file which includes the original illustrations4 ,see #eccaa-;h4htm or #eccaa-;h4zip3 7https3_/_/www4gutenberg4org_/cache_/epu b_/#eccaa_/pg#eccaa-;images4html7 or 7https3_/_/www4gutenberg4org_/files_/#ec caa_/eccaa-;h4zip7 ,images of the original pages are available through ,internet ,archive4 ,see https3_/_/archive4org_/details_/#efjajcc j,r4nlm4nih4gov ,,the ,,life ,,of ,,sir ,,isaac ,,newton4 99 99 99 99 99 99 ,,harper',s ,,family ,,library4 ,,designed ,,for ,,adult ,,persons4 8,books that you may carry to the fire1 and hold readily in your hand1 are the most useful after all4 ,a man will often look at them1 and be tempted to go on1 when he would have been frightened at books of a larger size1 and of a more erudite appearance40--,,dr4 ,,johnson4 ,the proprietors of the ,family ,library feel themselves stimulated to increased exertions by the distinguished favour with which it has already been received4 ,the volumes now before the public may be confidently appealed to as proofs of zeal on the part of the publishers to present to their readers a series of productions1 which1 as they are connected1 not with ephemeral1 but with permanent subjects1 may1 years hence as well as now1 be consulted for lively amusement as well as solid instruction4 ,to render this ,library still more worthy of patronage1 the proprietors propose incorporating in it such works of interest and value as may appear in the various ,libraries and ,miscellanies now preparing in ,europe1 particularly 8,constable's ,miscellany10 the 8,edinburgh ,cabinet0 ,library1 c4 ,all these productions1 as they emanate from the press1 will be submitted to literary gentlemen for inspection2 and none will be reprinted but such as shall be found calculated to sustain the exalted character which this ,library has already acquired4 ,several well-known authors have been engaged to prepare for it original works of an ,american character1 on ,history1 ,biography1 ,travels1 c4 c4 ,every distinct subject will in general be comprehended in one volume1 or at most in three volumes1 which may form either a portion of the series or a complete work by itself2 and each volume will be embellished with appropriate engravings4 ,the entire series will be the production of authors of eminence1 who have acquired celebrity by their literary labours1 and whose names1 as they appear in succession1 will afford the surest guarantee to the public for the satisfactory manner in which the subjects will be treated4 ,such is the plan by which it is intended to form an ,american ,family ,library1 comprising all that is valuable in those branches of knowledge which most happily unite entertainment with instruction4 ,the utmost care will be taken1 not only to exclude whatever can have an injurious influence on the mind1 but to embrace every thing calculated to strengthen the best and most salutary impressions4 ,with these arrangements and facilities1 the publishers flatter themselves that they shall be able to present to their fellow-citizens a work of unparalleled merit and cheapness1 embracing subjects adapted to all classes of readers1 and forming a body of literature deserving the praise of having instructed many1 and amused all2 and above every other species of eulogy1 of being fit to be introduced1 without reserve or exception1 by the father of a family to the domestic circle4 ,meanwhile1 the very low price at which it is charged renders more extensive patronage necessary for its support and prosecution4 ,the immediate encouragement1 therefore1 of those who approve its plan and execution is respectfully solicited4 ,the work may be obtained in complete sets1 or in separate numbers1 from the principal booksellers throughout the ,united ,states4 ,,opinions ,,of ,,the ,,family ,,library4 8,the publishers have hitherto fully deserved their daily increasing reputation by the good taste and judgment which have influenced the selections of works for the ,family ,library40--,albany ,daily ,advertiser4 8,the ,family ,library--,a title which1 from the valuable and entertaining matter the collection contains1 as well as from the careful style of its execution1 it well deserves4 ,no family1 indeed1 in which there are children to be brought up1 ought to be without this ,library1 as it furnishes the readiest resources for that education which ought to accompany or succeed that of the boarding-school or the academy1 and is infinitely more conducive than either to the cultivation of the intellect40--,monthly ,review4 8,it is the duty of every person having a family to put this excellent ,library into the hands of his children40--,n4 ,y4 ,mercantile ,advertiser4 8,it is one of the recommendations of the ,family ,library1 that it embraces a large circle of interesting matter1 of important information and agreeable entertainment1 in a concise manner and a cheap form4 ,it is eminently calculated for a popular series--published at a price so low1 that persons of the most moderate income may purchase it--combining a matter and a style that the most ordinary mind may comprehend it1 at the same time that it is calculated to raise the moral and intellectual character of the people40--,constellation4 8,we have repeatedly borne testimony to the utility of this work4 ,it is one of the best that has ever been issued from the ,american press1 and should be in the library of every family desirous of treasuring up useful knowledge40--,boston ,statesman4 8,we venture the assertion that there is no publication in the country more suitably adapted to the taste and requirements of the great mass of community1 or better calculated to raise the intellectual character of the middling classes of society1 than the ,family ,library40--,boston ,masonic ,mirror4 8,we have so often recommended this enterprising and useful publication 7the ,family ,library71 that we can here only add1 that each successive number appears to confirm its merited popularity40--,n4 ,y4 ,american4 8,the little volumes of this series truly comport with their title1 and are in themselves a ,family ,library40--,n4 ,y4 ,commercial ,advertiser4 8,we recommend the whole set of the ,family ,library as one of the cheapest means of affording pleasing instruction1 and imparting a proper pride in books1 with which we are acquainted40--,u4 ,s4 ,gazette4 8,it will prove instructing and amusing to all classes4 ,we are pleased to learn that the works comprising this ,library have become1 as they ought to be1 quite popular among the heads of families40--,n4 ,y4 ,gazette4 8,the ,family ,library is1 what its name implies1 a collection of various original works of the best kind1 containing reading useful and interesting to the family circle4 ,it is neatly printed1 and should be in every family that can afford it--the price being moderate40--,new-,england ,palladium4 8,we are pleased to see that the publishers have obtained sufficient encouragement to continue their valuable ,family ,library40--,baltimore ,republican4 8,the ,family ,library presents1 in a compendious and convenient form1 well-written histories of popular men1 kingdoms1 sciences1 c4 arranged and edited by able writers1 and drawn entirely from the most correct and accredited authorities4 ,it is1 as it professes to be1 a ,family ,library1 from which1 at little expense1 a household may prepare themselves for a consideration of those elementary subjects of education and society1 without a due acquaintance with which neither man nor woman has claim to be well bred1 or to take their proper place among those with whom they abide40--,charleston ,gazette4 ,,boy',s ,,and ,,girl',s ,,library4 ,,prospectus4 ,the ,publishers of the 8,,boy',s ,,and ,,girl',s ,,library0 propose1 under this title1 to issue a series of cheap but attractive volumes1 designed especially for the young4 ,the undertaking originates not in the impression that there does not already exist in the treasures of the reading world a large provision for this class of the community4 ,they are fully aware of the deep interest excited at the present day on the subject of the mental and moral training of the young1 and of the amount of talent and labour bestowed upon the production of works aiming both at the solid culture and the innocent entertainment of the inquisitive minds of children4 ,they would not therefore have their projected enterprise construed into an implication of the slightest disparagement of the merits of their predecessors in the same department4 ,indeed it is to the fact of the growing abundance rather than to the scarcity of useful productions of this description that the design of the present work is to be traced2 as they are desirous of creating a channel through which the products of the many able pens enlisted in the service of the young may be advantageously conveyed to the public4 ,the contemplated course of publications will more especially embrace such works as are adapted1 not to the extremes of early childhood or of advanced youth1 but to that intermediate space which lies between childhood and the opening of maturity1 when the trifles of the nursery and the simple lessons of the school-room have ceased to exercise their beneficial influence1 but before the taste for a higher order of mental pleasure has established a fixed ascendency in their stead4 ,in the selection of works intended for the rising generation in this plastic period of their existence1 when the elements of future character are receiving their moulding impress1 the ,publishers pledge themselves that the utmost care and scrupulosity shall be exercised4 ,they are fixed in their determination that nothing of a questionable tendency on the score of sentiment shall find admission into pages consecrated to the holy purpose of instructing the thoughts1 regulating the passions1 and settling the principles of the young4 ,in fine1 the ,publishers of the 8,boy's and ,girl's ,library0 would assure the ,public that an adequate patronage alone is wanting to induce and enable them to secure the services of the most gifted pens in our country in the proposed publication1 and thus to render it altogether worthy of the age and the object which calls it forth1 and of the countenance which they solicit for it4 ,illustration3 ,,sir4 ,g4 ,,kneller ,,pinx4 ,,eng4d ,,by ,,gimber4 ,,sir ,,isaac ,,newton4 ,,harper',s ,,family ,,library ,printed by ,r4 ,miller 99 99 99 99 99 99 ,harper's ,stereotype ,edition4 ,,the ,,life ,,of ,,sir ,,isaac ,,newton4 by ,,david ,,brewster1 ,,ll4,d4 ,f4,r4,s4 ,ergo vivida vis animi pervicit1 et extra ,processit longe flammantia mnia mundi2 ,atque omne immensum peragravit mente amimoque4 ,lucret4 lib4 i4 #a4 #gc4 ,illustration3 ,the ,birthplace of ,newton4 ,new-,york3 ,printed and ,published by ,j4 ,j4 ,harper2 ,no4 #hb ,cliff-,street1 and ,sold by the ,booksellers ,generally ,throughout the ,united ,states4 #ahcc4 ,,to ,,the ,,right ,,honourable ,,lord ,,braybrooke4 ,the kindness with which your lordship intrusted to me some very valuable materials for the composition of this volume has induced me to embrace the present opportunity of publicly acknowledging it4 ,but even if this personal obligation had been less powerful1 those literary attainments and that enlightened benevolence which reflect upon rank its highest lustre would have justified me in seeking for it the patronage of a name which they have so justly honoured4 ,,david ,,brewster4 ,allerly1 ,june #ast1 #ahca4 ,,preface4 ,as this is the only ,life of ,sir ,isaac ,newton on any considerable scale that has yet appeared1 ,i have experienced great difficulty in preparing it for the public4 ,the materials collected by preceding biographers were extremely scanty2 the particulars of his early life1 and even the historical details of his discoveries1 have been less perfectly preserved than those of his illustrious predecessors2 and it is not creditable to his disciples that they have allowed a whole century to elapse without any suitable record of the life and labours of a master who united every claim to their affection and gratitude4 ,in drawing up this volume1 ,i have obtained much assistance from the account of ,sir ,isaac ,newton in the ,biographia ,britannica2 from the letters to ,oldenburg1 and other papers in ,bishop ,horsley's edition of his works2 from ,turnor's ,collections for the ,history of the ,town and ,soke of ,grantham2 from ,m4 ,biot's excellent ,life of ,newton in the ,biographie ,universelle2 and from ,lord ,king's ,life and ,correspondence of ,locke4 ,although these works contain much important information respecting the ,life of ,newton1 yet ,i have been so fortunate as to obtain many new materials of considerable value4 ,to the kindness of ,lord ,braybrooke ,i have been indebted for the interesting correspondence of ,newton1 ,mr4 ,pepys1 and ,mr4 ,millington1 which is now published for the first time1 and which throws much light upon an event in the life of our author that has recently acquired an unexpected and a painful importance4 ,these letters1 when combined with those which passed between ,newton and ,locke1 and with a curious extract from the manuscript diary of ,mr4 ,abraham ,pryme1 kindly furnished to me by his collateral descendant ,professor ,pryme of ,cambridge1 fill up a blank in his history1 and have enabled me to delineate in its true character that temporary indisposition which1 from the view that has been taken of it by foreign philosophers1 has been the occasion of such deep distress to the friends of science and religion4 ,to ,professor ,whewell1 of ,cambridge1 ,i owe very great obligations for much valuable information4 ,professor ,rigaud1 of ,oxford1 to whose kindness ,i have on many other occasions been indebted1 supplied me with several important facts1 and with extracts from the diary of ,hearne in the ,bodleian ,library1 and from the original correspondence between ,newton and ,flamstead1 which the president of ,corpus ,christi ,college had for this purpose committed to his care2 and ,dr4 ,j4 ,c4 ,gregory1 of ,edinburgh1 the descendant of the illustrious inventor of the reflecting telescope1 allowed me to use his unpublished account of an autograph manuscript of ,sir ,isaac ,newton1 which was found among the papers of ,david ,gregory1 ,savilian ,professor of ,astronomy at ,oxford1 and which throws some light on the history of the ,principia4 ,i have been indebted to many other friends for the communication of books and facts1 but especially to ,sir ,william ,hamilton1 ,bart41 whose liberality in promoting literary inquiry is not limited to the circle of his friends4 ,d4 ,b4 ,allerly1 ,june #ast1 #ahca4 ,,contents4 ,page ,,chapter ,i4 ,the ,pre-eminence of ,sir ,isaac ,newton's ,reputation--,the ,interest attached to the ,study of his ,life and ,writings--,his ,birth and ,parentage--,his early ,education--,is sent to ,grantham ,school-- ,his early ,attachment to ,mechanical ,pursuits--,his ,windmill--,his ,water-clock--,his ,self-moving ,cart--,his ,sun-dials--,his ,preparation for the ,university #ag ,,chapter ,,ii4 ,newton enters ,trinity ,college1 ,cambridge--,origin of his ,propensity for ,mathematics--,he studies the ,geometry of ,descartes unassisted-- ,purchases a ,prism--,revises ,dr4 ,barrow's ,optical ,lectures--,dr4 ,barrow's ,opinion respecting ,colours--,takes his ,degrees--,is appointed a ,fellow of ,trinity ,college--,succeeds ,dr4 ,barrow in the ,lucasian ,chair of ,mathematics #bf ,,chapter ,,iii4 ,newton occupied in grinding ,hyperbolical ,lenses--,his first ,experiments with the ,prism made in #afff--;,he discovers the ,composition of ,white ,light1 and the different ,refrangibility of the ,rays which compose it--,abandons his ,attempts to improve ,refracting ,telescopes1 and resolves to attempt the ,construction of ,reflecting ones--,he quits ,cambridge on account of the ,plague--,constructs two ,reflecting ,telescopes in #affh1 the first ever executed--,one of them examined by the ,royal ,society1 and shown to the ,king--,he constructs a ,telescope with ,glass ,specula--,recent ,history of the ,reflecting ,telescope--,mr4 ,airy's ,glass ,specula--,hadley's ,reflecting ,telescopes--,short's--,herschel's--,ram age's--,lord ,oxmantown's #cj ,,chapter ,,iv4 ,he delivers a ,course of ,optical ,lectures at ,cambridge--,is elected ,fellow of the ,royal ,society--,he communicates to them his ,discoveries on the different ,refrangibility and ,nature of ,light-- ,popular ,account of them--,they involve him in various ,controversies-- ,his ,dispute with ,pardies--,linus--,lucas--,dr4 ,hooke and ,mr4 ,huygens-- ,the ,influence of these ,disputes on the mind of ,newton #dg ,,chapter ,v4 ,mistake of ,newton in supposing that the ,improvement of ,refracting ,telescopes was hopeless--,mr4 ,hall invents the ,achromatic ,telescope-- ,principles of the ,achromatic ,telescope explained--,it is reinvented by ,dollond1 and improved by future ,artists--,dr4 ,blair's ,aplanatic ,telescope--,mistakes in ,newton's ,analysis of the ,spectrum--,modern ,discoveries respecting the ,structure of the ,spectrum #fc ,,chapter ,,vi4 ,colours of thin ,plates first studied by ,boyle and ,hooke--,newton determines the ,law of their ,production--,his ,theory of ,fits of easy ,reflection and ,transmission--,colours of thick ,plates #ge ,,chapter ,,vii4 ,newton's ,theory of the ,colours of ,natural ,bodies explained-- ,objections to it stated--,new ,classification of ,colours--,outline of a new ,theory proposed #hb ,,chapter ,,viii4 ,newton's ,discoveries respecting the ,inflection or ,diffraction of ,light--,previous ,discoveries of ,grimaldi and ,dr4 ,hooke--,labours of succeeding ,philosophers--,law of ,interference of ,dr4 ,young-- ,fresnel's ,discoveries--,new ,theory of ,inflection on the ,hypothesis of the ,materiality of ,light #ih ,,chapter ,,ix4 ,miscellaneous ,optical ,researches of ,newton--,his ,experiments on ,refraction--,his ,conjecture respecting the ,inflammability of the ,diamond--,his ,law of ,double ,refraction--,his ,observations on the ,polarization of ,light--,newton's ,theory of ,light--,his 8,optics0 #ajf ,,chapter ,x4 ,astronomical ,discoveries of ,newton--,necessity of combined ,exertion to the completion of great ,discoveries--,sketch of the ,history or ,astronomy previous to the time of ,newton--,copernicus1 #adgc-aedc-- ,tycho ,brahe1 #aedf-afja--,kepler1 #aega-afca--;,galileo1 #aefd-afdb #aaj ,,chapter ,,xi4 ,the first ,idea of ,gravity occurs to ,newton in #afff--;,his first ,speculations upon it--,interrupted by his ,optical ,experiments--,he resumes the ,subject in consequence of a ,discussion with ,doctor ,hooke--,he discovers the true ,law of ,gravity and the ,cause of the ,planetary ,motions--,dr4 ,halley urges him to publish his ,principia-- ,his ,principles of ,natural ,philosophy--,proceedings of the ,royal ,society on this ,subject--,the ,principia appears in #afhg--;,general ,account of it1 and of the ,discoveries it contains--,they meet with great ,opposition1 owing to the ,prevalence of the ,cartesian ,system-- ,account of the ,reception and ,progress of the ,newtonian ,philosophy in ,foreign ,countries--,account of its ,progress and ,establishment in ,england #adj ,,chapter ,,xii4 ,doctrine of ,infinite ,quantities--,labours of ,pappus--,kepler--,cavaleri-- ,roberval--,fermat--,wallis--,newton discovers the ,binomial ,theorem and the ,doctrine of ,fluxions in #afjf--;,his ,manuscript ,work containing this ,doctrine communicated to his ,friends--,his ,treatise on ,fluxions--,his ,mathematical ,tracts--,his ,universal ,arithmetic--,his ,methodus ,differentialis--,his ,geometria ,analytica--,his ,solution of the ,problems proposed by ,bernouilli and ,leibnitz--,account of the celebrated ,dispute respecting the ,invention of ,fluxions--,commercium ,epistolicum--,report of the ,royal ,society--,general ,view of the ,controversy #afh ,,chapter ,,xiii4 ,james ,,ii4 attacks the ,privileges of the ,university of ,cambridge-- ,newton chosen one of the ,delegates to resist this ,encroachment--,he is elected a ,member of the ,convention ,parliament--,burning of his ,manuscript--,his supposed ,derangement of ,mind--,view taken of this by foreign ,philosophers--,his ,correspondence with ,mr4 ,pepys and ,mr4 ,locke at the time of his ,illness--,mr4 ,millington's ,letter to ,mr4 ,pepys on the subject of ,newton's ,illness--,refutation of the ,statement that he laboured under ,mental ,derangement #bjj ,,chapter ,,xiv4 ,no ,mark of ,national ,gratitude conferred upon ,newton--,friendship between him and ,charles ,montague1 afterward ,earl of ,halifax--,mr4 ,montague appointed ,chancellor of the ,exchequer in #afid--;,he resolves upon a ,recoinage--,nominates ,mr4 ,newton ,warden of the ,mint in #afie-- ,mr4 ,newton appointed ,master of the ,mint in #afii--,notice of the ,earl of ,halifax--,mr4 ,newton elected ,associate of the ,academy of ,sciences in #afii--,member for ,cambridge in #agja--;and ,president of the ,royal ,society in #agjc--,queen ,anne confers upon him the ,honour of ,knighthood in #agje--,second ,edition of the ,principia1 edited by ,cotes--,his ,conduct respecting ,mr4 ,ditton's ,method of finding the ,longitude #bbc ,,chapter ,,xv4 ,respect in which ,newton was held at the ,court of ,george ,i4--,the ,princess of ,wales delighted with his ,conversation--,leibnitz endeavours to prejudice the ,princess against ,sir ,isaac and ,locke-- ,controversy occasioned by his ,conduct--,the ,princess obtains a ,manuscript ,abstract of his ,system of ,chronology--,the ,abb ,conti is1 at her request1 allowed to take a ,copy of it on the promise of ,secrecy--,he prints it surreptitiously in ,french1 accompanied with a ,refutation by ,m4 ,freret--,sir ,isaac's ,defence of his ,system--,father ,souciet attacks it1 and is answered by ,dr4 ,halley--,sir ,isaac's larger ,work on ,chronology published after his ,death--,opinions respecting it--,sir ,isaac's ,paper on the ,form of the most ancient ,year #bcd ,,chapter ,,xvi4 ,theological ,studies of ,sir ,isaac--,their ,importance to ,christianity-- ,motives to which they have been ascribed--,opinions of ,biot and ,la ,place considered--,his ,theological ,researches begun before his supposed ,mental ,illness--,the ,date of these ,works fixed--,letters to ,locke--,account of his ,observations on ,prophecy--,his ,lexicon ,propheticum--,his ,four ,letters to ,dr4 ,bentley--,origin of ,newton's ,theological ,studies--,analogy between the ,book of ,nature and that of ,revelation #bdb ,,chapter ,,xvii4 ,the ,minor ,discoveries and ,inventions of ,newton--,his ,researches on ,heat--,on ,fire and ,flame--,on ,elective ,attraction--,on the ,structure of ,bodies--,his supposed ,attachment to ,alchymy--,his ,hypothesis respecting ,ether as the ,cause of ,light and ,gravity--,on the ,excitation of ,electricity in ,glass--,his ,reflecting ,sextant invented before #agjj--;,his ,reflecting ,microscope--,his ,prismatic ,reflector as a ,substitute for the small ,speculum of ,reflecting ,telescopes--,his ,method of varying the ,magnifying ,power of ,newtonian ,telescopes-- ,his ,experiments on ,impressions on the ,retina #bfe ,,chapter ,,xviii4 ,his ,acquaintance with ,dr4 ,pemberton--,who edits the ,third ,edition of the ,principia--,his first ,attack of ill ,health--,his ,recovery--,he is taken ill in consequence of attending the ,royal ,society--,his ,death on the #bjth ,march1 #agbg--;,his ,body lies in state--,his ,funeral--,he is buried in ,westminster ,abbey--,his ,monument described--,his ,epitaph-- ,a ,medal struck in honour of him--,roubiliac's full-length ,statue of him erected in ,cambridge--,division of his ,property--,his ,successors #bhd ,,chapter ,,xix4 ,permanence of ,newton's ,reputation--,character of his ,genius--,his ,method of ,investigation similar to that used by ,galileo--,error in ascribing his ,discoveries to the ,use of the ,methods recommended by ,lord ,bacon--,the ,pretensions of the ,baconian ,philosophy examined-- ,sir ,isaac ,newton's ,social ,character--,his great ,modesty--,the ,simplicity of his ,character--,his ,religious and ,moral ,character-- ,his ,hospitality and ,mode of ,life--,his ,generosity and ,charity--,his ,absence--,his ,personal ,appearance--,statues and ,pictures of him-- ,memorials and ,recollections of him #bib ,,appendix1 ,no4 ,i4--,observations on the ,family of ,sir ,isaac ,newton #cjg ,,appendix1 ,no4 ,,ii4--,letter from ,sir ,isaac ,newton to ,francis ,aston1 ,esq41 a young ,friend who was on the eve of setting out on his ,travels #caf ,,appendix1 ,no4 ,,iii4--8,a ,remarkable and ,curious ,conversation between ,sir ,isaac ,newton and ,mr4 ,conduit40 #cbj ,,life ,,of ,,sir ,,isaac ,,newton4 ,,chapter ,i4 ,the ,pre-eminence of ,sir ,isaac ,newton's ,reputation--,the ,interest attached to the ,study of his ,life and ,writings--,his ,birth and ,parentage--,his early ,education--,is sent to ,grantham ,school--,his early ,attachment to ,mechanical ,pursuits--,his ,windmill--,his ,waterclock--,his ,self-moving ,cart--,his ,sundials--,his ,preparation for the ,university4 ,the name of ,sir ,isaac ,newton has by general consent been placed at the head of those great men who have been the ornaments of their species4 ,however imposing be the attributes with which time has invested the sages and the heroes of antiquity1 the brightness of their fame has been eclipsed by the splendour of his reputation2 and neither the partiality of rival nations1 nor the vanity of a presumptuous age1 has ventured to dispute the ascendency of his genius4 ,the philosopher1#a indeed1 to whom posterity will probably assign the place next to ,newton1 has characterized the ,principia as pre-eminent above all the productions of human intellect1 and has thus divested of extravagance the contemporary encomium upon its author1 ,nec fas est propius mortali attingere ,divos4 ,,halley4 ,so near the gods--man cannot nearer go4 ,the biography of an individual so highly renowned cannot fail to excite a general interest4 ,though his course may have lain in the vale of private life1 and may have been unmarked with those dramatic events which throw a lustre even round perishable names1 yet the inquiring spirit will explore the history of a mind so richly endowed1--will study its intellectual and moral phases1 and will seek the shelter of its authority on those great questions which reason has abandoned to faith and hope4 ,if the conduct and opinions of men of ordinary talent are recorded for our instruction1 how interesting must it be to follow the most exalted genius through the incidents of common life2--to mark the steps by which he attained his lofty pre-eminence2 to see how he performs the functions of the social and the domestic compact2 how he exercises his lofty powers of invention and discovery2 how he comports himself in the arena of intellectual strife2 and in what sentiments1 and with what aspirations he quits the world which he has adorned4 ,in almost all these bearings1 the life and writings of ,sir ,isaac ,newton abound with the richest counsel4 ,here the philosopher will learn the art by which alone he can acquire an immortal name4 ,the moralist will trace the lineaments of a character adjusted to all the symmetry of which our imperfect nature is susceptible2 and the ,christian will contemplate with delight the high-priest of science quitting the study of the material universe1--the scene of his intellectual triumphs1--to investigate with humility and patience the mysteries of his faith4 99 99 99 99 99 ,sir ,isaac ,newton was born at ,woolsthorpe1 a hamlet in the parish of ,colsterworth1 in ,lincolnshire1 about six miles south of ,grantham1 on the #beth ,december1 ,o4 ,s41 #afdb1 exactly one year after ,galileo died1 and was baptized at ,colsterworth on the #ast ,january1 #afdb-c4 ,his father1 ,mr4 ,isaac ,newton1 died at the early age of thirty-six1 a little more than a year after the death of his father ,robert ,newton1 and only a few months after his marriage to ,harriet ,ayscough1 daughter of ,james ,ayscough of ,market ,overton in ,rutlandshire4 ,this lady was accordingly left in a state of pregnancy1 and appears to have given a premature birth to her only and posthumous child4 ,the helpless infant thus ushered into the world was of such an extremely diminutive size1#b and seemed of so perishable a frame1 that two women who were sent to ,lady ,pakenham's at ,north ,witham1 to bring some medicine to strengthen him1 did not expect to find him alive on their return4 ,providence1 however1 had otherwise decreed2 and that frail tenement which seemed scarcely able to imprison its immortal mind was destined to enjoy a vigorous maturity1 and to survive even the average term of human existence4 ,the estate of ,woolsthorpe1 in the manor-house of which this remarkable birth took place1 had been more than a hundred years in the possession of the family1 who came originally from ,newton in ,lancashire1 but who had1 previous to the purchase of ,woolsthorpe1 settled at ,westby1 in the county of ,lincoln4 ,the manor-house1 of which we have given an engraving1 is situated in a beautiful little valley1 remarkable for its copious wells of pure spring water1 on the west side of the river ,witham1 which has its origin in the neighbourhood1 and commands an agreeable prospect to the east towards ,colsterworth4 ,the manor of ,woolsthorpe was worth only #cjl4 per annum2 but ,mrs4 ,newton possessed another small estate at ,sewstern1#c which raised the annual value of their property to about #hjl42 and it is probable that the cultivation of the little farm on which she resided somewhat enlarged the limited income upon which she had to support herself1 and educate her child4 ,for three years ,mrs4 ,newton continued to watch over her tender charge with parental anxiety2 but in consequence of her marriage to the ,reverend ,barnabas ,smith1 rector of ,north ,witham1 about a mile south of ,woolsthorpe1 she left him under the care of her own mother4 ,at the usual age he was sent to two day-schools at ,skillington and ,stoke1 where he acquired the education which such seminaries afforded2 but when he reached his twelfth year he went to the public school at ,grantham1 taught by ,mr4 ,stokes1 and was boarded at the house of ,mr4 ,clark1 an apothecary in that town4 ,according to information which ,sir ,isaac himself gave to ,mr4 ,conduit1 he seems to have been very inattentive to his studies1 and very low in the school4 ,the boy1 however1 who was above him1 having one day given him a severe kick upon his stomach1 from which he suffered great pain1 ,isaac laboured incessantly till he got above him in the school1 and from that time he continued to rise till he was the head boy4 ,from the habits of application which this incident had led him to form1 the peculiar character of his mind was speedily displayed4 ,during the hours of play1 when the other boys were occupied with their amusements1 his mind was engrossed with mechanical contrivances1 either in imitation of something which he had seen1 or in execution of some original conception of his own4 ,for this purpose he provided himself with little saws1 hatchets1 hammers1 and all sorts of tools1 which he acquired the art of using with singular dexterity4 ,the principal pieces of mechanism which he thus constructed were a windmill1 a waterclock1 and a carriage put in motion by the person who sat in it4 ,when a windmill was erecting near ,grantham on the road to ,gunnerby1 ,isaac frequently attended the operations of the workmen1 and acquired such a thorough knowledge of the machinery that he completed a working model of it1 which excited universal admiration4 ,this model was frequently placed on the top of the house in which he lodged at ,grantham1 and was put in motion by the action of the wind upon its sails4 ,not content with this exact imitation of the original machine1 he conceived the idea of driving it by animal power1 and for this purpose he enclosed in it a mouse which he called the miller1 and which1 by acting upon a sort of treadwheel1 gave motion to the machine4 ,according to some accounts1 the mouse was made to advance by pulling a string attached to its tail1 while others allege that the power of the little agent was called forth by its unavailing attempts to reach a portion of corn placed above the wheel4 ,his waterclock was formed out of a box which he had solicited from ,mrs4 ,clark's brother4 ,it was about four feet high1 and of a proportional breadth1 somewhat like a common houseclock4 ,the index of the dialplate was turned by a piece of wood1 which either fell or rose by the action of dropping water4 ,as it stood in his own bedroom he supplied it every morning with the requisite quantity of water1 and it was used as a clock by ,mr4 ,clark's family1 and remained in the house long after its inventor had quitted ,grantham4#d ,his mechanical carriage was a vehicle with four wheels1 which was put in motion with a handle wrought by the person who sat in it1 but1 like ,merlin's chair1 it seems to have been used only on the smooth surface of a floor1 and not fitted to overcome the inequalities of a road4 ,although ,newton was at this time 8a sober1 silent1 thinking lad10 who scarcely ever joined in the ordinary games of his schoolfellows1 yet he took great pleasure in providing them with amusements of a scientific character4 ,he introduced into the school the flying of paper kites2 and he is said to have been at great pains in determining their best forms and proportions1 and in ascertaining the position and number of the points by which the string should be attached4 ,he made also paper lanterns1 by the light of which he went to school in the winter mornings1 and he frequently attached these lanterns to the tails of his kites in a dark night1 so as to inspire the country people with the belief that they were comets4 ,in the house where he lodged there were some female inmates in whose company he appears to have taken much pleasure4 ,one of these1 a ,miss ,storey1 sister to ,dr4 ,storey1 a physician at ,buckminster1 near ,colsterworth1 was two or three years younger than ,newton1 and to great personal attractions she seems to have added more than the usual allotment of female talent4 ,the society of this young lady and her companions was always preferred to that of his own schoolfellows1 and it was one of his most agreeable occupations to construct for them little tables and cupboards1 and other utensils for holding their dolls and their trinkets4 ,he had lived nearly six years in the same house with ,miss ,storey1 and there is reason to believe that their youthful friendship gradually rose to a higher passion2 but the smallness of her portion and the inadequacy of his own fortune appear to have prevented the consummation of their happiness4 ,miss ,storey was afterward twice married1 and under the name of ,mrs4 ,vincent1 ,dr4 ,stukely visited her at ,grantham in #agbg1 at the age of eighty-two1 and obtained from her many particulars respecting the early history of our author4 ,newton's esteem for her continued unabated during his life4 ,he regularly visited her when he went to ,lincolnshire1 and never failed to relieve her from little pecuniary difficulties which seem to have beset her family4 ,among the early passions of ,newton we must recount his love of drawing2 and even of writing verses4 ,his own room was furnished with pictures drawn1 coloured1 and framed by himself1 sometimes from copies1 but often from life4#e ,among these were portraits of ,dr4 ,donne1 ,mr4 ,stokes1 the master of ,grantham school1 and ,king ,charles ,i4 under whose picture were the following verses4 ,a secret art my soul requires to try1 ,if prayers can give me what the wars deny4 ,three crowns distinguished here1 in order do ,present their objects to my knowing view4 ,earth's crown1 thus at my feet ,i can disdain1 ,which heavy is1 and at the best but vain4 ,but now a crown of thorns ,i gladly greet1 ,sharp is this crown1 but not so sharp as sweet2 ,the crown of glory that ,i yonder see ,is full of bliss and of eternity4 ,these verses were repeated to ,dr4 ,stukely by ,mrs4 ,vincent1 who believed them to be written by ,sir ,isaac1 a circumstance which is the more probable1 as he himself assured ,mr4 ,conduit1 with some expression of pleasure1 that he 8excelled in making verses10 although he had been heard to express a contempt for poetical composition4 ,but while the mind of our young philosopher was principally occupied with the pursuits which we have now detailed1 it was not inattentive to the movements of the celestial bodies1 on which he was destined to throw such a brilliant light4 ,the imperfections of his waterclock had probably directed his thoughts to the more accurate measure of time which the motion of the sun afforded4 ,in the yard of the house where he lived1 he traced the varying movements of that luminary upon the walls and roofs of the buildings1 and by means of fixed pins he had marked out the hourly and half-hourly subdivisions4 ,one of these dials1 which went by the name of ,isaac's dial1 and was often referred to by the country people for the hour of the day1 appears to have been drawn solely from the observations of several years2 but we are not informed whether all the dials which he drew on the wall of his house at ,woolsthorpe1 and which existed after his death1 were of the same description1 or were projected from his knowledge of the doctrine of the sphere4 ,upon the death of the ,reverend ,mr4 ,smith in the year #afef1 his widow left the rectory of ,north ,witham1 and took up her residence at ,woolsthorpe along with her three children1 ,mary1 ,benjamin1 and ,hannah ,smith4 ,newton had now attained the fifteenth year of his age1 and had made great progress in his studies2 and as he was thought capable of being useful in the management of the farm and country business at ,woolsthorpe1 his mother1 chiefly from a motive of economy1 recalled him from the school at ,grantham4 ,in order to accustom him to the art of selling and buying1 two of the most important branches of rural labour1 he was frequently sent on ,saturday to ,grantham market to dispose of grain and other articles of farm produce1 and to purchase such necessaries as the family required4 ,as he had yet acquired no experience1 an old trustworthy servant generally accompanied him on these errands4 ,the inn which they patronised was the ,saracen's ,head at ,west ,gate2 but no sooner had they put up their horses than our young philosopher deserted his commercial concerns1 and betook himself to his former lodging in the apothecary's garret1 where a number of ,mr4 ,clark's old books afforded him abundance of entertainment till his aged guardian had executed the family commissions1 and announced to him the necessity of returning4 ,at other times he deserted his duties at an earlier stage1 and intrenched himself under a hedge by the way-side1 where he continued his studies till the servant returned from ,grantham4 ,the more immediate affairs of the farm were not more prosperous under his management than would have been his marketings at ,grantham4 ,the perusal of a book1 the execution of a model1 or the superintendence of a waterwheel of his own construction1 whirling the glittering spray from some neighbouring stream1 absorbed all his thoughts when the sheep were going astray1 and the cattle were devouring or treading down the corn4 ,mrs4 ,smith was soon convinced from experience that her son was not destined to cultivate the soil1 and as his passion for study1 and his dislike for every other occupation increased with his years1 she wisely resolved to give him all the advantages which education could confer4 ,he was accordingly sent back to ,grantham school1 where he continued for some months in busy preparation for his academical studies4 ,his uncle1 the ,reverend ,w4 ,ayscough1 who was rector of ,burton ,coggles1 about three miles east of ,woolsthorpe1 and who had himself studied at ,trinity ,college1 recommended to his nephew to enter that society1 and it was accordingly determined that he should proceed to ,cambridge at the approaching term4#f ,,chapter ,,ii4 ,newton enters ,trinity ,college1 ,cambridge--,origin of his ,propensity for ,mathematics--,he studies the ,geometry of ,descartes unassisted-- ,purchases a ,prism--,revises ,dr4 ,harrow's ,optical ,lectures--,dr4 ,barrow's ,opinion respecting ,colours--,takes his ,degrees--,is appointed a ,fellow of ,trinity ,college--,succeeds ,dr4 ,barrow in the ,lucasian ,chair of ,mathematics4 ,to a young mind thirsting for knowledge1 and ambitious of the distinction which it brings1 the transition from a village school to a university like that of ,cambridge1--from the absolute solitude of thought to the society of men imbued with all the literature and science of the age1--must be one of eventful interest4 ,to ,newton it was a source of peculiar excitement4 ,the history of science affords many examples where the young aspirant had been early initiated into her mysteries1 and had even exercised his powers of invention and discovery before he was admitted within the walls of a college2 but he who was to give philosophy her laws did not exhibit such early talent2 no friendly counsel regulated his youthful studies1 and no work of scientific eminence seems to have guided him in his course4 ,in yielding to the impulse of his mechanical genius1 his mind obeyed the laws of its own natural expansion1 and1 following the line of least resistance1 it was thus drawn aside from the strongholds with which it was destined to grapple4 ,when ,newton1 therefore1 arrived at ,trinity ,college1 he brought with him a more slender portion of science than falls to the lot of ordinary scholars2 but this state of his acquirements was perhaps not unfavourable to the development of his powers4 ,unexhausted by premature growth1 and invigorated by healthful repose1 his mind was the better fitted to make those vigorous and rapid shoots which soon covered with foliage and with fruit the genial soil to which it had been transferred4 ,cambridge was consequently the real birthplace of ,newton's genius4 ,her teachers fostered his earliest studies2--her institutions sustained his mightiest efforts2--and within her precincts were all his discoveries made and perfected4 ,when he was called to higher official functions1 his disciples kept up the pre-eminence of their master's philosophy1 and their successors have maintained this seat of learning in the fulness of its glory1 and rendered it the most distinguished among the universities of ,europe4 ,it was on the #eth of ,june1 #affj1 in the #ahth year of his age1 that ,newton was admitted into ,trinity ,college1 ,cambridge1 during the same year that ,dr4 ,barrow was elected professor of ,greek in the university4 ,his attention was first turned to the study of mathematics by a desire to inquire into the truth of judicial astrology2 and he is said to have discovered the folly of that study by erecting a figure with the aid of one or two of the problems of ,euclid4 ,the propositions contained in this ancient system of geometry he regarded as self-evident truths2 and without any preliminary study he made himself master of ,descartes's ,geometry by his genius and patient application4 ,this neglect of the elementary truths of geometry he afterward regarded as a mistake in his mathematical studies1 and he expressed to ,dr4 ,pemberton his regret that 8he had applied himself to the works of ,descartes1 and other algebraic writers1 before he had considered the elements of ,euclid with that attention which so excellent a writer deserved4#g ,dr4 ,wallis's ,arithmetic of ,infinites1 ,saunderson's ,logic1 and the ,optics of ,kepler were among the books which he had studied with care4 ,on these works he wrote comments during their perusal2 and so great was his progress1 that he is reported to have found himself more deeply versed in some branches of knowledge than the tutor who directed his studies4 ,neither history nor tradition has handed down to us any particular account of his progress during the first three years that he spent at ,cambridge4 ,it appears from a statement of his expenses1 that in #affd he purchased a prism1 for the purpose1 as has been said1 of examining ,descartes's theory of colours2 and it is stated by ,mr4 ,conduit1 that he soon established his own views on the subject1 and detected the errors in those of the ,french philosopher4 ,this1 however1 does not seem to have been the case4 ,had he discovered the composition of light in #affd or #affe1 it is not likely that he would have withheld it1 not only from the ,royal ,society1 but from his own friends at ,cambridge till the year #afga4 ,his friend and tutor1 ,dr4 ,barrow1 was made ,lucasian ,professor of ,mathematics in #affc1 and the optical lectures which he afterward delivered were published in #affi4 ,in the preface of this work he acknowledges his obligations to his colleague1 ,mr4 ,isaac ,newton1#h for having revised the ,,mss41 and corrected several oversights1 and made some important suggestions4 ,in the twelfth lecture there are some observations on the nature and origin of colours1 which ,newton could not have permitted his friend to publish had he been then in possession of their true theory4 ,according to ,dr4 ,barrow1 ,white is that which discharges a copious light equally clear in every direction2 ,black is that which does not emit light at all1 or which does it very sparingly4 ,red is that which emits a light more clear than usual1 but interrupted by shady interstices4 ,blue is that which discharges a rarified light1 as in bodies which consist of white and black particles arranged alternately4 ,green is nearly allied to blue4 ,yellow is a mixture of much white and a little red2 and ,purple consists of a great deal of blue mixed with a small portion of red4 ,the blue colour of the sea arises from the whiteness of the salt which it contains1 mixed with the blackness of the pure water in which the salt is dissolved2 and the blueness of the shadows of bodies1 seen at the same time by candle and daylight1 arises from the whiteness of the paper mixed with the faint light or blackness of the twilight4 ,these opinions savour so little of genuine philosophy that they must have attracted the observation of ,newton1 and had he discovered at that time that white was a mixture of all the colours1 and black a privation of them all1 he could not have permitted the absurd speculations of his master to pass uncorrected4 ,that ,newton had not distinguished himself by any positive discovery so early as #affd or #affe1 may be inferred also from the circumstances which attended the competition for the law fellowship of ,trinity ,college4 ,the candidates for this appointment were himself and ,mr4 ,robert ,uvedale2 and ,dr4 ,barrow1 then ,master of ,trinity1 having found them perfectly equal in their attainments1 conferred the fellowship on ,mr4 ,uvedale as the senior candidate4 ,in the books of the university1 ,newton is recorded as having been admitted sub-sizer in #affa4 ,he became a scholar in #affd4 ,in #affe he took his degree of ,bachelor of ,arts1 and in #afff1 in consequence of the breaking out of the plague1 he retired to ,woolsthorpe4 ,in #affg he was made ,junior ,fellow4 ,in #affh he took his degree of ,master of ,arts1 and in the same year he was appointed to a ,senior ,fellowship4 ,in #affi1 when ,dr4 ,barrow had resolved to devote his attention to theology1 he resigned the ,lucasian ,professorship of ,mathematics in favour of ,newton1 who may now be considered as having entered upon that brilliant career of discovery the history of which will form the subject of some of the following chapters4 ,,chapter ,,iii4 ,newton1 occupied in grinding ,hyperbolical ,lenses--,his first ,experiments with the ,prism made in #afff--;,he discovers the ,composition of ,white ,light1 and the different ,refrangibility of the ,rays which compose it--,abandons his ,attempts to improve ,refracting ,telescopes and resolves to attempt the ,construction of ,reflecting ones--,he quits ,cambridge on account of the ,plague--,constructs two ,reflecting ,telescopes in #affh1 the first ever executed--,one of them examined by the ,royal ,society1 and shown to the ,king--,he constructs a ,telescope with ,glass ,specula--,recent ,history of the ,reflecting ,telescope-- ,mr4 ,airy's ,glass ,specula--,hadley's ,reflecting ,telescopes--,short's-- ,herschel's--,ramage's--,lord ,oxmantown's4 ,the appointment of ,newton to the ,lucasian chair at ,cambridge seems to have been coeval with his grandest discoveries4 ,the first of these of which the date is well authenticated is that of the different refrangibility of the rays of light1 which he established in #afff4 ,the germ of the doctrine of universal gravitation seems to have presented itself to him in the same year1 or at least in #affg2 and 8in the year #afff or before0#i he was in possession of his method of fluxions1 and he had brought it to such a state in the beginning of #affi1 that he permitted ,dr4 ,barrow to communicate it to ,mr4 ,collins on the #bjth of ,june in that year4 ,although we have already mentioned1 on the authority of a written memorandum of ,newton himself1 that he purchased a prism at ,cambridge in #affd1 yet he does not appear to have made any use of it1 as he informs us that it was in #afff that he 8procured a triangular glass prism to try therewith the celebrated phenomena of colours40#aj ,during that year he had applied himself to the grinding of 8optic glasses1 of other figures than spherical10 and having1 no doubt1 experienced the impracticability of executing such lenses1 the idea of examining the phenomena of colour was one of those sagacious and fortunate impulses which more than once led him to discovery4 ,descartes in his ,dioptrice1 published in #afbi1 and more recently ,james ,gregory in his ,optica ,promota published in #affc1 had shown that parallel and diverging rays could be reflected or refracted1 with mathematical accuracy1 to a point or focus1 by giving the surface a parabolic1 an elliptical1 or a hyperbolic form1 or some other form not spherical4 ,descartes had even invented and described machines by which lenses of these shapes could be ground and polished1 and the perfection of the refracting telescope was supposed to depend on the degree of accuracy with which they could be executed4 ,in attempting to grind glasses that were not spherical1 ,newton seems to have conjectured that the defects of lenses1 and consequently of refracting telescopes1 might arise from some other cause than the imperfect convergency of rays to a single point1 and this conjecture was happily realized in those fine discoveries of which we shall now endeavour to give some account4 ,when ,newton began this inquiry1 philosophers of the highest genius were directing all the energies of their mind to the subject of light1 and to the improvement of the refracting telescope4 ,james ,gregory of ,aberdeen had invented his reflecting telescope4 ,descartes had explained the theory and exerted himself in perfecting the construction of the common refracting telescope1 and ,huygens had not only executed the magnificent instruments by which he discovered the ring and the satellites of ,saturn1 but had begun those splendid researches respecting the nature of light1 and the phenomena of double refraction1 which have led his successors to such brilliant discoveries4 ,newton1 therefore1 arose when the science of light was ready for some great accession1 and at the precise time when he was required to propagate the impulse which it had received from his illustrious predecessors4 ,the ignorance which then prevailed respecting the nature and origin of colours is sufficiently apparent from the account we have already given of ,dr4 ,barrow's speculations on this subject4 ,it was always supposed that light of every colour was equally refracted or bent out of its direction when it passed through any lens or prism1 or other refracting medium2 and though the exhibition of colours by the prism had been often made previous to the time of ,newton1 yet no philosopher seems to have attempted to analyze the phenomena4 ,illustration3 ,fig4 #a4 ,when he had procured his triangular glass prism1 a section of which is shown at ,,abc1 7fig4 #a17 he made a hole ,h in one of his window-shutters1 ,,sht1 and having darkened his chamber1 he let in a convenient quantity of the sun's light ,,rr1 which1 passing through the prism ,,abc1 was so refracted as to exhibit all the different colours on the wall at ,,mn1 forming an image about five times as long as it was broad4 8,it was at first10 says our author1 8a very pleasing divertisement to view the vivid and intense colours produced thereby10 but this pleasure was immediately succeeded by surprise at various circumstances which he had not expected4 ,according to the received laws of refraction1 he expected the image ,,mn to be circular1 like the white image at ,w1 which the sunbeam ,,rr had formed on the wall previous to the interposition of the prism2 but when he found it to be no less than five times larger than its breadth1 it 8excited in him a more than ordinary curiosity to examine from whence it might proceed4 ,he could scarcely think that the various thickness of the glass1 or the termination with shadow or darkness1 could have any influence on light to produce such an effect3 yet he thought it not amiss first to examine those circumstances1 and so find what would happen by transmitting light through parts of the glass of divers thicknesses1 or through holes in the window of divers bignesses1 or by setting the prism without 7on the other side of ,,st71 so that the light might pass through it and be refracted before it was terminated by the hole2 but he found none of these circumstances material4 ,the fashion of the colours was in all those cases the same40 ,newton next suspected that some unevenness in the glass1 or other accidental irregularity1 might cause the dilatation of the colours4 ,in order to try this1 he took another prism ,,bcb1 and placed it in such a manner that the light ,,rrw passing through them both might be refracted contrary ways1 and thus returned by ,,bcb into that course ,,rrw1 from which the prism ,,abc had diverted it1 for by this means he thought the regular effects of the prism ,,abc would be destroyed by the prism ,,bcb1 and the irregular ones more augmented by the multiplicity of refractions4 ,the result was1 that the light which was diffused by the first prism ,,abc into an oblong form1 was reduced by the second prism ,,bcb into a circular one ,w1 with as much regularity as when it did not pass through them at all2 so that whatever was the cause of the length of the image ,,mn1 it did not arise from any irregularity in the prism4 ,our author next proceeded to examine more critically what might be effected by the difference of the incidence of the rays proceeding from different parts of the sun's disk3 but by taking accurate measures of the lines and angles1 he found that the angle of the emergent rays should be #ca minutes equal to the sun's diameter1 whereas the real angle subtended by ,,mn at the hole ,h was #b #di4 ,but as this computation was founded on the hypothesis1 that the sine of the angle of incidence was proportional to the sine of the angle of refraction1 which from his own experience he could not imagine to be so erroneous as to make that angle but #ca1 which was in reality #b #di1 yet 8his curiosity caused him again to take up his prism0 ,,abc1 and having turned it round in both directions1 so as to make the rays ,,rr fall both with greater and with less obliquity upon the face ,,ac1 he found that the colours on the wall did not sensibly change their place2 and hence he obtained a decided proof that they could not be occasioned by a difference in the incidence of the light radiating from different parts of the sun's disk4 ,newton then began to suspect that the rays1 after passing through the prism1 might move in curve lines1 and1 in proportion to the different degrees of curvature1 might tend to different parts of the wall2 and this suspicion was strengthened by the recollection that he had often seen a tennis-ball struck with an oblique racket describe such a curve line4 ,in this case a circular and a progressive motion is communicated to the ball by the stroke1 and in consequence of this1 the direction of its motion was curvilineal1 so that if the rays of light were globular bodies1 they might acquire a circulating motion by their oblique passage out of one medium into another1 and thus move like the tennis-ball in a curve line4 ,notwithstanding1 however1 8this plausible ground of suspicion10 he could discover no such curvature in their direction1 and1 what was enough for his purpose1 he observed that the difference between the length ,,mn of the image1 and the diameter of the hole ,h1 was proportional to their distance ,,hm1 which could not have happened had the rays moved in curvilineal paths4 ,these different hypotheses1 or suspicions1 as ,newton calls them1 being thus gradually removed1 he was at length led to an experiment which determined beyond a doubt the true cause of the elongation of the coloured image4 ,having taken a board with a small hole in it1 he placed it behind the face ,,bc of the prism1 and close to it1 so that he could transmit through the hole any one of the colours in ,,mn1 and keep back all the rest4 ,when the hole1 for example1 was near ,c1 no other light but the red fell upon the wall at ,n4 ,he then placed behind ,n another board with a hole in it1 and behind this board he placed another prism1 so as to receive the red light at ,n1 which passed through this hole in the second board4 ,he then turned round the first prism ,,abc so as to make all the colours pass in succession through these two holes1 and he marked their places on the wall4 ,from the variation of these places1 he saw that the red rays at ,n were less refracted by the second prism than the orange rays1 the orange less than the yellow1 and so on1 the violet being more refracted than all the rest4 ,hence he drew the grand conclusion1 that light was not homogeneous1 but consisted of rays1 some of which were more refrangible than others4 ,as soon as this important truth was established1 ,sir ,isaac saw that a lens which refracts light exactly like a prism must also refract the differently coloured rays with different degrees of force1 bringing the violet rays to a focus nearer the glass than the red rays4 ,this is shown in fig4 #b1 where ,,ll is a convex lens1 and ,s1 ,l1 ,,sl rays of the sun falling upon it in parallel directions4 ,the violet rays existing in the white light ,,sl being more refrangible than the rest1 will be more refracted or bent1 and will meet at ,v1 forming there a violet image of the sun4 ,in like manner the yellow rays will form an image of the sun at ,y1 and so on1 the red rays1 which are the least refrangible1 being brought to a focus at ,r1 and there forming a red image of the sun4 ,illustration3 ,fig4 #b4 ,hence1 if we suppose ,,ll to be the object-glass of a telescope directed to the sun1 and ,,mm an eye-glass through which the eye at ,e sees magnified the image or picture of the sun formed by ,,ll1 it cannot see distinctly all the different images between ,r and ,v4 ,if it is adjusted so as to see distinctly the yellow image at ,y1 as it is in the figure1 it will not see distinctly either the red or violet images1 nor indeed any of them but the yellow one4 ,there will consequently be a distinct yellow image1 with indistinct images of all the other colours1 producing great confusion and indistinctness of vision4 ,as soon as ,sir ,isaac perceived this result of his discovery1 he abandoned his attempts to improve the refracting telescope1 and took into consideration the principle of reflection2 and as he found that rays of all colours were reflected regularly1 so that the angle of reflection was equal to the angle of incidence1 he concluded that1 upon this principle1 optical instruments might be brought to any degree of perfection imaginable1 provided a reflecting substance could be found which could polish as finely as glass1 and reflect as much light as glass transmits1 and provided a method of communicating to it a parabolic figure could be obtained4 ,these difficulties1 however1 appeared to him very great1 and he even thought them insuperable when he considered that1 as any irregularity in a reflecting surface makes the rays deviate five or six times more from their true path than similar irregularities in a refracting surface1 a much greater degree of nicety would be required in figuring reflecting specula than refracting lenses4 ,such was the progress of ,newton's optical discoveries1 when he was forced to quit ,cambridge in #afff by the plague which then desolated ,england1 and more than two years elapsed before he proceeded any farther4 ,in #affh he resumed the inquiry1 and having thought of a delicate method of polishing1 proper for metals1 by which1 as he conceived1 8the figure would be corrected to the last10 he began to put this method to the test of experiment4 ,at this time he was acquainted with the proposal of ,mr4 ,james ,gregory1 contained in his ,optica ,promota1 to construct a reflecting telescope with two concave specula1 the largest of which had a hole in the middle of the larger speculum1 to transmit the light to an eye-glass2#aa but he conceived that it would be an improvement on this instrument to place the eye-glass at the side of the tube1 and to reflect the rays to it by an oval plane speculum4 ,one of these instruments he actually executed with his own hands2 and he gave an account of it in a letter to a friend1 dated ,february #bc;d1 #affh-i1 a letter which is also remarkable for containing the first allusion to his discoveries respecting colours4 ,previous to this he was in correspondence on the subject with ,mr4 ,ent1 afterward ,sir ,george ,ent1 one of the original council of the ,royal ,society1 an eminent medical writer of his day1 and ,president of the ,college of ,physicians4 ,in a letter to ,mr4 ,ent he had promised an account of his telescope to their mutual friend1 and the letter to which we now allude contained the fulfilment of that promise4 ,the telescope was six inches long4 ,it bore an aperture in the large speculum something more than an inch1 and as the eye-glass was a plano-convex lens1 whose focal length was one-sixth or one-seventh of an inch1 it magnified about forty times1 which1 as ,newton remarks1 was more than any six-foot tube 7meaning refracting telescopes7 could do with distinctness4 ,on account of the badness of the materials1 however1 and the want of a good polish1 it represented objects less distinct than a six-feet tube1 though he still thought it would be equal to a three or four feet tube directed to common objects4 ,he had seen through it ,jupiter distinctly with his four satellites1 and also the horns or moon-like phases of ,venus1 though this last phenomenon required some niceness in adjusting the instrument4 ,although ,newton considered this little instrument as in itself contemptible1 yet he regarded it as an 8epitome of what might be done20 and he expressed his conviction that a six-feet telescope might be made after this method1 which would perform as well as a sixty or a hundred feet telescope made in the common way2 and that if a common refracting telescope could be made of the 8purest glass exquisitely polished1 with the best figure that any geometrician 7,descartes1 c47 hath or can design10 it would scarcely perform better than a common telescope4 ,this1 he adds1 may seem a paradoxical assertion1 yet he continues1 8it is the necessary consequence of some experiments which ,i have made concerning the nature of light40 ,the telescope now described possesses a very peculiar interest1 as being the first reflecting one which was ever executed and directed to the heavens4 ,james ,gregory1 indeed1 had attempted1 in #affd or #affe1 to construct his instrument4 ,he employed ,messrs4 ,rives and ,cox1 who were celebrated glass-grinders of that time1 to execute a concave speculum of six feet radius1 and likewise a small one2 but as they had failed in polishing the large one1 and as ,mr4 ,gregory was on the eve of going abroad1 he troubled himself no farther about the experiment1 and the tube of the telescope was never made4 ,some time afterward1 indeed1 he 8made some trials both with a little concave and convex speculum10 but1 8possessed with the fancy of the defective figure1 he would not be at the pains to fix every thing in its due distance40 ,such were the earliest attempts to construct the reflecting telescope1 that noble instrument which has since effected such splendid discoveries in astronomy4 ,looking back from the present advanced state of practical science1 how great is the contrast between the loose specula of ,gregory and the fine ,gregorian telescopes of ,hadley1 ,short1 and ,veitch1--between the humble six-inch tube of ,newton and the gigantic instruments of ,herschel and ,ramage4 ,the success of this first experiment inspired ,newton with fresh zeal1 and though his mind was now occupied with his optical discoveries1 with the elements of his method of fluxions1 and with the expanding germ of his theory of universal gravitation1 yet with all the ardour of youth he applied himself to the laborious operation of executing another reflecting telescope with his own hands4 ,this instrument1 which was better than the first1 though it lay by him several years1 excited some interest at ,cambridge2 and ,sir ,isaac himself informs us1 that one of the fellows of ,trinity ,college had completed a telescope of the same kind1 which he considered as somewhat superior to his own4 ,the existence of these telescopes having become known to the ,royal ,society1 ,newton was requested to send his instrument for examination to that learned body4 ,he accordingly transmitted it to ,mr4 ,oldenburg in ,december1 #afga1 and from this epoch his name began to acquire that celebrity by which it has been so peculiarly distinguished4 ,on the #aath of ,january1 #afgb1 it was announced to the ,royal ,society that his reflecting telescope had been shown to the king1 and had been examined by the president1 ,sir ,robert ,moray1 ,sir ,paul ,neale1 ,sir ,christopher ,wren1 and ,mr4 ,hook4 ,these gentlemen entertained so high an opinion of it1 that1 in order to secure the honour of the contrivance to its author1 they advised the inventor to send a drawing and description of it to ,mr4 ,huygens at ,paris4 ,mr4 ,oldenburg accordingly drew up a description of it in ,latin1 which1 after being corrected by ,mr4 ,newton1 was transmitted to that eminent philosopher4 ,this telescope1 of which the annexed is an accurate drawing1 is carefully preserved in the library of the ,royal ,society of ,london1 with the following inscription3-- 8,invented by ,sir ,isaac ,newton and made with his own hands1 #afga40 ,illustration3 ,fig4 #c4 ,sir ,isaac ,newton's ,reflecting ,telescope4 ,it does not appear that ,newton executed any other reflecting telescopes than the two we have mentioned4 ,he informs us that he repolished and greatly improved a fourteen-feet object-glass1 executed by a ,london artist1 and having proposed in #afgh to substitute glass reflectors in place of metallic specula1 he tried to make a reflecting telescope on this principle four feet long1 and with a magnifying power of #aej4 ,the glass was wrought by a ,london artist1 and though it seemed well finished1 yet1 when it was quicksilvered on its convex side1 it exhibited all over the glass innumerable inequalities1 which gave an indistinctness to every object4 ,he expresses1 however1 his conviction that nothing but good workmanship is wanting to perfect these telescopes1 and he recommends their consideration 8to the curious in figuring glasses40 ,for a period of fifty years this recommendation excited no notice4 ,at last ,mr4 ,james ,short of ,edinburgh1 an artist of consummate skill1 executed about the year #agcj no fewer than six reflecting telescopes with glass specula1 three of fifteen inches1 and three of nine inches in focal length4 ,he found it extremely troublesome to give them a true figure with parallel surfaces2 and several of them when finished turned out useless1 in consequence of the veins which then appeared in the glass4 ,although these instruments performed remarkably well1 yet the light was fainter than he expected1 and from this cause1 combined with the difficulty of finishing them1 he afterward devoted his labours solely to those with metallic specula4 ,at a later period1 in #ahbb1 ,mr4 ,g4 ,b4 ,airy of ,trinity ,college1 and one of the distinguished successors of ,newton in the ,lucasian chair1 resumed the consideration of glass specula1 and demonstrated that the aberration both of figure and of colour might be corrected in these instruments4 ,upon this ingenious principle ,mr4 ,airy executed more than one telescope1 but though the result of the experiment was such as to excite hopes of ultimate success1 yet the construction of such instruments is still a desideratum in practical science4 ,such were the attempts which ,sir ,isaac ,newton made to construct reflecting telescopes2 but notwithstanding the success of his labours1 neither the philosopher nor the practical optician seems to have had courage to pursue them4 ,a ,london artist1 indeed1 undertook to imitate these instruments2 but ,sir ,isaac informs us1 that 8he fell much short of what he had attained1 as he afterward understood by discoursing with the under workmen he had employed40 ,after a long period of fifty years1 ,john ,hadley1 ,esq4 of ,essex1 a ,fellow of the ,royal ,society1 began in #agai or #agbj to execute a reflecting telescope4 ,his scientific knowledge and his manual dexterity fitted him admirably for such a task1 and1 probably after many failures1 he constructed two large telescopes about five feet three inches long1 one of which1 with a speculum six inches in diameter1 was presented to the ,royal ,society in #agbc4 ,the celebrated ,dr4 ,bradley and the ,rev4 ,mr4 ,pound compared it with the great ,huygenian refractor #abc feet long4 ,it bore as high a magnifying power as the ,huygenian telescope3 it showed objects equally distinct1 though not altogether so clear and bright1 and it exhibited every celestial object that had been discovered by ,huygens1--the five satellites of ,saturn1 the shadow of ,jupiter's satellites on his disk1 the black list in ,saturn's ring1 and the edge of his shadow cast on the ring4 ,encouraged and instructed by ,mr4 ,hadley1 ,dr4 ,bradley began the construction of reflecting telescopes1 and succeeded so well that he would have completed one of them1 had he not been obliged to change his residence4 ,some time afterward he and the ,honourable ,samuel ,molyneux undertook the task together at ,kew1 and attempted to execute specula about twenty-six inches in focal length2 but notwithstanding ,dr4 ,bradley's former experience1 and ,mr4 ,hadley's frequent instructions1 it was a long time before they succeeded4 ,the first good instrument which they finished was in ,may1 #agbd4 ,it was twenty-six inches in focal length2 but they afterward completed a very large one of eight feet1 the largest that had ever been made4 ,the first of these instruments was afterward elegantly fitted up by ,mr4 ,molyneux1 and presented to his majesty ,john ,v4 ,king of ,portugal4 ,the great object of these two able astronomers was to reduce the method of making specula to such a degree of certainty that they could be manufactured for public sale4 ,mr4 ,hauksbee had indeed made a good one about three and a half feet long1 and had proceeded to the execution of two others1 one of six feet1 and another of twelve feet in focal length2 but ,mr4 ,scarlet and ,mr4 ,hearne1 having received all the information which ,mr4 ,molyneux had acquired1 constructed them for public sale2 and the reflecting telescope has ever since been an article of trade with every regular optician4 ,as ,sir ,isaac ,newton was at this time ,president of the ,royal ,society1 he had the high satisfaction of seeing his own invention become an instrument of public use1 and of great advantage to science1 and he no doubt felt the full influence of this triumph of his skill4 ,still1 however1 the reflecting telescope had not achieved any new discovery in the heavens4 ,the latest accession to astronomy had been made by the ordinary refractors of ,huygens1 labouring under all the imperfections of coloured light2 and this long pause in astronomical discovery seemed to indicate that man had carried to its farthest limits his power of penetrating into the depths of the universe4 ,this1 however1 was only one of those stationary positions from which human genius takes a new and a loftier elevation4 ,while the ,english opticians were thus practising the recent art of grinding specula1 ,mr4 ,james ,short of ,edinburgh was devoting to the subject all the energies of his youthful mind4 ,in #agcb1 and in the #bb;d year of his age1 he began his labours1 and he carried to such high perfection the art of grinding and polishing specula1 and of giving them the true parabolic figure1 that1 with a telescope fifteen inches in focal length1 he read in the ,philosophical ,transactions at the distance of #ejj feet1 and frequently saw the five satellites of ,saturn together1--a power which was beyond the reach even of ,hadley's six-feet instrument4 ,the celebrated ,maclaurin compared the telescopes of ,short with those made by the best ,london artists1 and so great was their superiority1 that his small telescopes were invariably superior to larger ones from ,london4 ,in #agdb1 after he had settled as an optician in the metropolis1 he executed for ,lord ,thomas ,spencer a reflecting telescope1 twelve feet in focal length1 for #fcjl42 in #ageb he completed one for the ,king of ,spain1 at the expense of #abjjl42 and a short time before his death1 which took place in #agfh1 he finished the specula of the large telescope which was mounted equatorially for the observatory of ,edinburgh by his brother ,thomas ,short1 who was offered twelve hundred guineas for it by the ,king of ,denmark4 ,although the superiority of these instruments1 which were all of the ,gregorian form1 demonstrated the value of the reflecting telescope1 yet no skilful hand had yet directed it to the heavens2 and it was reserved for ,dr4 ,herschel to employ it as an instrument of discovery1 to exhibit to the eye of man new worlds and new systems1 and to bring within the grasp of his reason those remote regions of space to which his imagination even had scarcely ventured to extend its power4 ,so early as #aggd he completed a five-feet ,newtonian reflector1 and he afterward executed no fewer than two hundred #g feet1 one hundred and fifty #aj feet1 and eighty #bj feet specula4 ,in #agha he began a reflector thirty feet long1 and having a speculum thirty-six inches in diameter2 and under the munificent patronage of ,george ,,iii4 he completed1 in #aghi1 his gigantic instrument forty feet long1 with a speculum forty-nine and a half inches in diameter4 ,the genius and perseverance which created instruments of such transcendent magnitude were not likely to terminate with their construction4 ,in the examination of the starry heavens1 the ultimate object of his labours1 ,dr4 ,herschel exhibited the same exalted qualifications1 and in a few years he rose from the level of humble life to the enjoyment of a name more glorious than that of the sages and warriors of ancient times1 and as immortal as the objects with which it will be for ever associated4 ,nor was it in the ardour of the spring of life that these triumphs of reason were achieved4 ,dr4 ,herschel had reached the middle of his course before his career of discovery began1 and it was in the autumn and winter of his days