,transcriber's ,note ,the punctuation and spelling from the original text have been faithfully preserved4 ,only obvious typographical errors have been corrected4 ,there are several mathematical formulas within the text4 ,they are represented as follows3 ,superscripts3 x#c ,subscripts3 x#c ,square ,root3 square root ,greek ,letters3 pi1 theta4 ,greek star names are represented as alpha1 gamma1 for example4 ,,pioneers ,,of ,,science ,illustration ,illustration3 ,,newton ,from the picture by ,kneller1 #afhi1 now at ,cambridge ,,pioneers ,,of ,,science ,,by ,,oliver ,,lodge1 ,f4,r4,s4 ,,professor ,,of ,,physics ,,in ,,victoria ,,university ,,college1 ,,liverpool ,,with ,,portraits ,,and ,,other ,,illustrations ,london ,,macmillan ,,and ,,co4 ,,and ,,new ,,york #ahic ,,richard ,,clay ,,and ,,sons1 ,,limited1 ,,london ,,and ,,bungay4 ,,preface ,this book takes its origin in a course of lectures on the history and progress of ,astronomy arranged for me in the year #ahhg by three of my colleagues 7,a4,c4,b41 ,j4,m41 ,g4,h4,r471 one of whom gave the course its name4 ,the lectures having been found interesting1 it was natural to write them out in full and publish4 ,if ,i may claim for them any merit1 ,i should say it consists in their simple statement and explanation of scientific facts and laws4 ,the biographical details are compiled from all readily available sources1 there is no novelty or originality about them2 though it is hoped that there may be some vividness4 ,i have simply tried to present a living figure of each ,pioneer in turn1 and to trace his influence on the progress of thought4 ,i am indebted to many biographers and writers1 among others to ,mr4 ,e4,j4,c4 ,morton1 whose excellent set of lives published by the ,s4,p4,c4,k4 saved me much trouble in the early part of the course4 ,as we approach recent times the subject grows more complex1 and the men more nearly contemporaries2 hence the biographical aspect diminishes and the scientific treatment becomes fuller1 but in no case has it been allowed to become technical and generally unreadable4 ,to the friends 7,c4,c4,c41 ,f4,w4,h4,m41 ,e4,f4,r47 who with great kindness have revised the proofs1 and have indicated places where the facts could be made more readily intelligible by a clearer statement1 ,i express my genuine gratitude4 ,,university ,,college1 ,,liverpool1 ,november1 #ahib4 ,,contents ,,part ,i ,,lecture ,i ,,page ,,copernicus ,,and ,,the ,,motion ,,of ,,the ,,earth #b ,,lecture ,,ii ,,tycho ,,brah ,,and ,,the ,,earliest ,,observatory #cb ,,lecture ,,iii ,,kepler ,,and ,,the ,,laws ,,of ,,planetary ,,motion #ef ,,lecture ,,iv ,,galileo ,,and ,,the ,,invention ,,of ,,the ,,telescope #hj ,,lecture ,v ,,galileo ,,and ,,the ,,inquisition #ajh ,,lecture ,,vi ,,descartes ,,and ,,his ,,theory ,,of ,,vortices #acf ,,lecture ,,vii ,,sir ,,isaac ,,newton #aei ,,lecture ,,viii ,,newton ,,and ,,the ,,law ,,of ,,gravitation #ahj ,,lecture ,,ix ,,newton',s ,,principia #bjc ,,part ,,ii ,,lecture ,x ,,roemer ,,and ,,bradley ,,and ,,the ,,velocity ,,of ,,light #bcb ,,lecture ,,xi ,,lagrange ,,and ,,laplace--,,the ,,stability ,,of ,,the ,,solar ,,system1 ,,and ,,the ,,nebular ,,hypothesis #bed ,,lecture ,,xii ,,herschel ,,and ,,the ,,motion ,,of ,,the ,,fixed ,,stars #bgc ,,lecture ,,xiii ,,the ,,discovery ,,of ,,the ,,asteroids #bid ,,lecture ,,xiv ,,bessel--,,the ,,distances ,,of ,,the ,,stars1 ,,and ,,the ,,discovery ,,of ,,stellar ,,planets #cjd ,,lecture ,,xv ,,the ,,discovery ,,of ,,neptune #cag ,,lecture ,,xvi ,,comets ,,and ,,meteors #cca ,,lecture ,,xvii ,,the ,,tides #cec ,,lecture ,,xviii ,,the ,,tides1 ,,and ,,planetary ,,evolution #cgi ,,illustrations ,,fig4 ,,page #a4 ,,archimedes #h #b4 ,,leonardo ,,da ,,vinci #aj #c4 ,,copernicus #ab #d4 ,,homeric ,,cosmogony #ae #e4 ,,egyptian ,,symbol ,,of ,,the ,,universe #af #f4 ,,hindoo ,,earth #ag #g4 ,,order ,,of ,,ancient ,,planets ,,corresponding ,,to ,,the ,,days ,,of ,,the ,,week #ai #h4 ,,ptolemaic ,,system #bj #i4 ,,specimens ,,of ,,apparent ,,paths ,,of ,,venus ,,and ,,of ,,mars ,,among ,,the ,,stars #ba #aj4 ,,apparent ,,epicyclic ,,orbits ,,of ,,jupiter ,,and ,,saturn #bb #aa4 ,,egyptian ,,system #bd #ab4 ,,true ,,orbits ,,of ,,earth ,,and ,,jupiter #be #ac4 ,,orbits ,,of ,,mercury ,,and ,,earth #be #ad4 ,,copernican ,,system ,,as ,,frequently ,,represented #bf #ae4 ,,slow ,,movement ,,of ,,the ,,north ,,pole ,,in ,a ,,circle ,,among ,,the ,,stars #bi #af4 ,,tychonic ,,system1 ,,showing ,,the ,,sun ,,with ,,all ,,the ,,planets ,,revolving ,,round ,,the ,,earth #ch #ag4 ,,portrait ,,of ,,tycho #da #ah4 ,,early ,,out-,,door ,,quadrant ,,of ,,tycho #dc #ai4 ,,map ,,of ,,denmark1 ,,showing ,,the ,,island ,,of ,,huen #de #bj4 ,,uraniburg #df #ba4 ,,astrolabe #dg #bb4 ,,tycho',s ,,large ,,sextant #dh #bc4 ,,the ,,quadrant ,,in ,,uraniburg #di #bd4 ,,tycho',s ,,form ,,of ,,transit ,,circle #ej #be4 ,a ,,modern ,,transit ,,circle #ea #bf4 ,,orbits ,,of ,,some ,,of ,,the ,,planets ,,drawn ,,to ,,scale #fj #bg4 ,,many-,,sided ,,polygon ,,or ,,approximate ,,circle ,,enveloped ,,by ,,straight ,,lines #fa #bh4 ,,kepler',s ,,idea ,,of ,,the ,,regular ,,solids #fb #bi4 ,,diagram ,,of ,,equant #fg #cj4 ,,excentric ,,circle ,,supposed ,,to ,,be ,,divided ,,into ,,equal ,,areas #fh #ca4 ,,mode ,,of ,,drawing ,,an ,,ellipse #gj #cb4 ,,kepler',s ,,diagram ,,proving ,,equable ,,description ,,of ,,areas ,,for ,,an ,,ellipse #ga #cc4 ,,diagram ,,of ,a ,,planet',s ,,velocity ,,in ,,different ,,parts ,,of ,,its ,,orbit #gb #cd4 ,,portrait ,,of ,,kepler #gf #ce4 ,,curve ,,described ,,by ,a ,,projectile #hb #cf4 ,,two ,,forms ,,of ,,pulsilogy #hg #cg4 ,,tower ,,of ,,pisa #ia #ch4 ,,view ,,of ,,the ,,half-,,moon ,,in ,,small ,,telescope #ig #ci4 ,,portion ,,of ,,the ,,lunar ,,surface ,,more ,,highly ,,magnified #ih #dj4 ,,another ,,portion ,,of ,,the ,,lunar ,,surface #ii #da4 ,,lunar ,,landscape ,,showing ,,earth #ajj #db4 ,,galileo',s ,,method ,,of ,,estimating ,,the ,,height ,,of ,,lunar ,,mountain #aja #dc4 ,,some ,,clusters ,,and ,,nebul #ajb #dd4 ,,stages ,,of ,,the ,,discovery ,,of ,,jupiter',s ,,satellites #ajc #de4 ,,eclipses ,,of ,,jupiter',s ,,satellites #aje #df4 ,,old ,,drawings ,,of ,,saturn ,,by ,,different ,,observers1 ,,with ,,the ,,imperfect ,,instruments ,,of ,,that ,,day #aaa #dg4 ,,phases ,,of ,,venus #aab #dh4 ,,sunspots ,,as ,,seen ,,with ,,low ,,power #aac #di4 ,a ,,portion ,,of ,,the ,,sun',s ,,disk ,,as ,,seen ,,in ,a ,,powerful ,,modern ,,telescope #aad #ej4 ,,saturn ,,and ,,his ,,rings #aae #ea4 ,,map ,,of ,,italy #aah #eb4 ,,portrait ,,of ,,galileo #abf #ec4 ,,portrait ,,of ,,descartes #adh #ed4 ,,descartes',s ,,eye ,,diagram #aea #ee4 ,,descartes',s ,,diagram ,,of ,,vortices ,,from ,,his ,,principia #aeb #ef4 ,,manor-,,house ,,of ,,woolsthorpe #afb #eg4 ,,projectile ,,diagram #agj #eh4 #aga #ei4 ,,diagrams ,,illustrative ,,of ,,those ,,near ,,the ,,beginning #agd #fj4 ,,of ,,newton',s ,,principia #age #fa-b4 #age #fc4 ,,prismatic ,,dispersion #ahb #fd4 ,a ,,single ,,constituent ,,of ,,white ,,light ,,is ,,capable ,,of ,,no ,,more ,,dispersion #ahc #fe4 ,,parallel ,,beam ,,passing ,,through ,a ,,lens #ahd #ff4 ,,newton',s ,,telescope #ahf #fg4 ,,the ,,sextant1 ,,as ,,now ,,made #ahg #fh4 ,,newton ,,when ,,young #aif #fi4 ,,sir ,,isaac ,,newton #bjj #gj4 ,,another ,,principia ,,diagram #bjg #ga4 ,,well-,,known ,,model ,,exhibiting ,,the ,,oblate ,,spheroidal ,,form ,,as ,a ,,consequence ,,of ,,spinning ,,about ,a ,,central ,,axis #bai #gb4 ,,jupiter #bba #gc4 ,,diagram ,,of ,,eye ,,looking ,,at ,a ,,light ,,reflected ,,in ,a ,,distant ,,mirror ,,through ,,the ,,teeth ,,of ,a ,,revolving ,,wheel #bch #gd4 ,,fizeau',s ,,wheel1 ,,showing ,,the ,,appearance ,,of ,,distant ,,image ,,seen ,,through ,,its ,,teeth #bci #ge4 ,,eclipses ,,of ,,one ,,of ,,jupiter',s ,,satellites #bda #gf4 ,a ,,transit ,,instrument ,,for ,,the ,,british ,,astronomical ,,expedition1 #ahgd #bdc #gg4 ,,diagram ,,of ,,equatorially ,,mounted ,,telescope #bde #gh4 ,,aberration ,,diagram #bej #gi4 ,,showing ,,the ,,three ,,conjunction ,,places ,,in ,,the ,,orbits ,,of ,,jupiter ,,and ,,saturn #bei #hj4 ,,lord ,,rosse',s ,,drawing ,,of ,,the ,,spiral ,,nebula ,,in ,,canes ,,venatici #bfi #ha4 ,,saturn #bga #hb4 ,,principle ,,of ,,newtonian ,,reflector #bgh #hc4 ,,herschel',s #dj-;,,foot ,,telescope #bhc #hd4 ,,william ,,herschel #bhe #he4 ,,caroline ,,herschel #bhg #hf4 ,,double ,,stars #bhh #hg4 ,,old ,,drawing ,,of ,,the ,,cluster ,,in ,,hercules #bij #hh4 ,,old ,,drawing ,,of ,,the ,,andromeda ,,nebula #bia #hi4 ,,the ,,great ,,nebula ,,in ,,orion #bib #ij4 ,,planetary ,,orbits ,,to ,,scale #big #ia4 ,,diagram ,,illustrating ,,parallax #cjg #ib4 ,,the ,k,,nigsberg ,,heliometer #cab #ic4 ,,perturbations ,,of ,,uranus #cbj #id4 ,,uranus' ,,and ,,neptune',s ,,relative ,,positions #cbe #ie4 ,,meteorite #ccc #if4 ,,meteor ,,stream ,,crossing ,,field ,,of ,,telescope #ccd #ig4 ,,diagram ,,of ,,direction ,,of ,,earth',s ,,orbital ,,motion #cce #ih4 ,,parabolic ,,and ,,elliptic ,,orbits #cdj #ii4 ,,orbit ,,of ,,halley',s ,,comet #cda #ajj4 ,,various ,,appearances ,,of ,,halley',s ,,comet ,,when ,,last ,,seen #cdb #aja4 ,,head ,,of ,,donati',s ,,comet ,,of #aheh #cdc #ajb4 ,,comet #cdd #ajc4 ,,encke',s ,,comet #cde #ajd4 ,,biela',s ,,comet ,,as ,,last ,,seen ,,in ,,two ,,portions #cdf #aje4 ,,radiant ,,point ,,perspective #cdh #ajf4 ,,present ,,orbit ,,of ,,november ,,meteors #cdi #ajg4 ,,orbit ,,of ,,november ,,meteors ,,before ,,and ,,after ,,encounter ,,with ,,uranus #cea #ajh4 ,,the ,,mersey #cee #aji4 ,,co-,,tidal ,,lines1 ,,showing ,,the ,,way ,,the ,,tidal ,,wave ,,reaches ,,the ,,british ,,isles ,,from ,,the ,,atlantic #cei #aaj4 ,,whirling ,,earth ,,model #cfd #aaa4 ,,earth ,,and ,,moon ,,model #cfe #aab4 ,,earth ,,and ,,moon 7,,earth',s ,,rotation ,,neglected7 #cff #aac4 ,,maps ,,showing ,,how ,,comparatively ,,free ,,from ,,land ,,obstruction ,,the ,,ocean ,,in ,,the ,,southern ,,hemisphere ,,is #cfi #aad4 ,,spring ,,and ,,neap ,,tides #cgj #aae4 ,,tidal ,,clock #cga #aaf4 ,,sir ,,william ,,thomson 7,,lord ,,kelvin7 #cgc #aag4 ,,tide-,,gauge ,,for ,,recording ,,local ,,tides #cge #aah4 ,,harmonic ,,analyzer #cge #aai4 ,,tide-,,predicter #cgf #abj4 ,,weekly ,,sheet ,,of ,,curves #cgg ,,pioneers ,,of ,,science ,,part ,i ,,from ,,dusk ,,to ,,daylight ,,dates ,,and ,,summary ,,of ,,facts ,,for ,,lecture ,i ,physical ,science of the ,ancients4 ,thales #fdj ,b4,c41 ,anaximander #faj ,b4,c41 ,,pythagoras #fjj ,b4,c41 ,anaxagoras #ejj ,b4,c41 ,eudoxus #djj ,b4,c41 ,,aristotle #chd ,b4,c41 ,aristarchus #cjj ,b4,c41 ,,archimedes #bhg ,b4,c41 ,eratosthenes #bgf ,b4,c41 ,,hipparchus #afj ,b4,c41 ,ptolemy #ajj ,a4,d4 ,science of the ,middle ,ages4 ,cultivated only among the ,arabs2 largely in the forms of astrology1 alchemy1 and algebra4 ,return of ,science to ,europe4 ,roger ,bacon #abdj1 ,leonardo da ,vinci #adhj1 7,printing #adee71 ,columbus #adib1 ,copernicus #aedc4 ,a sketch of ,copernik's life and work4 ,born #adgc at ,thorn in ,poland4 ,studied mathematics at ,bologna4 ,became an ecclesiastic4 ,lived at ,frauenburg near mouth of ,vistula4 ,substituted for the apparent motion of the heavens the real motion of the earth4 ,published tables of planetary motions4 ,motion still supposed to be in epicycles4 ,worked out his ideas for #cf years1 and finally dedicated his work to the ,pope4 ,died just as his book was printed1 aged #gb1 a century before the birth of ,newton4 ,a colossal statue by ,thorwaldsen erected at ,warsaw in #ahcj4 ,,pioneers ,,of ,,science ,,lecture ,i ,,copernicus ,,and ,,the ,,motion ,,of ,,the ,,earth ,the ordinary run of men live among phenomena of which they know nothing and care less4 ,they see bodies fall to the earth1 they hear sounds1 they kindle fires1 they see the heavens roll above them1 but of the causes and inner working of the whole they are ignorant1 and with their ignorance they are content4 ,understand the structure of a soap-bubble8 said a cultivated literary man whom ,i know2 ,i wouldn't cross the street to know it6 ,and if this is a prevalent attitude now1 what must have been the attitude in ancient times1 when mankind was emerging from savagery1 and when history seems composed of harassments by wars abroad and revolutions at home8 ,in the most violently disturbed times indeed1 those with which ordinary history is mainly occupied1 science is quite impossible4 ,it needs as its condition1 in order to flourish1 a fairly quiet1 untroubled state1 or else a cloister or university removed from the din and bustle of the political and commercial world4 ,in such places it has taken its rise1 and in such peaceful places and quiet times true science will continue to be cultivated4 ,the great bulk of mankind must always remain1 ,i suppose1 more or less careless of scientific research and scientific result1 except in so far as it affects their modes of locomotion1 their health and pleasure1 or their purse4 ,but among a people hurried and busy and preoccupied1 some in the pursuit of riches1 some in the pursuit of pleasure1 and some1 the majority1 in the struggle for existence1 there arise in every generation1 here and there1 one or two great souls--men who seem of another age and country1 who look upon the bustle and feverish activity and are not infected by it1 who watch others achieving prizes of riches and pleasure and are not disturbed1 who look on the world and the universe they are born in with quite other eyes4 ,to them it appears not as a bazaar to buy and to sell in2 not as a ladder to scramble up 7or down7 helter-skelter without knowing whither or why2 but as a fact--a great and mysterious fact--to be pondered over1 studied1 and perchance in some small measure understood4 ,by the multitude these men were sneered at as eccentric or feared as supernatural4 ,their calm1 clear1 contemplative attitude seemed either insane or diabolic2 and accordingly they have been pitied as enthusiasts or killed as blasphemers4 ,one of these great souls may have been a prophet or preacher1 and have called to his generation to bethink them of why and what they were1 to struggle less and meditate more1 to search for things of true value and not for dross4 ,another has been a poet or musician1 and has uttered in words or in song thoughts dimly possible to many men1 but by them unutterable and left inarticulate4 ,another has been influenced still more directly by the universe around him1 has felt at times overpowered by the mystery and solemnity of it all1 and has been impelled by a force stronger than himself to study it1 patiently1 slowly1 diligently2 content if he could gather a few crumbs of the great harvest of knowledge1 happy if he could grasp some great generalization or wide-embracing law1 and so in some small measure enter into the mind and thought of the ,designer of all this wondrous frame of things4 ,these last have been the men of science1 the great and heaven-born men of science2 and they are few4 ,in our own day1 amid the throng of inventions1 there are a multitude of small men using the name of science but working for their own ends1 jostling and scrambling just as they would jostle and scramble in any other trade or profession4 ,these may be workers1 they may and do advance knowledge1 but they are never pioneers4 ,not to them is it given to open out great tracts of unexplored territory1 or to view the promised land as from a mountain-top4 ,of them we shall not speak2 we will concern ourselves only with the greatest1 the epoch-making men1 to whose life and work we and all who come after them owe so much4 ,such a man was ,thales4 ,such was ,archimedes1 ,hipparchus1 ,copernicus4 ,such pre-eminently was ,newton4 ,now ,i am not going to attempt a history of science4 ,such a work in ten lectures would be absurd4 ,i intend to pick out a few salient names here and there1 and to study these in some detail1 rather than by attempting to deal with too many to lose individuality and distinctness4 ,we know so little of the great names of antiquity1 that they are for this purpose scarcely suitable4 ,in some departments the science of the ,greeks was remarkable1 though it is completely overshadowed by their philosophy2 yet it was largely based on what has proved to be a wrong method of procedure1 viz the introspective and conjectural1 rather than the inductive and experimental methods4 ,they investigated ,nature by studying their own minds1 by considering the meanings of words1 rather than by studying things and recording phenomena4 ,this wrong 7though by no means1 on the face of it1 absurd7 method was not pursued exclusively1 else would their science have been valueless1 but the influence it had was such as materially to detract from the value of their speculations and discoveries4 ,for when truth and falsehood are inextricably woven into a statement1 the truth is as hopelessly hidden as if it had never been stated1 for we have no criterion to distinguish the false from the true4 ,illustration3 ,,fig4 #a4--;,archimedes4 ,besides this1 however1 many of their discoveries were ultimately lost to the world1 some1 as at ,alexandria1 by fire--the bigoted work of a ,mohammedan conqueror--some by irruption of barbarians2 and all were buried so long and so completely by the night of the dark ages1 that they had to be rediscovered almost as absolutely and completely as though they had never been4 ,some of the names of antiquity we shall have occasion to refer to2 so ,i have arranged some of them in chronological order on page #d1 and as a representative one ,i may specially emphasize ,archimedes1 one of the greatest men of science there has ever been1 and the father of physics4 ,the only effective link between the old and the new science is afforded by the ,arabs4 ,the dark ages come as an utter gap in the scientific history of ,europe1 and for more than a thousand years there was not a scientific man of note except in ,arabia2 and with the ,arabs knowledge was so mixed up with magic and enchantment that one cannot contemplate it with any degree of satisfaction1 and little real progress was made4 ,in some of the ,waverley ,novels you can realize the state of matters in these times2 and you know how the only approach to science is through some ,arab sorcerer or astrologer1 maintained usually by a monarch1 and consulted upon all great occasions1 as the oracles were of old4 ,in the thirteenth century1 however1 a really great scientific man appeared1 who may be said to herald the dawn of modern science in ,europe4 ,this man was ,roger ,bacon4 ,he cannot be said to do more than herald it1 however1 for we must wait two hundred years for the next name of great magnitude2 moreover he was isolated1 and so far in advance of his time that he left no followers4 ,his own work suffered from the prevailing ignorance1 for he was persecuted and imprisoned1 not for the commonplace and natural reason that he frightened the ,church1 but merely because he was eccentric in his habits and knew too much4 ,the man ,i spoke of as coming two hundred years later is ,leonardo da ,vinci4 ,true he is best known as an artist1 but if you read his works you will come to the conclusion that he was the most scientific artist who ever lived4 ,he teaches the laws of perspective 7then new71 of light and shade1 of colour1 of the equilibrium of bodies1 and of a multitude of other matters where science touches on art--not always quite correctly according to modern ideas1 but in beautiful and precise language4 ,for clear and conscious power1 for wide-embracing knowledge and skill1 ,leonardo is one of the most remarkable men that ever lived4 ,about this time the tremendous invention of printing was achieved1 and ,columbus unwittingly discovered the ,new ,world4 ,the middle of the next century must be taken as the real dawn of modern science2 for the year #aedc marks the publication of the life-work of ,copernicus4 ,illustration3 ,,fig4 #b4--,leonardo da ,vinci4 ,nicolas ,copernik was his proper name4 ,copernicus is merely the ,latinized form of it1 according to the then prevailing fashion4 ,he was born at ,thorn1 in ,polish ,prussia1 in #adgc4 ,his father is believed to