent on the nature and direction of the energy which they contain2 and who can say that it will be impossible to control their action1 when the means of imparting and controlling energy shall have been investigated6 ,in the event of the discovery of a cheap method of producing gold1 the change which would certainly occur in our financial or currency system would be important1 if not revolutionary4 ,it has become the fashion at present with certain writers to scout the so-called quantitative theory of money as if it were an exposed fallacy4 ,now the quantitative theory of money rests on one of the most well-grounded and firmly established principles in political economy3 the trouble is that the writers in question do not understand it or even know what it is4 ,at present1 the production of gold barely keeps pace with the increasing demand for the metal as currency and in the arts1 but if that production were increased ten-fold1 the value of gold would decline and prices would go up astonishingly4 ,one of the objects which the better class of alchemists had in view was the making of gold to such an extent that it might become quite common and cease to be sought after by mankind4 ,one alchemical writer says3 ,would to ,god that all men might become adepts in our art1 for then gold1 the common idol of mankind1 would lose its value and we should prize it only for its scientific teaching4 ,,footnotes3 #b ,genesis vi1 #b4 ,,vi ,,the ,,fixation ,,of ,,mercury ,this is really one of the processes supposed to be involved in the transmutation of the metals and might1 therefore1 perhaps1 with propriety1 be included under that head4 ,but as it has received special attention in the apocryphal works of ,hermes ,trismegistus1 who is generally regarded as the ,father of ,alchemy1 it is frequently mentioned as one of the old scientific problems4 ,readers of ,scott's novel1 ,kenilworth1 may remember that ,wayland ,smith1 in his account of his former master1 ,demetrius ,doboobius1 describes him as a profound chemist who had made several efforts to fix mercury1 and judged himself to have made a fair hit at the philosopher's stone4 ,hermes1 or1 rather1 those who wrote over his name1 speaks in the jargon of the adepts1 about catching the flying bird1 by which is meant mercury1 and drowning it so that it may fly no more4 ,the usual means for effecting this was amalgamation with gold1 or some other metal or solution in some acid4 ,to the ancient chemists mercury must have been one of the most interesting of objects4 ,its great heaviness1 its metallic brilliancy1 and its wonderful mobility1 must all have combined to render it a subject for deep thought and an attractive object for experiment and investigation4 ,living in a warm climate1 as they did1 there was no means at their command by which its fluidity could be impaired4 ,this subtle substance seemed to defy the usual attempts to grasp it2 it rolled about like a solid sphere1 but offered no resistance to the touch1 and when pressed it split up into innumerable smaller globules so that the problem of fixing it must have had a strange fascination for the thoughtful alchemist1 especially when he found that1 on subjection to a comparatively moderate degree of heat1 this heavy metal disappeared in vapor and left not a trace behind4 ,i have often wondered what the old alchemists would have said if they had seen fluid mercury immersed in a clear liquid and brought out in the form of a lump of solid1 bright metal4 ,for1 although this is not in any sense a solution of the problem1 yet it is a most curious sight and one which was rarely seen before the discovery of the liquefaction of the gases4 ,to ,geber1 ,basil ,valentine1 ,van ,helmont1 ,helvetius1 and men of their day1 living in their climate1 this startling phenomenon would have seemed nothing short of a miracle4 ,in modern times the solidification of mercury had been frequently witnessed by these who dwelt in northern climates and by the skilful use of certain freezing mixtures made up of ordinary salts1 it is not difficult to exhibit this metal in the solid state at any time4 ,but it was not until the discovery of the liquefaction of carbonic acid1 nitrous oxide1 and other gases by ,faraday1 about #ahbc1 that the freezing of mercury became a common lecture-room experiment4 ,in the year #ahfb the writer delivered a course of lectures on chemistry1 in the city of ,rochester1 ,n4 ,y41 and during the progress of these lectures he reduced carbonic acid first to the liquid1 and then to the solid state1 in the form of a white snow4 ,the temperature of this snow was about -#hj deg4 ,cent4 7-#agf deg4 ,fahr47 and when it was mixed with ether and laid on a quantity of mercury1 the latter was quickly frozen4 ,in this way it was easy to make a hammer-head of frozen mercury and drive a nail with it4 ,another very interesting experiment was the freezing of a slender triangular bar of mercury which might be twisted1 bent1 and tied in a knot4 ,this was done by folding a long strip of very stiff paper so as to make an angular trough into which the mercury was poured4 ,this trough was then carefully leveled and a mixture of solid carbonic acid and ether was placed over the metal in the usual way4 ,in a few seconds the mercury was frozen quite solid so that it could be lifted out by means of two pairs of wooden forceps and bent and knotted at will4 ,but the most striking part of the experiment was the melting of this bar of mercury by means of a piece of ice4 ,the moment the ice touched the mercury1 the latter melted and fell down in drops in the same way that a bar of lead or solder melts when it is touched with a red-hot iron4 ,the melted mercury was allowed to fall into a tall ale-glass of water1 the temperature of which had been reduced as nearly as possible to the freezing point4 ,when the mercury came in contact with the cold water1 the latter began to freeze and by careful manipulation it was possible to freeze a tube of ice through the center of the column of water4 ,the effect of this under proper illumination was very striking4 ,owing to the fact that the specific heat or thermal capacity of mercury is only about one-thirtieth of that of water1 it requires a considerable amount of melted mercury to produce the desired result4 ,but these processes do not enable us to fix mercury in the alchemical sense2 the accomplishment of that still remains an unsolved problem1 and it is more than likely that it will remain so4 ,,vii ,,the ,,universal ,,medicine ,,and ,,the ,,elixir ,,of ,,life ,love of life is a characteristic of all animals1 man included1 and notwithstanding the fact that an occasional individual becomes so dissatisfied with his environment that he commits suicide1 and also in the face of the poet's assertion that protracted life is but protracted woe most men and women are of the same way of thinking as ,charmian1 the attendant on ,cleopatra1 and love long life better than figs4 ,and the force of this general feeling is appealed to in the only one of the ,mosaic commandments to which a promise is attached1 the inducement for honoring father and mother being that thy days may be long in the land that the ,lord thy ,god giveth thee4 ,no wonder then that the old alchemists dreamed of a universal medicine that would not only prevent or cure sickness but that would renew the youth of the aged and the feeble1 for in this1 as in most other attempts at discovery1 the wish was father to the thought4 ,that the renewal of youth in the aged was supposed to be within the ability of the magicians and gods of old1 we gather from the stories of ,medea and ,aeson and the ivory shoulder of ,pelops1 as referred to in ,shakespeare1 and explained in the ,shakespeare ,cyclopedia4 ,of the form of this supposed elixir we know very little for the language of the alchemists was so vague and mystical that it is often very difficult to ascertain their meaning with any approach to certainty4 ,the following1 which is a fair sample of their metaphorical modes of expressing themselves1 is found in the works of ,geber4 ,in one of his writings1 he exclaims3 ,bring me the six lepers that ,i may cleanse them4 ,modern commentators explain this as being his mode of telling his readers that he would convert into gold the six inferior or1 as they were called by the alchemists1 the six imperfect metals4 ,no wonder that ,dr4 ,johnson adopted the idea that the word gibberish 7anciently written geberish7 owed its origin to an epithet applied to the language of ,geber and his tribe4 ,some have claimed that the elixir and the philosopher's stone were one and the same thing1 and some of the writings of the old alchemists would seem to confirm this view4 ,thus1 at the close of a formula for preparing the philosopher's stone1 ,carolus ,musitanus gives the following admonition3 ,thus friend1 you have a description of the universal medicine1 not only for curing diseases and prolonging life1 but also for transmuting all metals into gold4 ,give therefore thanks to ,almighty ,god1 who1 taking pity on human calamities1 has at last revealed this inestimable treasure1 and made it known for the benefit of all4 ,and ,brande tells us that nearly all the alchemists attributed the power of prolonging life either to the philosopher's stone or to certain preparations of gold1 imagining possibly that the permanence of that metal might be transferred to the human system4 ,the celebrated ,descartes is said to have supported such opinions2 he told ,sir ,kenelm ,digby that although he would not venture to promise immortality1 he was certain that life might be lengthened to the period of that of the ,patriarchs4 ,his plan1 however1 seems to have been the very rational one of limiting all excess of diet and enjoining punctual and frugal meals4 ,it is an old saying that history repeats itself4 ,about forty years ago certain medical practitioners strongly urged the use of salts of gold in the treatment of disease1 and great hopes were entertained in regard to their efficacy4 ,and the ,keeley gold cure for drunkards is strongly in evidence1 even at the present day4 ,on the other hand1 some have held that the elixir was quite distinct from the stone by which metals might be transmuted into gold4 ,in the second part of ,king ,henry ,,iv1 ,falstaff 7,act ,,iii1 ,scene #b1 line #cee71 says of ,shallow3 it shall go hard but ,i will make him a philosopher's two stones to me1 and this saying of his has given considerable trouble to the commentators4 ,warburton's explanation of this expression is1 that there was two stones1 one of which was a universal medicine and the other a transmuter of base metals into gold4 ,and in ,churchyard's ,discourse and ,commendation of those that can make ,gold1 we read of ,remundus1 who ,wrate sundry workes1 as well doth yet appeare ,of stone for gold1 and shewed plaine and cleare ,a stone for health4 ,johnson and some others have objected to this explanation1 but it seems to be evident that ,falstaff meant that he would get health and wealth from ,shallow4 ,he got the wealth to the extent of a thousand pounds4 ,the intense desire which exists in the human bosom for an elixir that will cure all diseases1 and prolong life has made itself evident1 even in recent times1 and has called forth serious efforts on the part of men occupying prominent positions in the scientific world4 ,both in ,europe and in this country suggestions have been made of fluids which1 when injected into the veins of the old and the feeble1 would renew youth and impart fresh strength4 ,but alas6 the results thus far attained have been anything but gratifying1 and the probabilities against success in this direction are very strong4 ,the latest gleam of light comes from discoveries in connection with the radioactive elements1 as the reader will find1 on referring to ,sir ,william ,ramsay's utterance1 which is given at the close of the article on the ,transmutation of the ,metals1 on a preceding page4 ,,additional ,,follies ,in addition to the seven ,follies1 of which an account has been given in the preceding pages1 there are a few which deserve to be classed with them1 although they do not find a place in the usual lists4 ,these are known as ,,perpetual ,,lamps4 ,,the ,,alkahest ,,or ,,universal ,,solvent4 ,,palingenesy4 ,,the ,,powder ,,of ,,sympathy4 ,,perpetual ,,or ,,ever-,,burning ,,lamps ,part of the sepulchral rites of the ancients consisted in placing lighted lamps in the tombs or vaults in which the dead were laid1 and1 in many cases1 these lamps were carefully tended and kept continually burning4 ,some authors have claimed1 however1 that these men of old were able to construct lamps which burned perpetually and required no attention4 ,in number #cgi of the ,spectator there is an anecdote of some one having opened the sepulcher of the famous ,rosicrucius4 ,there he discovered a lamp burning which a statue of clock-work struck into pieces4 ,hence1 says the writer1 the disciples of this visionary claimed that he had made use of this method to show that he had re-invented the ever-burning lamps of the ancients4 ,and ,fortunio ,liceti wrote a book in which he collected a large number of stories about lamps1 said to have been found burning in tombs or vaults4 ,ozanam fills eight closely printed pages with a discussion of the subject4 ,attempts have been made to explain many of the facts upon which is based the claim that the ancients were able to construct perpetual lamps by the suggestion that the light sometimes seen on the opening of ancient tombs may have been due to the phosphorescence which is well known to arise during the decomposition of animal and vegetable matter4 ,decaying wood and dead fish are familiar objects which give out a light that is sufficient to render dimly visible the outlines of surrounding objects1 and such a light1 seen in the vicinity of an old lamp1 might give rise to the impression that the lamp had been actually burning and that it had been blown out by sudden exposure to a draft of air4 ,another supposition was that the flame1 which was supposed to have been seen1 may have been caused by the ignition of gases arising from the decomposition of dead bodies1 and set on fire by the flambeaux or candles of the investigators1 and it is quite possible that the occurrence of each of these phenomena may have given a certain degree of confirmation to preconceived ideas4 ,after the discovery of phosphorus in #affi1 by ,brandt and ,kunckel1 it was employed in the construction of luminous phials which could be carried in the pocket1 and which gave out sufficient light to enable the user to see the hands of a watch on a dark night4 ,directions for making these luminous phials are very simple1 and may be found in most of the books of experiments published prior to the introduction of the modern lucifer match4 ,they were also used for obtaining a light by means of the old matches1 which were tipped merely with a little sulphur1 and which could not be ignited by friction4 ,such a match1 after being dipped into one of these phosphorus bottles1 would readily take fire by slight friction1 and some persons preferred this contrivance to the old flint and steel1 partly1 no doubt1 because it was