that he reaped the full harvest of his glory4 ,the discovery of a new planet at the verge of the solar system was the first trophy of his skill1 and new double and multiple stars1 and new nebul1 and groups of celestial bodies were added in thousands to the system of the universe4 ,the spring-tide of knowledge which was thus let in upon the human mind continued for a while to spread its waves over ,europe2 but when it sank to its ebb in ,england1 there was no other bark left upon the strand but that of the ,deucalion of ,science1 whose home had been so long upon its waters4 ,during the life of ,dr4 ,herschel1 and during the reign1 and within the dominions of his royal patron1 four new planets were added to the solar system1 but they were detected by telescopes of ordinary power2 and we venture to state1 that since the reign of ,george ,,iii4 no attempt has been made to keep up the continuity of ,dr4 ,herschel's discoveries4 ,mr4 ,herschel1 his distinguished son1 has indeed completed more than one telescope of considerable size2 ,mr4 ,ramage1 of ,aberdeen1 has executed reflectors rivalling almost those of ,slough2--and ,lord ,oxmantown1 an ,irish nobleman of high promise1 is now engaged on an instrument of great size4 ,but what avail the enthusiasm and the efforts of individual minds in the intellectual rivalry of nations8 ,when the proud science of ,england pines in obscurity1 blighted by the absence of the royal favour1 and of the nation's sympathy2--when its chivalry fall unwept and unhonoured2--how can it sustain the conflict against the honoured and marshalled genius of foreign lands8 ,,chapter ,,iv4 ,he delivers a ,course of ,optical ,lectures at ,cambridge--,is elected ,fellow of the ,royal ,society--,he communicates to them his ,discoveries on the different ,refrangibility and ,nature of ,light--,popular ,account of them--,they involve him in various ,controversies--,his ,dispute with ,pardies--,linus--,lucas--,dr4 ,hooke and ,mr4 ,huygens--,the ,influence of these ,disputes on the ,mind of ,newton4 ,although ,newton delivered a course of lectures on optics in the ,university of ,cambridge in the years #affi1 #afgj1 and #afga1 containing his principal discoveries relative to the different refrangibility of light1 yet it is a singular circumstance1 that these discoveries should not have become public through the conversation or correspondence of his pupils4 ,the ,royal ,society had acquired no knowledge of them till the beginning of #afgb1 and his reputation in that body was founded chiefly on his reflecting telescope4 ,on the #bc;d ,december1 #afga1 the celebrated ,dr4 ,seth ,ward1 ,lord ,bishop of ,sarum1 who was the author of several able works on astronomy1 and had filled the astronomical chair at ,oxford1 proposed ,mr4 ,newton as a ,fellow of the ,royal ,society4 ,the satisfaction which he derived from this circumstance appears to have been considerable2 and in a letter to ,mr4 ,oldenburg1 of the #fth ,january1 he says1 8,i am very sensible of the honour done me by the ,bishop of ,sarum in proposing me a candidate2 and which1 ,i hope1 will be further conferred upon me by my election into the ,society2 and if so1 ,i shall endeavour to testify my gratitude1 by communicating what my poor and solitary endeavours can effect towards the promoting your philosophical designs40 ,his election accordingly took place on the #aath ,january1 the same day on which the ,society agreed to transmit a description of his telescope to ,mr4 ,huygens at ,paris4 ,the notice of his election1 and the thanks of the ,society for the communication of his telescope1 were conveyed in the same letter1 with an assurance that the ,society 8would take care that all right should be done him in the matter of this invention40 ,in his next letter to ,oldenburg1 written on the #ahth ,january1 #afga-b1 he announces his optical discoveries in the following remarkable manner3 8,i desire that in your next letter you would inform me for what time the ,society continue their weekly meetings2 because if they continue them for any time1 ,i am purposing them1 to be considered of and examined1 an account of a philosophical discovery which induced me to the making of the said telescope2 and ,i doubt not but will prove much more grateful than the communication of that instrument2 being in my judgment the oddest1 if not the most considerable detection which hath hitherto been made in the operations of nature40 ,this 8considerable detection0 was the discovery of the different refrangibility of the rays of light which we have already explained1 and which led to the construction of his reflecting telescope4 ,it was communicated to the ,royal ,society in a letter to ,mr4 ,oldenburg1 dated ,february #fth1 and excited great interest among its members4 ,the 8solemn thanks0 of the meeting were ordered to be transmitted to its author for his 8very ingenious discourse40 ,a desire was expressed to have it immediately printed1 both for the purpose of having it well considered by philosophers1 and for 8securing the considerable notices thereof to the author against the arrogations of others20 and ,dr4 ,seth ,ward1 ,bishop of ,salisbury1 ,mr4 ,boyle1 and ,dr4 ,hooke were desired to peruse and consider it1 and to bring in a report upon it to the ,society4 ,the kindness of this distinguished body1 and the anxiety which they had already evinced for his reputation1 excited on the part of ,newton a corresponding feeling1 and he gladly accepted of their proposal to publish his discourse in the monthly numbers in which the ,transactions were then given to the world4 8,it was an esteem10 says he1#ab 8of the ,royal ,society for most candid and able judges in philosophical matters1 encouraged me to present them with that discourse of light and colours1 which since they have so favourably accepted of1 ,i do earnestly desire you to return them my cordial thanks4 ,i before thought it a great favour to be made a member of that honourable body2 but ,i am now more sensible of the advantages2 for believe me1 sir1 ,i do not only esteem it a duty to concur with you in the promotion of real knowledge2 but a great privilege1 that1 instead of exposing discourses to a prejudiced and common multitude1 7by which means many truths have been baffled and lost71 ,i may with freedom apply myself to so judicious and impartial an assembly4 ,as to the printing of that letter1 ,i am satisfied in their judgment1 or else ,i should have thought it too straight and narrow for public view4 ,i designed it only to those that know how to improve upon hints of things2 and1 therefore1 to spare tediousness1 omitted many such remarks and experiments as might be collected by considering the assigned laws of refractions2 some of which ,i believe1 with the generality of men1 would yet be almost as taking as any ,i described4 ,but yet1 since the ,royal ,society have thought it fit to appear publicly1 ,i leave it to their pleasure3 and perhaps to supply the aforesaid defects1 ,i may send you some more of the experiments to second it 7if it be so thought fit71 in the ensuing ,transactions40 ,following the order which ,newton himself adopted1 we have1 in the preceding chapter1 given an account of the leading doctrine of the different refrangibility of light1 and of the attempts to improve the reflecting telescope which that discovery suggested4 ,we shall now1 therefore1 endeavour to make the reader acquainted with the other discoveries respecting colours which he at this time communicated to the ,royal ,society4 ,illustration3 ,fig4 #d4 ,having determined1 by experiments already described1 that a beam of white light1 as emitted from the sun1 consisted of seven different colours1 which possess different degrees of refrangibility1 he measured the relative extent of the coloured spaces1 and found them to have the proportions shown in fig4 #d1 which represents the prismatic spectrum1 and which is nothing more than an elongated image of the sun produced by the rays being separated in different degrees from their original direction1 the red being refracted least1 and the violet most powerfully4 ,if we consider light as consisting of minute particles of matter1 we may form some notion of its decomposition by the prism from the following popular illustration4 ,if we take steel filings of seven different degrees of fineness and mix them together1 there are two ways in which we may conceive the mass to be decomposed1 or1 what is the same thing1 all the seven different kinds of filings separated from each other4 ,by means of seven sieves of different degrees of fineness1 and so made that the finest will just transmit the finest powder and detain all the rest1 while the next in fineness transmits the two finest powders and detains all the rest1 and so on1 it is obvious that all the powders may be completely separated from each other4 ,if we again mix all the steel filings1 and laying them upon a table1 hold high above them a flat bar magnet1 so that none of the filings are attracted1 then if we bring the magnet nearer and nearer1 we shall come to a point where the finest filings are drawn up to it4 ,these being removed1 and the magnet brought nearer still1 the next finest powders will be attracted1 and so on till we have thus drawn out of the mass all the powders in a separate state4 ,we may conceive the bar magnet to be inclined to the surface of the steel filings1 and so moved over the mass1 that at the end nearest to them the heaviest or coarsest will be attracted1 and all the remotest and the finest or lighter filings1 while the rest are attracted to intermediate points1 so that the seven different filings are not only separated1 but are found adhering in separate patches to the surface of the flat magnet4 ,the first of these methods1 with the sieves1 may represent the process of decomposing light1 by which certain rays of white light are absorbed1 or stifled1 or stopped in passing through bodies1 while certain other rays are transmitted4 ,the second method may represent the process of decomposing light by refraction1 or by the attraction of certain rays farther from their original direction than other rays1 and the different patches of filings upon the flat magnet may represent the spaces on the spectrum4 ,when a beam of white light is decomposed into the seven different colours of the spectrum1 any particular colour1 when once separated from the rest1 is not susceptible of any change1 or farther decomposition1 whether it is refracted through prisms or reflected from mirrors4 ,it may become fainter or brighter1 but ,newton never could1 by any process1 alter its colour or its refrangibility4 ,among the various bodies which act upon light1 it is conceivable that there might have been some which acted least upon the violet rays and most upon the red rays4 ,newton1 however1 found that this never took place2 but that the same degree of refrangibility always belonged to the same colour1 and the same colour to the same degree of refrangibility4 ,having thus determined that the seven different colours of the spectrum were original or simple1 he was led to the conclusion that whiteness or white light is a compound of all the seven colours of the spectrum1 in the proportions in which they are represented in fig4 #d4 ,in order to prove this1 or what is called the recomposition of white light out of the seven colours1 he employed three different methods4 ,illustration3 ,fig4 #e4 ,when the beam ,,rr was separated into its elementary colours by the prism ,,abc1 he received the colours on another prism ,,bcb1 held either close to the first or a little behind it1 and by the opposite refraction of this prism they were all refracted back into a beam of white light ,,bw1 which formed a white circular image on the wall at ,w1 similar to what took place before any of the prisms were placed in its way4 ,the other method of recomposing white light consisted in making the spectrum fall upon a lens at some distance from it4 ,when a sheet of white paper was held behind the lens1 and removed to a proper distance1 the colours were all refracted into a circular spot1 and so blended as to reproduce light so perfectly white as not to differ sensibly from the direct light of the sun4 ,the last method of recomposing white light was one more suited to vulgar apprehension4 ,it consisted in attempting to compound a white by mixing the coloured powders used by painters4 ,he was aware that such colours1 from their very nature1 could not compose a pure white2 but even this imperfection in the experiment he removed by an ingenious device4 ,he accordingly mixed one part of red lead1 four parts of blue bice1 and a proper proportion of orpiment and verdigris4 ,this mixture was dun1 like wood newly cut1 or like the human skin4 ,he now took one-third of the mixture and rubbed it thickly on the floor of his room1 where the sun shone upon it through the opened casement1 and beside it1 in the shadow1 he laid a piece of white paper of the same size4 8,then going from them to the distance of twelve or eighteen feet1 so that he could not discern the unevenness of the surface of the powder nor the little shadows let fall from the gritty particles thereof2 the powder appeared intensely white1 so as to transcend even the paper itself in whiteness40 ,by adjusting the relative illumination of the powders and the paper1 he was able to make them both appear of the very same degree of whiteness4 8,for10 says he1 8when ,i was trying this1 a friend coming to visit me1 ,i stopped him at the door1 and before ,i told him what the colours were1 or what ,i was doing1 ,i asked him which of the two whites were the best1 and wherein they differed6 ,and after he had at that distance viewed them well1 he answered1 that they were both good whites1 and that he could not say which was best1 nor wherein their colours differed40 ,hence ,newton inferred that perfect whiteness may be compounded of different colours4 ,as all the various shades of colour which appear in the material world can be imitated by intercepting certain rays in the spectrum1 and uniting all the rest1 and as bodies always appear of the same colour as the light in which they are placed1 he concluded1 that the colours of natural bodies are not qualities inherent in the bodies themselves1 but arise from the disposition of the particles of each body to stop or absorb certain rays1 and thus to reflect more copiously the rays which are not thus absorbed4 ,no sooner were these discoveries given to the world than they were opposed with a degree of virulence and ignorance which have seldom been combined in scientific controversy4 ,unfortunately for ,newton1 the ,royal ,society contained few individuals of pre-eminent talent capable of appreciating the truth of his discoveries1 and of protecting him against the shafts of his envious and ignorant assailants4 ,this eminent body1 while they held his labours in the highest esteem1 were still of opinion that his discoveries were fair subjects of discussion1 and their secretary accordingly communicated to him all the papers which were written in opposition to his views4 ,the first of these was by a ,jesuit named ,ignatius ,pardies1 ,professor of ,mathematics at ,clermont1 who pretended that the elongation of the sun's image arose from the inequal incidence of the different rays on the first face of the prism1 although ,newton had demonstrated in his own discourse that this was not the case4 ,in ,april1 #afgb1 ,newton transmitted to ,oldenburg a decisive reply to the animadversions of ,pardies2 but1 unwilling to be vanquished1 this disciple of ,descartes took up a fresh position1 and maintained that the elongation of the spectrum might be explained by the diffusion of light on the hypothesis of ,grimaldi1 or by the diffusion of undulations on the hypothesis of ,hook4 ,newton again replied to these feeble reasonings2 but he contented himself with reiterating his original experiments1 and confirming them by more popular arguments1 and the vanquished ,jesuit wisely quitted the field4 ,another combatant soon sprung up in the person of one ,francis ,linus1 a physician in ,liege1#ac who1 on the #fth ,october1 #afgd1 addressed a letter to a friend in ,london1 containing animadversions on ,newton's doctrine of colours4 ,he boldly affirms1 that in a perfectly clear sky the image of the sun made by a prism is never elongated1 and that the spectrum observed by ,newton was not formed by the true sunbeams1 but by rays proceeding from some bright cloud4 ,in support of these assertions1 he appeals to frequently repeated experiments on the refractions and reflections of light which he had exhibited thirty years before to ,sir ,kenelm ,digby1 8who took notes upon them20 and he unblushingly states1 that1 if ,newton had used the same industry as he did1 he would never have 8taken so impossible a task in hand1 as to explain the difference between the length and breadth of the spectrum by the received laws of refraction40 ,when this letter was shown to ,newton1 he refused to answer it2 but a letter was sent to ,linus referring him to the answer to ,pardies1 and assuring him that the experiments on the spectrum were made when there was no bright cloud in the heavens4 ,this reply1 however1 did not satisfy the ,dutch experimentalist4 ,on the #beth ,february1 #afge1 he addressed another letter to his friend1 in which he gravely attempts to prove that the experiment of ,newton was not made in a clear day2--that the prism was not close to the hole1--and that the length of the spectrum was not perpendicular1 or parallel to the length of the prism4 ,such assertions could not but irritate even the patient mind of ,newton4 ,he more than once declined the earnest request of ,oldenburg to answer these observations2 he stated1 that1 as the dispute referred to matters of fact1 it could only be decided before competent witnesses1 and he referred to the testimony of those who had seen his experiments4 ,the entreaties of ,oldenburg1 however1 prevailed over his own better judgment1 and1 8lest ,mr4 ,linus should make the more stir10 this great man was compelled to draw up a long and explanatory reply to reasonings utterly contemptible1 and to assertions altogether unfounded4 ,this answer1 dated ,november #acth1 #afge1 could scarcely have been perused by ,linus1 who was dead on the #aeth ,december1 when his pupil ,mr4 ,gascoigne1 took up the gauntlet1 and declared that ,linus had shown to various persons in ,liege the experiment which proved the spectrum to be circular1 and that ,sir ,isaac could not be more confident on his side than they were on the other4 ,he admitted1 however1 that the different results might arise from different ways of placing the prism4 ,pleased with the 8handsome genius of ,mr4 ,gascoigne's letter10 ,newton replied even to it1 and suggested that the spectrum seen by ,linus may have been the circular one1 formed by one reflexion1 or1 what he thought more probable1 the circular one formed by two refractions1 and one intervening reflection from the base of the prism1 which would be coloured if the prism was not an isosceles one4 ,this suggestion seems to have enlightened the ,dutch philosophers4 ,mr4 ,gascoigne1 having no conveniences for making the experiments pointed out by ,newton1 requested ,mr4 ,lucas of ,liege to perform them in his own house4 ,this ingenious individual1 whose paper gave great satisfaction to ,newton1 and deserves the highest praise1 confirmed the leading results of the ,english philosopher2 but though the refracting angle of his prism was #fj and the refractions equal1 he never could obtain a spectrum whose length was more than from three to three and a half times its breadth1 while ,newton found the length to be five times its breadth4 ,in our author's reply1 he directs his attention principally to this point of difference4 ,he repeated his measures with each of the three angles of three different prisms1 and he affirmed that ,mr4 ,lucas might make sure to find the image as long or longer than he had yet done1 by taking a prism with plain surfaces1 and with an angle of #ff or #fg4 ,he admitted that the smallness of the angle in ,mr4 ,lucas's prism1 viz4 #fj1 did not account for the shortness of the spectrum which he obtained with it2 and he observed in one of his own prisms that the length of the image was greater in proportion to the refracting angle than it should have been2 an effect which he ascribes to its having a greater refractive power4 ,there is every reason to believe that the prism of ,lucas had actually a less dispersive power than that of ,newton2 and had the ,dutch philosopher measured its refractive power instead of guessing it1 or had ,newton been less confident than he was#ad that all other prisms must give a spectrum of the same length as his in relation to its refracting angle and its index of refraction1 the invention of the achromatic telescope would have been the necessary result4 ,the objections of ,lucas drove our author to experiments which he had never before made1--to measure accurately the lengths of the spectra with different prisms of different angles and different refractive powers2 and had the ,dutch philosopher maintained his position with more obstinacy1 he would have conferred a distinguished favour upon science1 and would have rewarded ,newton for all the vexation which had sprung from the minute discussion of his optical experiments4 ,such was the termination of his disputes with the ,dutch philosophers1 and it can scarcely be doubted that it cost him more trouble to detect the origin of his adversaries' blunders1 than to establish the great truths which they had attempted to overturn4 ,harassing as such a controversy must have been to a philosopher like ,newton1 yet it did not touch those deep-seated feelings which characterize the noble and generous mind4 ,no rival jealousy yet pointed the arguments of his opponents2--no charges of plagiarism were yet directed against his personal character4 ,these aggravations of scientific controversy1 however1 he was destined to endure2 and in the dispute which he was called to maintain both against ,hooke and ,huygens1 the agreeable consciousness of grappling with men of kindred powers was painfully imbittered by the personality and jealousy with which it was conducted4 ,dr4 ,robert ,hooke was about seven years older than ,newton1 and was one of the ninety-eight original or unelected members of the ,royal ,society4 ,he possessed great versatility of talent1 yet1 though his genius was of the most original cast1 and his acquirements extensive1 he had not devoted himself with fixed purpose to any particular branch of knowledge4 ,his numerous and ingenious inventions1 of which it is impossible to speak too highly1 gave to his studies a practical turn which unfitted him for that continuous labour which physical researches so imperiously demand4 ,the subjects of light1 however1 and of gravitation seem to have deeply occupied his thoughts before ,newton appeared in the same field1 and there can be no doubt that he had made considerable progress in both of these inquiries4 ,with a mind less divergent in its pursuits1 and more endowed with patience of thought1 he might have unveiled the mysteries in which both these subjects were enveloped1 and preoccupied the intellectual throne which was destined for his rival2 but the infirm state of his health1 the peevishness of temper which this occasioned1 the number of unfinished inventions from which he looked both for fortune and fame1 and1 above all1 his inordinate love of reputation1 distracted and broke down the energies of his powerful intellect4 ,in the more matured inquiries of his rivals he recognised1 and often truly1 his own incompleted speculations2 and when he saw others reaping the harvest for which he had prepared the ground1 and of which he had sown the seeds1 it was not easy to suppress the mortification which their success inspired4 ,in the history of science1 it has always been a difficult task to adjust the rival claims of competitors1 when the one was allowed to have completed what the other was acknowledged to have begun4 ,he who commences an inquiry1 and publishes his results1 often goes much farther than he has announced to the world1 and1 pushing his speculations into the very heart of the subject1 frequently submits them to the ear of friendship4 ,from the pedestal of his published labours his rival begins his researches1 and brings them to a successful issue2 while he has in reality done nothing more than complete and demonstrate the imperfect speculations of his predecessor4 ,to the world1 and to himself1 he is no doubt in the position of the principal discoverer3 but there is still some apology for his rival when he brings forward his unpublished labours2 and some excuse for the exercise of personal feeling1 when he measures the speed of his rival by his own proximity to the goal4 ,the conduct of ,dr4 ,hooke would have been viewed with some such feeling1 had not his arrogance on other occasions checked the natural current of our sympathy4 ,when ,newton presented his reflecting telescope to the ,royal ,society1 ,dr4 ,hooke not only criticised the instrument with undue severity1 but announced that he possessed an infallible method of perfecting all kinds of optical instruments1 so that 8whatever almost hath been in notion and imagination1 or desired in optics1 may be performed with great facility and truth40 ,hooke had been strongly impressed with the belief1 that light consisted in the undulations of a highly elastic medium pervading all bodies2 and1 guided by his experimental investigation of the phenomena of diffraction1 he had even announced the great principle of interference1 which has performed such an important part in modern science4 ,regarding himself1 therefore1 as in possession of the true theory of light1 he examined the discoveries of ,newton in their relation to his own speculative views1 and1 finding that their author was disposed to consider that element as consisting of material particles1 he did not scruple to reject doctrines which he believed to be incompatible with truth4 ,dr4 ,hooke was too accurate an observer not to admit the general correctness of ,newton's observations4 ,he allowed the existence of different refractions1 the unchangeableness of the simple colours1 and the production of white light by the union of all the colours of the spectrum2 but he maintained that the different refractions arose from the splitting and rarefying of ethereal pulses1 and that there are only two colours in nature1 viz4 red and violet1 which produce by their mixture all the rest1 and which are themselves formed by the two sides of a split pulse or undulation4 ,in reply to these observations1 ,newton wrote an able letter to ,oldenburg1 dated ,june #aa1 #afgb1 in which he examined with great boldness and force of argument the various objections of his opponent1 and maintained the truth of his doctrine of colours1 as independent of the two hypotheses respecting the origin and production of light4 ,he acknowledged his own partiality to the doctrine of the materiality of light2 he pointed out the defects of the undulatory theory2 he brought forward new experiments in confirmation of his former results2 and he refuted the opinions of ,hooke respecting the existence of only two simple colours4 ,no reply was made to the powerful arguments of ,newton2 and ,hooke contented himself with laying before the ,society his curious observations on the colours of soap-bubbles1 and of plates of air1 and in pursuing his experiments on the diffraction of light1 which1 after an interval of two years1 he laid before the same body4 ,after he had thus silenced the most powerful of his adversaries1 ,newton was again called upon to defend himself against a new enemy4 ,christian ,huygens1 an eminent mathematician and natural philosopher1 who1 like ,hooke1 had maintained the undulatory theory of light1 transmitted to ,oldenburg various animadversions on the ,newtonian doctrine2 but though his knowledge of optics was of the most extensive kind1 yet his objections were nearly as groundless as those of his less enlightened countryman4 ,attached to his own hypothesis respecting the nature of light1 namely1 to the system of undulation1 he seems1 like ,dr4 ,hooke1 to have regarded the discoveries of ,newton as calculated to overturn it2 but his principal objections related to the composition of colours1 and particularly of white light1 which he alleged could be obtained from the union of two colours1 yellow and blue4 ,to and similar objections1 ,newton replied that the colours in question were not simple yellows and blues1 but were compound colours1 in which1 together1 all the colours of the spectrum were themselves blended2 and though he evinced some strong traces of feeling at being again put upon his defence1 yet his high respect for ,huygens induced him to enter with patience on a fresh development of his doctrine4 ,huygens felt the reproof which the tone of this answer so gently conveyed1 and in writing to ,oldenburg1 he used the expression1 that ,mr4 ,newton 8maintained his doctrine with some concern40 ,to this our author replied1 8,as for ,mr4 ,huygens's expression1 ,i confess it was a little ungrateful to me1 to meet with objections which had been answered before1 without having the least reason given me why those answers were insufficient40 ,but though ,huygens appears in this controversy as a rash objector to the ,newtonian doctrine1 it was afterward the fate of ,newton to play a similar part against the ,dutch philosopher4 ,when ,huygens published his beautiful law of double refraction in ,iceland spar1 founded on the finest experimental analysis of the phenomena1 though presented as a result of the undulatory system1 ,newton not only rejected it1 but substituted for it another law entirely inconsistent with the experiments of ,huygens1 which ,newton himself had praised1 and with those of all succeeding philosophers4 ,the influence of these controversies on the mind of ,newton seems to have been highly exciting4 ,even the satisfaction of humbling all his antagonists he did not feel as a sufficient compensation for the disturbance of his tranquillity4 8,i intend10 says he1#ae 8to be no farther solicitous about matters of philosophy4 ,and therefore ,i hope you will not take it ill if you find me never doing any thing more in that kind2 or rather that you will favour me in my determination1 by preventing1 so far as you can conveniently1 any objections or other philosophical letters that may concern me40 ,in a subsequent letter in #afge1 he says1 8,i had some thoughts of writing a further discourse about colours1 to be read at one of your assemblies2 but find it yet against the grain to put pen to paper any more on that subject20 and in a letter to ,leibnitz1 dated ,december the #ith1 #afge1 he observes1 8,i was so persecuted with discussions arising from the publication of my theory of light1 that ,i blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow40 ,,chapter ,v4 ,mistake of ,newton in supposing that the ,improvement of ,refracting ,telescopes was hopeless--,mr4 ,hall invents the ,achromatic ,telescope-- ,principles of the ,achromatic ,telescope explained--,it is re-invented by ,dollond1 and improved by future ,artists--,dr4 ,blair's ,aplanatic ,telescope--,mistakes in ,newton's ,analysis of the ,spectrum--,modern ,discoveries respecting the ,structure of the ,spectrum4 ,the new doctrines of the composition of light1 and of the different refrangibility of the rays which compose it1 having been thus established upon an impregnable basis1 it will be interesting to take a general view of the changes which they have undergone since the time of ,newton1 and of their influence on the progress of optical discovery4 ,there is no fact in the history of science more singular than that ,newton should have believed that all bodies produced spectra of equal length1 or separated the red and violet rays to equal distances when the refraction of the mean rays was the same4 ,this opinion1 unsupported by experiments1 and not even sanctioned by any theoretical views1 seems to have been impressed upon his mind with all the force of an axiom4#af ,even the shortness of the spectrum observed by ,lucas did not rouse him to further inquiry2 and when1 under the influence of this blind conviction he pronounced the improvement of the refracting telescope to be desperate1 he checked for a long time the progress of this branch of science1 and furnished to future philosophers a lesson which cannot be too deeply studied4 ,in #agbi1 about two years after the death of ,sir ,isaac1 an individual unknown to science broke the spell in which the subject of the spectrum had been so singularly bound4 ,mr4 ,chester ,more ,hall1 of ,more ,hall in ,essex1 while studying the mechanism of the human eye1 was led to suppose that telescopes might be improved by a combination of lenses of different refractive powers1 and he actually completed several object-glasses upon this principle4 ,the steps by which he arrived at such a construction have not been recorded2 but it is obvious that he must have discovered what escaped the sagacity of ,newton1 that prisms made of different kinds of glass produced different degrees of separation of the red and violet rays1 or gave spectra of different lengths when the refraction of the middle ray of the spectrum was the same4 ,illustration3 ,fig4 #f4 ,in order to explain how such a property led him to the construction of a telescope without colour1 or an achromatic telescope1 let us take a lens ,,ll of crown or plate glass1 whose focal length ,,ly is about twelve inches4 ,when the sun's rays ,,sl1 ,,sl fall upon it1 the red will be refracted to ,r1 the yellow to ,y1 and the violet to ,v4 ,if we now place behind it a concave lens ll of the same glass1 and of the same focus or curvature1 it will be found1 both by experiment and by drawing the refracted rays1 according to the rules given in elementary works1 that the concave glass ll will refract the rays ,,lr1 ,,lr into ,,ls1 ,,ls1 and the rays ,,lv1 ,,lv into ,,ls1 ,,ls free of all colour2 but as these rays will be parallel1 the two lenses will not have a focus1 and consequently cannot form an image so as to be used as the object-glass of a telescope4 ,this is obvious from another consideration2 for since the curvatures of the convex and concave lenses are the same1 the two put together will be exactly the same as if they were formed out of a single piece of glass1 having parallel surfaces like a watch-glass1 so that the parallel rays of light ,,sl1 ,,sl will pass on in the same direction ,,ls1 ,,ls affected by equal and opposite refractions as in a piece of plane glass4 ,now1 since the convex lens ,,ll separated the white light ,,sl1 ,,sl into its component coloured rays1 ,,lv1 ,,lv being the extreme violet1 and ,,lr1 ,,lr the extreme red2 it follows that a similar concave lens of the same glass is capable of uniting into white light ,,ls1 ,,ls rays1 as much separated as ,,lv1 ,,lr are4 ,consequently1 if we take a concave lens ll of the same1 or of a greater refractive power than the convex one1 and having the power of uniting rays farther separated than ,,lv1 ,,lr are1 a less concavity in the lens ll will be sufficient to unite the rays ,,lv1 ,,lr into a white ray ,,ls2 but as the lens ll is now less concave than the lens ,,ll is convex1 the concavity will predominate1 and the uncoloured rays ,,ls1 ,,ls will no longer be parallel1 but will converge to some point ,o1 where they will form a colourless or achromatic image of the sun4 ,the effect now described may be obtained by making the convex lens ,,ll of crown or of plate glass1 and the concave one of flint glass1 or that of which wineglasses are made4 ,if the concave lens ll has a greater refractive power than ,,ll1 which is always the case1 the only effect of it will be to make the rays converge to a focus more remote than ,o1 or to render a less curvature necessary in ll1 if ,o is fixed for the focus of the combined lenses4 ,such is the principle of the achromatic telescope as constructed by ,mr4 ,hall4 ,this ingenious individual employed working opticians to grind his lenses1 and he furnished them with the radii of the surfaces1 which were adjusted to correct the aberration of figure as well as of colour4 ,his invention1 therefore1 was not an accidental combination of a convex and a concave lens of different kinds of glass1 which might have been made merely for experiment2 but it was a complete achromatic telescope1 founded on a thorough knowledge of the different dispersive powers of crown and flint glass4 ,it is a curious circumstance1 however1 in the history of the telescope1 that this invention was actually lost4 ,mr4 ,hall never published any account of his labours1 and it is probable that he kept them secret till he should be able to present his instrument to the public in a more perfect form2 and it was not till ,john ,dollond had discovered the property of light upon which the instrument depends1 and had actually constructed many fine telescopes1 that the previous labours of ,mr4 ,hall were laid before the public4#ag ,from this period the achromatic telescope underwent gradual improvement1 and by the successive labours of ,dollond1 ,ramsden1 ,blair1 ,tulley1 ,guinand1 ,lerebours1 and ,fraunhofer1 it has become one of the most valuable instruments in physical science4 ,although the achromatic telescope1 as constructed by ,dollond1 was founded on the principle that the spectra formed by crown and flint glass differed only in their relative lengths1 when the refraction of the mean ray was the same1 yet by a more minute examination of the best instruments1 it was found that they exhibited white or luminous objects tinged on one side with a green fringe1 and on the other with one of a claret colour4 ,these colours1 which did not arise from any defect of skill in the artist1 were found to arise from a difference in the extent of the coloured spaces in two equal spectra formed by crown and by flint glass4 ,this property was called the irrationality of the coloured spaces1 and the uncorrected colours which remained when the primary spectrum of the crown glass was corrected by the primary spectrum of the flint glass were called the secondary or residual spectrum4 ,by a happy contrivance1 which it would be out of place here to describe1 ,dr4 ,blair succeeded in correcting this secondary spectrum1 or in removing the green and claret-coloured fringes which appeared in the best telescopes1 and to this contrivance he gave the name of the ,aplanatic ,telescope4 ,but while ,newton thus overlooked these remarkable properties of the prismatic spectrum1 as formed by different bodies1 he committed some considerable mistakes in his examination of the spectrum which was under his own immediate examination4 ,it does not seem to have occurred to him that the relations of the coloured spaces must be greatly modified by the angular magnitude of the sun or the luminous body1 or aperture from which the spectrum is obtained2 and misled by an apparent analogy between the length of the coloured spaces and the divisions of a musical chord1#ah he adopted the latter1 as representing the proportion of the coloured spaces in every beam of white light4 ,had two other observers1 one situated in ,mercury1 and the other in ,jupiter1 studied the prismatic spectrum of the sun by the same instruments1 and with the same sagacity as ,newton1 it is demonstrable that they would have obtained very different results4 ,on account of the apparent magnitude of the sun in ,mercury1 the observer there would obtain a spectrum entirely without green1 having red1 orange1 and yellow at one end1 the white in the middle1 and terminated at the other end with blue and violet4 ,the observer in ,jupiter would1 on the contrary1 have obtained a spectrum in which the colours were much more condensed4 ,on the planet ,saturn a spectrum exactly similar would have been obtained1 notwithstanding the greater diminution of the sun's apparent diameter4 ,it may now be asked1 which of all these spectra are we to consider as exhibiting the number1 and arrangement1 and extent of the coloured spaces proper to be adopted as the true analysis of a solar ray4 ,the spectrum observed by ,newton has surely no claim to our notice1 merely because it was observed upon the surface of the earth4 ,the spectrum obtained in ,mercury affords no analysis at all of the incident beam1 the colours being almost all compound1 and not homogeneous1 and that of ,newton is liable to the same objection4 ,had ,newton examined his spectrum under the very same circumstances in winter and in summer1 he would have found the analysis of the beam more complete in summer1 on account of the diminution of the sun's diameter2 and1 therefore1 we are entitled to say that neither the number nor the extent of the coloured spaces1 as given by ,newton1 are those which belong to homogeneous and uncompounded light4 ,the spectrum obtained in ,jupiter and ,saturn is the only one where the analysis is complete1 as it is incapable of having its character altered by any farther diminution of the sun's diameter4 ,hence we are forced to conclude1 not only that the number and extent of the primitive homogeneous colours1 as given by ,newton1 are incorrect2 but that if he had attempted to analyze some of the primitive tints in the spectrum1 he would have found them decidedly composed of heterogeneous rays4 ,there is one consequence of these observations which is somewhat interesting4 ,a rainbow formed in summer1 when the sun's diameter is least1 must have its colours more condensed and homogeneous than in winter1 when the size of its disk is a maximum1 and when the upper or the under limb of the sun is eclipsed1 a rainbow formed at that time will lose entirely the yellow rays1 and have the green and the red in perfect contact4 ,for the same reason1 a rainbow formed in ,venus and ,mercury will be destitute of green rays1 and have a brilliant bow of white light separating two coloured arches2 while in ,mars1 ,jupiter1 ,saturn1 and the ,georgian planet1 the bow will exhibit only four homogeneous colours4 ,from his analysis of the solar spectrum1 ,newton concluded1 8that to the same degree of refrangibility ever belonged the same colour1 and to the same colour ever belonged the same degree of refrangibility20 and hence he inferred1 that red1 orange1 yellow1 green1 blue1 indigo1 and violet were primary and simple colours4 ,he admitted1 indeed1 that 8the same colours in specie with these primary ones may be also produced by composition4 ,for a mixture of yellow and blue makes green1 and of red and yellow makes orange20 but such compound colours were easily distinguished from the simple colours of the spectrum by the circumstance1 that they are always capable of being resolved by the action of the prism into the two colours which compose them4 ,this view of the composition of the spectrum might have long remained unchallenged1 had we not been able to apply to it a new mode of analysis4 ,though we cannot separate the green rays of the spectrum into yellow and blue by the refraction of prisms1 yet if we possessed any substance which had a specific attraction for blue rays1 and which stopped them in their course1 and allowed the yellow rays to pass1 we should thus analyze the green as effectually as if they were separated by refraction4 ,the substance which possesses this property is a purplish blue glass1 similar to that of which finger-glasses are made4 ,when we view through a piece of this glass1 about the twentieth of an inch thick1 a brilliant prismatic spectrum1 we find that it has exercised a most extraordinary absorptive action on the different colours which compose it4 ,the red part of the spectrum is divided into two red spaces1 separated by an interval entirely devoid of light4 ,next to the inner red space comes a space of bright yellow1 separated from the red by a visible interval4 ,after the yellow comes the green1 with an obscure space between them1 then follows the blue and the violet1 the last of which has suffered little or no diminution4 ,now it is very obvious1 that in this experiment1 the blue glass has actually absorbed the red rays1 which1 when mixed with the yellow on one side1 constituted orange1 and the blue rays1 which1 when mixed with the yellow on the other side1 constituted green1 so that the insulation of the yellow rays thus effected1 and the disappearance of the orange1 and of the greater part of the green light1 proves beyond a doubt that the orange and green colours in the spectrum are compound colours1 the former consisting of red and yellow rays1 and the latter of yellow and blue rays of the very same refrangibility4 ,if we compare the two red spaces of the spectrum seen through the blue glass with the red space seen without the blue glass1 it will be obvious that the red has experienced such an alteration in its tint by the action of the blue glass1 as would be effected by the absorption of a small portion of yellow rays2 and hence we conclude1 that the red of the spectrum contains a slight tinge of yellow1 and that the yellow space extends over more than one-half of the spectrum1 including the red1 orange1 yellow1 green1 and blue spaces4 ,i have found also that red light exists in the yellow space1 and it is certain that in the violet space red light exists in a state of combination with the blue rays4 ,from these and other facts which it would be out of place here to explain1 ,i conclude that the prismatic spectrum consists of three different spectra1 viz4 red1 yellow1 and blue1 all having the same length1 and all overlapping each other4 ,hence red1 yellow1 and blue rays of the very same refrangibility coexist at every point of the spectrum2 but the colour at any one point will be that of the predominant ray1 and will depend upon the relative distance of the point from the maximum ordinate of the curve which represents the intensity of the light of each of the three spectra4 ,illustration3 ,fig4 #g4 ,this structure of the spectrum1 which harmonizes with the old hypothesis of three simple colours1 will be understood from the annexed diagram1 where ,,mn is the spectrum of seven colours1 all compounded of the three simple ones1 red1 yellow1 and blue4 ,the ordinates of the curves ,r1 ,y1 and ,b will express the intensities of each colour at different points of the spectrum4 ,at the red extremity ,m of the spectrum1 the pure red is scarcely altered by the very slight intermixture of yellow and blue4 ,farther on in the red space1 the yellow begins to make the red incline to scarlet4 ,it then exists in sufficient quantity to form orange1 and1 as the red declines1 the yellow predominates over the feeble portion of red and blue which are mixed with it4 ,as the yellow decreases in intensity1 the increasing blue forms with it a good green1 and the blue rising to its maximum speedily overpowers the small portion of yellow and red4 ,when the blue becomes very faint1 the red exhibits its influence in converting it into violet1 and the yellow ceases to exercise a marked influence on the tint4 ,the influence of the red over the blue space is scarcely perceptible1 on account of the great intensity of the blue light2 but we may easily conceive it to reappear and form the violet light1 not only from the rapid decline of the blue light1 but from the greater influence of the red rays upon the retina4 ,these views may1 perhaps1 be more clearly understood by supposing that a certain portion of white light is actually formed at every point of the spectrum by the union of the requisite number of the three coloured rays that exist at any point4 ,the white light thus formed will add to the brilliancy without affecting the tint of the predominant colour4 ,in the violet space we may conceive the small portion of yellow which exists there to form white light with a part of the blue and a part of the red1 so that the resulting tint will be violet1 composed of the blue and the small remaining portion of red1 mixed with the white light4 ,this white light will possess the remarkable property of not being susceptible of decomposition by the analysis of the prism1 as it is composed of red1 yellow1 and blue rays of the very same refrangibility4 ,the insulation of this white light by the absorption of the predominant colours ,i have effected in the green1 yellow1 and red spaces1 and by the use of new absorbing media we may yet hope to exhibit it in some of the other colours1 particularly in the brightest part of the blue space1 where an obvious approximation to it takes place4 ,among the most important modern discoveries respecting the spectrum we must enumerate that of fixed dark and coloured lines1 which we owe to the sagacity of ,dr4 ,wollaston and ,m4 ,fraunhofer4 ,two or three of these lines were discovered by ,dr4 ,wollaston1 but nearly #fjj have been detected by means of the fine prisms and the magnificent apparatus of the ,bavarian optician4 ,these lines are parallel to one another1 and perpendicular to the length of the spectrum4 ,the largest occupy a space from #e to #aj in breadth4 ,sometimes they occur in well-defined lines1 and at other times in groups2 and in all spectra formed from solar light1 they preserve the same order and intensity1 and the same relative position to the coloured spaces1 whatever be the nature of the prism by which they are produced4 ,hence these lines are fixed points1 by which the relative dispersive powers of different media may be ascertained with a degree of accuracy hitherto unknown in this branch of science4 ,in the light of the fixed stars1 and in that of artificial flames1 a different system of lines is produced1 and this system remains unaltered1 whatever be the nature of the prism by which the spectrum is formed4 ,the most important fixed lines in the spectrum formed by light emitted from the sun1 whether it is reflected from the sky1 the clouds1 or the moon1 may be easily seen by looking at a narrow slit in the window-shutter of a dark room1 through a hollow prism formed of plates of parallel glass1 and filled with any fluid of a considerable dispersive power4 ,the slit should not greatly exceed the twentieth of an inch1 and the eye should look through the thinnest edge of the prism where there is the least thickness of fluid4 ,these lines ,i have found to be the boundaries of spaces within which the rays have particular affinities for particular bodies4 ,,chapter ,,vi4 ,colours of thin ,plates first studied by ,boyle and ,hooke--,newton determines the ,law of their ,production--,his ,theory of ,fits of ,easy ,reflection and ,transmission--,colours of thick ,plates4 ,in examining the nature and origin of colours as the component parts of white light1 the attention of ,newton was directed to the curious subject of the colours of thin plates1 and to its application to explain the colours of natural bodies4 ,his earliest researches on this subject were communicated1 in his ,discourse on ,light and ,colours1 to the ,royal ,society1 on the #ith ,december1 #afge1 and were read at subsequent meetings of that body4 ,this discourse contained fuller details respecting the composition and decomposition of light than he had given in his letter to ,oldenburg1 and was concluded with nine propositions1 showing how the colours of thin transparent plates stand related to those of all natural bodies4 ,the colours of thin plates seem to have been first observed by ,mr4 ,boyle4 ,dr4 ,hooke afterward studied them with some care1 and gave a correct account of the leading phenomena1 as exhibited in the coloured rings upon soap-bubbles1 and between plates of glass pressed together4 ,he recognised that the colour depended upon some certain thickness of the transparent plate1 but he acknowledges that he had attempted in vain to discover the relation between the thickness of the plate and the colour which it produced4 ,dr4 ,hooke succeeded in splitting a mineral substance1 called mica1 into films of such extreme thinness as to give brilliant colours4 ,one plate1 for example1 gave a yellow colour1 another a blue colour1 and the two together a deep purple2 but1 as plates which produced those colours were always less than the #ab1jjjth part of an inch thick1 it was quite impracticable1 by any contrivance yet discovered1 to measure their thickness1 and determine the law according to which the colour varied with the thickness of the film4 ,newton surmounted this difficulty by laying a double convex lens1 the radius of curvature of each side of which was fifty feet1 upon the flat surface of a plano-convex object-glass1 and in this way he obtained a plate of air or of space varying from the thinnest possible edge at the centre of the object-glass where it touched the plane surface1 to a considerable thickness at the circumference of the lens4 ,when light was allowed to fall upon the object-glass1 every different thickness of the plate of air between the object-glass gave different colours1 so that the point where the two object-glasses touched one another was the centre of a number of concentric coloured rings4 ,now1 as the curvature of the object-glass was known1 it was easy to calculate the thickness of the plate of air at which any particular colour appeared1 and thus to determine the law of the phenomena4 ,in order to understand how he proceeded1 let ,,ced be the convex surface of the one object-glass1 and ,,aeb the flat surface of the other4 ,let them touch at the point ,e1 and let homogeneous red rays fall upon them1 as shown in the figure4 ,at the point of contact ,e1 where the plate of air is inconceivably thin1 not a single ray of the pencil ,,re is reflected4 ,the light is wholly transmitted1 and1 consequently1 to an eye above ,e1 there will appear at ,e a black spot4 ,at a1 where the plate of air is thicker1 the red light ra is reflected in the direction aa1 and as the air has the same thickness in a circle round the point ,e1 the eye above ,e1 at a1 will see next the black spot ,e a ring of red light4 ,at m1 where the thickness of the air is a little greater than at a1 the light rm is all transmitted as at ,e1 and not a single ray suffers reflection1 so that to an eye above ,e at m there will be seen without the red ring a a dark ring m4 ,in like manner1 at greater thicknesses of the plate of air1 there is a succession of red and dark rings1 diminishing in breadth as shown in the diagram4 ,illustration3 ,fig4 #h4 ,when the same experiment was repeated in orange1 yellow1 green1 blue1 indigo1 and violet light1 the very same phenomenon was observed2 with this difference only1 that the rings were largest in red light1 and smallest in violet light1 and had intermediate magnitudes in the intermediate colours4 ,if the observer now places his eye below ,e1 so as to see the transmitted rays1 he will observe a set of rings as before1 but they will have a bright spot in their centre at ,e1 and the luminous rings will now correspond with those which were dark when seen by reflection1 as will be readily understood from inspecting the preceding diagram4 ,when the object-glasses are illuminated by white light1 the seven systems of rings1 formed by all the seven colours which compose white light1 will now be seen at once4 ,had the rings in each colour been all of the same diameter they would all have formed brilliant white rings1 separated by dark intervals2 but1 as they have all different diameters1 they will overlap one another1 producing rings of various colours by their mixture4 ,these colours1 reckoning from the centre ,e1 are as follows3-- #ast ,order4 ,black1 blue1 white1 yellow1 orange1 red4 #b;d ,order4 ,violet1 blue1 green1 yellow1 orange1 red4 #c;d ,order4 ,purple1 blue1 green1 yellow1 red1 bluish-red4 #dth ,order4 ,bluish-green1 green1 yellowish-green1 red4 #eth ,order4 ,greenish-blue1 red4 #fth ,order4 ,greenish-blue1 red4 ,by accurate measurements1 ,sir ,isaac found that the thicknesses of air at which the most luminous parts of the first rings were produced1 were in parts of an inch #a_/aghjjj1 #c_/aghjjj1 #e_/aghjjj1 #g_/aghjjj1 #i_/aghjjj1 #aa_/aghjjj4 ,if the medium or the substance of the thin plate is water1 as in the case of the soap-bubble1 which produces beautiful colours according to its different degrees of thinness1 the thicknesses at which the most luminous parts of the rings appear are produced at #a_/accf of the thickness at which they are produced in air1 and in the case of glass or mica at #a_/aebe of that thickness2 the numbers #a4ccf1 #a4ebe expressing the ratio of the sines of the angles of incidence and refraction in the substances which produce the colours4 ,from the phenomena thus briefly described1 ,sir ,isaac ,newton deduces that ingenious1 though hypothetical1 property of light1 called its fits of easy reflection and transmission4 ,this property consists in supposing that every particle of light from its first discharge from a luminous body possesses1 at equally distant intervals1 dispositions to be reflected from1 and transmitted through1 the surfaces of bodies upon which it is incident4 ,hence1 if a particle of light reaches a reflecting surface of glass when it is in its fit of reflection1 or in its disposition to be reflected1 it will yield more readily to the reflecting force of the surface2 and1 on the contrary1 if it reaches the same surface while in a fit of easy transmission1 or in a disposition to be transmitted1 it will yield with more difficulty to the reflecting force4 ,sir ,isaac has not ventured to inquire into the cause of this property2 but we may form a very intelligible idea of it by supposing1 that the particles of light have two attractive and two repulsive poles at the extremities of two axes at right angles to each other1 and that the particles revolve round their axes1 and at equidistant intervals bring one or other of these axes into the line of the direction in which the particle is moving4 ,if the attractive axis is in the line of the direction in which the particle moves when it reaches the refracting surface1 the particle will yield to the attractive force of the medium1 and be refracted and transmitted2 but if the repulsive axis is in the direction of the particle's motion when it reaches the surface1 it will yield to the repulsive force of the medium1 and be reflected from it4 ,the application of the theory of alternate fits of reflection and transmission to explain the colours of thin plates is very simple4 ,when the light falls upon the first surface ,,ab1 ,fig4 #h of the plate of air between ,,ab and ,,ced1 the rays that are in a fit of reflection are reflected1 and those that are in a fit of transmission are transmitted4 ,let us call ,f the length of a fit1 or the distance through which the particle of light moves while it passes from the state of being in a fit of reflection to the state of being in a fit of transmission4 ,now1 as all the particles of light transmitted through ,,ab were in a state of easy transmission when they entered ,,ab1 it is obvious1 that1 if the plate of air at ,e is so thin as to be less than one-half of ,f1 the particles of light will still be in their disposition to be transmitted1 and consequently the light will be all transmitted1 and none reflected at the curve surface at ,e4 ,when the plate becomes thicker towards a1 so that its thickness exceeds half of ,f1 the light will not reach the surface ,,ce till it has come under its fit of reflection1 and consequently at a the light will be all reflected1 and none transmitted4 ,as the thickness increases towards m1 the light will have come under its fit of transmission1 and so on1 the light being reflected at a1 l1 and transmitted at ,e1 m4 ,this will perhaps be still more easily understood from fig4 #i1 where we may suppose ,,aec to be a thin wedge of glass or any other transparent body4 ,when light is incident on the first surface ,,ae1 all the particles of it that are in a fit of easy reflection will be reflected1 and all those in a fit of easy transmission will be transmitted4 ,as the fits of transmission all commence at ,,ae1 let the first fit of transmission end when the particles of light have reached ab1 and the second when they have reached ef2 and let the fits of reflection commence at cd and gh4 ,then1 as the fit of transmission continues from ,,ae to ab1 all the light that falls upon the portion m,e of the second surface will be transmitted and none reflected1 so that to an eye above ,e the space m,e will appear black4 ,as the fit of reflection commences at ab1 and continues to cd1 all the light which falls upon the portion nm will be reflected1 and none transmitted2 and so on1 the light being transmitted at m,e and pn1 and reflected at nm and qp4 ,hence to an eye above ,e the wedge-shaped film of which ,,aec is a section will be covered with parallel bands or fringes of light separated by dark fringes of the same breadth1 and they will be all parallel to the thin edge of the plate1 a dark fringe corresponding to the thinnest edge4 ,to an eye placed below ,,ce1 similar fringes will be seen1 but the one corresponding to the thinnest edge m,e will be luminous4 ,illustration3 ,fig4 #i4 ,if the thickness of the plate does not vary according to a regular law as in fig4 #i1 but if1 like a film of blown glass1 it has numerous inequalities1 then the alternate fringes of light and darkness will vary with the thickness of the film1 and throughout the whole length of each fringe the thickness of the film will be the same4 ,we have supposed in the preceding illustration that the light employed is homogeneous4 ,if it is white1 then the differently coloured fringes will form by their superposition a system of fringes analogous to those seen between two object-glasses1 as already explained4 ,the same periodical colours which we have now described as exhibited by thin plates were discovered by ,newton in thick plates1 and he has explained them by means of the theory of fits2 but it would lead us beyond the limits of a popular work like this to enter into any details of his observations1 or to give an account of the numerous and important additions which this branch of optics has received from the discoveries of succeeding authors4 ,,chapter ,,vii4 ,newton's ,theory of the ,colours of ,natural ,bodies explained--,objections to it stated--,new ,classification of ,colours--,outline of a ,new ,theory proposed4 ,if the objects of the material world had been illuminated with white light1 all the particles of which possessed the same degree of refrangibility1 and were equally acted upon by the bodies on which they fall1 all nature would have shone with a leaden hue1 and all the combinations of external objects1 and all the features of the human countenance1 would have exhibited no other variety but that which they possess in a pencil sketch or a ,china-ink drawing4 ,the rainbow itself would have dwindled into a narrow arch of white light1--the stars would have shone through a gray sky1--and the mantle of a wintry twilight would have replaced the golden vesture of the rising and the setting sun4 ,but ,he who has exhibited such matchless skill in the organization of material bodies1 and such exquisite taste in the forms upon which they are modelled1 has superadded that ethereal beauty which enhances their more permanent qualities1 and presents them to us in the ever-varying colours of the spectrum4 ,without this the foliage of vegetable life might have filled the eye and fostered the fruit which it veils1--but the youthful green of its spring would have been blended with the dying yellow of its autumn4 ,without this the diamond might have displayed to science the beauty of its forms1 and yielded to the arts its adamantine virtues2--but it would have ceased to shine in the chaplet of beauty1 and to sparkle in the diadem of princes4 ,without this the human countenance might have expressed all the sympathies of the heart1 but the 8purple light of love0 would not have risen on the cheek1 nor the hectic flush been the herald of its decay4 ,the gay colouring with which the ,almighty has decked the pale marble of nature is not the result of any quality inherent in the coloured body1 or in the particles by which it may be tinged1 but is merely a property of the light in which they happen to be placed4 ,newton was the first person who placed this great truth in the clearest evidence4 ,he found that all bodies1 whatever were their peculiar colours1 exhibited these colours only in white light4 ,when they were illuminated by homogeneous red light they appeared red1 by homogeneous yellow light1 yellow1 and so on1 8their colours being most brisk and vivid under the influence of their own daylight colours40 ,the leaf of a plant1 for example1 appeared green in the white light of day1 because it had the property of reflecting that light in greater abundance than any other4 ,when it was placed in homogeneous red light1 it could no longer appear green1 because there was no green light to reflect2 but it reflected a portion of red light1 because there was some red in the compound green which it had the property of reflecting4 ,had the leaf originally reflected a pure homogeneous green1 unmixed with red1 and reflected no white light from its outer surface1 it would have appeared quite black in pure homogeneous red light1 as this light does not contain a single ray which the leaf was capable of reflecting4 ,hence the colours of material bodies are owing to the property which they possess of stopping certain rays of white light1 while they reflect or transmit to the eye the rest of the rays of which white light is composed4 ,so far the ,newtonian doctrine of colours is capable of rigid demonstration2 but its author was not content with carrying it thus far3 he sought to determine the manner in which particular rays are stopped1 while others are reflected or transmitted2 and the result of this profound inquiry was his theory of the colours of natural bodies1 which was communicated to the ,royal ,society on the #ajth ,february1 #afge4 ,this theory is perhaps the loftiest of all his speculations2 and though1 as a physical generalization1 it stands on a perishable basis1 and must soon be swept away in the progress of science1 it yet bears the deepest impress of the grasp of his powerful intellect4 ,the principles upon which this theory is founded are the following3-- #a4 ,bodies that have the greatest refractive powers reflect the greatest quantity of light2 and at the confines of equally refracting media there is no reflection4 #b4 ,the least particles of almost all natural bodies are in some measure transparent4 #c4 ,between the particles of bodies are many pores or spaces1 either empty or filled with media of less density than the particles4 #d4 ,the particles of bodies and their pores1 or the spaces between the particles1 have some definite size4 ,upon these principles ,newton explains the origin of transparency1 opacity1 and colour4 ,transparency he considers as arising from the particles and their intervals or pores being too small to cause reflection at their common surfaces1#ai so that all the light which enters transparent bodies passes through them without any portion of it being turned from its path by reflection4 ,if we could obtain1 for example1 a film of mica whose thickness does not exceed two-thirds of the millionth part of an inch1 all the light which fell upon it would pass through it1 and none would be reflected4 ,if this film was then cut into fragments1 a number of such fragments would constitute a bundle1 which would also transmit all the light which fell upon it1 and be perfectly transparent4 ,opacity in bodies arises1 he thinks1 from an opposite cause1 viz4 when the parts of bodies are of such a size as to be capable of reflecting the light which falls upon them1 in which case the light is 8stopped or stifled0 by the multitude of reflections4 ,the colours of natural bodies have1 in the ,newtonian hypothesis1 the same origin as the colours of thin plates1 their transparent particles1 according to their several sizes1 reflecting rays of one colour1 and transmitting those of another4 8,for if a thinned or plated body which1 being of an uneven thickness1 appears all over of one uniform colour1 should be slit into threads1 or broken into fragments of the same thickness with the plate or film1 every thread or fragment should keep its colour1 and consequently1 a heap of such threads or fragments should constitute a mass or powder of the same colour which the plate exhibited before it was broken3 and the parts of all natural bodies being like so many fragments of a plate1 must1 on the same grounds1 exhibit the same colour40 ,such is the theory of the colours of natural bodies1 stated as clearly and briefly as we can4 ,it has been very generally admitted by philosophers1 both of our own and of other countries1 and has been recently illustrated and defended by a ,french philosopher of distinguished eminence4 ,that this theory affords the true explanation of certain colours1 or1 to speak more correctly1 that certain colours in natural bodies are the colours of thin plates1 cannot be doubted2 but it will not be difficult to show that it is quite inapplicable to that great class of phenomena which may be considered as representing the colours of natural bodies4 ,the first objection to the ,newtonian theory is the total absence of all reflected light from the particles of transparent coloured media1 such as coloured gems1 coloured glasses1 and coloured fluids4 ,this objection was urged long ago by ,mr4 ,delaval1 who placed coloured fluids on black grounds1 and never could perceive the least trace of the reflected tints4 ,i have repeated the experiment with every precaution1 and with every variation that ,i could think of1 and ,i consider it as an established fact1 that in such coloured bodies the complementary reflected colour cannot be rendered visible4 ,if the fluid1 for example1 be red1 the green light from which the red has been separated ought to appear either directly by looking into the coloured mass1 or ought to be recognised by its influence in modifying the light really reflected2 but as it cannot be seen1 we must conclude that it has not been reflected1 but has been destroyed by some other property of the coloured body4 ,a similar objection may be drawn from the disappearance of the transmitted complementary colour in the leaves of plants and petals of flowers4 ,i have ascertained from numerous experiments1 that the transmitted colour is almost invariably the same with the reflected colour1 and that the same holds true with the coloured juices expressed from them4 ,the complementary tints are never seen1 and wherever there has been any thing like an approximation to two tints1 ,i have invariably found that it arose from there being two different coloured juices existing in different sides of the leaf4 ,in the phenomena of the light transmitted by coloured glasses1 there are some peculiarities which1 we think1 demonstrate that their colours are not those of thin plates4 ,the light1 for example1 transmitted through a particular kind of blue glass1 has a blue colour of such a peculiar composition that there is no blue in any of the orders of colours in thin plates which has any resemblance to it4 ,it is entirely destitute of the red rays which form the middle of the red space in the spectrum2 so that the particles on which the colour depends must reflect the middle red rays1 and transmit those on each side of it1--a property which cannot be deduced from the ,newtonian doctrine4 ,the explanation of opacity1 as arising from a multitude of reflections1 is liable to the same objection which we have urged against the explanation of colour4 ,in order to appreciate its weight1 we must distinguish opacity into two kinds1 namely1 the opacity of whiteness and the opacity of blackness4 ,those bodies which possess the power of reflection in the highest degree1 such as white metals1 chalk1 and plaster of ,paris1 never reflect more than one-half of the light which falls upon them4 ,the other half of the incident light is1 according to ,newton1 lost by a multitude of reflections4 ,but how is it lost8 ,reflection merely changes the direction of the particles of light1 so that they must again emerge from the body1 unless they are reflected into fixed returning orbits1 which detain them for ever in a state of motion within the body4 ,in the case of black opacity1 such as that of coal1 which reflects from its first surface only #a_/beth of the white light1 the difficulty is still greater1 and we cannot conceive how any system of interior reflections could so completely stifle #bd_/beths of the whole incident light1 without some of it returning to the eye in a visible form4 ,in determining the constitution of bodies that produce transparency and blackness1 the ,newtonian theory encounters a difficulty which its author has by no means surmounted4 ,transparency1 as we have already seen1 arises from the 8particles and their interstices being too small to cause reflections in their common surfaces10 that is1 they must be 8less than any of those which exhibit colours10 or 8less than is requisite to reflect the white and very faint blue of the first order4 ,but this is the very same constitution which produces blackness by reflection1 and in order to explain the cause of blackness by transmission1 or black opacity1 ,newton is obliged to introduce a new principle4 8,for the production of black10 says he1 8the corpuscles must be less than any of those which exhibit colours4 ,for at all greater sizes there is too much light reflected to constitute this colour4 ,but if they be supposed a little less than is requisite to reflect the white and very faint blue of the first order1 they will reflect so very little light as to appear intensely black1 and yet may perhaps variously refract#bj it to and fro within themselves so long1 until it happens to be stifled and lost1 by which means they will appear black in all positions of the eye1 without any transparency40 ,this very remarkable passage exhibits1 in a striking manner1 the perplexity in which our author was involved by the difficulties of his subject4 ,as the particles which produce blackness by reflection are necessarily so small as to exclude the existence of any reflective forces1 he cannot ascribe the loss of the intromitted light1 as he does in the case of white opacity1 to 8a multitude of reflections20 and therefore he is compelled to have recourse to refracting forces to perform the same office4 ,the reluctance with which he avails himself of this expedient is well marked in the mode of expression which he adopts2 and ,i am persuaded that when he wrote the above passage1 he felt the full force of the objections to this hypothesis1 which cannot fail to present themselves4 ,as the size of the particles which produce blackness are intermediate between those which produce transparency and those which produce colour1 approaching closely to the latter1 it is difficult to conceive why they should refract the intromitted light1 while the greater and smaller particles1 and even those almost of the same size1 should be destitute of that property4 ,it is1 besides1 not easy to understand how a refraction can take place within bodies which shall stifle all the light1 and prevent it from emerging4 ,nay1 we may admit the existence of such refractions1 and yet understand how1 by a compensation in their direction1 the refracted rays may all emerge from the opaque body4 ,the force of these objections is tacitly recognised in ,pemberton's ,view of ,sir ,isaac ,newton's ,philosophy2#ba and as ,newton not only read and approved of that work1 but even perused a great part of it along with its author1 we