have been a ,german4 ,he graduated at ,cracow as doctor in arts and medicine1 and was destined for the ecclesiastical profession4 ,the details of his life are few2 it seems to have been quiet and uneventful1 and we know very little about it4 ,he was instructed in astronomy at ,cracow1 and learnt mathematics at ,bologna4 ,thence he went to ,rome1 where he was made ,professor of ,mathematics2 and soon afterwards he went into orders4 ,on his return home1 he took charge of the principal church in his native place1 and became a canon4 ,at ,frauenburg1 near the mouth of the ,vistula1 he lived the remainder of his life4 ,we find him reporting on coinage for the ,government1 but otherwise he does not appear as having entered into the life of the times4 ,he was a quiet1 scholarly monk of studious habits1 and with a reputation which drew to him several earnest students1 who received viv voce instruction from him2 so1 in study and meditation1 his life passed4 ,he compiled tables of the planetary motions which were far more correct than any which had hitherto appeared1 and which remained serviceable for long afterwards4 ,the ,ptolemaic system of the heavens1 which had been the orthodox system all through the ,christian era1 he endeavoured to improve and simplify by the hypothesis that the sun was the centre of the system instead of the earth2 and the first consequences of this change he worked out for many years1 producing in the end a great book3 his one life-work4 ,this famous work1 ,de ,revolutionibus ,orbium ,coelestium1 embodied all his painstaking calculations1 applied his new system to each of the bodies in the solar system in succession1 and treated besides of much other recondite matter4 ,towards the close of his life it was put into type4 ,he can scarcely be said to have lived to see it appear1 for he was stricken with paralysis before its completion2 but a printed copy was brought to his bedside and put into his hands1 so that he might just feel it before he died4 ,illustration3 ,,fig4 #c4--;,copernicus4 ,that ,copernicus was a giant in intellect or power--such as had lived in the past1 and were destined to live in the near future--,i see no reason whatever to believe4 ,he was just a quiet1 earnest1 patient1 and ,god-fearing man1 a deep student1 an unbiassed thinker1 although with no specially brilliant or striking gifts2 yet to him it was given to effect such a revolution in the whole course of man's thoughts as is difficult to parallel4 ,you know what the outcome of his work was4 ,it proved--he did not merely speculate1 he proved--that the earth is a planet like the others1 and that it revolves round the sun4 ,yes1 it can be summed up in a sentence1 but what a revelation it contains4 ,if you have never made an effort to grasp the full significance of this discovery you will not appreciate it4 ,the doctrine is very familiar to us now1 we have heard it1 ,i suppose1 since we were four years old1 but can you realize it8 ,i know it was a long time before ,i could4 ,think of the solid earth1 with trees and houses1 cities and countries1 mountains and seas--think of the vast tracts of land in ,asia1 ,africa1 and ,america--and then picture the whole mass spinning like a top1 and rushing along its annual course round the sun at the rate of nineteen miles every second4 ,were we not accustomed to it1 the idea would be staggering4 ,no wonder it was received with incredulity4 ,but the difficulties of the conception are not only physical1 they are still more felt from the speculative and theological points of view4 ,with this last1 indeed1 the reconcilement cannot be considered complete even yet4 ,theologians do not1 indeed1 now deny the fact of the earth's subordination in the scheme of the universe1 but many of them ignore it and pass it by4 ,so soon as the ,church awoke to a perception of the tremendous and revolutionary import of the new doctrines1 it was bound to resist them or be false to its traditions4 ,for the whole tenor of men's thought must have been changed had they accepted it4 ,if the earth were not the central and all-important body in the universe1 if the sun and planets and stars were not attendant and subsidiary lights1 but were other worlds larger and perhaps superior to ours1 where was man's place in the universe8 and where were the doctrines they had maintained as irrefragable8 ,i by no means assert that the new doctrines were really utterly irreconcilable with the more essential parts of the old dogmas1 if only theologians had had patience and genius enough to consider the matter calmly4 ,i suppose that in that case they might have reached the amount of reconciliation at present attained1 and not only have left scientific truth in peace to spread as it could1 but might perhaps themselves have joined the band of earnest students and workers1 as so many of the higher ,catholic clergy do at the present day4 ,but this was too much to expect4 ,such a revelation was not to be accepted in a day or in a century--the easiest plan was to treat it as a heresy1 and try to crush it out4 ,not in ,copernik's life1 however1 did they perceive the dangerous tendency of the doctrine--partly because it was buried in a ponderous and learned treatise not likely to be easily understood2 partly1 perhaps1 because its propounder was himself an ecclesiastic2 mainly because he was a patient and judicious man1 not given to loud or intolerant assertion1 but content to state his views in quiet conversation1 and to let them gently spread for thirty years before he published them4 ,and1 when he did publish them1 he used the happy device of dedicating his great book to the ,pope1 and a cardinal bore the expense of printing it4 ,thus did the ,roman ,church stand sponsor to a system of truth against which it was destined in the next century to hurl its anathemas1 and to inflict on its conspicuous adherents torture1 imprisonment1 and death4 ,to realize the change of thought1 the utterly new view of the universe1 which the ,copernican theory introduced1 we must go back to preceding ages1 and try to recall the views which had been held as probable concerning the form of the earth and the motion of the heavenly bodies4 ,illustration3 ,,fig4 #d4--;,homeric ,cosmogony4 ,the earliest recorded notion of the earth is the very natural one that it is a flat area floating in an illimitable ocean4 ,the sun was a god who drove his chariot across the heavens once a day2 and ,anaxagoras was threatened with death and punished with banishment for teaching that the sun was only a ball of fire1 and that it might perhaps be as big as the country of ,greece4 ,the obvious difficulty as to how the sun got back to the east again every morning was got over--not by the conjecture that he went back in the dark1 nor by the idea that there was a fresh sun every day2 though1 indeed1 it was once believed that the moon was created once a month1 and periodically cut up into stars--but by the doctrine that in the northern part of the earth was a high range of mountains1 and that the sun travelled round on the surface of the sea behind these4 ,sometimes1 indeed1 you find a representation of the sun being rowed round in a boat4 ,later on it was perceived to be necessary that the sun should be able to travel beneath the earth1 and so the earth was supposed to be supported on pillars or on roots1 or to be a dome-shaped body floating in air--much like ,dean ,swift's island of ,laputa4 ,the elephant and tortoise of the ,hindu earth are1 no doubt1 emblematic or typical1 not literal4 ,illustration3 ,,fig4 #e4--;,egyptian ,symbol of the ,universe4 ,the earth a figure with leaves1 the heaven a figure with stars1 the principle of equilibrium and support1 the boats of the rising and setting sun4 ,aristotle1 however1 taught that the earth must be a sphere1 and used all the orthodox arguments of the present children's geography-books about the way you see ships at sea1 and about lunar eclipses4 ,to imagine a possible antipodes must1 however1 have been a tremendous difficulty in the way of this conception of a sphere1 and ,i scarcely suppose that any one can at that time have contemplated the possibility of such upside-down regions being inhabited4 ,i find that intelligent children invariably feel the greatest difficulty in realizing the existence of inhabitants on the opposite side of the earth4 ,stupid children1 like stupid persons in general1 will of course believe anything they are told1 and much good may the belief do them2 but the kind of difficulties felt by intelligent and thoughtful children are most instructive1 since it is quite certain that the early philosophers must have encountered and overcome those very same difficulties by their own genius4 ,illustration3 ,,fig4 #f4--;,hindoo ,earth4 ,however1 somehow or other the conception of a spherical earth was gradually grasped1 and the heavenly bodies were perceived all to revolve round it3 some moving regularly1 as the stars1 all fixed together into one spherical shell or firmament2 some moving irregularly and apparently anomalously--these irregular bodies were therefore called planets or wanderers4 ,seven of them were known1 viz4 ,moon1 ,mercury1 ,venus1 ,sun1 ,mars1 ,jupiter1 ,saturn1 and there is little doubt that this number seven1 so suggested1 is the origin of the seven days of the week4 ,the above order of the ancient planets is that of their supposed distance from the earth4 ,not always1 however1 are they thus quoted by the ancients3 sometimes the sun is supposed nearer than ,mercury or ,venus4 ,it has always been known that the moon was the nearest of the heavenly bodies2 and some rough notion of its distance was current4 ,mars1 ,jupiter1 and ,saturn were placed in that order because that is the order of their apparent motions1 and it was natural to suppose that the slowest moving bodies were the furthest off4 ,the order of the days of the week shows what astrologers considered to be the order of the planets2 on their system of each successive hour of the day being ruled over by the successive planets taken in order4 ,the diagram 7fig4 #g7 shows that if the ,sun rule the first hour of a certain day 7thereby giving its name to the day7 ,venus will rule the second hour1 ,mercury the third1 and so on2 the ,sun will thus be found to rule the eighth1 fifteenth1 and twenty-second hour of that day1 ,venus the twenty-third1 and ,mercury the twenty-fourth hour2 so the ,moon will rule the first hour of the next day1 which will therefore be ,monday4 ,on the same principle 7numbering round the hours successively1 with the arrows7 the first hour of the next day will be found to be ruled by ,mars1 or by the ,saxon deity corresponding thereto2 the first hour of the day after1 by ,mercury 7,mercredi71 and so on 7following the straight lines of the pattern74 ,the order of the planets round the circle counter-clockwise1 i4e4 the direction of their proper motions1 is that quoted above in the text4 ,to explain the motion of the planets and reduce them to any sort of law was a work of tremendous difficulty4 ,the greatest astronomer of ancient times was ,hipparchus1 and to him the system known as the ,ptolemaic system is no doubt largely due4 ,but it was delivered to the world mainly by ,ptolemy1 and goes by his name4 ,this was a fine piece of work1 and a great advance on anything that had gone before2 for although it is of course saturated with error1 still it is based on a large substratum of truth4 ,its superiority to all the previously mentioned systems is obvious4 ,and it really did in its more developed form describe the observed motions of the planets4 ,each planet was1 in the early stages of this system1 as taught1 say1 by ,eudoxus1 supposed to be set in a crystal sphere1 which revolved so as to carry the planet with it4 ,the sphere had to be of crystal to account for the visibility of other planets and the stars through it4 ,outside the seven planetary spheres1 arranged one inside the other1 was a still larger one in which were set the stars4 ,this was believed to turn all the others1 and was called the primum mobile4 ,the whole system was supposed to produce1 in its revolution1 for the few privileged to hear the music of the spheres1 a sound as of some magnificent harmony4 ,illustration3 ,,fig4 #g4--,order of ancient planets corresponding to the days of the week4 ,the enthusiastic disciples of ,pythagoras believed that their master was privileged to hear this noble chant2 and far be it from us to doubt that the rapt and absorbing pleasure of contemplating the harmony of nature1 to a man so eminently great as ,pythagoras1 must be truly and adequately represented by some such poetic conception4 ,illustration3 ,,fig4 #h4--,ptolemaic system4 ,the precise kind of motion supposed to be communicated from the primum mobile to the other spheres so as to produce the observed motions of the planets was modified and improved by various philosophers until it developed into the epicyclic train of ,hipparchus and of ,ptolemy4 ,it is very instructive to observe a planet 7say ,mars or ,jupiter7 night after night and plot down its place with reference to the fixed stars on a celestial globe or star-map4 ,or1 instead of direct observation by alignment with known stars1 it is easier to look out its right ascension and declination in ,whitaker's ,almanac1 and plot those down4 ,if this be done for a year or two1 it will be found that the motion of the planet is by no means regular1 but that though on the whole it advances it sometimes is stationary and sometimes goes back4#a ,illustration3 ,,fig4 #i4--,specimens of ,apparent paths of ,venus and of ,mars among the stars4 ,illustration3 ,,fig4 #aj4--;,apparent epicyclic orbits of ,jupiter and ,saturn2 the ,earth being supposed fixed at the centre1 with the ,sun revolving in a small circle4 ,a loop is made by each planet every year4 ,these stations and retrogressions of the planets were well known to the ancients4 ,it was not to be supposed for a moment that the crystal spheres were subject to any irregularity1 neither was uniform circular motion to be readily abandoned2 so it was surmised that the main sphere carried1 not the planet itself1 but the centre or axis of a subordinate sphere1 and that the planet was carried by this4 ,the minor sphere could be allowed to revolve at a different uniform pace from the main sphere1 and so a curve of some complexity could be obtained4 ,a curve described in space by a point of a circle or sphere1 which itself is carried along at the same time1 is some kind of cycloid2 if the centre of the tracing circle travels along a straight line1 we get the ordinary cycloid1 the curve traced in air by a nail on a coach-wheel2 but if the centre of the tracing circle be carried round another circle the curve described is called an epicycloid4 ,by such curves the planetary stations and retrogressions could be explained4 ,a large sphere would have to revolve once for a year of the particular planet1 carrying with it a subsidiary sphere in which the planet was fixed2 this latter sphere revolving once for a year of the earth4 ,the actual looped curve thus described is depicted for ,jupiter and ,saturn in the annexed diagram 7fig4 #aj47 ,it was long ago perceived that real material spheres were unnecessary2 such spheres indeed1 though possibly transparent to light1 would be impermeable to comets3 any other epicyclic gearing would serve1 and as a mere description of the motion it is simpler to think of a system of jointed bars1 one long arm carrying a shorter arm1 the two revolving at different rates1 and the end of the short one carrying the planet4 ,this does all that is needful for the first approximation to a planet's motion4 ,in so far as the motion cannot be thus truly stated1 the short arm may be supposed to carry another1 and that another1 and so on1 so that the resultant motion of the planet is compounded of a large number of circular motions of different periods2 by this device any required amount of complexity could be attained4 ,we shall return to this at greater length in ,lecture ,,iii4 ,the main features of the motion1 as shown in the diagram1 required only two arms for their expression2 one arm revolving with the average motion of the planet1 and the other revolving with the apparent motion of the sun1 and always pointing in the same direction as the single arm supposed to carry the sun4 ,this last fact is of course because the motion to be represented does not really belong to the planet at all1 but to the earth1 and so all the main epicyclic motions for the superior planets were the same4 ,as for the inferior planets 7,mercury and ,venus7 they only appear to oscillate like the bob of a pendulum about the sun1 and so it is very obvious that they must be really revolving round it4 ,an ancient ,egyptian system perceived this truth2 but the ,ptolemaic system imagined them to revolve round the earth like the rest1 with an artificial system of epicycles to prevent their ever getting far away from the neighbourhood of the sun4 ,it is easy now to see how the ,copernican system explains the main features of planetary motion1 the stations and retrogressions1 quite naturally and without any complexity4 ,illustration3 ,,fig4 #aa4--;,egyptian system4 ,let the outer circle represent the orbit of ,jupiter1 and the inner circle the orbit of the earth1 which is moving faster than ,jupiter 7since ,jupiter takes #dccb days to make one revolution72 then remember that the apparent position of ,jupiter is referred to the infinitely distant fixed stars and refer to fig4 #ab4 ,let ,e#a1 ,e#b1 c41 be successive positions of the earth2 ,j#a1 ,j#b1 c41 corresponding positions of ,jupiter4 ,produce the lines ,e#a ,j#a1 ,e#b ,j#b1 c41 to an enormously greater circle outside1 and it will be seen that the termination of these lines1 representing apparent positions of ,jupiter among the stars1 advances while the earth goes from ,e#a to ,e#c2 is almost stationary from somewhere about ,e#c to ,e#d2 and recedes from ,e#d to ,e#e2 so that evidently the recessions of ,jupiter are only apparent1 and are due to the orbital motion of the earth4 ,the apparent complications in the path of ,jupiter1 shown in ,fig4 #aj1 are seen to be caused simply by the motion of the earth1 and to be thus completely and easily explained4 ,illustration3 ,,fig4 #ab4--,true orbits of ,earth and ,jupiter4 ,the same thing for an inferior planet1 say ,mercury1 is even still more easily seen 7vide figure #ac74 ,the motion of ,mercury is direct from ,m'' to ,m'''1 retrograde from ,m''' to ,m''1 and stationary at ,m'' and ,m'''4 ,it appears to oscillate1 taking #gbe days for its direct swing1 and #dce for its return swing4 ,illustration3 ,,fig4 #ac4--,orbit of ,mercury and ,earth4 ,on this system no artificiality is required to prevent ,mercury's ever getting far from the sun3 the radius of its orbit limits its real and apparent excursions4 ,even if the earth were stationary1 the motions of ,mercury and ,venus would not be essentially modified1 but the stations and retrogressions of the superior planets1 ,mars1 ,jupiter1 c41 would wholly cease4 ,the complexity of the old mode of regarding apparent motion may be illustrated by the case of a traveller in a railway train unaware of his own motion4 ,it is as though trees1 hedges1 distant objects1 were all flying past him and contorting themselves as you may see the furrows of a ploughed field do when travelling1 while you yourself seem stationary amidst it all4 ,how great a simplicity would be introduced by the hypothesis that1 after all1 these things might be stationary and one's self moving4 ,illustration3 ,,fig4 #ad4--;,copernican system as frequently represented4 ,but the cometary orbit is a much later addition1 and no attempt is made to show the relative distances of the planets4 ,now you are not to suppose that the system of ,copernicus swept away the entire doctrine of epicycles2 that doctrine can hardly be said to be swept away even now4 ,as a description of a planet's motion it is not incorrect1 though it is geometrically cumbrous4 ,if you describe the motion of a