a novelty4 ,but these bottles were not in any sense perpetual1 the light being due to the slow oxidation of the phosphorus so that1 in a comparatively short time1 the luminosity of the materials ceased4 ,nevertheless1 it has been suggested that some form of these old luminous phials may have been the original perpetual lamp4 ,after the discovery of the phosphorescent qualities of barium sulphate or ,bolognian phosphorus1 as it was called1 it was thought that this might be a re-discovery of the long-lost art of making perpetual lamps4 ,but it is well known that this substance loses its phosphorescent power after being kept in the dark for some time1 and that occasional exposure to bright sun-light is one of the conditions absolutely essential to its giving out any light at all4 ,this condition does not exist in a dark tomb4 ,a few years ago phosphorescent salts of barium and calcium were employed in the manufacture of what was known as luminous paint4 ,these materials shine in the dark with brilliancy sufficient to enable the observer to read words and numbers traced with them1 but regular exposure to the rays of the sun or some other bright light is absolutely necessary to enable them to maintain their efficiency4 ,more recently it has been suggested that the ancients may have been acquainted with some form of radioactive matter like radium1 and that this was the secret of the lamps in question4 ,it is far more likely1 however1 that the reports of their perpetual lamps were based upon mere errors of observation4 ,the perpetual lamp is1 in chemistry1 the counterpart of perpetual motion in mechanics--both violate the fundamental principle of the conservation of energy4 ,and just as suggestions of impossible movements have been numerous in the case of perpetual motion1 so impossible devices and constructions have been suggested in regard to perpetual lamps4 ,prior to the development1 or even the suggestion of the law of the conservation of energy1 it was believed that it might be possible to find a liquid which would burn without being consumed1 and a wick which would feed the liquid to the flame without being itself destroyed4 ,dr4 ,plott suggested naphtha for the fluid and asbestos for the wick1 but since kerosene oil1 naphtha1 gasolene1 and other liquids of the kind have become common1 every housewife knows that as her lamp burns1 the oil1 of whatever kind it may be1 disappears4 ,under present conditions the construction of a perpetual lamp is not a severely felt want2 for constancy and brilliancy our present means of illumination are sufficient for almost all our requirements4 ,whether or not it would be possible to gather up those natural currents of electricity1 which are suspected to flow through and over the earth1 and utilize them for purposes of illumination1 however feeble1 it might be difficult to decide4 ,but such means of perpetual electric lighting would be similar to a perpetual motion derived from a mountain stream4 ,such natural means of illumination already exist1 and have existed for ages in the fire-giving wells of naphtha which are found on the shores of the ,caspian sea1 and in other parts of the east1 and which have long been objects of adoration to the fire-worshippers4 ,as for the outcome of present researches into the properties of radium1 polonium1 and similar substances1 and their possible applications1 it is too early to form even a surmise4 ,,the ,,alkahest ,,or ,,universal ,,solvent ,the production of a universal solvent or alkahest was one of the special problems of the alchemists in their general search for the philosopher's stone and the means of transmuting the so-called inferior metals into gold and silver4 ,their idea of the way in which it would aid them to attain these ends does not seem to be very clearly stated in any work that ,i have consulted2 probably they thought that a universal solvent would wash away all impurities from common materials and leave in absolute purity the higher substance1 which constituted the gold of the adepts4 ,but whatever their particular object may have been1 it is well known that much time and labor were expended in the fruitless search4 ,the futility of such attempts was very well exposed by the cynical sceptic1 who asked them what kind of vessel could they provide for holding such a liquid8 ,if its solvent powers are such that it dissolves everything1 it is very evident that it would dissolve the very material of the vessel in which it must be placed4 ,when hydrofluoric acid became a subject of investigation it was thought that its characteristics approached1 more nearly than those of any other substance known1 to those of the universal solvent1 and the very difficulty above suggested1 presented itself strongly to the chemists who experimented with it4 ,not only common metals but glass and porcelain were acted upon by this wonderfully energetic liquid and when attempts were made to isolate the fluorine1 even the platinum electrodes were corroded and destroyed4 ,vessels of pure silver and of lead served tolerably well1 but ,davy suggested that the most scientific method of constructing a containing vessel would be to use a compound in which fluorine was already present to the point of saturation4 ,as there is a limit to the amount of fluorine with which any base can combine1 such a vessel would be proof against its solvent action4 ,i am not aware1 however1 that the suggestion was ever carried into actual practice with success4 ,,palingenesy ,this singular delusion may have been partly due to errors of observation1 the instruments and methods of former times having been notably crude and unreliable4 ,this fact1 taken in connection with the wild theories upon which the natural sciences of the middle ages were based1 is a sufficient explanation of some of the extraordinary statements made by ,kircher1 ,schott1 ,digby1 and others4 ,by palingenesy these writers meant a certain chemical process by means of which a plant or an animal might be revived from its ashes4 ,in other words a sort of material resurrection4 ,most of the accounts given by the old authors go no further than to assert that by proper methods the ashes of plants1 when treated with water1 produce small forests of ferns and pines4 ,thus1 an ,english chemist1 named ,coxe1 asserts that having extracted and dissolved the essential salts of fern1 and then filtered the liquor1 he observed1 after leaving it at rest for five or six weeks1 a vegetation of small ferns adhering to the bottom of the vessel4 ,the same chemist1 having mixed northern potash with an equal quantity of sal ammoniac1 saw1 some time after1 a small forest of pines and other trees1 with which he was not acquainted1 rising from the bottom of the vessel4 ,and ,kircher tells us in his ,ars ,magnetica that he had a long-necked phial1 hermetically sealed1 containing the ashes of a plant which he could revive at pleasure by means of heat2 and that he showed this wonderful phenomenon to ,christina1 ,queen of ,sweden1 who was highly delighted with it4 ,unfortunately he left this valuable curiosity one cold day in his window and it was entirely destroyed by the frost4 ,father ,schott also asserts that he saw this chemical wonder which1 according to his account1 was a rose revived from its ashes4 ,and he adds that a certain prince having requested ,kircher to make him one of the same kind1 he chose rather to give up his own than to repeat the operation4 ,even the celebrated ,boyle1 though not very favorable to palingenesy1 relates that having dissolved in water some verdigris1 which1 as is well known1 is produced by combining copper with the acid of vinegar1 and having caused this water to congeal1 by means of artificial cold1 he observed1 at the surface of the ice1 small figures which had an exact resemblance to vines4 ,in this connection it is well to bear in mind that in ,boyle's time almost all vinegar was really what its name implies--sour wine 7vin aigre7--and verdigris or copper acetate was generally prepared by exposing copper plates to the action of refuse grapes which had been allowed to ferment and become sour4 ,therefore to him it might not have seemed so very improbable that the green crystals which appeared on the surface of the ice were1 in reality1 minute resuscitated grape-vines4 ,the explanation of these facts given by ,father ,kircher is worthy of the science of the times4 ,he tells us that the seminal virtue of each mixture is contained in its salts and these salts1 unalterable by their nature1 when put in motion by heat1 rise in the vessel through the liquor in which they are diffused4 ,being then at liberty to arrange themselves at pleasure1 they place themselves in that order in which they would be placed by the effect of vegetation1 or the same as they occupied before the body to which they belonged had been decomposed by the fire2 in short1 they form a plant1 or the phantom of a plant1 which has a perfect resemblance to the one destroyed4 ,that the operators have here mistaken for true vegetable growth the fern-like crystals of the salts which exist in the ashes of all plants is very obvious4 ,their knowledge of plant structure was exceedingly limited and their microscopes were so imperfect that imagination had free scope4 ,as seen under our modern microscopes1 there are few prettier sights than the crystallization of such salts as sal ammoniac1 potassic nitrate1 barium chloride1 etc4 ,the crystals are actually seen to grow and it would not require a very great stretch of the imagination to convince one that the growth is due to a living organism4 ,indeed1 this view has actually been taken in an article which recently appeared in a prominent magazine4 ,the writer of that article sees no difference between the mere aggregation of inorganic particles brought together by voltaic action and the building up of vital structures under the influence of organic forces4 ,this is simply materialism run mad4 ,perhaps the finest illustration of such crystallization is to be found in the deposition of silver from a solution of the nitrate as seen under the microscope4 ,a drop of the solution is placed on a glass slide and while the observer watches it through a low power1 a piece of copper wire or1 preferably1 a minute quantity of the amalgam of tin and mercury1 such as is used for silvering cheap looking glasses1 is brought into contact with it4 ,chemical decomposition at once sets in and then the silver thus deposited forms one element of a very minute voltaic couple and fresh crystals of silver are deposited upon the silver already thrown down4 ,when the illumination of this object under the microscope is properly managed1 the appearance1 which resembles that shown in ,fig4 #ah1 is exceedingly brilliant1 and beautiful beyond description4 ,illustration3 ,fig4 #ah4 ,that imagination played strange pranks in the observations of the older microscopists is shown by some of the engravings found in their books4 ,i have now before me a thick1 dumpy quarto in which the so-called seminal animalcules are depicted as little men and women1 and ,i have no doubt that1 to the eye of this early observer1 they had that appearance4 ,but the microscopists of to-day know better4 ,sir ,kenelm ,digby1 whose name is associated with the ,sympathetic ,powder1 tells us that he took the ashes of burnt crabs1 dissolved them in water and1 after subjecting the whole to a tedious process1 small crabs were produced in the liquor4 ,these were nourished with blood from the ox1 and1 after a time1 left to themselves in some stream where they throve and grew large4 ,now1 although ,evelyn1 in his diary1 declares that ,sir ,kenelm was an errant mountebank1 it is quite possible that he was honest in his account of his experiments and that he was merely led astray by the imperfection of his instruments of observation4 ,it is more than likely that the creatures which ,digby saw were entomostraca introduced in the form of ova which1 unless a good microscope be used1 are quite invisible4 ,these would develop rapidly and might easily be mistaken for some species of crab1 though1 when examined with proper instruments1 all resemblance vanishes4 ,when let loose in a running stream it would evidently be impossible to trace their identity and follow their growth4 ,but while some of these stories may have originated in errors of observation this will hardly explain some of the statements made by those who have advocated this strange doctrine4 ,father ,schott1 in his ,physica ,curiosa1 gives an account of the resurrection of a sparrow and actually gives an engraving in which the bird is shown in a bottle revived6 ,although the subject1 of itself1 is not worthy of a moment's consideration1 it deserves attention as an illustration of the extraordinary vagaries into which the human mind is liable to fall4 ,,the ,,powder ,,of ,,sympathy ,this curious occult method of curing wounds is indissolubly associated with the name of ,sir ,kenelm ,digby 7born #afjc1 died #affe71 though it was undoubtedly in use long before his time4 ,he himself tells us that he learned to make and apply the drug from a ,carmelite1 who had traveled in the east1 and whom he met in ,florence1 in #afbb4 ,the descendants of ,digby are still prominent in ,england1 and ,o4 ,w4 ,holmes1 in his ,one ,hundred ,days in ,europe1 tells us that he had met a ,sir ,kenelm ,digby1 a descendant of the famous ,sir ,kenelm of the seventeenth century1 and that he could hardly refrain from asking him if he had any of his ancestor's famous powder in his pocket4 ,digby was a student of chemistry1 or at least of the chemistry of those days1 and wrote books of ,recipes and the making of ,methington metheglin or mead8 ,syder1 etc4 ,he was1 as we have seen in the previous article1 a believer in palingenesy and made experiments with a view to substantiate that strange doctrine4 ,evelyn calls him an errant quack1 and he may have been given to quackery1 but then the loose scientific ideas of those days allowed a wide range in drawing conclusions which1 though they seem absurd to us1 may have appeared to be quite reasonable to the men of that time4 ,from his book on the subject1#c we learn that the wound was never to be brought into contact with the powder4 ,a bandage was to be taken from the wound1 immersed in the powder1 and kept there until the wound healed4 ,this beats the absent treatment of ,christian ,science6 ,the powder was simply pulverized vitriol1 that is1 ferric sulphate1 or sulphate of iron4 ,there was another and probably an older method of using sympathetic powders and salves2 this was to apply the supposed curative to the weapon which caused the wound1 instead of the wound itself4 ,in the ,lay of the ,last ,minstrel1 ,scott gives an account of the way in which the ,lady of ,buccleuch applied this occult surgery to the wound of ,william of ,deloraine3 ,she drew the splinter from the wound1 ,and with a charm she stanched the blood4 ,she bade the gash be cleansed and bound3 ,no longer by his couch she stood2 ,but she has ta'en the broken lance4 ,and washed it from the clotted gore1 ,and salved the splinter o'er and o'er4 ,william of ,deloraine1 in trance1 ,whene'er she turned it round and round ,twisted as