may fairly consider the opinion there stated to be his own4 8,for producing black1 the particles ought to be smaller than for exhibiting any of the colours1 viz4 of a size answering to the thickness of the bubble1 whereby reflecting little or no light1 it appears colourless2 but yet they must not be too small1 for that will make them transparent through deficiency of reflections in the inward parts of the body1 sufficient to stop the light from going through it2 but they must be of a size bordering upon that disposed to reflect the faint blue of the first order1 which affords an evident reason why blacks usually partake a little of that colour40 ,in this passage all idea of refraction is abandoned1 and that precise degree of size is assumed for the particles which leaves a small power of reflection1 which is deemed sufficient to prevent the body from becoming transparent2 that is1 sufficient to render it opaque or black4 ,the last objection which we shall state to this theory is one to which we attach great weight1 and1 as it is founded on discoveries and views which have been published since the time of ,newton1 we venture to believe1 that1 had he been aware of them1 he would never have proposed the theory which we are considering4 ,when light falls upon a thin film such as ,,aec1 fig4 #i1 p4 #hj1 so as to produce the colours of thin plates1 it follows1 from ,sir ,isaac ,newton's theory of fits1 that a portion of the light is1 as usual1 reflected at the first surface ,,ae1#bb while the light which forms the coloured image is that which is reflected from the second surface ,,ec1 so that all the colours of thin plates are diluted with the white light reflected from the first surface4 ,now1 in the modern theory1 which ascribes the colours of thin plates to the interference of the light reflected from the second surface ,,ec1 with the light reflected from the first surface ,,ae1 the resulting tint arises from the combination of these two pencils1 and consequently there is no white light reflected from the surface ,,ae4 ,in like manner1 when the thickness of the film is such that the two interfering pencils completely destroy one another1 and produce black1 there is not a ray of light reflected from the first surface4 ,here1 then1 we have a criterion for deciding between the theory of fits and the theory of interference2 for if there is no white light reflected from the first surface ,,ae1 the theory of fits must be rejected4 ,in a remarkable phenomenon of blackness arising from minute fibres1 which ,i have had occasion to describe1 there was no perceptible reflection from the surface of the fibres2#bc and ,m4 ,fresnel describes an experiment made to determine the same point1 and states the result of it to have been unequivocally in favour of the doctrine of interference4 ,in order to apply this important fact1 let us take a piece of coal1 one of the blackest and most opaque of all substances1 and which does not reflect to the eye a single ray out of those which enter its substance4 ,the size of its particles is so small1 that they are incapable of reflecting light4 ,when a number of these particles are placed together1 so as to form a surface1 and other particles behind them1 so as to form a solid1 they will not acquire by this process the power of reflection2 and consequently1 a piece of coal so composed should be destitute of the property of reflecting light from its first surface4 ,but this is not the case1--light is abundantly reflected from the first surface of the coal1 and consequently1 its elementary particles must possess the same power4 ,hence the blackness of coal must be ascribed to some other cause than to the minuteness of its transparent atoms4 ,to transparent bodies this argument has a similar application4 ,as their atoms are still less than those of black bodies1 their inability to reflect light is still greater1 and hence arises their transparency4 ,but the particles forming the surface of such bodies do reflect light1 and1 therefore1 their transparency must have another origin4 ,in the case of coloured bodies1 too1 the particles forming their surfaces reflect white light like those of all other bodies1 so that these particles cannot produce colour on the same principles as those of thin plates4 ,in many of those cases of colour which seem to depend upon the minuteness of the particles of the body1 the reflection of white light may nevertheless be observed1 but this will be found to arise from a thin transparent film1 behind which the colorific particles are placed4 ,whatever answer may be given to these objections1 we think it will be admitted by those who have studied the subject most profoundly1 that a satisfactory theory of the colours of natural bodies is still a desideratum in science4 ,how far we may be able to approach to it in the present state of optics the reader will judge from the following views4 ,colours may be arranged into seven classes1 each of which depends upon different principles4 #a4 ,transparent coloured fluids--transparent coloured gems--transparent coloured glasses--coloured powders--and the colours of the leaves and flowers of plants4 #b4 ,oxidations on metals--colours of ,labrador feldspar--colours of precious and hydrophanous opal1 and other opalescences--the colours of the feathers of birds1 of the wings of insects1 and of the scales of fishes4 #c4 ,superficial colours1 as those of mother-of-pearl and striated surfaces4 #d4 ,opalescences and colours in composite crystals having double refraction4 #e4 ,colours from the absorption of common and polarized light by doubly refracting crystals4 #f4 ,colours at the surfaces of media of different dispersive powers4 #g4 ,colours at the surface of media in which the reflecting forces extend to different distances1 or follow different laws4 ,the first two of these classes are the most important4 ,the ,newtonian theory appears to be strictly applicable to the phenomena of the second class2 but those of the first class cannot1 we conceive1 be referred to the same cause4 99 99 99 99 99 ,the rays of solar light possess several remarkable physical properties3 ,they heat--they illuminate--they promote chymical combination--they effect chymical decompositions--they impart magnetism to steel--they alter the colours of bodies--they communicate to plants and flowers their peculiar colours1 and are in many cases necessary to the development of their characteristic qualities4 ,it is impossible to admit for a moment that these varied effects are produced by a mere mechanical action1 or that they arise from the agitation of the particles of bodies by the vibration of the ether which is considered to be the cause of light4 ,whatever be the difficulties which attach to the theory which supposes light to consist of material particles1 we are compelled1 by its properties1 to admit that light acts as if it were material1 and that it enters into combinations with bodies1 in order to produce the effects which we have enumerated4 ,when a beam of light falls upon a body1 and the whole or a part of that which enters its substance totally disappears1 we are entitled to say1 that it is detained by some power exercised by the particles of the body over the particles of light4 ,when this light is said to be lost by a multitude of reflections or refractions1 the statement is not only hypothetical1 but it is an hypothesis incompatible with optical principles4 ,that the light detained within bodies has been stopped by the attractive force of the particles seems to be highly probable1 and the mind will not feel any repugnance to admit that the particles of all bodies1 whether solid1 fluid1 or ariform1 have a specific affinity for the particles of light4 ,considering light1 therefore1 as material1 it is not difficult to comprehend how it should1 like other elementary substances1 enter into combination with bodies1 and produce many chymical and physical effects1 but particularly the phenomena of transparency1 opacity1 and colour4 ,in transparent colourless bodies1 such as water and glass1 the intromitted light experiences a considerable loss1 because a certain number of its particles are attracted and detained by the atoms of the water or glass1 and the light which emerges is colourless1 because the particles exercise a proportional action over all the simple colours which compose white light4 ,when the transparent body has any decided colour1 such as those enumerated in ,class ,i41 then the particles of the body have exercised a specific attraction over those rays of white light which are complementary to those which compose the colour of the transmitted light4 ,if the transparent body1 for example1 is red1 then its particles have detained the green rays which entered into the incident light1 or certain other rays1 which with the red are necessary to compose white light4 ,in compound bodies1 like some of the artificial glasses1 the particles will attract and detain rays of light of different colours1 as may be seen by analyzing the transmitted light with a prism1 which will exhibit a spectrum deprived of all the rays which have been detained4 ,in black bodies the particles exercise a powerful attraction over light1 and detain all the intromitted rays4 ,when coloured bodies are opaque1 so as to exhibit their colours principally by reflection1 the light which is reflected back to the observer has received its colour from transmission through part of the thickness of the body1 or1 what is the same thing1 the colour reflected to the eye is complementary to that which has been detained by the particles of the body while the light is passing and repassing through a thickness terminated by the reflecting surfaces2 and as only a part of this light is reflected1 as in the case of leaves and flowers1 the transmitted light must have the same colour as the reflected light4 ,when coloured bodies exhibit two different colours complementary to each other1 the one seen by reflection and the other by transmission1 it is then highly probable that the colours are those of thin plates1 though there are still other optical principles to which they may be referred4 ,as the particles of bodies1 and the medium which unites them1 or1 as the different atoms of a compound body may have different dispersive powers1 while they exercise the same refractive force over a particular part of the spectrum1 the rays for which this compensation takes place will be transmitted1 while part of the complementary light is reflected4#bd ,or in cases where the refractive and dispersive powers are the same1 the reflective forces of the particles may vary according to a different law1 so that at the separating surfaces either white or coloured light may be reflected4#be ,in those cases of colour where the reflected and the transmitted tints are not complementary1 as in leaf-gold1 where the former is yellow and the latter green2--in leaf-silver1 where they are white and blue1 and in certain pieces of fir-wood1 where the reflected light is whitish yellow1 and the transmitted light a brilliant homogeneous red1 we may explain the separation of the colours either by the principles we have already laid down or by the doctrine of thin plates4 ,on the first principle1 the colour of the reflected light1 which is supposed to be the same as that of the transmitted light1 will be modified by the law according to which the particles of the body attract different rays out of the beam of white light4 ,in pitch1 for example1 the blue rays are first absorbed1 so that at small thicknesses the transmitted light is a fine yellow1 while1 by the action of a greater thickness1 the yellow itself is absorbed1 and the transmitted light is a bright homogeneous red4 ,now in leaf-gold the transmitted colour of thinner films than we can obtain may be yellow1 and1 consequently1 the light reflected from the first strata of interrupting faces will be yellow1 and will determine the predominant tint of the reflected light4 ,on the ,newtonian doctrine1 ,mr4 ,herschel has explained it by saying1 8that the transmitted rays have traversed the whole thickness of the medium1 and therefore undergo many more times the action of its atoms than those reflected1 especially those near the first surface to which the brighter part of the reflected colour is due40 ,the phenomena of the absorption of common and polarized light1 which ,i have described in another place1#bf throw much light on the subject of coloured bodies4 ,the relation of the absorbent action to the axes of double refraction1 and1 consequently1 to the poles of the molecules of the crystal1 shows how the particles of light attracted by the molecules of the body will vary1 both in their nature and number1 according to the direction in which they approach the molecules2 and explains how the colour of a body may be changed1 either temporarily or permanently1 by heat1 according as it produces a temporary or a permanent change in the relative position of the molecules4 ,this is not the place to enlarge on this subject2 but we may be permitted to apply the idea to the curious experiment of ,thenard on phosphorus4 ,when this substance is rendered pure by repeated distillation1 it is transparent1 and transmits yellow light2 but when it is thrown in a melted state into cold water1 it becomes jet black4 ,when again melted1 it resumes its original colour and transparency4 ,according to the ,newtonian theory1 we must suppose that the atoms of the phosphorus have been diminished in size by sudden cooling1--an effect which it is not easy to comprehend2 but1 according to the preceding views1 we may suppose that the atoms of the phosphorus have been forced by sudden cooling into relative positions quite different from those which they take when they slowly assume the solid state1 and their poles of maximum attraction1 in place of being turned to one another1 are turned in different directions1 and then allowed to exercise their full action in attracting the intromitted light1 and detaining it wholly within the body4#bg ,before concluding this chapter1 there is one topic peculiarly deserving our notice1 namely1 the change of colour produced in bodies by continued exposure to light4 ,the general effect of light is to diminish or dilute the colours of bodies1 and in many cases to deprive them entirely of their colour4 ,now1 it is not easy to understand how repeated undulations propagated through a body could diminish the size of its particles1 or how the same effect could be produced by a multitude of reflections from particle to particle4 ,but if light is attracted by the particles of bodies1 and combines with them1 it is easy to conceive that1 when the molecules of a body have combined with a great number of particles of a green colour1 for example1 their power of combination with others will be diminished1 and1 consequently1 the number of particles of any colour absorbed or detained must diminish with the time that the body has been exposed to light2 that is1 these particles must enter into the transmitted and reflected pencils1 and diminish the intensity of their colour4 ,if the body1 for example1 absorbs red light1 and transmits and reflects green1 then if the quantity of absorbed red light is diminished1 it will enter into the reflected and transmitted pencils1 and1 forming white light by its mixture with a portion of the green rays1 will actually dilute them in the same manner as if a portion of white light had been added4#bh ,,chapter ,,viii4 ,newton's ,discoveries respecting the ,inflection or ,diffraction of ,light--,previous ,discoveries of ,grimaldi and ,dr4 ,hooke--,labours of succeeding ,philosophers--,law of ,interference of ,dr4 ,young--,fresnel's ,discoveries--,new ,theory of ,inflection on the ,hypothesis of the ,materiality of ,light4 ,although the discoveries of ,newton respecting the ,inflection of ,light were first published in his ,optics in #agjd1 yet there is reason to think that they were made at a much earlier period4 ,sir ,isaac1 indeed1 informs us1 in his preface to that great work1 that the third book1 which contains these discoveries1 8was put together out of scattered papers20 and he adds at the end of his observations1 that 8he designed to repeat most of them with more care and exactness1 and to make some new ones for determining the manner how the rays of light are bent in their passage by bodies1 for making the fringes of colours with the dark lines between them4 ,but ,i was then interrupted1 and cannot now think of taking these things into consideration40 ,on the #ahth ,march1 #afgd1 ,dr4 ,hooke had read a valuable memoir on the phenomena of diffraction2 and1 as ,sir ,isaac makes no allusion whatever to this work1 it is the more probable that his 8scattered papers0 had been written previous to the communication of ,dr4 ,hooke's experiments4 ,the phenomena of the inflection of light were first discovered by ,francis ,maria ,grimaldi1 a learned ,jesuit1 who has described them in a posthumous work published in #affe1 two years after his death4#bi ,having admitted a beam of the sun's light through a small pin-hole in a piece of lead or card into a dark chamber1 he found that the light diverged from this aperture in the form of a cone1 and that the shadows of all bodies placed in this light were not only larger than might have been expected1 but were surrounded with three coloured fringes1 the nearest being the widest1 and the most remote the narrowest4 ,in strong light he discovered analogous fringes within the shadows of bodies1 which increased in number with the breadth of the body1 and became more distinct when the shadow was received obliquely and at a greater distance4 ,when two small apertures or pin-holes were placed so near each other that the cones of light formed by each of them intersected one another1 ,grimaldi observed1 that a spot common to the circumference of each1 or1 which is the same thing1 illuminated by rays from each cone1 was darker than the same spot when illuminated by either of the cones separately2 and he announces this remarkable fact in the following paradoxical proposition1 8that a body actually illuminated may become more dark by adding a light to that which it already receives40 ,without knowing what had been done by the ,italian philosopher1 our countryman1 ,dr4 ,robert ,hooke1 had been diligently occupied with the same subject4 ,in #afgb1 he communicated his first observations to the ,royal ,society1 and he then spoke of his paper as 8containing the discovery of a new property of light not mentioned by any optical writers before him40 ,in his paper of #afgd1 already mentioned1 and which is no doubt the one to which he alludes1 he has not only described the leading phenomena of the inflection1 or the deflection of light1 as he calls it1 but he has distinctly announced the doctrine of interference1 which has performed so great a part in the subsequent history of optics4#cj ,such was the state of the subject when ,newton directed to it his powers of acute and accurate observation4 ,his attention was turned only to the enlargement of the shadow1 and to the three fringes which surrounded it2 and he begins his observations by ascribing the discovery of these facts to ,grimaldi4 ,after taking exact measures of the diameter of the shadow of a human hair1 and of the breadth of the fringes at different distances behind it1 he discovered the remarkable fact that these diameters and breadths were not proportional to the distances from the hair at which they were measured4 ,in order to explain these phenomena1 ,newton supposed that the rays which passed by the edge of the hair are deflected or turned aside from it1 as if by a repulsive force1 the nearest rays suffering the greatest1 and those more remote a less degree of deflection4 ,illustration3 ,fig4 #aj4 ,thus1 if ,x1 fig4 #aj1 represents a section of the hair1 and ,,ab1 ,,cd1 ,,ef1 ,,gh1 c4 rays passing at different distances from ,x1 the ray ,,ab will be more deflected than ,,cd1 and will cross it at m1 the ray ,,cd will for the same reason cross ,,ef at n1 and ,,ef will cross ,,gh at o4 ,hence the curve or caustic formed by the intersections m1 n1 o1 c4 will be convex outward1 its curvature diminishing as it recedes from the vertex4 ,as none of the passing light can possibly enter within this curve1 it will form the boundary of the shadow of ,x4 ,the explanation given by ,sir ,isaac of the coloured fringes is less precise1 and can be inferred only from the two following queries4 #a4 8,do not the rays which differ in refrangibility differ also in flexibility1 and are they not1 by these different inflections separated from one another1 so as after separation to make the colours in the three fringes above described8 ,and after what manner are they inflected to make those fringes8 #b4 8,are not the rays of light in passing by the edges and sides of bodies bent several times backwards and forwards with a motion like that of an eel8 ,and do not the three fringes of light above mentioned arise from three such bendings80 ,the idea thus indistinctly thrown out in the preceding queries has been ingeniously interpreted by ,mr4 ,herschel in the manner represented in fig4 #aa1 where ,,ss are two rays passing by the edge of the body ,,mn4 ,these rays are supposed to undergo several bendings1 as at a1 b1 c1 and the particles of light are thrown off at one or other of the points of contrary flexure1 according to the state of their fits or other circumstances4 ,those that are thrown outwards in the direction a,a1 b,b1 c,c1 d,d1 will produce as many caustics by their intersections as there are deflected rays2 and each caustic1 when received on a screen at a distance1 will depict on it the brightest part or maximum of a fringe4 ,illustration3 ,fig4 #aa4 ,in this unsatisfactory state was the subject of the inflection of light left by ,sir ,isaac4 ,his inquiries were interrupted1 and never again renewed2 and though he himself found that the phenomena were the same1 8whether the hair was encompassed with air or with any other pellucid substance10 yet this important result does not seem to have shaken his conviction1 that the phenomena had their origin in the action of bodies upon light4 ,during two sets of experiments which ,i made on the inflection of light1 the first in #agih1 and the second in #ahab and #ahac1 ,i was desirous of examining the influence of density and refractive power over the fringes produced by inflection4 ,i compared the fringes formed by gold-leaf with those formed by masses of gold1--and those produced by films which gave the colours of thin plates with those formed by masses of the same substance4 ,i examined the influence of platinum1 diamond1 and cork in inflecting light1 the effect of non-reflecting grooves and spaces in polished metals1 and of cylinders of glass immersed in a mixture of oil of cassia and oil of olives of the same refractive power2 and1 as the fringes had the same magnitude and character under all these circumstances1 ,i concluded that they were not produced by any force inherent in the bodies themselves1 but arose from a property of the light itself1 which always showed itself when light was stopped in its progress4 ,dr4 ,thomas ,young1 who had supported with great ingenuity and force of argument the undulatory theory of light1 as maintained by ,hooke and ,huygens1 was the first who gave a plausible explanation of the inflection of light4 ,by interposing a small screen at ,b1 fig4 #aj1 and intercepting the rays that passed near the hair ,x1 he was surprised to find that all the fringes within the shadow disappeared4 ,the same effect took place when the screen intercepted the rays on the other side2 and hence he concluded1 that the rays on each side of the hair were necessary to the production of the inner fringes1 and that the fringes were produced by the interference of the rays that passed on one side of the hair with those that passed on the other side4 ,in order to account for the coloured fringes without the shadow1 ,dr4 ,young conceived that the rays which pass near the edge of the hair interfere with others1 which he supposes may be reflected after falling very obliquely upon its edge1--a supposition which1 if correct1 would certainly produce fringes very similar to those actually observed4 ,in pursuing these researches so successfully begun by ,dr4 ,young1 ,m4 ,fresnel had the good fortune to explain all the phenomena of inflection by means of the undulatory doctrine combined with the principle of interference4 ,in place of transmitting the light through a small aperture1 he caused it to diverge from the focus of a deep convex lens1 and instead of receiving the shadow and its fringes upon a smooth white surface1 as was done by ,newton1 he viewed them directly with his eye through a lens placed behind the shadow2 and by means of a microscope he was able to measure the dimensions of the fringes with the greatest exactness4 ,by this mode of observation he made the remarkable discovery1 that the inflection of the light depended on the distance of the inflecting body from the aperture or from the focus of divergence2#ca the fringes being observed to dilate as the body approached that focus1 and to contract as it receded from it1 their relative distances from each other1 and from the margin of the shadow continuing invariable4 ,in attempting to account for the formation of the exterior fringes1 ,m4 ,fresnel found it necessary to reject the supposition of ,dr4 ,young1 that they were owing to light reflected from the edge of the body4 ,he not only ascertained that the real place of the fringe was the #ag_/ajjth of a millimetre different from what it should be on that supposition1 but he found that the fringes preserved the same intensity of light1 whether the inflecting body had a round or a sharp edge1 and even when the edge was such as not to afford sufficient light for their production4 ,from this difficulty the undulatory theory speedily released him1 and he was led by its indications to consider the exterior fringes1 as produced by an infinite number of elementary waves of light emanating from a primitive wave when partly interrupted by an opaque body4 ,the various phenomena of inflection1 which had so long resisted every effort to generalize them1 having thus received so beautiful and satisfactory an explanation from the undulatory doctrine1 they must of course be regarded as affording to that doctrine the most powerful support1 while the ,newtonian hypothesis of the materiality of light is proportionally thrown into the shade4 ,it is impossible1 indeed1 even for national partiality to consider the views of ,newton as furnishing any explanation of the facts discovered by ,fresnel2 and1 as no attempt has been made by the small though able phalanx of his disciples to stay the decision with which1 on this count at least1 the doctrine of emission has been threatened1 we shall venture to suggest some principles by which the refractory phenomena may perhaps be yet brought within the pale of the ,newtonian theory4 ,that the particles of light1 like those of heat1 are endowed with a repulsive force which prevents them from accumulating when in a state of condensation1 or when they are detained by the absorptive action of opaque bodies1 will be readily admitted4 ,by this power a beam of light radiating from a luminous point has1 in every azimuth1 the same degree of intensity at the same distance from its centre of divergence2 but if we intercept a portion of such a beam by an opaque body1 the repulsive force of the light which formerly occupied its shadow is withdrawn1 and consequently the rays which pass near the body will be repelled into the shadow1 and will form1 by their interference with those similarly repelled on the other side1 the interior fringes1 which are parallel to the edges of the body4 ,the rays which pass at a greater distance will in like manner be bent towards the body1 but with less force1 and1 interfering with those rays which retain their primitive direction1 from the state of their fits or the position of their poles1 they will form the exterior fringes4 ,when the inflecting body is placed near the point of divergence1 the greater proximity of the rays will produce a greater repulsive force1 and consequently a greater inflection of the passing light2 while the removal of the body from the point of divergence will be accompanied with an increased distance of the particles1 an inferior repulsive force1 and a feebler inflection4 ,as the phenomena of inflection1 considered under this aspect1 arise from a property of the light itself1 it follows that they will remain invariable1 whatever be the nature or density of the body1 or the form of the edge which acts upon the passing rays4 ,,chapter ,,ix4 ,miscellaneous ,optical ,researches of ,newton--,his ,experiments on ,refraction--,his ,conjecture respecting the ,inflammability of the ,diamond--,his ,law of ,double ,refraction--,his ,observations on the ,polarization of ,light--,newton's ,theory of ,light--,his 8,optics40 ,before concluding our account of ,newton's optical discoveries1 it is necessary to notice some of his minor researches1 which1 though of inferior importance in the science of light1 have either exercised an influence over the progress of discovery1 or been associated with the history of other branches of knowledge4 ,one of the most curious of these inquiries related to the connexion between the refractive powers and the chymical composition of bodies4 ,having measured the refractive powers and the densities of twenty-two substances1 he found that the forces which reflect and refract light are very nearly proportional to the densities of the same bodies4 ,in this law1 however1 he noticed a remarkable exception in the case of unctuous and sulphureous bodies1 such as camphire1 olive oil1 linseed oil1 spirit of turpentine1 and diamond1 which have their refractive powers two or three times greater in respect of their densities than the other substances in the table1 while among themselves their refractive powers are proportional to their densities1 without any considerable variation4 ,hence he concluded that diamond 8is an unctuous substance coagulated10--a sagacious prediction1 which has been verified in the discoveries of modern chymistry4 ,the connexion between a high degree of inflammability and a great refracting force has been still more strongly established by the high refractive power which ,i detected in phosphorus1 and which was discovered in hydrogen by ,,mm4 ,biot and ,arago4 ,there is no part of the optical labours of ,newton which is less satisfactory than that which relates to the double refraction of light4 ,in #afij1 ,huygens1 published his admirable treatise on light1 in which he has given the law of double refraction in calcareous spar1 as deduced from his theory of light1 and as confirmed by direct experiment4 ,viewing it probably as a theoretical deduction1 ,newton seems to have regarded it as incorrect1 and though he has given ,huygens the credit of describing the phenomena more exactly than ,bartholinus1 yet1 without assigning any reason1 he rejected the law of the ,dutch philosopher1 and substituted another in its place4 ,these observations of our author form the subject of the twenty-fifth and twenty-sixth queries at the end of his ,optics1 which was published fourteen years after the appearance of ,huygens's work4 ,the law adopted by ,newton is not accompanied with any of the experiments from which it was deduced2 and though he has given it without expressing any doubt of its accuracy1 it is1 nevertheless1 entirely incompatible with observation1 and has been rejected by all succeeding philosophers4 ,in his speculations respecting the successive disappearance and reappearance of two of the four images which are formed when a luminous object is viewed through two rhombs of calcareous spar1 one of which is made to revolve upon the other1 ,newton has been more successful4 ,he concluded from these phenomena that every ray of light has two opposite sides originally endued with the property on which the unusual refraction depends1 and other two opposite sides not endued with that property2 and he suggested it as a subject for future inquiry1 whether there are not more properties of light by which the sides of the rays differ1 and are distinguished from one another4 ,this is the first occasion on which the idea of a polarity in the rays of light has been suggested4#cb ,from the various optical inquiries in which ,newton was engaged1 he was strongly impressed with the belief that light consists of small material particles emitted from shining substances1 and that these particles could be again recombined into solid matter1 so that 8gross bodies and light were convertible into one another40 ,he conceived also that the particles of solid bodies and of light exerted a mutual action upon each other1 the former being agitated and heated by the latter1 and the latter being attracted and repelled by the former1 with forces depending on the inertia of the luminous particles4 ,these forces he regarded as insensible at all measurable distances1 and he conceived that the distances between the particles of bodies were very small when compared with the extent of their sphere of attraction and repulsion4 ,with the exception of ,hooke1 ,huygens1 and ,euler1 almost all the contemporaries and successors of ,newton maintained the doctrine of the materiality of light4 ,it was first successfully assailed by ,dr4 ,thomas ,young1 and since that time it has been shaken to its foundation by those great discoveries which have illustrated the commencement of the present century4 ,the undulatory theory1 which has thus triumphed in its turn1 is still subject to grave difficulties1 and we fear another century must elapse before a final decision can be pronounced on this long-agitated question4 ,the most important of the optical discoveries of ,newton1 of which we have given a general history1 were communicated to the ,royal ,society in detached papers2 but the disputes in which they had involved their author made him hesitate about the publication of his other discoveries4 ,although he had drawn up a connected view of his labours under the title of 8,opticks1 or a ,treatise on the ,reflexions1 ,refractions1 ,inflexions1 and ,colours of ,light10 yet he resolved not to publish this work during the life of ,hooke1 by whose rival jealousy his tranquillity had been so frequently interrupted4 ,hooke1 however1 died in #agjb1 and the ,optics of ,newton appeared in ,english in #agjd4 ,dr4 ,samuel ,clark proposed a ,latin edition of it1 which appeared in #agjf1 and he was generously presented by ,sir ,isaac with #ejjl4 7or #ajjl4 for each of his five children71 as a token of the approbation and gratitude of the author4 ,both the ,english and the ,latin editions have been frequently reprinted both in ,england and on the ,continent1#cc and there perhaps never was a work of profound science so widely circulated4 ,,chapter ,x4 ,astronomical ,discoveries of ,newton--,necessity of combined ,exertion to the ,completion of great ,discoveries--,sketch of the ,history of ,astronomy previous to the ,time of ,newton--,copernicus1 #adgc-aedc-- ,tycho ,brahe1 #aedf-afja--,kepler1 #aega-afca--;,galileo1 #aefd-afdb4 ,from the optical labours of ,newton we now proceed to the history of his astronomical discoveries--those transcendent deductions of human reason by which he has secured to himself an immortal name1 and vindicated the intellectual dignity of his species4 ,pre-eminent as his triumphs have been1 it would be unjust to affirm that they were achieved by his single arm4 ,the torch of many a preceding age had thrown its light into the strongholds of the material universe1 and the grasp of many a powerful hand had pulled down the most impregnable of its defences4 ,an alliance1 indeed1 of many kindred spirits had been long struggling in this great cause1 and ,newton was but the leader of their mighty phalanx1--the director of their combined genius1--the general who won the victory1 and therefore wears its laurels4 ,the history of science presents us with no example of an individual mind throwing itself far in advance of its contemporaries4 ,it is only in the career of crime and ambition that reckless man takes the start of his species1 and1 uncurbed by moral and religious restraint1 erects an unholy dynasty upon the ruins of ancient and venerable institutions4 ,the achievements of intellectual power1 though often begun by one mind and completed by another1 have ever been the results of combined exertions4 ,slow in their growth1 they gradually approximate to a more perfect condition3--the variety in the phenomena of nature call forth a variety of intellectual gifts2--the powers of analysis and combination are applied to the humbler labours of observation and experiment1 and in the ordeal of rival inquiry truth is finally purified from error4 ,how different is it with those systems which the imagination rears1--those theories of wild import which are directed against the consciences and hopes of man4 ,the fatal upas-tree distils its poison in the spring as well as the autumn of its growth1 but the fruit which sustains life must have its bud prepared before the approach of winter1 its blossom expanded in the spring1 and its juices elaborated by the light and heat of the summer and the autumnal sun4 ,in the century which preceded the birth of ,newton the science of astronomy advanced with the most rapid steps4 ,emerging from the darkness of the middle ages1 the human mind seemed to rejoice in its new-born strength1 and to apply itself with elastic vigour to unfold the mechanism of the heavens4 ,the labours of ,hipparchus and ,ptolemy had indeed furnished many important epochs and supplied many valuable data2 but the cumbrous appendages of cycles and epicycles with which they explained the stations and retrogradations of the planets1 and the vulgar prejudices which a false interpretation of ,scripture had excited against a belief in the motion of the earth1 rendered it difficult even for great minds to escape from the trammels of authority1 and appeal to the simplicity of nature4 ,the sovereign of ,castile1 the generous and noble-minded ,alphonso1 had long before proscribed the rude expedients of his predecessors2 and when he declared that if the heavens were thus constituted1 he could have given the ,deity good advice1 he must not only have felt the absurdity of the prevailing system1 but must have obtained some foresight of a more simple arrangement4 ,but neither he nor the astronomers whom he so liberally protected seem to have established a better system1 and it was left to ,copernicus to enjoy the dignity of being the restorer of astronomy4 ,this great man1 a native of ,thorn in ,prussia1 following his father's profession1 began his career as a doctor of medicine1 but an accidental attendance on the mathematical lectures of ,brudzevius excited a love for astronomy1 which became the leading passion of his life4 ,quitting a profession uncongenial to such pursuits1 he went to ,bologna to study astronomy under ,dominic ,maria2 and after having enjoyed the friendship and instruction of that able philosopher1 he established himself at ,rome in the humble situation of a teacher of mathematics4 ,here he made numerous astronomical observations which served him as the basis of future researches2 but an event soon occurred which1 though it interrupted for a while his important studies1 placed him in a situation for pursuing them with new zeal4 ,the death of one of the canons enabled his uncle1 who was ,bishop of ,ermeland1 to appoint him to a canonry in the chapter of ,frauenburg1 where1 in a house situated on the brow of a mountain1 he continued1 in peaceful seclusion1 to carry on his astronomical observations4 ,during his residence at ,rome his talents had been so well appreciated1 that the ,bishop of ,fossombrona1 who presided over the council for reforming the calendar1 solicited the aid of ,copernicus in this desirable undertaking4 ,at first he entered warmly into the views of the council1 and charged himself with the determination of the length of the year and of the month1 and of the other motions of the sun and moon that seemed to be required2 but he found the task too irksome1 and probably felt that it would interfere with those interesting discoveries which had already begun to dawn upon his mind4 ,copernicus is said to have commenced his inquiries by an historical examination of the opinions of ancient authors on the system of the universe2 but it is more likely that he sought for the authority of their great names to countenance his peculiar views1 and that he was more desirous to present his own theory as one that he had received1 rather than as one which he had invented4 ,his mind had been long imbued with the idea that simplicity and harmony should characterize the arrangements of the planetary system1 and1 in the complication and disorder which reigned in the hypothesis of ,ptolemy1 he saw insuperable objections to its being regarded as a representation of nature4 ,in the opinions of the ,egyptian sages1 in those of ,pythagoras1 ,philolaus1 ,aristarchus1 and ,nicetas1 he recognised his own earliest conviction that the earth was not the centre of the universe2 but he appears to have considered it as still possible that our globe might perform some function in the system more important than that of the other planets2 and his attention was much occupied with the speculation of ,martianus ,capella1 who placed the sun between ,mars and the moon1 and made ,mercury and ,venus revolve round him as a centre2 and with the system of ,apollonius ,pergus1 who made all the planets revolve round the sun1 while the sun and moon were carried round the earth in the centre of the universe4 ,the examination1 however1 of these hypotheses gradually dispelled the difficulties with which the subject was beset2 and after the labours of more than thirty years1 he was permitted to see the true system of the heavens4 ,the sun he considered as immoveable in the centre of the system1 while the earth revolved between the orbits of ,venus and ,mars1 and produced by its rotation about its axis all the diurnal phenomena of the celestial sphere4 ,the precession of the equinoxes was thus referred to a slight motion of the earth's axis1 and the stations and retrogradations of the planets were the necessary consequence of their own motions combined with that of the earth about the sun4 ,these remarkable views were supported by numerous astronomical observations2 and in #aecj ,copernicus brought to a close his immortal work on the ,revolutions of the ,heavenly ,bodies4 ,but while we admire the genius which triumphed over so many difficulties1 we cannot fail to commend the extraordinary prudence with which he ushered his new system into the world4 ,aware of the prejudices1 and even of the hostility with which such a system would be received1 he resolved neither to startle the one nor provoke the other4 ,he allowed his opinions to circulate in the slow current of personal communication4 ,the points of opposition which they presented to established doctrines were gradually worn down1 and they insinuated themselves into reception among the ecclesiastical circles by the very reluctance of their author to bring them into notice4 ,in the year #aecd1 ,cardinal ,schonberg1 ,bishop of ,capua1 and ,gyse1 ,bishop of ,culm1 exerted all their influence to induce ,copernicus to lay his system before the world2 but he resisted their solicitations2 and it was not till #aeci that an accidental circumstance contributed to alter his resolution4 ,george ,rheticus1 professor of mathematics at ,wirtemberg1 having heard of the labours of ,copernicus1 resigned his chair1 and repaired to ,frauenberg to make himself master of his discoveries4 ,this zealous disciple prevailed upon his master to permit the publication of his system2 and they seem to have arranged a plan for giving it to the world without alarming the vigilance of the church1 or startling the prejudices of individuals4 ,under the disguise of a student of mathematics1 ,rheticus published in #aedj an account of the manuscript volume of ,copernicus4 ,this pamphlet was received without any disapprobation1 and its author was encouraged to reprint it at ,basle1 in #aeda1 with his own name4 ,the success of these publications1 and the flattering manner in which the new astronomy was received by several able writers1 induced ,copernicus to place his ,,mss4 in the hands of ,rheticus4 ,it was accordingly printed at the expense of ,cardinal ,schonberg1 and appeared at ,nuremberg in #aedc4 ,its illustrious author1 however1 did not live to peruse it4 ,a complete copy was handed to him in his last moments1 and he saw and touched it a few hours before his death4 ,this great work was dedicated to the ,holy ,pontiff1 in order1 as ,copernicus himself says1 that the authority of the head of the church might silence the calumnies of individuals who had attacked his views by arguments drawn from religion4 ,thus introduced1 the ,copernican system met with no ecclesiastical opposition1 and gradually made its way in spite of the ignorance and prejudices of the age4 ,among the astronomers who provided the materials of the ,newtonian philosophy the name of ,tycho ,brahe merits a conspicuous place4 ,descended from an ancient ,swedish family1 he was born at ,knudstorp1 in ,norway1 in #aedf1 three years after the death of ,copernicus4 ,the great eclipse of the sun which happened on the #bfth ,august1 #aefj1 while he was at the ,university of ,copenhagen1 attracted his notice3 and when he found that all its phenomena had been accurately predicted1 he was seized with the most irresistible passion to acquire the knowledge of a science so infallible in its results4 ,destined for the profession of the law1 his friends discouraged the pursuit which now engrossed his thoughts2 and such were the reproaches and even persecutions to which he was exposed1 that he quitted his country with the design of travelling through ,germany4 ,at the very commencement of his journey1 however1 an event occurred in which the impetuosity of his temper had nearly cost him his life4 ,at a wedding-feast in ,rostock1 a questionable point in geometry involved him in a dispute with a ,danish nobleman of the same temperament with himself2 and the two mathematicians resolved to settle the difference by the sword4 ,tycho1 however1 seems to have been second in the conflict1 for he lost the greater part of his nose1 and was obliged to supply its place by a substitute of gold and silver1 which a cement of glue attached to his face4 ,during his stay at ,augsburg he inspired the burgomaster of the city1 ,peter ,hainzell1 with a love of astronomy4 ,this public-spirited citizen erected an excellent observatory at his own expense1 and here ,tycho began that distinguished career which has placed him in the first rank of practical astronomers4 ,upon his return to ,copenhagen in #aegj1 he was received with every mark of respect4 ,the king invited him to court1 and persons of all ranks harassed him with their attentions4 ,at ,herritzvold1 near his native place1 the house of his maternal uncle afforded him a retreat from the gayeties of the capital1 and he was there offered every accommodation for the prosecution of his astronomical studies4 ,here1 however1 the passion of love and the pursuits of alchymy distracted his thoughts2 but though the peasant girl of whom he was enamoured was of easier attainment than the philosopher's stone1 the marriage produced an open quarrel with his relations1 which it required the interference of the king to allay4 ,in the tranquillity of domestic happiness1 ,tycho resumed his study of the heavens1 and in #aegb he enjoyed the singular good fortune of observing1 through all its variations1 the new star in ,cassiopeia1 which appeared with such extraordinary splendour as to be visible in the daytime1 and which gradually disappeared in the following year4 ,dissatisfied with his residence in ,denmark1 ,tycho resolved to settle in some distant country2 and having gone as far as ,venice in search of a suitable residence1 he at last fixed upon ,basle1 in ,switzerland4 ,the ,king of ,denmark1 however1 had learned his intention from the ,prince of ,hesse2 and when ,tycho returned to ,copenhagen to remove his family and his instruments1 his sovereign announced to him his resolution to detain him in his kingdom4 ,he presented him with the canonry of ,roschild1 with an income of #bjjj crowns per annum4 ,to this he added a pension of #ajjj crowns2 and he promised to give him the island of ,huen1 with a complete observatory erected under his own eye4 ,this generous offer was instantly accepted4 ,the celebrated observatory of ,uraniburg was established at the expense of about #bj1jjjl42 and in this magnificent retreat ,tycho continued for twenty-one years to enrich astronomy with the most valuable observations4 ,admiring disciples crowded to this sanctuary of the sciences to acquire the knowledge of the heavens2 and kings#cd and princes felt themselves honoured by becoming the guests of the great astronomer of the age4 ,one of the principal discoveries of ,tycho was that of the inequality of the moon's motion1 called the variation4 ,he detected1 also1 the annual equation which affects the place of her apogee and nodes1 and he determined the greatest and the least inclination of the lunar orbit4 ,his observations on the planets were numerous and precise1 and have formed the data of the present generalizations in astronomy4 ,though thus skilful in the observation of phenomena1 his mind was but little suited to investigate their cause1 and it was probably owing to this defect that he rejected the system of ,copernicus4 ,the vanity of giving his own name to another system was not likely to actuate a mind such as his1 and it was more probable that he was led to adopt the immobility of the earth1 and to make the sun1 with all his attendant planets1 circulate round it1 from the great difficulty which still presented itself by comparing the apparent diameter of the stars with the annual parallax of the earth's orbit4 ,the death of ,frederick in #aehh proved a severe calamity to ,tycho1 and to the science which he cultivated4 ,during the first years of the minority of ,christian ,,iv4 the regency continued the royal patronage to the observatory of ,uraniburg2 and in #aeib the young king paid a visit of some days to ,tycho1 and left him a gold chain in token of his favour4 ,the astronomer1 however1 had made himself enemies at court1 and the envy of his high reputation had probably added fresh malignity to the irritation of personal feelings4 ,under the ministry of ,wolchendorf1 a name for ever odious to science1 ,tycho's pension was stopped2--he was in #aeig deprived of the canonry of ,roschild1 and was thus forced1 with his wife and children1 to seek an asylum in a foreign land4 ,his friend1 ,henry ,rantzau1 of ,wansbeck1 under whose roof he found a hospitable shelter1 was fortunately acquainted with the emperor ,rodolph ,,ii41 who1 to his love of science1 added a passion for alchymy and astrology4 ,the reputation of ,tycho having already reached the imperial ear1 the recommendation of ,rantzau was scarcely necessary to ensure him his warmest friendship4 ,invited by the emperor1 he repaired in #aeii to ,prague1 where he met with the kindest reception4 ,a pension of three thousand crowns was immediately settled upon him1 and a commodious observatory erected for his use in the vicinity of that city4 ,here the exiled astronomer renewed with delight his interrupted labours1 and the gratitude which he cherished for the royal favour increased the satisfaction which he felt in having so unexpectedly found a resting-place for approaching age4 ,these prospects of better days were enhanced by the good fortune of receiving two such men as ,kepler and ,longomontanus for his pupils2 but the fallacy of human anticipation was here1 as in so many other cases1 strikingly displayed4 ,tycho was not aware of the inroads which both his labours and his disappointments had made upon his constitution4 ,though surrounded with affectionate friends and admiring disciples1 he was still an exile in a foreign land4 ,though his country had been base in its ingratitude1 it was yet the land which he loved1--the scene of his earliest affection1--the theatre of his scientific glory4 ,these feelings continually preyed upon his mind1 and his unsettled spirit was ever hovering among his native mountains4 ,in this condition he was attacked with a disease of the most painful kind1 and though the paroxysms of its agonies had lengthened intermissions1 yet he saw that death was approaching4 ,he implored his pupils to persevere in their scientific labours4 ,he conversed with ,kepler on some of the profoundest points of astronomy1 and with these secular occupations he mingled frequent acts of piety and devotion4 ,in this happy condition he expired without pain at the age of fifty-five1 the unquestionable victim of the councils of ,christian ,,iv4 ,notwithstanding the accessions which astronomy had received from the labours of ,copernicus and ,tycho1 no progress was yet made in developing the general laws of the system1 and scarcely an idea had been formed of the power by which the planets were retained in their orbits4 ,the labours of assiduous observers had supplied the materials for this purpose1 and ,kepler arose to lay the foundations of physical astronomy4 ,john ,kepler was born at ,wiel1 in ,wirtemberg1 in #aega4 ,he was educated for the church1 and discharged even some of the clerical functions2 but his devotion to science withdrew him from the study of theology4 ,having received mathematical instruction from the celebrated ,mstlinus1 he had made such progress in the science1 that he was invited in #aeid to fill the mathematical chair of ,gratz in ,styria4 ,endowed with a fertile imagination1 his mind was ever intent upon subtle and ingenious speculations4 ,in the year #aeif he published his peculiar views in a work on the ,harmonies and ,analogies of ,nature4 ,in this singular production1 he attempts to solve what he calls the great cosmographical mystery of the admirable proportion of the planetary orbits2 and by means of the six regular geometrical solids1#ce he endeavours to assign a reason why there are six planets1 and why the dimensions of their orbits and the time of their periodical revolutions were such as ,copernicus had found them4 ,if a cube1 for example1 were inserted in a sphere1 of which ,saturn's orbit was one of the great circles1 it would1 he supposed1 touch by its six planes the lesser sphere of ,jupiter2 and1 in like manner1 he proposes to determine1 by the aid of the other geometrical solids1 the magnitude of the spheres of the other planets4 ,a copy of this work was presented by its author to ,tycho ,brahe1 who had been too long versed in the severe realities of observation to attach any value to such wild theories4 ,he advised his young friend 8first to lay a solid foundation for his views by actual observation1 and then1 by ascending from these1 to strive to reach the causes of things20 and there is reason to think that1 by the aid of the whole ,baconian philosophy1 thus compressed by anticipation into a single sentence1 he abandoned for a while his visionary inquiries4 ,in the year #aeih ,kepler suffered persecution for his religious principles1 and was compelled to quit ,gratz2 but though he was recalled by the ,states of ,styria1 he felt his situation insecure1 and accepted of a pressing invitation from ,tycho to settle at ,prague1 and assist him in his calculations4 ,having arrived in ,bohemia in #afjj1 he was introduced by his friends to the ,emperor ,rodolph1 from whom he ever afterward received the kindest attention4 ,on the death of ,tycho in #afja1 he was appointed mathematician to the emperor1--a situation in which he was continued during the successive reigns of ,matthias and ,ferdinand2 but what was of more importance to science1 he was put in possession of the valuable collection of ,tycho's observations4 ,these observations were remarkably numerous2 and as the orbit of ,mars was more oval than that of any of the other planets1 they were peculiarly suitable for determining its real form4 ,the notions of harmony and symmetry in the construction of the solar system1 which had filled the mind of ,kepler1 necessarily led him to believe that the planets revolved with a uniform motion in circular orbits4 ,so firm1 indeed1 was this conviction1 that he made numerous attempts to represent the observations of ,tycho by this hypothesis4 ,the deviations were too great to be ascribed to errors of observation2 and in trying various other curves1 he was led to the discovery that ,mars revolved round the sun in an elliptical orbit1 in one of the foci of which the sun itself was placed4 ,the same observations enabled him to determine the dimensions of the planet's orbit1 and by comparing together the times in which ,mars passed over different portions of its orbit1 he found that they were to one another as the areas described by the lines drawn from the centre of the planet to the centre of the sun1 or1 in more technical terms1 that the radius vector describes equal areas in equal times4 ,these two remarkable discoveries1 the first that were ever made in physical astronomy1 were extended to all the other planets of the system1 and were communicated to the world in #afji1 in his 8,commentaries on the ,motions of the ,planet ,mars1 as deduced from the observations of ,tycho ,brahe40 ,although our author was conducted to these great laws by the patient examination of well-established facts1 his imagination was ever hurrying him among the wilds of conjecture4 ,convinced that the mean distances of the planets from the sun bore to one another some mysterious relation1 he not only compared them with the regular geometrical solids1 but also with the intervals of musical tones2 an idea which the ancient ,pythagoreans had suggested1 and which had been adopted by ,archimedes himself4 ,all these comparisons were fruitless2 and ,kepler was about to abandon an inquiry of about seventeen years' duration1 when1 on the #hth ,march1 #afah1 he conceived the idea of comparing the powers of the different members which express the planetary distances1 in place of the numbers themselves4 ,he compared the squares and the cubes of the distances with the same powers of the periodic times2 nay1 he tried even the squares of the times with the cubes of the distances2 but his hurry and impatience led him into an error of calculation1 and he rejected this law as having no existence in nature6 ,on the #aeth ,may1 his mind again reverted to the same notion1 and upon making the calculations anew1 and free from error1 he discovered the great law1 that the squares of the periodic times of any two planets are to one another as the cubes of their distances from the sun4 ,enchanted with this unexpected result1 he could scarcely trust his calculations2 and1 to use his own language1 he at first believed that he was dreaming1 and had taken for granted the very truth of which he was in search4 ,this brilliant discovery was published in #afai1 in his 8,harmony of the ,world20 a work dedicated to ,james ,,vi4 of ,scotland4 ,thus were established what have been called the three laws of ,kepler1--the motion of the planets in elliptical orbits1--the proportionality between the areas described and their times of description1--and the relations between the squares of the periodic times and the cubes of the distances4 ,the relation of the movements of the planets to the sun1 as the general centre of all their orbits1 could not fail to suggest to ,kepler that some power resided in that luminary by which these various motions were produced2 and he went so far as to conjecture that this power diminishes as the square of the distance of the body on which it was exerted2 but he immediately rejects this law1 and prefers that of the simple distances4 ,in his work on ,mars1 he speaks of gravity as a mutual and corporeal affection between similar bodies4 ,he maintained that the tides were occasioned by the moon's attraction1 and that the irregularities of the lunar motions1 as detected by ,tycho1 were owing to the joint actions of the sun and the earth2 but the relation between gravity1 as exhibited on the earth's surface1 and as conducting the planets in their orbits1 required more patience of thought than he could command1 and was accordingly left for the exercise of higher powers4 ,the misery in which ,kepler lived forms a painful contrast with the services which he performed to science4 ,the pension on which he subsisted was always in arrears1 and though the three emperors whose reigns he adorned directed their ministers to be more punctual in its payment1 the disobedience of their commands was a source of continued vexation to ,kepler4 ,when he retired to ,sagan1 in ,silesia1 to spend in retirement the remainder of his days1 his pecuniary difficulties became still more harassing4 ,necessity at last compelled him to apply personally for the arrears which were due2 and he accordingly set out in #afcj for ,ratisbon2 but in consequence of the great fatigue which so long a journey on horseback produced1 he was seized with a fever1 which carried him off on the #cjth ,november1 #afcj1 in the #eith year of his age4 ,while ,kepler was thus laying the foundation of physical astronomy1 ,galileo was busily employed in extending the boundaries of the solar system4 ,this distinguished philosopher was born at ,pisa in #aefd4 ,he was the son of a ,florentine nobleman1 and was educated for the medical profession2 but a passion for geometry took possession of his mind1 and called forth all his powers4 ,without the aid of a master1 he studied the writings of ,euclid and of ,archimedes2 and such were his acquirements1 that he was appointed by the ,grand-duke of ,tuscany to the mathematical chair of ,pisa in the twenty-fifth year of his age4 ,his opposition to the ,aristotelian philosophy gained him many enemies1 and at the end of three years he quitted ,pisa1 and accepted of an invitation to the professorship of mathematics at ,padua4 ,here he continued for eighteen years adorning the university by his name1 and diffusing around him a taste for the physical sciences4 ,with the exception of some contrivances of inferior importance1 ,galileo had distinguished himself by no discovery till he had reached the forty-fifth year of his age4 ,in the year #afji1 the same year in which ,kepler published his celebrated commentary on ,mars1 ,galileo paid a visit to ,venice1 where he heard1 in the course of conversation1 that a ,dutchman of the name of ,jansens had constructed and presented to ,prince ,maurice an instrument through which he saw distant objects magnified and rendered more distinct1 as if they had been brought nearer to the observer4 ,this report was credited by some and disbelieved by others2 but1 in the course of a few days1 ,galileo received a letter from ,james ,badovere at ,paris1 which placed beyond a doubt the existence of such an instrument4 ,the idea instantly filled his mind as one of the utmost importance to science2 and so thoroughly was he acquainted with the properties of lenses1 that he not only discovered the principle of its construction1 but was able to complete a telescope for his own use4 ,into one end of a leaden tube he fitted a spectacle-glass plane on one side and convex on the other1 and in the other end he placed another spectacle-glass concave on one side and plane on the other4 ,he then applied his eye to the concave glass1 and saw objects 8pretty large and pretty near him40 ,they appeared three times nearer1 and nine times larger in surface1 than to the naked eye4 ,he soon after made another1 which represented objects above sixty times larger2 and1 sparing neither labour nor expense1 he finally constructed an instrument so excellent1 as 8to show things almost a thousand times larger1 and above thirty times nearer to the naked eye40 ,there is1 perhaps1 no invention that science has presented to man so extraordinary in its nature1 and so boundless in its influence1 as that of the telescope4 ,to the uninstructed mind1 the power of seeing an object a thousand miles distant1 as large and nearly as distinct as if it were brought within a mile of the observer1 must seem almost miraculous2 and to the philosopher1 even1 who thoroughly comprehends the principles upon which it acts1 it must ever appear one of the most elegant applications of science4 ,to have been the first astronomer in whose hands such a gift was placed was a preference to which ,galileo owed much of his future reputation4 ,no sooner had he completed his telescope than he applied it to the heavens1 and on the #gth ,january1 #afah1 the first day of its use1 he saw round ,jupiter three bright little stars lying in a line parallel to the ecliptic1 two to the east1 and one to the west of the planet4 ,regarding them as ordinary stars1 he never thought of estimating their distances4 ,on the following day1 when he accidentally directed his telescope to ,jupiter1 he was surprised to see the three stars to the west of the planet4 ,to produce this effect it was requisite that the motion of ,jupiter should be direct1 though1 according to calculation1 it was actually retrograde4 ,in this dilemma he waited with impatience for the evening of the #ith1 but unfortunately the sky was covered with clouds4 ,on the #ajth he saw only two stars to the east--a circumstance which he was no longer able to explain by the motion of ,jupiter4 ,he was therefore compelled to ascribe the change to the stars themselves2 and upon repeating his observations on the #aath1 he no longer doubted that he had discovered three planets revolving round ,jupiter4 ,on the #acth ,january he for the first time saw the fourth satellite4#cf ,this discovery1 though of the utmost importance in itself1 derived an additional value from the light which it threw on the true system of the universe4 ,while the earth was the only planet enlightened by a moon1 it might naturally be supposed that it alone was habitable1 and was therefore entitled to the pre-eminence of occupying the centre of the system2 but the discovery of four moons round a much larger planet deprived this argument of its force1 and created a new analogy between the earth and the other planets4 ,when ,kepler received the 8,sidereal ,messenger10 the work in which ,galileo announced his discovery in #afaj1 he perused it with the deepest interest2 and while it confirmed and extended his substantial discoveries1 it dispelled at the same time some of those harmonic dreams which still hovered among his thoughts4 ,in the 8,dissertation0 which he published on the discovery of ,galileo1 he expresses his hope that satellites will be discovered round ,saturn and ,mars1--he conjectures that ,jupiter has a motion of rotation about his axis1--and states his surprise1 that1 after what had been written on the subject of telescopes by ,baptista ,porta1 they had not been earlier introduced into observatories4 ,in continuing his observations1 ,galileo applied his telescope to ,venus1 and in #afaj he discovered the phases of that planet1 which exhibited to him the various forms of the waxing and the waning moon4 ,this fact established beyond a doubt that the planet revolved round the sun1 and thus gave an additional blow to the ,ptolemaic system4 ,in his observations on the sun1 ,galileo discovered his spots1 and deduced from them the rotation of the central luminary4 ,he observed that the body of ,saturn had handles attached to it2 but he was unable to detect the form of its ring1 or render visible its minute satellites4 ,on the surface of the moon he discovered her mountains and valleys1 and determined the curious fact of her libration1 in virtue of which parts of the margin of her disk occasionally appear and disappear4 ,in the ,milky ,way he descried numerous minute stars which the unassisted eye was unable to perceive2 and as the largest fixed stars1 in place of being magnified by the telescope1 became actually minute brilliant points1 he inferred their immense distance as rendered necessary by the ,copernican hypothesis4 ,all his discoveries1 indeed1 furnished fresh arguments in favour of the new system2 and the order of the planets and their relation to a central sun may now be considered as established by incontrovertible evidence4 ,while ,galileo was occupied with these noble pursuits at ,pisa1 to which he had been recalled in #afaa1 his generous patron1 ,cosmo ,,ii4 ,grand-duke of ,tuscany1 invited him to ,florence1 that he might pursue with uninterrupted leisure his astronomical observations1 and carry on his correspondence with the ,german astronomers4 ,his fame had now resounded through all ,europe2--the strongholds of prejudice and ignorance were unbarred2--and the most obstinate adherents of ancient systems acknowledged the meridian power of the day-star of science4 ,galileo was ambitious of propagating the great truths which he contributed so powerfully to establish4 ,he never doubted that they would received with gratitude by all1--by the philosopher as the consummation of the greatest efforts of human genius1--and by the ,christian as the most transcendent displays of ,almighty power4 ,but he had mistaken the disposition of his species1 and the character of the age4 ,that same system of the heavens which had been discovered by the humble ecclesiastic of ,frauenberg1 which had been patronised by the kindness of a bishop1 and published at the expense of a cardinal1 and which the pope himself had sanctioned by the warmest reception1 was1 after the lapse of a hundred years1 doomed to the most violent opposition1 as subversive of the doctrines of the ,christian faith4 ,on no former occasion has the human mind exhibited such a fatal relapse into intolerance4 ,the age itself had improved in liberality2--the persecuted doctrines themselves had become more deserving of reception2--the light of the ,reformed faith had driven the ,catholics from some of their most obnoxious positions2--and yet1 under all these circumstances1 the church of ,rome unfurled her banner of persecution against the pride of ,italy1 against the ornament of his species1 and against truths immutable and eternal4 ,in consequence of complaints laid before the ,holy ,inquisition1 ,galileo was summoned to appear at ,rome in #afae1 to answer for the heretical opinions which he had promulgated4 ,he was charged with 8maintaining as true the false doctrine held by many1 that the sun was immoveable in the centre of the world1 and that the earth revolved with a diurnal motion2--with having certain disciples to whom he taught the same doctrine2--with keeping up a correspondence on the subject with several ,german mathematicians2--with having published letters on the solar spots1 in which he explained the same doctrine as true2--and with having glossed over with a false interpretation the passages of ,scripture which were urged against it40 ,the consideration of these charges came before a meeting of the ,inquisition1 which assembled on the #beth ,february1 #afaf2 and the court1 declaring their disposition to deal gently with the prisoner1 pronounced the following decree3--8,that ,cardinal ,bellarmine should enjoin ,galileo to renounce entirely the above-recited false opinions2 that1 on his refusal to do so1 he should be commanded by the commissary of the ,inquisition to abandon the said doctrine1 and to cease to teach and defend it2 and that1 if he did not obey this command1 he should be thrown into prison40 ,on the #bfth of ,february ,galileo appeared before ,cardinal ,bellarmine1 and1 after receiving from him a gentle admonition1 he was commanded by the commissary1 in the presence of a notary and witnesses1 to desist altogether from his erroneous opinions2 and it was declared to be unlawful for him in future to teach them in any way whatever1 either orally or in his writings4 ,to these commands ,galileo promised obedience1 and was dismissed from the ,inquisition4 ,the mildness of this sentence was no doubt partly owing to the influence of the ,grand-duke of ,tuscany1 and other persons of rank and influence at the papal court1 who took a deep interest in the issue of the trial4 ,dreading1 however1 that so slight a punishment might not have the effect of putting down the obnoxious doctrines1 the ,inquisition issued a decree denouncing the new opinions as false and contrary to the sacred writings1 and prohibiting the sale of every book in which they should be maintained4 ,thus liberated from his persecutors1 ,galileo returned to ,florence1 where he pursued his studies with his wonted diligence and ardour4 ,the recantation of his astronomical opinions was so formal and unreserved1 that ordinary prudence1 if not a sense of personal honour1 should have restrained him from unnecessarily bringing them before the world4 ,no anathema was pronounced against his scientific discoveries2 no interdict was laid upon the free exercise of his genius4 ,he was prohibited merely from teaching a doctrine which the church of ,rome considered to be injurious to its faith4 ,we might have expected1 therefore1 that a philosopher so conspicuous in the eyes of the world would have respected the prejudices1 however base1 of an institution whose decrees formed part of the law of the land1 and which possessed the power of life and death within the limits of its jurisdiction4 ,galileo1 however1 thought otherwise4 ,a sense of degradation#cg seems to have urged him to retaliate1 and before six years had elapsed1 he began to compose his 8,cosmical ,system1 or ,dialogues on the two greatest ,systems of the ,world1 the ,ptolemean and the ,copernican10 the concealed object of which is to establish the opinions which he had promised to abandon4 ,in this work the subject is discussed by three speakers1 ,sagredo1 ,salviatus1 and ,simplicius1 a peripatetic philosopher1 who defends the system of ,ptolemy with much skill against the overwhelming arguments of the rival disputants4 ,galileo hoped to escape notice by this indirect mode of propagating the new system1 and he obtained permission to publish his work1 which appeared at ,florence in #afcb4 ,the ,inquisition did not1 as might have been expected1 immediately summon ,galileo to their presence4 ,nearly a year elapsed before they gave any indication of their design2 and1 according to their own statement1 they did not even take the subject under consideration till they saw that the obnoxious tenets were every day gaining ground1 in consequence of the publication of the ,dialogues4 ,they then submitted the work to a careful examination1 and having found it to be a direct violation of the injunction which had been formerly intimated to its author1 they again cited him before their tribunal in #afcc4 ,the venerable sage1 now in his seventieth year1 was thus compelled to repair to ,rome1 and when he arrived he was committed to the apartments of the ,fiscal of the ,inquisition4 ,the unchangeable friendship1 however1 of the ,grand-duke of ,tuscany obtained a remission of this severity1 and ,galileo was allowed to reside at the house of the ,tuscan ambassador during the two months which the trial occupied4 ,when brought before the ,inquisition1 and examined upon oath1 he acknowledged that the ,dialogues were written by himself1 and that he obtained permission to publish them without notifying to the person who gave it that he had been prohibited from holding1 defending1 or teaching the heretical opinions4 ,he confessed also that the ,dialogues were composed in such a manner1 