railway train by stating that every point on the rim of each wheel describes a cycloid with reference to the earth1 and a circle with reference to the train1 and that the motion of the train is compounded of these cycloidal and circular motions1 you will not be saying what is false1 only what is cumbrous4 ,the ,ptolemaic system demanded large epicycles1 depending on the motion of the earth1 these are what ,copernicus overthrew2 but to express the minuter details of the motion smaller epicycles remained1 and grew more and more complex as observations increased in accuracy1 until a greater man than either ,copernicus or ,ptolemy1 viz4 ,kepler1 replaced them all by a simple ellipse4 ,one point ,i must not omit from this brief notice of the work of ,copernicus4 ,hipparchus had1 by most sagacious interpretation of certain observations of his1 discovered a remarkable phenomenon called the precession of the equinoxes4 ,it was a discovery of the first magnitude1 and such as would raise to great fame the man who should have made it in any period of the world's history1 even the present4 ,it is scarcely expressible in popular language1 and without some technical terms2 but ,i can try4 ,the plane of the earth's orbit produced into the sky gives the apparent path of the sun throughout a year4 ,this path is known as the ecliptic1 because eclipses only happen when the moon is in it4 ,the sun keeps to it accurately1 but the planets wander somewhat above and below it 7fig4 #i71 and the moon wanders a good deal4 ,it is manifest1 however1 in order that there may be an eclipse of any kind1 that a straight line must be able to be drawn through earth and moon and sun 7not necessarily through their centres of course71 and this is impossible unless some parts of the three bodies are in one plane1 viz4 the ecliptic1 or something very near it4 ,the ecliptic is a great circle of the sphere1 and is usually drawn on both celestial and terrestrial globes4 ,the earth's equator also produced into the sky1 where it may still be called the equator 7sometimes it is awkwardly called the equinoctial71 gives another great circle inclined to the ecliptic and cutting it at two opposite points1 labelled respectively ,aries symbol and ,libra symbol1 and together called the equinoxes4 ,the reason for the name is that when the sun is in that part of the ecliptic it is temporarily also on the equator1 and hence is symmetrically situated with respect to the earth's axis of rotation1 and consequently day and night are equal all over the earth4 ,well1 ,hipparchus found1 by plotting the position of the sun for a long time1#b that these points of intersection1 or equinoxes1 were not stationary from century to century1 but slowly moved among the stars1 moving as it were to meet the sun1 so that he gets back to one of these points again #bj minutes #bc-a_/d seconds before it has really completed a revolution1 i4e4 before the true year is fairly over4 ,this slow movement forward of the goal-post is called precession--the precession of the equinoxes4 7,one result of it is to shorten our years by about #bj minutes each2 for the shortened period has to be called a year1 because it is on the position of the sun with respect to the earth's axis that our seasons depend47 ,copernicus perceived that1 assuming the motion of the earth1 a clearer account of this motion could be given4 ,the ordinary approximate statement concerning the earth's axis is that it remains parallel to itself1 i4e4 has a fixed direction as the earth moves round the sun4 ,but if1 instead of being thus fixed1 it be supposed to have a slow movement of revolution1 so that it traces out a cone in the course of about #bf1jjj years1 then1 since the equator of course goes with it1 the motion of its intersection with the fixed ecliptic is so far accounted for4 ,that is to say1 the precession of the equinoxes is seen to be dependent on1 and caused by1 a slow conical movement of the earth's axis4 ,the prolongation of each end of the earth's axis into the sky1 or the celestial north and south poles1 will thus slowly trace out an approximate circle among the stars2 and the course of the north pole during historic time is exhibited in the annexed diagram4 ,it is now situated near one of the stars of the ,lesser ,bear1 which we therefore call the ,pole star2 but not always was it so1 nor will it be so in the future4 ,the position of the north pole #djjj years ago is shown in the figure2 and a revolution will be completed in something like #bf1jjj years4#c ,illustration3 ,,fig4 #ae4--,slow movement of the north pole in a circle among the stars4 7,copied from ,sir ,r4 ,ball47 ,this perception of the conical motion of the earth's axis was a beautiful generalization of ,copernik's1 whereby a multitude of facts were grouped into a single phenomenon4 ,of course he did not explain the motion of the axis itself4 ,he stated the fact that it so moved1 and ,i do not suppose it ever struck him to seek for an explanation4 ,an explanation was given later1 and that a most complete one2 but the idea even of seeking for it is a brilliant and striking one3 the achievement of the explanation by a single individual in the way it actually was accomplished is one of the most astounding things in the history of science2 and were it not that the same individual accomplished a dozen other things1 equally and some still more extraordinary1 we should rank that man as one of the greatest astronomers that ever lived4 ,as it is1 he is ,sir ,isaac ,newton4 ,we are to remember1 then1 as the life-work of ,copernicus1 that he placed the sun in its true place as the centre of the solar system1 instead of the earth2 that he greatly simplified the theory of planetary motion by this step1 and also by the simpler epicyclic chain which now sufficed1 and which he worked out mathematically2 that he exhibited the precession of the equinoxes 7discovered by ,hipparchus7 as due to a conical motion of the earth's axis2 and that1 by means of his simpler theory and more exact planetary tables1 he reduced to some sort of order the confused chaos of the ,ptolemaic system1 whose accumulation of complexity and of outstanding errors threatened to render astronomy impossible by the mere burden of its detail4 ,there are many imperfections in his system1 it is true2 but his great merit is that he dared to look at the facts of ,nature with his own eyes1 unhampered by the prejudice of centuries4 ,a system venerable with age1 and supported by great names1 was universally believed1 and had been believed for centuries4 ,to doubt this system1 and to seek after another and better one1 at a time when all men's minds were governed by tradition and authority1 and when to doubt was sin--this required a great mind and a high character4 ,such a mind and such a character had this monk of ,frauenburg4 ,and it is interesting to notice that the so-called religious scruples of smaller and less truly religious men did not affect ,copernicus2 it was no dread of consequences to one form of truth that led him to delay the publication of the other form of truth specially revealed to him4 ,in his dedication he says3-- ,if there be some babblers who1 though ignorant of all mathematics1 take upon them to judge of these things1 and dare to blame and cavil at my work1 because of some passage of ,scripture which they have wrested to their own purpose1 ,i regard them not1 and will not scruple to hold their judgment in contempt4 ,i will conclude with the words of one of his biographers 7,mr4 ,e4,j4,c4 ,morton73-- ,copernicus cannot be said to have flooded with light the dark places of nature--in the way that one stupendous mind subsequently did--but still1 as we look back through the long vista of the history of science1 the dim ,titanic figure of the old monk seems to rear itself out of the dull flats around it1 pierces with its head the mists that overshadow them1 and catches the first gleam of the rising sun1 '444 like some iron peak1 by the ,creator ,fired with the red glow of the rushing morn4' ,,dates ,,and ,,summary ,,of ,,facts ,,for ,,lecture ,,ii ,copernicus lived from #adgc to #aedc1 and was contemporary with ,paracelsus and ,raphael4 ,tycho ,brah from #aedf to #afja4 ,kepler from #aega to #afcj4 ,galileo from #aefd to #afdb4 ,gilbert from #aedj to #afjc4 ,francis ,bacon from #aefa to #afbf4 ,descartes from #aeif to #afej4 ,a sketch of ,tycho ,brah's life and work4 ,tycho was a ,danish noble1 born on his ancestral estate at ,knudstorp1 near ,helsinborg1 in #aedf4 ,adopted by his uncle1 and sent to the ,university of ,copenhagen to study law4 ,attracted to astronomy by the occurrence of an eclipse on its predicted day1 ,august #bast1 #aefj4 ,began to construct astronomical instruments1 especially a quadrant and a sextant4 ,observed at ,augsburg and ,wittenberg4 ,studied alchemy1 but was recalled to astronomy by the appearance of a new star4 ,overcame his aristocratic prejudices1 and delivered a course of lectures at ,copenhagen1 at the request of the king4 ,after this he married a peasant girl4 ,again travelled and observed in ,germany4 ,in #aegf was sent for to ,denmark by ,frederick ,,ii41 and established in the island of ,huen1 with an endowment enabling him to devote his life to astronomy4 ,built ,uraniburg1 furnished it with splendid instruments1 and became the founder of accurate instrumental astronomy4 ,his theories were poor1 but his observations were admirable4 ,in #aeib ,frederick died1 and five years later1 ,tycho was impoverished and practically banished4 ,after wandering till #aeii1 he was invited to ,prague by the ,emperor ,rudolf1 and there received ,john ,kepler among other pupils4 ,but the sentence of exile was too severe1 and he died in #afja1 aged #ed years4 ,a man of strong character1 untiring energy1 and devotion to accuracy1 his influence on astronomy has been immense4 ,,lecture ,,ii ,,tycho ,,brah ,,and ,,the ,,earliest ,,observatory ,we have seen how ,copernicus placed the earth in its true position in the solar system1 making it merely one of a number of other worlds revolving about a central luminary4 ,and observe that there are two phenomena to be thus accounted for and explained3 first1 the diurnal revolution of the heavens2 second1 the annual motion of the sun among the stars4 ,the effect of the diurnal motion is conspicuous to every one1 and explains the rising1 southing1 and setting of the whole visible firmament4 ,the effect of the annual motion1 i4e4 of the apparent annual motion1 of the sun among the stars1 is less obvious1 but it may be followed easily enough by observing the stars visible at any given time of evening at different seasons of the year4 ,at midnight1 for instance1 the position of the sun is definite1 viz4 due north always1 but the constellation which at that time is due south or is rising or setting varies with the time of year2 an interval of one month producing just the same effect on the appearance of the constellations as an interval of two hours does 7because the day contains twice as many hours as the year contains months71 e4g4 the sky looks the same at midnight on the #ast of ,october as it does at #aj p4m4 on the #ast of ,november4 ,all these simple consequences of the geocentric as opposed to the heliocentric point of view were pointed out by ,copernicus1 in addition to his greater work of constructing improved planetary tables on the basis of his theory4 ,but it must be admitted that he himself felt the hypothesis of the motion of the earth to be a difficulty4 ,its acceptance is by no means such an easy and childish matter as we are apt now to regard it1 and the hostility to it is not at all surprising4 ,the human race1 after having ridiculed and resisted the truth for a long time1 is apt to end in accepting it so blindly and unimaginatively as to fail to recognize the real achievement of its first propounders1 or the difficulties which they had to overcome4 ,the majority of men at the present day have grown accustomed to hear the motion of the earth spoken of3 their acceptance of it means nothing3 the attitude of the paradoxer who denies it is more intelligent4 ,it is not to be supposed that the idea of thus explaining some of the phenomena of the heavens1 especially the daily motion of the entire firmament1 by a diurnal rotation of the earth had not struck any one4 ,it was often at this time referred to as the ,pythagorean theory1 and it had been taught1 ,i believe1 by ,aristarchus4 ,but it was new to the modern world1 and it had the great weight of ,aristotle against it4 ,consequently1 for long after ,copernicus1 only a few leading spirits could be found to support it1 and the long-established venerable ,ptolemaic system continued to be taught in all ,universities4 ,the main objections to the motion of the earth were such as the following3-- #a4 ,the motion is unfelt and difficult to imagine4 ,that it is unfelt is due to its uniformity1 and can be explained mechanically4 ,that it is difficult to imagine is and remains true1 but a most important lesson we have to learn is that difficulty of conception is no valid argument against reality4 #b4 ,that the stars do not alter their relative positions according to the season of the year1 but the constellations preserve always the same aspect precisely1 even to careful measurement4 ,this is indeed a difficulty1 and a great one4 ,in ,june the earth is #ahd million miles away from where it was in ,december3 how can we see precisely the same fixed stars8 ,it is not possible1 unless they are at a practically infinite distance4 ,that is the only answer that can be given4 ,it was the tentative answer given by ,copernicus4 ,it is the correct answer4 ,not only from every position of the earth1 but from every planet of the solar system1 the same constellations are visible1 and the stars have the same aspect4 ,the whole immensity of the solar system shrinks to practically a point when confronted with the distance of the stars4 ,not1 however1 so entirely a speck as to resist the terrific accuracy of the present century1 and their microscopic relative displacement with the season of the year has now at length been detected1 and the distance of many thereby measured4 #c4 ,that1 if the earth revolved round the sun1 ,mercury and ,venus ought to show phases like the moon4 ,so they ought4 ,any globe must show phases if it live nearer the sun than we do and if we go round it1 for we shall see varying amounts of its illuminated half4 ,the only answer that ,copernicus could give to this was that they might be difficult to see without extra powers of sight1 but he ventured to predict that the phases would be seen if ever our powers of vision should be enhanced4 #d4 ,that if the earth moved1 or even revolved on its own axis1 a stone or other dropped body ought to be left far behind4 ,this difficulty is not a real one1 like the two last1 and it is based on an ignorance of the laws of mechanics1 which had not at that time been formulated4 ,we know now that a ball dropped from a high tower1 so far from lagging1 drops a minute trifle in front of the foot of a perpendicular1 because the top of the tower is moving a trace faster than the bottom1 by reason of the diurnal rotation4 ,but1 ignoring this1 a stone dropped from the lamp of a railway carriage drops in the centre of the floor1 whether the carriage be moving steadily or standing still2 a slant direction of fall could only be detected if the carriage were being accelerated or if the brake were applied4 ,a body dropped from a moving carriage shares the motion of the carriage1 and starts with that as its initial velocity4 ,a ball dropped from a moving balloon does not simply drop1 but starts off in whatever direction the car was moving1 its motion being immediately modified by gravity1 precisely in the same way as that of a thrown ball is modified4 ,this is1 indeed1 the whole philosophy of throwing--to drop a ball from a moving carriage4 ,the carriage is the hand1 and1 to throw far1 a run is taken and the body is jerked forward2 the arm is also moved as rapidly as possible on the shoulder as pivot4 ,the fore-arm can be moved still faster1 and the wrist-joint gives yet another motion3 the art of throwing is to bring all these to bear at the same instant1 and then just as they have all attained their maximum velocity to let the ball go4 ,it starts off with the initial velocity thus imparted1 and is abandoned to gravity4 ,if the vehicle were able to continue its motion steadily1 as a balloon does1 the ball when let go from it would appear to the occupant simply to drop2 and it would strike the ground at a spot vertically under the moving vehicle1 though by no means vertically below the place where it started4 ,the resistance of the air makes observations of this kind inaccurate1 except when performed inside a carriage so that the air shares in the motion4 ,otherwise a person could toss and catch a ball out of a train window just as well as if he were stationary2 though to a spectator outside he would seem to be using great skill to throw the ball in the parabola adapted to bring it back to his hand4 ,the same circumstance enhances the apparent difficulty of the circus rider's jumping feats4 ,all he has to do is to jump up and down on the horse2 the forward motion which carries him through hoops belongs to him by virtue of the motion of the horse1 without effort on his part4 ,thus1 then1 it happens that a stone dropped sixteen feet on the earth appears to fall straight down1 although its real path in space is a very flat trajectory of nineteen miles base and sixteen feet height2 nineteen miles being the distance traversed by the earth every second in the course of its annual journey round the sun4 ,no wonder that it was thought that bodies must be left behind if the earth was subject to such terrific speed as this4 ,all that ,copernicus could suggest on this head was that perhaps the atmosphere might help to carry things forward1 and enable them to keep pace with the earth4 ,there were thus several outstanding physical difficulties in the way of the acceptance of the ,copernican theory1 besides the ,biblical difficulty4 ,it was quite natural that the idea of the earth's motion should be repugnant1 and take a long time to sink into the minds of men2 and as scientific progress was vastly slower then than it is now1 we find not only all priests but even some astronomers one hundred years afterwards still imagining the earth to be at rest4 ,and among them was a very eminent one1 ,tycho ,brah4 ,it is interesting to note1 moreover1 that the argument about the motion of the earth being contrary to ,scripture appealed not only to ecclesiastics in those days1 but to scientific men also2 and ,tycho ,brah1 being a man of great piety1 and highly superstitious also1 was so much influenced by it1 that he endeavoured to devise some scheme by which the chief practical advantages of the ,copernican system could be retained1 and yet the earth be kept still at the centre of the whole4 ,this was done by making all the celestial sphere1 with stars and everything1 rotate round the earth once a day1 as in the ,ptolemaic scheme2 and then besides this making all the planets revolve round the sun1 and this to revolve round the earth4 ,such is the ,tychonic system4 ,so far as relative motion is concerned it comes to the same thing2 just as when you drop a book you may say either that the earth rises to meet the book1 or that the book falls to meet the earth4 ,or when a fly buzzes round your head1 you may say that you are revolving round the fly4 ,but the absurdity of making the whole gigantic system of sun and planets and stars revolve round our insignificant earth was too great to be swallowed by other astronomers after they had once had a taste of the ,copernican theory2 and accordingly the ,tychonic system died a speedy and an easy death at the same time as its inventor4 ,wherein then lay the magnitude of the man8--not in his theories1 which were puerile1 but in his observations1 which were magnificent4 ,he was the first observational astronomer1 the founder of the