if she galled his wound4 ,then to her maidens she did say1 ,that he should be whole man and sound1 ,within the course of a night and day4 ,full long she toiled1 for she did rue ,mishap to friend so stout and true4#d ,that no direct benefit could have been derived from such a mode of treatment must be obvious1 but ,de ,morgan very plausibly claims that in the then state of surgical and medical knowledge1 it was really the very best that could have been adopted4 ,his argument is as follows3 ,the sympathetic powder was that which cured by anointing the weapon with its salve instead of the wound4 ,i have been long convinced that it was efficacious4 ,the directions were to keep the wound clean and cool1 and to take care of diet1 rubbing the salve on the knife or sword4 ,if we remember the dreadful notions upon drugs which prevailed1 both as to quantity and quality1 we shall readily see that any way of not dressing the wound1 would have been useful4 ,if the physicians had taken the hint1 had been careful of diet1 etc41 and had poured the little barrels of medicine down the throat of a practicable doll1 they would have had their magical cures as well as the surgeons4 ,matters are much improved now2 the quantity of medicine given1 even by orthodox physicians1 would have been called infinitesimal by their professional ancestors4 ,accordingly1 the ,college of ,physicians has a right to abandon its motto1 which is1 ,ars longa1 vita brevis1 meaning1 ,practice is long1 so life is short4 ,as set forth by ,digby and others1 the use of the ,powder of ,sympathy is free from all taint of witchcraft or magic1 but1 in another form1 it was wholly dependent upon incantations and other magical performances4 ,this idea of sympathetic action was even carried so far as to lead to attempts to destroy or injure those whom the operator disliked4 ,in some cases this was done by moulding an image in wax which1 when formed under proper occult influences1 was supposed to have the power of transferring to the victim any injuries inflicted on the image4 ,into such images pins and knives were thrust in the hope that the living original would suffer the same pains and mutilations that would be inflicted if the knives or pins were thrust into him1 and sometimes the waxen form was held before the fire and allowed to melt away slowly in the hope that the prototype would also waste away1 and ultimately die4 ,shakespeare alludes to this in the play of ,king ,john4 ,in ,act v41 ,scene #d1 line #bd1 ,melun says3 ,a quantity of life ,which bleeds away1 even as a form of wax1 ,resolveth from his figure 'gainst the fire8 ,and ,hollinshed tells us that it was alleged against ,dame ,eleanor ,cobham and her confederates that they had devised an image of wax1 representing the king1 which1 by their sorcerie1 by little and little consumed1 intending thereby1 in conclusion1 to waste and destroy the king's person4 ,in these cases1 however1 the operator always depended upon certain occult or demoniacal influences1 or1 in other words1 upon the art of magic1 and therefore examples of this kind do not come within the scope of the present volume4 ,in the case of the ,powder of ,sympathy the results were supposed to be due entirely to natural causes4 ,,footnotes3 #c ,touching the ,cure of ,wounds by the ,powder of ,sympathy4 ,with ,instructions how to make the said ,powder4 ,rendered faithfully out of ,french into ,english by ,r4 ,white1 ,gent4 ,london1 #afeh4 #d ,canto ,,iii4 ,stanza #bc4 ,a ,,small ,,budget ,,of ,,paradoxes1 ,,illusions1 ,,and ,,marvels ,,the ,,fourth ,,dimension ,,and ,,the ,,possibility ,,of ,a ,,new ,,sense ,,and ,,new ,,sense-,,organ ,this subject has now found its way not only into semi-scientific works but into our general literature and magazines4 ,even our novel-writers have used suggestions from this hypothesis as part of the machinery of their plots so that it properly finds a place amongst the subjects discussed in this volume4 ,various attempts have been made to explain what is meant by the fourth dimension1 but it would seem that thus far the explanations which have been offered are1 to most minds1 vague and incomprehensible1 this latter condition arising from the fact that the ordinary mind is utterly unable to conceive of any such thing as a dimension which cannot be defined in terms of the three with which we are already familiar4 ,and ,i confess at the start that ,i labor under the superlative difficulty of not being able to form any conception of a fourth dimension1 and for this incapacity my only consolation is1 that in this respect ,i am not alone4 ,i have conversed upon the subject with many able mathematicians and physicists1 and in every case ,i found that they were in the same predicament as myself1 and where ,i have met men who professed to think it easy to form a conception of a fourth dimension1 ,i have found their ideas1 not only in regard to the new hypothesis1 but to its correlations with generally accepted physical facts1 to be nebulous and inaccurate4 ,it does not follow1 however1 that because myself and some others cannot form such a clear conception of a fourth dimension as we can of the third1 that1 therefore1 the theory is erroneous and the alleged conditions non-existent4 ,some minds of great power and acuteness have been incapable of mastering certain branches of science4 ,thus ,diderot1 who was associated with d',alembert1 the famous mathematician1 in the production of ,l',encyclopedie1 and who was not only a man of acknowledged ability1 but who1 at one time1 taught mathematics and wrote upon several mathematical subjects1 seems to have been unable to master the elements of algebra4 ,the following anecdote regarding his deficiency in this respect is given by ,thiebault and indorsed by ,professor ,de ,morgan3 ,at the invitation of the ,empress1 ,catherine ,,ii1 ,diderot paid a visit to the ,russian court4 ,he was a brilliant conversationalist and being quite free with his opinions1 he gave the younger members of the court circle a good deal of lively atheism4 ,the ,empress herself was very much amused1 but some of her councillors suggested that it might be desirable to check these expositions of strange doctrines4 ,as ,catherine did not like to put a direct muzzle on her guest's tongue1 the following plot was contrived4 ,diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of ,god and would give it to him before all the court if he desired to hear it4 ,diderot gladly consented1 and although the name of the mathematician is not given1 it is well known to have been ,euler4 ,he advanced toward ,diderot1 and said in ,french1 gravely1 and in a tone of perfect conviction3 ,monsieur1 7a bn7 _/ n x1 therefore1 ,god exists2 reply6 ,diderot1 to whom algebra was ,hebrew1 was embarrassed and disconcerted1 while peals of laughter rose on all sides4 ,he asked permission to return to ,france at once1 which was granted4 ,even such a mind as that of ,buckle1 who was generally acknowledged to be a keen-sighted thinker1 could not form any idea of a geometrical line--that is1 of a line without breadth or thickness1 a conception which has been grasped clearly and accurately by thousands of school-boys4 ,he therefore asserts1 positively1 that there are no lines without breadth1 and comes to the following extraordinary conclusions3 ,since1 however1 the breadth of the faintest line is so slight as to be incapable of measurement1 except by an instrument under the microscope1 it follows that the assumption that there can be lines without breadth is so nearly true that our senses1 when unassisted by art1 can not detect the error4 ,formerly1 and until the invention of the micrometer1 in the seventeenth century1 it was impossible to detect it at all4 ,hence1 the conclusions of the geometrician approximate so closely to truth that we are justified in accepting them as true4 ,the flaw is too minute to be perceived4 ,but that there is a flaw appears to me certain4 ,it appears certain that1 whenever something is kept back in the premises1 something must be wanting in the conclusion4 ,in all such cases1 the field of inquiry has not been entirely covered2 and part of the preliminary facts being suppressed1 it must1 ,i think1 be admitted that complete truth be unattainable1 and that no problem in geometry has been exhaustively solved4#e ,the fallacy which underlies ,mr4 ,buckle's contention is thus clearly exposed by the author of ,the ,natural ,history of ,hell4 ,if it be conceded that lines have breadth1 then all we have to do is to assign some definite breadth to each line--say the one-thousandth of an inch--and allow for it4 ,but the lines of the geometer have no breadth4 ,all the micrometers of which ,mr4 ,buckle speaks depend1 either directly or indirectly1 upon lines for their graduations1 and the positions of these lines are indicated by rulings or scratches4 ,now1 in even the finest of these rulings1 as1 for example1 those of ,nobert or ,fasoldt1 where the ruling or scratching1 together with its accompanying space1 amounts to no more than the one hundred and fifty thousandth part of an inch1 the scratch has a perceptible breadth4 ,but this broad scratch is not the line recognized by the microscopist1 to say nothing of the geometer4 ,the true line is a line which lies in the very center of this scratch and it is certain that this central line has absolutely no breadth at all4#f ,it must be very evident that if ,mr4 ,buckle's contention that geometrical lines have breadth were true1 then some of the fundamental axioms of geometry must be false4 ,it could no longer hold true that the whole is equal to all its parts taken together1 for if we divide a square or a circle into two parts by means of a line which has breadth1 the two parts cannot be equal to the whole as it formerly was4 ,as a matter of fact1 ,mr4 ,buckle's lines are saw-cuts1 not geometrical lines4 ,geometrical points1 lines1 and surfaces1 have no material existence and can have none4 ,an ideal conception and a material existence are two very different things4 ,a very interesting book#g has been written on the movements and feelings of the inhabitants of a world of two dimensions4 ,nevertheless1 if we know anything at all1 we know that such a world could not have any actual existence and when we attempt to form any mental conception of it and its inhabitants1 we are compelled to adopt1 to a certain extent1 the idea of the third dimension4 ,but at the same time we must remember that since the ordinary mechanic and the school-boy who has studied geometry1 find no difficulty in conceiving of points without magnitude1 lines without breadth1 and surfaces without thickness--conceptions which seem to have been impossible to ,buckle1 a man of acknowledged ability--it may be possible that minds constituted slightly differently from that of myself and some others1 might1 perhaps1 be able to form a conception of a fourth dimension4 ,leaving out of consideration the speculations of those who have woven this idea into romances and day-dreams we find that the hypothesis of a fourth dimension has been presented by two very different classes of thinkers1 and the discussion has been carried on from two very different standpoints4 ,the first suggestion of this hypothesis seems to have come from ,kant and ,gauss and to have had a purely metaphysical origin1 for1 although attempts have been made to trace the idea back to the famous phantoms of ,plato1 it is evident that the ideas then advanced had nothing in common with the modern theory of the existence of a fourth dimension4 ,the first hint seems to have been a purely mathematical one and did not attract any very general attention4 ,it was1 however1 seized upon by a certain branch of the transcendentalists1 closely allied to the spiritualists1 and was exploited by them as a possible explanation of some curious and mysterious phenomena and feats exhibited by certain ,indian and ,european devotees4 ,this may have been done merely for the purpose of mystifying and confounding their adversaries by bringing forward a striking illustration of ,hamlet's famous dictum-- ,there are more things in heaven and earth1 ,horatio1 ,than are dreamt of in your philosophy4 ,a very fair statement of this view is thus given by ,edward ,carpenter3#h ,there is another idea which modern science has been familiarizing us with1 and which is bringing us towards the same conception--that1 namely1 of the fourth dimension4 ,the supposition that the actual world has four space-dimensions instead of three makes many things conceivable which otherwise would be incredible4 ,it makes it conceivable that apparently separate objects1 e4 g41 distinct people1 are really physically united2 that things apparently sundered by enormous distances of space are really quite together2 that a person or other object might pass in and out of a closed room without disturbance of walls1 doors or windows1 etc41 and if this fourth dimension were to become a factor of our consciousness it is obvious that we should have means of knowledge which1 to the ordinary sense1 would appear simply miraculous4 ,there is much1 apparently1 to suggest that the consciousness attained to by the ,indian gnanis in their degree1 and by hypnotic subjects in theirs1 is of this fourth dimensional order4 ,as a solid is related to its own surface1 so1 it would appear1 is the cosmic consciousness related to the ordinary consciousness4 ,the phases of the personal consciousness are but different facets of the other consciousness2 and experiences which seem remote from each other in the individual are perhaps all equally near in the universal4 ,space itself1 as we know it1 may be practically annihilated in the consciousness of a larger space1 of which it is but the superficies2 and a person living in ,london may not unlikely find that he has a back door opening quite simply and unceremoniously out in ,bombay4 ,on the other hand1 the mathematicians1 looking at it as a purely speculative idea1 have endeavored to arrive at definite conclusions in regard to what would be the condition of things if the universe really exists in a fourth1 or even in some higher dimension4 ,professor ,w4 ,w4 ,r4 ,ball tells us that the conception of a world of more than three dimensions is facilitated by the fact that there is no difficulty in imagining a world confined to only two dimensions--which we may take for simplicity to be plane--though equally well it might be a spherical or other surface4 ,we may picture the inhabitants of flatland as moving either on the surface of a plane or between two parallel and adjacent planes4 ,they could move in any direction along the plane1 but they could not move perpendicularly to it1 and would have no consciousness that such a motion was possible4 ,we may suppose them to have no thickness1 in which case they would be mere geometrical abstractions2 or we may think of them as having a small but uniform thickness1 in which case they would be realities4 4 4 4 4 4 ,if an inhabitant of flatland was able to move in three dimensions1 he would be credited with supernatural powers by those who were unable so to move2 for he could appear or disappear at will2 could 7so far as they could tell7 create matter or