that the arguments in favour of the ,copernican system1 though given as partly false1 were yet managed in such a manner that they were more likely to confirm than overturn its doctrines2 but that this error1 which was not intentional1 arose from the natural desire of making an ingenious defence of false propositions1 and of opinions that had the semblance of probability4 ,after receiving these confessions and excuses1 the ,inquisition allowed ,galileo a proper time for giving in his defence2 but this seems to have consisted solely in bringing forward the certificate of ,cardinal ,bellarmine already mentioned1 which made no allusion to the promise under which ,galileo had come never to defend1 nor teach in any way whatever1 the ,copernican doctrines4 ,the court held this defence to be an aggravation of the crime rather than an excuse for it1 and proceeded to pronounce a sentence which will be ever memorable in the history of the human mind4 ,invoking the name of our ,saviour1 they declare1 that ,galileo had made himself liable to the suspicion of heresy1 by believing the doctrine1 contrary to ,scripture1 that the sun was the centre of the earth's orbit1 and did not move from east to west2 and by defending as probable the opinion that the earth moved1 and was not the centre of the world2 and that he had thus incurred all the censures and penalties which were enacted by the church against such offences2--but that he should be absolved from these penalties1 provided he sincerely abjured and cursed all the errors and heresies contained in the formula of the church1 which should be submitted to him4 ,that so grave and pernicious a crime should not pass altogether unpunished1 that he might become more cautious in future1 and might be an example to others to abstain from such offences1 they decreed that his ,dialogues should be prohibited by a formal edict1--that he should be condemned to the prison of the ,inquisition during pleasure1--and that1 during the three following years1 he should recite once a week the seven penitential psalms4 ,this sentence was subscribed by seven cardinals2 and on the #bb;d ,june1 #afcc1 ,galileo signed an abjuration humiliating to himself and degrading to philosophy4 ,at the age of seventy1 on his bended knees1 and with his right hand resting on the ,holy ,evangelists1 did this patriarch of science avow his present and his past belief in all the dogmas of the ,romish ,church1 abandon as false and heretical the doctrine of the earth's motion and of the sun's immobility1 and pledge himself to denounce to the ,inquisition any other person who was even suspected of heresy4 ,he abjured1 cursed1 and detested those eternal and immutable truths which the ,almighty had permitted him to be the first to establish4 ,what a mortifying picture of moral depravity and intellectual weakness6 ,if the unholy zeal of the assembly of cardinals has been branded with infamy1 what must we think of the venerable sage whose gray hairs were entwined with the chaplet of immortality1 quailing under the fear of man1 and sacrificing the convictions of his conscience and the deductions of his reason at the altar of a base superstition8 ,had ,galileo but added the courage of the martyr to the wisdom of the sage1--had he carried the glance of his indignant eye round the circle of his judges1--had he lifted his hands to heaven1 and called the living ,god to witness the truth and immutability of his opinions1 the bigotry of his enemies would have been disarmed1 and science would have enjoyed a memorable triumph4 ,the great truths of the ,copernican system1 instead of being considered as heretical1 had been actually adopted by many pious members of the ,catholic church1 and even some of its dignitaries did not scruple to defend it openly4 ,previous to the first persecution of ,galileo in #afae1 a ,neapolitan nobleman1 ,vincenzio ,caraffa1 a person equally distinguished by his piety and birth1 had solicited ,paul ,anthony ,foscarinus1 a learned ,carmelite monk1 to illustrate and defend the new system of the universe4 ,with this request the ecclesiastic speedily complied2 and in the pamphlet which he completed on the #fth ,january1 #afae1 he defends the ,copernican system with much boldness and ingenuity2 he reconciles the various passages of ,scripture with the new doctrine1 and he expresses the hope that such an attempt1 now made for the first time1 will prove agreeable to philosophers1 but particularly to those very learned men1 ,galileo ,galilei1 ,john ,kepler1 and all the members of the ,lyncean ,academy1 who1 he believes1 entertain the same opinion4 ,this remarkable production1 written from the convent of the ,carmelites at ,naples1 is dedicated to the very ,reverend ,sebastian ,fantoni1 general of the order of ,carmelites1 and was published at ,florence1 with the sanction of the ecclesiastical authorities1 in #afcj2 three years before the second persecution of ,galileo4 ,it would be interesting to know the state of public feeling in ,italy when ,galileo was doomed to the prisons of the ,inquisition4 ,no appeal seems to have been made against so cruel a sentence2 and neither in remonstrance nor in derision does an individual voice seem to have been raised4 ,the master spirits of the age looked with sullen indifference on the persecution of exalted genius2 and ,galileo lay in chains1 deserted and unpitied4 ,this unrebuked triumph of his enemies was perhaps favourable to the object of their vengeance4 ,resistance might have heightened the rigour of a sentence1 which submission seems to have alleviated4 ,the interference of some eminent individuals of ,rome1 among whom we have no doubt that the ,grand-duke of ,tuscany was the most influential1 induced ,pope ,urban ,,viii41 not only to shorten the period1 but to soften the rigour of ,galileo's imprisonment4 ,from the dungeon of the ,inquisition1 where he had remained only four days1 he was transported to the ambassador's palace in the ,garden de ,medici at ,rome2 and when his health had begun to suffer1 he was permitted to leave the metropolis2 and would have been allowed to return to ,florence1 but as the plague raged in that city1 he was sent1 in ,july1 #afcc1 to the archiepiscopal palace of ,sienna1 the residence of the ,archbishop ,piccolimini1 where he carried on and completed his valuable investigations respecting the resistance of solids4 ,here he continued five months1 when1 in consequence of the disappearance of the plague at ,florence1 he was allowed to retire to his villa at ,bellosguardo1 and afterward to that of ,arcetri in the vicinity of ,florence4 ,though ,galileo was now1 to a certain degree1 liberated from the power of man1 yet the afflicting dispensations of ,providence began to fall thickly around him4 ,no sooner had he returned to ,arcetri1 than his favourite daughter1 ,maria1 was seized with a dangerous illness1 which soon terminated in her death4 ,he was himself attacked with hernia1 palpitation of the heart1 loss of appetite1 and the most oppressive melancholy2 and though he solicited permission to repair to ,florence for medical assistance1 yet this deed of mercy was denied him4 ,in #afch1 however1 the pope permitted him to pay a visit to ,florence1 and his friend1 ,father ,castelli1 was allowed to visit him in the company of an officer of the ,inquisition4 ,but this indulgence was soon withdrawn1 and at the end of a few months he was remanded to ,arcetri4 ,the sight of his right eye had begun to fail in #afcf1 from an opacity of the cornea4 ,in #afcg his left eye was attacked with the same complaint2 so that in a few months he was affected with total and incurable blindness4 ,before this calamity had supervened1 he had noticed the curious phenomenon of the moon's libration1 in consequence of which1 parts of her visible disk that are exposed to view at one time are withdrawn at another4 ,he succeeded in explaining two of the causes of this curious phenomenon1 viz4 the different distances of the observer from the line joining the centre of the earth and the moon1 which produces the diurnal libration1 and the unequal motion of the moon in her orbit1 which produces the libration in longitude4 ,it was left1 however1 to ,hevelius to discover the libration in latitude1 which arises from the inclination of her axis being a little less than a right angle to the ecliptic2 and to ,lagrange to discover the spheroidal libration1 or that which arises from the action of the earth upon the lunar spheroid4 ,the sorrows with which ,galileo was now beset1 seemed to have disarmed the severity of the ,inquisition4 ,he was freely permitted to enjoy the society of his friends1 who now thronged around him to express their respect and their sympathy4 ,the ,grand-duke of ,tuscany was his frequent visiter1 and ,gassendi1 ,deodati1 and our countryman ,milton went to ,italy for the purpose of visiting him4 ,he entertained his friends with the warmest hospitality1 and though simple and abstemious in his diet1 yet he was fond of good wine1 and seems even in his last days to have paid particular attention to the excellence of his cellar4 ,although ,galileo had nearly lost his hearing as well as his sight1 yet his intellectual faculties were unimpaired2 and while his mind was occupied in considering the force of percussion1 he was seized with fever and palpitation of the heart1 which1 after two months' illness1 terminated his life on the #hth of ,january1 #afdb4 ,among the predecessors of ,newton in astronomical research we must not omit the names of ,bouillaud 7,bullialdus71 ,borelli1 and ,dr4 ,hooke4 ,ismael ,bouillaud1 a native of ,laon in ,france1 and the author of several valuable astronomical works1 has derived more reputation from a single sentence in his ,astronomica ,philolaica1 published in #afde1 than from all the rest of his labours4 ,he was not a believer in the doctrine of attraction1 which1 as we have already seen1 had been broached by ,copernicus1 and discovered by ,kepler2 but in speaking of that power as the cause of the planetary motions1 he remarks1 8that if attraction existed1 it would decrease as the square of the distance40 ,the influence of gravity was still more distinctly developed by ,borelli1 a ,neapolitan philosopher1 who published in #afff a work on ,jupiter's satellites4#ch ,in this work he maintains1 that all the planets perform their motions round the sun according to a general law2 that the satellites of ,jupiter and of ,saturn move round their primary planets in the same manner as the moon does round the earth1 and that they all revolve round the sun1 which is the only source of any virtue1 and that this virtue attaches them1 and unites them so that they cannot recede from their centre of action4#ci ,our countryman ,dr4 ,robert ,hooke seems to have devoted much of his attention to the cause of the planetary motions4 ,on the #bast ,march1 #afff1 he read to the ,royal ,society an account of a series of experiments for determining if bodies experience any variation in their weight at different distances from the centre of the earth4 ,his experiments1 as ,hooke himself saw1 were by no means satisfactory1 and hence he was led to the ingenious idea of measuring the force of gravity by observing1 at different altitudes1 the rate of a pendulum clock4 ,about two months afterward1 he exhibited to the ,society an approximate representation of the forces which retain the planets in their orbits1 in the paths described by a circular pendulum impelled with different degrees of force2 but though this experiment illustrated the production of a curvilineal motion1 by combining a tangential force with a central power of attraction1 yet it was only an illustration1 and could not lead to the true cause of the planetary motions4 ,at a later period1 however1 viz4 in #afgd1 ,hooke resumed the subject in a dissertation entitled 8,an ,attempt to prove the ,motion of the ,earth from ,observation10 which contains the following remarkable observations upon gravity3-- 8,i shall hereafter explain a system of the world differing in many particulars from any yet known1 answering in all things to the common rules of mechanical motions4 ,this depends upon three suppositions3--first1 that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres1 whereby they attract1 not only their own parts1 and keep them from flying from them1 as we may observe the earth to do1 but that they also do attract all the other celestial bodies that are within the sphere of their activity1 and consequently1 that not only the sun and moon have an influence upon the body and motion of the earth1 and the earth upon them1 but that ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn1 also1 by their attractive powers1 have a considerable influence upon its motion1 as in the same manner the corresponding attractive power of the earth hath a considerable influence upon every one of their motions also4 ,the second supposition is this1 that all bodies whatsoever that are put into a direct and simple motion will so continue to move forward in a straight line1 till they are1 by some other effectual powers1 deflected1 and sent into a motion describing a circle1 ellipsis1 or some other more compounded curve line4 ,the third supposition is1 that those attractive powers are so much the more powerful in operating by how much the nearer the body wrought upon is to their own centres4 ,now1 what these several degrees are ,i have not yet experimentally verified2 but it is a notion which1 if fully prosecuted1 as it ought to be1 will mightily assist the astronomers to reduce all the celestial motions to a certain rule1 which ,i doubt will never be done without it4 ,he that understands the nature of the circular pendulum and circular motion will easily understand the whole of this principle1 and will know where to find directions in nature for the true stating thereof4 ,this ,i only hint at present to such as have ability and opportunity of prosecuting this inquiry1 and are not wanting of industry for observing and calculating1 wishing heartily such may be found1 having myself many other things in hand1 which ,i would first complete1 and therefore cannot so well attend it4 ,but this ,i do not promise the undertaker1 that he will find all the great motions of the world to be influenced by this principle1 and that the true understanding thereof will be the true perfection of astronomy40 ,this passage1 which has been considered as a remarkable one by the philosophers of every country1 has1 we think1 been misapprehended by ,m4 ,delambre1 when he asserts that every thing which it contains 8is to be found expressly in ,kepler40#dj ,,chapter ,,xi4 ,the first ,idea of ,gravity occurs to ,newton in #afff--;,his first ,speculations upon it--,interrupted by his ,optical ,experiments--,he resumes the ,subject in consequence of a ,discussion with ,dr4 ,hooke-- ,he discovers the true ,law of ,gravity and the ,cause of the ,planetary ,motions--,dr4 ,halley urges him to publish his ,principia--,his ,principles of ,natural ,philosophy--,proceedings of the ,royal ,society on this ,subject--,the ,principia appears in #afhg--;,general ,account of it1 and of the ,discoveries it contains--,they meet with great ,opposition1 owing to the ,prevalence of the ,cartesian ,system--,account of the ,reception and ,progress of the ,newtonian ,philosophy in foreign ,countries--,account of its ,progress and ,establishment in ,england4 ,such is a brief sketch of the labours and lives of those illustrious men who prepared the science of astronomy for the application of ,newton's genius4 ,copernicus had determined the arrangement and general movements of the planetary bodies3 ,kepler had proved that they moved in elliptical orbits2 that their radii vectores described arcs proportional to the times2 and that their periodic times were related to their distances4 ,galileo had added to the universe a whole system of secondary planets2 and several astronomers had distinctly referred the motion of the heavenly bodies to the power of attraction4 ,in the year #afff1 when the plague had driven ,newton from ,cambridge1 he was sitting alone in the garden at ,woolsthorpe1 and reflecting on the nature of gravity1--that remarkable power which causes all bodies to descend towards the centre of the earth4 ,as this power is not found to suffer any sensible diminution at the greatest distance from the earth's centre to which we can reach1 being as powerful at the tops of the highest mountains as at the bottom of the deepest mines1 he conceived it highly probable1 that it must extend much farther than was usually supposed4 ,no sooner had this happy conjecture occurred to his mind1 than he considered what would be the effect of its extending as far as the moon4 ,that her motion must be influenced by such a power he did not for a moment doubt2 and a little reflection convinced him that it might be sufficient for retaining that luminary in her orbit round the earth4 ,though the force of gravity suffers no sensible diminution at those small distances from the earth's centre at which we can place ourselves1 yet he thought it very possible1 that1 at the distance of the moon1 it might differ much in strength from what it is on the earth4 ,in order to form some estimate of the degree of its diminution1 he considered that1 if the moon be retained in her orbit by the force of gravity1 the primary planets must also be carried round the sun by the same power2 and by comparing the periods of the different planets with their distances from the sun1 he found1 that if they were retained in their orbits by any power like gravity1 its force must decrease in the duplicate proportion1#da or as the squares of their distances from the sun4 ,in drawing this conclusion1 he supposed the planets to move in orbits perfectly circular1 and having the sun in their centre4 ,having thus obtained the law of the force by which the planets were drawn to the sun1 his next object was to ascertain if such a force1 emanating from the earth and directed to the moon1 was sufficient1 when diminished in the duplicate ratio of the distance1 to retain her in her orbit4 ,in performing this calculation1 it was necessary to compare the space through which heavy bodies fall in a second at a given distance from the centre of the earth1 viz4 at its surface1 with the space through which the moon1 as it were1 falls to the earth in a second of time while revolving in a circular orbit4 ,being at a distance from books when he made this computation1 he adopted the common estimate of the earth's diameter then in use among geographers and navigators1 and supposed that each degree of latitude contained sixty ,english miles4 ,in this way he found that the force which retains the moon in her orbit1 as deduced from the force which occasions the fall of heavy bodies to the earth's surface1 was one-sixth greater than that which is actually observed in her circular orbit4 ,this difference threw a doubt upon all his speculations2 but1 unwilling to abandon what seemed to be otherwise so plausible1 he endeavoured to account for the difference of the two forces1 by supposing that some other cause#db must have been united with the force of gravity in producing so great a velocity of the moon in her circular orbit4 ,as this new cause1 however1 was beyond the reach of observation1 he discontinued all further inquiries into the subject1 and concealed from his friends the speculations in which he had been employed4 ,after his return to ,cambridge in #afff1 his attention was occupied with those optical discoveries of which we have given an account in a preceding chapter2 but he had no sooner brought them to a close than his mind reverted to the great subject of the planetary motions4 ,upon the death of ,oldenburg in ,august1 #afgh1 ,dr4 ,hooke was appointed secretary to the ,royal ,society2 and as this learned body had requested the opinion of ,newton about a system of physical astronomy1 he addressed a letter to ,dr4 ,hooke on the #bhth ,november1 #afgi4 ,in this letter he proposed a direct experiment for verifying the motion of the earth1 viz4 by observing whether or not bodies that fall from a considerable height descend in a vertical direction1 for if the earth were at rest the body would describe exactly a vertical line1 whereas if it revolved round its axis1 the falling body must deviate from the vertical line towards the east4 ,the ,royal ,society attached great value to the idea thus casually suggested2 and ,dr4 ,hooke was appointed to put it to the test of experiment4 ,being thus led to consider the subject more attentively1 he wrote to ,newton1 that wherever the direction of gravity was oblique to the axis on which the earth revolved1 that is1 in every part of the earth except the equator1 falling bodies should approach to the equator1 and the deviation from the vertical1 in place of being exactly to the east1 as ,newton maintained1 should be to the south-east of the point from which the body began to move4 ,newton acknowledged that this conclusion was correct in theory1 and ,dr4 ,hooke is said to have given an experimental demonstration of it before the ,royal ,society in ,december1 #afgi4dc ,newton had erroneously concluded that the path of the falling body would be a spiral2 but ,dr4 ,hooke1 on the same occasion on which he made the preceding experiment1 read a paper to the ,society1 in which he proved that the path of the body would be an eccentric ellipse in vacuo1 and an ellipti-spiral1 if the body moved in a resisting medium4#dd ,this correction of ,newton's error1 and the discovery that a projectile would move in an elliptical orbit when under the influence of a force varying in the inverse ratio of the square of the distance1 led ,newton1 as he himself informs us in his letter to ,halley1#de to discover 8the theorem by which he afterward examined the ellipsis10 and to demonstrate the celebrated proposition1 that a planet acted upon by an attractive force varying inversely as the squares of the distances will describe an elliptical orbit1 in one of whose foci the attractive force resides4 ,but though ,newton had thus discovered the true cause of all the celestial motions1 he did not yet possess any evidence that such a force actually resided in the sun and planets4 ,the failure of his former attempt to identify the law of falling bodies at the earth's surface with that which guided the moon in her orbit threw a doubt over all his speculations1 and prevented him from giving any account of them to the public4 ,an accident1 however1 of a very interesting nature induced him to resume his former inquiries1 and enabled him to bring them to a close4 ,in ,june1 #afhb1 when he was attending a meeting of the ,royal ,society of ,london1 the measurement of a degree of the meridian1 executed by ,m4 ,picard in #afgi1 became the subject of conversation4 ,newton took a memorandum of the result obtained by the ,french astronomer1 and having deduced from it the diameter of the earth1 he immediately resumed his calculation of #affe1 and began to repeat it with these new data4 ,in the progress of the calculation he saw that the result which he had formerly expected was likely to be produced1 and he was thrown into such a state of nervous irritability that he was unable to carry on the calculation4 ,in this state of mind he intrusted it to one of his friends1 and he had the high satisfaction of finding his former views amply realized4 ,the force of gravity which regulated the fall of bodies at the earth's surface1 when diminished as the square of the moon's distance from the earth1 was found to be almost exactly equal to the centrifugal force of the moon as deduced from her observed distance and velocity4 ,the influence of such a result upon such a mind may be more easily conceived than described4 ,the whole material universe was spread out before him2--the sun with all his attending planets2--the planets with all their satellites2--the comets wheeling in every direction in their eccentric orbits2--and the systems of the fixed stars stretching to the remotest limits of space4 ,all the varied and complicated movements of the heavens1 in short1 must have been at once presented to his mind1 as the necessary result of that law which he had established in reference to the earth and the moon4 ,after extending this law to the other bodies of the system1 he composed a series of propositions on the motion of the primary planets about the sun1 which were sent to ,london about the end of #afhc1 and were soon afterward communicated to the ,royal ,society4#df ,about this period other philosophers had been occupied with the same subject4 ,sir ,christopher ,wren had many years before endeavoured to explain the planetary motions 8by the composition of a descent towards the sun1 and an impressed motion2 but he at length gave it over1 not finding the means of doing it40 ,in ,january1 #afhc-d1 ,dr4 ,halley had concluded1 from ,kepler's ,law of the ,periods and ,distances1 that the centripetal force decreased in the reciprocal proportion of the squares of the distances1 and having one day met ,sir ,christopher ,wren and ,dr4 ,hooke1 the latter affirmed that he had demonstrated upon that principle all the laws of the celestial motions4 ,dr4 ,halley confessed that his attempts were unsuccessful1 and ,sir ,christopher1 in order to encourage the inquiry1 offered to present a book of forty shillings' value to either of the two philosophers who should1 in the space of two months1 bring him a convincing demonstration of it4 ,hooke persisted in the declaration that he possessed the method1 but avowed it to be his intention to conceal it for some time4 ,he promised1 however1 to show it to ,sir ,christopher2 but there is every reason to believe that this promise was never fulfilled4 ,in ,august1 #afhd1 ,dr4 ,halley went to ,cambridge for the express purpose of consulting ,newton on this interesting subject4 ,newton assured him that he had brought this demonstration to perfection1 and promised him a copy of it4 ,this copy was received in ,november by the doctor1 who made a second visit to ,cambridge1 in order to induce its author to have it inserted in the register book of the society4 ,on the #ajth of ,december1 ,dr4 ,halley announced to the society1 that he had seen at ,cambridge ,mr4 ,newton's treatise ,de ,motu ,corporum1 which he had promised to send to the society to be entered upon their register2 and ,dr4 ,halley was desired to unite with ,mr4 ,paget1 master of the mathematical school in ,christ's ,hospital1 in reminding ,mr4 ,newton of his promise 8for securing the invention to himself till such time as he can be at leisure to publish it40 ,on the #beth ,february ,mr4 ,aston1 the secretary1 communicated a letter from ,mr4 ,newton1 in which he expressed his willingness 8to enter in the register his notions about motion1 and his intentions to fit them suddenly for the press40 ,the progress of his work was1 however1 interrupted by a visit of five or six weeks which he made in ,lincolnshire2 but he proceeded with such diligence on his return1 that he was able to transmit the manuscript to ,london before the end of ,april4 ,this manuscript1 entitled ,philosophi ,naturalis ,principia ,mathematica1 and dedicated to the society1 was presented by ,dr4 ,vincent on the #bhth ,april1 #afhf1 when ,sir ,john ,hoskins1 the vice-president1 and the particular friend of ,dr4 ,hooke1 was in the chair4 ,dr4 ,vincent passed a just encomium on the novelty and dignity of the subject2 and another member added1 that 8,mr4 ,newton had carried the thing so far1 that there was no more to be added40 ,to these remarks the vice-president replied1 that the method 8was so much the more to be prized as it was both invented and perfected at the same time40 ,dr4 ,hooke took offence at these remarks1 and blamed ,sir ,john for not having mentioned 8what he had discovered to him20 but the vice-president did not seem to recollect any such communication1 and the consequence of this discussion was1 that 8these two1 who till then were the most inseparable cronies1 have since scarcely seen one another1 and are utterly fallen out40 ,after the breaking up of the meeting1 the society adjourned to the coffee-house1 where ,dr4 ,hooke stated that he not only had made the same discovery1 but had given the first hint of it to ,newton4 ,an account of these proceedings was communicated to ,newton through two different channels4 ,in a letter dated ,may #bb;d1 ,dr4 ,halley wrote to him 8that ,mr4 ,hooke has some pretensions upon the invention of the rule of the decrease of gravity being reciprocally as the squares of the distances from the centre4 ,he says you had the notion from him1 though he owns the demonstration of the curves generated thereby to be wholly your own4 ,how much of this is so you know best1 as likewise what you have to do in this matter4 ,only ,mr4 ,hooke seems to expect you would make some mention of him in the preface1 which it is possible you may see reason to prefix40 ,this communication from ,dr4 ,halley induced our author1 on the #bjth ,june1 to address a long letter to him1 in which he gives a minute and able refutation of ,hooke's claims2 but before this letter was despatched1 another correspondent1 who had received his information from one of the members that were present1 informed ,newton 8that ,hooke made a great stir1 pretending that he had all from him1 and desiring they would see that he had justice done him40 ,this fresh charge seems to have ruffled the tranquillity of ,newton2 and he accordingly added an angry and satirical postscript1 in which he treats ,hooke with little ceremony1 and goes so far as to conjecture that ,hooke might have acquired his knowledge of the law from a letter of his own to ,huygens1 directed to ,oldenburg1 and dated ,january #adth1 #afgb-c4 8,my letter to ,hugenius was directed to ,mr4 ,oldenburg1 who used to keep the originals4 ,his papers came into ,mr4 ,hooke's possession4 ,mr4 ,hooke1 knowing my hand1 might have the curiosity to look into that letter1 and there take the notion of comparing the forces of the planets arising from their circular motion2 and so what he wrote to me afterward about the rate of gravity might be nothing but the fruit of my own garden40 ,in replying to this letter1 ,dr4 ,halley assured him that ,hooke's 8manner of claiming the discovery had been represented to him in worse colours than it ought1 and that he neither made public application to the society for justice1 nor pretended that you had all from him40 ,the effect of this assurance was to make ,newton regret that he had written the angry postscript to his letter2 and in replying to ,halley on the #adth ,july1 #afhf1 he not only expresses his regret1 but recounts the different new ideas which he had acquired from ,hooke's correspondence1 and suggests it as the best method 8of compromising the present dispute10 to add a scholium1 in which ,wren1 ,hooke1 and ,halley are acknowledged to have independently deduced the law of gravity from the second law of ,kepler4#dg ,at the meeting of the #bhth ,april1 at which the manuscript of the ,principia was presented to the ,royal ,society1 it was agreed that the printing of it should be referred to the council2 that a letter of thanks should be written to its author2 and at a meeting of the council on the #aith ,may1 it was resolved that the ,,mss4 should be printed at the society's expense1 and that ,dr4 ,halley should superintend it while going through the press4 ,these resolutions were communicated by ,dr4 ,halley in a letter dated the #bb;d ,may2 and in ,newton's reply on the #bjth ,june already mentioned1 he makes the following observations3 8,the proof you sent me ,i like very well4 ,i designed the whole to consist of three books2 the second was finished last summer1 being short1 and only wants transcribing1 and drawing the cuts fairly4 ,some new propositions ,i have since thought on1 which ,i can as well let alone4 ,the third wants the theory of comets4 ,in autumn last ,i spent two months in calculation to no purpose for want of a good method1 which made me afterward return to the first book1 and enlarge it with diverse propositions1 some relating to comets1 others to other things found out last winter4 ,the third ,i now design to suppress4 ,philosophy is such an impertinently litigious lady1 that a man had as good be engaged in lawsuits as have to do with her4 ,i found it so formerly1 and now ,i can no sooner come near her again but she gives me warning4 ,the first two books without the third will not so well bear the title of ,philosophi ,naturalis ,principia ,mathematica2 and therefore ,i had altered it to this1 ,de ,motu ,corporum ,libri duo4 ,but after second thoughts ,i retain the former title4 ,it will help the sale of the book1 which ,i ought not to diminish now 'tis yours40 ,in replying to this letter on the #bith ,june1 ,dr4 ,halley regrets that our author's tranquillity should have been thus disturbed by envious rivals2 and implores him in the name of the society not to suppress the third book4 8,i must again beg you10 says he1 8not to let your resentments run so high as to deprive us of your third book1 wherein your applications of your mathematical doctrine to the theory of comets1 and several curious experiments1 which1 as ,i guess by what you write ought to compose it1 will undoubtedly render it acceptable to those who will call themselves philosophers without mathematics1 which are much the greater number40 ,to these solicitations ,newton seems to have readily yielded4 ,his second book was sent to the society1 and presented on the #b;d ,march1 #afhf-g4 ,the third book was also transmitted1 and presented on the #fth ,april1 and the whole work was completed and published in the month of ,may1 #afhg4 ,such is a brief account of the publication of a work which is memorable1 not only in the annals of one science or of one country1 but which will form an epoch in the history of the world1 and will ever be regarded as the brightest page in the records of human reason4 ,we shall endeavour to convey to the reader some idea of its contents1 and of the brilliant discoveries which it disseminated over ,europe4 ,the ,principia consists of three books4 ,the first and second1 which occupy three-fourths of the work1 are entitled1 ,on the ,motion of ,bodies2 and the third bears the title1 ,on the ,system of the ,world4 ,the first two books contain the mathematical principles of philosophy1 namely1 the laws and conditions of motions and forces2 and they are illustrated with several philosophical scholia1 which treat of some of the most general and best established points in philosophy1 such as the density and resistance of bodies1 spaces void of matter1 and the motion of sound and light4 ,the object of the third book is to deduce from these principles the constitution of the system of the world2 and this book has been drawn up in as popular a style as possible1 in order that it may be generally read4 ,the great discovery which characterizes the ,principia is that of the principle of universal gravitation1 as deduced from the motion of the moon1 and from the three great facts or laws discovered by ,kepler4 ,this principle is1 that every particle of matter is attracted by1 or gravitates to1 every other particle of matter1 with a force inversely proportional to the squares of their distances4 ,from the first law of ,kepler1 namely1 the proportionality of the areas to the times of their description1 ,newton inferred that the force which kept the planet in its orbit was always directed to the sun2 and from the second law of ,kepler1 that every planet moves in an ellipse with the sun in one of its foci1 he drew the still more general inference1 that the force by which the planet moves round that focus varies inversely as the square of its distance from the focus4 ,as this law was true in the motion of satellites round their primary planets1 ,newton deduced the equality of gravity in all the heavenly bodies towards the sun1 upon the supposition that they are equally distant from its centre2 and in the case of terrestrial bodies1 he succeeded in verifying this truth by numerous and accurate experiments4 ,by taking a more general view of the subject1 ,newton demonstrated that a conic section was the only curve in which a body could move when acted upon by a force varying inversely as the square of the distance2 and he established the conditions depending on the velocity and the primitive position of the body1 which were requisite to make it describe a circular1 an elliptical1 a parabolic1 or a hyperbolic orbit4 ,notwithstanding the generality and importance of these results1 it still remained to be determined whether the force resided in the centres of the planets1 or belonged to each individual particle of which they were composed4 ,newton removed this uncertainty by demonstrating1 that if a spherical body acts upon a distant body with a force varying as the distance of this body from the centre of the sphere1 the same effect will be produced as if each of its particles acted upon the distant body according to the same law4 ,and hence it follows that the spheres1 whether they are of uniform density1 or consist of concentric layers1 with densities varying according to any law whatever1 will act upon each other in the same manner as if their force resided in their centres alone4 ,but as the bodies of the solar system are very nearly spherical1 they will all act upon one another1 and upon bodies placed on their surface1 as if they were so many centres of attraction2 and therefore we obtain the law of gravity which subsists between spherical bodies1 namely1 that one sphere will act upon another with a force directly proportional to the quantity of matter1 and inversely as the square of the distance between the centres of the spheres4 ,from the equality of action and reaction1 to which no exception can be found1 ,newton concluded that the sun gravitated to the planets1 and the planets to their satellites2 and the earth itself to the stone which falls upon its surface2 and1 consequently1 that the two mutually gravitating bodies approached to one another with velocities inversely proportional to their quantities of matter4 ,having established this universal law1 ,newton was enabled1 not only to determine the weight which the same body would have at the surface of the sun and the planets1 but even to calculate the quantity of matter in the sun1 and in all the planets that had satellites1 and even to determine the density or specific gravity of the matter of which they were composed4 ,in this way he found that the weight of the same body would be twenty-three times greater at the surface of the sun than at the surface of the earth1 and that the density of the earth was four times greater than that of the sun1 the planets increasing in density as they receded from the centre of the system4 ,if the peculiar genius of ,newton has been displayed in his investigation of the law of universal gravitation1 it shines with no less lustre in the patience and sagacity with which he traced the consequences of this fertile principle4 ,the discovery of the spheroidal form of ,jupiter by ,cassini had probably directed the attention of ,newton to the determination of its cause1 and consequently to the investigation of the true figure of the earth4 ,the spherical form of the planets have been ascribed by ,copernicus to the gravity or natural appetency of their parts2 but upon considering the earth as a body revolving upon its axis1 ,newton quickly saw that the figure arising from the mutual attraction of its parts must be modified by another force arising from its rotation4 ,when a body revolves upon an axis1 the velocity of rotation increases from the poles1 where it is nothing1 to the equator1 where it is a maximum4 ,in consequence of this velocity the bodies on the earth's surface have a tendency to fly off from it1 and this tendency increases with the velocity4 ,hence arises a centrifugal force which acts in combination with a force of gravity1 and which ,newton found to be the #bhith part of the force of gravity at the equator1 and decreasing1 as the cosine of the latitude1 from the equator to the poles4 ,the great predominance of gravity over the centrifugal force prevents the latter from carrying off any bodies from the earth's surface1 but the weight of all bodies is diminished by the centrifugal force1 so that the weight of any body is greater at the poles than it is at the equator4 ,if we now suppose the waters at the pole to communicate with those at the equator by means of a canal1 one branch of which goes from the pole to the centre of the earth1 and the other from the centre of the earth to the equator1 then the polar branch of the canal will be heavier than the equatorial branch1 in consequence of its weight not being diminished by the centrifugal force1 and1 therefore1 in order that the two columns may be in equilibrio1 the equatorial one must be lengthened4 ,newton found that the length of the polar must be to that of the equatorial canal as #bbi to #bcj1 or that the earth's polar radius must be seventeen miles less than its equatorial radius2 that is1 that the figure of the earth is an oblate spheroid1 formed by the revolution of an ellipse round its lesser axis4 ,hence it follows1 that the intensity of gravity at any point of the earth's surface is in the inverse ratio of the distance of that point from the centre1 and1 consequently1 that it diminishes from the equator to the poles1--a result which he confirmed by the fact1 that clocks required to have their pendulums shortened in order to beat true time when carried from ,europe towards the equator4 ,the next subject to which ,newton applied the principle of gravity was the tides of the ocean4 ,the philosophers of all ages have recognised the connexion between the phenomena of the tides and the position of the moon4 ,the ,college of ,jesuits at ,coimbra1 and subsequently ,antonio de ,dominis and ,kepler1 distinctly referred the tides to the attraction of the waters of the earth by the moon1 but so imperfect was the explanation which was thus given of the phenomena1 that ,galileo ridiculed the idea of lunar attraction1 and substituted for it a fallacious explanation of his own4 ,that the moon is the principal cause of the tides is obvious from the well-known fact1 that it is high water at any given place about the time when she is in the meridian of that place2 and that the sun performs a secondary part in their production may be proved from the circumstance1 that the highest tides take place when the sun1 the moon1 and the earth are in the same straight line1 that is1 when the force of the sun conspires with that of the moon1 and that the lowest tides take place when the lines drawn from the sun and moon to the earth are at right angles to each other1 that is1 when the force of the sun acts in opposition to that of the moon4 ,the most perplexing phenomenon in the tides of the ocean1 and one which is still a stumbling-block to persons slightly acquainted with the theory of attraction1 is the existence of high water on the side of the earth opposite to the moon1 as well as on the side next the moon4 ,to maintain that the attraction of the moon at the same instant draws the waters of the ocean towards herself1 and also draws them from the earth in an opposite direction1 seems at first sight paradoxical2 but the difficulty vanishes when we consider the earth1 or rather the centre of the earth1 and the water on each side of it as three distinct bodies placed at different distances from the moon1 and consequently attracted with forces inversely proportional to the squares of their distances4 ,the water nearest the moon will be much more powerfully attracted than the centre of the earth1 and the centre of the earth more powerfully than the water farthest from the moon4 ,the consequence of this must be1 that the waters nearest the moon will be drawn away from the centre of the earth1 and will consequently rise from their level1 while the centre of the earth will be drawn away from the waters opposite the moon1 which will1 as it were1 be left behind1 and consequently be in the same situation as if they were raised from the earth in a direction opposite to that in which they are attracted by the moon4 ,hence the effect of the moon's action upon the earth is to draw its fluid parts into the form of an oblong spheroid1 the axis of which passes through the moon4 ,as the action of the sun will produce the very same effect1 though in a smaller degree1 the tide at any place will depend on the relative position of these two spheroids1 and will be always equal either to the sum or to the difference of the effects of the two luminaries4 ,at the time of new and full moon the two spheroids will have their axes coincident1 and the height of the tide1 which will then be a spring one1 will be equal to the sum of the elevations produced in each spheroid considered separately1 while at the first and third quarters the axes of the spheroids will be at right angles to each other1 and the height of the tide1 which will then be a neap one1 will be equal to the difference of the elevations produced in each separate spheroid4 ,by comparing the spring and neap tides1 ,newton found that the force with which the sun acted upon the waters of the earth was to that with which the sun acted upon them as #d4dh to #a2--that the force of the moon produced a tide of #h4fc feet2--that of the sun one of #a4ic feet2--and both of them combined1 one of #aj ,french feet1--a result which in the open sea does not deviate much from observation4 ,having thus ascertained the force of the moon on the waters of our globe1 he found that the quantity of matter in the moon was to that in the earth as #a to #dj1 and the density of the moon to that of the earth as #aa to #i4 ,the motions of the moon1 so much within the reach of our own observation1 presented a fine field for the application of the theory of universal gravitation4 ,the irregularities exhibited in the lunar motions had been known in the time of ,hipparchus and ,ptolemy4 ,tycho had discovered the great inequality called the variation1 amounting to #cg1 and depending on the alternate acceleration and retardation of the moon in every quarter of a revolution1 and he had also ascertained the existence of the annual equation4 ,of these two inequalities ,newton gave a most satisfactory explanation4 ,the action of the sun upon the moon may be always resolved into two1 one acting in the direction of the line joining the moon and earth1 and consequently tending to increase or diminish the moon's gravity to the earth1 and the other in a direction at right angles to this1 and consequently tending to accelerate or retard the motion in her orbit4 ,now1 it was found by ,newton that this last force was reduced to nothing1 or vanished at the syzigies or quadratures1 so that at these four points the moon described areas proportional to the times4 ,the instant1 however1 that the moon quits these positions1 the force under consideration1 which we may call the tangential force1 begins1 and it reaches its maximum in the four octants4 ,the force1 therefore1 compounded of these two elements of the solar force1 or the diagonal of the parallelogram which they form1 is no longer directed to the earth's centre1 but deviates from it at a maximum about #cj minutes1 and therefore affects the angular motion of the moon1 the motion being accelerated in passing from the quadratures to the syzigies1 and retarded in passing from the syzigies to the quadratures4 ,hence the velocity is in its mean state in the octants1 a maximum in the syzigies1 and a minimum in the quadratures4 ,upon considering the influence of the solar force in diminishing or increasing the moon's gravity to the earth1 ,newton saw that her distance and her periodic time must from this cause be subject to change1 and in this way he accounted for the annual equation observed by ,tycho4 ,by the application of similar principles1 he explained the cause of the motion of the apsides1 or of the greater axis of the moon's orbit1 which has an angular progressive motion of #c #d nearly in the course of one lunation2 and he showed that the retrogradation of the nodes1 amounting to #c #aj daily1 arose from one of the elements of the solar force being exerted in the plane of the ecliptic1 and not in the plane of the moon's orbit1 the effect of which was to draw the moon down to the plane of the ecliptic1 and thus cause the line of the nodes1 or the intersection of these two planes1 to move in a direction opposite to that of the moon4 ,the lunar theory thus blocked out by ,newton1 required for its completion the labours of another century4 ,the imperfections of the fluxionary calculus prevented him from explaining the other inequalities of the moon's motions1 and it was reserved to ,euler1 ,d',alembert1 ,clairaut1 ,mayer1 and ,laplace to bring the lunar tables to a high degree of perfection1 and to enable the navigator to determine his longitude at sea with a degree of precision which the most sanguine astronomer could scarcely have anticipated4 ,by the consideration of the retrograde motion of the moon's nodes1 ,newton was led to discover the cause of the remarkable phenomenon of the precession of the equinoctial points1 which moved #ej annually1 and completed the circuit of the heavens in #be1ibj years4 ,kepler had declared himself incapable of assigning any cause for this motion1 and we do not believe that any other astronomer ever made the attempt4 ,from the spheroidal form of the earth1 it may be regarded as a sphere with a spheroidal ring surrounding its equator1 one-half of the ring being above the plane of the ecliptic and the other half below it4 ,considering this excess of matter as a system of satellites adhering to the earth's surface1 ,newton saw that the combined actions of the sun and moon upon these satellites tended to produce a retrogradation in the nodes of the circles which they described in their diurnal rotation1 and that the sum of all the tendencies being communicated to the whole mass of the planet1 ought to produce a slow retrogradation of the equinoctial points4 ,the effect produced by the motion of the sun he found to be #dj1 and that produced by the action of the moon #aj4 ,although there could be little doubt that the comets were retained in their orbits by the same laws which regulated the motions of the planets1 yet it was difficult to put this opinion to the test of observation4 ,the visibility of comets only in a small part of their orbits rendered it difficult to ascertain their distance and periodic times1 and as their periods were probably of great length1 it was impossible to correct approximate results by repeated observation4 ,newton1 however1 removed this difficulty1 by showing how to determine the orbit of a comet1 namely1 the form and position of the orbit and the periodic time1 by three observations4 ,by applying this method to the comet of #afhj1 he calculated the elements of its orbit1 and from the agreement of the computed places with those which were observed1 he justly inferred that the motions of comets were regulated by the same laws as those of the planetary bodies4 ,this result was one of great importance2 for as the comets enter our system in every possible direction1 and at all angles with the ecliptic1 and as a great part of their orbits extend far beyond the limits of the solar system1 it demonstrated the existence of gravity in spaces far removed beyond the planet1 and proved that the law of the inverse ratio of the squares of the distance was true in every possible direction1 and at very remote distances from the centre of our system4#dh ,such is a brief view of the leading discoveries which the ,principia first announced to the world4 ,the grandeur of the subjects of which it treats1 the beautiful simplicity of the system which it unfolds1 the clear and concise reasoning by which that system is explained1 and the irresistible evidence by which it is supported might have ensured it the warmest admiration of contemporary mathematicians1 and the most welcome reception in all the schools of philosophy throughout ,europe4 ,this1 however1 is not the way in which great truths are generally received4 ,though the astronomical discoveries of ,newton were not assailed by the class of ignorant pretenders who attacked his optical writings1 yet they were every where resisted by the errors and prejudices which had taken a deep hold even of the strongest minds4 ,the philosophy of ,descartes was predominant throughout ,europe4 ,appealing to the imagination1 and not to the reason of mankind1 it was quickly received into popular favour1 and the same causes which facilitated its introduction extended its influence1 and completed its dominion over the human mind4 ,in explaining all the movements of the heavenly bodies by a system of vortices in a fluid medium diffused through the universe1 ,descartes had seized upon an analogy of the most alluring and deceitful kind4 ,those who had seen heavy bodies revolving in the eddies of a whirlpool1 or in the gyrations of a vessel of water thrown into a circular motion1 had no difficulty in conceiving how the planets might revolve round the sun by analogous movements4 ,the mind instantly grasped at an explanation of so palpable a character1 and which required for its development neither the exercise of patient thought nor the aid of mathematical skill4 ,the talent and perspicuity with which the ,cartesian system was expounded1 and the show of experiments with which it was sustained1 contributed powerfully to its adoption1 while it derived a still higher sanction from the excellent character and the unaffected piety of its author4 ,thus intrenched1 as the ,cartesian system was1 in the strongholds of the human mind1 and fortified by its most obstinate prejudices1 it was not to be wondered at that the pure and sublime doctrines of the ,principia were distrustfully received and perseveringly resisted4 ,the uninstructed mind could not readily admit the idea1 that the great masses of the planets were suspended in empty space1 and retained in their orbits by an invisible influence residing in the sun2 and even those philosophers who had been accustomed to the rigour of true scientific research1 and who possessed sufficient mathematical skill for the examination of the ,newtonian doctrines1 viewed them at first as reviving the occult qualities of the ancient physics1 and resisted their introduction with a pertinacity which it is not easy to explain4 ,prejudiced1 no doubt1 in favour of his own metaphysical views1 ,leibnitz himself misapprehended the principles of the ,newtonian philosophy1 and endeavoured to demonstrate the truths in the ,principia by the application of different principles4 ,huygens1 who above all other men was qualified to appreciate the new philosophy1 rejected the doctrine of gravitation as existing between the individual particles of matter1 and received it only as an attribute of the planetary masses4 ,john ,bernouilli1 one of the first mathematicians of his age1 opposed the philosophy of ,newton4 ,mairan1 in the early part of his life1 was a strenuous defender of the system of vortices4 ,cassini and ,maraldi were quite ignorant of the ,principia1 and occupied themselves with the most absurd methods of calculating the orbits of comets long after the ,newtonian method had been established on the most impregnable foundation2 and even ,fontenelle1 a man of liberal views and extensive information1 continued1 throughout the whole of his life1 to maintain the doctrines of ,descartes4 ,the ,chevalier ,louville of ,paris had adopted the ,newtonian philosophy before #agbj4 ,s',gravesande had introduced it into the ,dutch universities at a somewhat earlier period1 and ,maupertuis1 in consequence of a visit which he paid to ,england in #agbh1 became a zealous defender of it2 but notwithstanding these and some other examples that might be quoted1 we must admit the truth of the remark of ,voltaire1 that though ,newton survived the publication of the ,principia more than forty years1 yet at the time of his death he had not above twenty followers out of ,england4 ,with regard to the progress of the ,newtonian philosophy in ,england1 some difference of opinion has been entertained4 ,professor ,playfair gives the following account of it4 8,in the universities of ,england1 though the ,aristotelian physics had made an obstinate resistance1 they had been supplanted by the ,cartesian1 which became firmly established about the time when their foundation began to be sapped by the general progress of science1 and particularly by the discoveries of ,newton4 ,for more than thirty years after the publication of these discoveries1 the system of vortices kept its ground2 and a translation from the ,french into ,latin of the ,physics of ,rohault1 a work entirely ,cartesian1 continued at ,cambridge to be the text for philosophical instruction4 ,about the year #agah1 a new and more elegant translation of the same book was published by ,dr4 ,samuel ,clarke1 with the addition of notes1 in which that profound and ingenious writer explained the views of ,newton on the principal objects of discussion1 so that the notes contained virtually a refutation of the text2 they did so1 however1 only virtually1 all appearance of argument and controversy being carefully avoided4 ,whether this escaped the notice of the learned doctor or not is uncertain1 but the new translation1 from its better ,latinity1 and the name of the editor1 was readily admitted to all the academical honours which the old one had enjoyed4 ,thus the stratagem of ,dr4 ,clarke completely succeeded2 the tutor might prelect from the text1 but the pupil would sometimes look into the notes2 and error is never so sure of being exposed as when the truth is placed close to it1 side by side1 without any thing to alarm prejudice1 or awaken from its lethargy the dread of innovation4 ,thus1 therefore1 the ,newtonian philosophy first entered the university of ,cambridge under the protection of the ,cartesian40 ,to this passage ,professor ,playfair adds the following as a note3-- 8,the universities of ,st4 ,andrew's and ,edinburgh were1 ,i believe1 the first in ,britain where the ,newtonian philosophy was made the subject of the academical prelections4 ,for this distinction they are indebted to ,james and ,david ,gregory1 the first in some respects the rival1 but both the friends of ,newton4 ,whiston bewails1 in the anguish of his heart1 the difference1 in this respect1 between those universities and his own4 ,david ,gregory taught in ,edinburgh for several years prior to #afij1 when he removed to ,oxford2 and ,whiston says1 #8,he had already caused several of his scholars to keep acts1 as we call them1 upon several branches of the ,newtonian philosophy1 while we at ,cambridge1 poor wretches1 were ignominiously studying the fictitious hypotheses of the ,cartesians4'#di ,i do not1 however1 mean to say1 that from this date the ,cartesian philosophy was expelled from those universities2 the ,physics of ,rohault were still in use as a text-book1--at least occasionally1 to a much later period than this1 and a great deal1 no doubt1 depended on the character of the individual4 ,professor ,keill introduced the ,newtonian philosophy in his lectures at ,oxford in #afig2 but the instructions of the tutors1 which constitute the real and efficient system of the university1 were not cast in that mould till long afterward40 ,adopting the same view of the subject1 ,mr4 ,dugald ,stewart has stated1 8that the philosophy of ,newton was publicly taught by ,david ,gregory at ,edinburgh1 and by his brother1 ,james ,gregory1 at ,st4 ,andrew's1#ej before it was able to supplant the vortices of ,descartes in that very university of which ,newton was a member4 ,it was in the ,scottish universities that the philosophy of ,locke1 as well as that of ,newton1 was first adopted as a branch of academical education40 ,anxious as we should have been to have awarded to ,scotland the honour of having first adopted the ,newtonian philosophy1 yet a regard for historical truth compels us to take a different view of the subject4 ,it is well known that ,sir ,isaac ,newton delivered lectures on his own philosophy from the ,lucasian chair before the publication of the ,principia2 and in the very page of ,whiston's life quoted by ,professor ,playfair1 he informs us that he had heard him read such lectures in the public schools1 though at that time he did not at all understand them4 ,newton continued to lecture till #afii1 and occasionally1 we presume1 till #agjc1 when ,whiston became his successor1 having been appointed his deputy in #afii4 ,in both of these capacities ,whiston delivered in the public schools a course of lectures on astronomy1 and a course of physico-mathematical lectures1 in which the mathematical philosophy of ,newton was explained and demonstrated1 and both these courses were published1 the one in #agjg1 and the other in #agaj1 8for the use of the young men in the university40 ,in #agjg1 the celebrated blind mathematician ,nicholas ,saunderson took up his residence in ,christ's ,college without being admitted a member of that body4 ,the society not only allotted to him apartments1 but gave him the free use of their library4 ,with the concurrence of ,whiston he delivered a course of lectures 8on the ,principia1 ,optics1 and ,universal ,arithmetic of ,newton10 and the popularity of these lectures was so great1 that ,sir ,isaac corresponded on the subject of them with their author2 and on the ejection of ,whiston from the ,lucasian chair in #agaa1 ,saunderson was appointed his successor4 ,in this important office he continued to teach the ,newtonian philosophy till the time of his death1 which took place in #agci4 ,but while the ,newtonian philosophy was thus regularly taught in ,cambridge1 after the publication of the ,principia1 there were not wanting other exertions for accelerating its progress4 ,about #afid1 the celebrated ,dr4 ,samuel ,clarke1 while an under-graduate1 defended1 in the public schools1 a question taken from the ,newtonian philosophy2 and his translation of ,rohault's ,physics1 which contains references in the notes to the ,principia1 and which was published in #afig 7and not in #agah1 as stated by ,professor ,playfair71 shows how early the ,cartesian system was attacked by the disciples of ,newton4 ,the author of the ,life of ,saunderson informs us1 that public exercises or acts founded on every part of the ,newtonian system were very common about #agjg1 and so general were such studies in the university1 that the ,principia rose to four times its original price4#ea ,one of the most ardent votaries of the ,newtonian philosophy was ,dr4 ,laughton1 who had been tutor in ,clare ,hall from #afid1 and it is probable that during the whole1 or at least a greater part1 of his tutorship he had inculcated the same doctrines4 ,in #agji-aj1 when he was proctor of that college1 instead of appointing a moderator1 he discharged the office himself1 and devoted his most active exertions to the promotion of mathematical knowledge4 ,previous to this1 he had even published a paper of questions on the ,newtonian philosophy1 which appear to have been used as theses for disputations2 and such was his ardour and learning that they powerfully contributed to the popularity of his college4 ,between #agjf and #agaf1 the year of his death1 the celebrated ,roger ,cotes1 the friend and disciple of ,newton1 filled the ,plumian chair of astronomy and experimental philosophy at ,cambridge4 ,during this period he edited the second edition of the ,principia1 which he enriched with an admirable preface1 and thus contributed1 by his writings as well as by his lectures1 to advance the philosophy of his master4 ,about the same time1 the learned ,dr4 ,bentley1 who first made known the philosophy of his friend to the readers of general literature1 filled the high office of master of ,trinity ,college1 and could not fail to have exerted his utmost influence in propagating doctrines which he so greatly admired4 ,had any opposition been offered to the introduction of the true system of the universe1 the talents and influence of these individuals would have immediately suppressed it2 but no such opposition seems to have been made2 and though there may have been individuals at ,cambridge ignorant of mathematical science1 who adhered to the system of ,descartes1 and patronised the study of the ,physics of ,rohault1 yet it is probable that similar persons existed in the universities of ,edinburgh and ,st4 ,andrew's2 and we cannot regard their adherence to error as disproving the general fact1 that the philosophy of ,newton was quickly introduced into all the universities of ,great ,britain4 ,but while the mathematical principles of the ,newtonian system were ably expounded in our seats of learning1 its physical truths were generally studied1 and were explained and communicated to the public by various lecturers on experimental philosophy4 ,the celebrated ,locke1 who was incapable of understanding the ,principia from his want of mathematical knowledge1 inquired of ,huygens if all the mathematical propositions in that work were true4 ,when he was assured that he might depend upon their certainty1 he took them for granted1 and carefully examined the reasonings and corollaries deduced from them4 ,in this manner he acquired a knowledge of the physical truths in the ,principia1 and became a firm believer in the discoveries which it contained4 ,in the same manner he studied the treatise on ,optics1 and made himself master of every part of it which was not mathematical4#eb ,from a manuscript of ,sir ,isaac ,newton's1 entitled 8,a demonstration that the planets1 by their gravity towards the sun1 may move in ellipses1#ec found among the papers of ,mr4 ,locke1 and published by ,lord ,king10 it would appear that he himself had been at considerable trouble in explaining to his friend that interesting doctrine4 ,this manuscript is endorsed1 8,mr4 ,newton1 ,march1 #afhi40 ,it begins with three hypotheses 7the first two being the two laws of motion1 and the third the parallelogram of motion71 which introduce the proposition of the proportionality of the areas to the times in motions round an immoveable centre of attraction4#ed ,three lemmas1 containing properties of the ellipse1 then prepare the reader for the celebrated proposition1 that when a body moves in an ellipse1#ee the attraction is reciprocally as the square of the distance of the body from the focus to which it is attracted4 ,these propositions are demonstrated in a more popular manner than in the ,principia1 but there can be no doubt that1 even in their present modified form1 they were beyond the capacity of ,mr4 ,locke4 ,dr4 ,john ,keill was the first person who publicly taught natural philosophy by experiments4 ,desaguliers informs us that this author 8laid down very simple propositions1 which he proved by experiments1 and from these he deduced others more compound1 which he still confirmed by experiments1 till he had instructed his auditors in the laws of motion1 the principles of hydrostatics and optics1 and some of the chief propositions of ,sir ,isaac ,newton concerning light and colours4 ,he began these courses in ,oxford about the year #agjd or #agje1 and in that way introduced the love of the ,newtonian philosophy40 ,when ,dr4 ,keill left the university1 ,desaguliers began to teach the ,newtonian philosophy by experiments4 ,he commenced his lectures at ,harthall in ,oxford1 in #agaj1 and delivered more than a hundred and twenty courses2 and when he went to settle in ,london in #agac1 he informs us that he found 8the ,newtonian philosophy generally received among persons of all ranks and professions1 and even among the ladies by the help of experiments40 ,such were the steps by which the ,newtonian philosophy was established in ,great ,britain4 ,from the time of the publication of the ,principia1 its mathematical doctrines formed a regular part of academical education2 and before twenty years had elapsed1 its physical truths were communicated to the public in popular lectures illustrated by experiments1 and accommodated to the capacities of those who were not versed in mathematical knowledge4 ,the ,cartesian system1 though it may have lingered for a while in the recesses of our universities1 was soon overturned2 and long before his death1 ,newton enjoyed the high satisfaction of seeing his philosophy triumphant in his native land4 ,,chapter ,,xii4 ,doctrine of ,infinite ,quantities--,labours of ,pappus--,kepler--,cavaleri-- ,roberval--,fermat--,wallis--,newton discovers the ,binomial ,theorem--and the ,doctrine of ,fluxions in #afff--;,his ,manuscript ,work containing this ,doctrine communicated to his ,friends--,his ,treatise on ,fluxions-- ,his ,mathematical ,tracts--,his ,universal ,arithmetic--,his ,methodus ,differentialis--,his ,geometria ,analytica--,his ,solution of the ,problems proposed by ,bernouilli and ,leibnitz--,account of the celebrated ,dispute respecting the ,invention of ,fluxions--,commercium ,epistolicum-- ,report of the ,royal ,society--,general ,view of the ,controversy4 ,previous to the time of ,newton1 the doctrine of infinite quantities had been the subject of profound study4 ,the ancients made the first step in this curious inquiry by a rude though ingenious attempt to determine the area of curves4 ,the method of exhaustions which was used for this purpose consisted in finding a given rectilineal area to which the inscribed and circumscribed polygonal figures continually approached by increasing the number of their sides4 ,this area was obviously the area of the curve1 and in the case of the parabola it was found by ,archimedes to be two-thirds of the area formed by multiplying the ordinate by the abscissa4 ,although the synthetical demonstration of the results was perfectly conclusive1 yet the method itself was limited and imperfect4 ,the celebrated ,pappus of ,alexandria followed ,archimedes in the same inquiries2 and in his demonstration of the property of the centre of gravity of a plane figure1 by which we may determine the solid formed by its revolution1 he has shadowed forth the discoveries of later times4 ,in his curious tract on ,stereometry1 published in #afae1 ,kepler made some advances in the doctrine of infinitesimals4 ,prompted to the task by a dispute with the seller of some casks of wine1 he studied the measurement of solids formed by the revolution of a curve round any line whatever4 ,in solving some of the simplest of these problems1 he conceived a circle to be formed of an infinite number of triangles having all their vertices in the centre1 and their infinitely small bases in the circumference of the circle1 and by thus rendering familiar the idea of quantities infinitely great and infinitely small1 he gave an impulse to this branch of mathematics4 ,the failure of ,kepler1 too1 in solving some of the more difficult of the problems which he himself proposed roused the attention of geometers1 and seems particularly to have attracted the notice of ,cavaleri4 ,this ingenious mathematician was born at ,milan in #aeih1 and was ,professor of ,geometry at ,bologna4 ,in his method of ,indivisibles1 which was published in #afce1 he considered a line as composed of an infinite number of points1 a surface of an infinite number of lines1 and a solid of an infinite number of surfaces2 and he lays it down as an axiom that the infinite sums of such lines and surfaces have the same ratio when compared with the linear or superficial unit1 as the surfaces and solids which are to be determined4 ,as it is not true that an infinite number of infinitely small points can make a line1 or an infinite number of infinitely small lines a surface1 ,pascal removed this verbal difficulty by considering a line as composed of an infinite number of infinitely short lines1 a surface as composed of an infinite number of infinitely narrow parallelograms1 and a solid of an infinite number of infinitely thin solids4 ,but1 independent of this correction1 the conclusions deduced by ,cavaleri are rigorously true1 and his method of ascertaining the ratios of areas and solids to one another1 and the theorems which he deduced from it may be considered as forming an era in mathematics4 ,by the application of this method1 ,roberval and ,toricelli showed that the area of the cycloid is three times that of its generating circle1 and the former extended the method of ,cavaleri to the case where the powers of the terms of the arithmetical progression to be summed were fractional4 ,in applying the doctrine of infinitely small quantities to determine the tangents of curves1 and the maxima and minima of their ordinates1 both ,roberval and ,fermat made a near approach to the invention of fluxions--so near indeed that both ,lagrange and ,laplace#ef have pronounced the latter to be the true inventer of the differential calculus4 ,roberval supposed the point which describes a curve to be actuated by two motions1 by the composition of which it moves in the direction of a tangent2 and had he possessed the method of fluxions1 he could1 in every case1 have determined the relative velocities of these motions1 which depend on the nature of the curve1 and consequently the direction of the tangent which he assumed to be in the diagonal of a parallelogram whose sides had the same ratio as the velocities4 ,but as he was able to determine these velocities only in the conic sections1 c4 his ingenious method had but few applications4 ,the labours of ,peter ,fermat1 a counsellor of the parliament of ,toulouse1 approached still nearer to the fluxionary calculus4 ,in his method of determining the maxima and minima of the ordinates of curves1 he substitutes x e for the independent variable x in the function which is to become a maximum1 and as these two expressions should be equal when e becomes infinitely small or #j1 he frees this equation from surds and radicals1 and after dividing the whole by e1 e is made #j1 and the equation for the maximum is thus obtained4 ,upon a similar principle he founded his method of drawing tangents to curves4 ,but though the methods thus used by ,fermat are in principle the same with those which connect the theory of tangents and of maxima and minima with the analytical method of exhibiting the differential calculus1 yet it is a singular example of national partiality to consider the inventer of these methods as the inventer of the method of fluxions4 8,one might be led10 says ,mr4 ,herschel1 8to suppose by ,laplace's expression that the calculus of finite differences had then already assumed a systematic form1 and that ,fermat had actually observed the relation between the two calculi1 and derived the one from the other4 ,the latter conclusion would scarcely be less correct than the former4 ,no method can justly be regarded as bearing any analogy to the differential calculus which does not lay down a system of rules 7no matter on what considerations founded1 by what names called1 or by what extraneous matter enveloped7 by means of which the second term of the development of any function of x e in powers of e1 can be correctly calculated1 #8qu extendet se1' to use ,newton's expression1 #8citra ullum molestum calculum in terminis surdis que ac in integris procedens4' ,it would be strange to suppose ,fermat or any other in possession of such a method before any single surd quantity had ever been developed in a series4 ,but1 in point of fact1 his writings present no trace of the kind2 and this1 though fatal to his claim1 is allowed by both the geometers cited4 ,hear ,lagrange's candid avowal4 #8,il fait disparaitre dans cette