splendid system of practical astronomy which has culminated in the present ,greenwich ,observatory4 ,illustration3 ,,fig4 #af4--,tychonic system showing the sun with all the planets revolving round the earth4 ,up to ,tycho the only astronomical measurements had been of the rudest kind4 ,copernicus even improved upon what had gone before1 with measuring rules made with his own hands4 ,ptolemy's observations could never be trusted to half a degree4 ,tycho introduced accuracy before undreamed of1 and though his measurements1 reckoned by modern ideas1 are of course almost ludicrously rough 7remember no such thing as a telescope or microscope was then dreamed of71 yet1 estimated by the era in which they were made1 they are marvels of accuracy1 and not a single mistake due to carelessness has ever been detected in them4 ,in fact they may be depended on almost to minutes of arc1 i4e4 to sixtieths of a degree4 ,for certain purposes connected with the proper motion of stars they are still appealed to1 and they served as the certain and trustworthy data for succeeding generations of theorists to work upon4 ,it was long1 indeed1 after ,tycho's death before observations approaching in accuracy to his were again made4 ,in every sense1 therefore1 he was a pioneer3 let us proceed to trace his history4 ,born the eldest son of a noble family--as noble and ignorant as sixteen undisputed quarterings could make them1 as one of his biographers says--in a period when1 even more than at present1 killing and hunting were the only natural aristocratic pursuits1 when all study was regarded as something only fit for monks1 and when science was looked at askance as something unsavoury1 useless1 and semi-diabolic1 there was little in his introduction to the world urging him in the direction where his genius lay4 ,of course he was destined for a soldier2 but fortunately his uncle1 ,george ,brah1 a more educated man than his father1 having no son of his own1 was anxious to adopt him1 and though not permitted to do so for a time1 succeeded in getting his way on the birth of a second son1 ,steno--who1 by the way1 ultimately became ,privy ,councillor to the ,king of ,denmark4 ,tycho's uncle gave him what he would never have got at home--a good education2 and ultimately put him to study law4 ,at the age of thirteen he entered the ,university of ,copenhagen1 and while there occurred the determining influence of his life4 ,an eclipse of the sun in those days was not regarded with the cold-blooded inquisitiveness or matter-of-fact apathy1 according as there is or is not anything to be learnt from it1 with which such an event is now regarded4 ,every occurrence in the heavens was then believed to carry with it the destiny of nations and the fate of individuals1 and accordingly was of surpassing interest4 ,ever since the time of ,hipparchus it had been possible for some capable man here and there to predict the occurrence of eclipses pretty closely4 ,the thing is not difficult4 ,the prediction was not1 indeed1 to the minute and second1 as it is now2 but the day could usually be hit upon pretty accurately some time ahead1 much as we now manage to hit upon the return of a comet--barring accidents2 and the hour could be predicted as the event approached4 ,well1 the boy ,tycho1 among others1 watched for this eclipse on ,august #bast1 #aefj2 and when it appeared at its appointed time1 every instinct for the marvellous1 dormant in his strong nature1 awoke to strenuous life1 and he determined to understand for himself a science permitting such wonderful possibilities of prediction4 ,he was sent to ,leipzig with a tutor to go on with his study of law1 but he seems to have done as little law as possible3 he spent all his money on books and instruments1 and sat up half the night studying and watching the stars4 ,in #aefc he observed a conjunction of ,jupiter and ,saturn1 the precursor1 and cause as he thought it1 of the great plague4 ,he found that the old planetary tables were as much as a month in error in fixing this event1 and even the ,copernican tables were several days out2 so he formed the resolve to devote his life to improving astronomical tables4 ,this resolve he executed with a vengeance4 ,his first instrument was a jointed ruler with sights for fixing the position of planets with respect to the stars1 and observing their stations and retrogressions4 ,by thus measuring the angles between a planet and two fixed stars1 its position can be plotted down on a celestial map or globe4 ,illustration3 ,,fig4 #ag4--,portrait of ,tycho4 ,in #aefe his uncle ,george died1 and made ,tycho his heir4 ,he returned to ,denmark1 but met with nothing but ridicule and contempt for his absurd drivelling away of time over useless pursuits4 ,so he went back to ,germany--first to ,wittenberg1 thence1 driven by the plague1 to ,rostock4 ,here his fiery nature led him into an absurd though somewhat dangerous adventure4 ,a quarrel at some feast1 on a mathematical point1 with a countryman1 ,manderupius1 led to the fixing of a duel1 and it was fought with swords at #g p4m4 at the end of ,december1 when1 if there was any light at all1 it must have been of a flickering and unsatisfactory nature4 ,the result of this insane performance was that ,tycho got his nose cut clean off4 ,he managed however to construct an artificial one1 some say of gold and silver1 some say of putty and brass2 but whatever it was made of there is no doubt that he wore it for the rest of his life1 and it is a most famous feature4 ,it excited generally far more interest than his astronomical researches4 ,it is said1 moreover1 to have very fairly resembled the original1 but whether this remark was made by a friend or by an enemy ,i cannot say4 ,one account says that he used to carry about with him a box of cement to apply whenever his nose came off1 which it periodically did4 ,about this time he visited ,augsburg1 met with some kindred and enlightened spirits in that town1 and with much enthusiasm and spirit constructed a great quadrant4 ,these early instruments were tremendous affairs4 ,a great number of workmen were employed upon this quadrant1 and it took twenty men to carry it to its place and erect it4 ,it stood in the open air for five years1 and then was destroyed by a storm4 ,with it he made many observations4 ,illustration3 ,,fig4 #ah4--;,early out-door quadrant of ,tycho2 for observing altitudes by help of the sights ,d1 ,l and the plumb line4 ,on his return to ,denmark in #aega1 his fame preceded him1 and he was much better received2 and in order to increase his power of constructing instruments he took up the study of alchemy1 and like the rest of the persuasion tried to make gold4 ,the precious metals were by many old philosophers considered to be related in some way to the heavenly bodies3 silver to the moon1 for instance--as we still see by the name lunar caustic applied to nitrate of silver2 gold to the sun1 copper to ,mars1 lead to ,saturn4 ,hence astronomy and alchemy often went together4 ,tycho all his life combined a little alchemy with his astronomical labours1 and he constructed a wonderful patent medicine to cure all disorders1 which had as wide a circulation in ,europe in its time as ,holloway's pills2 he gives a tremendous receipt for it1 with liquid gold and all manner of ingredients in it2 among them1 however1 occurs a little antimony--a well-known sudorific--and to this1 no doubt1 whatever efficacy the medicine possessed was due4 ,so he might have gone on wasting his time1 were it not that in ,november1 #aegb1 a new star made its appearance1 as they have done occasionally before and since4 ,on the average one may say that about every fifty years a new star of fair magnitude makes its temporary appearance4 ,they are now known to be the result of some catastrophe or collision1 whereby immense masses of incandescent gas are produced4 ,this one seen by ,tycho became as bright as ,jupiter1 and then died away in about a year and a half4 ,tycho observed all its changes1 and endeavoured to measure its distance from the earth1 with the result that it was proved to belong to the region of the fixed stars1 at an immeasurable distance1 and was not some nearer and more trivial phenomenon4 ,he was asked by the ,university of ,copenhagen to give a course of lectures on astronomy2 but this was a step he felt some aristocratic aversion to1 until a little friendly pressure was brought to bear upon him by a request from the king1 and delivered they were4 ,he now seems to have finally thrown off his aristocratic prejudices1 and to have indulged himself in treading on the corns of nearly all the high and mighty people he came into contact with4 ,in short1 he became what we might now call a violent ,radical2 but he was a good-hearted man1 nevertheless1 and many are the tales told of his visits to sick peasants1 of his consulting the stars as to their fate--all in perfect good faith--and of the medicines which he concocted and prescribed for them4 ,the daughter of one of these peasants he married1 and very happy the marriage seems to have been4 ,illustration3 ,,fig4 #ai4--,map of ,denmark1 showing the island of ,huen4 ,walker ,boutallse4 ,now comes the crowning episode in ,tycho's life4 ,frederick ,,ii41 realizing how eminent a man they had among them1 and how much he could do if only he had the means--for we must understand that ,tycho1 though of good family and well off1 was by no means what we would call a wealthy man--,frederick ,,ii4 made him a splendid and enlightened offer4 ,the offer was this3 that if ,tycho would agree to settle down and make his astronomical observations in ,denmark1 he should have an estate in ,norway settled upon him1 a pension of #djj a year for life1 a site for a large observatory1 and #bj1jjj to build it with4 ,illustration3 ,,fig4 #bj4--,uraniburg4 ,illustration3 ,,fig4 #ba4--;,astrolabe4 ,an old instrument with sights for marking the positions of the celestial bodies roughly4 ,a sort of skeleton celestial globe4 ,illustration3 ,,sextans ,,astronomicvs ,,trigonicvs ,,pro ,,distantiis rimandis4 ,,fig4 #bb4--,tycho's large sextant2 for measuring the angular distance between two bodies by direct sighting4 ,well1 if ever money was well spent1 this was4 ,by its means ,denmark before long headed the nations of ,europe in the matter of science--a thing it has not done before or since4 ,the site granted was the island of ,huen1 between ,copenhagen and ,elsinore2 and here the most magnificent observatory ever built was raised1 and called ,uraniburg--the castle of the heavens4 ,it was built on a hill in the centre of the island1 and included gardens1 printing shops1 laboratory1 dwelling-houses1 and four observatories--all furnished with the most splendid instruments that ,tycho could devise1 and that could then be constructed4 ,it was decorated with pictures and sculptures of eminent men1 and altogether was a most gorgeous place4 #bj1jjj no doubt went far in those days1 but the original grant was supplemented by ,tycho himself1 who is said to have spent another equal sum out of his own pocket on the place4 ,illustration3 ,,qvadrans ,,maximvs ,,chalibeus ,,quadrato ,,inclusus1 ,,et ,horizonti ,azimuthali chalybeo insistens4 ,,fig4 #bc4--,the ,quadrant in ,uraniburg2 or altitude and azimuth instrument4 ,for twenty years this great temple of science was continually worked in by him1 and he soon became the foremost scientific man in ,europe4 ,philosophers1 statesmen1 and occasionally kings1 came to visit the great astronomer1 and to inspect his curiosities4 ,illustration3 ,,qvadrans ,,mvralis ,,sive ,,tichonicus4 ,,fig4 #bd4--,tycho's form of transit circle4 ,the method of utilising the extremely uniform rotation of the earth by watching the planets and stars as they cross the meridian1 and recording their times of transit2 observing also at the same time their meridian altitudes 7see observer ,f71 was the invention of ,tycho1 and constitutes his greatest achievement4 ,his method is followed to this day in all observatories4 ,illustration3 ,,fig4 #be4--;,a modern transit circle1 showing essentially the same parts as in ,tycho's instrument1 viz4 the observer watching the transit1 the clock1 the recorder of the observation1 and the graduated circle2 the latter to be read by a second observer4 ,and very wholesome for some of these great personages must have been the treatment they met with4 ,for ,tycho was no respecter of persons4 ,his humbly-born wife sat at the head of the table1 whoever was there2 and he would snub and contradict a chancellor just as soon as he would a serf4 ,whatever form his pride may have taken when a youth1 in his maturity it impelled him to ignore differences of rank not substantially justified1 and he seemed to take a delight in exposing the ignorance of shallow titled persons1 to whom contradiction and exposure were most unusual experiences4 ,for sick peasants he would take no end of trouble1 and went about doctoring them for nothing1 till he set all the professional doctors against him2 so that when his day of misfortune came1 as come it did1 their influence was not wanting to help to ruin one who spoilt their practice1 and whom they derided as a quack4 ,but some of the great ignorant folk who came to visit his temple of science1 and to inspect its curiosities1 felt themselves insulted--not always without reason4 ,he kept a tame maniac in the house1 named ,lep1 and he used to regard the sayings of this personage as oracular1 presaging future events1 and far better worth listening to than ordinary conversation4 ,consequently he used to have him at his banquets and feed him himself2 and whenever ,lep opened his mouth to speak1 every one else was peremptorily ordered to hold his tongue1 so that ,lep's words might be written down4 ,in fact it was something like an exaggerated edition of ,betsy ,trotwood and ,mr4 ,dick4 ,it must have been an odd dinner party 7says ,prof4 ,stuart71 with this strange1 wild1 terribly clever man1 with his red hair and brazen nose1 sometimes flashing with wit and knowledge1 sometimes making the whole company1 princes and servants alike1 hold their peace and listen humbly to the ravings of a poor imbecile4 ,to people he despised he did not show his serious instruments4 ,he had other attractions1 in the shape of a lot of toy machinery1 little windmills1 and queer doors1 and golden globes1 and all manner of ingenious tricks and automata1 many of which he had made himself1 and these he used to show them instead2 and no doubt they were well enough pleased with them4 ,those of the visitors1 however1 who really cared to see and understand his instruments1 went away enchanted with his genius and hospitality4 ,i may1 perhaps1 be producing an unfair impression of imperiousness and insolence4 ,tycho was fiery1 no doubt1 but ,i think we should wrong him if we considered him insolent4 ,most of the nobles of his day were haughty persons1 accustomed to deal with serfs1 and very likely to sneer at and trample on any meek man of science whom they could easily despise4 ,so ,tycho was not meek2 he stood up for the honour of his science1 and paid them back in their own coin1 with perhaps a little interest4 ,that this behaviour was not worldly-wise is true enough1 but ,i know of no commandment enjoining us to be worldly-wise4 ,if we knew more about his so-called imbecile protg we should probably find some reason for the interest which ,tycho took in him4 ,whether he was what is now called a clairvoyant or not1 ,tycho evidently regarded his utterances as oracular1 and of course when one is receiving what may be a revelation from heaven it is natural to suppress ordinary conversation4 ,among the noble visitors whom he received and entertained1 it is interesting to notice ,james ,i4 of ,england1 who spent eight days at ,uraniburg on the occasion of his marriage with ,anne of ,denmark in #aeij1 and seems to have been deeply impressed by his visit4 ,among other gifts1 ,james presented ,tycho with a dog 7depicted in ,fig4 #bd71 and this same animal was subsequently the cause of trouble4 ,for it seems that one day the ,chancellor of ,denmark1 ,walchendorf1 brutally kicked the poor beast2 and ,tycho1 who was very fond of animals1 gave him a piece of his mind in no measured language4 ,walchendorf went home determined to ruin him4 ,king ,frederick1 however1 remained his true friend1 doubtless partly influenced thereto by his ,queen ,sophia1 an enlightened woman who paid many visits to ,uraniburg1 and knew ,tycho well4 ,but unfortunately ,frederick died2 and his son1 a mere boy1 came to the throne4 ,now was the time for the people whom ,tycho had offended1 for those who were jealous of his great fame and importance1 as well as for those who cast longing eyes on his estate and endowments4 ,the boy-king1 too1 unfortunately paid a visit to ,tycho1 and1 venturing upon a decided opinion on some recondite subject1 received a quiet setting down which he ill relished4 ,letters written by ,tycho about this time are full of foreboding4 ,he greatly dreads having to leave ,uraniburg1 with which his whole life has for twenty years been bound up4 ,he tries to comfort himself with the thought that1 wherever he is sent1 he will have the same heavens and the same stars over his head4 ,gradually his ,norwegian estate and his pension were taken away1 and in five years poverty compelled him to abandon his magnificent temple1 and to take a small house in ,copenhagen4 ,not content with this1 ,walchendorf got a ,royal ,commission appointed to inquire into the value of his astronomical labours4 ,this sapient body reported that his work was not only useless1 but noxious2 and soon after he was attacked by the populace in the public street4 ,nothing was left for him now but to leave the country1 and he went into ,germany1 leaving his wife and instruments to follow him whenever he could find a home for them4 ,his wanderings in this dark time--some two years--are not quite clear2 but at last the enlightened ,emperor of ,bohemia1 ,rudolph ,,ii41 invited him to settle in ,prague4 ,thither he repaired1 a castle was given him as an observatory1 a house in the city1 and #cjjj crowns a year for life4 ,so his instruments were set up once more1 students flocked to hear him and to receive work at his hands--among them a poor youth1 ,john ,kepler1 to whom he was very kind1 and who became1 as you know1 a still greater man than his master4 ,but the spirit of ,tycho was broken1 and though some good work was done at ,prague--more observations made1 and the ,rudolphine tables begun--yet the hand of death was upon him4 ,a painful disease seized him1 attended with sleeplessness and temporary delirium1 during the paroxysms of which he frequently exclaimed1 ,ne frustra vixisse videar4 7,oh that it may not appear that ,i have lived in vain67 ,quietly1 however1 at last1 and surrounded by his friends and relatives1 this fierce1 passionate soul passed away1 on the #bdth of ,october1 #afja4 ,his beloved instruments1 which were almost a part of himself1 were stored by ,rudolph in a museum with scrupulous care1 until the taking of ,prague by the ,elector ,palatine's troops4 ,in this disturbed time they got smashed1 dispersed1 and converted to other purposes4 ,one thing only was saved--the great brass globe1 which some thirty years after was recognized by a later king of ,denmark as having belonged to ,tycho1 and deposited in the ,library of the ,academy of ,sciences at ,copenhagen1 where ,i believe it is to this day4 ,the island of ,huen was overrun by the ,danish nobility1 and nothing now remains of ,uraniburg but a mound of earth and two pits4 ,as to the real work of ,tycho1 that has become immortal enough1--chiefly through the labours of his friend and scholar whose life we shall consider in the next lecture4 ,,summary ,,of ,,facts ,,for ,,lecture ,,iii ,life and work of ,kepler4 ,kepler was born in ,december1 #aega1 at ,weil in ,wrtemberg4 ,father an officer in the duke's army1 mother something of a virago1 both very poor4 ,kepler was utilized as a tavern pot-boy1 but ultimately sent to a charity school1 