destroy it1 and would be free from so many constraints to which the other inhabitants were subject that his actions would be inexplicable to them4 4 4 4 4 4 ,our conscious life is in three dimensions1 and naturally the idea occurs whether there may not be a fourth dimension4 ,no inhabitant of flatland could realize what life in three dimensions would mean1 though1 if he evolved an analytical geometry applicable to the world in which he lived1 he might be able to extend it so as to obtain results true of that world in three dimensions which would be to him unknown and inconceivable4 ,similarly we cannot realize what life in four dimensions is like1 though we can use analytical geometry to obtain results true of that world1 or even of worlds of higher dimensions4 ,moreover1 the analogy of our position to the inhabitants of flatland enables us to form some idea of how inhabitants of space of four dimensions would regard us4 4 4 4 4 4 ,if a finite solid was passed slowly through flatland1 the inhabitants would be conscious only of that part of it which was in their plane4 ,thus they would see the shape of the object gradually change and ultimately vanish4 ,in the same way1 if a body of four dimensions was passed through our space1 we should be conscious of it only as a solid body 7namely1 the section of the body by our space7 whose form and appearance gradually changed and perhaps ultimately vanished4 ,it has been suggested that the birth1 growth1 life1 and death of animals1 may be explained thus as the passage of finite four-dimensional bodies through our three-dimensional space4 ,attempts have been made to construct drawings and models showing a four-dimensional body4 ,the success of such attempts has not been very encouraging4 ,investigators of this class look upon the actuality of a fourth dimension as an unsolved question1 but they hold that1 provided we could see our way clear to adopt it1 it would open up wondrous possibilities in the way of explaining abstruse and hitherto inexplicable physical conditions and phenomena4 ,there is obviously no limit to such speculations1 provided we assume the existence of such conditions as are needed for our purpose4 ,too often1 however1 those who indulge in such day-dreams begin by assuming the impossible1 and end by imagining the absurd4 ,we have so little positive knowledge in regard to the ultimate constitution of matter and even in regard to the actual character of the objects around us1 which are revealed to us through our senses1 that the field in which our imagination may revel is boundless4 ,perhaps some day the humanity of the present will merge itself into a new race1 endowed with new senses1 whose revelations are to us1 for the present1 at least1 utterly inconceivable4 ,the possibility of such a development may be rendered more clear if we imagine the existence of a race devoid of the sense of hearing1 and without the organs necessary to that sense4 ,they certainly could form no idea of sound1 far less could they enjoy music or oratory1 such as afford us so much delight4 ,and1 if one or more of our race should visit these people1 how very strange to them would appear those curious appendages1 called ears1 which project from the sides of our heads1 and how inexplicable to them would be the movements and expressions of intelligence which we show when we talk or sing8 ,it is certain that no development of the physical or mathematical sciences could give them any idea whatever of the sensations which sound1 in its various modifications1 imparts to us1 and neither can any progress in that direction enable us to acquire any idea of the revelations which a new sense might open up to us4 ,nevertheless1 it seems to me that the development of new senses and new sense organs is not only more likely to be possible1 but that it is actually more probable1 than any revelation in regard to a fourth dimension4 ,,footnotes3 #e ,history of ,civilization in ,england4 ,american edition1 ,vol4 ,,ii1 page #cdb4 #f ,the ,natural ,history of ,hell1 by ,john ,phillipson1 page #cg4 #g ,flatland1 by ,e4 ,a4 ,abbott4 ,london1 #ahhd4 #h ,from ,adam's ,peak to ,elephanta-- page #afj4 ,,how ,a ,,space ,,may ,,be ,,apparently ,,enlarged ,,by ,,changing ,,its ,,shape ,the following is a curious illustration of the errors to which careless observers may be subject3 ,draw a square1 like ,fig4 #ai1 and divide the sides into #h parts each4 ,join the points of division in opposite sides so as to divide the whole square into #fd small squares4 ,then draw the lines shown in black and cut up the drawing into four pieces4 ,the lines indicating the cuts have been made quite heavy so as to show up clearly1 but on the actual card they may be made quite light4 ,now1 put the four pieces together1 so as to form the rectangle shown in ,fig4 #bj4 ,unless the scale1 to which the drawing is made is quite large and the work very accurate1 it will seem that the rectangle contains #e squares one way and #ac the other which1 when multiplied together1 give #fe for the number of small squares1 being an apparent gain of one square by the simple process of cutting4 ,illustration3 ,fig4 #ai4 ,illustration3 ,fig4 #bj4 ,this paradox is very apt to puzzle those who are not familiar with accurate drawings4 ,of course1 every person of common sense knows that the card or drawing is not made any larger by cutting it1 but where does the #feth small square come from8 ,on careful examination it will be seen that the line ,,ab1 ,fig4 #bj1 is not quite straight and the three parts into which it is divided are thus enabled to gain enough to make one of the small squares4 ,on a small scale this deviation from the straight line is not very obvious1 but make a larger drawing1 and make it carefully1 and it will readily be seen how the trick is done4 ,,can ,a ,,man ,,lift ,,himself ,,by ,,the ,,straps ,,of ,,his ,,boots8 ,i think it was the elder ,stephenson1 the famous engineer1 who told a man who claimed the honor of having invented a perpetual motion1 that when he could lift himself over a fence by taking hold of his waist-band1 he might hope to accomplish his object4 ,and the query which serves as a title for this article has long been propounded as one of the physical impossibilities4 ,and yet1 perhaps1 it might be possible to invent a waist-band or a boot-strap by which this apparently impossible feat might be accomplished6 ,travelers in ,mexico frequently bring home beans which jump about when laid on a table4 ,they are well-known as jumping beans and have often been a puzzle to those who were not familiar with the facts in the case4 ,each bean contains the larva of a species of beetle and this affords a clue to the secret4 ,but the question at once comes up3 ,how is the insect able to move1 not only itself1 but its house as well1 without some purchase or direct contact with the table8 ,the explanation is simple4 ,the hollow bean is elastic and the insect has strength enough to bend it slightly2 when the insect suddenly relaxes its effort and allows the bean to spring back to its former shape1 the reaction on the table moves the bean4 ,a man placed in a perfectly rigid box could never move himself by pressing on the sides1 but if the box were elastic and could be bent by the strength of the man inside1 it might be made to move4 ,a somewhat analogous result1 but depending on different principles1 is attained in certain curious boat races which are held at some ,english regattas and which is explained by ,prof4 ,w4 ,w4 ,rouse ,ball1 in his ,mathematical ,recreations and ,problems4 ,he says that it affords a somewhat curious illustration of the fact that commonly a boat is built so as to make the resistance to motion straight forward less than that to motion in the opposite direction4 ,the only thing supplied to the crew is a coil of rope1 and they have 7without leaving the boat7 to propel it from one point to another as rapidly as possible4 ,the motion is given by tying one end of the rope to the afterthwart1 and giving the other end a series of violent jerks in a direction parallel to the keel4 ,the effect of each jerk is to compress the boat4 ,left to itself the boat tends to resume its original shape1 but the resistance to the motion through the water of the stern is much greater than that of the bow1 hence1 on the whole1 the motion is forwards4 ,i am told that in still water a pace of two or three miles an hour can be thus attained4 ,,how ,a ,,spider ,,lifted ,a ,,snake ,one of the most interesting books in natural history is a work on ,insect ,architecture1 by ,rennie4 ,but if the architecture of insect homes is wonderful1 the engineering displayed by these creatures is equally marvellous4 ,long before man had thought of the saw1 the saw-fly had used the same tool1 made after the same fashion1 and used in the same way for the purpose of making slits in the branches of trees so that she might have a secure place in which to deposit her eggs4 ,the carpenter bee1 with only the tools which nature has given her1 cuts a round hole1 the full diameter of her body1 through thick boards1 and so makes a tunnel by which she can have a safe retreat1 in which to rear her young4 ,the tumble-bug1 without derrick or machinery1 rolls over large masses of dirt many times her own weight1 and the sexton beetle will1 in a few hours1 bury beneath the ground the carcass of a comparatively large animal4 ,all these feats require a degree of instinct which in a reasoning creature would be called engineering skill1 but none of them are as wonderful as the feats performed by the spider4 ,this extraordinary little animal has the faculty of propelling her threads directly against the wind1 and by means of her slender cords she can haul up and suspend bodies which are many times her own weight4 ,some years ago a paragraph went the rounds of the papers in which it was said that a spider had suspended an unfortunate mouse1 raising it up from the ground1 and leaving it to perish miserably between heaven and earth4 ,would-be philosophers made great fun of this statement1 and ridiculed it unmercifully4 ,i know not how true it was1 but ,i know that it might have been true4 ,some years ago1 in the village of ,havana1 in the ,state of ,new ,york1 a spider entangled a milk-snake in her threads1 and actually raised it some distance from the ground1 and this1 too1 in spite of the struggles of the reptile1 which was alive4 ,by what process of engineering did the comparatively small and feeble insect succeed in overcoming and lifting up by mechanical means1 the mouse or the snake8 ,the solution is easy enough if we only give the question a little thought4 ,the spider is furnished with one of the most efficient mechanical implements known to engineers1 viz41 a strong elastic thread4 ,that the thread is strong is well known4 ,indeed1 there are few substances that will support a greater strain than the silk of the silkworm1 or the spider2 careful experiment having shown that for equal sizes the strength of these fibers exceeds that of common iron4 ,but notwithstanding its strength1 the spider's thread alone would be useless as a mechanical power if it were not for its elasticity4 ,the spider has no blocks or pulleys1 and1 therefore1 it cannot cause the thread to divide up and run in different directions1 but the elasticity of the thread more than makes up for this1 and renders possible the lifting of an animal much heavier than a mouse or a snake4 ,this may require a little explanation4 ,let us suppose that a child can lift a six-pound weight one foot high and do this twenty times a minute4 ,furnish him with #cej rubber bands1 each capable of pulling six pounds through one foot when stretched4 ,let these bands be attached to a wooden platform on which stand a pair of horses weighing #b1ajj lbs41 or rather more than a ton4 ,if now the child will go to work and stretch these rubber bands1 singly1 hooking each one up1 as it is stretched1 in less than twenty minutes he will have raised the pair of horses one foot6 ,we thus see that the elasticity of the rubber bands enables the child to divide the weight of the horses into #cej pieces of six pounds each1 and at the rate of a little less than one every three seconds1 he lifts all these separate pieces one foot1 so that the child easily lifts this enormous weight4 ,each spider's thread acts like one of the elastic rubber bands4 ,let us suppose that the mouse or the snake weighed half an ounce and that each thread is capable of supporting a grain and a half4 ,the spider would have to connect the mouse with the point from which it was to be suspended with #aej threads1 and if the little quadruped was once swung off his feet1 he would be powerless4 ,by pulling successively on each thread and shortening it a little1 the mouse or snake might be raised to any height within the capacity of the building or structure in which the work was done4 ,so that to those who have ridiculed the story we may justly say3 ,there are more things in heaven and earth than are dreamed of in your philosophy4 ,what object the spider could have had in this work ,i am unable to see4 ,it may have been a dread of the harm which the mouse or snake might work1 or it may have been the hope that the decaying carcass would attract flies which would furnish food for the engineer4 ,i can vouch for the truth of the snake story1 however1 and the object of this article is to explain and render credible a very extraordinary feat of insect engineering4 ,,how ,,the ,,shadow ,,may ,,be ,,made ,,to ,,move ,,backward ,,on ,,the ,,sun-,,dial ,in the twentieth chapter of ,,ii ,kings1 at the eleventh verse we read1 that ,isaiah the prophet cried unto the ,lord1 and he brought the shadow ten degrees backward1 by which it had gone down in the dial of ,ahaz4 ,it is a curious fact1 first pointed out by ,nonez1 the famous cosmographer and mathematician of the sixteenth century1 but not generally known1 that by tilting a sun-dial through the proper angle1 the shadow at certain periods of the year can be made1 for a short time1 to move backwards on the dial4 ,this was used by the ,french encyclopaedists as a rationalistic explanation of the miracle which is related at the opening of this article4 ,the reader who is curious in such matters will find directions for constructing a dial1 for any latitude1 on which the shadow shall retrograde or move backwards1 in ,ozanam's ,recreations in ,science and ,natural ,philosophy1 ,riddle's edition1 page #ebi4 ,professor ,ball in his ,mathematical ,recreations1 page #bad1 gives a very clear explanation of the phenomenon4 ,the subject is somewhat too technical for these pages4 ,,how ,a ,,watch ,,may ,,be ,,used ,,as ,a ,,compass ,several years ago a correspondent of ,truth 7,london7 gave the following simple directions for finding the points of the compass by means of the ordinary pocket watch3 ,point the hour hand to the sun1 and south is exactly half way between the hour hand and twelve on the watch1 counting forward up to noon1 but backward after the sun has passed the meridian4 ,professor ,ball1 in his ,mathematical ,recreations and ,problems1 gives more complete directions and explanations4 ,he says3 ,the position of the sun relative to