equation1' that of the maximum between x and e1 #8les radicaux et les fractions s'il y en 4' ,laplace1 too1 declares that #8il savoit etendre son calcul aux fonctions irrationelles en se debarrassant des irrationalits par l'elevation des radicaux aux puissances4' ,this is at once giving up the point in question4 ,it is allowing unequivocally that ,fermat in these processes only took a circuitous route to avoid a difficulty which it is one of the most express objects of the differential calculus to face and surmount4 ,the whole claim of the ,french geometer arises from a confusion 7too often made7 of the calculus and its applications1 the means and the end1 under the sweeping head of #8nouveaux calculs' on the one hand1 and an assertion somewhat too unqualified1 advanced in the warmth and generality of a preface1 on the other40#eg ,the discoveries of ,fermat were improved and simplified by ,hudde1 ,huygens1 and ,barrow2 and by the publication of the ,arithmetic of ,infinites by ,dr4 ,wallis1 ,savilian professor of geometry at ,oxford1 mathematicians were conducted to the very entrance of a new and untrodden field of discovery4 ,this distinguished author had effected the quadrature of all curves whose ordinates can be expressed by any direct integral powers2 and though he had extended his conclusions to the cases where the ordinates are expressed by the inverse or fractional powers1 yet he failed in its application4 ,nicolas ,mercator 7,kauffman7 surmounted the difficulty by which ,wallis had been baffled1 by the continued division of the numerator by the denominator to infinity1 and then applying ,wallis's method to the resulting positive powers4 ,in this way he obtained1 in #affg1 the first general quadrature of the hyperbola1 and1 at the same time1 gave the regular development of a function in series4 ,in order to obtain the quadrature of the circle1 ,dr4 ,wallis considered that if the equations of the curves of which he had given the quadrature were arranged in a series1 beginning with the most simple1 these areas would form another series4 ,he saw also that the equation of the circle was intermediate between the first and second terms of the first series1 or between the equation of a straight line and that of a parabola1 and hence he concluded1 that by interpolating a term between the first and second term of the second series1 he would obtain the area of the circle4 ,in pursuing this singularly beautiful thought1 ,dr4 ,wallis did not succeed in obtaining the indefinite quadrature of the circle1 because he did not employ general exponents2 but he was led to express the entire area of the circle by a fraction1 the numerator and denominator of which are each obtained by the continued multiplication of a certain series of numbers4 ,such was the state of this branch of mathematical science1 when ,newton1 at an early age1 directed to it the vigour of his mind4 ,at the very beginning of his mathematical studies1 when the works of ,dr4 ,wallis fell into his hands1 he was led to consider how he could interpolate the general values of the areas in the second series of that mathematician4 ,with this view he investigated the arithmetical law of the coefficients of the series1 and obtained a general method of interpolating1 not only the series above referred to1 but also other series4 ,these were the first steps taken by ,newton1 and1 as he himself informs us1 they would have entirely escaped from his memory if he had not1 a few weeks before1#eh found the notes which he made upon the subject4 ,when he had obtained this method1 it occurred to him that the very same process was applicable to the ordinates1 and1 by following out this idea1 he discovered the general method of reducing radical quantities composed of several terms into infinite series1 and was thus led to the discovery of the celebrated ,binomial ,theorem4 ,he now neglected entirely his methods of interpolation1 and employed that theorem alone as the easiest and most direct method for the quadratures of curves1 and in the solution of many questions which had not even been attempted by the most skilful mathematicians4 ,after having applied the ,binomial theorem to the rectification of curves1 and to the determination of the surfaces and contents of solids1 and the position of their centres of gravity1 he discovered the general principle of deducing the areas of curves from the ordinate1 by considering the area as a nascent quantity1 increasing by continual fluxion in the proportion of the length of the ordinate1 and supposing the abscissa to increase uniformly in proportion to the time4 ,in imitation of ,cavalerius1 he called the momentary increment of a line a point1 though it is not a geometrical point1 but an infinitely short line2 and the momentary increment of an area or surface he called a line1 though it is not a geometrical line1 but an infinitely narrow surface4 ,by thus regarding lines as generated by the motion of points1 surfaces by the motions of lines1 and solids by the motion of surfaces1 and by considering that the ordinates1 absciss1 c4 of curves thus formed1 vary according to a regular law depending on the equation of the curve1 he deduces from this equation the velocities with which these quantities are generated2 and by the rules of infinite series he obtains the ultimate value of the quantity required4 ,to the velocities with which every line or quantity is generated1 ,newton gave the name of ,fluxions1 and to the lines or quantities themselves that of ,fluents4 ,this method constitutes the doctrine of fluxions which ,newton had invented previous to #afff1 when the breaking out of the plague at ,cambridge drove him from that city1 and turned his attention to other subjects4 ,but though ,newton had not communicated this great invention to any of his friends1 he composed his treatise1 entitled ,analysis per equationes numero terminorum infinitas1 in which the principle of fluxions and its numerous applications are clearly pointed out4 ,in the month of ,june1 #affi1 he communicated this work to ,dr4 ,barrow1 who mentions it in a letter to ,mr4 ,collins1 dated the #bjth ,june1 #affi1 as the production of a friend of his residing at ,cambridge1 who possesses a fine genius for such inquiries4 ,on the #cast ,july1 he transmitted the work to ,collins2 and having received his approbation of it1 he informs him that the name of the author of it was ,newton1 a fellow of his own college1 and a young man who had only two years before taken his degree of ,m4,a4 ,collins took a copy of this treatise1 and returned the original to ,dr4 ,barrow2 and this copy having been found among ,collins's papers by his friend ,mr4 ,william ,jones1 and compared with the original manuscript borrowed from ,newton1 it was published with the consent of ,newton in #agaa1 nearly fifty years after it was written4 ,though the discoveries contained in this treatise were not at first given to the world1 yet they were made generally known to mathematicians by the correspondence of ,collins1 who communicated them to ,james ,gregory2 to ,,mm4 ,bertet and ,vernon in ,france2 to ,slusius in ,holland2 to ,borelli in ,italy2 and to ,strode1 ,townsend1 and ,oldenburg1 in letters dated between #affi and #afgb4 ,hitherto the method of fluxions was known only to the friends of ,newton and their correspondents2 but1 in the first edition of the ,principia1 which appeared in #afhg1 he published1 for the first time1 the fundamental principle of the fluxionary calculus1 in the second lemma of the second book4 ,no information1 however1 is here given respecting the algorithm or notation of the calculus2 and it was not till #afic-e8 that it was communicated to the mathematical world in the second volume of ,dr4 ,wallis's works1 which were published in that year4 ,this information was extracted from two letters of ,newton written in #afib4 ,about the year #afgb1 ,newton had undertaken to publish an edition of ,kinckhuysen's ,algebra1 with notes and additions4 ,he therefore drew up a treatise1 entitled1 ,a ,method of ,fluxions1 which he proposed as an introduction to that work2 but the fear of being involved in disputes about this new discovery1 or perhaps the wish to render it more complete1 or to have the sole advantage of employing it in his physical researches1 induced him to abandon this design4 ,at a later period of his life he again resolved to give it to the world2 but it did not appear till after his death1 when it was translated into ,english1 and published in #agcf1 with a commentary by ,mr4 ,john ,colson1 ,professor of ,mathematics in ,cambridge4#ei ,to the first edition of ,newton's ,optics1 which appeared in #agjd1 there were added two mathematical treatises1 entitled1 ,tractatus duo de speciebus et magnitudine figurarum curvilinearum1 the one bearing the title of ,tractatus de ,quadratura ,curvarum1 and the other ,enumeratio linearum tertii ordinis4 ,the first contains an explanation of the doctrine of fluxions1 and of its application to the quadrature of curves2 and the second a classification of seventy-two curves of the third order1 with an account of their properties4 ,the reason for publishing these two tracts in his ,optics 7in the subsequent editions of which they are omitted7 is thus stated in the advertisement3--8,in a letter written to ,m4 ,leibnitz in the year #afgi1 and published by ,dr4 ,wallis1 ,i mentioned a method by which ,i had found some general theorems about squaring curvilinear figures on comparing them with the conic sections1 or other the simplest figures with which they might be compared4 ,and some years ago ,i lent out a manuscript containing such theorems2 and having since met with some things copied out of it1 ,i have on this occasion made it public1 prefixing to it an introduction1 and joining a scholium concerning that method4 ,and ,i have joined with it another small tract concerning the curvilineal figures of the second kind1 which was also written many years ago1 and made known to some friends1 who have solicited the making it public40 ,in the year #agjg1 ,mr4 ,whiston published the algebraical lectures which ,newton had1 during nine years1 delivered at ,cambridge1 under the title of ,arithmetica ,universalis1 sive de ,compositione et ,resolutione ,arithmetica ,liber4 ,we are not accurately informed how ,mr4 ,whiston obtained possession of this work2 but it is stated by one of the editors of the ,english edition1 that 8,mr4 ,whiston thinking it a pity that so noble and useful a work should be doomed to a college confinement1 obtained leave to make it public40 ,it was soon afterward translated into ,english by ,mr4 ,ralphson2 and a second edition of it1 with improvements by the author1 was published at ,london in #agab1 by ,dr4 ,machin1 secretary to the ,royal ,society4 ,with the view of stimulating mathematicians to write annotations on this admirable work1 the celebrated ,s',gravesande published a tract1 entitled1 ,specimen ,commentarii in ,arithmeticam ,universalem2 and ,maclaurin's ,algebra seems to have been drawn up in consequence of this appeal4 ,among the mathematical works of ,newton we must not omit to enumerate a small tract entitled1 ,methodus ,differentialis1 which was published with his consent in #agaa4 ,it consists of six propositions1 which contain a method of drawing a parabolic curve through any given number of points1 and which are useful for constructing tables by the interpolation of series1 and for solving problems depending on the quadrature of curves4 ,another mathematical treatise of ,newton's was published for the first time in #aggi1 in ,dr4 ,horsley's edition of his works4#fj ,it is entitled1 ,artis ,analytic ,specimina1 vel ,geometria ,analytica4 ,in editing this work1 which occupies about #acj quarto pages1 ,dr4 ,horsley used three manuscripts1 one of which was in the handwriting of the author2 another1 written in an unknown hand1 was given by ,mr4 ,william ,jones to the ,honourable ,charles ,cavendish2 and a third1 copied from this by ,mr4 ,james ,wilson1 the editor of ,robins's works1 was given to ,dr4 ,horsley by ,mr4 ,john ,nourse1 bookseller to the king4 ,dr4 ,horsley has divided it into twelve chapters1 which treat of infinite series2 of the reduction of affected equations2 of the specious resolution of equations2 of the doctrine of fluxions2 of maxima and minima2 of drawing tangents to curves2 of the radius of curvature2 of the quadrature of curves2 of the area of curves which are comparable with the conic sections2 of the construction of mechanical problems1 and on finding the lengths of curves4 ,in enumerating the mathematical works of our author1 we must not overlook his solutions of the celebrated problems proposed by ,bernouilli and ,leibnitz4 ,on the ,kalends of ,january1 #afig1 ,john ,bernouilli addressed a letter to the most distinguished mathematicians in ,europe1#fa challenging them to solve the two following problems3 #a4 ,to determine the curve line connecting two given points which are at different distances from the horizon1 and not in the same vertical line1 along which a body passing by its own gravity1 and beginning to move at the upper point1 shall descend to the lower point in the shortest time possible4 #b4 ,to find a curve line of this property that the two segments of a right line drawn from a given point through the curve1 being raised to any given power1 and taken together1 may make every where the same sum4 ,on the day after he received these problems1 ,newton addressed to ,mr4 ,charles ,montague1 the ,president of the ,royal ,society1 a solution of them both4 ,he announced that the curve required in the first problem must be a cycloid1 and he gave a method of determining it4 ,he solved also the second problem1 and he showed that by the same method other curves might be found which shall cut off three or more segments having the like properties4 ,leibnitz1 who was struck with the beauty of the problem1 requested ,bernouilli1 who had allowed six months for its solution1 to extend the period to twelve months4 ,this delay was readily granted1 solutions were obtained from ,newton1 ,leibnitz1 and the ,marquis de ,l',hopital2 and although that of ,newton was anonymous1 yet ,bernouilli recognised in it his powerful mind1 8tanquam10 says he1 8ex ungue leonem10 as the lion is known by his claw4 ,the last mathematical effort of our author was made with his usual success1 in solving a problem which ,leibnitz proposed in #agaf1 in a letter to the ,abb ,conti1 8for the purpose1 as he expressed it1 of feeling the pulse of the ,english analysts40 ,the object of this problem was to determine the curve which should cut at right angles an infinity of curves of a given nature1 but expressible by the same equation4 ,newton received this problem about five o'clock in the afternoon1 as he was returning from the ,mint2 and though the problem was extremely difficult1 and he himself much fatigued with business1 yet he finished the solution of it before he went to bed4 ,such is a brief account of the mathematical writings of ,sir ,isaac ,newton1 not one of which were voluntarily communicated to the world by himself4 ,the publication of his ,universal ,arithmetic is said to have been a breach of confidence on the part of ,whiston2 and1 however this may be1 it was an unfinished work1 never designed for the public4 ,the publication of his ,quadrature of ,curves1 and of his ,enumeration of ,curve ,lines1 was rendered necessary1 in consequence of plagiarisms from the manuscripts of them which he had lent to his friends1 and the rest of his analytical writings did not appear till after his death4 ,it is not easy to penetrate into the motives by which this great man was on these occasions actuated4 ,if his object was to keep possession of his discoveries till he had brought them to a higher degree of perfection1 we may approve of the propriety1 though we cannot admire the prudence of such a step4 ,if he wished to retain to himself his own methods1 in order that he alone might have the advantage of them in prosecuting his physical inquiries1 we cannot reconcile so selfish a measure with that openness and generosity of character which marked the whole of his life4 ,if he withheld his labours from the world in order to avoid the disputes and contentions to which they might give rise1 he adopted the very worst method of securing his tranquillity4 ,that this was the leading motive under which he acted1 there is little reason to doubt4 ,the early delay in the publication of his method of fluxions1 after the breaking out of the plague at ,cambridge1 was probably owing to his not having completed the algorithm of that calculus2 but no apology can be made for the imprudence of withholding it any longer from the public4 ,had he published this noble discovery even previous to #afgc1 when his great rival had not even entered upon those studies which led him to the same method1 he would have secured to himself the undivided honour of the invention1 and ,leibnitz could have aspired to no other fame but that of an improver of the doctrine of fluxions4 ,but he unfortunately acted otherwise4 ,he announced to his friends that he possessed a method of great generality and power2 he communicated to them a general account of its principles and applications2 and the information which was thus conveyed directed the attention of mathematicians to subjects to which they might not have otherwise applied their powers4 ,in this way the discoveries which he had previously made were made subsequently by others2 and ,leibnitz1 in place of appearing in the theatre of science as the disciple and the follower of ,newton1 stood forth with all the dignity of a rival2 and1 by the early publication of his discoveries had nearly placed himself on the throne which ,newton was destined to ascend4 ,it would be inconsistent with the popular nature of a work like this1 to enter into a detailed history of the dispute between ,newton and ,leibnitz respecting the invention of fluxions4 ,a brief and general account of it1 however1 is indispensable4 ,in the beginning of #afgc1 ,leibnitz came to ,london in the suite of the ,duke of ,hanover1 and he became acquainted with the great men who then adorned the capital of ,england4 ,among these was ,oldenburg1 a countryman of his own1 who was then secretary to the ,royal ,society4 ,about the beginning of ,march1 in the same year1 ,leibnitz went to ,paris1 where1 with the assistance of ,huygens1 he devoted himself to the study of the higher geometry4 ,in the month of ,july he renewed his correspondence with ,oldenburg1 and he communicated to him some of the discoveries which he had made relative to series1 particularly the series for a circular arc in terms of the tangent4 ,oldenburg informed him in return of the discoveries on series which had been made by ,newton and ,gregory2 and in #afgf ,newton communicated to him1 through ,oldenburg1 a letter of fifteen closely printed quarto pages1 containing many of his analytical discoveries1 and stating that he possessed a general method of drawing tangents1 which he thought it necessary to conceal in two sentences of transposed characters4 ,in this letter neither the method of fluxions nor any of its principles are communicated2 but the superiority of the method over all others is so fully described1 that ,leibnitz could scarcely fail to discover that ,newton possessed that secret of which geometers had so long been in quest4 ,had ,leibnitz at the time of receiving this letter been entirely ignorant of his own differential method1 the information thus conveyed to him by ,newton could not fail to stimulate his curiosity1 and excite his mightiest efforts to obtain possession of so great a secret4 ,that this new method was intimately connected with the subject of series was clearly indicated by ,newton2 and as ,leibnitz was deeply versed in this branch of analysis1 it is far from improbable that a mind of such strength and acuteness might attain his object by direct investigation4 ,that this was the case may be inferred from his letter to ,oldenburg 7to be communicated to ,newton7 of the #bast ,june1 #afgg1 where he mentions that he had for some time been in possession of a method of drawing tangents more general than that of ,slusius1 namely1 by the differences of ordinates4 ,he then proceeds with the utmost frankness to explain this method1 which was no other than the differential calculus4 ,he describes the algorithm which he had adopted1 the formation of differential equations1 and the application of the calculus to various geometrical and analytical questions4 ,no answer seems to have been returned to this letter either by ,newton or ,oldenburg1 and1 with the exception of a short letter from ,leibnitz to ,oldenburg1 dated #abth ,july1 #afgg1 no further correspondence seems to have taken place4 ,this1 no doubt1 arose from the death of ,oldenburg in the month of ,august1 #afgg1fb when the two rival geometers pursued their researches with all the ardour which the greatness of the subject was so well calculated to inspire4 ,in the hands of ,leibnitz the differential calculus made rapid progress4 ,in the ,acta ,eruditorum1 which was published at ,leipsic in ,november1 #afhd1 he gave the first account of it1 describing its algorithm in the same manner as he had done in his letter to ,oldenburg1 and pointing out its application to the drawing of tangents1 and the determination of maxima and minima4 ,he makes a remote reference to the similar calculus of ,newton1 but lays no claim to the sole invention of the differential method4 ,in the same work for ,june1 #afhf1 he resumes the subject2 and when ,newton had not published a single word upon fluxions1 and had not even made known his notation1 the differential calculus was making rapid advances on the ,continent1 and in the hands of ,james and ,john ,bernouilli had proved the means of solving some of the most important and difficult problems4 ,the silence of ,newton was at last broken1 and in the second lemma of the second book of the ,principia1 he explained the fundamental principle of the fluxionary calculus4 ,his explanation1 which occupied only three pages1 was terminated with the following scholium3--8,in a correspondence which took place about ten years ago between that very skilful geometer1 ,g4 ,g4 ,leibnitz1 and myself1 ,i announced to him that ,i possessed a method of determining maxima and minima1 of drawing tangents1 and of performing similar operations which was equally applicable to rational and irrational quantities1 and concealed the same in transposed letters involving this sentence1 7data equatione quotcunque fluentes quantitates involvente1 fluxiones invenire et vice versa74 ,this illustrious man replied that he also had fallen on a method of the same kind1 and he communicated to me his method which scarcely differed from mine except in the notation and in the idea of the generation of quantities40#fc ,this celebrated scholium1 which is so often referred to in the present controversy1 has1 in our opinion1 been much misapprehended4 ,while ,m4 ,biot considers it as 8eternalizing the rights of ,leibnitz by recognising them in the ,principia10 ,professor ,playfair regards it as containing 8a highly favourable opinion on the subject of the discoveries of ,leibnitz40 ,to us it appears to be nothing more than the simple statement of the fact1 that the method communicated by ,leibnitz was nearly the same as his own2 and this much he might have said1 whether he believed that ,leibnitz had seen the fluxionary calculus among the papers of ,collins1 or was the independent inventor of his own4 ,it is more than probable1 indeed1 that when ,newton wrote this scholium he regarded ,leibnitz as a second inventor2 but when he found that ,leibnitz and his friends had showed a willingness to believe1 and had even ventured to throw out the suspicion1 that he himself had borrowed the doctrine of fluxions from the differential calculus1 he seems to have altered the opinion which he had formed of his rival1 and to have been willing in his turn to retort the charge4 ,this change of opinion was brought about by a series of circumstances over which he had no control4 ,m4 ,nicolas ,fatio de ,duillier1 a ,swiss mathematician1 resident in ,london1 communicated to the ,royal ,society1 in #afii1 a paper on the line of quickest descent1 which contains the following observations3--8,compelled by the evidence of facts1 ,i hold ,newton to have been the first inventor of this calculus1 and the earliest by several years2 and whether ,leibnitz1 the second inventor1 has borrowed any thing from the other1 ,i would prefer to my own judgment that of those who have seen the letters and other copies of the same manuscripts of ,newton40 ,this imprudent remark1 which by no means amounts to a charge of plagiarism1 for ,leibnitz is actually designated the second inventor1 may be considered as showing that the ,english mathematicians had been cherishing suspicions unfavourable to ,leibnitz1 and there can be no doubt that a feeling had long prevailed that this mathematician either had1 or might have seen1 among the papers of ,collins1 the 8,analysis per ,equationes1 c410 which contained the principles of the fluxionary method4 ,leibnitz replied to the remark of ,duillier with much good feeling4 ,he appealed to the facts as exhibited in his correspondence with ,oldenburg2 he referred to ,newton's scholium as a testimony in his favour2 and1 without disputing or acknowledging the priority of ,newton's claim1 he asserted his own right to the invention of the differential calculus4 ,fatio transmitted a reply to the ,leipsic ,acts2 but the editor refused to insert it4 ,the dispute1 therefore1 terminated1 and the feelings of the contending parties continued for some time in a state of repose1 though ready to break out on the slightest provocation4 ,when ,newton's ,optics appeared in #agjd1 accompanied by his ,treatise on the ,quadrature of ,curves1 and his enumeration of lines of the third order1 the editor of the ,leipsic ,acts 7whom ,newton supposed to be ,leibnitz himself7 took occasion to review the first of these tracts4 ,after giving an imperfect analysis of its contents1 he compared the method of fluxions with the differential calculus1 and1 in a sentence of some ambiguity1 he states that ,newton employed fluxions in place of the differences of ,leibnitz1 and made use of them in his ,principia in the same manner as ,honoratus ,fabri1 in his ,synopsis of ,geometry1 had substituted progressive motion in place of the indivisibles of ,cavaleri4#fd ,as ,fabri1 therefore1 was not the inventor of the method which is here referred to1 but borrowed it from ,cavaleri1 and only changed the mode of its expression1 there can be no doubt that the artful insinuation contained in the above passage was intended to convey the impression that ,newton had stolen his method of fluxions from ,leibnitz4 ,the indirect character of this attack1 in place of mitigating its severity1 renders it doubly odious2 and we are persuaded that no candid reader can peruse the passage without a strong conviction that it justifies1 in the fullest manner1 the indignant feelings which it excited among the ,english philosophers4 ,if ,leibnitz was the author of the review1 or if he was in any way a party to it1 he merited the full measure of rebuke which was dealt out to him by the friends of ,newton1 and deserved those severe reprisals which doubtless imbittered the rest of his days4 ,he who dared to accuse a man like ,newton1 or indeed any man holding a fair character in society1 with the odious crime of plagiarism1 placed himself without the pale of the ordinary courtesies of life1 and deserved to have the same charge thrown back upon himself4 ,the man who conceives his fellow to be capable of such intellectual felony1 avows the possibility of himself committing it1 and almost substantiates the weakest evidence of the worst accusers4 ,dr4 ,keill1 as the representative of ,newton's friends1 could not brook this base attack upon his countryman4 ,in a letter printed in the ,philosophical ,transactions for #agjh1 he maintained that ,newton was 8beyond all doubt0 the first inventor of fluxions4 ,he referred for a direct proof of this to his letters published by ,wallis2 and he asserted 8that the same calculus was afterward published by ,leibnitz1 the name and the mode of notation being changed40 ,if the reader is disposed to consider this passage as retorting the charge of plagiarism upon ,leibnitz1 he will readily admit that the mode of its expression is neither so coarse nor so insidious as that which is used by the writer in the ,leipsic ,acts4 ,in a letter to ,hans ,sloane1 dated ,march1 #agaa1 ,leibnitz complained to the ,royal ,society of the treatment he had received4 ,he expressed his conviction that ,keill had erred more from rashness of judgment than from any improper motive1 and that he did not regard the accusation as a calumny2 and he requested that the society would oblige ,mr4 ,keill to disown publicly the injurious sense which his words might bear4 ,when this letter was read to the society1 ,keill justified himself to ,sir ,isaac ,newton and the other members by showing them the obnoxious review of the ,quadrature of ,curves in the ,leipsic ,acts4 ,they all agreed in attaching the same injurious meaning to the passage which we formerly quoted1 and authorized ,keill to explain and defend his statement4 ,he accordingly addressed a letter to ,sir ,hans ,sloane1 which was read at the society on the #bdth ,may1 #agaa1 and a copy of which was ordered to be sent to ,leibnitz4 ,in this letter1 which is one of considerable length1 he declares that he never meant to state that ,leibnitz knew either the name of ,newton's method or the form of notation1 and that the real meaning of the passage was1 8that ,newton was the first inventor of fluxions or of the differential calculus1 and that he had given1 in two letters to ,oldenburg1 and which he had transmitted to ,leibnitz1 indications of it sufficiently intelligible to an acute mind1 from which ,leibnitz derived1 or at least might derive1 the principles of his calculus40 ,the charge of plagiarism which ,leibnitz thought was implied in the former letter of his antagonist is here greatly modified1 if not altogether denied4 ,keill expresses only an opinion that the letter seen by ,leibnitz contained intelligible indications of the fluxionary calculus4 ,even if this opinion were correct1 it is no proof that ,leibnitz either saw these indications or availed himself of them1 or if he did perceive them1 it might have been in consequence of his having previously been in possession of the differential calculus1 or having enjoyed some distant view of it4 ,leibnitz should1 therefore1 have allowed the dispute to terminate here2 for no ingenuity on his part1 and no additional facts1 could affect an opinion which any other person as well as ,keill was entitled to maintain4 ,leibnitz1 however1 took a different view of the subject1 and wrote a letter to ,sir ,hans ,sloane1 dated ,december #ai1 #agaa1 which excited new feelings1 and involved him in new embarrassments4 ,insensible to the mitigation which had been kindly impressed upon the supposed charge against his honour1 he alleges that ,keill had attacked his candour and sincerity more openly than before2--that he acted without any authority from ,sir ,isaac ,newton1 who was the party interested2--and that it was in vain to justify his proceedings by referring to the provocation in the ,leipsic ,acts1 because in that journal no injustice had been done to any party1 but every one had received what was his due4 ,he branded ,keill with the odious appellation of an upstart1 and one little acquainted with the circumstances of the case2#fe he called upon the society to silence his vain and unjust clamours1#ff which1 he believed1 were disapproved by ,newton himself1 who was well acquainted with the facts1 and who1 he was persuaded1 would willingly give his opinion on the matter4 ,this unfortunate letter was doubtless the cause of all the rancour and controversy which so speedily followed1 and it placed his antagonist in a new and a more favourable position4 ,it may be correct1 though few will admit it1 that ,keill's second letter was more injurious than the first2 but it was not true that ,keill acted without the authority of ,newton1 because ,keill's letter was approved of and transmitted by the ,royal ,society1 of which ,newton was the president1 and therefore became the act of that body4 ,the obnoxious part1 however1 of ,leibnitz's letter consisted in his appropriating to himself the opinions of the reviewer in the ,leipsic ,acts1 by declaring that1 in a review which charged ,newton with plagiarism1 every person had got what was his due4 ,the whole character of the controversy was now changed3 ,leibnitz places himself in the position of the party who had first disturbed the tranquillity of science by maligning its most distinguished ornament2 and the ,royal ,society was imperiously called upon to throw all the light they could upon a transaction which had exposed their venerable president to so false a charge4 ,the society1 too1 had become a party to the question1 by their approbation and transmission of ,keill's second letter1 and were on that account alone bound to vindicate the step which they had taken4 ,when the letter of ,leibnitz1 therefore1 was read1 ,keill appealed to the registers of the society for the proofs of what he had advanced2 ,sir ,isaac also expressed his displeasure at the obnoxious passage in the ,leipsic ,review1 and at the defence of it by ,leibnitz1 and he left it to the society to act as they thought proper4 ,a committee was therefore appointed on the #aath ,march1 consisting of ,dr4 ,arbuthnot1 ,mr4 ,hill1 ,dr4 ,halley1 ,mr4 ,jones1 ,mr4 ,machin1 and ,mr4 ,burnet1 who were instructed to examine the ancient registers of the society1 to inquire into the dispute1 and to produce such documents as they should find1 together with their own opinions on the subject4 ,on the #bdth ,april the committee produced the following report3-- 8,we have consulted the letters and letter-books in the custody of the ,royal ,society1 and those found among the papers of ,mr4 ,john ,collins1 dated between the years #affi and #afgg1 inclusive2 and showed them to such as knew and avouched the hands of ,mr4 ,barrow1 ,mr4 ,collins1 ,mr4 ,oldenburg1 and ,mr4 ,leibnitz2 and compared those of ,mr4 ,gregory with one another1 and with copies of some of them taken in the hand of ,mr4 ,collins2 and have extracted from them what relates to the matter referred to us2 all which extracts herewith delivered to you we believe to be genuine and authentic4 ,and by these letters and papers we find1-- 8,i4 ,mr4 ,leibnitz was in ,london in the beginning of the year #afgc2 and went thence1 in or about ,march1 to ,paris1 where he kept a correspondence with ,mr4 ,collins by means of ,mr4 ,oldenburg1 till about ,september1 #afgf1 and then returned by ,london and ,amsterdam to ,hanover3 and that ,mr4 ,collins was very free in communicating to able mathematicians what he had received from ,mr4 ,newton and ,mr4 ,gregory4 8,,ii4 ,that when ,mr4 ,leibnitz was the first time in ,london1 he contended for the invention of another differential method properly so called2 and1 notwithstanding that he was shown by ,dr4 ,pell that it was ,newton's method1 persisted in maintaining it to be his own invention1 by reason that he had found it by himself without knowing what ,newton had done before1 and had much improved it4 ,and we find no mention of his having any other differential method than ,newton's before his letter of the #bast of ,june1 #afgg1 which was a year after a copy of ,mr4 ,newton's letter of the #ajth of ,december1 #afgb1 had been sent to ,paris to be communicated to him2 and above four years after1 ,mr4 ,collins began to communicate that letter to his correspondent2 in which letter the method of fluxions was sufficiently described to any intelligent person4 8,,iii4 ,that by ,mr4 ,newton's letter of the #acth of ,june1 #afgf1 it appears that he had the method of fluxions above five years before the writing of that letter4 ,and by his ,analysis per quationes numero ,terminorum ,infinitas1 communicated by ,dr4 ,barrow to ,mr4 ,collins in ,july1 #affi1 we find that he had invented the method before that time4 8,,iv4 ,that the differential method is one and the same with the method of fluxions1 excepting the name and mode of notation2 ,mr4 ,leibnitz calling those quantities differences which ,mr4 ,newton calls moments or fluxions2 and marking them with the letter d--a mark not used by ,mr4 ,newton4 8,and therefore we take the proper question to be not who invented this or that method1 but who was the first inventor of the method4 ,and we believe that those who have reputed ,mr4 ,leibnitz the first inventor knew little or nothing of his correspondence with ,mr4 ,collins and ,mr4 ,oldenburg long before1 nor of ,mr4 ,newton's having that method above fifteen years before ,mr4 ,leibnitz began to publish it in the ,acta ,eruditorum of ,leipsic4 8,for which reason we reckon ,mr4 ,newton the first inventor2 and are of opinion that ,mr4 ,keill1 in asserting the same1 has been no ways injurious to ,mr4 ,leibnitz4 ,and we submit to the judgment of the society whether the extract and papers now presented to you1 together with what is extant to the same purpose in ,dr4 ,wallis's third volume1 may not deserve to be made public40 ,this report being read1 the society unanimously ordered the collection of letters and manuscripts to be printed1 and appointed ,dr4 ,halley1 ,mr4 ,jones1 and ,mr4 ,machin to superintend the press4 ,complete copies of it1 under the title of ,commercium ,epistolicum ,d4 ,johannis ,collins et aliorum de analysi promota1 were laid before the society on the #hth ,january1 #agac1 and ,sir ,isaac ,newton1 as president1 ordered a copy to be delivered to each person of the committee appointed for that purpose1 to examine it before its publication4 ,leibnitz received information of the appearance of the ,commercium ,epistolicum when he was at ,vienna2 and 8being satisfied10 as he expresses it1 8that it must contain malicious falsehoods1 ,i did not think proper to send for it by post1 but wrote to ,m4 ,bernouilli to give me his sentiments4 ,m4 ,bernouilli wrote me a letter dated at ,basle1 ,june #gth1 #agac1 in which he said that it appeared probable that ,sir ,isaac ,newton had formed his calculus after having seen mine40#fg ,this letter was published by a friend of ,leibnitz1 with reflections1 in a loose sheet entitled ,charta ,volans1 and dated ,july #bi1 #agac4 ,it was widely circulated without either the name of the author1 printer1 or place of publication1 and was communicated to the ,journal ,literaire by another friend of ,leibnitz1 who added remarks of his own1 and stated1 that when ,newton published the ,principia in #afhg1 he did not understand the true differential method2 and that he took his fluxions from ,leibnitz4 ,in this state of the controversy1 ,mr4 ,chamberlayne conceived the design of reconciling the two distinguished philosophers2 and in a letter dated ,april #bh1 #agad1fh he addressed himself to ,leibnitz1 who was still at ,vienna4 ,in replying to this letter1 ,leibnitz declared that he had given no occasion for the dispute2 8that ,newton procured a book to be published1 which was written purposely to discredit him1 and sent it to ,germany1 c4 as in the name of the society20 and he stated that there was room to doubt whether ,newton knew his invention before he had it of him4 ,mr4 ,chamberlayne communicated this letter to ,sir ,isaac ,newton1 who replied that ,leibnitz had attacked his reputation in #agje1 by intimating that he had borrowed from him the method of fluxions2 that if ,mr4 ,c4 could point out to him any thing in which he had injured ,mr4 ,leibnitz1 he would give him satisfaction2 that he would not retract things which he knew to be true2 and that he believed that the ,royal ,society had done no injustice by the publication of the ,commercium ,epistolicum4 ,the ,royal ,society1 having learned that ,leibnitz complained of their having condemned him unheard1 inserted a declaration in their journals on the #bjth ,may1 #agad1 that they did not pretend that the report of their committee should pass for a decision of the society4 ,mr4 ,chamberlayne sent a copy of this to ,leibnitz1 along with ,sir ,isaac's letter1 and ,dr4 ,keill's answer to the papers inserted in the ,journal ,literaire4 ,after perusing these documents1 ,m4 ,leibnitz replied1 8that ,sir ,isaac's letter was written with very little civility2 that he was not in a humour to put himself in a passion against such people2 that there were other letters among those of ,oldenburg and ,collins which should have been published2 and that on his return to ,hanover1 he would be able to publish a ,commercium ,epistolicum which would be of service to the history of learning40 ,when this letter was read to the ,royal ,society1 ,sir ,isaac remarked1 that the last part of it injuriously accused the society of having made a partial selection of papers for the ,commercium ,epistolicum2 that he did not interfere in any way in the publication of that work1 and had even withheld from the committee two letters1 one from ,leibnitz in #afic1 and another from ,wallis in #afie1 which were highly favourable to his cause4 ,he stated that he did not think it right for ,m4 ,leibnitz himself1 but that1 if he had letters to produce in his favour1 that they might be published in the ,philosophical ,transactions1 or in ,germany4 ,about this time the ,abb ,conti1 a noble ,venetian1 came to ,england4 ,he was a correspondent of ,leibnitz1 and in a letter which he had received soon after his arrival1#fi he enters upon his dispute with ,newton4 ,he charges the ,english 8with wishing to pass for almost the only inventors40 ,he declares 8that ,bernouilli had judged rightly in saying that ,newton did not possess before him the infinitesimal characteristic and algorithm40 ,he remarks that ,newton preceded him only in series2 and he confesses that during his second visit to ,england1 8,collins showed him part of his correspondence10 or1 as he afterward expresses it1 he saw 8some of the letters of ,newton at ,mr4 ,collins's40 ,he then attacks ,sir ,isaac's philosophy1 particularly his opinions about gravity and vacuum1 the intervention of ,god for the preservation of his creatures2 and he accuses him of reviving the occult qualities of the schools4 ,but the most remarkable passage in this letter is the following3 8,i am a great friend of experimental philosophy1 but ,newton deviates much from it when he pretends that all matter is heavy1 or that each particle of matter attracts every other particle40 ,the above letter to the ,abb ,conti was generally shown in ,london1 and came to be much talked of at court1 in consequence of ,leibnitz having been privy counsellor to the ,elector of ,hanover when that prince ascended the throne of ,england4 ,many persons of distinction1 and particularly the ,abb ,conti1 urged ,newton to reply to ,leibnitz's letter1 but he resisted all their solicitations4 ,one day1 however1 ,king ,george ,i4 inquired when ,sir ,isaac ,newton's answer to ,leibnitz would appear2 and when ,sir ,isaac heard this1 he addressed a long reply to the ,abb ,conti1 dated ,february #bfth1 ,o4 ,s4 #agae-af4 ,this letter1 written with dignified severity1 is a triumphant refutation of the allegations of his adversary2 and the following passage deserves to be quoted1 as connected with that branch of the dispute which relates to ,leibnitz's having seen part of ,newton's letters to ,mr4 ,collins4 8,he complains of the committee of the ,royal ,society1 as if they had acted partially in omitting what made against me2 but he fails in proving the accusation4 ,for he instances in a paragraph concerning my ignorance1 pretending that they omitted it1 and yet you will find it in the ,commercium ,epistolicum1 p4 #edg1 lines #b1 #c1 and ,i am not ashamed of it4 ,he saith that he saw this paragraph in the hands of ,mr4 ,collins when he was in ,london the second time1 that is in ,october1 #afgf4 ,it is in my letter of the #bdth of ,october1 #afgf1 and therefore he then saw that letter4 ,and in that and some other letters writ before that time1 ,i described my method of fluxions2 and in the same letter ,i described also two general methods of series1 one of which is now claimed from me by ,mr4 ,leibnitz40 ,the letter concludes with the following paragraph3 8,but as he has lately attacked me with an accusation which amounts to plagiary2 if he goes on to accuse me1 it lies upon him by the laws of all nations to prove his accusations1 on pain of being accounted guilty of calumny4 ,he hath hitherto written letters to his correspondents full of affirmations1 complaints1 and reflections1 without proving any thing4 ,but he is the aggressor1 and it lies upon him to prove the charge40 ,in transmitting this letter to ,leibnitz1 the ,abb ,conti informed him that he himself had read with great attention1 and without the least prejudice1 the ,commercium ,epistolicum1 and the little piece#gj that contains the extract2 that he had also seen at the ,royal ,society the original papers of the ,commercium ,epistolicum1 and some other original pieces relating to it4 8,from all this10 says he1 8,i infer1 that1 if all the digressions are cut off1 the only point is1 whether ,sir ,isaac ,newton had the method of fluxions or infinitesimals before you1 or whether you had it before him4 ,you published it first1 it is true1 but you have owned also that ,sir ,isaac ,newton had given many hints of it in his letters to ,mr4 ,oldenburg and others4 ,this is proved very largely in the ,commercium1 and in the extract of it4 ,what answer do you give8 ,this is still wanting to the public1 in order to form an exact judgment of the affair40 ,the ,abb adds1 that ,mr4 ,leibnitz's own friends waited for his answer with great impatience1 and that they thought he could not dispense with answering1 if not ,dr4 ,keill1 at least ,sir ,isaac ,newton himself1 who had given him a defiance in express terms4 ,leibnitz was not long in complying with this request4 ,he addressed a letter to the ,abb ,conti1 dated ,april #ith1 #agaf1 but he sent it through ,m4 ,ramond at ,paris1 to communicate it to others4 ,when it was received by the ,abb ,conti1 ,newton wrote observations upon it1 which were communicated only to some of his friends1 and which1 while they placed his defence on the most impregnable basis1 at the same time threw much light on the early history of his mathematical discoveries4 ,the death of ,leibnitz on the #adth ,november1 #agaf1 put an end to this controversy1 and ,newton some time afterward published the correspondence with the ,abb ,conti1 which had hitherto been only privately circulated among the friends of the disputants4#ga ,in #agbb1 a new edition of the ,commercium ,epistolicum was published1 and there was prefixed to it a general review of its contents1 which has been falsely ascribed to ,newton4#gb ,when the third edition of the ,principia was published in #agbe1 the celebrated scholium which we have already quoted1 and in which ,leibnitz's differential calculus was mentioned1 was struck out either by ,newton or by the editor4 ,this step was perhaps rash and ill-advised2 but as the scholium had been adduced by ,leibnitz and others as a proof that ,newton acknowledged him to be an independent inventor of the calculus1--an interpretation which it does not bear1 and which ,newton expressly states he never intended it to bear1--he was justified in withdrawing a passage which had been so erroneously interpreted1 and so greatly misapplied4 ,in viewing this controversy1 at the distance of more than a century1 when the passions of the individual combatants have been allayed1 and national jealousies extinguished1 it is not difficult to form a correct estimate of the conduct and claims of the two rival analysts4 ,by the unanimous verdict of all nations1 it has been decided that ,newton invented fluxions at least ten years before ,leibnitz4 ,some of the letters of ,newton which bore reference to this great discovery were perused by the ,german mathematician2 but there is no evidence whatever that he borrowed his differential calculus from these letters4 ,newton was therefore the first inventor1 and ,leibnitz the second4 ,it was impossible that the former could have been a plagiarist2 but it was possible for the latter4 ,had the letters of ,newton contained even stronger indications than they do of the new calculus1 no evidence short of proof could have justified any allegation against ,leibnitz's honour4 ,the talents which he displayed in the improvement of the calculus showed that he was capable of inventing it2 and his character stood sufficiently high to repel every suspicion of his integrity4 ,but if it would have been criminal to charge ,leibnitz with plagiarism1 what must we think of those who dared to accuse ,newton of borrowing his fluxions from ,leibnitz8 ,this odious accusation was made by ,leibnitz himself1 and by ,bernouilli2 and we have seen that the former repeated it again and again1 as if his own good name rested on the destruction of that of his rival4 ,it was this charge against ,newton that gave rise to the attack of ,keill1 and the publication of the ,commercium ,epistolicum2 and1 notwithstanding this high provocation1 the committee of the ,royal ,society contented themselves with asserting ,newton's priority1 without retorting the charge of plagiarism upon his rival4 ,although an attempt has been recently made to place the conduct of ,leibnitz on the same level with that of ,newton1 yet the circumstances of the case will by no means justify such a comparison4 ,the conduct of ,newton was at all times dignified and just4 ,he knew his rights1 and he boldly claimed them4 ,conscious of his integrity1 he spurned with indignation the charge of plagiarism with which an ungenerous rival had so insidiously loaded him2 and if there was one step in his frank and unhesitating procedure which posterity can blame it is his omission1 in the third edition of the ,principia1 of the references to the differential calculus of ,leibnitz4 ,this omission1 however1 was perfectly just4 ,the scholium which he had left out was a mere historical statement of the fact1 that the ,german mathematician had sent him a method which was the same as his own2 and when he found that this simple assertion had been held by ,leibnitz and others as a recognition of his independent claim to the invention1 he was bound either to omit it altogether1 or to enter into explanations which might have involved him in a new controversy4 ,the conduct of ,leibnitz was not marked with the same noble lineaments4 ,that he was the aggressor is universally allowed4 ,that he first dared to breathe the charge of plagiarism against ,newton1 and that he often referred to it1 has been sufficiently apparent2 and when arguments failed him he had recourse to threats--declaring that he would publish another ,commercium ,epistolicum1 though he had no appropriate letters to produce4 ,all this is now matter of history2 and we may find some apology for it in his excited feelings1 and in the insinuations which were occasionally thrown out against the originality of his discovery2 but for other parts of his conduct we seek in vain for an excuse4 ,when he assailed the philosophy of ,newton in his letters to the ,abb ,conti1 he exhibited perhaps only the petty feelings of a rival2 but when he dared to calumniate that great man in his correspondence with the ,princess of ,wales1 by whom he was respected and beloved2 when he ventured to represent the ,newtonian philosophy as physically false1 and as dangerous to religion2 and when he founded these accusations on passages in the ,principia and the ,optics glowing with all the fervour of genuine piety1 he cast a blot upon his name1 which all his talents as a philosopher1 and all his virtues as a man1 will never be able to efface4 ,,chapter ,,xiii4 ,james ,,ii4 attacks the ,privileges of the ,university of ,cambridge-- ,newton chosen one of the ,delegates to resist this ,encroachment--,he is elected a ,member of the ,convention ,parliament--,burning of his ,manuscripts--,his supposed ,derangement of ,mind--,view taken of this by foreign ,philosophers--,his ,correspondence with ,mr4 ,pepys and ,mr4 ,locke at the time of his ,illness--,mr4 ,millington's ,letter to ,mr4 ,pepys on the subject of ,newton's ,illness--,refutation of the ,statement that he laboured under ,mental ,derangement4 ,from the year #affi1 when ,newton was installed in the ,lucasian chair1 till #afie1 when he ceased to reside in ,cambridge1 he seems to have been seldom absent from his college more than three or four weeks in the year4 ,in #afge1 he received a dispensation from ,charles ,,ii4 to continue in his fellowship of ,trinity ,college without taking orders1 and we have already seen in the preceding chapter how his time was occupied till the publication of the ,principia in #afhg4 ,an event now occurred which drew ,newton from the seclusion of his studies1 and placed him upon the theatre of public life4 ,desirous of re-establishing the ,catholic faith in its former supremacy1 ,king ,james ,,ii4 had begun to assail the rights and privileges of his ,protestant subjects4 ,among other illegal acts1 he sent his letter of mandamus to the ,university of ,cambridge to order ,father ,francis1 an ignorant monk of the ,benedictine order1 to be received as master of arts1 and to enjoy all the privileges of this degree1 without taking the oaths of allegiance and supremacy4 ,the university speedily perceived the consequences which might arise from such a measure4 ,independent of the infringement of their rights which such an order involved1 it was obvious that the highest interests of the university were endangered1 and that ,roman ,catholics might soon become a majority in the convocation4 ,they therefore unanimously refused to listen to the royal order1 and they did this with a firmness of purpose which irritated the despotic court4 ,the king reiterated his commands1 and accompanied them with the severest threatenings in case of disobedience4 ,the ,catholics were not idle in supporting the views of the sovereign4 ,the honorary degree of ,m4,a4 which conveys no civil rights to its possessor1 having been formerly given to the secretary of the ambassador from ,morocco1 it was triumphantly urged that the ,university of ,cambridge had a greater regard for a ,mahometan than for a ,roman ,catholic1 and was more obsequious to the ambassador from ,morocco than to their own lawful sovereign4 ,though this reasoning might impose upon the ignorant1 it produced little effect upon the members of the university4 ,a few weak-minded individuals1 however1 were disposed to yield a reluctant consent to the royal wishes4 ,they proposed to confer the degree1 and at the same time to resolve that it should not in future be regarded as a precedent4 ,to this it was replied1 that the very act of submission in one case would be a stronger argument for continuing the practice than any such resolution would be against its repetition4 ,the university accordingly remained firm in their original decision4 ,the vice-chancellor was summoned before the ecclesiastical commission to answer for this act of contempt4 ,newton was among the number of those who resisted the wishes of the court1 and he was consequently chosen one of the nine delegates who were appointed to defend the independence of the university4 ,these delegates appeared before the ,high ,court4 ,they maintained that not a single precedent could be found to justify so extraordinary a measure2 and they showed that ,charles ,,ii4 had1 under similar circumstances1 been pleased to withdraw his mandamus4 ,this representation had its full weight1 and the king was induced to abandon his design4#gc ,the part which ,newton had taken in this affair1 and the high character which he now held in the scientific world1 induced his friends to propose him as member of parliament for the university4 ,he was accordingly elected in #afhh1 though by a very narrow majority1#gd and he sat in the ,convention ,parliament till its dissolution4 ,in the year #afhh and #afhi1 ,newton was absent from ,cambridge during the greater part of the year1 owing1 we presume1 to his attendance in parliament2 but it appears from the books of the ,university that from #afij to #afie he was seldom absent1 and must therefore have renounced his parliamentary duties4 ,during his stay in ,london he had no doubt experienced the unsuitableness of his income to the new circumstances in which he was placed1 and it is probable that this was the cause of the limitation of his residence to ,cambridge4 ,his income was certainly very confined1 and but little suited to the generosity of his disposition4 ,demands were doubtless made upon it by some of his less wealthy relatives2 and there is reason to think that he himself1 as well as his influential friends1 had been looking forward to some act of liberality on the part of the government4 ,an event however occurred which will ever form an epoch in his history2 and it is a singular circumstance1 that this incident has been for more than a century unknown to his own countrymen1 and has been accidentally brought to light by the examination of the manuscripts of ,huygens4 ,this event has been magnified into a temporary aberration of mind1 which is said to have arisen from a cause scarcely adequate to its production4 ,while he was attending divine service in a winter morning1 he had left in his study a favourite little dog called ,diamond4 ,upon returning from chapel he found that it had overturned a lighted taper on his desk1 which set fire to several papers on which he had recorded the results of some optical experiments4 ,these papers are said to have contained the labours of many years1 and it has been stated that when ,mr4 ,newton perceived the magnitude of his loss1 he exclaimed1 8,oh1 ,diamond1 ,diamond1 little do you know the mischief you have done me60 ,it is a curious circumstance that ,newton never refers to the experiments which he is said to have lost on this occasion1 and his nephew1 ,mr4 ,conduit1 makes no allusion to the event itself4 ,the distress1 however which it occasioned is said to have been so deep as to affect even the powers of his understanding4 ,this extraordinary effect was first communicated to the world in the ,life of ,newton by ,m4 ,biot1 who received the following account of it from the celebrated ,m4 ,van ,swinden4 8,there is among the manuscripts of the celebrated ,huygens a small journal in folio1 in which he used to note down different occurrences4 ,it is side 1 ,no4 #h1 p4 #aab1 in the catalogue of the library of ,leyden4 ,the following extract is written by ,huygens himself1 with whose handwriting ,i am well acquainted1 having had occasion to peruse several of his manuscripts and autograph letters4 #8,on the #bith ,may1 #afid1 ,m4 ,colin1#ge a ,scotsman1 informed me that eighteen months ago the illustrious geometer1 ,isaac ,newton1 had become insane1 either in consequence of his too intense application to his studies1 or from excessive grief at having lost1 by fire1 his chymical laboratory and several manuscripts4 ,when he came to the ,archbishop of ,cambridge1 he made some observations which indicated an alienation of mind4 ,he was immediately taken care of by his friends1 who confined him to his house and applied remedies1 by means of which he had now so far recovered his health that he began to understand the ,principia4'0 ,huygens mentioned this circumstance to ,leibnitz1 in a letter dated #hth ,june1 #afid1 to which ,leibnitz replies in a letter dated the #bc;d1 8,i am very glad that ,i received information of the cure of ,mr4 ,newton1 at the same time that ,i first heard of his illness1 which doubtless must have been very alarming4 #8,it is to men like you and him1 sir1 that ,i wish a long life4'0 ,the first publication of the preceding statement produced a strong sensation among the friends and admirers of ,newton4 ,they could not easily believe in the prostration of that intellectual strength which had unbarred the strongholds of the universe4 ,the unbroken equanimity of ,newton's mind1 the purity of his moral character1 his temperate and abstemious life1 his ardent and unaffected piety1 and the weakness of his imaginative powers1 all indicated a mind which was not likely to be overset by any affliction to which it could be exposed4 ,the loss of a few experimental records could never have disturbed the equilibrium of a mind like his4 ,if they were the records of discoveries1 the discoveries themselves indestructible would have been afterward given to the world4 ,if they were merely the details of experimental results1 a little time could have easily reproduced them4 ,had these records contained the first fruits of early genius--of obscure talent1 on which fame had not yet shed its rays1 we might have supposed that the first blight of such early ambition would have unsettled the stability of an untried mind4 ,but ,newton was satiated with fame4 ,his mightiest discoveries were completed and diffused over all ,europe1 and he must have felt himself placed on the loftiest pinnacle of earthly ambition4 ,the incredulity which such views could not fail to encourage was increased by the novelty of the information4 ,no ,english biographer had ever alluded to such an event4 ,history and tradition were equally silent1 and it was not easy to believe that the ,lucasian ,professor of ,mathematics at ,cambridge1 a member of the ,english parliament1 and the first philosopher in ,europe could have lost his reason without the dreadful fact being known to his own countrymen4 ,but if the friends of ,newton were surprised by the nature of the intelligence1 they were distressed at the view which was taken of it by foreign philosophers4 ,while one maintained that the intellectual exertions of ,newton had terminated with the publication of the ,principia1 and that the derangement of his mind was the cause of his abandoning the sciences1 others indirectly questioned the sincerity of his religious views1 and ascribed to the aberration of his mind those theological pursuits which gilded his declining age4 8,but the fact10 says ,m4 ,biot1 8of the derangement of his intellect1 whatever may have been the cause of it1 will explain why1 after the publication of the ,principia in #afhg1 ,newton1 though only forty-five years old1 never more published a new work on any branch of science1 but contented himself with giving to the world those which he had composed long before that epoch1 confining himself to the completion of those parts which might require development4 ,we may also remark1 that even these developments appear always to be derived from experiments and observations formerly made1 such as the additions to the second edition of the ,principia1 published in #agac1 the experiments on thick plates1 those on diffraction1 and the chymical queries placed at the end of the ,optics in #agjd2 for in giving an account of these experiments ,newton distinctly says that they were taken from ancient manuscripts which he had formerly composed2 and he adds1 that though he felt the necessity of extending them1 or rendering them more perfect1 he was not able to resolve to do this1 these matters being no longer in his way4 ,thus it appears that though he had recovered his health sufficiently to understand all his researches1 and even in some cases to make additions to them1 and useful alterations1 as appears from the second edition of the ,principia1 for which he kept up a very active mathematical correspondence with ,mr4 ,cotes1 yet he did not wish to undertake new labours in those departments of science where he had done so much1 and where he so distinctly saw what remained to be done40 ,under the influence of the same opinion1 ,m4 ,biot finds 8it extremely probable that his dissertation on the scale of heat was written before the fire in his laboratory20 he describes ,newton's conduct about the longitude bill as 8almost puerile on so solemn an occasion1 and one which might lead to the strangest conclusions1 particularly if we refer it to the fatal accident which ,newton had suffered in #afie40 ,the celebrated ,marquis de la ,place viewed the illness of ,newton in a light still more painful to his friends4 ,he maintained that he never recovered the vigour of his intellect1 and he was persuaded that ,newton's theological inquiries did not commence till after that afflicting epoch of his life4 ,he even commissioned ,professor ,gautier of ,geneva to make inquiries on this subject during his visit to ,england1 as if it concerned the interests of truth and justice to show that ,newton became a ,christian and a theological writer only after the decay of his strength and the eclipse of his reason4 ,such having been the consequences of the disclosure of ,newton's illness by the manuscript of ,huygens1 ,i felt it to be a sacred duty to the memory of that great man1 to the feelings of his countrymen1 and to the interests of ,christianity itself1 to inquire into the nature and history of that indisposition which seems to have been so much misrepresented and misapplied4 ,from the ignorance of so extraordinary an event which has prevailed for such a long period in ,england1 it might have been urged with some plausibility that ,huygens had mistaken the real import of the information that was conveyed to him2 or that the ,scotchman from whom he received it had propagated an idle and a groundless rumour4 ,but we are1 fortunately1 not confined to this very reasonable mode of defence4 ,there exists at ,cambridge a manuscript journal written by ,mr4 ,abraham de la ,pryme1 who was a student in the university while ,newton was a fellow of ,trinity4 ,this manuscript is entitled 8,ephemeris ,vit1 or ,diary of my own ,life1 containing an account likewise of the most observable and remarkable things that ,i have taken notice of from my youth up hitherto40 ,mr4 de la ,pryme was born in #afga1 and begins the diary in #afhe4 ,this manuscript is in the possession of his collateral descendant1 ,george ,pryme1 ,esq41 ,professor of ,political ,economy at ,cambridge1 to whom ,i have been indebted for the following extract4 8#afib1 ,february #c;d4--,what ,i heard to-day ,i must relate4 ,there is one ,mr4 ,newton 7whom ,i have very oft seen71 ,fellow of ,trinity ,college1 that is mighty famous for his learning1 being a most excellent mathematician1 philosopher1 divine1 c4 ,he has been ,fellow of the ,royal ,society these many years2 and among other very learned books and tracts1 he's written one upon the mathematical principles of philosophy1 which has got him a mighty name1 he having received1 especially from ,scotland1 abundance of congratulatory letters for the same2 but of all the books that he ever wrote1 there was one of colours and light1 established upon thousands of experiments which he had been twenty years of making1 and which had cost him many hundred of pounds4 ,this book1 which he valued so much1 and which was so much talked of1 had the ill luck to perish and be utterly lost just when the learned author was almost at putting a conclusion at the same1 after this manner3 ,in a winter's morning1 leaving it among his other papers on his study table while he went to chapel1 the candle1 which he had unfortunately left burning there too1 catched hold by some means of other papers1 and they fired the aforesaid book1 and utterly consumed it and several other valuable writings2 and1 which is most wonderful1 did no further mischief4 ,but when ,mr4 ,newton came from chapel1 and had seen what was done1 every one thought he would have run mad1 he was so troubled thereat that he was not himself for a month after4 ,a long account of this his system of light and colours you may find in the ,transactions of the ,royal ,society1 which he had sent up to them long before this sad mischance happened unto him40 ,from this extract we are enabled to fix the approximate date of the accident by which ,newton lost his papers4 ,it must have been previous to the #c;d ,january1 #afib1 a month before the date of the extract2 but if we fix it by the dates in ,huygens's manuscript1 we should place it about the #bith ,november1 #afib1 eighteen months previous to the conversation between ,collins and ,huygens4 ,the manner in which ,mr4 ,pryme refers to ,newton's state of mind is that which is used every day when we speak of the loss of tranquillity which arises from the ordinary afflictions of life2 and the meaning of the passage amounts to nothing more than that ,newton was very much troubled by the destruction of his papers1 and did not recover his serenity1 and return to his usual occupations1 for a month4 ,the very phrase that 8every person thought he would have run mad0 is in itself a proof that no such effect was produced2 and1 whatever degree of indisposition may be implied in the phrase 8he was not himself for a month after10 we are entitled to infer that one month was the period of its duration1 and that previous to the #c;d ,february1 #afib1 the date of ,mr4 ,pryme's memorandum1 8,newton was himself again40 ,these facts and dates cannot be reconciled with those in ,huygens's manuscript4 ,it appears from that document1 that1 so late as ,may1 #afid1 ,newton had only so far recovered his health as to begin to again understand the ,principia4 ,his supposed malady1 therefore1 was in force from the #c;d of ,january1 #afib1 till the month of ,may1 #afid1--;a period of more than two years4 ,now1 it is a most important circumstance1 which ,m4 ,biot ought to have known1 that in the very middle of this period1 ,newton wrote his four celebrated letters to ,dr4 ,bentley on the ,existence of a ,deity1--letters which evince a power of thought and a serenity of mind absolutely incompatible even with the slightest obscuration of his faculties4 ,no man can peruse these letters without the conviction that their author then possessed the full vigour of his reason1 and was capable of understanding the most profound parts of his writings4 ,the first of these letters was written on the #ajth ,december1 #afib1 the second on the #agth ,january1 #afic1 the third on the #beth ,february1 and the #dth on the #aath#gf ,february1 #afic4 ,his mind was1 therefore1 strong and vigorous on these four occasions2 and as the letters were written at the express request of ,dr4 ,bentley1 who had been appointed to deliver the lecture founded by ,mr4 ,boyle for vindicating the fundamental principles of natural and revealed religion1 we must consider such a request as showing his opinion of the strength and freshness of his friend's mental powers4 ,in #afib1 ,newton1 at the request of ,dr4 ,wallis1 transmitted to him the first proposition of his book on quadratures1 with examples of it in first1 second1 and third fluxions4#gg ,these examples were written in consequence of an application from his friend2 and the author of the review of the ,commercium ,epistolicum1 in which this fact is quoted1 draws the conclusion1 that he had not at that time forgotten his method of second fluxions4 ,it appears1 also1 from the second book of the ,optics1#gh that in the month of ,june1 #afib1 he had been occupied with the subject of haloes1 and had made accurate observations both on the colours and the diameters of the rings in a halo which he had then seen around the sun4 ,but though these facts stand in direct contradiction to the statement recorded by ,huygens1 the reader will be naturally anxious to know the real nature and extent of the indisposition to which it refers4 ,the following letters1#gi written by ,newton himself1 ,mr4 ,pepys1 ,secretary to the ,admiralty1 and ,mr4 ,millington of ,magdalene ,college1 ,cambridge1 will throw much light upon the subject4 ,newton1 as will be presently seen1 had fallen into a bad state of health some time in #afib1 in consequence of which both his sleep and his appetite were greatly affected4 ,about the middle of ,september1 #afic1 he had been kept awake for five nights by this nervous disorder1 and in this condition he wrote the following letter to ,mr4 ,pepys3 ,sept4 #ac1 #afic4 8,,sir1 8,some time after ,mr4 ,millington had delivered your message1 he pressed me to see you the next time ,i went to ,london4 ,i was averse2 but upon his pressing consented1 before ,i considered what ,i did1 for ,i am extremely troubled at the embroilment ,i am in1 and have neither ate nor slept well this twelvemonth1 nor have my former consistency of mind4 ,i never designed to get any thing by your interest1 nor by ,king ,james's favour1 but am now sensible that ,i must withdraw from your acquaintance1 and see neither you nor the rest of my friends any more1 if ,i may but leave them quietly4 ,i beg your pardon for saying ,i would see you again1 and rest your most humble and most obedient servant1 8,,is4 ,,newton40 ,from this letter we learn1 on his own authority1 that his complaint had lasted for a twelvemonth1 and that during that twelvemonth he neither ate nor slept well1 nor enjoyed his former consistency of mind4 ,it is not easy to understand exactly what is meant by not enjoying his former consistency of mind2 but whatever be its import1 it is obvious that he must have been in a state of mind so sound as to enable him to compose the four letters to ,bentley1 all of which were written during the twelvemonth here referred to4 ,on the receipt of this letter1 his friend ,mr4 ,pepys seems to have written to ,mr4 ,millington of ,magdalene ,college to inquire after ,mr4 ,newton's health2 but the inquiry having been made in a vague manner1 an answer equally vague was returned4 ,mr4 ,pepys1 however1 who seems to have been deeply anxious about ,newton's health1 addressed the following more explicit letter to his friend ,mr4 ,millington3-- ,septemb4 #bf1 #afic4 8,,sir1 8,after acknowledging your many old favours1 give me leave to do it a little more particularly upon occasion of the new one conveyed to me by my nephew ,jackson4 ,though1 at the same time1 ,i must acknowledge myself not at the ease ,i would be glad to be at in reference to the excellent ,mr4 ,newton2 concerning whom 7methinks7 your answer labours under the same kind of restraint which 7to tell you the truth7 my asking did4 ,for ,i was loth at first dash to tell you that ,i had lately received a letter from him so surprising to me for the inconsistency of every part of it1 as to be put into great disorder by it1 from the concernment ,i have for him1 lest it should arise from that which of all mankind ,i should least dread from him and most lament for1--,i mean a discomposure in head1 or mind1 or both4 ,let me therefore beg you1 sir1 having now told you the true ground of the trouble ,i lately gave you1 to let me know the very truth of the matter1 as far at least as comes within your knowledge4 ,for ,i own too great an esteem for ,mr4 ,newton1 as for a public good1 to be able to let any doubt in me of this kind concerning him lie a moment uncleared1 where ,i can have any hopes of helping it4 ,i am1 with great truth and respect1 dear sir1 your most humble1 and most affectionate servant1 8,s4 ,,pepys40 ,to this letter ,mr4 ,millington made the following reply3-- ,coll4 ,magd4 ,camb4 ,sept4 the #cj1 #afic4 8,,honor',d ,,sir1 8,coming home from a journey on the #bhth instant at night1 ,i met with your letter which you were pleased to honour me with of the #bfth4 ,i am much troubled ,i was not at home in time for the post1 that ,i might as soon as possible put you out of your generous payne that you are in for the worthy ,mr4 ,newton4 ,i was1 ,i must confess1 