and thence to the ,university of ,tbingen4 ,health extremely delicate2 he was liable to violent attacks all his life4 ,studied mathematics1 and accepted an astronomical lectureship at ,graz as the first post which offered4 ,endeavoured to discover some connection between the number of the planets1 their times of revolution1 and their distances from the sun4 ,ultimately hit upon his fanciful regular-solid hypothesis1 and published his first book in #aeig4 ,in #aeii was invited by ,tycho to ,prague1 and there appointed ,imperial mathematician1 at a handsome but seldom paid salary4 ,observed the new star of #afjd4 ,endeavoured to find the law of refraction of light from ,vitellio's measurements1 but failed4 ,analyzed ,tycho's observations to find the true law of motion of ,mars4 ,after incredible labour1 through innumerable wrong guesses1 and six years of almost incessant calculation1 he at length emerged in his two laws--discoveries which swept away all epicycles1 deferents1 equants1 and other remnants of the ,greek system1 and ushered in the dawn of modern astronomy4 ,,law ,i4 ,planets move in ellipses1 with the ,sun in one focus4 ,,law ,,ii4 ,the radius vector 7or line joining sun and planet7 sweeps out equal areas in equal times4 ,published his second book containing these laws in #afji4 ,death of ,rudolph in #afab1 and subsequent increased misery and misfortune of ,kepler4 ,ultimately discovered the connection between the times and distances of the planets for which he had been groping all his mature life1 and announced it in #afah3-- ,,law ,,iii4 ,the square of the time of revolution 7or year7 of each planet is proportional to the cube of its mean distance from the sun4 ,the book in which this law was published 7,on ,celestial ,harmonies7 was dedicated to ,james of ,england4 ,in #afbj had to intervene to protect his mother from being tortured for witchcraft4 ,accepted a professorship at ,linz4 ,published the ,rudolphine tables in #afbg1 embodying ,tycho's observations and his own theory4 ,made a last effort to overcome his poverty by getting the arrears of his salary paid at ,prague1 but was unsuccessful1 and1 contracting brain fever on the journey1 died in ,november1 #afcj1 aged #ei4 ,a man of keen imagination1 indomitable perseverance1 and uncompromising love of truth1 ,kepler overcame ill-health1 poverty1 and misfortune1 and placed himself in the very highest rank of scientific men4 ,his laws1 so extraordinarily discovered1 introduced order and simplicity into what else would have been a chaos of detailed observations2 and they served as a secure basis for the splendid erection made on them by ,newton4 ,seven planets of the ,ptolemaic system-- ,moon1 ,mercury1 ,venus1 ,sun1 ,mars1 ,jupiter1 ,saturn4 ,six planets of the ,copernican system-- ,mercury1 ,venus1 ,earth1 ,mars1 ,jupiter1 ,saturn4 ,the five regular solids1 in appropriate order-- ,octahedron1 ,icosahedron1 ,dodecahedron1 ,tetrahedron1 ,cube4 ,table illustrating ,kepler's third law4 ---------------------------------------- -------------------------- ,mean distance ,length ,cube of the ,square of the ,planet4 from ,sun4 of ,year4 ,distance4 ,time4 ,d ,t ,d#c ,t#b ---------------------------------------- -------------------------- ,mercury #chga #bdjhd #jehja #jehja ,venus #gbcc #faeai #cghde #cghdf ,earth #ajjjj #ajjjj #ajjjj #ajjjj ,mars #aebcg #ahhjh #cecge #cecge ,jupiter #ebjbh #aahfb #adjhc #adjgj ,saturn #iechh #bideg #hfgib #hfggj ---------------------------------------- -------------------------- ,the length of the earth's year is #cfebef days2 its mean distance from the sun1 taken above as unity1 is #ib1jjj1jjj miles4 ,,lecture ,,iii ,,kepler ,,and ,,the ,,laws ,,of ,,planetary ,,motion ,it is difficult to imagine a stronger contrast between two men engaged in the same branch of science than exists between ,tycho ,brah1 the subject of last lecture1 and ,kepler1 our subject on the present occasion4 ,the one1 rich1 noble1 vigorous1 passionate1 strong in mechanical ingenuity and experimental skill1 but not above the average in theoretical and mathematical power4 ,the other1 poor1 sickly1 devoid of experimental gifts1 and unfitted by nature for accurate observation1 but strong almost beyond competition in speculative subtlety and innate mathematical perception4 ,the one is the complement of the other2 and from the fact of their following each other so closely arose the most surprising benefits to science4 ,the outward life of ,kepler is to a large extent a mere record of poverty and misfortune4 ,i shall only sketch in its broad features1 so that we may have more time to attend to his work4 ,he was born 7so his biographer assures us7 in longitude #bi #g'1 latitude #dh #ed'1 on the #bast of ,december1 #aega4 ,his parents seem to have been of fair condition1 but by reason1 it is said1 of his becoming surety for a friend1 the father lost all his slender income1 and was reduced to keeping a tavern4 ,young ,john ,kepler was thereupon taken from school1 and employed as pot-boy between the ages of nine and twelve4 ,he was a sickly lad1 subject to violent illnesses from the cradle1 so that his life was frequently despaired of4 ,ultimately he was sent to a monastic school and thence to the ,university of ,tbingen1 where he graduated second on the list4 ,meanwhile home affairs had gone to rack and ruin4 ,his father abandoned the home1 and later died abroad4 ,the mother quarrelled with all her relations1 including her son ,john2 who was therefore glad to get away as soon as possible4 ,all his connection with astronomy up to this time had been the hearing the ,copernican theory expounded in ,university lectures1 and defending it in a college debating society4 ,an astronomical lectureship at ,graz happening to offer itself1 he was urged to take it1 and agreed to do so1 though stipulating that it should not debar him from some more brilliant profession when there was a chance4 ,for astronomy in those days seems to have ranked as a minor science1 like mineralogy or meteorology now4 ,it had little of the special dignity with which the labours of ,kepler himself were destined so greatly to aid in endowing it4 ,well1 he speedily became a thorough ,copernican1 and as he had a most singularly restless and inquisitive mind1 full of appreciation of everything relating to number and magnitude--was a born speculator and thinker just as ,mozart was a born musician1 or ,bidder a born calculator--he was agitated by questions such as these3 ,why are there exactly six planets8 ,is there any connection between their orbital distances1 or between their orbits and the times of describing them8 ,these things tormented him1 and he thought about them day and night4 ,it is characteristic of the spirit of the times--this questioning why there should be six planets4 ,nowadays1 we should simply record the fact and look out for a seventh4 ,then1 some occult property of the number six was groped for1 such as that it was equal to #a #b #c and likewise equal to #a #b #c1 and so on4 ,many fine reasons had been given for the seven planets of the ,ptolemaic system 7see1 for instance1 p4 #ajf71 but for the six planets of the ,copernican system the reasons were not so cogent4 ,again1 with respect to their successive distances from the sun1 some law would seem to regulate their distance1 but it was not known4 7,parenthetically ,i may remark that it is not known even now3 a crude empirical statement known as ,bode's law--see page #bid--;is all that has been discovered47 ,once more1 the further the planet the slower it moved2 there seemed to be some law connecting speed and distance4 ,this also ,kepler made continual attempts to discover4 ,illustration3 ,,fig4 #bf4--,orbits of some of the planets drawn to scale3 showing the gap between ,mars and ,jupiter4 ,one of his ideas concerning the law of the successive distances was based on the inscription of a triangle in a circle4 ,if you inscribe in a circle a large number of equilateral triangles1 they envelop another circle bearing a definite ratio to the first3 these might do for the orbits of two planets 7see ,fig4 #bg74 ,then try inscribing and circumscribing squares1 hexagons1 and other figures1 and see if the circles thus defined would correspond to the several planetary orbits4 ,but they would not give any satisfactory result4 ,brooding over this disappointment1 the idea of trying solid figures suddenly strikes him4 ,what have plane figures to do with the celestial orbits8 he cries out2 inscribe the regular solids4 ,and then--brilliant idea--he remembers that there are but five4 ,euclid had shown that there could be only five regular solids4#d ,the number evidently corresponds to the gaps between the six planets4 ,the reason of there being only six seems to be attained4 ,this coincidence assures him he is on the right track1 and with great enthusiasm and hope he represents the earth's orbit by a sphere as the norm and measure of all2 round it he circumscribes a dodecahedron1 and puts another sphere round that1 which is approximately the orbit of ,mars2 round that1 again1 a tetrahedron1 the corners of which mark the sphere of the orbit of ,jupiter2 round that sphere1 again1 he places a cube1 which roughly gives the orbit of ,saturn4 ,illustration3 ,,fig4 #bg4--,many-sided polygon or approximate circle enveloped by straight lines1 as for instance by a number of equilateral triangles4 ,on the other hand1 he inscribes in the sphere of the earth's orbit an icosahedron2 and inside the sphere determined by that1 an octahedron2 which figures he takes to inclose the spheres of ,venus and of ,mercury respectively4 ,the imagined discovery is purely fictitious and accidental4 ,first of all1 eight planets are now known2 and secondly1 their real distances agree only very approximately with ,kepler's hypothesis4 ,illustration3 ,,fig4 #bh4--;,frameworks with inscribed and circumscribed spheres1 representing the five regular solids distributed as ,kepler supposed them to be among the planetary orbits4 7,see ,summary at beginning of this lecture1 p4 #eg47 ,nevertheless1 the idea gave him great delight4 ,he says3--,the intense pleasure ,i have received from this discovery can never be told in words4 ,i regretted no more the time wasted2 ,i tired of no labour2 ,i shunned no toil of reckoning1 days and nights spent in calculation1 until ,i could see whether my hypothesis would agree with the orbits of ,copernicus1 or whether my joy was to vanish into air4 ,he then went on to speculate as to the cause of the planets' motion4 ,the old idea was that they were carried round by angels or celestial intelligences4 ,kepler tried to establish some propelling force emanating from the sun1 like the spokes of a windmill4 ,this first book of his brought him into notice1 and served as an introduction to ,tycho and to ,galileo4 ,tycho ,brah was at this time at ,prague under the patronage of the ,emperor ,rudolph2 and as he was known to have by far the best planetary observations of any man living1 ,kepler wrote to him to know if he might come and examine them so as to perfect his theory4 ,tycho immediately replied1 ,come1 not as a stranger1 but as a very welcome friend2 come and share in my observations with such instruments as ,i have with me1 and as a dearly beloved associate4 ,after this visit1 ,tycho wrote again1 offering him the post of mathematical assistant1 which after hesitation was accepted4 ,part of the hesitation ,kepler expresses by saying that for observations his sight was dull1 and for mechanical operations his hand was awkward4 ,he suffered much from weak eyes1 and dare not expose himself to night air4 ,in all this he was1 of course1 the antipodes of ,tycho1 but in mathematical skill he was greatly his superior4 ,on his way to ,prague he was seized with one of his periodical illnesses1 and all his means were exhausted by the time he could set forward again1 so that he had to apply for help to ,tycho4 ,it is clear1 indeed1 that for some time now he subsisted entirely on the bounty of ,tycho1 and he expresses himself most deeply grateful for all the kindness he received from that noble and distinguished man1 the head of the scientific world at that date4 ,to illustrate ,tycho's kindness and generosity1 ,i must read you a letter written to him by ,kepler4 ,it seems that ,kepler1 on one of his absences from ,prague1 driven half mad with poverty and trouble1 fell foul of ,tycho1 whom he thought to be behaving badly in money matters to him and his family1 and wrote him a violent letter full of reproaches and insults4 ,tycho's secretary replied quietly enough1 pointing out the groundlessness and ingratitude of the accusation4 ,kepler repents instantly1 and replies3-- ,,most ,,noble ,,tycho1 7these are the words of his letter71 how shall ,i enumerate or rightly estimate your benefits conferred on me8 ,for two months you have liberally and gratuitously maintained me1 and my whole family2 you have provided for all my wishes2 you have done me every possible kindness2 you have communicated to me everything you hold most dear2 no one1 by word or deed1 has intentionally injured me in anything2 in short1 not to your children1 your wife1 or yourself have you shown more indulgence than to me4 ,this being so1 as ,i am anxious to put on record1 ,i cannot reflect without consternation that ,i should have been so given up by ,god to my own intemperance as to shut my eyes on all these benefits2 that1 instead of modest and respectful gratitude1 ,i should indulge for three weeks in continual moroseness towards all your family1 in headlong passion and the utmost insolence towards yourself1 who possess so many claims on my veneration1 from your noble family1 your extraordinary learning1 and distinguished reputation4 ,whatever ,i have said or written against the person1 the fame1 the honour1 and the learning of your excellency2 or whatever1 in any other way1 ,i have injuriously spoken or written 7if they admit no other more favourable interpretation71 as1 to my grief1 ,i have spoken and written many things1 and more than ,i can remember2 all and everything ,i recant1 and freely and honestly declare and profess to be groundless1 false1 and incapable of proof4 ,tycho accepted the apology thus heartily rendered1 and the temporary breach was permanently healed4 ,in #afja1 ,kepler was appointed ,imperial mathematician1 to assist ,tycho in his calculations4 ,the ,emperor ,rudolph did a good piece of work in thus maintaining these two eminent men1 but it is quite clear that it was as astrologers that he valued them2 and all he cared for in the planetary motions was limited to their supposed effect on his own and his kingdom's destiny4 ,he seems to have been politically a weak and superstitious prince1 who was letting his kingdom get into hopeless confusion1 and entangling himself in all manner of political complications4 ,while ,bohemia suffered1 however1 the world has benefited at his hands2 and the tables upon which ,tycho was now engaged are well called the ,rudolphine tables4 ,these tables of planetary motion ,tycho had always regarded as the main work of his life2 but he died before they were finished1 and on his death-bed he intrusted the completion of them to ,kepler1 who loyally undertook their charge4 ,the ,imperial funds were by this time1 however1 so taxed by wars and other difficulties that the tables could only be proceeded with very slowly1 a staff of calculators being out of the question4 ,in fact1 ,kepler could not get even his own salary paid3 he got orders1 and promises1 and drafts on estates for it2 but when the time came for them to be honoured they were worthless1 and he had no power to enforce his claims4 ,so everything but brooding had to be abandoned as too expensive1 and he proceeded to study optics4 ,he gave a very accurate explanation of the action of the human eye1 and made many hypotheses1 some of them shrewd and close to the mark1 concerning the law of refraction of light in dense media3 but though several minor points of interest turned up1 nothing of the first magnitude came out of this long research4 ,the true law of refraction was discovered some years after by a ,dutch professor1 ,willebrod ,snell4 ,we must now devote a little time to the main work of ,kepler's life4 ,all the time he had been at ,prague he had been making a severe study of the motion of the planet ,mars1 analyzing minutely ,tycho's books of observations1 in order to find out1 if possible1 the true theory of his motion4 ,aristotle had taught that circular motion was the only perfect and natural motion1 and that the heavenly bodies therefore necessarily moved in circles4 ,so firmly had this idea become rooted in men's minds1 that no one ever seems to have contemplated the possibility of its being false or meaningless4 ,when ,hipparchus and others found that1 as a matter of fact1 the planets did not revolve in simple circles1 they did not try other curves1 as we should at once do now1 but they tried combinations of circles1 as we saw in ,lecture ,i4 ,the small circle carried by a bigger one was called an ,epicycle4 ,the carrying circle was called the ,deferent4 ,if for any reason the earth had to be placed out of the centre1 the main planetary orbit was called an ,excentric1 and so on4 ,but although the planetary paths might be roughly represented by a combination of circles1 their speeds could not1 on the hypothesis of uniform motion in each circle round the earth as a fixed body4 ,hence was introduced the idea of an ,equant1 i4e4 an arbitrary point1 not the earth1 about which the speed might be uniform4 ,copernicus1 by making the sun the centre1 had been able to simplify a good deal of this1 and to abolish the equant4 ,but now that ,kepler had the accurate observations of ,tycho to refer to1 he found immense difficulty in obtaining the true positions of the planets for long together on any such theory4 ,he specially attacked the motion of the planet ,mars1 because that was sufficiently rapid in its changes for a considerable collection of data to have accumulated with respect to it4 ,he tried all manner of circular orbits for the earth and for ,mars1 placing them in all sorts of aspects with respect to the sun4 ,the problem to be solved was to choose such an orbit and such a law of speed1 for both the earth and ,mars1 that a line joining them1 produced out to the stars1 should always mark correctly the apparent position of ,mars as seen from the earth4 ,he had to arrange the size of the orbits that suited best1 then the positions of their centres1 both being supposed excentric with respect to the sun2 but he could not get any such arrangement to work with uniform motion about the sun4 ,so he reintroduced the equant1 and thus had another variable at his disposal--in fact1 two1 for he had an equant for the earth and another for ,mars1 getting a pattern of the kind suggested in ,fig4 #bi4 ,the equants might divide the line in any arbitrary ratio4 ,all sorts of combinations had to be tried1 the relative positions of the earth and ,mars to be worked out for each1 and compared with ,tycho's recorded observations4 ,it was easy to get them to agree for a short time1 but sooner or later a discrepancy showed itself4 ,illustration3 ,,fig4 #bi4--,s represents the sun2 ,,ec1 the centre of the earth's orbit1 to be placed as best suited2 ,,mc1 the same for ,mars2 ,,ee1 the earth's equant1 or point about which the earth uniformly revolved 7i4e4 the point determining the law of speed about the sun71 likewise to be placed anywhere1 but supposed to be in the line joining ,s to ,,ec2 ,,me1 the same thing for ,mars2 with 8,,me for an alternative hypothesis that perhaps ,mars' equant was on line joining ,,ec with ,,mc4 ,i need not say that all these attempts and gropings1 thus briefly summarized1 entailed enormous labour1 and required not only great pertinacity1 but a most singularly constituted mind1 that could thus continue groping in the dark without a possible ray of theory to illuminate its search4 ,grope he did1 however1 with unexampled diligence4 ,at length he hit upon a point that seemed nearly