the points of the compass determines the solar time4 ,conversely1 if we take the time given by a watch as being the solar time 7and it will differ from it only by a few minutes at the most71 and we observe the position of the sun1 we can find the points of the compass4 ,to do this it is sufficient to point the hour-hand to the sun and then the direction which bisects the angle between the hour and the figure ,,xii will point due south4 ,for instance1 if it is four o'clock in the afternoon1 it is sufficient to point the hour-hand 7which is then at the figure ,,iiii7 to the sun1 and the figure ,,ii on the watch will indicate the direction of south4 ,again1 if it is eight o'clock in the morning1 we must point the hour-hand 7which is then at the figure ,,viii7 to the sun1 and the figure ,x on the watch gives the south point of the compass4 ,between the hours of six in the morning and six in the evening the angle between the hour and ,,xii1 which must be bisected is less than #ahj degrees1 but at other times the angle to be bisected is greater than #ahj degrees2 or perhaps it is simpler to say that at other times the rule gives the north point and not the south point4 ,the reason is as follows3 ,at noon the sun is due south1 and it makes one complete circuit round the points of the compass in #bd hours4 ,the hour-hand of a watch also makes one complete circuit in #ab hours4 ,hence1 if the watch is held with its face in the plane of the ecliptic1 and the figure ,,xii on the dial is pointed to the south1 both the hour-hand and the sun will be in that direction at noon4 ,both move round in the same direction1 but the angular velocity of the hour-hand is twice as great as that of the sun4 ,hence the rule4 ,the greatest error due to the neglect of the equation of time is less than #b degrees4 ,of course1 in practice1 most people would hold the face of the watch horizontal1 and in our latitude 7that of ,london7 no serious error would thus be introduced4 ,in the southern hemisphere1 or in any tropical country where at noon the sun is due north1 the rule will give the north point instead of the south4 ,,micrography ,,or ,,minute ,,writing ,,and ,,microphotography ,minute works of art have always excited the curiosity and commanded the admiration of the average man4 ,consequently ,cicero thought it worth while to record that the entire ,iliad of ,homer had been written upon parchment in characters so fine that the copy could be enclosed in a nutshell4 ,this has always been regarded as a marvelous feat4 ,there is in the ,french ,cabinet of ,medals a seal1 said to have belonged to ,michael ,angelo1 the fabrication of which must date from a very remote epoch1 and upon which fifteen figures have been engraved in a circular space of fourteen millimeters 74#ee inch7 in diameter4 ,these figures cannot be distinguished by the naked eye4 ,the ,ten ,commandments have been engraved in characters so fine that they could be stamped upon one side of a nickle five-cent piece1 and on several occasions the ,lord's ,prayer has been engraved on one side of a gold dollar1 the diameter of which is six-tenths of an inch4 ,i have also seen it written with a pen within a circle which measured four-tenths of an inch in diameter4 ,in the ,harleian manuscript1 #ecj1 there is an account of a rare piece of work1 brought to pass by ,peter ,bales1 an ,englishman1 and a clerk of the chancery4 ,d',israeli tells us that it was ,the whole ,bible in an ,english walnut1 no bigger than a hen's egg4 ,the nut holdeth the book3 there are as many leaves in his little book as in the great ,bible1 and he hath written as much in one of his little leaves as a great leaf of the ,bible4 ,by most people1 such achievements are considered marvels of skill1 and the newspaper accounts of them which are published always attract special attention4 ,and it must be acknowledged that such work requires good eyes1 steady nerves1 and very delicate control of the muscles4 ,but with ordinary writing materials there are certain mechanical limitations which must prevent even the most skilful from going very far in this direction4 ,these limitations are imposed by the fiber or grain of the paper and the construction of the ordinary pen1 neither of which can be carried beyond a certain very moderate degree of fineness4 ,of course1 the paper that is chosen will be selected on account of its hard1 even-grained surface1 and the pen will be chosen on account of the quality of its material and its shape1 and the point is always carefully dressed on a whetstone so as to have both halves of the nib equal in strength and length1 and the ends smooth and delicate4 ,when due preparation has been made1 and when the eyes and nerves of the writer are in good condition1 the smallness of the distinctly readable letters that may be produced is wonderful4 ,and in this connection it is an interesting fact that in many mechanical operations1 writing included1 the hand is far more delicate than the eye4 ,that which the unaided eye can see to write1 the unaided eye can see to read1 but the hand1 without the assistance or guidance of the eye1 can produce writing so minute that the best eyes cannot see to read it1 and yet1 when viewed under a microscope1 it is found to compare favorably with the best writing of ordinary size4 ,and those who are conversant with the more delicate operations of practical mechanics1 know that this is no exceptional case4 ,the only aid given by the eye in the case of such minute writing is the arrangement of the lines1 otherwise the writing could be done as well with the eyes shut as open4 ,since the mechanical limitations which we have noted prevent us from going very far with the instruments and materials mentioned1 the next step is to adopt a finer surface and a sharper point4 ,these conditions may be found in the fine glazed cards and the metal pencils or styles used by card writers4 ,in these cards the surface is nearly homogeneous1 that is to say1 free from fibers1 and the point of the metal pencil may be made as sharp as a needle1 but to utilize these conditions to the fullest extent1 it is necessary to aid the eye1 and a magnifier is1 therefore1 brought into use4 ,under a powerful glass the hand may be so guided by the eye that the writing produced cannot be read by the unaided vision4 ,the specimens of fine writing thus far described have been produced directly by the hand under the guidance either of a magnifier or the simple sense of motion4 ,just how far it would be possible to go by these means has never been determined1 so far as ,i know1 but those who have examined the specimens of selected diatoms and insect scales in which objects that are utterly invisible to the naked eye are arranged with great accuracy so as to form the most beautiful figures1 can readily believe that a combination of microscopical dexterity and skill in penmanship might easily go far beyond anything that has yet been accomplished in this direction1 either in ancient or modern times4 ,but by means of a very simple mechanical arrangement1 the motion of the hand in every direction may be accurately reduced or enlarged to almost any extent1 and it thus becomes possible to form letters which are inconceivably small4 ,the instrument by which this is accomplished is known as a pantagraph1 and it has1 within a few years1 become quite popular as a means of reducing or enlarging pictures of various kinds1 including crayon reproductions of photographs4 ,its construction and use are1 therefore1 very generally understood4 ,it was by means of a very finely-made instrument embodying the principles of the pantagraph that the extraordinarily fine work which we are about to describe was accomplished4 ,it is obvious1 however1 that in order to produce very fine writing we must use a very fine pen or point and the finer the point the sooner does it wear out1 so that in a very short time the lines which go to form the letters become thick and blurred and the work is rendered illegible4 ,as a consequence of this1 when the finest specimens of writing are required1 it is necessary to abandon the use of ordinary points and surfaces and to resort to the use of the diamond for a pen1 and glass for a surface upon which to write4 ,one of the earliest attempts in this direction was that of ,m4 ,froment1 of ,paris1 who engraved on glass1 within a circle1 the one-thirtieth of an inch in diameter1 the ,coat of ,arms of ,england--lion1 unicorn1 and crown--with the following inscription1 partly in ,roman letters1 partly in script3 ,honi soit qui mal y pense1 ,her ,most ,gracious ,majesty1 ,queen ,victoria1 and ,his ,royal ,highness1 ,prince ,albert1 ,dieu et mon droit4 ,written on occasion of the ,great ,exhibition1 by ,froment1 a ,paris1 #ahea4 ,the late ,dr4 ,barnard1 ,president of ,columbia ,college1 had in his possession a copy of the device borne by the seal of ,columbia ,college1 ,new ,york1 executed for him by ,m4 ,dumoulin-,froment1 within a circle less than three one-hundredths of an inch in diameter1 in which are embraced four human figures and various other objects1 together with inscriptions in ,latin1 ,greek1 and ,hebrew1 all clearly legible4 ,in this device the rising sun is represented in the horizon1 the diameter of the disk being about three one-thousandths of an inch4 ,this disk has been cross-hatched by the draughtsman in the original design from which the copy was made2 and the copy shows the marks of the cross-hatching with perfect distinctness4 ,when this beautiful and delicate drawing is brought clearly out by a suitably adjusted illumination1 the lines appear as if traced by a smooth point in a surface of opaque ice4 ,lardner1 in his book on the ,microscope1 published in #ahef1 gives a wood cut which shows the first piece of engraving magnified #abj diameters1 but he said that he was not at liberty to describe the method by which it was done4 ,as happens in almost all such cases1 however1 the very secrecy with which the process was surrounded naturally stimulated others to rival or surpass it1 and ,mr4 ,n4 ,peters1 a ,london banker1 turned his attention to the subject and soon invented a machine which produced results far exceeding anything that ,m4 ,froment had accomplished4 ,on ,april #be1 #ahee1 ,mr4 ,farrants read before the ,microscopical ,society of ,london a full account of the ,peters machine1 with which the inventor had written the ,lord's ,prayer 7in the ordinary writing character1 without abbreviation or contraction of any kind71 in a space not exceeding the one hundred and fifty-thousandth of a square inch4 ,seven years later1 ,mr4 ,farrants1 as ,president of the ,microscopical ,society1 described further improvements in the machine of ,mr4 ,peters1 and made the following statement3 ,the ,lord's ,prayer has been written and may be read in the one-three hundred and fifty-six thousandth of an ,english square inch4 ,the measurements of one of these specimens was verified by ,dr4 ,bowerbank1 with a difference of not more than one five-millionth of an inch1 and that difference1 small as it is1 arose from his not including the prolongation of the letter f in the sentence 'deliver us from evil'2 so he made the area occupied by the writing less than that stated above4 ,some idea of the minuteness of the characters in these specimens may be obtained from the statement that the whole ,bible and ,testament1 in writing of the same size1 might be placed twenty-two times on the surface of a square inch4 ,the grounds for this startling assertion are as follows3 ,the ,bible and ,testament together1 in the ,english language1 are said to contain #c1eff1dhj letters4 ,the number of letters in the ,lord's ,prayer1 as written1 ending in the sentence1 'deliver us from evil1' is #bbc1 whence1 as #c1eff1dhj divided by #bbc1 is equal to #ae1ibb1 it appears that the ,bible and ,testament together contain the same number of letters as the ,lord's ,prayer written #af1jjj times2 if then the prayer were written in #a-af1jjj of an inch1 the ,bible and ,testament in writing of the same size would be contained by one square inch2 but as #a-cef1jjjth of an inch is one twenty-secondth part of #a-ae1ibb of an inch1 it follows that the ,bible and ,testament1 in writing of that size1 would occupy less space than one twenty-secondth of a square inch4 ,it only now remains to be seen that1 minute as are the letters written by this machine1 they are characterized by a clearness and precision of form which proves that the moving parts of the machine1 while possessing the utmost delicacy of freedom1 are absolutely destitute of shake1 a union of requisites very difficult of fulfilment1 but quite indispensable to the satisfactory performance of the apparatus4 ,i have no information in regard to the present whereabouts of any of the specimens turned out by ,mr4 ,peters1 and inquiry in ,london1 among persons likely to know1 has not supplied any information on the subject4 ,there was1 however1 another micrographer1 ,mr4 ,william ,webb1 of ,london1 who succeeded in producing some marvellous results4 ,epigrams and also the ,lord's ,prayer written in the one-thousandth part of a square inch have been freely distributed4 ,mr4 ,webb also produced a few copies of the second chapter of the ,gospel1 according to ,st4 ,john1 written on the scale of the whole ,bible1 to a little more than three-quarters of a square inch1 and of the ,lord's ,prayer written on the scale of the whole ,bible eight times on a square inch4 ,mr4 ,webb died about fifteen years ago1 and ,i believe he has had no successor in the art4 ,specimens of his work are quite scarce1 most of them having found their way into the cabinets of public ,museums and ,societies1 who are unwilling to part with them4 ,the late ,dr4 ,woodward1 ,director of the ,army ,medical ,museum1 ,washington1 ,d4,c41 procured two of them on special order for the ,museum4 ,mr4 ,webb had brought out these fine writings as tests for certain qualities of the microscope1 and it was to serve as tests for high-power objectives that ,dr4 ,woodward procured the specimens now in the microscopical department of the ,museum4 ,i am so fortunate as to have in my possession two specimen's of ,mr4 ,webb's work4 ,one is an ordinary microscopical glass slide1 three inches by one1 and in the center is a square speck which measures #a-deth of an inch on the side4 ,upon this square is written the whole of the second chapter of the ,gospel according to ,st4 ,john--the chapter which contains the account of the marriage in ,cana of ,galilee4 ,in order to estimate the space which the whole ,bible would occupy if written on the same scale as this chapter1 ,i have made the following calculation which1 ,i think1 will be more easily followed and checked by my readers1 than that of ,mr4 ,farrants4 ,the text of the old version of the ,bible1 as published in minion by the ,american ,bible ,society1 contains #abgb pages1 exclusive of title pages and blanks4 ,each page contains two columns of #eh lines each1 making #aaf lines to the page4 ,this includes the headings of the chapters and the synopses of their contents1 which are1 therefore1 thrown in to make good measure4 ,we have1 therefore1 #abgb pages of #aaf lines each1 making a total of #adg1eeb lines4 ,the second chapter of ,st4 ,john has #be verses containing #ie lines1 and is written on the #a-bjbeth of an inch1 or1 in other words1 it would go #bjbe times on a square inch4 ,a square inch would1 therefore1 contain #ie x #bjbe or #aib1cge lines4 ,this number 7#aib1cge71 divided by the number of lines in the ,bible 7#adg1eeb71 gives #a4cjg1 which is the number of times the ,bible might be written on a square inch in letters of the same size4 ,in other words1 the whole ,bible might be written on 4#gg inch1 or very little more than three-quarters of a square inch4 ,perhaps the following gives a more impressive illustration3 ,the ,united ,states silver quarter of a dollar is 4#ie inch in diameter1 so that the surface of each side is 4#gjg of a square inch4 ,the whole ,bible would1 therefore1 very nearly go on one side of a quarter of a dollar4 ,if the blank spaces at the heads of the chapters and the synopses of contents were left out1 it would easily go on one side4 ,the second specimen1 which ,i have of ,mr4 ,webb's writing1 is a copy of the ,lord's ,prayer written on a scale of eight ,bibles to the square inch4 ,according to a statement kindly sent me by the superintendent of the ,united ,states ,mint at ,philadelphia1 the diameter of the last issued gold dollar1 and also of the silver half-dime1 is six-tenths of an inch4 ,this gives 4#bhbg of a square inch as the area of the surface of one side1 and1 therefore1 the whole ,bible might be written more than two and a quarter times on one side of either the gold dollar or the silver half dime4 ,such numerical and space relations are far beyond the power of any ordinary mind to grasp4 ,with the aid of a microscope we can see the object and compare with other magnifications the rate at which it is enlarged1 and a person of even the most ordinary education can follow the calculation and understand why the statements are true1 but the final result1 like the duration of eternity or the immensity of space1 conveys no definite idea to our minds4 ,but at the same time we must carefully distinguish between our want of power to grasp these ideas and our inability to form a conception of some inconceivable subject1 such as a fourth dimension or the mode of action of a new sense4 ,wonderful as these achievements are1 there is another branch of the microscopic art which1 from the practical applications that have been made of it1 is even more interesting4 ,this is the art of microphotography4 ,about the middle of the last century ,mr4 ,j4 ,b4 ,dancer1 of ,manchester1 ,england1 produced certain minute photographs of well-known pictures and statues which commanded the universal attention of the microscopists of that day1 and for a time formed the center of attraction at all microscopical exhibitions4 ,they have now1 however1 become so common that they receive no special notice4 ,mr4 ,dancer and other artists also produced copies of the ,lord's ,prayer1 the ,creed1 the ,declaration of ,independence1 etc41 on such a scale that the ,lord's ,prayer might be covered with the head of a common pin1 and yet1 when viewed under a very moderate magnifying power1 every letter was clear and distinct4 ,i have now before me a slip of glass1 three inches long and one inch wide1 in the center of which is an oval photograph which occupies less than the #a-bjjth of a square inch4 ,this photograph contains the ,declaration of ,independence with the signatures of all the signers1 surrounded by portraits of the ,presidents and the seals of the original thirteen ,states4 ,under a moderate power every line is clear and distinct4 ,in the same way copies of such famous pictures as ,landseer's ,stag at ,bay1 although almost invisible to the naked eye1 come out beautifully clear and distinct under the microscope1 so that it has been suggested that one might have an extensive picture gallery in a small box1 or pack away copies of all the books in the ,congressional ,library in a small hand-bag4 ,with such means at our command1 it would be a simple matter to condense a bulky dispatch into a few little films1 which might be carried in a quill or concealed in ways which would have been impossible with the original4 ,if ,major ,andre had been able to avail himself of this mode of reducing the bulk of the original papers1 he might have carried1 without danger of discovery1 those reports which caused his capture and led to his death4 ,and hereafter the ordinary methods of searching suspected spies will have to be exchanged for one that is more efficient4 ,the most interesting application of microphotography1 of which we have any record1 occurred during the ,franco-,prussian war in #ahgj-ga4 ,illustration3 ,fig4 #ba4 ,on ,september #ba1 #ahgj1 the ,germans so completely surrounded the ,french capitol1 that all communication by roads1 railways1 and telegraphs1 was cut off and the only way of escape from the city was through the air4 ,on ,april #bc1 the first balloon left ,paris1 and in a short time after that1 a regular balloon post was established1 letters and packages being sent out at intervals of three to seven days4 ,in order to get news back to the city1 carrier pigeons were employed1 and at first the letters were simply written on very thin paper and enclosed in quills which were fastened to the middle tail-feather of the bird1 as shown in the engraving1 ,fig4 #ba4 ,it is1 of course1 needless to say1 that the ordinary pictures of doves with letters tied round their necks or love-notes attached to their wings1 are all mere romance4 ,a bird loaded in that way would soon fall a prey to its enemies4 ,as it was1 some of the pigeons were shot by ,german gunners or captured by hawks trained by the ,germans for the purpose1 but the great majority got safely through4 ,written communications1 however1 were of necessity1 bulky and heavy1 and therefore ,m4 ,dagron1 a ,parisian photographer1 suggested that the news be printed in large sheets of which microphotographs could be made and transferred to collodion positives which might then be stripped from the glass and would be very light4 ,this was done2 the collodion pellicles measuring about ten centimeters 7four inches7 square and containing about three thousand average messages4 ,eighteen of these pellicles weighed less than one gramme 7fifteen grains7 and were easily carried by a single pigeon4 ,the pigeons having been bred in ,paris and sent out by balloons1 always returned to their dove-cotes in that city4 ,m4 ,dagron left ,paris by balloon on ,november #ab1 and after a most adventurous voyage1 being nearly captured by a ,german patrol1 he reached ,tours and there established his headquarters1 and organized a regular system of communication with the capitol4 ,the results were most satisfactory1 upwards of two and a half millions of messages having been sent into the city4 ,even postal orders1 and drafts were transmitted in this way and duly honored4 ,and thus through the pigeon-post1 aided by microphotography1 ,paris was enabled to keep in touch with the outer world1 and the anxiety of thousands of families was relieved4 ,it is not likely1 however1 that the pigeon-post will ever again come into use for this purpose2 our interest in it is now merely historical1 for in the next great siege1 if we ever have one1 the wireless telegraph will no doubt take its place and messages1 which no hawks can capture and no guns can destroy1 will be sent directly over the heads of the besiegers4 ,but let us hope and pray1 that the savage and unnecessary war which is now being waged in the east will be the last1 and that in the near future1 two or more of the great nations of the globe will so police the world1 that peace on earth and good will toward men will everywhere prevail4 ,,illusions ,,of ,,the ,,senses ,our senses have been called the ,five ,gateways of ,knowledge because all that we know of the world in which we live reaches the mind1 either directly or indirectly1 through these avenues4 ,from the ivory palace1 in which she dwells apart1 and which we call the skull1 the mind sends forth her scouts--sight1 hearing1 feeling1 taste1 and smell--bidding them bring in reports of all that is going on around her1 and if the information which they furnish should be untrue or distorted1 the most dire results might follow4 ,she1 therefore1 frequently compares the tale that is told by one with the reports from the others1 and in this way it is found that under some conditions these reporters are anything but reliable2 the stories which they tell are often distorted and untrue1 and in some cases their tales have no foundation whatever in fact1 but are the unsubstantial fabric of a vision4 ,it is1 therefore1 of the greatest importance to us1 that we should find out the points on which these information bearers are most likely to be deceived so that we may guard against the errors into which they would otherwise certainly lead us4 ,all the senses are liable to be imposed upon under certain conditions4 ,the senses of taste and of smell are frequently the subject of phantom smells and tastes1 which are as vivid as the sensations produced by physical causes acting in the regular way4 ,even those comparatively new senses#i which have been differentiated from the sense of touch and which1 with the original five1 make up the mystic number seven1 are very untrustworthy guides under certain circumstances4 ,thus we all know how the sense of heat may be deceived by the old experiment of placing one hand in a bowl of cold water and the other in a bowl of hot water1 and then1 after a few minutes1 placing both hands together in a bowl of tepid water2 the hand1 which has been in the cold water will feel warm1 while that which has just been taken from the hot water1 will feel quite cold4 ,we have all experienced the deceptions to which the sense of hearing exposes us4 ,who has not heard sounds which had no existence except in our own sensations8 ,and every one is familiar with the illusions to which we are liable when under the influence of a skilful ventriloquist4 ,even the sense of touch1 which most of us regard as infallible1 is liable to gross deception4 ,when we have felt anything we are always confident as to its shape1 number1 hardness1 etc41 but the following very simple experiment shows that this confidence may be misplaced3 ,illustration3 ,fig4 #bb4 ,take a large pea or a small marble or bullet and place it on the table or in the palm of the left hand4 ,then cross the fingers of the right hand as shown in the engraving1 ,fig4 #bb1 the second finger crossing the first1 and place them on the ball1 so that the latter may lie between the fingers1 as figured in the cut4 ,if the pea or ball be now rolled about1 the sensation is apparently that given by two peas under the fingers1 and this illusion is so strong that it cannot be dispelled by calling in any of the other senses 7the sense of sight for example7 as is usually the case under similar circumstances4 ,we may try and try1 but it will only be after considerable experience that we shall learn to disregard the apparent impression that there are two balls4 ,the cause of this illusion is readily found4 ,in the ordinary position of the fingers the same ball cannot touch at the same time the exterior sides of two adjoining fingers4 ,when the two fingers are crossed1 the conditions are exceptionally changed1 but the instinctive interpretation remains the same1 unless a frequent repetition of the experiment has overcome the effect of our first education on this point4 ,the experiment1 in fact has to be repeated a great number of times to make the illusion become less and less appreciable4 ,but of all the senses1 that of sight is the most liable to error and illusion1 as the following simple illustrations will show4 ,illustration3 ,fig4 #bc4 ,illustration3 ,fig4 #bd4 ,in ,fig4 #bc a black spot has been placed on a white ground1 and in ,fig4 #bd a white spot is placed on a black ground2 which is the larger1 the black spot or the white one8 ,to every eye the white spot will appear to be the largest1 but as a matter of fact they are both the same size4 ,this curious effect is attributed by ,helmholtz to what is called irradiation4 ,the eye may also be greatly deceived even in regard to the length of lines placed side by side4 ,thus1 in ,fig4 #be a thin vertical line stands upon a thick horizontal one2 although the two lines are of precisely the same length1 the vertical one seems to be considerably longer than the other4 ,illustration3 ,fig4 #be4 ,in ,figs4 #bf and #bg a series of vertical and horizontal lines are shown1 and in both forms the space that is covered seems to be longer one way than the other4 ,as a matter of fact the space in each case is a perfect square1 and the apparent difference in width and height depends upon whether the lines are vertical or horizontal4 ,illustration3 ,fig4 #bf4 ,illustration3 ,fig4 #bg4 ,advantage is taken of this curious illusion in decorating rooms and in selecting dresses4 ,stout ladies of taste avoid dress goods having horizontal stripes1 and ladies of the opposite conformation avoid those in which the stripes are vertical4 ,but the greatest discrepancy is seen in ,figs4 #bh and #bi1 the middle line in ,fig4 #bi appearing to be much longer than in ,fig4 #bh4 ,careful measurement will show that they are both of precisely the same length1 the apparent difference being due to the arrangement of the divergent lines at the ends4 ,illustration3 ,fig4 #bh4 ,illustration3 ,fig4 #bi4 ,illustration3 ,fig4 #cj4 ,converging lines have a curious effect upon apparent size4 ,thus in ,fig4 #cj we have a wall and three posts1 and if asked which of the posts was the highest1 most persons would name ,c1 but measurement will show that ,a is the highest and that ,c is the shortest4 ,illustration3 ,fig4 #ca4 ,a still more striking effect is produced in two parallel lines by crossing them with a series of oblique lines as seen in ,figs4 #ca and #cb4 ,in ,fig4 #ca the horizontal lines seem to be much closer at the right-hand ends than at the left1 but accurate measurement will show that they are strictly parallel4 ,by changing the direction of the oblique lines1 as shown in ,fig4 #cb1 the horizontal lines appear to be crooked although they are perfectly straight4 ,illustration3 ,fig4 #cb4 ,all these curious illusions are1 however1 far surpassed by an experiment which we will now proceed to describe4 ,,footnotes3 #i ,the old and generally recognized list of the senses is as follows3 ,sight1 ,hearing1 ,smell1 ,taste1 and ,touch4 ,this is the list enumerated by ,john ,bunyan in his famous work1 ,the ,holie ,warre4 ,it has1 however1 been pointed out that the sense which enables us to recognize heat is not quite the same as that of touch and modern physiologists have therefore set apart1 as a distinct sense1 the power by which we recognize heat4 ,the same had been previously done in the case of the sense of ,muscular ,resistance but1 as the author of ,the ,natural ,history of ,hell says1 when we differentiate the ',sense of ,heat1' and the ',sense of ,resistance' from the ,sense of ,touch1 we may set up new signposts1 but we do not open up any new 'gateways'1 things still remain as they were of old1 and every