very much surprised at the inquiry you were pleased to make by your nephew about the message that ,mr4 ,newton made the ground of his letter to you1 for ,i was very sure ,i never either received from you or delivered to him any such1 and therefore ,i went immediately to wayt upon him1 with a design to discourse him about the matter1 but1 he was out of town1 and since ,i have not seen him1 till upon the #bhth ,i met him at ,huntingdon1 where1 upon his own accord1 and before ,i had time to ask him any question1 he told me that he had writt to you a very odd letter1 at which he was much concerned2 added1 that it was in a distemper that much seized his head1 and that kept him awake for above five nights together1 which upon occasion he desired ,i would represent to you1 and beg your pardon1 he being very much ashamed1 he should be so rude to a person for whom he hath so great an honour4 ,he is now very well1 and1 though ,i fear he is under some small degree of melancholy1 yet ,i think there is no reason to suspect it hath at all touched his understanding1 and ,i hope never will2 and so ,i am sure all ought to wish that love learning or the honour of our nation1 which it is a sign how much it is looked after1 when such a person as ,mr4 ,newton lyes so neglected by those in power4 ,and thus1 honoured sir1 ,i have made you acquainted with all ,i know of the cause of such inconsistencys in the letter of so excellent a person2 and ,i hope it will remove the doubts and fears you are1 with so much compassion and publickness of spirit1 pleased to entertain about ,mr4 ,newton2 but if ,i should have been wanting in any thing tending to the more full satisfaction1 ,i shall1 upon the least notice1 endeavour to amend it with all gratitude and truth4 ,honored sir1 your most faithfull and most obedient servant1 8,,joh4 ,,millington40 ,mr4 ,pepys was perfectly satisfied with this answer1 as appears from the following letter3-- ,october #c;d1 #afic4 8,,sir1 8,you have delivered me from a fear that indeed gave me much trouble1 and from my very heart ,i thank you for it2 an evil to ,mr4 ,newton being what every good man must feel for his own sake as well as his4 ,god grant it may stopp here4 ,and for the kind reflection hee has since made upon his letter to mee1 ,i dare not take upon mee to judge what answer ,i should make him to it1 or whether any or no2 and therefore pray that you will bee pleased either to bestow on mee what directions you see fitt for my own guidance towards him in it1 or to say to him in my name1 but your own pleasure1 whatever you think may be most welcome to him upon it1 and most expressive of my regard and affectionate esteem of him1 and concernment for him4 99 99 99 ,dear sir1 your most humble and most faithful servant1 8,s4 ,,pepys40 ,it does not appear from the memoirs of ,mr4 ,pepys whether he ever returned any answer to the letter of ,mr4 ,newton which occasioned this correspondence2 but we find that in less than two months after the date of the preceding letter1 an opportunity occurred of introducing to him a ,mr4 ,smith1 who wished to have his opinion on some problem in the doctrine of chances4 ,this letter from ,pepys is dated ,november #bb;d1 #afic4 ,sir ,isaac replied to it on the #bfth ,november1 and wrote to ,pepys again on the #afth ,december1 #afic2 and in both these letters he enters fully into the discussion of the mathematical question which had been submitted to his judgment4#hj ,it is obvious1 from ,newton's letter to ,mr4 ,pepys1 that the subject of his receiving some favour from the government had been a matter of anxiety with himself1 and of discussion among his friends4#ha ,mr4 ,millington was no doubt referring to this anxiety1 when he represents ,newton as an honour to the nation1 and expresses his surprise 8that such a person should lye so neglected by those in power40 ,and we find the same subject distinctly referred to in two letters written to ,mr4 ,locke during the preceding year4 ,in one of these1 dated ,january #bfth1 #afia-b1 he says1 8,being fully convinced that ,mr4 ,montague1 upon an old grudge which ,i thought had been worn out1 is false to me1 ,i have done with him1 and intend to sit still1 unless my ,lord ,monmouth be still my friend40 ,mr4 ,locke seems to have assured him of the continued friendship of this nobleman1 and ,mr4 ,newton1 still referring to the same topic1 in a letter dated ,february #afth1 #afia-b1 remarks1 8,i am very glad ,lord ,monmouth is still my friend1 but intend not to give his lordship and you any farther trouble4 ,my inclinations are to sit still40 ,in a later letter to ,mr4 ,locke1 dated ,september1 #afic1 and given below1 he asks his pardon for saying or thinking that there was a design to sell him an office4 ,in these letters ,mr4 ,newton no doubt referred to some appointment in ,london which he was solicitous to obtain1 and which ,mr4 ,montague and his other friends may have failed in procuring4 ,this opinion is confirmed by the letter of ,mr4 ,montague announcing to him his appointment to the wardenship of the mint1 in which he says that he is very glad he can at last give him good proof of his friendship4 ,in the same month in which ,newton wrote to ,mr4 ,pepys1 we find him in correspondence with ,mr4 ,locke4 ,displeased with his opinions respecting innate ideas1 he had rashly stated that they struck at the root of all morality2 and that he regarded the author of such doctrines as a ,hobbist4 ,upon reconsidering these opinions1 he addressed the following remarkable letter to ,locke1 written three days after his letter to ,mr4 ,pepys1 and consequently during the illness under which he then laboured4 8,,sir1 8,being of opinion that you endeavoured to embroil me with women1 and by other means1 ,i was so much affected with it1 as that when one told me you were sickly and would not live1 ,i answered1 'twere better if you were dead4 ,i desire you to forgive me this uncharitableness2 for ,i am now satisfied that what you have done is just1 and ,i beg your pardon for my having hard thoughts of you for it1 and for representing that you struck at the root of morality1 in a principle you laid in your book of ideas1 and designed to pursue in another book1 and that ,i took you for a ,hobbist4#hb ,i beg your pardon also for saying or thinking that there was a design to sell me an office1 or to embroil me4--,i am your most humble and unfortunate servant1 8,,is4 ,,newton4 8,at the ,bull1 in ,shoreditch1 ,london1 ,sept4 #afth1 #afic40 ,to this letter ,locke returned the following answer1 so nobly distinguished by philosophical magnanimity and ,christian charity3-- ,oates1 ,oct4 #eth1 #afic4 8,,sir1 8,i have been1 ever since ,i first knew you1 so entirely and sincerely your friend1 and thought you so much mine1 that ,i could not have believed what you tell me of yourself had ,i had it from anybody else4 ,and1 though ,i cannot but be mightily troubled that you should have had so many wrong and unjust thoughts of me1 yet next to the return of good offices1 such as from a sincere good-will ,i have ever done you1 ,i receive your acknowledgment of the contrary as the kindest thing you have done me1 since it gives me hopes ,i have not lost a friend ,i so much valued4 ,after what your letter expresses1 ,i shall not need to say any thing to justify myself to you4 ,i shall always think your own reflection on my carriage1 both to you and all mankind1 will sufficiently do that4 ,instead of that1 give me leave to assure you that ,i am more ready to forgive you than you can be to desire it2 and ,i do it so freely and fully1 that ,i wish for nothing more than the opportunity to convince you that ,i truly love and esteem you1 and that ,i have the same good-will for you as if nothing of this had happened4 ,to confirm this to you more fully1 ,i should be glad to meet you any where1 and the rather1 because the conclusion of your letter makes me apprehend it would not be wholly useless to you4 ,but whether you think it fit or not1 ,i leave wholly to you4 ,i shall always be ready to serve you to my utmost1 in any way you shall like1 and shall only need your commands or permission to do it4 8,my book is going to press for a second edition2 and1 though ,i can answer for the design with which ,i write it1 yet1 since you have so opportunely given me notice of what you have said of it1 ,i should take it as a favour if you would point out to me the places that gave occasion to that censure1 that1 by explaining myself better1 ,i may avoid being mistaken by others1 or unawares doing the least prejudice to truth or virtue4 ,i am sure you are so much a friend to them both1 that1 were you none to me1 ,i could expect this from you4 ,but ,i cannot doubt but you would do a great deal more than this for my sake1 who1 after all1 have all the concern of a friend for you1 wish you extremely well1 and am1 without compliment1 c40#hc ,to this letter ,newton made the following reply3-- 8,,sir1 8,the last winter1 by sleeping too often by my fire1 ,i got an ill habit of sleeping2 and a distemper1 which this summer has been epidemical1 put me farther out of order1 so that when ,i wrote to you1 ,i had not slept an hour a night for a fortnight together1 and for five days together not a wink4 ,i remember ,i wrote to you1 but what ,i said of your book ,i remember not4 ,if you please to send me a transcript of that passage1 ,i will give you an account of it if ,i can4--,i am your most humble servant1 8,,is4 ,,newton4 8,cambridge1 ,oct4 #eth1 #afic40 ,although the first of these letters evinces the existence of a nervous irritability which could not fail to arise from want of appetite and of rest1 yet it is obvious that its author was in the full possession of his mental powers4 ,the answer of ,mr4 ,locke1 indeed1 is written upon that supposition2 and it deserves to be remarked1 that ,mr4 ,dugald ,stewart1 who first published a portion of these letters1 never imagines for a moment that ,newton was labouring under any mental alienation4 ,the opinion entertained by ,laplace1 that ,newton devoted his attention to theology only in the latter part of his life1 may be considered as deriving some countenance from the fact1 that the celebrated general scholium at the end of the second edition of the ,principia1 published in #agac1 did not appear in the first edition of that work4 ,this argument has been ably controverted by ,dr4 ,j4 ,c4 ,gregory of ,edinburgh1 on the authority of a manuscript of ,newton1 which seems to have been transmitted to his ancestor1 ,dr4 ,david ,gregory1 between the years #afhg and #afih4 ,this manuscript1 which consists of twelve folio pages in ,newton's handwriting1 contains1 in the form of additions and scholia to some propositions in the third book of the ,principia1 an account of the opinions of the ancient philosophers on gravitation and motion1 and on natural theology1 with various quotations from their works4 ,attached to this manuscript are three very curious paragraphs4 ,the first two appear to have been the original draught of the general scholium already referred to2 and the third relates to the subject of an ethereal medium1 respecting which he maintains an opinion diametrically opposite to that which he afterward published at the end of his ,optics4#hd ,the first paragraph expresses nearly the same ideas as some sentences in the scholium beginning 8,deus summus est ens ternum1 infinitum1 absolute perfectum20#he and it is remarkable that the second paragraph is found only in the third edition of the ,principia1 which appeared in #agbf1 the year before ,newton's death4 ,in the middle of the year #afid1 about the time when our author is said to be beginning to understand the ,principia1 we find him occupied with the difficult and profound subject of the lunar theory4 ,in order to procure observations for verifying the equations which he had deduced from the theory of gravity1 he paid a visit to ,flamstead1 at the ,royal ,observatory of ,greenwich1 on the #ast ,september1 #afid1 when he received from him a series of lunar observations4 ,on the #gth of ,october he wrote to ,flamstead that he had compared the observations with his theory1 and had satisfied himself that by both together 8the moon's theory may be reduced to a good degree of exactness1 perhaps to the exactness of two or three minutes40 ,he wrote him again on the #bdth ,october1 and the correspondence was continued till #afih1 ,newton making constant application for observations to compare with his theory of the planetary motions2 while ,flamstead1 not sufficiently aware of the importance of the inquiry1 received his requests as if they were idle intrusions in which the interests of science were but slightly concerned4#hf ,in reviewing the details which we have now given respecting the health and occupations of ,newton from the beginning of #afib till #afie1 it is impossible to draw any other conclusion than that he possessed a sound mind1 and was perfectly capable of carrying on his mathematical1 his metaphysical1 and his astronomical inquiries4 ,his friend and admirer1 ,mr4 ,pepys1 residing within fifty miles of ,cambridge1 had never heard of his being attacked with any illness till he inferred it from the letter to himself written in ,september1 #afic4 ,mr4 ,millington1 who lived in the same university1 had been equally unacquainted with any such attack1 and1 after a personal interview with ,newton1 for the express purpose of ascertaining the state of his health1 he assures ,mr4 ,pepys 8that he is very well1--that he fears he is under some small degree of melancholy1 but that there is no reason to suspect that it hath at all touched his understanding40 ,during this period of bodily indisposition1 his mind1 though in a state of nervous irritability1 and disturbed by want of rest1 was capable of putting forth its highest powers4 ,at the request of ,dr4 ,wallis he drew up an example of one of his propositions on the quadrature of curves in second fluxions4 ,he composed1 at the desire of ,dr4 ,bentley1 his profound and beautiful letters on the existence of the ,deity4 ,he was requested by ,locke to reconsider his opinions on the subject of innate ideas2 and we find him grappling with the difficulties of the lunar theory4 ,but with all these proofs of a vigorous mind1 a diminution of his mental powers has been rashly inferred from the cessation of his great discoveries1 and from his unwillingness to enter upon new investigations4 ,the facts1 however1 here assumed are as incorrect as the inference which is drawn from them4 ,the ambition of fame is a youthful passion1 which is softened1 if not subdued1 by age4 ,success diminishes its ardour1 and early pre-eminence often extinguishes it4 ,before the middle period of life ,newton was invested with all the insignia of immortality2 but endowed with a native humility of mind1 and animated with those hopes which teach us to form an humble estimate of human greatness1 he was satisfied with the laurels which he had won1 and he sought only to perfect and complete his labours4 ,his mind was principally bent on the improvement of the ,principia2 but he occasionally diverged into new fields of scientific research1--he solved problems of great difficulty which had been proposed to try his strength1--and he devoted much of his time to profound inquiries in chronology and in theological literature4 ,the powers of his mind were therefore in full requisition2 and1 when we consider that he was called to the discharge of high official functions which forced him into public life1 and compelled him to direct his genius into new channels1 we can scarcely be surprised that he ceased to produce any original works on abstract science4 ,in the direction of the affairs of the mint1 and of the ,royal ,society1 to which we shall now follow him1 he found ample occupation for his time2 while the leisure of his declining years was devoted to those exalted studies in which philosophy yields to the supremacy of faith1 and hope administers to the aspirations of genius4 ,,chapter ,,xiv4 ,no ,mark of ,national ,gratitude conferred upon ,newton--,friendship between him and ,charles ,montague1 afterward ,earl of ,halifax--,mr4 ,montague appointed ,chancellor of the ,exchequer in #afid--;,he resolves upon a ,recoinage--,nominates ,mr4 ,newton ,warden of the ,mint in #afie-- ,mr4 ,newton appointed ,master of the ,mint in #afii--,notice of the ,earl of ,halifax--,mr4 ,newton elected ,associate of the ,academy of ,sciences in #afii--,member for ,cambridge in #agja--;and ,president of the ,royal ,society in #agjc--,queen ,anne confers upon him the ,honour of ,knighthood in #agje--,second ,edition of the ,principia1 edited by ,cotes--,his ,conduct respecting ,mr4 ,ditton's ,method of finding the ,longitude4 ,hitherto we have viewed ,newton chiefly as a philosopher leading a life of seclusion within the walls of a college1 and either engaged in the duties of his professorship1 or ardently occupied in mathematical and scientific inquiries4 ,he had now reached the fifty-third year of his age1 and while those of his own standing at the university had been receiving high appointments in the church1 or lucrative offices in the state1 he still remained without any mark of the respect or gratitude of his country4 ,all ,europe indeed had been offering incense to his name1 and ,englishmen themselves boasted of him as the pride of their country and the ornament of their species1 but he was left in comparative poverty1#hg with no other income than the salary of his professorship1 eked out with the small rental of his paternal inheritance4 ,such disregard of the highest genius1 dignified by the highest virtue1 could have taken place only in ,england1 and we should have ascribed it to the turbulence of the age in which he lived1 had we not seen1 in the history of another century1 that the successive governments which preside over the destinies of our country have never been able either to feel or to recognise the true nobility of genius4 ,among his friends at ,cambridge ,newton had the honour of numbering ,charles ,montague1 grandson of ,henry ,earl of ,manchester1 a young man of high promise1 and every way worthy of his friendship4 ,though devoted to literary pursuits1 and twenty years younger than ,newton1 he cherished for the philosopher all the veneration of a disciple1 and his affection for him gathered new strength as he rose to the highest honours and offices of the state4 ,in the year #afhd we find him co-operating with ,newton in the establishment of a philosophical society at ,cambridge2 but though both of them had made personal application to different individuals to become members1 yet the plan failed1 from the want1 as ,newton expresses it1 of persons willing to try experiments4 ,mr4 ,montague sat along with ,newton in the convention parliament1 and such were the powers which he displayed in that assembly as a public speaker1 that he was appointed a commissioner of the treasury1 and soon afterward a privy counsellor4 ,in these situations his talents and knowledge of business were highly conspicuous1 and in #afid he was appointed chancellor of the exchequer4 ,the current coin of the nation having been adulterated and debased1 one of his earliest designs was to recoin it and restore it to its intrinsic value4 ,this scheme1 however1 met with great opposition4 ,it was characterized as a wild project1 unsuitable to a period of war1 as highly injurious to the interests of commerce1 and as likely to sap the foundation of the government4 ,but he had weighed the subject too deeply1 and had intrenched himself behind opinions too impartial and too well-founded1 to be driven from a measure which the best interests of his country seemed to require4 ,the persons whom ,mr4 ,montague had consulted about the recoinage were ,newton1 ,locke1 and ,halley1 and in consequence of ,mr4 ,overton1 the warden of the mint1 having been appointed a commissioner of customs1 he embraced the opportunity which was thus offered of serving his friend and his country by recommending ,newton to that important office4 ,the notice of this appointment was conveyed in the following letter to ,newton4 ,london1 #aith ,march1 #afie4 8,,sir1 8,i am very glad that1 at last1 ,i can give you a good proof of my friendship1 and the esteem the king has of your merits4 ,mr4 ,overton1 the warden of the mint1 is made one of the commissioners of the customs1 and the king has promised me to make ,mr4 ,newton warden of the mint4 ,the office is the most proper for you4 ',tis the chief office in the mint1 'tis worth five or six hundred pounds per annum1 and has not too much business to require more attendance than you can spare4 ,i desire that you will come up as soon as you can1 and ,i will take care of your warrant in the mean time4 ,let me see you as soon as you come to town1 that ,i may carry you to kiss the king's hand4 ,i believe you may have a lodging near me4--,i am1 c4 ,,charles ,,montague40 ,in this new situation the mathematical and chymical knowledge of our author was of great service to the nation1 and he became eminently useful in carrying on the recoinage1 which was completed in the short space of two years4 ,in the year #afii1 he was promoted to the mastership of the mint1--an office which was worth twelve or fifteen hundred pounds per annum1 and which he held during the remainder of his life4 ,in this situation he wrote an official report on the ,coinage1 which has been published2 and he drew up a table of ,assays of ,foreign ,coins1 which is printed at the end of ,dr4 ,arbuthnot's ,tables of ,ancient ,coins1 ,weights1 and ,measures1 which appeared in #agbg4 ,while our author filled the inferior office of warden of the mint1 he retained his professorship at ,cambridge2 but upon his promotion in #afii1 he appointed ,mr4 ,whiston to be his deputy1 with all the emoluments of the office2 and when he resigned the chair in #agjc1 he succeeded in getting him nominated his successor4 ,the appointment of ,newton to the mastership of the mint must have been peculiarly gratifying to the ,royal ,society1 and it was probably from a feeling of gratitude to ,mr4 ,montague1 as much as from a regard for his talents1 that this able statesman was elected president of that learned body on the #cjth ,november1 #afie4 ,this office he held for three years1 and on the #cjth ,january1 #afig1 ,newton had the satisfaction of addressing to him his solution of the celebrated problems proposed by ,john ,bernouilli4 ,this accomplished nobleman was created ,earl of ,halifax in #agjj1 and after the death of his first wife he conceived a strong attachment for ,mrs4 ,catharine ,barton1 the widow of ,colonel ,barton1 and the niece of ,newton4 ,this lady was young1 gay1 and beautiful1 and though she did not escape the censures of her contemporaries1 she was regarded by those who knew her as a woman of strict honour and virtue4 ,we are not acquainted with the causes which prevented her union with the ,earl of ,halifax1 but so great was the esteem and affection which he bore her1 that in the will in which he left #ajjl4 to ,mr4 ,newton1 he bequeathed to his niece a very large portion of his fortune4 ,this distinguished statesman died in #agae1 in the fifty-fourth year of his age4 ,himself a poet and an elegant writer1 he was the liberal patron of genius1 and he numbered among his intimate friends ,congreve1 ,halley1 ,prior1 ,tickell1 ,steele1 and ,pope4 ,his conduct to ,newton will be for ever remembered in the annals of science4 ,the sages of every nation and of every age will pronounce with affection the name of ,charles ,montague1 and the persecuted science of ,england will continue to deplore that he was the first and the last ,english minister who honoured genius by his friendship and rewarded it by his patronage4 ,the elevation of ,mr4 ,newton to the highest offices in the mint was followed by other marks of honour4 ,the ,royal ,academy of ,sciences at ,paris having been empowered by a new charter granted in #afii1 to admit a very small number of foreign associates1 ,newton was elected a member of that distinguished body4 ,in the year #agja1 on the assembling of a new parliament1 he was re-elected one of the members for the ,university of ,cambridge4#hh ,in #agjc he was chosen ,president of the ,royal ,society of ,london1 and he was annually re-elected to this office during the remaining twenty-five years of his life4 ,on the #afth of ,april1 #agje1 when ,queen ,anne was living at the royal residence of ,newmarket1 she went with ,prince ,george of ,denmark and the rest of the court to visit the ,university of ,cambridge4 ,after the meeting of the ,regia ,consilia1 her majesty held a court at ,trinity ,lodge1 the residence of ,dr4 ,bentley1 then master of ,trinity2 where the honour of knighthood was conferred upon ,mr4 ,newton1 ,mr4 ,john ,ellis1 the vice-chancellor1 and ,mr4 ,james ,montague1 the university counsel4#hi ,on the dissolution of the parliament1 which took place in #agje1 ,sir ,isaac was again a candidate for the representation of the ,university1 but notwithstanding the recent expression of the royal favour1 he lost his election by a very great majority4#ij ,this singular result was perhaps owing to the loss of that personal influence which his residence in the university could not fail to command1 though it is more probable that the ministry preferred the candidates of a more obsequious character1 and that the electors looked for advantages which ,sir ,isaac ,newton was not able to obtain for them4 ,although the first edition of the ,principia had been for some time sold off1 and copies of it had become extremely rare1 yet ,sir ,isaac's attention was so much occupied with his professional avocations that he could not find leisure for preparing a new edition4 ,dr4 ,bentley1 who had repeatedly urged him to this task1 at last succeeded1 by engaging ,roger ,cotes1 ,plumian ,professor of ,astronomy at ,cambridge1 to superintend its publication at the university press4 ,in ,june1 #agji1 ,sir ,isaac committed this important trust to his young friend2 and about the middle of ,july he promised to send him in the course of a fortnight his own revised copy of the work4 ,business1 however1 seems to have intervened1 and ,mr4 ,cotes was obliged to remind ,sir ,isaac of his promise1 which he did in the following letter3-- ,cambridge1 ,aug4 #ahth1 #agji4 8,,sir1 8,the earnest desire ,i have to see a new edition of your ,principia makes me somewhat impatient till we receive your copy of it1 which you were pleased to promise me about the middle of last month you would send down in about a fortnight's time4 ,i hope you will pardon me for this uneasiness1 from which ,i cannot free myself1 and for giving you this trouble to let you know it4 ,i have been so much obliged by yourself and by your book1 that 7,i desire you to believe me7 ,i think myself bound in gratitude to take all the care ,i possibly can that it shall be correct4--,your obliged servant1 8,,roger ,,cotes4 8,for ,sir ,isaac ,newton1 at his house in ,jermyn-street1 near ,st4 ,james's ,church1 ,westminster40 ,this was the first letter of that celebrated correspondence1 consisting of nearly three hundred letters1 in which ,sir ,isaac and ,mr4 ,cotes discussed the various improvements which were thought necessary in a new edition of the ,principia4 ,this valuable collection of letters is preserved in the library of ,trinity ,college2 and we cannot refrain from repeating the wish expressed by ,dr4 ,monk1 8that one of the many accomplished ,newtonians who are resident in that society would favour the world by publishing the whole collection40 ,when the work was at last printed1 ,mr4 ,cotes expressed a wish that ,dr4 ,bentley should write the preface to it1 but it was the opinion both of ,sir ,isaac and ,dr4 ,bentley that the preface should come from the pen of ,mr4 ,cotes himself4 ,this he accordingly undertook2 but previous to its execution he addressed the following letter to ,dr4 ,bentley1 in order to learn from ,sir ,isaac the particular view with which it should be written4 ,march #ajth1 #agab-ac4 8,,sir1 8,i received what you wrote to me in ,sir ,isaac's letter4 ,i will set about the index in a day or two4 ,as for the preface1 ,i should be glad to know from ,sir ,isaac with what view he thinks proper to have it written4 ,you know the book has been received abroad with some disadvantage1 and the cause of it may be easily guessed at4 ,the ,commercium ,epistolicum1 lately published by order of the ,royal ,society1 gives such indubitable proofs of ,mr4 ,leibnitz's want of candour1 that ,i shall not scruple in the least to speak out the full truth of the matter1 if it be thought convenient4 ,there are some pieces of his looking this way which deserve a censure1 as his ,tentamen de motuum clestium causis4 ,if ,sir ,isaac is willing that something of this nature may be done1 ,i should be glad if1 while ,i am making the index1 he would consider of it1 and put down a few notes of what he thinks most material to be insisted on4 ,this ,i say upon supposition that ,i write the preface myself4 ,but ,i think it will be much more advisable that you1 or he1 or both of you should write it while you are in town4 ,you may depend upon it ,i will own it1 and defend it as well as ,i can1 if hereafter there be occasion4--,i am sir1 c40 ,we are not acquainted with the instructions which were given to ,mr4 ,cotes in consequence of this application2 but it appears from the preface itself1 which contains a long and able summary of the ,newtonian philosophy1 that ,sir ,isaac had prohibited any personal reference to the conduct of ,leibnitz4 ,the general preface is dated #abth ,may1 #agac1 and in a subsidiary preface of only a few lines1 dated ,march #bhth1 #agac1 ,sir ,isaac mentions the leading alterations which had been made in this edition4 ,the determination of the forces by which bodies may revolve in given orbits was simplified and enlarged4 ,the theory of the resistance of fluids was more accurately investigated1 and confirmed by new experiments4 ,the theory of the moon and the precession of the equinoxes were more fully deduced from their principles2 and the theory of comets was confirmed by several examples of their orbits more accurately computed4 ,in the year #agad1 several captains and owners of merchant vessels petitioned the ,house of ,commons to consider the propriety of bringing in a bill to reward inventions for promoting the discovery of the longitude at sea4 ,a committee was appointed to investigate the subject1 and ,mr4 ,ditton and ,mr4 ,whiston1 having thought of a new method of finding the longitude1 submitted it to the committee4 ,four members of the ,royal ,society1 viz4 ,sir ,isaac ,newton1 ,dr4 ,halley1 ,mr4 ,cotes1 and ,dr4 ,clarke1 were examined on the subject1 along with ,mr4 ,ditton and ,mr4 ,whiston4 ,the last three of these philosophers stated their opinions verbally4 ,mr4 ,cotes considered the proposed scheme as correct in theory and on shore1 and both he and ,dr4 ,halley were of opinion that expensive experiments would be requisite4 ,newton1 when called upon for his opinion1 read the following memorandum1 which deserves to be recorded4 8,for determining the longitude at sea there have been several projects1 true in theory1 but difficult to execute4 8#a4 ,one is by a watch to keep time exactly2 but by reason of the motion of the ship1 the variation of heat and cold1 wet or dry1 and the difference of gravity in different latitudes1 such a watch hath not yet been made4 8#b4 ,another is by the eclipses of ,jupiter's satellites2 but by reason of the length of telescopes requisite to observe them1 and the motion of a ship at sea1 those eclipses cannot yet be there observed4 8#c4 ,a third is by the place of the moon2 but her theory is not yet exact enough for that purpose2 it is exact enough to determine the longitude within two or three degrees1 but not within a degree4 8#d4 ,a fourth is ,mr4 ,ditton's project1 and this is rather for keeping an account of the longitude at sea than for finding it1 if at any time it should be lost1 as it may easily be in cloudy weather4 ,how far this is practicable1 and with what charge1 they that are skilled in sea affairs are best able to judge4 ,in sailing by this method1 whenever they are to pass over very deep seas1 they must sail due east or west2 they must first sail into the latitude of the next place to which they are going beyond it1 and then keep due east or west till they come at that place4 ,in the first three ways there must be a watch regulated by a spring1 and rectified every visible sunrise and sunset1 to tell the hour of the day or night4 ,in the fourth way such a watch is not necessary4 ,in the first way there must be two watches1 this and the other above mentioned4 ,in any of the first three ways1 it may be of some service to find the longitude within a degree1 and of much more service to find it within forty minutes1 or half a degree if it may1 and the success may deserve rewards accordingly4 ,in the fourth way1 it is easier to enable seamen to know their distance and bearing from the shore #dj1 #fj1 or #hj miles off1 than to cross the seas2 and some part of the reward may be given when the first is performed on the coast of ,great ,britain for the safety of ships coming home2 and the rest when seamen shall be enabled to sail to an assigned remote harbour without losing their longitude if it may be40 ,the committee brought up their report on the #aath ,june1 and recommended that a bill should be introduced into parliament for the purpose of rewarding inventions or discoveries connected with the determination of the longitude4 ,the bill passed the ,house of ,commons on the #c;d ,july1 and was agreed to by the ,lords on the #hth of the same month4#ia ,in giving an account of this transaction1#ib ,mr4 ,whiston states1 that nobody understood ,sir ,isaac's paper1 and that after sitting down he obstinately kept silence1 though he was much pressed to explain himself more distinctly4 ,at last1 seeing that the scheme was likely to be rejected1 ,whiston ventured to say that ,sir ,isaac did not wish to explain more through fear of compromising himself1 but that he really approved of the plan4 ,sir ,isaac1 he goes on to say1 repeated word for word what ,whiston had said4 ,this is the part of ,mr4 ,newton's conduct which ,m4 ,biot has described as puerile1 and 8tending to confirm the fact of the aberration of his intellect in #afic40 ,before we can admit such a censure we must be satisfied with the correctness of ,whiston's statement4 ,newton's paper is perfectly intelligible1 and we may easily understand how he might have approved of ,mr4 ,ditton's plan as ingenious and practicable under particular circumstances1 though he did not think it of that paramount importance which would have authorized the ,house of ,commons to distinguish it by a parliamentary reward4 ,the conflict between public duty and a disposition to promote the interests of ,mr4 ,whiston and ,mr4 ,ditton was no doubt the cause of that embarrassment of manner which the former of these mathematicians has so unkindly brought before the public4 ,,chapter ,,xv4 ,respect in which ,newton was held at the ,court of ,george ,i4--,the ,princess of ,wales delighted with his ,conversation--,leibnitz endeavours to prejudice the ,princess against ,sir ,isaac and ,locke-- ,controversy occasioned by his ,conduct--,the ,princess obtains a ,manuscript ,abstract of his ,system of ,chronology--,the ,abb ,conti is1 at her request1 allowed to take a ,copy of it on the promise of ,secresy--,he prints it surreptitiously in ,french1 accompanied with a ,refutation by ,m4 ,freret--,sir ,isaac's ,defence of his ,system--,father ,souciet attacks it--and is answered by ,dr4 ,halley--,sir ,isaac's larger ,work on ,chronology published after his ,death--,opinions respecting it-- ,sir ,isaac's ,paper on the ,form of the most ancient ,year4 ,on the accession of ,george ,i4 to the ,british throne in #agad1 ,sir ,isaac ,newton became an object of interest at court4 ,his high situation under government1 his splendid reputation1 his spotless character1 and1 above all1 his unaffected piety attracted the attention of the ,princess of ,wales1 afterward queen-consort to ,george ,,ii4 ,this lady1 who possessed a highly cultivated mind1 derived the greatest pleasure from conversing with ,newton and corresponding with ,leibnitz4 ,in all her difficulties1 she received from ,sir ,isaac that information and assistance which she had elsewhere sought in vain1 and she was often heard to declare in public that she thought herself fortunate in living at a time which enabled her to enjoy the conversation of so great a genius4 ,but while ,newton was thus esteemed by the house of ,hanover1 ,leibnitz1 his great rival1 endeavoured to weaken and undermine his influence4 ,in his correspondence with the princess1 he represented the ,newtonian philosophy1 not only as physically false1 but as injurious to the interests of religion4 ,he asserted that natural religion was rapidly declining in ,england1 and he supported this position by referring to the works of ,locke1 and to the beautiful and pious sentiments contained in the #bhth query at the end of the ,optics4 ,he represented the principles of these great men as precisely the same with those of the materialists1 and thus endeavoured to degrade the character of ,english philosophers4 ,these attacks of ,leibnitz became subjects of conversation at court1 and when they reached the ear of the king1 his majesty expressed his expectation that ,sir ,isaac ,newton would draw up a reply4 ,he accordingly entered the lists on the mathematical part of the controversy1 and left the philosophical part of it to ,dr4 ,clarke1 who was a full match for the ,german philosopher4 ,the correspondence which thus took place was carefully perused by the princess1 and from the estimation in which ,sir ,isaac continued to be held1 we may infer that the views of the ,english philosopher were not very remote from her own4 ,when ,sir ,isaac was one day conversing with her royal highness on some points of ancient history1 he was led to mention to her1 and to explain1 a new system of chronology which he composed during his residence at ,cambridge1 where he was in the habit1 as he himself expresses it1 8of refreshing himself with history and chronology when he was weary with other studies40 ,the princess was so much pleased with his ingenious system1 that she subsequently1 in the year #agah1 sent a message by the ,abb ,conti to ,sir ,isaac1 requesting him to speak with her1 and she1 on this occasion1 requested a copy of the interesting work which contained his system of chronology4 ,sir ,isaac informed her that it existed merely in separate papers1 which were not only in a state of confusion1 but which contained a very imperfect view of the subject1 and he promised1 in a few days1 to draw up an abstract of it for her own private use1 and on the condition that it should not be communicated to any other person4 ,some time after the princess received the manuscript1 she requested that the ,abb ,conti might be allowed to have a copy of it4 ,sir ,isaac granted this request1 and the ,abb was informed that he received a copy of the manuscript with ,sir ,isaac's leave1 and at the princess's request1 and that it was to be kept secret4#ic ,the manuscript which was thus rashly put into the hands of a foreigner was entitled 8,a ,short ,chronicle from the ,first ,memory of ,things in ,europe to the ,conquest of ,persia by ,alexander the ,great40 ,it consists of about twenty-four quarto printed pages1#id with an introduction of four pages1 in which ,sir ,isaac states that he 8does not pretend to be exact to a year1 that there may be errors of five or ten years1 and sometimes twenty1 but not much above40 ,the ,abb ,conti kept his promise of secrecy during his residence in ,england1 but he no sooner reached ,paris than he communicated it to ,m4 ,freret1 a learned antiquarian1 who not only translated it1 but drew up observations upon it for the purpose of refuting some of its principal results4 ,sir ,isaac was unacquainted with this transaction till he was informed of it by the ,french bookseller1 ,m4 ,cavalier1 who requested his leave to publish it1 and charged one of his friends in ,london to procure ,sir ,isaac's answer1 which was as follows3-- 8,i remember that ,i wrote a ,chronological index for a particular friend1 on condition that it should not be communicated4 ,as ,i have not seen the manuscript which you have under my name1 ,i know not whether it be the same4 ,that which ,i wrote was not at all done with design to publish it4 ,i intend not to meddle with that which hath been given you under my name1 nor to give any consent to the publishing of it4--,i am your very humble servant1 8,,isaac ,,newton4 8,london1 ,may #bgth1 #agbe1 ,o4 ,s40 ,before this letter was written1 viz4 on the #bast ,may1 the bookseller had received the royal privilege for printing the work2 and when it was completed1 he sent a copy in a present to ,sir ,isaac1 who received it on the #aath ,november1 #agbe4 ,it was entitled1 ,abreg de ,chronologie de ,m4 ,le ,chevalier ,newton1 fait par lui-meme1 et traduit sur le manuscript ,anglais1 and was accompanied with observations by ,m4 ,freret1#ie the object of which was to refute the leading points of the system4#if ,an advertisement was prefixed to it1 in which the bookseller defends himself for printing it without the author's leave1 on the ground that he had written three letters to obtain permission1 and had declared that he would take ,sir ,isaac's silence for consent4 ,when ,sir ,isaac received this work1 he drew up a paper entitled1 ,remarks on the ,observations made on a ,chronological ,index of ,sir ,isaac ,newton1 translated into ,french by the ,observator1 and published at ,paris1 which was printed in the ,philosophical ,transactions for #agbe4ig ,in this paper ,sir ,isaac gives a history of the transaction1--charges the ,abb ,conti with a breach of promise1 and blames the publisher for having asked his leave to print the translation without sending him a copy for his perusal1 without acquainting him with the name of the translator1 and without announcing his intention of printing along with it a refutation of the original4 ,the observations made by the translator against the conclusions deduced by the author were founded on an imperfect knowledge of ,sir ,isaac's system2 and they are so specious1 that ,halley himself confesses that he was at first prejudiced in favour of the observations1 taking the calculations for granted1 and not having seen ,sir ,isaac's work4 ,to all the observations of ,m4 ,freret ,sir ,isaac returned a triumphant answer4 ,this presumptuous antiquary had ventured to state at the end of his observations1 8that he believed he had stated enough concerning the epochs of the ,argonauts1 and the length of generations1 to make people cautious about the rest2 for these are the two foundations of all this new system of chronology40 ,he founds his arguments against the epochs of the ,argonauts1 as fixed by our author1 on the supposition that ,sir ,isaac places the vernal equinox at the time of the ,argonautic expedition in the middle of the sign of ,aries1 whereas ,sir ,isaac places it in the middle of the constellation1--a point corresponding with the middle of the back of ,aries1 or #h from the first star of ,aries4 ,this position of the colure is assigned on the authority of ,eudoxus1 as given by ,hipparchus1 who says that the colure passed over the back of ,aries4 ,setting out with this mistake1 ,m4 ,freret concludes that the ,argonautic expedition took place #ecb years earlier than ,sir ,isaac made it4 ,his second objection to the new system relates to the length of generations1 which he says is made only #ah or #bj years4 ,sir ,isaac1 on the contrary1 reckons a generation at #cc years1 or #c generations at #ajj2 and it was the lengths of the reigns of kings that he made #ah or #bj years4 ,this deduction he founds on the reigns of #fd ,french kings4 ,now1 the ancient ,greeks and ,egyptians reckoned the length of a reign equal to that of a generation2 and it was by correcting this mistake1 and adopting a measure founded on fact1 that ,sir ,isaac placed the ,argonautic expedition forty-four years after the death of ,solomon1 and fixed some of the other points of his system4 ,this answer of ,sir ,isaac's to the objections of ,freret called into the field a fresh antagonist1 ,father ,souciet1 who published five dissertations on the new chronology4 ,these dissertations were written in a tone highly reprehensible2 and the friends of ,sir ,isaac1 being apprehensive that the manner in which his system was attacked would affect him more than the arguments themselves1 prevailed upon a friend to draw up an abstract of ,souciet's objections1 stripped of the 8extraordinary ornaments with which they were clothed40 ,the perusal of these objections had no other effect upon him than to convince him of the ignorance of their author2 and he was induced to read the entire work1 which produced no change in his opinion4 ,in consequence of these discussions1 ,sir ,isaac was prevailed upon to prepare his larger work for the press4 ,he had nearly completed it at the time of his death1 and it was published in #agbh1 under the title of ,the ,chronology of ,ancient ,kingdoms amended1 to which is prefixed a short ,chronicle1 from the first memory of ,things in ,europe to the ,conquest of ,persia by ,alexander the ,great4 ,it was dedicated to the queen by ,mr4 ,conduit1 and consists of six chapters3 #a4 ,on the ,chronology of the ,greeks2#ih #b4 ,of the ,empire of ,egypt2 #c4 ,of the ,assyrian ,empire2 #d4 ,of the two contemporary ,empires of the ,babylonians and ,medes2 #e4 ,a ,description of the ,temple of ,solomon2 #f4 ,of the ,empire of the ,persians4 ,the sixth chapter was not copied out with the other five1 which makes it doubtful whether or not it was intended for publication2 but as it was found among his papers1 and appeared to be a continuation of the same work1 it was thought right to add it to the other five chapters4#ii ,after the death of ,newton1 ,dr4 ,halley1 who had not yet seen the larger work1 felt himself called upon1 both as astronomer-royal and as the friend of the author1 to reply to the first and last dissertations of ,father ,souciet1 which were chiefly astronomical2 and in two papers printed in the ,philosophical ,transactions for #agbg1ajj he has done this in a most convincing and learned argument4 ,among the supporters of the views of ,newton1 we may enumerate ,dr4 ,reid1 ,nauze1 and some other writers2 and among its opponents1 ,m4 ,freret1 who left behind him a posthumous work on the subject1 ,m4 ,fourmond1 ,mr4 ,a4 ,bedford1 ,dr4 ,shuckford1 ,dr4 ,middleton1 ,whiston1 and the late ,m4 ,delambre4 ,the object of ,m4 ,fourmond is to show the uncertainty of the astronomical argument1 arising on the one hand from the vague account of the ancient sphere as given by ,hipparchus2 and1 on the other1 from the extreme rudeness of ancient astronomical observations4 ,delambre has taken a similar view of the subject3 he regards the observations of ancient astronomers as too incorrect to form the basis of a system of chronology2 and he maintains1 that if we admit the accuracy of the details in the sphere of ,eudoxus1 and suppose them all to belong to the same epoch1 all the stars which it contains ought at that epoch to be found in the place where they are marked1 and we might thence verify the accuracy1 and ascertain the state of the observations4 ,it follows1 however1 from such an examination1 that the sphere would indicate almost as many different epochs as it contains stars4 ,some of them even had not1 in the time of ,eudoxus1 arrived at the position which had been for a long time attributed to them1 and will not even reach it for three hundred years to come1 and on this account he considers it impossible to deduce any chronological conclusions from such a rude mass of errors4 ,but however well-founded these observations may be1 we agree in opinion with ,m4 ,daunou1#aja 8that they are not sufficient to establish a new system1 and we must regard the system of ,newton as a great fact in the history of chronological science1 and as confirming the observation of ,varro1 that the stage of history does not commence till the first ,olympiad40 ,among the chronological writings of ,sir ,isaac ,newton we must enumerate his letter to a person of distinction who had desired his opinion of the learned ,bishop ,lloyd's hypothesis concerning the form of the most ancient year4 ,this hypothesis was sent by the ,bishop of ,worcester to ,dr4 ,prideaux4 ,sir ,isaac remarks1 that it is filled with many excellent observations on the ancient year2 but he does not 8find it proved that any ancient nations used a year of twelve months and #cfj days without correcting it from time to time by the luminaries1 to make the months keep to the course of the moon1 and the year to the course of the sun1 and returns of the seasons and fruits of the earth40 ,after examining the years of all the nations of antiquity1 he concludes1 8that no other years are to be met with among the ancients but such as were either luni-solar1 or solar or lunar1 or the calendars of these years40 ,a practical year1 he adds1 of #cfj days is none of these4 ,the beginning of such a year would have run round the four seasons in seventy years1 and such a notable revolution would have been mentioned in history1 and is not to be asserted without proving it4#ajb ,,chapter ,,xvi4 ,theological ,studies of ,sir ,isaac--,their ,importance to ,christianity-- ,motives to which they have been ascribed--,opinions of ,biot and ,laplace considered--,his ,theological ,researches begun before his supposed ,mental ,illness--,the ,date of these ,works fixed--,letters to ,locke--,account of his ,observations on ,prophecy--,his ,historical ,account of two notable ,corruptions of ,scripture--,his ,lexicon ,propheticum--,his ,four ,letters to ,dr4 ,bentley--,origin of ,newton's ,theological ,studies--,analogy between the ,book of ,nature and that of ,revelation4 ,the history of the theological studies of ,sir ,isaac ,newton will ever be regarded as one of the most interesting portions of his life4 ,that he who among all the individuals of his species possessed the highest intellectual powers was not only a learned and profound divine1 but a firm believer in the great doctrines of religion1 is one of the proudest triumphs of the ,christian faith4 ,had he distinguished himself only by an external respect for the offices and duties of religion2 and had he left merely in his last words an acknowledgment of his faith1 his piety would have been regarded as a prudent submission to popular feeling1 and his last aspirations would have been ascribed to the decay or to the extinction of his transcendent powers4 ,but he had been a ,christian from his youth1 and though never intended for the church1 yet he interchanged the study of the ,scriptures with that of the laws of the material universe2 and from the examination of the works of the ,supreme ,creator he found it to be no abrupt transition to investigate the revelation of his will1 and to contemplate the immortal destinies of mankind4 ,but when the religious habits of ,sir ,isaac ,newton could not be ascribed to an ambition of popularity1 to the influence of weak health1 or to the force of professional impulse1 it became necessary for the apostles of infidelity to refer it to some extraordinary cause4 ,his supposed insanity was therefore eagerly seized upon by some as affording a plausible origin for his religious principles2 while others1 without any view of supporting the cause of skepticism1 ascribed his theological researches to the habits of the age in which he lived1 and to a desire of promoting political liberty1 by turning against the abetters of despotism those powerful weapons which the ,scriptures supplied4 ,the anxiety evinced by ,m4 de ,laplace to refer his religious writings to a late period of his life seems to have been felt also by ,m4 ,biot1 who has gone so far as to fix the very date of one of his most important works1 and thus to establish the suspicions of his colleague4 8,from the nature of the subject10#ajc says he1 8and from certain indications which ,newton seems to give at the beginning of his dissertation1 we may conjecture with probability that he composed it at the time when the errors of ,whiston1 and a work of ,dr4 ,clarke on the same subject1 drew upon them the attacks of all the theologians of ,england1 which would place the date between the years #agab and #agai4 ,it would then be truly a prodigy to remark1 that a man of from seventy-two to seventy-five years of age was able to compose1 rapidly1 as he leads us to believe1 so extensive a piece of sacred criticism1 of literary history1 and even of bibliography1 where an erudition the most vast1 the most varied1 and the most ready always supports an argument well arranged and powerfully combined4 99 99 99 ,at this epoch of the life of ,newton the reading of religious books had become one of his most habitual occupations1 and after he had performed the duties of his office1 they formed1 along with the conversation of his friends1 his principal amusement4 ,he had then almost ceased to care for the sciences1 and1 as we have already remarked1 since the fatal epoch of #afic1 he gave to the world only three really new scientific productions40 ,notwithstanding the prodigy which it involves1 ,m4 ,biot has adopted #agab-agai as the date of this critical dissertation2--it is regarded as the composition of a man of seventy-two or seventy-five2--the reading of religious works is stated to have become one of his most habitual occupations1 and such reading is said to have been one of his principal amusements2 and all this is associated with 8the fatal epoch of #afic10 as if his illness at that time had been the cause of his abandoning science and betaking himself to theology4 ,carrying on the same views1 ,m4 ,biot asks1 in reference to ,sir ,isaac's work on ,prophecy1 8,how a mind of the character and force of ,newton's1 so habituated to the severity of mathematical considerations1 so exercised in the observation of real phenomena1 and so well aware of the conditions by which truth is to be discovered1 could put together such a number of conjectures without noticing the extreme improbability of his interpretations from the infinite number of arbitrary postulates on which he has founded them80 ,we would apply the same question to the reasoning by which ,m4 ,biot fixes the date of the critical dissertation2 and we would ask how so eminent a philosopher could hazard such frivolous conjectures upon a subject on which he had not a single fact to guide his inquiries4 ,the obvious tendency1 though not the design1 of the conclusion at which he arrives is injurious to the memory of ,newton1 as well as to the interests of religion2 and these considerations might have checked the temerity of speculation1 even if it had been founded on better data4 ,the ,newtonian interpretation of the ,prophecies1 and especially that part which ,m4 ,biot characterizes as unhappily stamped with the spirit of prejudice1 has been adopted by men of the soundest and most unprejudiced minds2 and in addition to the moral and historical evidence by which it is supported1 it may yet be exhibited in all the fulness of demonstration4 ,but the speculation of ,biot respecting the date of ,newton's theological works was never maintained by any other person than himself1 and is capable of being disproved by the most incontrovertible evidence4 ,we have already seen1 in the extract from ,mr4 ,pryme's manuscript1 that previous to #afib1 when a shade is supposed to have passed over his gifted mind1 ,newton was well known by the appellation of an 8excellent divine10--a character which could not have been acquired without the devotion of many years to theological researches2 but1 important as this argument would have been1 we are fortunately not left to so general a defence4 ,the correspondence of ,newton with ,locke1 recently published by ,lord ,king1 places it beyond a doubt that he had begun his researches respecting the ,prophecies before the year #afia1--;before the forty-ninth year of his age1 and before the 8fatal epoch of #afic40 ,the following letter shows that he had previously discussed this subject with his friend3-- ,cambridge1 ,feb4 #g1 #afij-a4 8,,sir1 8,i am sorry your journey proved to so little purpose1 though it delivered you from the trouble of the company the day after4 ,you have obliged me by mentioning me to my friends at ,london1 and ,i must thank both you and my ,lady ,masham for your civilities at ,oates1 and for not thinking that ,i made a long stay there4 ,i hope we shall meet again in due time1 and then ,i should be glad to have your judgment upon some of my mystical fancies4 ,the ,son of ,man1 ,dan4 vii4 ,i take to be the same with the ,word of ,god upon the ,white ,horse in ,heaven1 ,apoc4 xii41 for both are to rule the nations with a rod of iron2 but whence are you certain that the ,ancient of ,days is ,christ8 ,does ,christ anywhere sit upon the throne8 ,if ,sir ,francis ,masham be at ,oates1 present1 ,i pray1 my service to him1 with his lady1 ,mrs4 ,cudworth1 and ,mrs4 ,masham4 ,dr4 ,covel is not in ,cambridge4--,i am your affectionate and humble servant1 8,,is4 ,,newton4 8,know you the meaning of ,dan4 x4 #ba4 ,there is none that holdeth with me in these things but ,mich4 the prince40 ,having thus determined the date of those investigations which constitute his observations on the prophecies of holy writ1 particularly the prophecies of ,daniel and the ,apocalypse1 we shall proceed to fix the latest date of his historical account of two notable corruptions of the ,scripture1 in a letter to a friend4 ,this work seems to have been a very early production of our author4 ,it was written in the form of a letter to ,mr4 ,locke1 and at that time ,sir ,isaac seems to have been anxious for its publication4 ,afraid1 however1 of being again led into a controversy1 and dreading the intolerance to which he might be exposed1 he requested ,mr4 ,locke1 who was at that time meditating a voyage to ,holland1 to get it translated into ,french1 and published on the ,continent4 ,having abandoned his design of visiting ,holland1 ,locke transmitted the manuscript1 without ,newton's name1 to his learned friend ,m4 ,le ,clerc1 in ,holland2 and it appears1 from a letter of ,le ,clerc's to ,locke1 that he must have received it before the #aath ,april1 #afia4 ,m4 ,le ,clerc delayed for a long time to take any steps regarding its publication2 but in a letter dated ,january #bjth1 #afib1 he announced to ,locke his intention of publishing the tract in ,latin4 ,when this plan was communicated to ,sir ,isaac1 he became alarmed at the risk of detection1 and resolved to stop the publication of his manuscript4 ,this resolution was intimated to ,mr4 ,locke in the following letter3 ,cambridge1 ,feb4 #afth1 #afia-b4 8,,sir1 8,your former letters came not to my hand1 but this ,i have4 ,i was of opinion my papers had lain still1 and am sorry to hear there is news about them4 ,let me entreat you to stop their translation and impression so soon as you can2 for ,i design to suppress them4 ,if your friend hath been at any pains and charge1 ,i will repay it1 and gratify him4 ,i am very glad my ,lord ,monmouth is till my friend1 but intend not to give his lordship and you any farther trouble4 ,my inclinations are to sit still4 ,i am to beg his lordship's pardon for pressing into his company the last time ,i saw him4 ,i had not done it1 but that ,mr4 ,paulin pressed me into the room4 ,miracles1 of good credit1 continued in the church for about two or three hundred years4 ,gregorius ,thaumaturgus had his name from thence1 and was one of the latest who was eminent for that gift2 but of their number and frequency ,i am not able to give you a just account4 ,the history of those ages is very imperfect4 ,mr4 ,paulin told me you had writ for some of ,mr4 ,boyle's red earth1 and by that ,i knew you had the receipt4--,your most affectionate and humble servant1 8,,is4 ,,newton40 ,hence we see that this celebrated treatise1 which ,biot alleges to have been written between #agab and #agai1 was actually in the hands of ,le ,clerc in ,holland previous to the #aath ,april1 #afia1 and consequently previous to the time of the supposed insanity of its author4 ,mr4 ,locke lost no time in obeying the request of his friend4 ,le ,clerc instantly stopped the publication of the letter1 and1 as he had never learned the name of the author1 he deposited the manuscript1 which was in the handwriting of ,mr4 ,locke1 in the library of the ,remonstrants1 where it was afterward found1 and was published at ,london in #aged1 under the title of ,two letters from ,sir ,isaac ,newton to ,m4 ,le ,clerc1--a form which had never been given to it by its author4 ,the copy thus published was a very imperfect one1 wanting both the beginning#ajd and the end1 and erroneous in many places2 but ,dr4 ,horsley has published a genuine edition1 which has the form of a single letter to a friend1 and was copied from a manuscript in ,sir ,isaac ,newton's handwriting1 in the possession of the ,rev4 ,dr4 ,ekins1 ,dean of ,carlisle4 ,having thus determined as accurately as possible the dates of the principal theological writings of ,sir ,isaac1 we shall now proceed to give some account of their contents4 ,the ,observations on the ,prophecies of ,daniel and the ,apocalypse of ,st4 ,john were published in ,london in #agcc1 in one volume #dto4 ,the work is divided into two parts1 the first of which treats of the ,prophecies of ,daniel1 and the second of the ,apocalypse of ,st4 ,john4 ,it begins with an account of the different books which compose the ,old ,testament2 and as the author considers ,daniel to be the most distinct in the order of time1 and the easiest to be understood1 he makes him the key to all the prophetic books in those matters which relate to the 8last time40 ,he next considers the figurative language of the prophets1 which he regards as taken 8from the analogy between the world natural and an empire or kingdom considered as a world politic20 the heavens and the things therein representing thrones and dynasties2 the earth1 with the things therein1 the inferior people2 and the lowest parts of the earth the most miserable of the people4 ,the sun is put for the whole race of kings1 the moon for the body of the common people1 and the stars for subordinate princes and rulers4 ,in the earth1 the dry land and the waters are put for the people of several nations4 ,animals and vegetables are also put for the people of several regions4 ,when a beast or man is put for a kingdom1 his parts and qualities are put for the analogous parts and qualities of the kingdom2 and when a man is taken in a mystical sense1 his qualities are often signified by his actions1 and by the circumstances and things about him4 ,in applying these principles he begins with the vision of the image composed of four different metals4 ,this image he considers as representing a body of four great nations which should reign in succession over the earth1 viz4 the people of ,babylonia1 the ,persians1 the ,greeks1 and the ,romans2 while the stone cut out without hands is a new kingdom which should arise after the four1 conquer all those nations1 become very great1 and endure to the end of time4 ,the vision of the four beasts is the prophecy of the four empires repeated1 with several new additions4 ,the lion with eagles' wings was the kingdom of ,babylon and ,media1 which overthrew the ,assyrian power4 ,the beast like a bear was the ,persian empire1 and its three ribs were the kingdoms of ,sardis1 ,babylon1 and ,egypt4 ,the third beast1 like a leopard1 was the ,greek empire1 and its four heads and four wings were the kingdoms of ,cassander1 ,lysimachus1 ,ptolemy1 and ,seleucus4 ,the fourth beast1 with its great iron teeth1 was the ,roman empire1 and its ten horns were the ten kingdoms into which it was broken in the reign of ,theodosius the ,great4 ,in the fifth chapter ,sir ,isaac treats of the kingdoms represented by the feet of the image composed of iron and clay which did not stick to one another1 and which were of different strength4 ,these were the ,gothic tribes called ,ostrogoths1 ,visigoths1 ,vandals1 ,gepid1 ,lombards1 ,burgundians1 ,alans1 c42 all of whom had the same manners and customs1 and spoke the same language1 and who1 about the year #daf ,a4 ,c4 were all quietly settled in several kingdoms within the empire1 not only by conquest1 but by grants of emperor4 ,in the sixth chapter he treats of the ten kingdoms represented by the ten horns of the fourth beast1 into which the western empire became divided about the time when ,rome was besieged and taken by the ,goths4 ,these kingdoms were1 #a4 ,the kingdom of the ,vandals and ,alans in ,spain and ,africa4 #b4 ,the kingdom of ,suevians in ,spain4 #c4 ,the kingdom of the ,visigoths4 #d4 ,the kingdom of the ,alans in ,gaul4 #e4 ,the kingdom of the ,burgundians4 #f4 ,the kingdom of the ,franks4 #g4 ,the kingdom of the ,britains4 #h4 ,the kingdom of the ,huns4 #i4 ,the kingdom of the ,lombards4 #aj4 ,the kingdom of ,ravenna4 ,some of these kingdoms at length fell1 and new ones sprung up2 but whatever was their subsequent number1 they still retain the name of the ten kings from their first number4 ,the eleventh horn of ,daniel's fourth beast is shown in chapter vii4 to be the ,church of ,rome in its triple character of a seer1 a prophet1 and a king2 and its power to change times and laws is copiously illustrated in chapter viii4 ,in the ninth chapter our author treats of the kingdom represented in ,daniel by the ram and he-goat1 the ram indicating the kingdom of the ,medes and ,persians from the beginning of the four empires1 and the he-goat the kingdom of the ,greeks to the end of them4 ,the prophecy of the seventy weeks1 which had hitherto been restricted to the first coming of our ,saviour1 is shown to be a prediction of all the main periods relating to the coming of the ,messiah1 the times of his birth and death1 the time of his rejection by the ,jews1 the duration of the ,jewish war by which he caused the city and sanctuary to be destroyed1 and the time of his second coming4 ,in the eleventh chapter ,sir ,isaac treats with great sagacity and acuteness of the time of our ,saviour's birth and passion1--a subject which had perplexed all preceding commentators4 ,after explaining in the twelfth chapter the last prophecy of ,daniel1 namely1 that of the scripture of truth1 which he considers as a commentary on the vision of the ram and he-goat1 he proceeds in the thirteenth chapter to the prophecy of the king who did according to his will1 and magnified himself above every god1 and honoured ,mahuzzims1 and regarded not the desire of women4 ,he shows that the ,greek empire1 after the division of the ,roman empire into the ,greek and ,latin empires1 became the king who in matters of religion did according to his will1 and in legislation exalted and magnified himself above every god4 ,in the second part of his work on the ,apocalypse of ,st4 ,john1 ,sir ,isaac treats1 #ast1 ,of the time when the prophecy was written1 which he conceives to have been during ,john's exile in ,patmos1 and before the epistle to the ,hebrews and the epistles of ,peter were written1 which in his opinion have a reference to the ,apocalypse2 #b;dly1 ,of the scene of the vision1 and the relation which the ,apocalypse has to the book of the law of ,moses1 and to the worship of ,god in the temple2 and1 #c;dly1 ,of the relation which the ,apocalypse has to the prophecies of ,daniel1 and of the subject of the prophecy itself4 ,sir ,isaac regards the prophecies of the ,old and ,new ,testaments1 not as given to gratify men's curiosities1 by enabling them to foreknow things1 but that after they were fulfilled1 they might be interpreted by the event1 and afford convincing arguments that the world is governed by ,providence1 he considers that there is so much of this prophecy already fulfilled as to afford to the diligent student sufficient instances of ,god's providence2 and he adds1 that 8among the interpreters of the last age1 there is scarce one of note who hath not made some discovery worth knowing1 and thence it seems one may gather that ,god is about opening these mysteries4 ,the success of others10 he continues1 8put me upon considering it1 and if ,i have done any thing which may be useful to following writers1 ,i have my design40 ,such is a brief abstract of this ingenious work1 which is characterized by great learning1 and marked with the sagacity of its distinguished author4 ,the same qualities of his mind are equally conspicuous in his ,historical ,account of ,two ,notable ,corruptions of ,scripture4 ,this celebrated treatise relates to two texts in the ,epistles of ,st4 ,john and ,st4 ,paul4 ,the first of these is in #a ,john v4 #g4 8,for there are three that bear record in heaven1 the ,father1 the ,son1 and the ,holy ,ghost1 and these three are one40 ,this text he considers as a gross corruption of ,scripture1 which had its origin among the ,latins1 who interpreted the ,spirit1 ,water1 and ,blood to be the ,father1 ,son1 and ,holy ,ghost1 in order to prove them one4 ,with the same view ,jerome inserted the ,trinity in express words in his version4 ,the ,latins marked his variations in the margins of their books2 and in the twelfth and following centuries1 when the disputations of the schoolmen were at their height1 the variation began to creep into the text in transcribing4 ,after the invention of printing1 it crept out of the ,latin into the printed ,greek1 contrary to the authority of all the ,greek manuscripts and ancient versions2 and from the ,venetian press it went soon after into ,greece4 ,after proving these positions ,sir ,isaac gives the following paraphrase of this remarkable passage1 which is given in italics4 8,who is he that overcometh the world1 but he that believeth that ,jesus is the ,son of ,god1 that ,son spoken of in the ,psalms1 where he saith1 #8thou art my ,son2 this day have ,i begotten thee4' ,this is he that1 after the ,jews had long expected him1 came1 first in a mortal body1 by baptism of water1 and then in an immortal one1 by shedding his blood upon the cross and rising again from the dead2 not by water only1 but by water and blood2 being the ,son of ,god1 as well by his resurrection from the dead 7,acts xiii4 #cc71 as by his supernatural birth of the virgin 7,luke i4 #ce74 ,and it is the ,spirit also that1 together with the water and blood1 beareth witness of the truth of his coming2 because the ,spirit is truth2 and so a fit and unexceptionable witness4 ,for there are three that bear record of his coming2 the ,spirit1 which he promised to send1 and which was since shed forth upon us in the form of cloven tongues1 and in various gifts2 the baptism of water1 wherein ,god testified #8this is my beloved ,son2' and the shedding of his blood1 accompanied with his resurrection1 whereby he became the most faithful martyr1 or witness1 of this truth4 ,and these three1 the spirit1 the baptism1 and passion of ,christ1 agree in witnessing one and the same thing 7namely1 that the ,son of ,god is come72 and1 therefore1 their evidence is strong3 for the law requires but two consenting witnesses1 and here we have three3 and if we receive the witness of men1 the threefold witness of ,god1 which he bare of his ,son1 by declaring at his baptism #8this is my beloved ,son1' by raising him from the dead1 and by pouring out his ,spirit on us1 is greater2 and1 therefore1 ought to be more readily received40 ,while the ,latin ,church was corrupting the preceding text1 the ,greek ,church was doing the same to ,st4 ,paul's #ast ,epistle to ,timothy iii4 #af4 ,great is the mystery of godliness1 ,god manifest in the flesh4 ,according to ,sir ,isaac1 this reading was effected by changing into 1 the abbreviation of 1 and after proving this by a learned and ingenious examination of ancient manuscripts1 he concludes that the reading should be ,great is the mystery of ,godliness who 7viz4 our ,saviour7 was manifest in the flesh4 ,as this learned dissertation had the effect of depriving the defenders of the doctrine of the ,trinity of the aid of two leading texts1 ,sir ,isaac ,newton has been regarded as an ,antitrinitarian2 but such a conclusion is not warranted by any thing which he has published2#aje and he distinctly warns us1 that his object was solely to 8purge the truth of things spurious40 ,we are disposed1 on the contrary1 to think that he declares his belief in the doctrine of the ,trinity when he says1 8,in the eastern nations1 and for a long time in the western1 the faith subsisted without this text2 and it is rather a danger to religion than an advantage1 to make it now lean upon a bruised reed4 ,there cannot be better service done to the truth than to purge it of things spurious2 and therefore1 knowing your prudence and calmness of temper1 ,i am confident ,i shall not offend you by telling you my mind plainly2 especially since it is no article of faith1 no point of discipline1 nothing but a criticism concerning a text of ,scripture which ,i am going to write about40 ,the word faith in the preceding passage cannot mean faith in the ,scriptures in general1 but faith in the particular doctrine of the ,trinity2 for it is this article of faith only to which the author refers when he deprecates its leaning on a bruised reed4 ,but1 whatever be the meaning of this passage1 we know that ,sir ,isaac was greatly offended at ,mr4 ,whiston for having represented him as an ,arian2 and so much did he resent the conduct of his friend in ascribing to him heretical opinions1 that he would not permit him to be elected a ,fellow of the ,royal ,society while he was ,president4#ajf ,the only other religious works which were composed by ,sir ,isaac ,newton were his ,lexicon ,propheticum1 to which was added a ,dissertation on the sacred cubit of the ,jews1 and ,four ,letters addressed to ,dr4 ,bentley1 containing some arguments in proof of a ,deity4 ,the ,lexicon ,propheticum was left incomplete1 and has not been published2 but the ,latin ,dissertation which was appended to it1 in which he shows that the cubit was about #bf ,roman unci1 was published in #agcg among the ,miscellaneous ,works of ,mr4 ,john ,greaves4 ,upon the death of the ,honourable ,robert ,boyle1 on the #cjth of ,december1 #afia1 it was found1 by a codicil to his will1 that he had left a revenue of #ejl4 per annum to establish a lectureship1 in which eight discourses were to be preached annually in one of the churches of the metropolis1 in illustration of the evidences of ,christianity1 and in opposition to the principles of infidelity4 ,dr4 ,bentley1 though a very young man1 was appointed to preach the first course of sermons1 and the manner in which he discharged this important duty gave the highest satisfaction1 not only to the trustees of the lectureship1 but to the public in general4 ,in the first six lectures ,bentley exposed the folly of atheism even in reference to the present life1 and derived powerful arguments for the existence of a ,deity from the faculties of the soul1 and the structure and functions of the human frame4 ,in order to complete his plan1 he proposed to devote his seventh and eighth lectures to the demonstration of a ,divine ,providence from the physical constitution of the universe1 as established in the ,principia4 ,in order to qualify himself for this task1 he received from ,sir ,isaac written directions respecting a list of books necessary to be perused previous to the study of that work2#ajg and having