right4 ,he thought he had found the truth2 but no1 before long the position of the planet1 as calculated1 and as recorded by ,tycho1 differed by eight minutes of arc1 or about one-eighth of a degree4 ,could the observation be wrong by this small amount8 ,no1 he had known ,tycho1 and knew that he was never wrong eight minutes in an observation4 ,so he set out the whole weary way again1 and said that with those eight minutes he would yet find out the law of the universe4 ,he proceeded to see if by making the planet librate1 or the plane of its orbit tilt up and down1 anything could be done4 ,he was rewarded by finding that at any rate the plane of the orbit did not tilt up and down3 it was fixed1 and this was a simplification on ,copernicus's theory4 ,it is not an absolute fixture1 but the changes are very small 7see ,laplace1 page #bff74 ,illustration3 ,,fig4 #cj4--;,excentric circle supposed to be divided into equal areas4 ,the sun1 ,s1 being placed at a selected point1 it was possible to represent the varying speed of a planet by saying that it moved from ,a to ,b1 from ,b to ,c1 and so on1 in equal times4 ,at last he thought of giving up the idea of uniform circular motion1 and of trying varying circular motion1 say inversely as its distance from the sun4 ,to simplify calculation1 he divided the orbit into triangles1 and tried if making the triangles equal would do4 ,a great piece of luck1 they did beautifully3 the rate of description of areas 7not arcs7 is uniform4 ,over this discovery he greatly rejoices4 ,he feels as though he had been carrying on a war against the planet and had triumphed2 but his gratulation was premature4 ,before long fresh little errors appeared1 and grew in importance4 ,thus he announces it himself3-- ,while thus triumphing over ,mars1 and preparing for him1 as for one already vanquished1 tabular prisons and equated excentric fetters1 it is buzzed here and there that the victory is vain1 and that the war is raging anew as violently as before4 ,for the enemy left at home a despised captive has burst all the chains of the equations1 and broken forth from the prisons of the tables4 ,still1 a part of the truth had been gained1 and was not to be abandoned any more4 ,the law of speed was fixed3 that which is now known as his second law4 ,but what about the shape of the orbit--,was it after all possible that ,aristotle1 and every philosopher since ,aristotle1 had been wrong8 that circular motion was not the perfect and natural motion1 but that planets might move in some other closed curve8 ,suppose he tried an oval4 ,well1 there are a great variety of ovals1 and several were tried3 with the result that they could be made to answer better than a circle1 but still were not right4 ,now1 however1 the geometrical and mathematical difficulties of calculation1 which before had been tedious and oppressive1 threatened to become overwhelming2 and it is with a rising sense of despondency that ,kepler sees his six years' unremitting labour leading deeper and deeper into complication4 ,one most disheartening circumstance appeared1 viz4 that when he made the circuit oval his law of equable description of areas broke down4 ,that seemed to require the circular orbit1 and yet no circular orbit was quite accurate4 ,while thinking and pondering for weeks and months over this new dilemma and complication of difficulties1 till his brain reeled1 an accidental ray of light broke upon him in a way not now intelligible1 or barely intelligible4 ,half the extreme breadth intercepted between the circle and oval was #dbi_/ajj1jjj of the radius1 and he remembered that the optical inequality of ,mars was also about #dbi_/ajj1jjj4 ,this coincidence1 in his own words1 woke him out of sleep2 and for some reason or other impelled him instantly to try making the planet oscillate in the diameter of its epicycle instead of revolve round it--a singular idea1 but ,copernicus had had a similar one to explain the motions of ,mercury4 ,illustration3 ,,fig4 #ca4--,mode of drawing an ellipse4 ,the two pins ,f are the foci4 ,away he started through his calculations again4 ,a long course of work night and day was rewarded by finding that he was now able to hit off the motions better than before2 but what a singularly complicated motion it was4 ,could it be expressed no more simply8 ,yes1 the curve so described by the planet is a comparatively simple one3 it is a special kind of oval--the ellipse4 ,strange that he had not thought of it before4 ,it was a famous curve1 for the ,greek geometers had studied it as one of the sections of a cone1 but it was not so well known in ,kepler's time4 ,the fact that the planets move in it has raised it to the first importance1 and it is familiar enough to us now4 ,but did it satisfy the law of speed8 ,could the rate of description of areas be uniform with it8 ,well1 he tried the ellipse1 and to his inexpressible delight he found that it did satisfy the condition of equable description of areas1 if the sun was in one focus4 ,so1 moving the planet in a selected ellipse1 with the sun in one focus1 at a speed given by the equable area description1 its position agreed with ,tycho's observations within the limits of the error of experiment4 ,mars was finally conquered1 and remains in his prison-house to this day4 ,the orbit was found4 ,illustration3 ,,fig4 #cb4 ,in a paroxysm of delight ,kepler celebrates his victory by a triumphant figure1 sketched actually on his geometrical diagram--the diagram which proves that the law of equable description of areas can hold good with an ellipse4 ,the above is a tracing of it4 ,such is a crude and bald sketch of the steps by which ,kepler rose to his great generalizations--the two laws which have immortalized his name4 ,all the complications of epicycle1 equant1 deferent1 excentric1 and the like1 were swept at once away1 and an orbit of striking and beautiful properties substituted4 ,well might he be called1 as he was1 the legislator1 or law interpreter1 of the heavens4 ,illustration3 ,,fig4 #cc4--;,if ,s is the sun1 a planet or comet moves from ,p to ,p#a1 from ,p#b to ,p#c1 and from ,p#d to ,p#e in the same time2 if the shaded areas are equal4 ,he concludes his book on the motions of ,mars with a half comic appeal to the ,emperor to provide him with the sinews of war for an attack on ,mars's relations--father ,jupiter1 brother ,mercury1 and the rest--but the death of his unhappy patron in #afab put an end to all these schemes1 and reduced ,kepler to the utmost misery4 ,while at ,prague his salary was in continual arrear1 and it was with difficulty that he could provide sustenance for his family4 ,he had been there eleven years1 but they had been hard years of poverty1 and he could leave without regret were it not that he should have to leave ,tycho's instruments and observations behind him4 ,while he was hesitating what best to do1 and reduced to the verge of despair1 his wife1 who had long been suffering from low spirits and despondency1 and his three children1 were taken ill2 one of the sons died of small-pox1 and the wife eleven days after of low fever and epilepsy4 ,no money could be got at ,prague1 so after a short time he accepted a professorship at ,linz1 and withdrew with his two quite young remaining children4 ,he provided for himself now partly by publishing a prophesying almanack1 a sort of ,zadkiel arrangement--a thing which he despised1 but the support of which he could not afford to do without4 ,he is continually attacking and throwing sarcasm at astrology1 but it was the only thing for which people would pay him1 and on it after a fashion he lived4 ,we do not find that his circumstances were ever prosperous1 and though #h1jjj crowns were due to him from ,bohemia he could not manage to get them paid4 ,about this time occurred a singular interruption to his work4 ,his old mother1 of whose fierce temper something has already been indicated1 had been engaged in a law-suit for some years near their old home in ,wrtemberg4 ,a change of judge having in process of time occurred1 the defendant saw his way to turn the tables on the old lady by accusing her of sorcery4 ,she was sent to prison1 and condemned to the torture1 with the usual intelligent idea of extracting a voluntary confession4 ,kepler had to hurry from ,linz to interpose4 ,he succeeded in saving her from the torture1 but she remained in prison for a year or so4 ,her spirit1 however1 was unbroken1 for no sooner was she released than she commenced a fresh action against her accuser4 ,but fresh trouble was averted by the death of the poor old dame at the age of nearly eighty4 ,this narration renders the unflagging energy shown by her son in his mathematical wrestlings less surprising4 ,interspersed with these domestic troubles1 and with harassing and unsuccessful attempts to get his rights1 he still brooded over his old problem of some possible connection between the distances of the planets from the sun and their times of revolution1 i4e4 the length of their years4 ,it might well have been that there was no connection1 that it was purely imaginary1 like his old idea of the law of the successive distances of the planets1 and like so many others of the guesses and fancies which he entertained and spent his energies in probing4 ,but fortunately this time there was a connection1 and he lived to have the joy of discovering it4 ,the connection is this1 that if one compares the distance of the different planets from the sun with the length of time they take to go round him1 the cube of the respective distances is proportional to the square of the corresponding times4 ,in other words1 the ratio of r#c to ,t#b for every planet is the same4 ,or1 again1 the length of a planet's year depends on the #c_/bth power of its distance from the sun4 ,or1 once more1 the speed of each planet in its orbit is as the inverse square-root of its distance from the sun4 ,the product of the distance into the square of the speed is the same for each planet4 ,this 7however stated7 is called ,kepler's third law4 ,it welds the planets together1 and shows them to be one system4 ,his rapture on detecting the law was unbounded1 and he breaks out into an exulting rhapsody3-- ,what ,i prophesied two-and-twenty years ago1 as soon as ,i discovered the five solids among the heavenly orbits--what ,i firmly believed long before ,i had seen ,ptolemy's ,harmonies--what ,i had promised my friends in the title of this book1 which ,i named before ,i was sure of my discovery--what sixteen years ago1 ,i urged as a thing to be sought--that for which ,i joined ,tycho ,brah1 for which ,i settled in ,prague1 for which ,i have devoted the best part of my life to astronomical contemplations1 at length ,i have brought to light1 and recognized its truth beyond my most sanguine expectations4 ,it is not eighteen months since ,i got the first glimpse of light1 three months since the dawn1 very few days since the unveiled sun1 most admirable to gaze upon1 burst upon me4 ,nothing holds me2 ,i will indulge my sacred fury2 ,i will triumph over mankind by the honest confession that ,i have stolen the golden vases of the ,egyptians to build up a tabernacle for my ,god far away from the confines of ,egypt4 ,if you forgive me1 ,i rejoice2 if you are angry1 ,i can bear it2 the die is cast1 the book is written1 to be read either now or by posterity1 ,i care not which2 it may well wait a century for a reader1 as ,god has waited six thousand years for an observer4 ,soon after this great work his third book appeared3 it was an epitome of the ,copernican theory1 a clear and fairly popular exposition of it1 which had the honour of being at once suppressed and placed on the list of books prohibited by the ,church1 side by side with the work of ,copernicus himself1 ,de ,revolutionibus ,orbium ,coelestium4 ,this honour1 however1 gave ,kepler no satisfaction--it rather occasioned him dismay1 especially as it deprived him of all pecuniary benefit1 and made it almost impossible for him to get a publisher to undertake another book4 ,still he worked on at the ,rudolphine tables of ,tycho1 and ultimately1 with some small help from ,vienna1 completed them2 but he could not get the means to print them4 ,he applied to the ,court till he was sick of applying3 they lay idle four years4 ,at last he determined to pay for the type himself4 ,what he paid it with1 ,god knows1 but he did pay it1 and he did bring out the tables1 and so was faithful to the behest of his friend4 ,this great publication marks an era in astronomy4 ,they were the first really accurate tables which navigators ever possessed2 they were the precursors of our present ,nautical ,almanack4 ,after this1 the ,grand ,duke of ,tuscany sent ,kepler a golden chain1 which is interesting inasmuch as it must really have come from ,galileo1 who was in high favour at the ,italian ,court at this time4 ,once more ,kepler made a determined attempt to get his arrears of salary paid1 and rescue himself and family from their bitter poverty4 ,he travelled to ,prague on purpose1 attended the imperial meeting1 and pleaded his own cause1 but it was all fruitless2 and exhausted by the journey1 weakened by over-study1 and disheartened by the failure1 he caught a fever1 and died in his fifty-ninth year4 ,his body was buried at ,ratisbon1 and a century ago a proposal was made to erect a marble monument to his memory1 but nothing was done4 ,it matters little one way or the other whether ,germany1 having almost refused him bread during his life1 should1 a century and a half after his death1 offer him a stone4 ,illustration3 ,,fig4 #cd4--,portrait of ,kepler1 older4 ,the contiguity of the lives of ,kepler and ,tycho furnishes a moral too obvious to need pointing out4 ,what ,kepler might have achieved had he been relieved of those ghastly struggles for subsistence one cannot tell1 but this much is clear1 that had ,tycho been subjected to the same misfortune1 instead of being born rich and being assisted by generous and enlightened patrons1 he could have accomplished very little4 ,his instruments1 his observatory--the tools by which he did his work--would have been impossible for him4 ,frederick and ,sophia of ,denmark1 and ,rudolph of ,bohemia1 are therefore to be remembered as co-workers with him4 ,kepler1 with his ill-health and inferior physical energy1 was unable to command the like advantages4 ,much1 nevertheless1 he did2 more one cannot but feel he might have done had he been properly helped4 ,besides1 the world would have been free from the reproach of accepting the fruits of his bright genius while condemning the worker to a life of misery1 relieved only by the beauty of his own thoughts and the ecstasy awakened in him by the harmony and precision of ,nature4 ,concerning the method of ,kepler1 the mode by which he made his discoveries1 we must remember that he gives us an account of all the steps1 unsuccessful as well as successful1 by which he travelled4 ,he maps out his route like a traveller4 ,in fact he compares himself to ,columbus or ,magellan1 voyaging into unknown lands1 and recording his wandering route4 ,this being remembered1 it will be found that his methods do not differ so utterly from those used by other philosophers in like case4 ,his imagination was perhaps more luxuriant and was allowed freer play than most men's1 but it was nevertheless always controlled by rigid examination and comparison of hypotheses with fact4 ,brewster says of him3--,ardent1 restless1 burning to distinguish himself by discovery1 he attempted everything2 and once having obtained a glimpse of a clue1 no labour was too hard in following or verifying it4 ,a few of his attempts succeeded--a multitude failed4 ,those which failed seem to us now fanciful1 those which succeeded appear to us sublime4 ,but his methods were the same4 ,when in search of what really existed he sometimes found it2 when in pursuit of a chimra he could not but fail2 but in either case he displayed the same great qualities1 and that obstinate perseverance which must conquer all difficulties except those really insurmountable4 ,to realize what he did for astronomy1 it is necessary for us now to consider some science still in its infancy4 ,astronomy is so clear and so thoroughly explored now1 that it is difficult to put oneself into a contemporary attitude4 ,but take some other science still barely developed3 meteorology1 for instance4 ,the science of the weather1 the succession of winds and rain1 sunshine and frost1 clouds and fog1 is now very much in the condition of astronomy before ,kepler4 ,we have passed through the stage of ascribing atmospheric disturbances--thunderstorms1 cyclones1 earthquakes1 and the like--to supernatural agency2 we have had our ,copernican era3 not perhaps brought about by a single individual1 but still achieved4 ,something of the laws of cyclone and anticyclone are known1 and rude weather predictions across the ,atlantic are roughly possible4 ,barometers and thermometers and anemometers1 and all their tribe1 represent the astronomical instruments in the island of ,huen2 and our numerous meteorological observatories1 with their continual record of events1 represent the work of ,tycho ,brah4 ,observation is heaped on observation2 tables are compiled2 volumes are filled with data2 the hours of sunshine are recorded1 the fall of rain1 the moisture in the air1 the kind of clouds1 the temperature--millions of facts2 but where is the ,kepler to study and brood over them8 ,where is the man to spend his life in evolving the beginnings of law and order from the midst of all this chaos8 ,perhaps as a man he may not come1 but his era will come4 ,through this stage the science must pass1 ere it is ready for the commanding intellect of a ,newton4 ,but what a work it will be for the man1 whoever he be that undertakes it--a fearful monotonous grind of calculation1 hypothesis1 hypothesis1 calculation1 a desperate and groping endeavour to reconcile theories with facts4 ,a life of such labour1 crowned by three brilliant discoveries1 the world owes 7and too late recognizes its obligation7 to the harshly treated ,german genius1 ,kepler4 ,,summary ,,of ,,facts ,,for ,,lectures ,,iv ,,and ,v ,in #aefd1 ,michael ,angelo died and ,galileo was born2 in #afdb1 ,galileo died and ,newton was born4 ,milton lived from #afjh to #afgd4 ,for teaching the plurality of worlds1 with other heterodox doctrines1 and refusing to recant1 ,bruno1 after six years' imprisonment in ,rome1 was burnt at the stake on the #afth of ,february1 #afjj ,a4,d4 ,a natural death in the dungeons of the ,inquisition saved ,antonio de ,dominis1 the explainer of the rainbow1 from the same fate1 but his body and books were publicly burned at ,rome in #afbd4 ,the persecution of ,galileo began in #afae1 became intense in #afcb1 and so lasted till his death and after4 99 99 99 99 99 ,galileo ,galilei1 eldest son of ,vincenzo de ,bonajuti de ,galilei1 a noble ,florentine1 was born at ,pisa1 #ahth of ,february1 #aefd4 ,at the age of #ag was sent to the ,university of ,pisa to study medicine4 ,observed the swing of a pendulum and applied it to count pulse-beats4 ,read ,euclid and ,archimedes1 and could be kept at medicine no more4 ,at #bf was appointed ,lecturer in ,mathematics at ,pisa4 ,read ,bruno and became smitten with the ,copernican theory4 ,controverted the ,aristotelians concerning falling bodies1 at ,pisa4 ,hence became unpopular and accepted a chair at ,padua1 #aeib4 ,invented a thermometer4 ,wrote on astronomy1 adopting the ,ptolemaic system provisionally1 and so opened up a correspondence with ,kepler1 with whom he formed a friendship4 ,lectured on the new star of #afjd1 and publicly renounced the old systems of astronomy4 ,invented a calculating compass or ,gunter's scale4 ,in #afji invented a telescope1 after hearing of a ,dutch optician's discovery4 ,invented the microscope soon after4 ,rapidly completed a better telescope and began a survey of the heavens4 ,on the #hth of ,january1 #afaj1 discovered ,jupiter's satellites4 ,observed the mountains in the moon1 and roughly measured their height4 ,explained the visibility of the new moon by earth-shine4 ,was invited to the ,grand ,ducal ,court of ,tuscany by ,cosmo de ,medici1 and appointed philosopher to that personage4 ,discovered innumerable new stars1 and the nebul4 ,observed a triple appearance of ,saturn4 ,discovered the phases of ,venus predicted by ,copernicus1 and spots on the sun4 ,wrote on floating bodies4 ,tried to get his satellites utilized for determining longitude at sea4 ,went to ,rome to defend the ,copernican system1 then under official discussion1 and as a result was formally forbidden ever to teach it4 ,on the accession of ,pope ,urban ,,viii4 in #afbc1 ,galileo again visited ,rome to pay his respects1 and was well received4 ,in #afcb appeared his ,dialogues on the ,ptolemaic and ,copernican systems4 ,summoned to ,rome1 practically imprisoned1 and rigorously questioned4 ,was made to recant #bbnd of ,june1 #afcc4 ,forbidden evermore to publish anything1 or to teach1 or receive friends4 ,retired to ,arcetri in broken down health4 ,death of his favourite daughter1 ,sister ,maria ,celeste4 ,wrote and meditated on the laws of motion4 ,discovered the moon's libration4 ,in #afcg he became blind4 ,the rigour was then slightly relaxed and many visited him3 among them ,john ,milton4 ,died #hth of ,january1 #afdb1 aged #gh4 ,as a prisoner of the ,inquisition his right to make a will or to be buried in consecrated ground was disputed4 ,many of his manuscripts were destroyed4 ,galileo1 besides being a singularly clear-headed thinker and experimental genius1 was also something of a musician1 a poet1 and an artist4 ,he was full of humour as well as of solid common-sense1 and his literary style is brilliant4 ,of his scientific achievements those now reckoned most weighty1 are the discovery of the ,laws of ,motion1 and the laying of the foundations of ,mechanics4 ,particulars of ,jupiter's ,satellites1 ,illustrating their obedience to ,kepler's third law4 ---------------------------------------- ---------------------------------- ,distance ,t#b ,time of from ---- ,satellite4,diameter revolution ,jupiter1 ,t#b d#c d#c miles4 in hours4 in ,jovian which is miles 7,t7 radii4 practically 7d7 constant4 ---------------------------------------- ---------------------------- ,no4 #a4 #bdcg #dbdg #fjdi #ahjcg #bbadd #hadi ,no4 #b4 #bahh #hebc #ifbc #gbfda #hiaaa #haeb ,no4 #c4 #cege #agggb #aecej #bidhh #ciafh #haec ,no4 #d4 #cjei #djjec #bfiih #afjdbf #aifgi #haeb ---------------------------------------- ---------------------------------- ,the diameter of ,jupiter is #he1hbc miles4 ,falling ,bodies4 ,since all bodies fall at the same rate1 except for the disturbing effect of the resistance of the air1 a statement of their rates of fall is of interest4 ,in one second a freely falling body near the earth is found to drop #af feet4 ,in two seconds it drops #fd feet altogether1 viz4 #af feet in the first1 and #dh feet in the next second2 because at the beginning of every second after the first it has the accumulated velocity of preceding seconds4 ,the height fallen by a dropped body is not proportional to the time simply1 but to what is rather absurdly called the square of the time1 i4e4 the time multiplied by itself4 ,for instance1 in #c seconds it drops #i #af #add feet2 in #d seconds #af #af1 or #bef feet1 and so on4 ,the distances travelled in #a1 #b1 #c1 #d1 c41 seconds by a body dropped from rest and not appreciably resisted by the air1 are #a1 #d1 #i1 #af1 #be1 c41 respectively1 each multiplied by the constant #af feet4 ,another way of stating the law is to say that the heights travelled in successive seconds proceed in the proportion #a1 #c1 #e1 #g1 #i1 c42 again multiplied by #af feet in each case4 ,illustration3 ,,fig4 #ce4--;,curve described by a projectile1 showing how it drops from the line of fire1 ,o ,d1 in successive seconds1 the same distances ,,ap1 ,,bq1 ,,cr1 c41 as are stated above for a dropped body4 ,all this was experimentally established by ,galileo4 ,a body takes half a second to drop #d feet2 and a quarter of a second to drop #a foot4 ,the easiest way of estimating a quarter of a second with some accuracy is to drop a bullet one foot4 ,a bullet thrown or shot in any direction falls just as much as if merely dropped2 but instead of falling from the starting-point it drops vertically from the line of fire4 7,see fig4 #ce74 ,the rate of fall depends on the intensity of gravity2 if it could be doubled1 a body would fall twice as far in the same time2 but to make it fall a given distance in half the time the intensity of gravity would have to be quadrupled4 ,at a place where the intensity of gravity is #a_/cfjj of what it is here1 a body would fall as far in a minute as it now falls in a second4 ,such a place occurs at about the distance of the moon 7cf4 page #agg74 ,the fact that the height fallen through is proportional to the square of the time proves that the attraction of the earth or the intensity of gravity is sensibly constant throughout ordinary small ranges4 ,over great distances of fall1 gravity cannot be considered constant2 so for things falling through great spaces the ,galilean law of the square of the time does not hold4 ,the fact that things near the earth fall #af feet in the first second proves that the intensity of ordinary terrestrial gravity is #cb ,british units of force per pound of matter4 ,the fact that all bodies fall at the same rate 7when the resistance of the air is eliminated71 proves that weight is proportional to mass2 or more explicitly1 that the gravitative attraction of the earth on matter near its surface depends on the amount of that matter1 as estimated by its inertia1 and on nothing else4 ,,lecture ,,iv ,,galileo ,,and ,,the ,,invention ,,of ,,the ,,telescope ,contemporary with the life of ,kepler1 but overlapping it at both ends1 comes the great and eventful life of ,galileo ,galilei1#e a man whose influence on the development of human thought has been greater than that of any man whom we have yet considered1 and upon whom1 therefore1 it is necessary for us1 in order to carry out the plan of these lectures1 to bestow much time4 ,a man of great and wide culture1 a so-called universal genius1 it is as an experimental philosopher that he takes the first rank4 ,in this capacity he must be placed alongside of ,archimedes1 and it is pretty certain that between the two there was no man of magnitude equal to either in experimental philosophy4 ,it is perhaps too bold a speculation1 but ,i venture to doubt whether in succeeding generations we find his equal in the domain of purely experimental science until we come to ,faraday4 ,faraday was no doubt his superior1 but ,i know of no other of whom the like can unhesitatingly be said4 ,in mathematical and deductive science1 of course1 it is quite otherwise4 ,kepler1 for instance1 and many men before and since1 have far excelled ,galileo in mathematical skill and power1 though at the same time his achievements in this department are by no means to be despised4 ,born at ,pisa three centuries ago1 on the very day that ,michael ,angelo lay dying in ,rome1 he inherited from his father a noble name1 cultivated tastes1 a keen love of truth1 and an impoverished patrimony4 ,vincenzo de ,galilei1 a descendant of the important ,bonajuti family1 was himself a mathematician and a musician1 and in a book of his still extant he declares himself in favour of free and open inquiry into scientific matters1 unrestrained by the weight of authority and tradition4 ,in all probability the son imbibed these precepts3 certainly he acted on them4 ,vincenzo1 having himself experienced the unremunerative character of scientific work1 had a horror of his son's taking to it1 especially as in his boyhood he was always constructing ingenious mechanical toys1 and exhibiting other marks of precocity4 ,so the son was destined for business--to be1 in fact1 a cloth-dealer4 ,but he was to receive a good education first1 and was sent to an excellent convent school4 ,here he made rapid progress1 and soon excelled in all branches of classics and literature4 ,he delighted in poetry1 and in later years wrote several essays on ,dante1 ,tasso1 and ,ariosto1 besides composing some tolerable poems himself4 ,he played skilfully on several musical instruments1 especially on the lute1 of which indeed he became a master1 and on which he solaced himself when quite an old man4 ,besides this he seems to have had some skill as an artist1 which was useful afterwards in illustrating his discoveries1 and to have had a fine sensibility as an art critic1 for we find several eminent painters of that day acknowledging the value of the opinion of the young ,galileo4 ,perceiving all this display of ability1 the father wisely came to the conclusion that the selling of woollen stuffs would hardly satisfy his aspirations for long1 and that it was worth a sacrifice to send him to the ,university4 ,so to the ,university of his native town he went1 with the avowed object of studying medicine1 that career seeming the most likely to be profitable4 ,old ,vincenzo's horror of mathematics or science as a means of obtaining a livelihood is justified by the fact that while the ,university ,professor of ,medicine received #b1jjj scudi a year1 the ,professor of ,mathematics had only #fj1 that is #ac a year1 or #g-a_/b;d4 a day4 ,so the son had been kept properly ignorant of such poverty-stricken subjects1 and to study medicine he went4 ,but his natural bent showed itself even here4 ,for praying one day in the ,cathedral1 like a good ,catholic as he was all his life1 his attention was arrested by the great lamp which1 after lighting it1 the verger had left swinging to and fro4 ,galileo proceeded to time its swings by the only watch he possessed--viz41 his own pulse4 ,he noticed that the time of swing remained as near as he could tell the same1 notwithstanding the fact that the swings were getting smaller and smaller4 ,by subsequent experiment he verified the law1 and the isochronism of the pendulum was discovered4 ,an immensely important practical discovery this1 for upon it all modern clocks are based2 and ,huyghens soon applied it to the astronomical clock1 which up to that time had been a crude and quite untrustworthy instrument4 ,the best clock which ,tycho ,brah could get for his observatory was inferior to one that may now be purchased for a few shillings2 and this change is owing to the discovery of the pendulum by ,galileo4 ,not that he applied it to clocks2 he was not thinking of astronomy1 he was thinking of medicine1 and wanted to count people's pulses4 ,the pendulum served2 and pulsilogies1 as they were called1 were thus introduced to and used by medical practitioners4 ,the ,tuscan ,court came to ,pisa for the summer months1 for it was then a seaside place1 and among the suite was ,ostillio ,ricci1 a distinguished mathematician and old friend of the ,galileo family4 ,the youth visited him1 and one day1 it is said1 heard a lesson in ,euclid being given by ,ricci to the pages while he stood outside the door entranced4 ,anyhow he implored ,ricci to help him into some knowledge of mathematics1 and the old man willingly consented4 ,so he mastered ,euclid and passed on to ,archimedes1 for whom he acquired a great veneration4 ,his father soon heard of this obnoxious proclivity1 and did what he could to divert him back to medicine again4 ,but it was no use4 ,underneath his ,galen and ,hippocrates were secreted copies of ,euclid and ,archimedes1 to be studied at every available opportunity4 ,old ,vincenzo perceived the bent of genius to be too strong for him1 and at last gave way4 ,illustration3 ,,fig4 #cf4--,two forms of pulsilogy4 ,the string is wound up till the swinging weight keeps time with the pulse1 and the position of a bead or of an index connected with the string is then read on a scale or dial4 ,with prodigious rapidity the released philosopher now assimilated the elements of mathematics and physics1 and at twenty-six we find him appointed for three years to the ,university ,chair of ,mathematics1 and enjoying the paternally dreaded stipend of #g-a_/b;d4 a day4 ,now it was that he pondered over the laws of falling bodies4 ,he verified1 by experiment1 the fact that the velocity acquired by falling down any slope of given height was independent of the angle of slope4 ,also1 that the height fallen through was proportional to the square of the time4 ,another thing he found experimentally was that all bodies1 heavy and light1 fell at the same rate1 striking the ground at the same time4#f ,now this was clean contrary to what he had been taught4 ,the physics of those days were a simple reproduction of statements in old books4 ,aristotle had asserted certain things to be true1 and these were universally believed4 ,no one thought of trying the thing to see if it really were so4 ,the idea of making an experiment would have savoured of impiety1 because it seemed to tend towards scepticism1 and cast a doubt on a reverend authority4 ,young ,galileo1 with all the energy and imprudence of youth 7what a blessing that youth has a little imprudence and disregard of consequences in pursuing a high ideal671 as soon as he perceived that his instructors were wrong on the subject of falling bodies1 instantly informed them of the fact4 ,whether he expected them to be pleased or not is a question4 ,anyhow1 they were not pleased1 but were much annoyed by his impertinent arrogance4 ,it is1 perhaps1 difficult for us now to appreciate precisely their position4 ,these doctrines of antiquity1 which had come down hoary with age1 and the discovery of which had reawakened learning and quickened intellectual life1 were accepted less as a science or a philosophy1 than as a religion4 ,had they regarded ,aristotle as a verbally inspired writer1 they could not have received his statements with more unhesitating conviction4 ,in any dispute as to a question of fact1 such as the one before us concerning the laws of falling bodies1 their method was not to make an experiment1 but to turn over the pages of ,aristotle2 and he who could quote chapter and verse of this great writer was held to settle the question and raise it above the reach of controversy4 ,it is very necessary for us to realize this state of things clearly1 because otherwise the attitude of the learned of those days towards every new discovery seems stupid and almost insane4 ,they had a crystallized system of truth1 perfect1 symmetrical--it wanted no novelty1 no additions2 every addition or growth was an imperfection1 an excrescence1 a deformity4 ,progress was unnecessary and undesired4 ,the ,church had a rigid system of dogma1 which must be accepted in its entirety on pain of being treated as a heretic4 ,philosophers had a cast-iron system of truth to match--a system founded upon ,aristotle--and so interwoven with the great theological dogmas that to question one was almost equivalent to casting doubt upon the other4 ,in such an atmosphere true science was impossible4 ,the life-blood of science is growth1 expansion1 freedom1 development4 ,before it could appear it must throw off these old shackles of centuries4 ,it must burst its old skin1 and emerge1 worn with the struggle1 weakly and unprotected1 but free and able to grow and to expand4 ,the conflict was inevitable1 and it was severe4 ,is it over yet8 ,i fear not quite1 though so nearly as to disturb science hardly at all4 ,then it was different2 it was terrible4 ,honour to the men who bore the first shock of the battle6 ,now ,aristotle had said that bodies fell at rates depending on their weight4 ,a #e lb4 weight would fall five times as quick as a #a lb4 weight2 a #ej lb4 weight fifty times as quick1 and so on4 ,why he said so nobody knows4 ,he cannot have tried4 ,he was not above trying experiments1 like his smaller disciples2 but probably it never occurred to him to doubt the fact4 ,it seems so natural that a heavy body should fall quicker than a light one2 and perhaps he thought of a stone and a feather1 and was satisfied4 ,galileo1 however1 asserted that the weight did not matter a bit1 that everything fell at the same rate 7even a stone and a feather1 but for the resistance of the air71 and would reach the ground in the same time4 ,and he was not content to be pooh-poohed and snubbed4 ,he knew he was right1 and he was determined to make every one see the facts as he saw them4 ,so one morning1 before the assembled ,university1 he ascended the famous leaning tower1 taking with him a #ajj lb4 shot and a #a lb4 shot4 ,he balanced them on the edge of the tower1 and let them drop together4 ,together they fell1 and together they struck the ground4 ,the simultaneous clang of those two weights sounded the death-knell of the old system of philosophy1 and heralded the birth of the new4 ,but was the change sudden8 ,were his opponents convinced8 ,not a jot4 ,though they had seen with their eyes1 and heard with their ears1 the full light of heaven shining upon them1 they went back muttering and discontented to their musty old volumes and their garrets1 there to invent occult reasons for denying the validity of the observation1 and for referring it to some unknown disturbing cause4 ,they saw that if they gave way on this one point they would be letting go their anchorage1 and henceforward would be liable to drift along with the tide1 not knowing whither4 ,they dared not do this4 ,no2 they must cling to the old traditions2 they could not cast away their rotting ropes and sail out on to the free ocean of ,god's truth in a spirit of fearless faith4 ,illustration3 ,,fig4 #cg4--,tower of ,pisa4 ,yet they had received a shock3 as by a breath of fresh salt breeze and a dash of spray in their faces1 they had been awakened out of their comfortable lethargy4 ,they felt the approach of a new era4 ,yes1 it was a shock2 and they hated the young ,galileo for giving it them--hated him with the sullen hatred of men who fight for a lost and dying cause4 ,we need scarcely blame these men2 at least we need not blame them overmuch4 ,to say that they acted as they did is to say that they were human1 were narrow-minded1 and were the apostles of a lost cause4 ,but they could not know this2 they had no experience of the past to guide them2 the conditions under which they found themselves were novel1 and had to be met for the first time4 ,conduct which was excusable then would be unpardonable now1 in the light of all this experience to guide us4 ,are there any now who practically repeat their error1 and resist new truth8 who cling to any old anchorage of dogma1 and refuse to rise with the tide of advancing knowledge8 ,there may be some even now4 ,well1 the unpopularity of ,galileo smouldered for a time1 until1 by another noble imprudence1 he managed to offend a semi-royal personage1 ,giovanni de ,medici1 by giving his real opinion1 when consulted1 about a machine which de ,medici had invented for cleaning out the harbour of ,leghorn4 ,he said it was as useless as it in fact turned out to be4 ,through the influence of the mortified inventor he lost favour at ,court2 and his enemies took advantage of the fact to render his chair untenable4 ,he resigned before his three years were up1 and retired to ,florence4 ,his father at this time died1 and the family were left in narrow circumstances4 ,he had a brother and three sisters to provide for4 ,he was offered a professorship at ,padua for six years by the ,senate of ,venice1 and willingly accepted it4 ,now began a very successful career4 ,his introductory address was marked by brilliant eloquence1 and his lectures soon acquired fame4 ,he wrote for his pupils on the laws of motion1 on fortifications1 on sundials1 on mechanics1 and on the celestial globe3 some of these papers are now lost1 others have been printed during the present century4 ,kepler sent him a copy of his new book1 ,mysterium ,cosmographicum1 and ,galileo in thanking him for it writes him the following letter3--#g ,i count myself happy1 in the search after truth1 to have so great an ally as yourself1 and one who is so great a friend of the truth itself4 ,it is really