messenger from the material world around us must enter the ivory palace of the skull through one of the old and well-known ways4 ,,objects ,,apparently ,,seen ,,through ,a ,,hole ,,in ,,the ,,hand ,the following curious experiment always excites surprise1 and as ,i have met with very few persons who have ever heard of it1 ,i republish it from ,the ,young ,scientist1 for ,november1 #ahhj4 ,it throws a good deal of light upon the facts connected with vision4 ,illustration3 ,fig4 #cc4 ,procure a paste-board tube about seven or eight inches long and an inch or so in diameter1 or roll up a strip of any kind of stiff paper so as to form a tube4 ,holding this tube in the left hand1 look through it with the left eye1 the right eye also being kept open4 ,then bring the right hand into the position shown in the engraving1 ,fig4 #cc1 the edge opposite the thumb being about in line with the right-hand side of the tube4 ,or the right hand may rest against the right-hand side of the tube1 near the end farthest from the eye4 ,this cuts off entirely the view of the object by the right eye1 yet strange to say the object will still remain apparently visible to both eyes through a hole in the hand1 as shown by the dotted lines in the engraving6 ,in other words1 it will appear to us as if there was actually a hole through the hand1 the object being seen through that hole4 ,the result is startlingly realistic1 and forms one of the simplest and most interesting experiments known4 ,this singular optical illusion is evidently due to the sympathy which exists between the two eyes1 from our habit of blending the images formed in both eyes so as to give a single image4 ,,looking ,,through ,a ,,solid ,,brick ,a very common exhibition by street showmen1 and one which never fails to excite surprise and draw a crowd1 is the apparatus by which a person is apparently enabled to look through a brick4 ,mounted on a simple-looking stand are a couple of tubes which look like a telescope cut in two in the middle4 ,looking through what most people take for a telescope1 we are not surprised when we see clearly the people1 buildings1 trees1 etc41 beyond it1 but this natural expectation is turned into the most startled surprise when it is found that the view of these objects is not cut off by placing a common brick between the two parts of the telescope and directly in the apparent line of vision1 as shown in the accompanying illustration1 ,fig4 #cd4 ,illustration3 ,fig4 #cd4 ,in truth1 however1 the observer looks round the brick instead of through it1 and this he is enabled to do by means of four mirrors ingeniously arranged as shown in the engraving4 ,as the mirrors and the lower connecting tube are concealed1 and the upright tubes supporting the pretended telescope1 though hollow1 appear to be solid1 it is not very easy for those who are not in the secret to discover the trick4 ,of course any number of fake explanations are given by the showman who always manages to keep up with the times and exploit the latest mystery4 ,at one time it was psychic force1 then ,roentgen or ,x-rays2 lately it has been attributed to the mysterious effects of radium6 ,this illustration is more properly a delusion2 there is no illusion about it4 ,,curious ,,arithmetical ,,problems ,,the ,,chess-,,board ,,problem ,an ,arabian author1 ,al ,sephadi1 relates the following curious anecdote3 ,a mathematician named ,sessa1 the son of ,dahar1 the subject of an ,indian ,prince1 having invented the game of chess1 his sovereign was highly pleased with the invention1 and wishing to confer on him some reward worthy of his magnificence1 desired him to ask whatever he thought proper1 assuring him that it should be granted4 ,the mathematician1 however1 only asked for a grain of wheat for the first square of the chess-board1 two for the second1 four for the third1 and so on to the last1 or sixty-fourth4 ,the prince at first was almost incensed at this demand1 conceiving that it was ill-suited to his liberality4 ,by the advice of his courtiers1 however1 he ordered his vizier to comply with ,sessa's request1 but the minister was much astonished when1 having caused the quantity of wheat necessary to fulfil the prince's order to be calculated1 he found that all the grain in the royal granaries1 and even all that in those of his subjects and in all ,asia1 would not be sufficient4 ,he therefore informed the prince1 who sent for the mathematician1 and candidly acknowledged that he was not rich enough to be able to comply with his demand1 the ingenuity of which astonished him still more than the game he had invented4 ,it will be found by calculation that the sixty-fourth term of the double progression1 beginning with unity1 is #i1bbc1cgb1jcf1hed1gge1hjh1 and the sum of all the terms of this double progression1 beginning with unity1 may be obtained by doubling the last term and subtracting the first from the sum4 ,the number1 therefore1 of the grains of wheat required to satisfy ,sessa's demand will be #ah1ddf1gdd1jgc1gji1eea1fae4 ,now1 if a pint contains #i1baf grains of wheat1 a gallon will contain #gc1gbh1 and a bushel 7#h gallons7 will contain #ehi1ghd4 ,dividing the number of grains by this quantity1 we get #ca1bgd1iig1dab1bie for the number of bushels necessary to discharge the promise of the ,indian prince4 ,and if we suppose that one acre of land is capable of producing in one year1 thirty bushels of wheat1 it would require #a1jdb1dii1iac1gdc acres1 which is more than eight times the entire surface of the globe2 for the diameter of the earth being taken at #g1icj miles1 its whole surface1 including land and water1 will amount to very little more than #abf1dcg1hhi1agg square acres4 ,if the price of a bushel of wheat be estimated at one dollar1 the value of the above quantity probably exceeds that of all the riches on the earth4 ,,the ,,nail ,,problem ,a gentleman took a fancy to a horse1 and the dealer1 to induce him to buy1 offered the animal for the value of the twenty-fourth nail in his shoe1 reckoning one cent for the first nail1 two for the second1 four for the third1 and so on4 ,the gentleman1 thinking the price very low1 accepted the offer4 ,what was the price of the horse8 ,on calculating1 it will be found that the twenty-fourth term of the progression #a1 #b1 #d1 #h1 #af1 etc41 is #h1chh1fjh1 or #hc1hhf4jh1 a sum which is more than any horse1 even the best ,arabian1 was ever sold for4 ,had the price of the horse been fixed at the value of all the nails1 the sum would have been double the above price less the first term1 or #afg1ggb4ae4 ,a ,,question ,,of ,,population ,the following note on the result of unrestrained propagation for one hundred generations is taken from ,familiar ,lectures on ,scientific ,subjects1 by ,sir ,john ,f4 ,w4 ,herschel3 ,for the benefit of those who discuss the subjects of population1 war1 pestilence1 famine1 etc41 it may be as well to mention that the number of human beings living at the end of the hundredth generation1 commencing from a single pair1 doubling at each generation 7say in thirty years71 and allowing for each man1 woman1 and child1 an average space of four feet in height and one foot square1 would form a vertical column1 having for its base the whole surface of the earth and sea spread out into a plane1 and for its height #c1fgd times the sun's distance from the earth6 ,the number of human strata thus piled1 one on the other1 would amount to #dfj1gij1jjj1jjj1jjj4 ,in this connection the following facts in regard to the present population of the globe may be of interest3 ,the present population of the entire globe is estimated by the best statisticians at between fourteen and fifteen hundred millions of persons4 ,this number would easily find standing-room on one half of ,long ,island1 in the ,state of ,new ,york4 ,if this entire population were to be brought to the ,united ,states1 we could easily give every man1 woman1 and child1 one acre and a half each1 or a nice little farm of seven acres and a half to every family1 consisting of a man1 his wife1 and three children4 ,this question has also an important bearing on the preservation of animals which1 in limited numbers1 are harmless and even desirable4 ,in ,australia1 where the restraints on increase are slight1 the rabbit soon becomes not only a nuisance but a menace1 and in this country the migratory thrush or robin1 as it is generally called1 has been so protected in some localities that it threatens to destroy the small fruit industry4 ,,how ,,to ,,become ,a ,,millionaire ,many plans have been suggested for getting rich quickly1 and some of these are so plausible and alluring that multitudes have been induced to invest in them the savings which had been accumulated by hard labor and severe economy4 ,it is needless to say that1 except in the case of a few stool-pigeons1 who were allowed to make large profits so that their success might deceive others and lead them into the net1 all these projects have led to disaster or ruin4 ,it is a curious fact1 however1 that some of those who invested in such get-rich-quickly schemes were probably fully aware of their fraudulent character and went into the speculation with their eyes open in the hope that they might be allowed to become the stool-pigeons1 and in this way come out of the enterprise with a large balance on the right side4 ,no regret can be felt when a bird of this kind gets plucked4 ,but by the following simple method every one may become his own promoter and in a short time accumulate a respectable fortune4 ,it would seem that almost any one could save one cent for the first day of the month1 two cents for the second1 four for the third1 and so on4 ,now if you will do this for thirty days we will guarantee you the possession of quite a nice little fortune4 ,see how easy it is to become a millionaire on paper1 and by the way1 it is only on paper that such schemes ever succeed4 ,if1 however1 you should have any doubt in regard to your ability to lay aside the required amount each day1 perhaps you can induce some prosperous and avaricious employer to accept the following tempting proposition3 ,offer to work for him for a year1 provided he pays you one cent for the first week1 two cents for the second1 four for the third1 and so on to the end of the term4 ,surely your services would increase in value in a corresponding ratio1 and many business men would gladly accept your terms4 ,we ourselves have had such a proposition accepted over and over again2 the only difficulty was that when we insisted upon security for the last instalment of our wages1 our would-be employers could never come to time4 ,and we would strongly urge upon our readers that if they ever make such a bargain1 they get full security for the last payment for they will find that when it becomes due there will not be money enough in the whole world to satisfy the claim4 ,the entire amount of all the money in circulation among all the nations of the world 7not the wealth7 is estimated at somewhat less than #ae1jjj1jjj1jjj1 and the last payment would amount to fifteen hundred times that immense sum4 ,the ,french have a proverb that it is the first step that costs 7c'est le premier pas qui coute7 but in this case it is the last step that costs and it costs with a vengeance4 ,while on this subject let me suggest to my readers to figure up the amount of which they will be possessed if they will begin at fifteen years of age and save ten cents per week for sixty years1 depositing the money in a savings bank as often as it reaches the amount required for a deposit1 and adding the interest every six months4 ,most persons will be surprised at the result4 ,,the ,,actual ,,cost ,,and ,,present ,,value ,,of ,,the ,,first ,,folio ,,shakespeare ,seven years after the death of ,shakespeare1 his collected works were published in a large folio volume1 now known as ,the ,first ,folio ,shakespeare4 ,this was in the year #afbc4 ,the price at which the volume was originally sold was one pound1 but perhaps we ought to take into consideration the fact that at that time money had a value1 or purchasing power1 at least eight times that which it has at present2 ,halliwell-,phillips estimates it at from twelve to twenty times its present value4 ,for this circumstance1 however1 full allowance may be made by multiplying the ultimate result by the proper number4 ,this folio is regarded as the most valuable printed book in the ,english language--the last copy that was offered for sale in good condition having brought the record price of nearly #i1jjj1 so that it is safe to assume that a perfect copy1 in the condition in which it left the publisher's hands1 would readily command #aj1jjj1 and the question now arises3 ,what would be the comparative value of the present price1 #aj1jjj1 and of the original price 7one pound7 placed at interest and compounded every year since #afbc8 ,over and over again ,i have heard it said that the purchasers of the ,first ,folio had made a splendid investment and the same remark is frequently used in reference to the purchase of books in general1 irrespective of the present intellectual use that may be made of them4 ,let us make the comparison4 ,money placed at compound interest at six per cent1 a little more than doubles itself in twelve years4 ,at the present time and for a few years back1 six per cent is a high rate1 but it is a very low rate for the average4 ,during a large part of the time money brought eight1 ten1 and twelve per cent per annum1 and even within the half century just past it brought seven per cent during a large portion of the time4 ,now1 between #afbc and #ahii1 there are #bc periods1 of #ab years each1 and at double progression the twenty-third term1 beginning with unity1 would be #h1chh1fjh4 ,this1 therefore1 would be the amount1 in pounds1 which the volume had cost up to #ahii4 ,in dollars it would be #dj1gid1hgh4hh4 ,an article which costs forty millions of dollars1 and sells for ten thousand dollars1 cannot be called a very good financial investment4 ,from a literary or intellectual standpoint1 however1 the subject presents an entirely different aspect4 ,some time ago ,i asked one of the foremost ,shakespearian scholars in the world if he had a copy of the ,first ,folio4 ,his reply was that he could not afford it2 that it would not be wise for him to lose #djj to #ejj per year for the mere sake of ownership1 when for a very slight expenditure for time and railway fare he could consult any one of half-a-dozen copies whenever he required to do so4 ,,arithmetical ,,puzzles ,a good-sized volume might be filled with the various arithmetical puzzles which have been propounded4 ,they range from a method of discovering the number which any one may think of to a solution of the famous question3 ,how old is ,ann8 ,of the following cases one may be considered a catch question1 while the other is an interesting problem4 ,a country woman1 carrying eggs to a garrison where she had three guards to pass1 sold at the first1 half the number she had and half an egg more2 at the second1 the half of what remained and half an egg more2 at the third the half of the remainder and half an egg more2 when she arrived at the market-place she had three dozen still to