made himself master of the system which it contained1 he applied it with irresistible force of argument to establish the existence of an overruling mind4 ,previous to the publication of these lectures1 ,bentley encountered a difficulty which he was not able to solve1 and he prudently transmitted to ,sir ,isaac during #afib a series of queries on the subject4 ,this difficulty occurred in an argument urged by ,lucretius1 to prove the eternity of the world from an hypothesis of deriving the frame of it by mechanical principles from matter endowed with an innate power of gravity1 and evenly scattered throughout the heavens4 ,sir ,isaac willingly entered upon the consideration of the subject1 and transmitted his sentiments to ,dr4 ,bentley in the four letters which have been noticed in a preceding chapter4 ,in the first#ajh of these letters ,sir ,isaac mentions that when he wrote his treatise about our system1 viz4 the ,third ,book of the ,principia1 8he had an eye upon such principles as might work1 with considering men1 for the belief of a ,deity1 and he expresses his happiness that it has been found useful for that purpose4 ,in answering the first query of ,dr4 ,bentley1 the exact import of which we do not know1 he states1 that1 if matter were evenly diffused through a finite space1 and endowed with innate gravity1 it would fall down into the middle of the space1 and form one great spherical mass2 but if it were diffused through an infinite space1 some of it would collect into one mass1 and some into another1 so as to form an infinite number of great masses4 ,in this manner the sun and stars might be formed if the matter were of a lucid nature4 ,but he thinks it inexplicable by natural causes1 and to be ascribed to the counsel and contrivance of a voluntary ,agent1 that the matter should divide itself into two sorts1 part of it composing a shining body like the sun1 and part an opaque body like the planets4 ,had a natural and blind cause1 without contrivance and design1 placed the earth in the centre of the moon's orbit1 and ,jupiter in the centre of his system of satellites1 and the sun in the centre of the planetary system1 the sun would have been a body like ,jupiter and the earth1 that is1 without light and heat1 and consequently he knows no reason why there is only one body qualified to give light and heat to all the rest1 but because the ,author of the system thought it convenient1 and because one was sufficient to warm and enlighten all the rest4 ,to the second query of ,dr4 ,bentley1 he replies that the motions which the planets now have could not spring from any natural cause alone1 but were impressed by an intelligent ,agent4 8,to make such a system with all its motions required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets1 and the gravitating powers resulting from thence2 the several distances of the primary planets from the sun1 and of the secondary ones from ,saturn1 ,jupiter1 and the earth1 and the velocities with which those planets could revolve about those quantities of matter in the central bodies2 and to compare and adjust all these things together in so great a variety of bodies1 argues that cause to be not blind and fortuitous1 but very well skilled in mechanics and geometry40 ,in the second#aji letter1 he admits that the spherical mass formed by the aggregation of particles would affect the figure of the space in which the matter was diffused1 provided the matter descends directly downwards to that body1 and the body has no diurnal rotation2 but he states1 that by earthquakes loosening the parts of this solid1 the protuberance might sink a little by their weight1 and the mass by degrees approach a spherical figure4 ,he then proceeds to correct an error of ,dr4 ,bentley's in supposing that all infinites are equal4 ,he admits that gravity might put the planets in motion1 but he maintains that1 without the ,divine power1 it could never give them such a circulating motion as they have about the sun1 because a proper quantity of a transverse motion is necessary for this purpose2 and he concludes that he is compelled to ascribe the frame of this system to an intelligent ,agent4 ,the third letter contains opinions confirming or correcting several positions which ,dr4 ,bentley had laid down1 and he concludes it with a curious examination of the opinion of ,plato1 that the motion of the planets is such as if they had been all created by ,god in some region very remote from our system1 and let fall from thence towards the sun1 their falling motion being turned aside into a transverse one whenever they arrived at their several orbits4 ,sir ,isaac shows that there is no common place such as that conjectured by ,plato1 provided the gravitating power of the sun remains constant2 but that ,plato's affirmation is true if we suppose the gravitating power of the sun to be doubled at that moment of time when they all arrive at their several orbits4 8,if we suppose10 says he1 8the gravity of all the planets towards the sun to be of such a quantity as it really is1 and that the motions of the planets are turned upwards1 every planet will ascend to twice its height from the sun4 ,saturn will ascend till he be twice as high from the sun as he is at present1 and no higher2 ,jupiter will ascend as high again as at present1 that is1 a little above the orb of ,saturn2 ,mercury will ascend to twice his present height1 that is1 to the orb of ,venus2 and so of the rest2 and then1 by falling down again from the places to which they ascended1 they will arise again at their several orbs with the same velocities they had at first1 and with which they now revolve4 8,but if so soon as their motions by which they revolve are turned upwards1 the gravitating power of the sun1 by which their ascent is perpetually retarded1 be diminished by one-half1 they will now ascend perpetually1 and all of them1 at all equal distances from the sun1 will be equally swift4 ,mercury1 when he arrives at the orb of ,venus1 will be as swift as ,venus2 and he and ,venus1 when they arrive at the orb of the earth1 will be as swift as the earth2 and so of the rest4 ,if they begin all of them to ascend at once1 and ascend in the same line1 they will constantly1 in ascending1 become nearer and nearer together1 and their motions will constantly approach to an equality1 and become at length slower than any motion assignable4 ,suppose1 therefore1 that they ascended till they were almost contiguous1 and their motions inconsiderably little1 and that all their motions were at the same moment of time turned back again1 or1 which comes almost to the same thing1 that they were only deprived of their motions1 and let fall at that time1 they would all at once arrive at their several orbs1 each with the velocity it had at first2 and if their motions were then turned sideways1 and at the same time the gravitating power of the sun doubled1 that it might be strong enough to retain them in their orbs1 they would revolve in them as before their ascent4 ,but if the gravitating power of the sun was not doubled1 they would go away from their orbs into the highest heavens in parabolical lines40#aaj ,in the fourth letter#aaa he states1 that the hypothesis that matter is at first evenly diffused through the universe is in his opinion inconsistent with the hypothesis of innate gravity without a supernatural power to reconcile them1 and therefore it infers a ,deity4 8,for if there be innate gravity1 it is impossible now for the matter of the earth and all the planets and stars to fly up from them1 and become evenly spread throughout all the heavens without a supernatural power2 and certainly that which can never be hereafter without a supernatural power1 could never be heretofore without the same power40 ,these letters1 of which we have endeavoured to give a brief summary1 will well repay the most attentive perusal by the philosopher as well as the divine4 ,they are written with much perspicuity of language and great power of thought1 and they contain results which incontestably prove that their author was fully master of his noblest faculties1 and comprehended the profoundest parts of his own writings4#aab ,the logical acuteness1 the varied erudition1 and the absolute freedom from all prejudice which shine throughout the theological writings of ,newton1 might have protected them from the charge of having been written in his old age1 and at a time when a failure of mind was supposed to have unfitted him for his mathematical investigations4 ,but it is fortunate for his reputation1 as well as for the interests of ,christianity1 that we have been able to prove the incorrectness of such insinuations1 and to exhibit the most irrefragable evidence that all the theological writings of ,newton were composed in the vigour of his life1 and before the crisis of that bodily disorder which is supposed to have affected his reason4 ,the able letters to ,dr4 ,bentley were even written in the middle of that period when want of sleep and appetite had disturbed the serenity of his mind1 and enable us to prove that this disturbance1 whatever was its amount1 never affected the higher functions of his understanding4 ,when a philosopher of distinguished eminence1 and we believe not inimical to the ,christian faith1 has found it necessary to make a laboured apology for a man like ,newton writing on theological subjects1 and has been led to render that apology more complete by referring this class of his labours to a mind debilitated by age and weakened by its previous aberrations1 it may be expected from an ,english biographer1 and one who acknowledges the importance of revealed truth1 and the paramount interest of such subjects above all secular studies1 to suggest the true origin of ,newton's theological inquiries4 ,when a mind of great and acknowledged power first directs its energies to the study of the material universe1 no indications of order attract his notice1 and no proofs of design call forth his admiration4 ,in the starry firmament he sees no bodies of stupendous magnitude1 and no distances of immeasurable span4 ,the two great luminaries appear vastly inferior in magnitude to many objects around him1 and the greatest distances in the heavens seem even inferior to those which his own eye can embrace on the surface of the earth4 ,the planets1 when observed with care1 are seen to have a motion among the fixed stars1 and to vary in their magnitude and distances1 but these changes appear to follow no law4 ,sometimes they move to the east1 sometimes to the west1 sometimes towards the north1 and sometimes towards the south1 and at other times they are absolutely stationary4 ,no system1 in short1 appears1 and no general law seems to direct their motions4 ,by the observations and inquiries of astronomers1 however1 during successive ages1 a regular system has been recognised in this chaos of moving bodies1 and the magnitudes1 distances1 and revolutions of every planet which composes it has been determined with the most extraordinary accuracy4 ,minds fitted and prepared for this species of inquiry are capable of understanding the great variety of evidence by which the truth of the planetary system is established2 but thousands of individuals who are even distinguished in other branches of knowledge are incapable of such researches1 and view with a skeptical eye the great and irrefragable truths of astronomy4 ,that the sun is stationary in the centre of our system1--that the earth moves round the sun1 and round its own axis1--that the earth is #hjjj miles in diameter1 and the sun one hundred and ten times as large1--that the earth's orbit is #aij millions of miles in breadth1--and that if this immense space were filled with light1 it would appear only like a luminous point at the nearest fixed star1--are positions absolutely unintelligible and incredible to all who have not carefully studied the subject4 ,to millions of our species1 then1 the great book of nature is absolutely sealed1 though it is in the power of all to unfold its pages1 and to peruse those glowing passages which proclaim the power and wisdom of its mighty ,author4 ,the book of revelation exhibits to us the same peculiarities as that of nature4 ,to the ordinary eye it presents no immediate indications of its ,divine origin4 ,events apparently insignificant--supernatural interferences seemingly unnecessary--doctrines almost contradictory--and prophecies nearly unintelligible occupy its pages4 ,the history of the fall of man--of the introduction of moral and physical evil--the prediction of a ,messiah--the actual advent of our ,saviour--his instructions--his miracles--his death--his resurrection--and the subsequent propagation of his religion by the unlettered fishermen of ,galilee1 are each a stumbling block to the wisdom of this world4 ,the youthful and vigorous mind1 when first summoned to peruse the ,scriptures1 turns from them with disappointment4 ,it recognises in them no profound science--no secular wisdom--no ,divine eloquence--no disclosures of nature's secrets--no direct impress of an ,almighty hand4 ,but1 though the system of revealed truth which this book contains is1 like that of the universe1 concealed from common observation1 yet the labours of centuries have established its ,divine origin1 and developed in all its order and beauty the great plan of human restoration4 ,in the chaos of its incidents we discover the whole history of our species1 whether it is delineated in events that are past or shadowed forth in those which are to come1--from the creation of man and the origin of evil1 to the extinction of his earthly dynasty and the commencement of his immortal career4 ,the antiquity and authenticity of the books which compose the sacred canon1--the fulfilment of its prophecies1--the miraculous works of its founder1--his death and resurrection1 have been demonstrated to all who are capable of appreciating the force of historical evidence2 and in the poetical and prose compositions of the inspired authors we discover a system of doctrine and a code of morality traced in characters as distinct and legible as the most unerring truths in the material world4 ,false systems of religion have indeed been deduced from the sacred record1--as false systems of the universe have sprung from the study of the book of nature1--but the very prevalence of a false system proves the existence of one that is true2 and though the two classes of facts necessarily depend on different kinds of evidence1 yet we scruple not to say that the ,copernican system is not more demonstrably true than the system of theological truth contained in the ,bible4 ,if men of high powers1 then1 are still found1 who are insensible to the evidence which sustains the system of the universe1 need we wonder that there are others whose minds are shut against the effulgent evidence which intrenches the strongholds of our faith4 ,if such1 then1 is the character of the ,christian faith1 we need not be surprised that it was embraced and expounded by such a genius as ,sir ,isaac ,newton4 ,cherishing its doctrines1 and leaning on its promises1 he felt it his duty1 as it was his pleasure1 to apply to it that intellectual strength which had successfully surmounted the difficulties of the material universe4 ,the fame which that success procured him he could not but feel to be the breath of popular applause1 which administered only to his personal feelings2 but the investigation of the sacred mysteries1 while it prepared his own mind for its final destiny1 was calculated to promote the spiritual interests of thousands4 ,this noble impulse he did not hesitate to obey1 and by thus uniting philosophy with religion1 he dissolved the league which genius had formed with skepticism1 and added to the cloud of witnesses the brightest name of ancient or of modern times4 ,,chapter ,,xvii4 ,the minor ,discoveries and ,inventions of ,newton--,his ,researches on ,heat--,on ,fire and ,flame--,on ,elective ,attraction--,on the ,structure of ,bodies--,his supposed ,attachment to ,alchymy--,his ,hypothesis respecting ,ether as the ,cause of ,light and ,gravity--,on the ,excitation of ,electricity in ,glass--,his ,reflecting ,sextant invented before #agjj-- ,his ,reflecting ,microscope--,his ,prismatic ,reflector as a ,substitute for the small ,speculum of ,reflecting ,telescopes--,his ,method of varying the ,magnifying ,power of ,newtonian ,telescopes--,his ,experiments on ,impressions on the ,retina4 ,in the preceding chapters we have given an account of the principal labours of ,sir ,isaac ,newton2 but there still remain to be noticed several of his minor discoveries and inventions1 which could not properly be introduced under any general head4 ,the most important of these1 perhaps1 are his chymical researches1 which he seems to have pursued with more or less diligence from the time when he first witnessed the practical operations of chymistry during his residence at the apothecary's at ,grantham4 ,his first chymical experiments were probably made on the alloys of metals1 for the purpose of obtaining a good metallic composition for the specula of reflecting telescopes4 ,in his paper on thin plates he treats of the combinations of solids and fluids2 but he enters more largely on these and other subjects in the queries published at the end of his ,optics4 ,one of his most important chymical papers is his ,tabula quantitatum et graduum caloris1 which was published in the ,philosophical ,transactions4 ,this short paper contains a comparative scale of temperature from that of melting ice to that of a small kitchen coal-fire4 ,the following are the principal points of the scale1 the intermediate degrees of heat having been determined with great care4 ,degrees ,equal ,parts of ,heat4 of ,heat4 #j #j ,freezing point of water4 #a #ab ,blood-heat4 #b #bd ,heat of melting wax4 #c #dh ,melting point of equal parts of tin and bismuth4 #d #if ,melting point of lead4 #e #aib ,heat of a small coal-fire4 ,the first column of this table contains the degrees of heat in arithmetical progression1 and the second in geometrical progression1--the second degree being twice as great as the first1 and so on4 ,it is obvious from this table1 that the heat at which equal parts of tin and bismuth melt is four times greater than that of blood-heat1 the heat of melting lead eight times greater1 and the heat of a small coal-fire sixteen times greater4 ,this table was constructed by the help of a thermometer1 and of red-hot iron4 ,by the former he measured all heats as far as that of melting tin2 and by the latter he measured all the higher heats4 ,for the heat which heated iron loses in a given time is as the total heat of the iron2 and therefore1 if the times of cooling are taken equal1 the heats will be in a geometrical progression1 and may therefore be easily found by a table of logarithms4 ,he found by a thermometer constructed with linseed oil1 that if the oil1 when the thermometer was placed in melting snow1 occupied a space of #ajjj parts1 the same oil1 rarefied with one degree of heat1 or that of the human body1 occupied a space of #ajbef2 in the heat of water beginning to boil1 a space of #ajgje2 in the heat of water boiling violently1 #ajgbe2 in the heat of melted tin beginning to cool1 and putting on the consistency of an amalgam1 #aaeaf1 and when the tin had become solid1 #aadif4 ,hence the oil was rarefied in the ratio of #dj to #ci by the heat of the human body2 of #ae to #ad by the heat of boiling water2 of #ae to #ac in the heat of melting tin beginning to solidify2 and of #bc to #bj in the same tin when solid4 ,the rarefaction of air was1 with the same heat1 ten times greater than that of oil1 and the rarefaction of oil fifteen times greater than that of spirit of wine4 ,by making the heats of oil proportional to its rarefaction1 and by calling the heat of the human body #ab parts1 we obtain the heat of water beginning to boil1 #cc2 of water boiling violently1 #cd2 of melted tin beginning to solidify1 #gb2 and of the same become solid1 #gj4 ,sir ,isaac then heated a sufficiently thick piece of iron till it was red-hot2 and having fixed it in a cold place1 where the wind blew uniformly1 he put upon it small pieces of different metals and other fusible bodies1 and noted the times of cooling1 till all the particles1 having lost their fluidity1 grew cold1 and the heat of the iron was equal to that of the human body4 ,then1 by assuming that the excesses of the heats of the iron and of the solidified particles of metal above the heat of the atmosphere1 were in geometrical progression when the times were in arithmetical progression1 all the heats were obtained4 ,the iron was placed in a current of air1 in order that the air heated by the iron might always be carried away by the wind1 and that cold air might replace it with a uniform motion2 for thus equal parts of the air were heated in equal times1 and received a heat proportional to that of the iron4 ,but the heats thus found had the same ratio to one another with the heats found by the thermometer2 and hence he was right in assuming that the rarefactions of the oil were proportional to its heats4 ,another short chymical paper by ,sir ,isaac ,newton has been published by ,dr4 ,horsley4 ,it is entitled ,de ,natura ,acidorum1 but is principally occupied with a number of brief opinions on chymical subjects4 ,this paper was written later than #afhg1 as it bears a reference to the ,principia2 and the most important facts which it contains seem to have been more distinctly reproduced in the queries at the end of the ,optics4 ,the most important of these queries relate to fire1 flame1 and electric attractions1 and as they were revised in the year #agaf and #agag1 they may be regarded as containing the most matured opinions of their author4 ,fire he regards as a body heated so hot as to emit light copiously1 and flame as a vapour1 fume1 or exhalation heated so hot as to shine4 ,in his long query on elective attractions1 he considers the small particles of bodies as acting upon one another at distances so minute as to escape observation4 ,when salt of tartar deliquesces1 he supposes that this arises from an attraction between the saline particles and the aqueous particles held in solution in the atmosphere1 and to the same attraction he ascribes it that the water will not distil from the salt of tartar without great heat4 ,for the same reason sulphuric acid attracts water powerfully1 and parts with it with great difficulty4 ,when this attractive force becomes very powerful1 as in the union between sulphuric acid and water1 so as to make the particles 8coalesce with violence10 and rush towards one another with an accelerated motion1 heat is produced by the mixture of the two fluids4 ,in like manner1 he explains the production of flame from the mixture of cold fluids1--the action of fulminating powders1--the combination of iron filings with sulphur1--and all the other chymical phenomena of precipitation1 combination1 solution1 and crystallization1 and the mechanical phenomena of cohesion and capillary attraction4 ,he ascribes hot springs1 volcanoes1 fire-damps1 mineral coruscations1 earthquakes1 hot suffocating exhalations1 hurricanes1 lightning1 thunder1 fiery meteors1 subterraneous explosions1 land-slips1 ebullitions of the sea1 and waterspouts1 to sulphureous steams abounding in the bowels of the earth1 and fermenting with minerals1 or escaping into the atmosphere1 where they ferment with acid vapours fitted to promote fermentation4 ,in explaining the structure of solid bodies1 he is of opinion1 8that the smallest particles of matter may cohere by the strongest attractions1 and compose bigger particles of weaker virtue2 and many of these may cohere and compose bigger particles whose virtue is still weaker2 and so on for divers successions1 until the progression end in the biggest particles1 on which the operations in chymistry and the colours of natural bodies depend1 and which1 by adhering1 compose bodies of a sensible magnitude4 ,if the body is compact1 and bends or yields inward to pression1 without any sliding of its parts1 it is hard and elastic1 returning to its figure with a force rising from the mutual attraction of its parts4 ,if the parts slide upon one another1 the body is malleable or soft4 ,if they slip easily1 and are of a fit size to be agitated by heat1 and the heat is big enough to keep them in agitation1 the body is fluid2 and if it be apt to stick to things1 it is humid2 and the drops of every fluid affect a round figure1 by the mutual attraction of their parts1 as the globe of the earth and sea affects a round figure1 by the mutual attraction of its parts1 by gravity40 ,sir ,isaac then supposes1 that1 as the attractive force of bodies can reach but to a small distance from them1 8a repulsive virtue ought to succeed20 and he considers such a virtue as following from the reflection of the rays of light1 the rays being repelled without the immediate contact of the reflecting body1 and also from the emission of light1 the ray1 as soon as it is shaken off from a shining body by the vibrating motion of the parts of the body1 getting beyond the reach of attraction1 and being driven away with exceeding great velocity by the force of reflection4#aac ,many of the chymical views which ,sir ,isaac thus published in the form of queries were in his own lifetime illustrated and confirmed by ,dr4 ,stephen ,hales1 in his book on ,vegetable ,statics1--a work of great originality1 which contains the germ of some of the finest discoveries in modern chymistry4 ,although there is no reason to suppose that ,sir ,isaac ,newton was a believer in the doctrines of alchymy1 yet we are informed by the ,reverend ,mr4 ,law that he had been a diligent student of ,jacob ,behmen's writings1 and that there were found among his papers copious abstracts from them in his own handwriting4#aad ,he states also that ,sir ,isaac1 together with one ,dr4 ,newton1 his relation1 had1 in the earlier part of his life1 set up furnaces1 and were for several months at work in quest of the philosopher's tincture4 ,these statements may receive some confirmation from the fact1 that there exist among the ,portsmouth papers many sheets1 in ,sir ,isaac's own writing1 of ,flammel's ,explication of ,hieroglyphic ,figures1 and in another hand1 many sheets of ,william ,yworth's ,processus ,mysterii ,magni ,philosophicus1 and also from the manner in which ,sir ,isaac requests ,mr4 ,aston to inquire after one ,borry in ,holland1 who always went clothed in green1 and who was said to possess valuable secrets2 but ,mr4 ,law has weakened the force of his own testimony1 when he asserts that ,newton borrowed the doctrine of attraction from ,behmen's first three propositions of eternal nature4 ,on the #gth ,december1 #afge1 ,sir ,isaac ,newton communicated to the ,royal ,society a paper entitled ,an hypothesis explaining properties of light1 in which he1 for the first time1 introduces his opinions respecting ether1 and employs them to explain the nature of light1 and the cause of gravity4 8,he was induced10 he says1 8to do this1 because he had observed the heads of some great virtuosos to run much upon hypotheses1 and he therefore gave one which he was inclined to consider as the most probable1 if he were obliged to adopt one40#aae ,this hypothesis seems to have been afterward a subject of discussion between him and ,mr4 ,boyle1 to whom he promised to communicate his opinion more fully in writing4 ,he accordingly addressed to him a long letter1 dated ,february #bhth1 #afgh-i1 in which he explains his views respecting ether1 and employs them to account for the refraction of light1--the cohesion of two polished pieces of metal in an exhausted receiver1--the adhesion of quicksilver to glass tubes1--the cohesion of the parts of all bodies1--the cause of filtration1--the phenomena of capillary attraction1--the action of menstrua on bodies1--the transmutation of gross compact substances into aerial ones1--and the cause of gravity4 ,from the language used in this paper1 we should be led to suppose that ,sir ,isaac had entirely forgotten that he had formerly treated the general subject of ether1 and applied it to the explanation of gravity4 8,i shall set down10 says he1 8one conjecture more which came into my mind now as ,i was writing this letter2 it is about the cause of gravity10 which he goes on to explain2#aaf and he concludes by saying1 that 8he has so little fancy to things of this nature1 that1 had not your encouragement moved me to it1 ,i should never1 ,i think1 thus far have set pen to paper about them40 ,these opinions1 however1 about the existence of ether1 ,newton seems to have subsequently renounced2 for in the manuscript in the possession of ,dr4 ,j4 ,c4 ,gregory1 which we have already mentioned1 and which was written previous to #agjb1 he states1 that ether is neither obvious to our senses1 nor supported by any arguments1 but is a gratuitous assumption1 which1 if we are to trust to reason and to our senses1 must be banished from the nature of things2 and he goes on to establish1 by various arguments1 the validity of this opinion4 ,this renunciation of his former hypothesis probably arose from his having examined more carefully some of the phenomena which he endeavoured to explain by it4 ,those of capillary attraction1 for example1 he had ascribed to the ether 8standing rarer in the very sensible cavities of the capillary tubes than without them10 whereas he afterward discovered their true cause1 and ascribed them to the reciprocal attraction of the tube and the fluid4 ,but1 however this may be1 there can be no doubt that he resumed his early opinions before the publication of his ,optics1 which may be considered as containing his views upon this subject4 ,the queries which contain these opinions are the #ahth-#bdth1 all of which appeared for the first time in the second ,english edition of the ,optics4 ,if a body is either heated or loses its heat when placed in vacuo1 he ascribes the conveyance of the heat in both cases 8to the vibration of a much subtiler medium than air20 and he considers this medium as the same with that by which light is refracted and reflected1 and by whose vibrations light communicates heat to bodies1 and is put into fits of easy reflection and transmission4 ,this ethereal medium1 according to our author1 is exceedingly more rare and more elastic than air4 ,it pervades all bodies1 and is expanded through all the heavens4 ,it is much rarer within the dense bodies of the sun1 stars1 planets1 and comets1 than in the celestial spaces between them1 and also more rare within glass1 water1 c4 than in the free and open spaces void of air and other grosser bodies4 ,in passing out of glass1 water1 c4 and other dense bodies into empty space1 it grows denser and denser by degrees1 and this gradual condensation extends to some distance from the bodies4 ,owing to its great elasticity1 and1 consequently1 its efforts to spread in all directions1 it presses against itself1 and1 consequently1 against the solid particles of bodies1 so as to make them continually approach to one another1 the body being impelled from the denser parts of the medium towards the rarer with all that power which we call gravity4 ,in employing this medium to explain the nature of light1 ,newton does not suppose1 with ,descartes1 ,hooke1 ,huygens1 and others1 that light is nothing more than the impression of those undulations on the retina4 ,he regards light as a peculiar substance1 composed of heterogeneous particles thrown off with great velocity1 and in all directions1 from luminous bodies2 and he supposes that these particles while passing through the ether1 excite in it vibrations or pulses which accelerate or retard the particles of light1 and thus throw them into their alternate fits of easy reflection and transmission4 ,hence1 if a ray of light falls upon a transparent body1 in which the ether consists of strata of variable density1 the particles of light acted upon by the vibrations which they create will be urged with an accelerated velocity in entering the body1 while their velocity will be retarded in quitting it4 ,in this manner he conceives the phenomena of refraction to be produced1 and he shows how in such a case the refraction would be regulated by the law of the sines4 ,in order that the ethereal medium may produce the fits of easy reflection and transmission1 he conceives that its vibrations must be swifter than light4 ,he computes its elasticity to be #dij1jjj1jjj1jjj times greater than that of air1 in proportion to its density1 and about #fjj1jjj1jjj times more rare than water1 from which he infers that the resistance which it would oppose to the motions of the planets would not be sensible in #aj1jjj years4 ,he considers that the functions of vision and hearing may be performed chiefly by the vibrations of this medium1 executed in the bottom of the eye1 or in the auditory nerve by the rays of light1 and propagated through the solid1 pellucid1 and uniform capillamenta of the optic or auditory nerves into the place of sensation2 and he is of opinion that animal motion may be performed by the vibrations of the same medium1 excited in the brain by the power of the will1 and propagated from thence by the solid1 pellucid1 and uniform capillamenta of the nerves into the muscles for contracting and dilating them4 ,in the registers of the ,royal ,society there exist several letters#aag on the excitation of electricity in glass1 which were occasioned by an experiment of this kind having been mentioned in ,sir ,isaac's hypothesis of light4 ,the society had ordered the experiment to be tried at their meeting of the #afth ,december1 #afge2 but1 in order to secure its success1 ,mr4 ,oldenburg wrote to ,sir ,isaac for a more particular account of it4 ,sir ,isaac being thus 8put upon recollecting himself a little farther about it10 remembers that he made the experiment with a glass fixed at the distance of the #a_/c;d of an inch from one end of a brass hoop1 and only the #a_/hth of an inch from the other4 ,small pieces of thin paper were then laid upon the table2 when the glass was laid above them and rubbed1 the pieces of paper leaped from the one part of the glass to the other1 and twirled about in the air4 ,notwithstanding this explicit account of the experiment1 it entirely failed at the ,royal ,society1 and the secretary was desired to request the loan of ,sir ,isaac's apparatus1 and to inquire whether or not he had secured the papers from being moved by the air1 which might have somewhere stole in4 ,in a letter1 dated #bast ,december1 ,sir ,isaac recommended to the society to rub the glass 8with stuff whose threads may rake its surface1 and1 if that will not do1 to rub it with the fingers' ends to and fro1 and knock them as often upon the glass40 ,these directions enabled the society to succeed with the experiment on the #acth ,january1 #afgf1 when they used a scrubbing brush of short hog's bristles1 and the heft of a knife made with whalebone4 ,among the minor inventions of ,sir ,isaac ,newton1 we must enumerate his reflecting instrument for observing the moon's distance from the fixed stars at sea4 ,the description of this instrument was communicated to ,dr4 ,halley in the year #agjj2 but1 either from having mislaid the manuscript1 or from attaching no value to the invention1 he never communicated it to the ,royal ,society1 and it remained among his papers till after his death in #agdb1 when it was published in the ,philosophical ,transactions4 ,the following is ,sir ,isaac's own description of it as communicated to ,dr4 ,halley4 8,in the annexed figure ,,pqrs denotes a plate of brass1 accurately divided in the limb ,,dq1 into degrees1 minutes1 and #a_/ab minutes1 by a diagonal scale2 and the degrees1 and minutes1 and #a_/ab minutes1 counted for degrees1 minutes1 and #a_/f minutes4 ,,ab is a telescope three or four feet long1 fixed on the edge of that brass plate4 ,g is a speculum fixed on the brass plate perpendicularly as near as may be to the object-glass of the telescope1 so as to be inclined forty-five degrees to the axis of the telescope1 and intercept half the light which would otherwise come through the telescope to the eye4 ,,cd is a moveable index turning about the centre ,c1 and1 with its fiducial edge1 showing the degrees1 minutes1 and #a_/f minutes on the limb of the brass plate ,,pq2 the centre ,c must be over against the middle of the speculum ,g4 ,h is another speculum1 parallel to the former1 when the fiducial edge of index falls on #j #j #j2 so that the same star may then appear through the telescope in one and the same place1 both by the direct rays and by the reflexed ones2 but if the index be turned1 the star shall appear in two places1 whose distance is showed on the brass limb by the index4 ,illustration3 ,fig4 #ab4 8,by this instrument the distance of the moon from any fixed star is thus observed3 view the star through the perspicil by the direct light1 and the moon by the reflexed 7or on the contrary72 and turn the index till the star touch the limb of the moon1 and the index shall show on the brass limb of the instrument the distance of the star from the moon's limb2 and though the instrument shake by the motion of the ship at sea1 yet the moon and star will move together as if they did really touch one another in the heavens2 so that an observation may be made as exactly at sea as at land4 8,and by the same instrument may be observed exactly the altitudes of the moon and stars1 by bringing them to the horizon2 and thereby the latitude and times of observation may be determined more exactly than by the ways now in use4 8,in the time of the observation1 if the instrument move angularly about the axis of the telescope1 the star will move in a tangent of the moon's limb1 or of the horizon2 but the observation may notwithstanding be made exactly1 by noting when the line described by the star is a tangent to the moon's limb1 or to the horizon4 8,to make the instrument useful1 the telescope ought to take in a large angle2 and to make the observation true1 let the star touch the moon's limb1 not on the outside1 but on the inside40 ,this ingenious contrivance is obviously the very same invention as that which ,mr4 ,hadley produced in #agca1 and which1 under the name of ,hadley's ,quadrant1 has been of so great service in navigation4 ,the merit of its first invention must therefore be transferred to ,sir ,isaac ,newton4 ,in the year #afgb1 ,sir ,isaac communicated to ,mr4 ,oldenburg his design for a microscope1 which he considered to be as capable of improvement as the telescope1 and perhaps more so1 because it requires only one speculum4 ,this microscope is shown in the annexed diagram1 where ,,ab is the object-metal1 ,,cd the eye-glass1 ,f their common focus1 and ,o the other focus of the metal in which the object is placed4 ,this ingenious idea has been greatly improved in modern times by ,professor ,amici1 who makes ,,ab a portion of an ellipsoid1 whose foci are ,o and ,f1 and who places a small plain speculum between ,o and ,,ab1 in order to reflect the object1 which is placed on one side ,,ap1 for the purpose of being illuminated4 ,illustration3 ,fig4 #ac4 ,in another letter to ,mr4 ,oldenburg1 dated ,july #aath in the same year1 he suggests another improvement in microscopes1 which is to 8illuminate the object in a darkened room with the light of any convenient colour not too much compounded3 for by that means the microscope will1 with distinctness1 bear a deeper charge and larger aperture1 especially if its construction be such as ,i may hereafter describe40#aah ,this happy idea ,i have some years ago succeeded in realizing1 by illuminating microscopic objects with the light of a monochromatic lamp1 which discharges a copious flame of pure yellow light of definite refrangibility4#aai ,illustration3 ,fig4 #ad4 ,illustration3 ,fig4 #ae4 ,in order to remedy the evils arising from the weak reflecting power of speculum metal1 and from its tarnishing by exposure to the air1 ,sir ,isaac proposed to substitute for the small oval speculum a triangular prism of glass or crystal ,,abc4 ,its side ,,ab ba he supposes to perform the office of that metal1 by reflecting towards the eye-glass the light which comes from the concave speculum ,,df1 fig4 #ac1 whose light he supposes to enter into this prism at its side ,,cb bc1 and lest any colours should be produced by the refraction of these planes1 it is requisite that the angles of the prism at ,aa and ,bb be precisely equal4 ,this may be done most conveniently1 by making them half right angles1 and consequently the third angle at ,cc a right one4 ,the plane ,,ab ba will reflect all the light incident upon it2 but in order to exclude unnecessary light1 it will be proper to cover it all over with some black substance excepting two circular spaces of the planes ,ac and ,bc1 through which the useful light may pass4 ,the length of the prism should be such that its sides ,ac and ,bc may be square1 and so much of the angles ,b and b as are superfluous ought to be ground off1 to give passage for as much light as is possible from the object to the speculum4 ,illustration3 ,fig4 #af4 ,one great advantage of this prism1 which cannot be obtained from the oval metal1 is1 that without using two glasses the object may be erected1 and the magnifying power of the telescope varied at pleasure1 by merely varying the distances of the speculum1 the prism1 and the eye-glass4 ,this will be understood from fig4 #af1 where ,,ai represents the great concave speculum1 ,,ef the eye-glass1 and ,,bcd the prism of glass1 whose sides ,,bc and ,,cd are not flat1 but spherically convex4 ,the rays which come from ,g1 the focus of the great speculum ,,ai1 will1 by the refraction of the first side ,,bc1 be reduced to parallelism1 and after reflection from the base ,,cd1 will be made by the refraction of the next side ,,bd to converge to the focus ,h of the eye-glass ,,ef4 ,if we now bring the prism ,,bcd nearer the image at ,g1 the point ,h will recede from ,,bd1 and the image formed there will be greater than that at ,g1 and if we remove the prism ,,bcd from ,g1 the point ,h will approach to ,,bd1 and the image at ,h will be less than that at ,g4 ,the prism ,,bcd performs the same part as a convex lens1 ,g and ,h being its conjugate foci1 and the relative size of the images formed at these points being proportional to their distance from the lens4 ,this construction would be a good one for varying optically the angular distance of a pair of wires placed in the focus of the eye-glass ,,ef2 and by bisecting the lenticular prism ,,bcd1 and giving the halves a slight inclination1 we should be able to separate and to close the two images or disks which would thus be produced1 and thus form a double image micrometer4 ,among the minor and detached labours of ,sir ,isaac1 we must not omit his curious experiments on the action of light upon the retina4 ,locke seems to have wished his opinion respecting a fact stated in ,boyle's ,book on ,colours1 and in a letter from ,cambridge1 dated ,june #cjth1 #afia1 he communicated to his friend the following very remarkable observations made by himself4 8,the observation you mention in ,mr4 ,boyle's book of colours ,i once made upon myself with the hazard of my eyes4 ,the manner was this2 ,i looked a very little while upon the sun in the looking-glass with my right eye1 and then turned my eyes into a dark corner of my chamber1 and winked1 to observe the impression made1 and the circles of colours which encompassed it1 and how they decayed by degrees1 and at last vanished4 ,this ,i repeated a second and a third time4 ,at the third time1 when the phantasm of light and colours about it were almost vanished1 intending my fancy upon them to see their last appearance1 ,i found1 to my amazement1 that they began to return1 and by little and little to become as lively and vivid as when ,i had newly looked upon the sun4 ,but when ,i ceased to intend my fancy upon them1 they vanished again4 ,after this1 ,i found1 that as often as ,i went into the dark1 and intended my mind upon them1 as when a man looks earnestly to see any thing which is difficult to be seen1 ,i could make the phantasm return without looking any more upon the sun2 and the oftener ,i made it return1 the more easily ,i could make it return again4 ,and at length1 by repeating this without looking any more upon the sun1 ,i made such an impression on my eye1 that1 if ,i looked upon the clouds1 or a book1 or any bright object1 ,i saw upon it a round bright spot of light like the sun1 and1 which is still stranger1 though ,i looked upon the sun with my right eye only1 and not with my left1 yet my fancy began to make an impression upon my left eye1 as well as upon my right4 ,for if ,i shut my right eye1 or looked upon a book or the clouds with my left eye1 ,i could see the spectrum of the sun almost as plain as with my right eye1 if ,i did but intend my fancy a little while upon it2 for at first1 if ,i shut my right eye1 and looked with my left1 the spectrum of the sun did not appear till ,i intended my fancy upon it2 but by repeating1 this appeared every time more easily4 ,and now1 in a few hours' time1 ,i had brought my eyes to such a pass1 that ,i could look upon no bright object with either eye but ,i saw the sun before me1 so that ,i durst neither write nor read2 but to recover the use of my eyes1 shut myself up in my chamber made dark1 for three days together1 and used all means to divert my imagination from the sun4 ,for if ,i thought upon him1 ,i presently saw his picture1 though ,i was in the dark4 ,but by keeping in the dark1 and employing my mind about other things1 ,i began in three or four days to have some use of my eyes again2 and1 by forbearing to look upon bright objects1 recovered them pretty well1 though not so well but that1 for some months after1 the spectrum of the sun began to return as often as ,i began to meditate upon the phenomena1 even though ,i lay in bed at midnight with my curtains drawn4 ,but now ,i have been very well for many years1 though ,i am apt to think1 if ,i durst venture my eyes1 ,i could still make the phantasm return by the power of my fancy4 ,this story ,i tell you1 to let you understand1 that in the observation related by ,mr4 ,boyle1 the man's fancy probably concurred with the impression made by the sun's light to produce that phantasm of the sun which he constantly saw in bright objects4 ,and so your question about the cause of this phantasm involves another about the power of fancy1 which ,i must confess is too hard a knot for me to untie4 ,to place this effect in a constant motion is hard1 because the sun ought then to appear perpetually4 ,it seems rather to consist in a disposition of the sensorium to move the imagination strongly1 and to be easily moved1 both by the imagination and by the light1 as often as bright objects are looked upon40 ,these observations possess in many respects a high degree of interest4 ,the fact of the transmission of the impression from the retina of the one eye to that of the other is particularly important2 and it deserves to be remarked1 as a singular coincidence1 that ,i had occasion to observe and to describe the same phenomena above twenty years ago1#abj and long before the observations of ,sir ,isaac were communicated to the scientific world4 ,,chapter ,,xviii4 ,his ,acquaintance with ,dr4 ,pemberton1 who edits the ,third ,edition of the ,principia--,his first ,attack of ill ,health--,his ,recovery--,he is taken ill in consequence of attending the ,royal ,society--,his ,death on the #bjth ,march1 #agbg--;,his ,body lies in state--,his ,funeral--,he is buried in ,westminster ,abbey--,his ,monument described--,his ,epitaph--,a ,medal struck in honour of him--,roubiliac's full-length ,statue of him erected in ,cambridge--,division of his ,property--,his ,successors4 ,about the year #agbb1 ,sir ,isaac was desirous of publishing a third edition of his ,principia1 and the premature death of ,mr4 ,cotes having deprived him of his valuable aid1 he had the good fortune to become acquainted with ,dr4 ,henry ,pemberton1 a young and accomplished physician1 who had cultivated mathematical learning with considerable success4 ,m4 ,poleni1 an eminent professor in the ,university of ,padua1 having endeavoured1 on the authority of a new experiment1 to overturn the common opinion respecting the force of bodies in motion1 and to establish that of ,leibnitz in its place1 ,dr4 ,pemberton transmitted to ,dr4 ,mead a demonstration of its inaccuracy4 ,dr4 ,mead communicated this paper to ,sir ,isaac1 who not only highly approved of it1 but added a demonstration of his own1 drawn from another consideration of the subject2 and this was printed without his name1 as a postscript to ,pemberton's paper1 when it appeared in the ,transactions4#aba ,in a short time after the commencement of their acquaintance1 ,sir ,isaac engaged ,dr4 ,pemberton to superintend the new edition of the ,principia4 ,in discharging this duty1 ,dr4 ,pemberton had occasion to make many remarks on this work1 which ,sir ,isaac always received with the utmost goodness1 and the new edition appeared with numerous alterations in #agbf4 ,on the occasions upon which he had personal intercourse with ,sir ,isaac1 and which were necessarily numerous1 he endeavoured to learn his opinions on various mathematical subjects1 and to obtain some historical information respecting his inventions and discoveries4 ,sir ,isaac entered freely into all these topics and during the conversations which took place1 and while they were reading together ,dr4 ,pemberton's popular account of ,sir ,isaac's discoveries1 he obtained the most perfect evidence that1 though his memory was much decayed1 yet he was fully able to understand his own writings4 ,during the last twenty years of his life1 which he spent in ,london1 the charge of his domestic concerns devolved upon his beautiful and accomplished niece1 ,mrs4 ,catharine ,barton1 the wife of ,colonel ,barton1 for whom1 as we have already seen1 the ,earl of ,halifax had conceived the warmest affection4 ,this lady1 who had been educated at her uncle's expense1 married ,mr4 ,conduit1 and continued to reside with her husband in ,sir ,isaac's house till the time of his death4 ,in the year #agbb1 when he had reached the eightieth year of his age1 he was seized with an incontinence of urine1 which was ascribed to stone in the bladder1 and was considered incurable4 ,by means of a strict regimen1 however1 and other precautions1 he was enabled to alleviate his complaint1 and to procure long intervals of ease4 ,at this time he gave up the use of his carriage1 and always went out in a chair4 ,he declined all invitations to dinner1 and at his own house he had only small parties4 ,in his diet he was extremely temperate4 ,though he took a little butcher meat1 yet the principal articles of his food were broth1 vegetables1 and fruit1 of which he always ate very heartily4 ,in spite of all his precautions1 however1 he experienced a return of his old complaint1 and in ,august1 #agbd1 he passed a stone the size of a pea1 which came away in two pieces1 the one at the distance of two days from the other4 ,after some months of tolerable good health1 he was seized in ,january1 #agbe1 with a violent cough and inflammation of the lungs2 and in consequence of this attack1 he was prevailed upon1 with some difficulty1 to take up his residence at ,kensington1 where his health experienced a decided improvement4 ,in ,february1 #agbe1 he was attacked in both his feet with a fit of the gout1 of which he had received a slight warning a few years before1 and the effect of this new complaint was to produce a great and beneficial change in his general health4 ,on ,sunday the #gth ,march1 when his head was clearer and his memory stronger than ,mr4 ,conduit had known it to be for some time1 he entered into a long conversation on various subjects in astronomy4 ,he explained to ,mr4 ,conduit how comets might be formed out of the light of vapours discharged from the sun and the fixed stars as the centres of systems4 ,he conceived that these luminaries were replenished by the same comets being again returned to them2 and upon this principle he explained the extraordinary lights which were seen among the fixed stars by ,hipparchus1 ,tycho ,brahe1 and ,kepler's disciples1 and which he supposed to arise from the additional fuel which they received4#abb ,notwithstanding the improvement which his health had experienced1 his indisposition was still sufficiently severe to unfit him for the discharge of his duties at the mint2 and as his old deputy was confined with the dropsy1 he was desirous in #agbe of resigning his office to ,mr4 ,conduit4 ,difficulties probably were experienced in making this arrangement1 but his nephew discharged for him all the duties of his office2 and during the last year of his life he hardly ever went to the mint4 ,but though every kind of motion was calculated to aggravate his complaint1 and though he had derived from absolute rest and from the air at ,kensington the highest benefit1 yet great difficulty was experienced in preventing him from occasionally going to town4 ,feeling himself able for the journey1 he went to ,london on ,tuesday the #bhth of ,february1 #agbg1 to preside at a meeting of the ,royal ,society4 ,on the following day ,mr4 ,conduit considered him better than he had been for many years1 and ,sir ,isaac was himself so sensible of this improvement in his health1 that he assured his nephew that on the ,sunday preceding1 he had slept from eleven o'clock at night till eight o'clock next morning without waking4 ,he had undergone1 however1 great fatigue in attending the meeting of the ,royal ,society1 and in paying and receiving visits1 and the consequence of this was a violent return of his former complaint4 ,he returned to ,kensington on ,saturday the #dth ,march1 and was attended by ,dr4 ,mead and ,dr4 ,cheselden1 who pronounced his disease to be stone1 and held out no hopes of his recovery4 ,from the time of his last journey to ,london he had experienced violent fits of pain with very short intermissions2 and though the drops of sweat ran down his face during these severe paroxysms1 yet he never uttered a cry or a complaint1 or displayed the least marks of peevishness or impatience2 but during the short intervals of relief which occurred1 he smiled and conversed with his usual gayety and cheerfulness4 ,on ,wednesday the #aeth of ,march he seemed a little better2 and slight1 though groundless hopes were entertained of his recovery4 ,on the morning of ,saturday the #ahth he read the newspapers1 and carried on a pretty long conversation with ,dr4 ,mead1 when all his senses and faculties were strong and vigorous2 but at six o'clock of the same evening he became insensible1 and he continued in that state during the whole of ,sunday1 and till ,monday the #bjth1 when he expired between one and two o'clock in the morning1 in the eighty-fifth year of his age4 ,his body was removed from ,kensington to ,london1 and on ,tuesday the #bhth ,march it lay in state in the ,jerusalem ,chamber1 and was thence conveyed to ,westminster ,abbey1 where it was buried near the entrance into the choir on the left-hand4 ,the pall was supported by the ,lord ,high ,chancellor1 the ,dukes of ,roxburghe and ,montrose1 and the ,earls of ,pembroke1 ,sussex1 and ,macclesfield1 who were ,fellows of the ,royal ,society4 ,the ,hon4 ,sir ,michael ,newton1 ,knight of the ,bath1 was chief mourner1 and was followed by some other relations1 and several distinguished characters who were intimately acquainted with the deceased4 ,the funeral service was performed by the ,bishop of ,rochester1 attended by the prebend and choir4 ,sensible of the high honour which they derived from their connexion with so distinguished a philosopher1 the relations of ,sir ,isaac ,newton who inherited his personal estate1#abc agreed to devote #ejjl4 to the erection of a monument to his memory1 and the dean and chapter of ,westminster appropriated for it a place in the most conspicuous part of the ,abbey1 which had often been refused to the greatest of our nobility4 ,this monument was erected in #agca4 ,on the front of a sarcophagus resting on a pedestal are sculptured in basso-relievo youths bearing in their hands the emblems of ,sir ,isaac's principal discoveries4 ,one carries a prism1 another a reflecting telescope1 a third is weighing the sun and planets with a steelyard1 a fourth is employed about a furnace1 and two others are loaded with money newly coined4 ,on the sarcophagus is placed the figure of ,sir ,isaac in a cumbent posture1 with his elbow resting on several of his works4 ,two youths stand before him with a scroll1 on which is drawn a remarkable diagram relative to the solar system1 and above that is a converging series4 ,behind the sarcophagus is a pyramid1 from the middle of which rises a globe in mezzo-relievo1 upon which several of the constellations are drawn1 in order to show the path of the comet of #afha1 whose period ,sir ,isaac had determined1 and also the position of the solstitial colure mentioned by ,hipparchus1 and by means of which ,sir ,isaac had1 in his ,chronology1 fixed the time of the ,argonautic expedition4 ,a figure of ,astronomy as ,queen of the ,sciences sits weeping on the ,globe with a sceptre in her hand1 and a star surmounts the summit of the pyramid4 ,the following epitaph is inscribed on the monument4 ,hic situs est ,isaacus ,newton1 ,eques ,auratus1 ,qui ,animi ,vi prope divina1 ,planetarum ,motus1 ,figuras1 ,cometarum ,semitas1 ,oceanique stus1 ,sua ,mathesi facem preferente1 ,primus demonstravit4 ,radiorum ,lucis dissimilitudines1 ,colorumque inde nascentium ,proprietates1 ,quas nemo antea vel suspicatus erat1 pervestigavit1 ,natur1 ,antiquitates1 ,s4 ,scriptur1 ,sedulus1 sagax1 fidus ,interpres1 ,dei ,opt4 ,max4 ,majestatem ,philosophia asseruit1 ,evangelii simplicitatem moribus expressit4 ,sibi gratulentur ,mortales1 tale tantumque extitisse1 ,,humani ,,generis ,,decus4 ,natus xxv4 ,decemb4 ,,mdcxlii4 ,obiit4 xx4 ,mar4 ,,mdccxxvii4 ,of which the following is a literal translation3 ,here lies ,isaac ,newton1 ,knight1 ,who1 by a ,vigour of ,mind almost supernatural1 ,first demonstrated ,the ,motions and ,figures of the ,planets1 ,the ,paths of the ,comets1 and the ,tides of the ,ocean4 ,he diligently investigated ,the different ,refrangibilities of the ,rays of ,light1 ,and the ,properties of the ,colours to which they give rise4 ,an assiduous1 sagacious1 and faithful ,interpreter ,of ,nature1 ,antiquity1 and the ,holy ,scriptures1 ,he asserted in his ,philosophy the ,majesty of ,god1 ,and exhibited in his conduct the ,simplicity of the ,gospel4 ,let ,mortals rejoice ,that there has existed such and so great ,,an ,,ornament ,,of ,,human ,,nature4 ,born #beth ,dec4 #afdb1 ,died #bjth ,march1 #agbg4 ,in the beginning of #agca1 a medal was struck at the ,tower in honour of ,sir ,isaac ,newton4 ,it had on one side the head of the philosopher1 with the motto1 ,felix cognoscere causas1 and on the reverse a figure representing the mathematics4 ,on the #dth ,february1 #agee1 a magnificent full-length statue of ,sir ,isaac ,newton in white marble was erected in the antechapel of ,trinity ,college4 ,he is represented standing on a pedestal in a loose gown1 holding a prism1 and looking upwards with an expression of the deepest thought4 ,on the pedestal is the inscription1 ,qui genus humanum ingenio superavit4 ,who surpassed all men in genius4 ,this statue1 executed by ,roubiliac1 was erected at the expense of ,dr4 ,robert ,smith1 the author of the ,compleat ,system of ,optics1 and professor of astronomy and experimental philosophy at ,cambridge4--,it has been thus described by a modern poet3 ,hark where the organ1 full and clear1 ,with loud hosannas charms the ear2 ,behold1 a prism within his hands1 ,absorbed in thought great ,newton stands ,such was his brow1 and looks serene1 ,his serious gait and musing mien1 ,when taught on eagle wings to fly1 ,he traced the wonders of the sky2 ,the chambers of the sun explored1 ,where tints of thousand hues were stored4 ,dr4 ,smith likewise bequeathed the sum of #ejjl4 for executing a painting on glass for the window at the south end of ,trinity ,college1 ,cambridge4 ,the subject represents the presentation of ,sir ,isaac ,newton to his majesty ,george ,,iii41 who is seated under a canopy with a laurel chaplet in his hand1 and attended by the ,british ,minerva1 apparently advising him to reward merit in the person of the great philosopher4 ,below the throne1 the ,lord ,chancellor ,bacon is proposing to register the reward about to be conferred upon ,sir ,isaac4 ,the original drawing of this absurd picture was executed by ,cypriani1 and cost one hundred guineas4 ,the personal estate of ,sir ,isaac ,newton1 which was worth about #cb1jjjl41 was divided among his four nephews and four nieces of the half-blood1 the grandchildren of his mother by the ,reverend ,mr4 ,smith4 ,the family estates of ,woolsthorpe and ,sustern he bequeathed to ,john ,newton1 the heir-at-law1 whose great-grandfather was ,sir ,isaac's uncle4 ,this gentleman does not seem to have sufficiently valued the bequest1 for he sold them in #agcb1 to ,edmund ,turnor of ,stoke ,rocheford4#abd ,a short time before his death1 ,sir ,isaac gave away an estate in ,berkshire to the sons and daughter of a brother of ,mrs4 ,conduit1 who1 in consequence of their father dying before ,sir ,isaac1 had no share in the personal estate2 and he also gave an estate of the same value1 which he bought at ,kensington1 to ,catharine1 the only daughter of ,mr4 ,conduit1 who afterward married ,mr4 ,wallop1 the eldest son of ,lord ,lymington4 ,this lady was afterward ,viscountess ,lymington1 and the estate of ,kensington descended to the late ,earl of ,portsmouth1 by whom it was sold4 ,sir ,isaac was succeeded as master and warden in the mint by his nephew1 ,john ,conduit1 ,esq41 who wrote a treatise on the gold and silver coin1 and who died in #agcg1 leaving behind him his wife and daughter1 the former of whom died in #agci1 in the #eith year of her age4 ,,chapter ,,xix4 ,permanence of ,newton's ,reputation--,character of his ,genius--,his ,methods of ,investigation similar to that used by ,galileo--,error in ascribing his ,discoveries to the ,use of the ,methods recommended by ,lord ,bacon--,the ,pretensions of the ,baconian ,philosophy examined--,sir ,isaac ,newton's social ,character--,his great ,modesty--,the ,simplicity of his ,character--,his religious and moral ,character--,his ,hospitality and ,mode of ,life--,his ,generosity and ,charity--,his ,absence--,his personal ,appearance--,statues and ,pictures of him--,memorials and ,recollections of him4 ,such were the last days of ,sir ,isaac ,newton1 and such the last laurels which were shed over his grave4 ,a century of discoveries has since his day been added to science2 but brilliant as these discoveries are1 they have not obliterated the minutest of his labours1 and have served only to brighten the halo which encircles his name4 ,the achievements of genius1 like the source from which they spring1 are indestructible4 ,acts of legislation and deeds of war may confer a high celebrity1 but the reputation which they bring is only local and transient2 and while they are hailed by the nation which they benefit1 they are reprobated by the people whom they ruin or enslave4 ,the labours of science1 on the contrary1 bear along with them no counterpart of evil4 ,they are the liberal bequests of great minds to every individual of their race1 and wherever they are welcomed and honoured they become the solace of private life1 and the ornament and bulwark of the commonwealth4 ,the importance of ,sir ,isaac ,newton's discoveries has been sufficiently exhibited in the preceding chapters3 the peculiar character of his genius1 and the method which he pursued in his inquiries1 can be gathered only from the study of his works1 and from the history of his individual labours4 ,were we to judge of the qualities of his mind from the early age at which he made his principal discoveries1 and from the rapidity of their succession1 we should be led to ascribe to him that quickness of penetration1 and that exuberance of invention1 which is more characteristic of poetical than of philosophical genius4 ,but we must recollect that ,newton was placed in the most favourable circumstances for the development of his powers4 ,the flower of his youth and the vigour of his manhood were entirely devoted to science4 ,no injudicious guardian controlled his ruling passion1 and no ungenial studies or professional toils interrupted the continuity of his pursuits4 ,his discoveries were1 therefore1 the fruit of persevering and unbroken study2 and he himself declared1 that whatever service he had done to the public was not owing to any extraordinary sagacity1 but solely to industry and patient thought4 ,initiated early into the abstractions of geometry1 he was deeply imbued with her cautious spirit2 and if his acquisitions were not made with the rapidity of intuition1 they were at least firmly secured2 and the grasp which he took of his subject was proportional to the mental labour which it had exhausted4 ,overlooking what was trivial1 and separating what was extraneous1 he bore down with instinctive sagacity on the prominences of his subject1 and having thus grappled with its difficulties1 he never failed to intrench himself in its strongholds4 ,to the highest powers of invention ,newton added1 what so seldom accompanies them1 the talent of simplifying and communicating his profoundest speculations4#abe ,in the economy of her distributions1 nature is seldom thus lavish of her intellectual gifts4 ,the inspired genius which creates is rarely conferred along with the matured judgment which combines1 and yet without the exertion of both the fabric of human wisdom could never have been reared4 ,though a ray from heaven kindled the vestal fire1 yet an humble priesthood was required to keep alive the flame4 ,the method of investigating truth by observation and experiment1 so successfully pursued in the ,principia1 has been ascribed by some modern writers of great celebrity to ,lord ,bacon2 and ,sir ,isaac ,newton is represented as having owed all his discoveries to the application of the principles of that distinguished writer4 ,one of the greatest admirers of ,lord ,bacon has gone so far as to characterize him as a man who has had no rival in the times which are past1 and as likely to have none in those which are to come4 ,in a eulogy so overstrained as this1 we feel that the language of panegyric has passed into that of idolatry2 and we are desirous of weighing the force of arguments which tend to depose ,newton from the high-priesthood of nature1 and to unsettle the proud destinies of ,copernicus1 ,galileo1 and ,kepler4 ,that ,bacon was a man of powerful genius1 and endowed with varied and profound talent1--the most skilful logician1--the most nervous and eloquent writer of the age which he adorned1 are points which have been established by universal suffrage4 ,the study of ancient systems had early impressed him with the conviction that experiment and observation were the only sure guides in physical inquiries2 and1 ignorant though he was of the methods1 the principles1 and the details of the mathematical sciences1 his ambition prompted him to aim at the construction of an artificial system by which the laws of nature might be investigated1 and which might direct the inquiries of philosophers in every future age4 ,the necessity of experimental research1 and of advancing gradually from the study of facts to the determination of their cause1 though the groundwork of ,bacon's method1 is a doctrine which was not only inculcated but successfully followed by preceding philosophers4 ,in a letter from ,tycho ,brahe to ,kepler1 this industrious astronomer urges his pupil 8to lay a solid foundation for his views by actual observation1 and then by ascending from these to strive to reach the causes of things20 and it was no doubt under the influence of this advice that ,kepler submitted his wildest fancies to the test of observation1 and was conducted to his most splendid discoveries4 ,the reasonings of ,copernicus1 who preceded ,bacon by more than a century1 were all founded upon the most legitimate induction4 ,dr4 ,gilbert had exhibited in his treatise on the magnet#abf the most perfect specimen of physical research4 ,leonardo da ,vinci had described in the clearest manner the proper method of philosophical investigation2#abg and the whole scientific career of ,galileo was one continued example of the most sagacious application of observation and experiment to the discovery of general laws4 ,the names of ,paracelsus1 ,van ,helmont1 and ,cardan have been ranged in opposition to this constellation of great names1 and while it is admitted that even they had thrown off the yoke of the schools1 and had succeeded in experimental research1 their credulity and their pretensions have been adduced as a proof that to the 8bulk of philosophers0 the method of induction was unknown4 ,the fault of this argument consists in the conclusion being infinitely more general than the fact4 ,the errors of these men were not founded on their ignorance1 but on their presumption4 ,they wanted the patience of philosophy and not her methods4 ,an excess of vanity1 a waywardness of fancy1 and an insatiable appetite for that species of passing fame which is derived from eccentricity of opinion1 moulded the reasonings and disfigured the writings of these ingenious men2 and it can scarcely admit of a doubt1 that1 had they lived in the present age1 their philosophical character would have received the same impress from the peculiarity of their tempers and dispositions4 ,this is an experiment1 however1 which cannot now be made2 but the history of modern science supplies the defect1 and the experience of every man furnishes a proof that in the present age there are many philosophers of elevated talents and inventive genius who are as impatient of experimental research as ,paracelsus1 as fanciful as ,cardan1 and as presumptuous as ,van ,helmont4 ,having thus shown that the distinguished philosophers who flourished before ,bacon were perfect masters both of the principles and practice of inductive research1 it becomes interesting to inquire whether or not the philosophers who succeeded him acknowledged any obligation to his system1 or derived the slightest advantage from his precepts4 ,if ,bacon constructed a method to which modern science owes its existence1 we shall find its cultivators grateful for the gift1 and offering the richest incense at the shrine of a benefactor whose generous labours conducted them to immortality4 ,no such testimonies1 however1 are to be found4 ,nearly two hundred years have gone by1 teeming with the richest fruits of human genius1 and no grateful disciple has appeared to vindicate the rights of the alleged legislator of science4 ,even ,newton1 who was born and educated after the publication of the ,novum ,organon1 never mentions the name of ,bacon or his system1 and the amiable and indefatigable ,boyle treated him with the same disrespectful silence4 ,when we are told1 therefore1 that ,newton owed all his discoveries to the method of ,bacon1 nothing more can be meant than that he proceeded in that path of observation and experiment which had been so warmly recommended in the ,novum ,organon2 but it ought to have been added1 that the same method was practised by his predecessors1--that ,newton possessed no secret that was not used by ,galileo and ,copernicus1--and that he would have enriched science with the same splendid discoveries if the name and the writings of ,bacon had never been heard of4 ,from this view of the subject we shall now proceed to examine the ,baconian process itself1 and consider if it possesses any merit as an artificial method of discovery1 or if it is at all capable of being employed1 for this purpose1 even in the humblest walks of scientific inquiry4 ,the process of ,lord ,bacon was1 we believe1 never tried by any philosopher but himself4 ,as the subject of its application1 he selected that of heat4 ,with his usual erudition1 he collected all the facts which science could supply1--he arranged them in tables1--he cross-questioned them with all the subtlety of a pleader1--he combined them with all the sagacity of a judge1--and he conjured with them by all the magic of his exclusive processes4 ,but1 after all this display of physical logic1 nature thus interrogated was still silent4 ,the oracle which he had himself established refused to give its responses1 and the ministering priest was driven with discomfiture from his own shrine4 ,this example1 in short1 of the application of his system1 will remain to future ages as a memorable instance of the absurdity of attempting to fetter discovery by any artificial rules4 ,nothing even in mathematical science can be more certain than that a collection of scientific facts are of themselves incapable of leading to discovery1 or to the determination of general laws1 unless they contain the predominating fact or relation in which the discovery mainly resides4 ,a vertical column of arch-stones possesses more strength than the same materials arranged in an arch without the key-stone4 ,however nicely they are adjusted1 and however nobly the arch may spring1 it never can possess either equilibrium or stability4 ,in this comparison all the facts are supposed to be necessary to the final result2 but1 in the inductive method1 it is impossible to ascertain the relative importance of any facts1 or even to determine if the facts have any value at all1 till the master-fact which constitutes the discovery has crowned the zealous efforts of the aspiring philosopher4 ,the mind then returns to the dark and barren waste over which it has been hovering2 and by the guidance of this single torch it embraces1 under the comprehensive grasp of general principles1 the multifarious and insulated phenomena which had formerly neither value nor connexion4 ,hence it must be obvious to the most superficial thinker1 that discovery consists either in the detection of some concealed relation--some deep-seated affinity which baffles ordinary research1 or in the discovery of some simple fact which is connected by slender ramifications with the subject to be investigated2 but which1 when once detected1 carries us back by its divergence to all the phenomena which it embraces and explains4 ,in order to give additional support to these views1 it would be interesting to ascertain the general character of the process by which a mind of acknowledged power actually proceeds in the path of successful inquiry4 ,the history of science does not furnish us with much information on this head1 and if it is to be found at all1 it must be gleaned from the biographies of eminent men4 ,whatever this process may be in its details1 if it has any1 there cannot be the slightest doubt that in its generalities at least it is the very reverse of the method of induction4 ,the impatience of genius spurns the restraints of mechanical rules1 and never will submit to the plodding drudgery of inductive discipline4 ,the discovery of a new fact unfits even a patient mind for deliberate inquiry4 ,conscious of having added to science what had escaped the sagacity of former ages1 the ambitious spirit invests its new acquisition with an importance which does not belong to it4 ,he imagines a thousand consequences to flow from his discovery3 he forms innumerable theories to explain it1 and he exhausts his fancy in trying all its possible relations to recognised difficulties and unexplained facts4 ,the reins1 however1 thus freely given to his imagination1 are speedily drawn up4 ,his wildest conceptions are all subjected to the rigid test of experiment1 and he has thus been hurried by the excursions of his own fancy into new and fertile paths1 far removed from ordinary observation4 ,here the peculiar character of his own genius displays itself by the invention of methods of trying his own speculations1 and he is thus often led to new discoveries far more important and general than that by which he began his inquiry4 ,for a confirmation of these views1 we may refer to the ,history of ,kepler's ,discoveries2 and if we do not recognise them to the same extent in the labours of ,newton1 it is because he kept back his discoveries till they were nearly perfected1 and therefore withheld the successive steps of his inquiries4 ,the social character of ,sir ,isaac ,newton was such as might have been expected from his intellectual attainments4 ,he was modest1 candid1 and affable1 and without any of the eccentricities of genius1 suiting himself to every company1 and speaking of himself and others in such a manner that he was never even suspected of vanity4 8,but this10 says ,dr4 ,pemberton1 8,i immediately discovered in him1 which at once both surprised and charmed me4 ,neither his extreme great age nor his universal reputation had rendered him stiff in opinion1 or in any degree elated4 ,of this ,i had occasion to have almost daily experience4 ,the remarks ,i continually sent him by letters on the ,principia were received with the utmost goodness4 ,these were so far from being any ways displeasing to him1 that on the contrary it occasioned him to speak many kind things of me to my friends1 and to honour me with a public testimony of his good opinion40 ,the modesty of ,sir ,isaac ,newton in reference to his great discoveries was not founded on any indifference to the fame which they conferred1 or upon any erroneous judgment of their importance to science4 ,the whole of his life proves1 that he knew his place as a philosopher1 and was determined to assert and vindicate his rights4 ,his modesty arose from the depth and extent of his knowledge1 which showed him what a small portion of nature he had been able to examine1 and how much remained to be explored in the same field in which he had himself laboured4 ,in the magnitude of the comparison he recognised his own littleness2 and a short time before his death he uttered this memorable sentiment3--8,i do not know what ,i may appear to the world2 but to myself ,i seem to have been only like a boy playing on the seashore1 and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary1 while the great ocean of truth lay all undiscovered before me40 ,what a lesson to the vanity and presumption of philosophers1--to those especially who have never even found the smoother pebble or the prettier shell6 ,what a preparation for the latest inquiries1 and the last views of the decaying spirit1--for those inspired doctrines which alone can throw a light over the dark ocean of undiscovered truth6 ,the native simplicity of ,sir ,isaac ,newton's mind is finely portrayed in the affecting letter in which he acknowledges to ,locke that he had thought and spoken of him uncharitably2 and the humility and candour in which he asks forgiveness could have emanated only from a mind as noble as it was pure4 ,in the religious and moral character of our author there is much to admire and to imitate4 ,while he exhibited in his life and writings an ardent regard for the general interests of religion1 he was at the same time a firm believer in revelation4 ,he was too deeply versed in the ,scriptures1 and too much imbued with their spirit1 to judge harshly of other men who took different views of them from himself4 ,he cherished the great principles of religious toleration1 and never scrupled to express his abhorrence of persecution1 even in its mildest form4 ,immorality and impiety he never permitted to pass unreproved2 and when ,dr4 ,halley#abh ventured to say any thing disrespectful to religion1 he invariably checked him1 and said1 8,i have studied these things1--you have not40#abi ,after ,sir ,isaac ,newton took up his residence in ,london1 he lived in a very handsome style1 and kept his carriage1 with an establishment of three male and three female servants4 ,in his own house he was hospitable and kind1 and on proper occasions he gave splendid entertainments1 though without ostentation or vanity4 ,his own diet was frugal1 and his dress was always simple2 but on one occasion1 when he opposed the ,honourable ,mr4 ,annesley in #agje1 as a candidate for the university1 he is said to have put on a suit of laced clothes4 ,his generosity and charity had no bounds1 and he used to remark1 that they who gave away nothing till they died never gave at all4 ,though his wealth had become considerable by a prudent economy1 yet he had always a contempt for money1 and he spent a considerable part of his income in relieving the poor1 in assisting his relations1 and in encouraging ingenuity and learning4 ,the sums which he gave to his relations at different times were enormous2#acj and in #agbd he wrote a letter to the ,lord ,provost of ,edinburgh1 offering to contribute #bjl4 per annum to a provision for ,mr4 ,maclaurin1 provided he accepted the situation of assistant to ,mr4 ,james ,gregory1 who was professor of mathematics in the university4 ,the habits of deep meditation which ,sir ,isaac ,newton had acquired1 though they did not show themselves in his intercourse with society1 exercised their full influence over his mind when in the midst of his own family4 ,absorbed in thought he would often sit down on his bedside after he rose1 and remain there for hours without dressing himself1 occupied with some interesting investigation which had fixed his attention4 ,owing to the same absence of mind1 he neglected to take the requisite quantity of nourishment1 and it was therefore often necessary to remind him of his meals4#aca ,sir ,isaac ,newton is supposed to have had little knowledge of the world1 and to have been very ignorant of the habits of society4 ,this opinion has1 we think1 been rashly deduced from a letter which he wrote in the twenty-seventh year of his age to his young friend1 ,francis ,aston1 ,esq41 who was about to set out on his travels4 ,this letter is a highly interesting production2 and while it shows much knowledge of the human heart1 it throws a strong light upon the character and opinions of its author4 ,in his personal appearance1 ,sir ,isaac ,newton was not above the middle size1 and in the latter part of his life was inclined to be corpulent4 ,according to ,mr4 ,conduit 8he had a very lively and piercing eye1 a comely and gracious aspect1 with a fine head of hair as white as silver1 without any baldness1 and when his peruke was off was a venerable sight40 ,bishop ,atterbury asserts1#acb on the other hand1 that the lively and piercing eye did not belong to ,sir ,isaac during the last twenty years of his life4 8,indeed10 says he1 8in the whole air of his face and make there was nothing of that penetrating sagacity which appears in his compositions4 ,he had something rather languid in his look and manner which did not raise any great expectation in those who did not know him40 ,this opinion of ,bishop ,atterbury is confirmed by an observation of ,mr4 ,thomas ,hearne1#acc who says 8that ,sir ,isaac was a man of no very promising aspect4 ,he was a short1 well-set man4 ,he was full of thought1 and spoke very little in company1 so that his conversation was not agreeable4 ,when he rode in his coach1 one arm would be out of his coach on one side and the other on the other40 ,sir ,isaac never wore spectacles1 and never 8lost more than one tooth to the day of his death40 ,besides the statue of ,sir ,isaac ,newton executed by ,roubiliac1 there is a bust of him by the same artist in the library of ,trinity ,college1 ,cambridge4 ,several good paintings of him are extant4 ,two of these are in the hall of the ,royal ,society of ,london1 and have1 we believe1 been often engraved4 ,another1 by ,vanderbank1 is in the apartments of the ,master's lodge in ,trinity ,college1 and has been engraved by ,vertue4 ,another1 by ,valentine ,ritts1 is in the landing-place near the entrance to ,trinity ,college library2 but the best1 from which our engraving is copied1 was painted by ,sir ,godfrey ,kneller1 and is in the possession of ,lord ,egremont at ,petworth4 ,in the university library there is preserved a cast taken from his face after death4 ,every memorial of so great a man as ,sir ,isaac ,newton has been preserved and cherished with peculiar veneration4 ,his house at ,woolsthorpe1 of which we have given an engraving1 has been religiously protected by ,mr4 ,turnor of ,stoke ,rocheford1 the proprietor4 ,dr4 ,stukeley1 who visited it in ,sir ,isaac's lifetime1 on the #acth ,october1 #agba1 gives the following description of it in his letter to ,dr4 ,mead1 written in #agbg3 8',tis built of stone as is the way of the country hereabouts1 and a reasonable good one4 ,they led me up stairs and showed me ,sir ,isaac's study1 where ,i suppose he studied when in the country in his younger days1 or perhaps when he visited his mother from the university4 ,i observed the shelves were of his own making1 being pieces of deal boxes which probably he sent his books and clothes down in on those occasions4 ,there were some years ago two or three hundred books in it of his father-in-law1 ,mr4 ,smith1 which ,sir ,isaac gave to ,dr4 ,newton of our town40#acd ,when the house was repaired in #agih1 a tablet of white marble was put up by ,mr4 ,turnor in the room where ,sir ,isaac was born1 with the following inscription3 8,sir ,isaac ,newton1 son of ,john ,newton1 ,lord of the manor of ,woolsthorpe1 was born in this room on the #beth ,december1 #afdb40 ,nature and ,nature's laws lay hid in night1 ,god said1 8,let ,newton be10 and all was light4 ,the following lines have been written upon the house3 ,here ,newton dawned1 here lofty wisdom woke1 ,and to a wondering world divinely spoke4 ,if ,tully glowed1 when ,phdrus' steps he trode1 ,or fancy formed ,philosophy a god2 ,if sages still for ,homer's birth contend ,the ,sons of ,science at this dome must bend4 ,all hail the shrine6 ,all hail the natal day1 ,cam boasts his noon1--,this ,cot his morning ray4 ,the house is now occupied by a person of the name of ,john ,wollerton4 ,it still contains the two dials made by ,newton1 but the styles of both are wanting4 ,the celebrated apple-tree1 the fall of one of the apples of which is said to have turned the attention of ,newton to the subject of gravity1 was destroyed by wind about four years ago2 but ,mr4 ,turnor has preserved it in the form of a chair4#ace ,the chambers which ,sir ,isaac inhabited at ,cambridge are known by tradition4 ,they are the apartments next to the great gate of ,trinity ,college1 and it is believed that they then communicated by a staircase with the observatory in the ,great ,tower1--an observatory which was furnished by the contributions of ,newton1 ,cotes1 and others4 ,his telescope1 represented in fig4 #c1 page #da1 is preserved in the library of the ,royal ,society of ,london1 and his globe1 his universal ring-dial1 quadrant1 compass1 and a reflecting telescope said to have belonged to him1 in the library of ,trinity ,college4 ,there is also in the same collection a long and curled lock of his silver white hair4 ,the door of his bookcase is in the ,museum of the ,royal ,society of ,edinburgh4 ,the manuscripts1 letters1 and other papers of ,newton have been preserved in different collections4 ,his correspondence with ,cotes relative to the second edition of the ,principia1 and amounting to between sixty and a hundred letters1 a considerable portion of the manuscript of that work1 and two or three letters to ,dr4 ,keill on the ,leibnitzian controversy1 are preserved in the library of ,trinity ,college1 ,cambridge4 ,newton's letters to ,flamstead1 about thirty-four in number1 are deposited in the library of ,corpus ,christi ,college1 ,oxford4#acf ,several letters of ,newton1 and1 we believe1 the original specimen which he drew up of the ,principia1 exist among the papers of ,mr4 ,william ,jones 7the father of ,sir ,william ,jones71 which are preserved at ,shirburn ,castle1 in the library of ,lord ,macclesfield4 ,but the great mass of ,newton's papers came into the possession of the ,portsmouth family through his niece1 ,lady ,lymington1 and have been safely preserved by that noble family4 ,there is reason to believe that they contain nothing which could be peculiarly interesting to science2 but as the correspondence of ,newton with contemporary philosophers must throw considerable light on his personal history1 we trust that it will ere long be given to the public4 ,,appendix4 ,no4 ,i4 ,,observations ,,on ,,the ,,family ,,of ,,sir ,,isaac ,,newton4 ,in the year #agje1 ,sir ,isaac gave into the ,herald's ,office an elaborate pedigree1 stating upon oath that he had reason to believe that ,john ,newton of ,westby1 in the county of ,lincoln1 was his great-grandfather's father1 and that this was the same ,john ,newton who was buried in ,basingthorpe church1 on the #bb;d ,december1 #aefc4 ,this ,john ,newton had four sons1 ,john1 ,thomas1 ,richard1 and ,william ,newton of ,gunnerly1 the last of whom was great-grandfather to ,sir ,john ,newton1 ,bart41 of ,hather4 ,sir ,isaac considered himself as descended from the eldest of these1 he having1 by tradition from his kindred ever since he can remember1 reckoned himself next of kin 7among the ,newtons7 to ,sir ,john ,newton's family4 ,the pedigree1 founded upon these and other considerations1 was accompanied by a certificate from ,sir ,john ,newton1 of ,thorpe1 ,bart41 who states that he had heard his father speak of ,sir ,isaac ,newton as of his relation and kinsman1 and that he himself believed that ,sir ,isaac was descended from ,john ,newton1 son to ,john ,newton of ,westby1 but knoweth not in what particular manner4 ,the pedigree of ,sir ,isaac1 as entered at the ,herald's ,office1 does not seem to have been satisfactory either to himself or to his successors1 as it could not be traced with certainty beyond his grandfather2 and it will be seen from the following interesting correspondence1 that upon making further researches1 he had found some reason to believe that he was of ,scotch extraction4 ,extract of a ,letter from the ,reverend ,dr4 ,reid of ,glasgow to ,dr4 ,gregory of ,edinburgh1 dated #adth ,march1 #aghd4 8,i send you on the other page an anecdote respecting ,sir ,isaac ,newton1 which ,i do not remember whether ,i ever happened to mention to you in conversation4 ,if his descent be not clearly ascertained 7as ,i think it is not in the books ,i have seen71 might it not be worth while to inquire if evidence can be found to confirm the account which he is said to have given of himself4 ,sheriff ,cross was very zealous about it when death put a stop to his inquiries4 8,when ,i lived in old ,aberdeen above twenty years ago1 ,i happened to be conversing over a pipe of tobacco with a gentleman of that country1 who had been lately at ,edinburgh4 ,he told me that he had been often in company with ,mr4 ,hepburn of ,keith1 with whom ,i had the honour of some acquaintance4 ,he said that1 speaking of ,sir ,isaac ,newton1 ,mr4 ,hepburn mentioned an anecdote1 which he had from ,mr4 ,james ,gregory1 professor of mathematics at ,edinburgh1 which was to this purpose3 8,mr4 ,gregory1 being at ,london for some time after he resigned the mathematical chair1 was often with ,sir ,isaac ,newton4 ,one day ,sir ,isaac said to him1 #8,gregory1 ,i believe you don't know that ,i am connected with ,scotland4'--#8,pray how1 ,sir ,isaac8' said ,gregory4 ,sir ,isaac said he was told that his grandfather was a gentleman of ,east ,lothian2 that he came to ,london with ,king ,james at his accession to the crown of ,england1 and there spent his fortune1 as many more did at that time1 by which his son 7,sir ,isaac's father7 was reduced to mean circumstances4 ,to this ,gregory bluntly replied1 #8,newton a gentleman of ,east ,lothian1 ,i never heard of a gentleman of ,east ,lothian of that name4' ,upon this ,sir ,isaac said1 #8that being very young when his father died1 he had it only by tradition1 and it might be a mistake2' and immediately turned the conversation to another subject4 8,i confess ,i suspected that the gentleman who was my author had given some colouring to this story1 and therefore ,i never mentioned it for a good many years4 8,after ,i removed to ,glasgow1 ,i came to be very intimately acquainted with ,mr4 ,cross1 then sheriff of ,lanark1 and one day at his own house mentioned this story1 without naming my author1 of whom ,i expressed some diffidence4 8,the sheriff immediately took it up as a matter worth being inquired into4 ,he said he was well acquainted with ,mr4 ,hepburn of ,keith 7who was then alive71 and that he would write him to know whether he ever heard ,mr4 ,gregory say that he had such a conversation with ,sir ,isaac ,newton4 ,he said he knew that ,mr4 ,keith1 the ambassador1 was also intimate with ,mr4 ,gregory1 and that he would write him to the same purpose4 8,some time after1 ,mr4 ,cross told me that he had answers from both the gentlemen above mentioned1 and that both remembered to have heard ,mr4 ,gregory mention the conversation between him and ,sir ,isaac ,newton1 to the purpose above narrated1 and at the same time acknowledged that they had made no further inquiry about the matter4 8,mr4 ,cross1 however1 continued the inquiry1 and a short time before his death told me that all he had learned was1 that there is1 or was lately1 a baronet's family of the name of ,newton in ,west ,lothian or ,mid ,lothian 7,i have forgot which73 that there is a tradition in that family that ,sir ,isaac ,newton wrote a letter to the old knight that then was 7,i think ,sir ,john ,newton of ,newton was his name71 desiring to know what children1 and particularly what sons he had1 their age1 and what professions they intended3 that the old baronet never deigned to return an answer to this letter1 which his family was sorry for1 as they thought ,sir ,isaac might have intended to do something for them40 ,several years after this letter was written1 a ,mr4 ,barron1 a relation of ,sir ,isaac ,newton1 seems to have been making inquiries respecting the family of his ancestor1 and in consequence of this the late ,professor ,robison applied to ,dr4 ,reid1 to obtain from him a more particular account of the remarkable conversation between ,sir ,isaac and ,mr4 ,james ,gregory referred to in the preceding letter4 ,in answer to this request1 ,dr4 ,reid wrote the following letter1 for which ,i was indebted to ,john ,robison1 ,esq4 ,sec4 ,r4 ,s4 ,e41 who found it among his father's manuscripts4 ,letter from ,dr4 ,reid to ,professor ,robison respecting the ,family of ,sir ,isaac ,newton4 8,,dear ,,sir1 8,i am very glad to learn by yours of ,april #d1 that a ,mr4 ,barron1 a near relation of ,sir ,isaac ,newton1 is anxious to inquire into the descent of that great man1 as the family cannot trace it farther1 with any certainty1 than his grandfather4 ,i therefore1 as you desire1 send you a precise account of all ,i know2 and am glad to have this opportunity1 before ,i die1 of putting this information in hands that will make the proper use of it1 if it shall be found of any use4 8,several years before ,i left ,aberdeen 7which ,i did in #agfd71 ,mr4 ,douglas of ,feckel1 the father of ,sylvester ,douglas1 now a barrister at ,london1 told me1 that having been lately at ,edinburgh1 he was often in company with ,mr4 ,hepburn of ,keith1 a gentleman of whom ,i had some acquaintance1 by his lodging a night at my house at ,new ,machar1 when he was in the rebel army in #agde4 ,that ,mr4 ,hepburn told him that he had heard ,mr4 ,james ,gregory1 professor of mathematics1 ,edinburgh1 say1 that being one day in familiar conversation with ,sir ,isaac ,newton at ,london1 ,sir ,isaac said1 #8,gregory1 ,i believe you don't know that ,i am a ,scotchman4'--#8,pray1 how is that8' said ,gregory4 ,sir ,isaac said he was informed that his grandfather 7or great-grandfather7 was a gentleman of ,east 7or ,west7 ,lothian3 that he went to ,london with ,king ,james the ,i4 at his accession to the crown of ,england3 and that he attended the court in expectation1 as many others did1 until he spent his fortune1 by which means his family was reduced to low circumstances4 ,at the time this was told me ,mr4 ,gregory was dead1 otherwise ,i should have had his own testimony1 for he was my mother's brother4 ,i likewise thought at that time that it had been certainly known that ,sir ,isaac had been descended from an old ,english family1 as ,i think is said in his eloge before the ,academy of ,sciences at ,paris1 and therefore ,i never mentioned what ,i had heard for many years1 believing that there must be some mistake in it4 8,some years after ,i came to ,glasgow1 ,i mentioned 7,i believe for the first time7 what ,i had heard to have been said by ,mr4 ,hepburn to ,mr4 ,cross1 late sheriff of this county1 whom you will remember4 ,mr4 ,cross was moved by this account1 and immediately said1 #8,i know ,mr4 ,hepburn very well1 and ,i know he was intimate with ,mr4 ,gregory3 ,i shall write him this same night1 to know whether he heard ,mr4 ,gregory say so or not4' ,after some reflection1 he added1 #8,i know that ,mr4 ,keith1 the ambassador1 was also an intimate acquaintance of ,mr4 ,gregory1 and as he is at present in ,edinburgh1 ,i shall likewise write to him this night4' 8,the next time ,i waited on ,mr4 ,cross he told me that he had wrote both to ,mr4 ,hepburn and ,mr4 ,keith1 and had an answer from both1 and that both of them testified that they had several times heard ,mr4 ,james ,gregory say1 that ,sir ,isaac ,newton told him what is above expressed1 but that neither they nor ,mr4 ,gregory1 as far as they knew1 ever made any further inquiry into the matter4 ,this appeared very strange both to ,mr4 ,cross and me1 and he said he would reproach them for their indifference1 and would make inquiry as soon as he was able4 8,he lived but a short time after this1 and in the last conversation ,i had with him upon the subject1 he said1 that all he had yet learned was1 that there was a ,sir ,john ,newton of ,newton in one of the counties of ,lothian 7but ,i have forgot which71 some of whose children were yet alive3 that they reported that their father1 ,sir ,john1 had a letter from ,sir ,isaac ,newton1 desiring to know the state of his family1 what children he had1 particularly what sons1 and in what way they were4 ,the old knight never returned an answer to this letter1 thinking probably that ,sir ,isaac was some upstart1 who wanted to claim a relation to his worshipful house4 ,this omission the children regretted1 conceiving that ,sir ,isaac might have had a view of doing something for their benefit4 8,after this ,i mentioned occasionally in conversation what ,i knew1 hoping that these facts might lead to some more certain discovery1 but ,i found more coldness about the matter than ,i thought it deserved4 ,i wrote an account of it to ,dr4 ,gregory1 your colleague1 that he might impart it to any member of the ,antiquarian ,society who he judged might have the curiosity to trace the matter further4 8,in the year #aghg1 my colleague1 ,mr4 ,patrick ,wilson1 professor of astronomy1 having been in ,london1 told me on his return that he had met accidentally with a ,james ,hutton1 ,esq4 of ,pimlico1 ,westminster1 a near relation of ,sir ,isaac ,newton1#acg to whom he mentioned what he had heard from me with respect to ,sir ,isaac's descent1 and that ,i wished much to know something more decisive on that subject4 ,mr4 ,hutton said1 if ,i pleased to write to him he would give me all the information he could give4 ,i wrote him accordingly1 and had a very polite answer1 dated at ,bath1 #beth ,december1 #aghg1 which is now before me4 ,he says1 #8,i shall be glad when ,i return to ,london1 if ,i can find in some old notes of my mother any thing that may fix the certainty of ,sir ,isaac's descent4 ,if he spoke so to ,mr4 ,james ,gregory1 it is most certain he spoke truth4 ,but ,sir ,isaac's grandfather1 not his great-grandfather1 must be the person who came from ,scotland with ,king ,james ,i4 ,if ,i find any thing to the purpose1 ,i will take care it shall reach you4' 8,in consequence of this letter ,i expected another from ,mr4 ,hutton when he should return to ,london1 but have never had any4 ,mr4 ,wilson told me he was a very old man1 and whether he be dead or alive ,i know not4 8,this is all ,i know of the matter1 and for the facts above mentioned ,i pledge my veracity4 ,i am much obliged to you1 dear sir1 for the kind expressions of your affection and esteem1 which1 ,i assure you1 are mutual on my part1 and ,i sincerely sympathize with you on your afflicting state of health1 which makes you consider yourself as out of the world1 and despair of seeing me any more4 8,i have been long out of the world by deafness and extreme old age4 ,i hope1 however1 if we should not meet again in this world1 that we shall meet and renew our acquaintance in another4 ,in the mean time1 ,i am with great esteem1 dear sir1 yours affectionately1 8,,tho4 ,,reid4 8,glasgow ,college1 0#abth ,april1 #agib40 ,this curious letter ,i published in the ,ed4 ,phil4 ,journal for ,october #a1 #ahbj4 ,it excited the particular attention of the late ,george ,chalmers1 ,esq41 who sent me an elaborate letter upon the subject2 but as ,i was at that time in the expectation of obtaining some important information through other channels1 this letter was not published4 ,this hope1 however1 has been disappointed4 ,a careful search has been made through the charter-chest of the ,newtons of ,newton in ,east ,lothian1 by ,mr4 ,richard ,hay ,newton1 the representative of that family1 but no document whatever has been found that can throw the least light upon the matter4 ,it deserves to be remarked1 however1 that ,sir ,richard ,newton1 the alleged correspondent of ,sir ,isaac1 appears to have destroyed his correspondence2 for though the charter-chest contains the letters of his predecessors for some generations1 yet there is not a single epistolary document either of his own or of his lady's4 ,hitherto the evidence of ,sir ,isaac's ,scottish descent has been derived chiefly from his conversation with ,mr4 ,james ,gregory2 but ,i am enabled1 by the kindness of ,mr4 ,robison1 to corroborate this evidence by the following information1 derived1 as will be seen1 from the family of the ,newtons of ,newton4 ,among various memoranda in the handwriting of ,professor ,robison1 who at one time proposed to write the life of ,sir ,isaac1 are the following3-- 8#ast1 ,lord ,henderland informed me in a letter dated ,march1 #agid1 that he had heard from his infancy that ,sir ,isaac considered himself as descended from the family of ,newton of ,newton4 ,this he heard from his uncle ,richard ,newton of ,newton 7who was third son of ,lord ,william ,hay of ,newhall730 8,he said that ,sir ,isaac wrote to ,scotland to learn whether any descendants of that family remained1 and this 7it was thought7 with the view to leave some of his fortune to the family possessing the estate with the title of baronet4 ,mr4 ,newton1 not having this honour1 and being a shy man1 did not encourage the correspondence1 because he did not consider himself as of kin to ,sir ,isaac1 c40 8#b;d1 ,information communicated to me by ,hay ,newton1 ,esq41 of that ilk1 #ahth ,august1 #ahjj40 8,the late ,sir ,richard ,newton of ,newton1 ,bart41 chief of that name1 having no male children1 settled the estate and barony of ,newton in ,east ,lothian county upon his relation ,richard ,hay ,newton1 ,esq41 son of ,lord ,william ,hay40#ach--8;,it cannot be discovered how long the family of ,newton have been in possession of the barony1 there being no tradition concerning that circumstance further than that they came originally from ,england at a very distant period1 and settled on these lands40--8,the celebrated ,sir ,isaac ,newton was a distant relation of the family1 and corresponded with the last baronet1 the above-mentioned ,sir ,richard ,newton40 ,the preceding documents furnish the most complete evidence that the conversation respecting ,sir ,isaac ,newton's family took place between him and ,mr4 ,gregory2 and the testimony of ,lord ,henderland proves that his own uncle1 ,richard ,newton of ,newton1 the immediate successor of ,sir ,richard ,newton1 with whom ,sir ,isaac corresponded1 was perfectly confident that such a correspondence took place4 ,all these circumstances prove that ,sir ,isaac ,newton could not trace his pedigree with any certainty beyond his grandfather1 and that there were two different traditions in his family1--one which referred his descent to ,john ,newton of ,westby1 and the other to a gentleman of ,east ,lothian who accompanied ,king ,james ,,vi4 to ,england4 ,in the first of these traditions he seems to have placed most confidence in #agje1 when he drew out his traditionary pedigree2 but as the conversation with ,professor ,james ,gregory respecting his ,scotch extraction took place twenty years afterward1 namely1 between #agbe and #agbg1 it is probable that he had discovered the incorrectness of his first opinions1 or at least was disposed to attach more importance to the other tradition respecting his descent from a ,scotch family4 ,in the letter addressed to me by the learned ,george ,chalmers1 ,esq4 ,i find the following observations respecting the immediate relations of ,sir ,isaac4 8,the ,newtons of ,woolsthorpe10 says he1 8who were merely yeomen farmers1 were not by any means opulent4 ,the son of ,sir ,isaac's father's brother was a carpenter called ,john4 ,he was afterward appointed gamekeeper to ,sir ,isaac1 as lord of the manor1 and died at the age of sixty in #agbe4 ,this ,john had a son1 ,robert1 7,john87 who was ,sir ,isaac's second cousin1 and who became possessed of the whole land estates at and near ,woolsthorpe1 which belonged to the great ,newton1 as his heir-at-law4#aci ,robert 7,john87 became a worthless and dissolute person1 who very soon wasted this ancient patrimony1 and falling down with a tobacco-pipe in his mouth when he was drunk1 it broke in his throat1 and put an end to his life at the age of thirty years1 in #agcg40 ,no4 ,,ii4 ,,letter ,,from ,,sir ,,isaac ,,newton ,,to ,,francis ,,aston1 ,,esq41 ,a ,,young ,,friend ,,who ,,was ,,on ,,the ,,eve ,,of ,,setting ,,out ,,upon ,,his ,,travels4 ,mr4 ,aston was elected a ,fellow of the ,royal ,society in #afgh4 ,he held the office of ,secretary between #afha and #afhe2 and he was the author of some observations on certain unknown ancient characters1 which were published in the ,philosophical ,transactions for #afic4 ,this letter has been referred to in pages #bgj and #cjc1 and was written when ,newton was only twenty-six years of age4 ,it is in every respect an interesting document4 8,trinity ,college1 ,cambridge1 ,may #ah1 #affi4 8,,sir1 8,since in your letter you give mee so much liberty of spending my judgement about what may be to your advantage in travelling1 ,i shall do it more freely than perhaps otherwise would have been decent4 ,first1 then1 ,i will lay down some general rules1 most of which1 ,i believe1 you have considered already2 but if any of them be new to you1 they may excuse the rest2 if none at all1 yet is my punishment more in writing than yours in reading4 8,when you come into any fresh company1 #a4 ,observe their humours4 #b4 ,suit your own carriage thereto1 by which insinuation you will make their converse more free and open4 #c4 ,let your discours be more in querys and doubtings than peremptory assertions or disputings1 it being the designe of travellers to learne1 not to teach4 ,besides1 it will persuade your acquaintance that you have the greater esteem of them1 and soe make them more ready to communicate what they know to you2 whereas nothing sooner occasions disrespect and quarrels than peremtorinesse4 ,you will find little or no advantage in seeming wiser or much more ignorant than your company4 #d4 ,seldom discommend any thing though never so bad1 or doe it but moderately1 lest you bee unexpectedly forced to an unhansom retraction4 ,it is safer to commend any thing more than it deserves1 than to discommend a thing soe much as it deserves2 for commendations meet not soe often with oppositions1 or1 at least1 are not usually soe ill resented by men that think otherwise1 as discommendations2 and you will insinuate into men's favour by nothing sooner than seeming to approve and commend what they like2 but beware of doing it by a comparison4 #e4 ,if you bee affronted1 it is better1 in a forraine country1 to pass it by in silence1 and with a jest1 though with some dishonour1 than to endeavour revenge2 for1 in the first case1 your credit's ne'er the worse when you return into ,england1 or come into other company that have not heard of the quarrell4 ,but1 in the second case1 you may beare the marks of the quarrell while you live1 if you outlive it at all4 ,but1 if you find yourself unavoidably engaged1 'tis best1 ,i think1 if you can command your passion and language1 to keep them pretty evenly at some certain moderate pitch1 not much hightning them to exasperate your adversary1 or provoke his friends1 nor letting them grow overmuch dejected to make him insult4 ,in a word1 if you can keep reason above passion1 that and watchfullnesse will be your best defendants4 ,to which purpose you may consider1 that1 though such excuses as this1--,he provok't mee so much ,i could not forbear1--may pass among friends1 yet amongst strangers they are insignificant1 and only argue a traveller's weaknesse4 8,to these ,i may add some general heads for inquirys or observations1 such as at present ,i can think on4 ,as1 #a4 ,to observe the policys1 wealth1 and state-affairs of nations1 so far as a solitary traveller may conveniently doe4 #b4 ,their impositions upon all sorts of people1 trades1 or commoditys1 that are remarkable4 #c4 ,their laws and customs1 how far they differ from ours4 #d4 ,their trades and arts wherein they excell or come short of us in ,england4 #e4 ,such fortifications as you shall meet with1 their fashion1 strength1 and advantages for defence1 and other such military affairs as are considerable4 #f4 ,the power and respect belonging to their degrees of nobility or magistracy4 #g4 ,it will not be time mispent to make a catalogue of the names and excellencys of those men that are most wise1 learned1 or esteemed in any nation4 #h4 ,observe the mechanisme and manner of guiding ships4 #i4 ,observe the products of nature in several places1 especially in mines1 with the circumstances of mining and of extracting metals or minerals out of their oare1 and of refining them2 and if you meet with any transmutations out of their own species into another 7as out of iron into copper1 out of any metall into quicksilver1 out of one salt into another1 or into an insipid body1 c471 those1 above all1 will be worth your noting1 being the most luciferous1 and many times lucriferous experiments too1 in philosophy4 #aj4 ,the prices of diet and other things4 #aa4 ,and the staple commoditys of places4 8,these generals 7such as at present ,i could think of71 if they will serve for nothing else1 yet they may assist you in drawing up a modell to regulate your travells by4 ,as for particulars1 these that follow are all that ,i can now think of1 viz4 ,whether at ,schemnitium1 in ,hungary 7where there are mines of gold1 copper1 iron1 vitrioll1 antimony1 c471 they change iron into copper by dissolving it in a vitriolate water1 which they find in cavitys of rocks in the mines1 and then melting the slimy solution in a strong fire1 which in the cooling proves copper4 ,the like is said to be done in other places1 which ,i cannot now remember2 perhaps1 too1 it may be done in ,italy4 ,for about twenty or thirty years agone there was a certain vitrioll came from thence 7called ,roman vitrioll71 but of a nobler virtue than that which is now called by that name2 which vitrioll is not now to be gotten1 because1 perhaps1 they make a greater gain by some such trick as turning iron into copper with it than by selling it4 #b4 ,whether1 in ,hungary1 ,sclavonia1 ,bohemia1 near the town ,eila1 or at the mountains of ,bohemia near ,silesia1 there be rivers whose waters are impregnated with gold2 perhaps1 the gold being dissolved by some corrosive waters like aqua regis1 and the solution carried along with the streame1 that runs through the mines4 ,and whether the practice of laying mercury in the rivers1 till it be tinged with gold1 and then straining the mercury through leather1 that the gold may stay behind1 be a secret yet1 or openly practised4 #c4 ,there is newly contrived1 in ,holland1 a mill to grind glasses plane withall1 and ,i think polishing them too2 perhaps it will be worth the while to see it4 #d4 ,there is in ,holland one ---- ,borry1 who some years since was imprisoned by the ,pope1 to have extorted from him secrets 7as ,i am told7 of great worth1 both as to medicine and profit1 but he escaped into ,holland1 where they have granted him a guard4 ,i think he usually goes clothed in green4 ,pray inquire what you can of him1 and whether his ingenuity be any profit to the ,dutch4 ,you may inform yourself whether the ,dutch have any tricks to keep their ships from being all worm-eaten in their voyages to the ,indies4 ,whether pendulum clocks do any service in finding out the longitude1 c4 8,i am very weary1 and shall not stay to part with a long compliment1 only ,i wish you a good journey1 and ,god be with you4 8,,is4 ,,newton4 8,pray let us hear from you in your travells4 ,i have given your two books to ,dr4 ,arrowsmith40 ,no4 ,,iii4 8,a ,,remarkable ,,and ,,curious ,,conversation ,,between ,,sir ,,isaac ,,newton ,,and ,,mr4 ,,conduit40 8,i was on ,sunday night1 the #gth of ,march1 #agbd-e1 at ,kensington with ,sir ,isaac ,newton1 in his lodgings1 just after he was come out of a fit of the gout1 which he had had in both his feet1 for the first time1 in the eighty-third year of his age4 ,he was better after it1 and his head clearer1 and memory stronger than ,i had known them for some time4 ,he then repeated to me1 by way of discourse1 very distinctly1 though rather in answer to my queries than in one continued narration1 what he had often hinted to me before1 viz4 that it was his conjecture 7he would affirm nothing7 that there was a sort of revolution in the heavenly bodies2 that the vapours and light emitted by the sun1 which had their sediment as water and other matter1 had gathered themselves by degrees into a body1 and attracted more matter from the planets1 and at last made a secondary planet 7viz4 one of those that go round another planet7 and then by gathering to them1 and attracting more matter1 became a primary planet2 and then by increasing still became a comet1 which after certain revolutions1 by coming nearer and nearer to the sun1 had all its volatile parts condensed1 and became a matter fit to recruit and replenish the sun 7which must waste by the constant heat and light it emitted7 as a fagot would this fire if put into it 7we were sitting by a wood fire71 and that that would probably be the effect of the comet of #afhj1 sooner or later1 for1 by the observations made upon it1 it appeared1 before it came near the sun1 with a tail only two or three degrees long2 but by the heat it contracted in going so near the sun1 it seemed to have a tail of thirty or forty degrees when it went from it2 that he could not say when this comet would drop into the sun2 it might perhaps have five or six revolutions more first1 but whenever it did it would so much increase the heat of the sun that this earth would be burnt1 and no animals in it could live4 ,that he took the three phenomena seen by ,hipparchus1 ,tycho ,brahe1 and ,kepler's disciples to have been of this kind1 for he could not otherwise account for an extraordinary light as those were1 appearing all at once among the fixed stars 7all which he took to be suns enlightening other planets as our sun does ours7 as big as ,mercury or ,venus seems to us1 and gradually diminishing for sixteen months1 and then sinking into nothing4 ,he seemed to doubt whether there were not intelligent beings superior to us who superintended these revolutions of the heavenly bodies by the direction of the ,supreme ,being4 ,he appeared also to be very clearly of opinion that the inhabitants of this world were of a short date1 and alleged as one reason for that opinion1 that all arts1 as letters1 ships1 printing1 needle1 c41 were discovered within the memory of history1 which could not have happened if the world had been eternal2 and that there were visible marks of ruin upon it which could not be effected by a flood only4 ,when ,i asked him how this earth could have been repeopled if ever it had undergone the same fate it was threatened with hereafter by the comet of #afhj1 he answered1 that required the power of a ,creator4 ,he said he took all the planets to be composed of the same matter with this earth1 viz4 earth1 water1 stones1 c41 but variously concocted4 ,i asked him why he would not publish his conjectures as conjectures1 and instanced that ,kepler had communicated his2 and though he had not gone near so far as ,kepler1 yet ,kepler's guesses were so just and happy that they had been proved and demonstrated by him4 ,his answer was1 #8,i do not deal in conjectures4' ,but upon my talking to him about the four observations that had been made of the comet of #afhj1 at #egd years' distance1 and asking him the particular times1 he opened his ,principia1 which laid on the table1 and showed me there the particular periods1 viz4 #ast1 the ,julium ,sidus1 in the time of ,justinian1 in #aajf1 in #afhj4 ,and ,i1 observing that he said there of that comet1 #8incidet in corpus solis1' and in the next paragraph adds1 #8stell fix refici possunt1' told him ,i thought he owned there what we had been talking about1 viz4 that the comet would drop into the sun1 and that fixed stars were recruited and replenished by comets when they dropped into them2 and1 consequently1 that the sun would be recruited too2 and asked him why he would not own as freely what he thought of the sun as well as what he thought of the fixed stars4 ,he said1 #8that concerned us more2' and1 laughing1 added1 #8that he had said enough for people to know his meaning4'0 ,the preceding paper1 with the title prefixed to it1 was first published by ,mr4 ,turnor in his ,collections1 c4 p4 #agb4 ,it was found among the ,portsmouth manuscripts1 in the handwriting of ,mr4 ,conduit4 ,,the ,,end4 ,,footnotes #a ,the ,marquis ,la ,place4--,see ,systme du ,monde1 p4 #ccf4 #b ,sir ,isaac ,newton told ,mr4 ,conduit1 that he had often heard his mother say that when he was born he was so little that they might have put him into a quart mug4 #c ,in ,leicestershire1 and about three miles south-east of ,woolsthorpe4 #d 8,i remember once10 says ,dr4 ,stukely1 8when ,i was deputy to ,dr4 ,hailey1 secretary at the ,royal ,society1 ,sir ,isaac talked of these kind of instruments4 ,that he observed the chief inconvenience in them was1 that the hole through which the water is transmitted being necessarily very small1 was subject to be furred up by impurities in the water1 as those made with sand will wear bigger1 which at length causes an inequality in time40--,stukely's ,letter to ,dr4 ,mead4--,turnor's ,collections1 p4 #agg4 #e ,mr4 ,clark informed ,dr4 ,stukely that the walls of the room in which ,sir ,isaac lodged were covered with charcoal drawings of birds1 beasts1 men1 ships1 and mathematical figures1 all of which were very well designed4 #f 8,one of his uncles10 says ,m4 ,biot1 8having one day found him under a hedge with a book in his hand and entirely absorbed in meditation1 took it from him1 and found that he was occupied in the solution of a mathematical problem4 ,struck with finding so serious and so active a disposition at so early an age1 he urged his mother no longer to thwart him1 and to send him back to ,grantham to continue his studies40 ,i have omitted this anecdote in the text1 as ,i cannot find it in ,turner's ,collections1 from which ,m4 ,biot derived his details of ,newton's infancy1 nor in any other work4 #g ,pemberton's ,view of ,sir ,isaac ,newton's ,philosophy4 ,pref4 #h ,peregregi vir indolis ac insignis periti4--,epist ad4 ,lect4 #i ,see ,newton's ,letter to the ,abb ,conti1 dated ,february #bf1 #agae-af1 in the ,additamenta ,comm4 ,epistolici4 #aj ,newtoni ,opera1 tom4 iv4 p4 #bje1 ,letter to ,oldenburg4 #aa ,m4 ,biot1 in his ,life of ,newton1 has stated that ,newton was preceded in the invention of the reflecting telescope by ,gregory1 but probably without knowing it4 ,it is quite certain1 however1 that ,newton was acquainted with ,gregory's invention1 as appears from the following avowal of it4 8,when ,i first applied myself to try the effects of reflection1 ,mr4 ,gregory's ,optica ,promota 7printed in the year #affc7 having fallen into my hands1 where there is an instrument described with a hole in the midst of the object-glass1 to transmit the light to an eye-glass placed behind it1 ,i had thence an occasion of considering that sort of construction1 and found their disadvantages so great1 that ,i saw it necessary before ,i attempted any thing in the practice to alter the design of them1 and place the eye-glass at the side of the tube rather than at the middle40--,letter to ,oldenburg1 ,may #dth1 #afgb4 #ab ,letter to ,oldenburg1 ,february #aj1 #afga4 #ac ,this gentleman was the author of a paper in the ,philosophical ,transactions1 entitled 8,optical ,assertions concerning the ,rainbow40 ,how such a paper could be published by so learned a body seems in the present day utterly incomprehensible4 ,the dials which ,linus erected at ,liege1 and which were the originals of those formerly in the ,priory ,gardens in ,london1 are noticed in the ,philosophical ,transactions for #agjc4 ,in one of them the hours were distinguished by touch4 #ad ,newton speaks with singular positiveness on this subject4 8,for ,i know10 says he1 8that ,mr4 ,lucas's observations cannot hold where the refracting angle of the prism is full #fj1 and the day is clear1 and the full length of the colours is measured1 and the breadth of the image answers to the sun's diameter2 and seeing ,i am well assured of the truth and exactness of my own observations1 ,i shall be unwilling to be diverted by any other experiments from having a fair end made of this in the first place40 ,on the supposition that his prism was one of very low dispersive power1 ,mr4 ,lucas might1 with perfect truth1 have used the very same language towards ,newton4 #ae ,letter to ,oldenburg in #afgb1 containing his first reply to ,huygens4 #af ,in an experiment made by ,newton1 he had occasion to counteract the refraction of a prism of glass by another prism of water2 and had he completed the experiment1 and studied the result of it1 he could not have failed to observe a quantity of uncorrected colour1 which would have led him to the discovery of the different dispersive powers of bodies4 ,but in order to increase the refractive power of the water1 he mixed with it a little sugar of lead1 the high dispersive power of which seems to have rendered the dispersive power of the water equal to that of the glass1 and thus to have corrected the uncompensated colour of the glass prism4 #ag ,see the article ,,optics in the ,edinburgh ,encyclopdia1 vol xv4 p4 #dgi1 note4 #ah 8,this result was obtained10 as ,newton says1 8by an assistant whose eyes were more critical than mine1 and who1 by right lines drawn across the spectrum1 noted the confines of the colours4 ,and this operation being divers times repeated both on the same and on several papers1 ,i found that the observations agreed well enough with one another40--,,optics1 ,part ,,ii4 ,book ,,iii4 #ai ,optics1 ,book ii4 ,prop4 iv4 #bj ,in the same paragraph1 when speaking of black bodies becoming hot1 and burning sooner than others1 he says that their 8effect may proceed partly from the multitude of refractions in a little room and partly from the easy commotion of so very small corpuscles40--,optics1 ,part iii4 ,prop4 vii4 p4 #bce4 #ba ,see page #ced4 #bb ,when ,newton speaks of bodies losing their reflecting power from their thinness he means the reflecting power of their second surfaces1 as is evident from the reason he assigns4--,see ,optics1 ,part iii4 ,prop4 xiii4 p4 #beg4 #bc ,edinburgh ,journal of ,science1 ,no4 #a4 p4 #ajh4 #bd ,see the ,phil4 ,trans4 #ahbi1 ,part ,i4 p4 #ahi4 #be ,idem4 #bf ,phil4 ,trans4 #ahai1 p4 #aa4 #bg ,if this view of the matter be just1 we should expect that the specific gravity of the black would exceed that of the yellow phosphorus4 #bh ,since the two preceding chapters were written1 ,i have had occasion to confirm and extend the views which they contain by many new experiments4 #bi ,physico-,mathesis de ,lumine coloribus et iride aliisque annexis4 ,bonon4 #affe4 #cj ,this doctrine is thus announced4 #a4 ,that the same rays of light falling upon the same point of an object will turn into all sorts of colours by the various inclination of the object4 #b4 ,that colours begin to appear when two pulses of light are blended so well and so near together that the sense takes them for one4 #ca ,this effect is so great1 that at the distance of four inches from the point of divergence1 the angular inflexion of the red rays of the first fringe is #ab #f1 while at the distance of about twenty feet1 it is only #c #ee4 #cb ,see the twenty-ninth query at the end of his ,optics1 where the sides of a ray are compared with the poles of a magnet4 #cc ,the ,english edition was reprinted at ,london in #agad1 #agba1 and #agcj1 and the ,latin one at ,london in #agjf1 #agai1 #agba1 #agbh1 at ,lausanne in #agdj1 and at ,padua in #aggc4 #cd ,when ,james ,i4 went to ,copenhagen in #aeij1 to conclude his marriage with the ,princess ,anne of ,denmark1 he spent eight days under the roof of ,tycho at ,uraniburg4 ,as a token of his gratitude1 he composed a set of ,latin verses in honour of the astronomer1 and left him a magnificent present at his departure4 ,he gave him also his royal license for the publication of his works in ,england1 and accompanied it with the following complimentary letter3-- 8,nor am ,i acquainted with these things on the relation of others1 or from a mere perusal of your works1 but ,i have seen them with my own eyes1 and heard them with my own ears1 in your residence at ,uraniburg1 during the various learned and agreeable conversations which ,i there held with you1 which even now affect my mind to such a degree1 that it is difficult to decide whether ,i recollect them with greater pleasure or admiration40 #ce ,the cube1 the sphere1 the tetrahedron1 the octohedron1 the dodecahedron1 and the icosahedron4 #cf ,simon ,marius1 mathematician to the ,marquis of ,brandenburg1 assures us that he discovered the satellites of ,jupiter in ,november1 #afji4 #cg ,it is distinctly stated in the sentence of the ,inquisition1 that ,galileo's enemies had charged him with having abjured his opinions in #afaf1 and affirmed that he had been punished by the ,inquisition4 ,in order to refute these calumnies1 ,galileo applied to ,cardinal ,bellarmine for a certificate to prove that he neither abjured his opinions nor suffered any punishment for them2 but that the doctrine of the motion of the earth and the stability of the sun was only denounced to him as contrary to ,scripture1 and as one which could not be defended or maintained4 ,cardinal ,bellarmine drew up such a certificate in his own handwriting4 #ch ,theoric ,medicearum planetarum ex causis physicis deduct4 ,flor4 #afff1 #dto4 #ci ,m4 ,delambre maintains that these views of ,borelli are only those of ,kepler slightly modified4 ,newton and ,huygens have attached to them a greater value4 ,the last of these philosophers remarks1 8,refert ,plutarchus1 fuisse jam olim qui putaret ideo manere lunam in orbe suo1 quod vis recedendi a terra1 ob motum circularem1 inhiberetur pari vi gravitatis1 qua ad terram accedere conaretur4 ,idemque vo nostro1 non de luna tantum sed et planetis ceteris statuit ,alphonsus ,borellus1 ut nempe primariis eorum gravitas esset solem versus2 lunis vero ad terram1 ,jovem ac ,saturnum quos comitantur40--,huygen1 ,cosmotheor1 lib4 ii42 ,opera1 t4 ii4 p4 #gbj4 #dj ,hist4 de l',astronomie aux ,dix-huitieme ,sicle1 p4 #i4 #da 8,but for the duplicate proportion1 ,i gathered it from ,kepler's theorem about twenty years ago40--,newton's ,letter to ,halley1 ,july #ad1 #afhf4 #db ,whiston asserts that this cause was supposed by ,newton to be something analogous to the vortices of ,descartes4--,see ,whiston's ,memoirs of himself1 p4 #bca4 #dc ,waller's ,life of ,hooke1 p4 #bb4 #dd ,ibid4 #de ,july #bg1 #afhf1 ,biog4 ,brit4 p4 #bffb4 #df ,commercium ,epistolicum1 ,no4 #g4 #dg ,this ,scholium is added to ,prop4 iv4 lib4 i4 coroll4 #f4 #dh ,in writing to ,flamstead1 ,newton requests from him the long diameters of the orbits of ,jupiter and ,saturn1 that he 8may see how the sesquialteral proportion fills the heavens40 #di ,whiston's ,memoirs of his own ,life4 #ej 8,dr4 ,reid states1 that ,james ,gregory1 ,professor of ,philosophy at ,st4 ,andrew's1 printed a thesis at ,edinburgh in #afij1 containing twenty-five positions1 of which twenty-two were a compend of ,newton's ,principia40 #ea ,nichols's ,literary ,anecdotes1 vol4 iii4 p4 #cbb4 ,cotes states in his preface to the second edition of the ,principia1 that copies of the first edition could only be obtained at an immense price4 #eb ,preface to ,desaguliers's ,experimental ,philosophy4 ,dr4 ,desaguliers states that he was told this anecdote several times by ,sir ,isaac ,newton himself4 #ec ,the ,life of ,john ,locke1 p4 #bji-bae1 ,lond4 #ahbi4 #ed ,principia1 lib4 i4 prop4 i4 #ee ,ib4 lib4 i4 prop4 xi4 #ef 8,on peut regarder ,fermat10 says ,lagrange1 8comme le premier inventeur des nouveaux calculs20 and ,laplace observes1 8,il paraitque ,fermat le veritable inventeur du calcul differentiel1 l'ait envisag comme un cas particulier de celui des differences10 c4 #eg ,art4 ,mathematics1 in the ,edinburgh ,encyclopdia1 volume xiii4 p4 #cfe4 #eh ,these facts are mentioned in ,newton's letter to ,oldenburgh1 ,october #bd1 #afgf4 #ei ,dr4 ,pemberton informs us that he had prevailed upon ,sir ,isaac to publish this treatise during his lifetime1 and that he had for this purpose examined all the calculations and prepared part of the figures4 ,but as the latter part of the treatise had never been finished1 ,sir ,isaac was about to let him have other papers to supply what was wanting1 when his death put a stop to the plan4--,preface to ,pemberton's ,view of ,sir ,isaac ,newton's ,philosophy4 #fj ,isaci ,newtoni ,opera qu extant omnia1 vol4 i4 p4 #chh-eai4 #fa 8,acutissimis qui toto orbe florent ,mathematicis40 #fb ,henry ,oldenburg1 whose name is so intimately associated with the history of ,newton's discoveries1 was born at ,bremen1 and was consul from that town to ,london during the usurpation of ,cromwell4 ,having lost his office1 and being compelled to seek the means of subsistence1 he became tutor to an ,english nobleman1 whom he accompanied to ,oxford in #afef4 ,during his residence in that city he became acquainted with the philosophers who established the ,royal ,society1 and upon the death of ,william ,crown1 the first secretary1 he was appointed in #affc1 joint secretary along with ,mr4 ,wilkins4 ,he kept up an extensive correspondence with the philosophers of all nations1 and he was the author of several papers in the ,philosophical ,transactions1 and of some works which have not acquired much celebrity4 ,he died at ,charlton1 near ,greenwich1 in ,august1 #afgg4 #fc ,these words in brackets are in the second edition1 but not in the first4 #fd ,as this passage is of essential importance in this controversy1 we shall give it in the original4 8,pro differentiis igitur ,leibnitianis ,d4 ,newtonus adhibet1 semperque adhibuit1 fluxiones1 qu sunt quam proxime ut fluentium augmenta1 qualibus temporis particulis quam minimis genita2 iisque tam in suis ,principiis ,natur ,mathematicis1 tum in aliis postea editis1 eleganter est usus2 quem admodum et ,honoratus ,fabrius in sua ,synopsi ,geometrica1 motuumque progressus ,cavallerian methodo substituit40 #fe ,homine docto1 sed novo1 et parum perito rerum ante actarum cognitare4 #ff ,van et injust vociferationes4 #fg ,letter to ,count ,bothman in ,des ,maizeaux's ,recueil de diverses pieces1 tom4 ii4 p4 #dd1 #de4 #fh ,see ,des ,maizeaux1 tom4 ii4 p4 #aaf4 #fi ,written in ,november or ,december1 #agae4 #gj ,this is the ,recensio ,commercii ,epistolici1 or review of it1 which was first published in the ,phil4 ,trans4 #agae4 #ga ,m4 ,biot remarks1 that the animosity of ,newton was not calmed by the death of ,leibnitz1 for he had no sooner heard of it than he caused to be printed two manuscript letters of ,leibnitz1 written in the preceding year1 accompanying them with a very bitter refutation 7en les accompagnant d'un refutation tres-amere74 ,who that reads this sentence does not believe that the bitter refutation was written after ,leibnitz's death8 ,the animosity could not be shown by the simple publication of the letters4 ,it could reside only in the bitterness of the refutation4 ,the implied charge is untrue2 the bitter refutation was written before ,leibnitz's death1 and consequently he showed no animosity over the grave of his rival2 and in our opinion none even before his death4 #gb ,m4 ,biot states that ,sir ,isaac ,newton caused this edition of the ,commercium ,epistolicum to be printed2 that ,sir ,isaac placed at the head of it a partial abstract of the collection2 and that this abstract appeared to have been written by himself4 ,these groundless charges may be placed1 without any refutation1 beside the assertion of ,montucla1 that ,newton wrote the notes 7les notes7 on the ,commercium ,epistolicum2 and the equally incorrect statement of ,la ,croix1 that ,newton added to it notes 7des notes71 with his own hand4 ,we should not have noticed the charges of ,m4 ,biot1 had he not adduced them as proofs of ,newton's animosity to ,leibnitz after his death4 ,see ,mr4 ,herschel's ,history of ,mathematics in the ,edinburgh ,encyclopdia1 vol4 xiii4 p4 #cfh1 note4 #gc ,see ,burnet's ,history of his own ,times1 vol4 i4 p4 #fig4 ,lond4 #agbd4 #gd ,the other candidates were ,sir ,robert ,sawyer and ,mr4 ,finch1 and the votes stood thus4 ,sir ,robert ,sawyer1 #abe ,mr4 ,newton1 #abb ,mr4 ,finch1 #aag #ge ,this ,m4 ,colin was probably a young bachelor of arts whom ,newton seems afterward to have employed in some of his calculations4 ,these bachelors were distinguished by the title of ,dominus1 and it was usual to translate this word and to call them ,sir4 ,in a letter from ,newton to ,flamstead1 dated ,cambridge1 ,june #bith1 #afie1 is the following passage3 8,i want not your calculations1 but your observations only1 for besides myself and my servant1 ,sir ,collins 7whom ,i can employ for a little money1 which ,i value not7 tells me that he can calculate an eclipse and work truly40 #gf ,they are thus dated in ,horsley's edition of ,newton's ,works1 the fourth letter having an earlier date than the third4 #gg ,see ,newtoni ,opera1 tom4 iv4 p4 #dhj1 and ,wallasii ,opera1 #afic1 tom4 ii4 p4 #cia-cif4 #gh ,optics1 part iv4 obs4 #ac4 #gi ,for these letters ,i have been indebted to the kindness of ,lord ,braybrooke4 #hj ,these three letters have been published by ,lord ,braybrooke in the ,life and ,correspondence of ,mr4 ,pepys4 #ha ,this anxiety will be understood from the fact that1 by an order of council dated ,january #bhth1 #afgd-e1 ,mr4 ,newton was excused from making the usual payments of one shilling per week1 8on account of his low circumstances1 as he represented40 #hb ,the system of ,hobbes was at this time very prevalent4 ,according to ,dr4 ,bentley1 8the taverns and coffee-houses1 nay1 ,westminster ,hall and the very churches1 were full of it20 and he was convinced from personal observation1 that 8not one ,english infidel in a hundred was other than a ,hobbist40--,monk's ,life of ,bentley1 p4 #ca4 #hc ,the draft of this letter is endorsed 8,j4 ,l4 to ,i4 ,newton40 #hd ,dr4 ,gregory concludes his account of this manuscript1 which he has kindly permitted me to read1 in the following words3--8,i do not know whether it is true1 as stated by ,huygens1 #8,newtonum incidisse in ,phrenitim2' but ,i think every gentleman who examines this manuscript will be of opinion that he must have thoroughly recovered from his phrenitis before he wrote either the ,commentary on the ,opinions of the ,ancients1 or the ,sketch of his own ,theological and ,philosophical ,opinions which it contains40 #he ,this paragraph is as follows3--8,deum esse ens summe perfectum concedunt omnes4 ,entis autem summe perfecti ,idea est ut sit substantia1 una1 simplex1 indivisibilis1 viva et vivifica1 ubique semper necessario existens1 summe intelligens omnia1 libere volens bona1 voluntate efficiens possibilia1 effectibus nobilioribus similitudinem propriam quantum fieri potest communicans1 omnia in se continens tanquam eorum principium et locus1 omnia per presentiam substantialem cernens et regens1 et cum rebus omnibus1 secundum leges accuratas ut natur totius fundamentum et causa constanter co-operans1 nisi ubi aliter agere bonum est40 #hf ,the following extract1 characteristic of ,flamstead's manner1 is from a letter to ,newton dated ,january #f1 #afih-i4 8,upon hearing occasionally that you had sent a letter to ,dr4 ,wallis about the parallax of the fixed stars to be printed1 and that you had mentioned me therein with respect to the theory of the moon1 ,i was concerned to be publicly brought upon the state about what1 perhaps1 will never be fitted for the public1 and thereby the world put into an expectation of what perhaps they are never likely to have4 ,i do not love to be printed upon every occasion1 much less to be dunned and teased by foreigners about mathematical things1 or to be thought by your own people to be trifling away my time when ,i should be about the king's business40 ,on the first of the above passages in italics ,flamstead has the following memorandum3--8,when ,mr4 ,halley boasts 'tis done1 and given to him as a secret1 tells the ,society so and foreigners40 ,in the second passage in italics1 ,mr4 ,flamstead refers1 in a note1 to ,mr4 ,colson's letter to him1 in which he seems to have represented practical astronomy as trifling4 ,mr4 ,flamstead adds1 8,was ,mr4 ,newton a trifler when he read mathematics for a salary at ,cambridge3 surely1 then1 astronomy is of some good use1 though his place be more beneficial40 ,for these extracts from the original manuscript in the collection of ,corpus ,christi ,college1 ,oxford1 ,i have been indebted to the kindness of ,professor ,rigaud of ,oxford4 #hg ,see page #bae1 note4 #hh ,the candidates in #agja were as follows3 ,mr4 ,henry ,boyle1 afterward ,lord ,carleton1 #ahj ,both of ,trinity ,mr4 ,newton #afa ,college4 ,mr4 ,hammond #fd #hi ,the banquet which was on this occasion given in the college hall to the royal visiter seems to have cost about #ajjjl41 and the university was obliged to borrow #ejjl41 to defray the expense of it4--,monk's ,life of ,bentley1 p4 #adc1 #add4 #ij ,the candidates in #agje were as follows3 ,the ,hon4 ,arthur ,annesley #ahb ,hon4 ,dixie ,windsor #agj ,mr4 ,godolphin #afb ,sir ,isaac ,newton #aag #ia ,journals of the ,house of ,commons1 vol4 xvii4 p4 #fgg1 #gaf4 #ib ,whiston's 8,longitude ,discovered40 ,lond #agch4 #ic ,this anecdote concerning the ,chronological manuscript is not correctly given in the ,biographia ,britannica1 and in some of the other lives of ,newton4 ,i have followed implicitly ,newton's own account of it in the ,phil4 ,trans4 #agbe1 vol4 xxxiii4 ,no4 #chi1 p4 #cae4 #id ,m4 ,biot has supposed that this abstract was an imperfect edition of ,newton's work on ,chronology4 #ie ,father ,souciet was supposed by ,halley and others to have been the author of these observations1 but there is no doubt that they were written by ,m4 ,freret4 #if ,it is stated in the ,biogr4 ,britannica1 ,art4 ,newton1 that the copy of the ,french translation was not accompanied with the refutation4 ,though the reverse of this is not distinctly stated by ,sir ,isaac himself1 yet it may be inferred from his observations4 #ig ,vol4 xxxiii4 ,no4 #chi1 p4 #cae4 #ih ,according to ,whiston1 ,sir ,isaac wrote out eighteen copies of this chapter with his own hand1 differing little from one another4--,whiston's ,life1 p4 #ci4 #ii ,this work is the first article in the fifth volume of ,dr4 ,hersley's edition of ,newton's works4 ,the next article in the volume is entitled1 8,a ,short ,chronicle from a ,,ms41 the property of the ,reverend ,dr4 ,ekins1 ,dean of ,carlisle20 which is nothing more than the abstract of the ,chronology already printed in the same volume4 ,we cannot even conjecture the reasons for publishing it1 especially as it is less perfect than the abstract1 two or three dates being wanting4 #ajj ,see vol4 xxxiv4 p4 #bje1 and vol4 xxxv4 p4 #bif4 #aja ,see an excellent view of this chronological controversy in an able note by ,m4 ,daunou1 attached to ,biot's ,life of ,newton in the ,biog4 ,universelle1 tom4 xxxi4 p4 #ahj4 #ajb ,this letter is published without any date in the ,gentleman's ,magazine for #agee1 vol4 xxv4 p4 #c4 ,it bears internal evidence of being genuine4 #ajc ,his ,historical ,account of two notable ,corruptions of the ,scriptures4 #ej pp quarto4 #ajd ,the editor supplied the beginning down to the #acth page1 where he mentions in a note that 8thus far is not ,sir ,isaac's40 #aje ,m4 ,biot has well remarked that there is absolutely nothing in the writings of ,newton to justify1 or even to authorize1 the idea that he was an ,antitrinitarian4 ,this passage is strangely omitted in the ,english translation of ,biot's ,life of ,newton4 ,we do not know upon what authority ,dr4 ,thomson states1 in his ,history of the ,royal ,society1 that ,newton 8did not believe in the ,trinity10 and that ,dr4 ,horsley considered ,newton's papers unfit for publication1 because they contained proofs of his hostility to that doctrine4 #ajf ,whiston's ,memoirs of his own ,life1 p4 #agh1 #bdi1 #bej4 ,edit4 #agec4 #ajg ,dr4 ,monk's ,life of ,bentley1 p4 #ca4 #ajh ,dated ,december #ajth1 #afib4 ,this letter is endorsed1 in ,bentley's hand1 8,mr4 ,newton's answer to some queries sent by me after ,i had preached my two last sermons40--,monk's ,life of ,bentley1 p4 #cd1 note4 #aji ,dated ,jan4 #agth1 #afib-c4 #aaj 8,these things10 says he1 8follow from my ,princip4 ,math4 lib4 i4 prop4 #cc1 #cd1 #ce1 #cf40 #aaa ,dated ,february #aath1 #afic4 #aab ,the originals of these four letters to ,bentley 8were given by ,dr4 ,richard ,bentley to ,cumberland1 his nephew1 and executor1 while a student at ,trinity ,college1 and were printed by him in a separate pamphlet in #agef4 ,this publication was reviewed by ,dr4 ,samuel ,johnson in the ,literary ,magazine1 vol4 i4 p4 #hi4 ,see ,johnson's ,works1 vol4 ii4 p4 #cbh4 ,the original letters are preserved in ,trinity ,college1 to which society they were given by ,cumberland a short time before his death40--,monk's ,life of ,bentley1 p4 #cc1 note4 #aac ,mr4 ,herschel1 in his ,treatise on ,light1 #eec1 has maintained that ,newton's ,doctrine of ,reflection is accordant with the idea that the attractive force extends beyond the repulsive or reflecting force4 ,in the query above referred to1 ,sir ,isaac1 in the most distinct manner1 places the sphere of the reflecting force without that of the attractive one4 #aad ,in a tract annexed to his ,appeal to all that doubt or disbelieve the truths of the ,gospel4 ,see ,gent4 ,mag4 #aghb1 vol4 iii4 p4 #bbg1 #bci4 ,it is stated in a letter of ,mr4 ,law's1 quoted in this magazine1 that ,charles ,i4 was a diligent reader and admirer of ,jacob ,behmen2 that he sent a well-qualified person from ,england to ,goerlitz1 in ,upper ,lusatia1 to acquire the ,german language1 and to collect every anecdote he could meet with there relative to this great alchymist4 #aae ,in a letter to ,dr4 ,halley1 dated ,june #bjth1 #afhf1 ,sir ,isaac refers to this paper1 and observes1 that it is only to be looked upon as one of his guesses that he did not rely upon4 #aaf ,see page #bgc4 #aag ,see ,newtoni ,opera1 by ,horsley1 vol4 iv4 p4 #cge-chb4 #aah ,sir ,isaac does not seem to have afterward described this construction4 #aai ,see ,edinburgh ,transactions1 vol4 ix4 p4 #dcc1 and the ,edinburgh ,journal of ,science1 ,july1 #ahbi1 ,no4 ,i4 ,new ,series1 p4 #ajh4 #abj ,art4 ,accidental ,colours in the ,edinburgh ,encyclopdia4 #aba ,see ,phil4 ,trans4 #agbb1 vol4 xxxiii4 p4 #eg4 #abb ,this conversation1 originally copied from ,mr4 ,conduit's handwriting1 is given in the ,appendix1 ,no4 iii4 p4 #cbj4 #abc ,these were the three children of his half-brother ,smith1 the three children of his half-sister ,pilkington1 and the two daughters of his half-sister ,barton1 all of whom survived ,sir ,isaac4 ,new ,anecdotes of ,sir ,isaac ,newton1 by ,j4 ,h41 a ,gentleman of his ,mother's ,family4 ,see ,annual ,register1 #aggf1 vol4 xix4 p4 #be of ,characters4 ,the author of this paper was ,james ,hutton1 ,esq4 of ,pimlico4 #abd ,turnor's ,collections1 c4 p4 #aeh4 ,see ,,appendix1 p4 #caf4 #abe ,this valuable faculty characterizes all his writings1 whether theological1 chymical1 or mathematical2 but it is peculiarly displayed in his treatise on ,universal ,arithmetic1 and in his ,optical ,lectures4 #abf ,de ,magnete1 p4 #db1 #eb1 #afi1 and ,pref4 p4 #cj4 #abg ,the following passages from ,leonardo da ,vinci are very striking3 8,theory is the general1 and practice the soldiers4 8,experiment is the interpreter of the artifices of nature4 ,it never deceives us2 it is our judgment itself which sometimes deceives us1 because we expect from it effects which are contrary to experiment4 ,we must consult experiment by varying the circumstances till we have deduced from it general laws2 for it is it which furnishes true laws4 8,in the study of the sciences which depend on mathematics1 those who do not consult nature1 but authors1 are not the children of nature2 they are only her grandchildren4 ,nature alone is the master of true genius4 8,in treating any particular subject1 ,i would first of all make some experiments1 because my design is first to refer to experiment1 and then to demonstrate why bodies are constrained to act in such a manner4 ,this is the method which we ought to follow in investigating the phenomena of nature4 ,it is very true that nature begins by reasoning and ends with experiment2 but it matters not1 we must take the opposite course2 as ,i have said1 we must begin by experiment1 and endeavour by its means to discover general principles40 ,thus1 says ,venturi1 spoke ,leonard a century before ,bacon1 and thus1 we add1 did ,leonard tell philosophers all that they required for the proper investigation of general laws4 ,see ,essai sur les uvrages physico-mathematiques de ,leonard de ,vinci1 par ,j4 ,b4 ,venturi4 ,paris1 #agii1 p4 #cb1 #cc1 c4 ,see also ,carlo ,amoretti's ,memorie storiche su la vita gli studi e le ,opere de ,lionardo da ,vinci4 ,milano1 #ahjd4 #abh ,mr4 ,hearne1 in a memorandum dated ,april #dth1 #agbf1 states1 that a great quarrel happened between ,sir ,isaac ,newton and ,mr4 ,halley4 ,if this is true1 the difference is likely to have originated in ,halley's impiety4 #abi ,professor ,rigaud of ,oxford heard this anecdote from ,dr4 ,maskelyne4 #acj 8,he was very kind to all the ,ayscoughs4 ,to one he gave #hjjl41 to another #bjjl41 and to a third #ajjl41 and many other sums2 and other engagements did he enter into also for them4 ,he was the ready assistant of all who were any way related to him1--to their children and grandchildren40--,annual ,register1 #aggf1 vol4 xix4 p4 #be4 ,sir ,isaac gave some donations to the chapel and parish of ,colsterworth4 ,hearne says 8that he promised to become a benefactor to the ,royal ,society1 but failed40 #aca ,the following anecdote of ,sir ,isaac's absence has been published1 but ,i cannot vouch for its authenticity4 ,his intimate friend ,dr4 ,stukely1 who had been deputy to ,dr4 ,halley as secretary to the ,royal ,society1 was one day shown into ,sir ,isaac's dining-room1 where his dinner had been for some time served up4 ,dr4 ,stukely waited for a considerable time1 and getting impatient1 he removed the cover from a chicken1 which he ate1 replacing the bones under the cover4 ,in a short time ,sir ,isaac entered the room1 and after the usual compliments sat down to his dinner1 but on taking off the cover1 and seeing nothing but bones1 he remarked1 8,how absent we philosophers are4 ,i really thought that ,i had not dined40 #acb ,epistolary ,correspondence1 vol4 i4 p4 #ahj1 sec4 #gg4 #acc ,,ms4 ,memoranda in the ,bodleian ,library4 #acd ,turnor's ,collections1 p4 #agf4 #ace ,the anecdote of the falling apple is mentioned neither by ,dr4 ,stukely nor by ,mr4 ,conduit1 and as ,i have not been able to find any authority for it whatever1 ,i did not feel myself at liberty to use it4 #acf ,in the ,monthly ,review for ,august1 #ahbi1 p4 #eic1 it is stated1 that the correspondence between ,newton and ,flamstead1 from #afhj to #afih1 exists in the ,sloane collection of ,manuscripts in the ,british ,museum4 ,professor ,rigaud1 however1 has had the kindness to inquire into the accuracy of this statement1 and he has ascertained that these letters are merely copies1 which ,dr4 ,birch had made from the originals at ,oxford4 #acg ,see page #bhh1 note4 #ach ,this entail was executed in #agbd1 a year or two before ,sir ,richard's death4--,d4 ,b4 #aci ,see p4 #bia4 99 99 99 99 99 99 ,transcriber's note3 ,punctuation1 hyphenation1 and spelling were made consistent when a predominant preference was found in this book2 otherwise they were not changed4 ,many abbreviations1 and some sentences1 did not end with periods4 ,transcriber added missing periods only at the ends of sentences1 and did not attempt to resolve other inconsistencies4 ,simple typographical errors were corrected2 occasional unpaired quotation marks retained4 ,ambiguous hyphens at the ends of lines were retained4 ,in some letters1 the salutations and dates were printed on the same line1 and the signatures sometimes were printed on the same lines as the end of the body4 ,in this e,book1 the dates always appear above the salutations and the signatures are on their own lines4 ,superscripts were used only as abbreviations for names and words1 not in mathematical expressions1 and have been printed as normal lower-case letters in the ,plain ,text version of this e,book4 ,the ,transcriber did not review the spelling of non-,english words4 ,second page 7unnumbered71 last line3 8with whom they abide40 ,the word shown here as 8abide0 was poorly printed and unclear4 ,at the bottom of the ,title page1 the date is 8#ahcc02 at the bottom of the cover1 the date is 8#ahce04 ,page #ff3 8piece of plane glass0 was printed that way4 ,page #ff3 ,transcriber added the comma in 8and ,,lr1 ,,lr the extreme red04 ,page #gj3 ,transcriber added italics to 8makes orange04 ,page #abf3 8on the #gth ,january1 #afah0 should be 8#afaj04 ,page #cjf referred to ,newton's telescope being shown in 8fig4 #a01 but it actually is in 8fig4 #c0 and is referenced that way in this e,book4 ,page #cba3 ,the opening parenthesis before 8viz4 one of those that go round another0 has no matching closing parenthesis4 ,transcriber added a closing parenthesis after 8round another planet01 but that may not be where it belongs4