sell4 ,how was this possible without breaking any of the eggs8 ,at first view1 this problem seems impossible1 for how can half an egg be sold without breaking any8 ,but by taking the greater half of an odd number we take the exact half and half an egg more4 ,if she had #bie eggs before she came to the first guard1 she would there sell #adh1 leaving her #adg4 ,at the next she sold #gd1 leaving her #gc4 ,at the next she sold #cg1 leaving her three dozen4 ,the second problem is as follows3 ,after the ,romans had captured ,jotopat1 ,josephus and forty other ,jews sought shelter in a cave1 but the refugees were so frightened that1 with the exception of ,josephus himself and one other1 they resolved to kill themselves rather than fall into the hands of their enemies4 ,failing to dissuade them from this horrid purpose1 ,josephus used his authority as their chief to insist that they put each other to death in an orderly manner4 ,they were therefore arranged round a circle1 and every third man was killed until but two men remained1 the understanding being that they were to commit suicide4 ,by placing himself and the other man in the #cast and #afth places1 they were the last that were left1 and in this way they escaped death4 ,,archimedes ,,and ,,his ,,fulcrum ,next to that of ,euclid1 the name of ,archimedes is probably that which is the best known of all the mathematicians and mechanics of antiquity1 and this is in great part due to the two famous sayings which have been attributed to him1 one being ,eureka--,i have found it1 uttered when he discovered the method now universally in use for finding the specific gravity of bodies1 and the other being the equally famous dictum which he is said to have addressed to ,hiero1 ,king of ,sicily1--,give me a fulcrum and ,i will raise the earth from its place4 ,that ,archimedes1 provided he had been immortal1 could have carried out his promise1 is mathematically certain1 but it occurred to ,ozanam to calculate the length of time which it would take him to move the earth only one inch1 supposing his machine constructed and mathematically perfect2 that is to say1 without friction1 without gravity1 and in complete equilibrium1 and the following is the result3 ,for this purpose we shall suppose that the matter of which the earth is composed weighs #cjj pounds per cubic foot1 this being about the ascertained average4 ,if the diameter of the earth be #g1icj miles1 the whole globe will be found to contain #bfa1ajg1daa1gfe cubic miles1 which make #a1dbc1dii1abj1hhb1edd1fdj1jjj cubic yards1 or #ch1dcd1dgf1bfc1hbh1gje1bhj1jjj cubic feet1 and allowing #cjj pounds to each cubic foot1 we shall have #aa1ecj1cdb1hgi1adh1faa1ehd1jjj1jjj for the weight of the earth in pounds4 ,now1 we know1 by the laws of mechanics1 that1 whatever be the construction of a machine1 the space passed over by the weight1 is to that passed over by the moving power1 in the reciprocal ratio of the latter to the former4 ,it is known also1 that a man can act with an effort equal only to about #cj pounds for eight or ten hours1 without intermission1 and with a velocity of about #aj1jjj feet per hour4 ,if then we suppose the machine of ,archimedes to be put in motion by means of a crank1 and that the force continually applied to it is equal to #cj pounds1 then with the velocity of #aj1jjj feet per hour1 to raise the earth one inch the moving power must pass over the space of #chd1cdd1gfb1fch1bhg1jeb1hjj1jjj inches2 and if this space be divided by #aj1jjj feet or #abj1jjj inches1 we shall have for a quotient #c1bjb1hgc1jba1ihe1gbe1ddj1 which will be the number of hours required for this motion4 ,but as a year contains #h1gff hours1 a century will contain #hgf1fjj2 and if we divide the above number of hours by the latter1 the quotient1 #c1fec1gde1agf1hjc1 will be the number of centuries during which it would be necessary to make the crank of the machine continually turn in order to move the earth only one inch4 ,we have omitted the fraction of a century as being of little consequence in a calculation of this kind4 ,the machine is also supposed to be constantly in action1 but if it should be worked only eight hours each day1 the time required would be three times as long4 ,so that while it is true that ,archimedes could move the world1 the space through which he could have moved it1 during his whole life1 from infancy to old age1 is so small that even if multiplied two hundred million times it could not be measured by even the most delicate of our modern measuring instruments4 ,there is a modern saying which has become almost as famous amongst ,english-speaking peoples as is that of ,archimedes to the world at large4 ,it is that which ,bulwer ,lytton puts into the mouth of ,richelieu1 in his well-known play of that name3 ,beneath the rule of men entirely great ,,the ,,pen ,,is ,,mightier ,,than ,,the ,,sword4 ,about thirty years ago it occurred to the writer that these two epigrammatic sayings--that of ,archimedes and that of ,bulwer ,lytton1 might be symbolized in an allegorical drawing which would forcibly express the ideas which they contain1 and the question immediately arose--,where will ,archimedes get his fulcrum and what can he use as a lever8 ,and the mental answer was3 ,let the pen be the lever and the printing press the fulcrum1 while the sword1 used for the same purpose but resting on glory1 or in other words1 having no substantial fulcrum1 breaks in the attempt4 ,the little engraving which1 with a new motto1 forms a fitting tail-piece to this volume1 was the outcome4 ,it is true that the pen is mighty1 and in the hands of philosophers and diplomats it accomplishes much1 but it is only when resting on the printing press that it is provided with that fulcrum which enables it to raise the world by diffusing knowledge1 inculcating morality1 and providing pleasure and culture for humanity at large4 ,when assigned to such a task the sword breaks1 and well it may4 ,but we have a well-grounded hope that through the influence of the pen and the printing press there will soon come an era of universal ,illustration3 ,peace on ,earth and ,good ,will ,toward ,men4 ,,index ,absurdities in perpetual motion1 #db ,accuracy of modern methods of squaring the circle1 #ag ,adams1 perpetual motion1 #ga ,ahaz1 dial of1 #acc ,air1 liquid1 #fe ,alkahest1 or universal solvent1 #ajd ,altar of ,apollo1 #cj ,angelo1 ,michael1 finely engraved seal1 #acf ,angle1 ,trisection of1 #cc ,apollo1 ,altar of1 #cj ,approximations to ratio of diameter to circumference of circle1 #ag ,de ,morgan's ,illustration of1 #ah ,new ,illustration of1 #ai ,archimedean screw1 #di ,archimedes1 area of circle1 #ac ,ratio of circumference to diameter1 #ad ,archimedes and his fulcrum1 #aga ,arithmetic of the ancients1 #ae ,arithmetical problems1 #afc ,chess-board problem1 #afc ,nail problem1 #afd ,a question of population1 #afe ,how to become a millionaire1 #aff ,cost of first folio ,shakespeare1 #afh ,arithmetical puzzles1 #agj ,archimedes and his fulcrum1 #aga ,army ,medical ,museum1 #adb ,ball1 ,prof4 ,w4 ,w4 ,r41 #ci1 #abi1 #acc1 #acd ,balloons for conveying letters1 #adg ,balls--proportion of weight to diameter1 #cb ,bean1 jumping1 #abh ,bells kept ringing for eight years1 #da ,bible in walnut shell1 #acf ,bible1 written at rate of #bb to square inch1 #ada ,boat-race without oars1 #abi ,bolognian phosphorus1 #ajb ,boots--lifting oneself by straps of1 #abh ,boyle and palingenesy1 #ajg ,bramwell1 ,sir ,frederick1 #ch ,brick1 to look through1 #aea ,buckle and geometrical lines1 #aai ,budget of ,paradoxes1 ,de ,morgan1 #f1 #ah1 #aah ,carbon bisulphide for perpetual motion1 #fg ,capillary attraction1 #ec ,carpenter1 ,edward--fourth dimension1 #abb ,catherine ,,ii1 #aah ,century of ,inventions1 #gd ,chess-board problem1 #afc ,child lifting two horses1 #aca ,perpetual motion by a1 #fd ,circle1 squaring the1 #i ,supposed reward for squaring the1 #i ,resolution of ,royal ,academy of ,sciences on1 #aj ,what the problem is1 #ab ,approximation to1 by ,archimedes1 #ad ,jews1 ratio accepted by1 #ac ,egyptians1 ratio accepted by1 #ad ,symbol for ratio introduced by ,euler1 #ad ,graphical approximations1 #bb ,circumference of circle1 to find1 when diameter is given1 #bb ,clock that requires no winding1 #ch ,columbia ,college seal1 #adj ,column of ,de ,luc1 #dj ,compass1 watch used as a1 #acd ,congreve1 ,sir ,william1 #ec ,cube1 duplication of1 #ch ,crystallization seen by microscope1 #ajh ,mistaken for palingenesy1 #ajj ,dancer--microphotographs1 #add ,dangerous1 fascination of the1 #a ,declaration of ,independence1 #ade ,de ,luc's column1 #dj ,de ,morgan--,legend of ,michael ,scott1 #f ,ignorance v4 learning1 #h ,illustration of accuracy of modern attempts to square the circle1 #ah ,budget of ,paradoxes1 #f1 #ah ,trisection of angle1 #cd1 #aah ,on powder of sympathy1 #aab ,anecdote of ,diderot1 #aah ,dial of ,ahaz1 #acc ,diderot1 anecdote of1 #aah ,digby1 ,sir ,kenelm1 and palingenesy1 #aji ,sir ,kenelm and powder of sympathy1 #aaa ,dircks1 #ef1 #ga1 #ge ,discoveries1 valuable1 not due to perpetual-motion-mongers1 #cf ,duplication of the cube1 #cj ,elixir of life1 #ie ,engineering1 insect1 #acj ,euler1 #ad1 #aah ,fallacies in perpetual motion1 #fe ,falstaff and the philosopher's stone1 #ig ,faraday's discovery1 #ic ,farrants1 ,prest4 ,royal ,mic4 ,soc1 #adj ,figure1 a1 enlarged by cutting1 #abf ,first folio ,shakespeare1 cost of1 #afh ,fixation of mercury1 #ib ,follies of ,science1 ,the ,seven1 #b ,d',israeli's list1 #b ,an inappropriate term1 #c ,fourth dimension--conception of1 #aag ,flatland1 #abj ,kant and ,gauss1 #aba ,spiritualists1 #aba ,edward ,carpenter on1 #abb ,possibility of a new sense1 #abc ,frauds in perpetual motion1 #fi ,freezing of mercury1 #ic ,froment1 micrographs1 #aci ,gases1 liquefaction of1 #ic ,geiser's clock1 #ga ,geometrical quadrature impossible1 #ba ,gibberish1 origin of word1 #if ,god1 demonstration of existence of1 #aah ,hammer made of solid mercury1 #ic ,hand1 to look through1 #aef ,heat and cold1 illusions1 #aej ,hesse1 ,landgrave of1 #gg ,hindoos1 ratio accepted by1 #af ,holmes1 ,o4 ,w41 and powder of sympathy1 #aaa ,homer's ,iliad in nutshell1 #acf ,honecourt1 ,wilars de1 #db ,horses lifted by child1 #aca ,hydrofluoric acid1 #ajd ,hydrostatic paradox1 #df ,iliad of ,homer in nutshell1 #acf ,impossible1 fascination of the1 #a ,insect engineering1 #acj ,irradiation1 #aeb ,jews1 ratio accepted by the1 #ac ,keeley gold cure1 #ig ,keeley motor1 #fi ,kircher and palingenesy1 #ajf ,lacomme1 on squaring circle1 #bg ,lamps1 ever-burning1 #ajj ,library1 ,congressional1 in hand-bag1 #ade ,light from electric earth-currents1 #ajc ,lines1 geometrical1 #aai ,lines1 direction of1 deceptive1 #aed ,length of1 deceptive1 #aec ,liquid air1 #fe ,lodge1 ,sir ,oliver1 on conservation of energy1 #e ,longitude1 relation of squaring the circle to1 #aj ,mc,arthur1 on arithmetic of ancients1 #ae ,machin1 #af ,magnetism for perpetual motion1 #fa ,man lifting himself1 #abh ,mathematicians--how they go to heaven1 #h ,mercury1 fixation of1 #ib ,freezing of1 #ic ,metals4 ,see ,transmutation4 ,metius1 ,peter1 #af ,micrography1 or minute writing1 #acf ,homer in a nutshell1 #acf ,michael ,angelo's seal1 #acf ,ten ,commandments1 #acf ,bible in a nutshell1 #acf ,earliest micrographic engraving1 #aci ,micrographic copy of seal of ,columbia ,college1 #aci ,peters' machine1 #ada ,lord's ,prayer written at rate of #bb ,bibles to square inch1 #ada ,webb's fine writing1 #adb ,calculation in regard to1 #adc ,microphotographs by ,dancer1 #add ,pigeon-post in ,franco-,prussian ,war1 #adf ,millionaire1 to become a1 #aff ,miracle--dial of ,ahaz1 #acc ,morgan4 ,see ,de ,morgan4 ,morton1 ,president ,henry1 #ff ,motion1 perpetual4 ,see ,perpetual motion4 ,muir1 ,prof4 ,on ,archimedes1 #ad ,musitanus1 ,carolus1 #if ,nail problem1 #afd ,nicomedean line1 #bi ,orffyreus--his real name1 #gg ,his fraudulent machine1 #gg ,overbalancing wheels1 #dc ,paint1 luminous1 #ajb ,palingenesy1 #ajf ,patent office ,u4 ,s4 and perpetual motion1 #db ,pen mightier than the sword1 #agc ,perpetual lamps1 #ajj ,perpetual motion1 #cf ,what the problem is1 #cg ,clock that requires no winding1 #ch ,watch wound by walking1 #ci ,clock wound by tides1 #da ,by electricity1 #da ,absurdities1 #db ,overbalancing wheels1 #dc ,dr4 ,young1 on1 #dd ,bellows action1 #de ,hydrostatic paradox1 #df ,bishop ,wilkins1 #dh ,archimedean screw1 #di ,archimedean screw1 by mercury1 #ea ,congreve's1 by capillary attraction1 #ec ,tube and balls1 #ef ,tube and rope1 #ei ,magnetism1 #fa ,self-moving railway carriage1 #fc ,a child's perpetual motion1 #fd ,fallacies1 #fe ,liquid air1 #fe ,bisulphide of carbon1 #ff ,frauds1 #fi ,keeley motor1 #fi ,geiser's clock1 #ga ,adams1 #ga ,redhoeffer1 #gb ,lukens1 #gb ,how to stop the machine1 #gc ,marquis of ,worcester1 #gd ,dircks' model1 #ge ,orffyreus1 #gg ,possibility of1 #gh ,peters' micrographs1 #ada ,philosopher's stone1 #ig ,phosphorus1 discovery of1 #aja ,pigeon-post1 #adf ,population1 a question of1 #afe ,power1 the1 of the future1 #dj ,ptolemy1 on the circle1 #ae ,puzzles1 arithmetical1 #agj ,railway carriage1 self-moving1 #fc ,ramsay1 ,sir ,william1 #hj1 #ih ,ratio of diameter to circumference carried to #abg places1 #ag ,redhoeffer's perpetual motion1 #gb ,rosicrucius1 #ajj ,rutherford1 #af ,schott1 ,father1 and palingenesy1 #ajg ,schweirs1 ,dr41 #eb ,scott1 ,michael1 and his slave demons1 #f ,scott1 ,sir ,walter1 legend of the great ,wizard1 #f ,powder of sympathy1 #aab ,self-moving railway carriage1 #fc ,senses--illusions of1 #adh ,taste and smell1 #adi ,heat and cold1 #aej ,hearing1 #aej ,touch1 #aej ,sight--size of spot1 #aeb ,length of lines1 #aec ,direction of lines1 #aed ,objects seen through hand1 #aef ,looking through a brick1 #aeh ,sense1 possibility of a new1 #abc ,shadow going backward on dial1 #acc ,shakespeare1 cost of first folio1 #afh ,philosopher's stone1 #ig ,witchcraft1 #aad ,shanks--value of ratio carried to #gjg places1 #af ,sharp1 ,abraham1 #af ,sight1 sense of1 deceived1 #aeb ,smith1 ,james1 on squaring circle1 #bh ,snake lifted by spider1 #acj ,solvent1 universal1 #ajd ,space enlarged by cutting1 #abf ,spider lifting a snake1 #acj ,sun-dial--shadow going backward1 #acc ,taste and smell--illusions1 #adi ,tides1 clock moved by1 #dj ,will be the great source of power of the future1 #dj ,time it would take ,archimedes to move the world1 #aga ,touch1 sense of1 deceived1 #aej ,transmutation of the metals1 #gi ,ancient fables1 #gi ,hermes ,trismegistus1 #hj ,treatises not allegorical1 #ha ,seven metals1 #hb ,metals named after planets1 #hb ,methods of cheating1 #hc ,brief of the ,golden ,calf1 #hd ,story of unknown ,italian1 #hg ,possibility of effecting1 #hh ,sir ,william ,ramsay1 #hi ,effect of such discovery on our currency system1 #ij ,tribune1 ,new ,york1 #bi ,trisection of angle1 #cc ,tube and balls1 #ef ,tube and rope1 #ei ,universal medicine4 ,see ,elixir of ,life4 ,van ,ceulen1 ,rudolph1 #af ,wallich1 ,dr41 #ce ,watch that is wound by walking1 #ci ,used as a compass1 #acd ,webb micrographs1 #adb ,whewell's refutation of #c-a_/h ratio1 #bh ,wilkins1 ,bishop1 #dh ,witchcraft or magic1 #aac ,worcester1 ,marquis of1 #gd ,writing1 fine1 #aci ,young1 ,dr4 ,thomas1 #dd