pitiful that there are so few who seek truth1 and who do not pursue a perverse method of philosophising4 ,but this is not the place to mourn over the miseries of our times1 but to congratulate you on your splendid discoveries in confirmation of truth4 ,i shall read your book to the end1 sure of finding much that is excellent in it4 ,i shall do so with the more pleasure1 because ,i have been for many years an adherent of the ,copernican system1 and it explains to me the causes of many of the appearances of nature which are quite unintelligible on the commonly accepted hypothesis4 ,i have collected many arguments for the purpose of refuting the latter2 but ,i do not venture to bring them to the light of publicity1 for fear of sharing the fate of our master1 ,copernicus1 who1 although he has earned immortal fame with some1 yet with very many 7so great is the number of fools7 has become an object of ridicule and scorn4 ,i should certainly venture to publish my speculations if there were more people like you4 ,but this not being the case1 ,i refrain from such an undertaking4 ,kepler urged him to publish his arguments in favour of the ,copernican theory1 but he hesitated for the present1 knowing that his declaration would be received with ridicule and opposition1 and thinking it wiser to get rather more firmly seated in his chair before encountering the storm of controversy4 ,the six years passed away1 and the ,venetian ,senate1 anxious not to lose so bright an ornament1 renewed his appointment for another six years at a largely increased salary4 ,soon after this appeared a new star1 the stella nova of #afjd1 not the one ,tycho had seen--that was in #aegb--;but the same that ,kepler was so much interested in4 ,galileo gave a course of three lectures upon it to a great audience4 ,at the first the theatre was over-crowded1 so he had to adjourn to a hall holding #ajjj persons4 ,at the next he had to lecture in the open air4 ,he took occasion to rebuke his hearers for thronging to hear about an ephemeral novelty1 while for the much more wonderful and important truths about the permanent stars and facts of nature they had but deaf ears4 ,but the main point he brought out concerning the new star was that it upset the received ,aristotelian doctrine of the immutability of the heavens4 ,according to that doctrine the heavens were unchangeable1 perfect1 subject neither to growth nor to decay4 ,here was a body1 not a meteor but a real distant star1 which had not been visible and which would shortly fade away again1 but which meanwhile was brighter than ,jupiter4 ,the staff of petrified professorial wisdom were annoyed at the appearance of the star1 still more at ,galileo's calling public attention to it2 and controversy began at ,padua4 ,however1 he accepted it2 and now boldly threw down the gauntlet in favour of the ,copernican theory1 utterly repudiating the old ,ptolemaic system which up to that time he had taught in the schools according to established custom4 ,the earth no longer the only world to which all else in the firmament were obsequious attendants1 but a mere insignificant speck among the host of heaven6 ,man no longer the centre and cynosure of creation1 but1 as it were1 an insect crawling on the surface of this little speck6 ,all this not set down in crabbed ,latin in dry folios for a few learned monks1 as in ,copernicus's time1 but promulgated and argued in rich ,italian1 illustrated by analogy1 by experiment1 and with cultured wit2 taught not to a few scholars here and there in musty libraries1 but proclaimed in the vernacular to the whole populace with all the energy and enthusiasm of a recent convert and a master of language6 ,had a bombshell been exploded among the fossilized professors it had been less disturbing4 ,but there was worse in store for them4 ,a ,dutch optician1 ,hans ,lippershey by name1 of ,middleburg1 had in his shop a curious toy1 rigged up1 it is said1 by an apprentice1 and made out of a couple of spectacle lenses1 whereby1 if one looked through it1 the weather-cock of a neighbouring church spire was seen nearer and upside down4 ,the tale goes that the ,marquis ,spinola1 happening to call at the shop1 was struck with the toy and bought it4 ,he showed it to ,prince ,maurice of ,nassau1 who thought of using it for military reconnoitring4 ,all this is trivial4 ,what is important is that some faint and inaccurate echo of this news found its way to ,padua1 and into the ears of ,galileo4 ,the seed fell on good soil4 ,all that night he sat up and pondered4 ,he knew about lenses and magnifying glasses4 ,he had read ,kepler's theory of the eye1 and had himself lectured on optics4 ,could he not hit on the device and make an instrument capable of bringing the heavenly bodies nearer8 ,who knew what marvels he might not so perceive6 ,by morning he had some schemes ready to try1 and one of them was successful4 ,singularly enough it was not the same plan as the ,dutch optician's1 it was another mode of achieving the same end4 ,he took an old small organ pipe1 jammed a suitably chosen spectacle glass into either end1 one convex the other concave1 and behold1 he had the half of a wretchedly bad opera glass capable of magnifying three times4 ,it was better than the ,dutchman's1 however2 it did not invert4 ,it is easy to understand the general principle of a telescope4 ,a general knowledge of the common magnifying glass may be assumed4 ,roger ,bacon knew about lenses2 and the ancients often refer to them1 though usually as burning glasses4 ,the magnifying power of globes of water must have been noticed soon after the discovery of glass and the art of working it4 ,a magnifying glass is most simply thought of as an additional lens to the eye4 ,the eye has a lens by which ordinary vision is accomplished1 an extra glass lens strengthens it and enables objects to be seen nearer and therefore apparently bigger4 ,but to apply a magnifying glass to distant objects is impossible4 ,in order to magnify distant objects1 another function of lenses has also to be employed1 viz41 their power of forming real images1 the power on which their use as burning-glasses depends3 for the best focus is an image of the sun4 ,although the object itself is inaccessible1 the image of it is by no means so1 and to the image a magnifier can be applied4 ,this is exactly what is done in the telescope2 the object glass or large lens forms an image1 which is then looked at through a magnifying glass or eye-piece4 ,of course the image is nothing like so big as the object4 ,for astronomical objects it is almost infinitely less2 still it is an exact representation at an accessible place1 and no one expects a telescope to show distant bodies as big as they really are4 ,all it does is to show them bigger than they could be seen without it4 ,but if the objects are not distant1 the same principle may still be applied1 and two lenses may be used1 one to form an image1 the other to magnify it2 only if the object can be put where we please1 we can easily place it so that its image is already much bigger than the object even before magnification by the eye lens4 ,this is the compound microscope1 the invention of which soon followed the telescope4 ,in fact the two instruments shade off into one another1 so that the reading telescope or reading microscope of a laboratory 7for reading thermometers1 and small divisions generally7 goes by either name at random4 ,the arrangement so far described depicts things on the retina the unaccustomed way up4 ,by using a concave glass instead of a convex1 and placing it so as to prevent any image being formed1 except on the retina direct1 this inconvenience is avoided4 ,illustration3 ,,fig4 #ch4--,view of the half-moon in small telescope4 ,the darker regions1 or plains1 used to be called seas4 ,such a thing as ,galileo made may now be bought at a toy-shop for ,i suppose half a crown1 and yet what a potentiality lay in that glazed optic tube1 as ,milton called it4 ,away he went with it to ,venice and showed it to the ,signoria1 to their great astonishment4 ,many noblemen and senators1 says ,galileo1 though of advanced age1 mounted to the top of one of the highest towers to watch the ships1 which were visible through my glass two hours before they were seen entering the harbour1 for it makes a thing fifty miles off as near and clear as if it were only five4 ,among the people too the instrument excited the greatest astonishment and interest1 so that he was nearly mobbed4 ,the ,senate hinted to him that a present of the instrument would not be unacceptable1 so ,galileo took the hint and made another for them4 ,illustration3 ,,fig4 #ci4--,portion of the lunar surface more highly magnified1 showing the shadows of a mountain range1 deep pits1 and other details4 ,they immediately doubled his salary at ,padua1 making it #ajjj florins1 and confirmed him in the enjoyment of it for life4 ,he now eagerly began the construction of a larger and better instrument4 ,grinding the lenses with his own hands with consummate skill1 he succeeded in making a telescope magnifying thirty times4 ,thus equipped he was ready to begin a survey of the heavens4 ,illustration3 ,,fig4 #dj4--;,another portion of the lunar surface1 showing a so-called crater or vast lava pool and other evidences of ancient heat unmodified by water4 ,the first object he carefully examined was naturally the moon4 ,he found there everything at first sight very like the earth1 mountains and valleys1 craters and plains1 rocks1 and apparently seas4 ,you may imagine the hostility excited among the ,aristotelian philosophers1 especially no doubt those he had left behind at ,pisa1 on the ground of his spoiling the pure1 smooth1 crystalline1 celestial face of the moon as they had thought it1 and making it harsh and rugged and like so vile and ignoble a body as the earth4 ,illustration3 ,,fig4 #da4--,lunar landscape showing earth4 ,the earth would be a stationary object in the moon's sky3 its only apparent motion being a slow oscillation as of a pendulum 7the result of the moon's libration74 ,he went further1 however1 into heterodoxy than this--he not only made the moon like the earth1 but he made the earth shine like the moon4 ,the visibility of the old moon in the new moon's arms he explained by earth-shine4 ,leonardo had given the same explanation a century before4 ,now one of the many stock arguments against ,copernican theory of the earth being a planet like the rest was that the earth was dull and dark and did not shine4 ,galileo argued that it shone just as much as the moon does1 and in fact rather more--especially if it be covered with clouds4 ,one reason of the peculiar brilliancy of ,venus is that she is a very cloudy planet4#h ,seen from the moon the earth would look exactly as the moon does to us1 only a little brighter and sixteen times as big 7four times the diameter74 ,illustration3 ,,fig4 #db4--;,galileo's method of estimating the height of lunar mountain4 ,,ab',,bc is the illuminated half of the moon4 ,,sa is a solar ray just catching the peak of the mountain ,m4 ,then by geometry1 as ,,mn is to ,,ma1 so is ,,ma to ,,mb'2 whence the height of the mountain1 ,,mn1 can be determined4 ,the earth and spectator are supposed to be somewhere in the direction ,,ba produced1 i4e4 towards the top of the page4 ,galileo made a very good estimate of the height of lunar mountains1 of which many are five miles high and some as much as seven4 ,he did this simply by measuring from the half-moon's straight edge the distance at which their peaks caught the rising or setting sun4 ,the above simple diagram shows that as this distance is to the diameter of the moon1 so is the height of the sun-tipped mountain to the aforesaid distance4 ,wherever ,galileo turned his telescope new stars appeared4 ,the ,milky ,way1 which had so puzzled the ancients1 was found to be composed of stars4 ,stars that appeared single to the eye were some of them found to be double2 and at intervals were found hazy nebulous wisps1 some of which seemed to be star clusters1 while others seemed only a fleecy cloud4 ,illustration3 ,,fig4 #dc4--,some clusters and nebul4 ,illustration3 ,,fig4 #dd4--;,jupiter's satellites1 showing the stages of their discovery4 ,now we come to his most brilliant1 at least his most sensational1 discovery4 ,examining ,jupiter minutely on ,january #g1 #afaj1 he noticed three little stars near it1 which he noted down as fixing its then position4 ,on the following night ,jupiter had moved to the other side of the three stars4 ,this was natural enough1 but was it moving the right way8 ,on examination it appeared not4 ,was it possible the tables were wrong8 ,the next evening was cloudy1 and he had to curb his feverish impatience4 ,on the #ajth there were only two1 and those on the other side4 ,on the #aath two again1 but one bigger than the other4 ,on the #abth the three re-appeared1 and on the #acth there were four4 ,no more appeared4 ,jupiter then had moons like the earth1 four of them in fact1 and they revolved round him in periods which were soon determined4 ,the reason why they were not all visible at first1 and why their visibility so rapidly changes1 is because they revolve round him almost in the plane of our vision1 so that sometimes they are in front and sometimes behind him1 while again at other times they plunge into his shadow and are thus eclipsed from the light of the sun which enables us to see them4 ,a large modern telescope will show the moons when in front of ,jupiter1 but small telescopes will only show them when clear of the disk and shadow4 ,often all four can be thus seen1 but three or two is a very common amount of visibility4 ,quite a small telescope1 such as a ship's telescope1 if held steadily1 suffices to show the satellites of ,jupiter1 and very interesting objects they are4 ,they are of habitable size1 and may be important worlds for all we know to the contrary4 ,the news of the discovery soon spread and excited the greatest interest and astonishment4 ,many of course refused to believe it4 ,some there were who having been shown them refused to believe their eyes1 and asserted that although the telescope acted well enough for terrestrial objects1 it was altogether false and illusory when applied to the heavens4 ,others took the safer ground of refusing to look through the glass4 ,one of these who would not look at the satellites happened to die soon afterwards4 ,i hope1 says ,galileo1 that he saw them on his way to heaven4 ,the way in which ,kepler received the news is characteristic1 though by adding four to the supposed number of planets it might have seemed to upset his notions about the five regular solids4 ,he says1#i ,i was sitting idle at home thinking of you1 most excellent ,galileo1 and your letters1 when the news was brought me of the discovery of four planets by the help of the double eye-glass4 ,wachenfels stopped his carriage at my door to tell me1 when such a fit of wonder seized me at a report which seemed so very absurd1 and ,i was thrown into such agitation at seeing an old dispute between us decided in this way1 that between his joy1 my colouring1 and the laughter of us both1 confounded as we were by such a novelty1 we were hardly capable1 he of speaking1 or ,i of listening4444 ,on our separating1 ,i immediately fell to thinking how there could be any addition to the number of planets without overturning my ,mysterium ,cosmographicon1 published thirteen years ago1 according to which ,euclid's five regular solids do not allow more than six planets round the sun4 ,but ,i am so far from disbelieving the existence of the four circumjovial planets that ,i long for a telescope to anticipate you if possible in discovering two round ,mars 7as the proportion seems to me to require7 six or eight round ,saturn1 and one each round ,mercury and ,venus4 ,illustration3 ,,fig4 #de4--;,eclipses of ,jupiter's satellites4 ,the diagram shows the first 7i4e4 the nearest7 moon in ,jupiter's shadow1 the second as passing between earth and ,jupiter1 and appearing to transit his disk1 the third as on the verge of entering his shadow1 and the fourth quite plainly and separately visible4 ,as an illustration of the opposite school1 ,i will take the following extract from ,francesco ,sizzi1 a ,florentine astronomer1 who argues against the discovery thus3-- ,there are seven windows in the head1 two nostrils1 two eyes1 two ears1 and a mouth2 so in the heavens there are two favourable stars1 two unpropitious1 two luminaries1 and ,mercury alone undecided and indifferent4 ,from which and many other similar phenomena of nature1 such as the seven metals1 c41 which it were tedious to enumerate1 we gather that the number of planets is necessarily seven4 ,moreover1 the satellites are invisible to the naked eye1 and therefore can have no influence on the earth1 and therefore would be useless1 and therefore do not exist4 ,besides1 the ,jews and other ancient nations as well as modern ,europeans have adopted the division of the week into seven days1 and have named them from the seven planets3 now if we increase the number of the planets this whole system falls to the ground4 ,to these arguments ,galileo replied that whatever their force might be as a reason for believing beforehand that no more than seven planets would be discovered1 they hardly seemed of sufficient weight to destroy the new ones when actually seen4 ,writing to ,kepler at this time1 ,galileo ejaculates3 ,oh1 my dear ,kepler1 how ,i wish that we could have one hearty laugh together6 ,here1 at ,padua1 is the principal professor of philosophy whom ,i have repeatedly and urgently requested to look at the moon and planets through my glass1 which he pertinaciously refuses to do4 ,why are you not here8 ,what shouts of laughter we should have at this glorious folly6 ,and to hear the professor of philosophy at ,pisa labouring before the grand duke with logical arguments1 as if with magical incantations1 to charm the new planets out of the sky4 ,a young ,german protg of ,kepler1 ,martin ,horkey1 was travelling in ,italy1 and meeting ,galileo at ,bologna was favoured with a view through his telescope4 ,but supposing that ,kepler must necessarily be jealous of such great discoveries1 and thinking to please him1 he writes1 ,i cannot tell what to think about these observations4 ,they are stupendous1 they are wonderful1 but whether they are true or false ,i cannot tell4 ,he concludes1 ,i will never concede his four new planets to that ,italian from ,padua though ,i die for it4 ,so he published a pamphlet asserting that reflected rays and optical illusions were the sole cause of the appearance1 and that the only use of the imaginary planets was to gratify ,galileo's thirst for gold and notoriety4 ,when after this performance he paid a visit to his old instructor ,kepler1 he got a reception which astonished him4 ,however1 he pleaded so hard to be forgiven that ,kepler restored him to partial favour1 on this condition1 that he was to look again at the satellites1 and this time to see them and own that they were there4 ,by degrees the enemies of ,galileo were compelled to confess to the truth of the discovery1 and the next step was to outdo him4 ,scheiner counted five1 ,rheiter nine1 and others went as high as twelve4 ,some of these were imaginary1 some were fixed stars1 and four satellites only are known to this day4#aj ,here1 close to the summit of his greatness1 we must leave him for a time4 ,a few steps more and he will be on the brow of the hill2 a short piece of table-land1 and then the descent begins4 ,,lecture ,v ,,galileo ,,and ,,the ,,inquisition ,one sinister event occurred while ,galileo was at ,padua1 some time before the era we have now arrived at1 before the invention of the telescope--two years indeed after he had first gone to ,padua2 an event not directly concerning ,galileo1 but which ,i must mention because it must have shadowed his life both at the time and long afterwards4 ,it was the execution of ,giordano ,bruno for heresy4 ,this eminent philosopher had travelled largely1 had lived some time in ,england1 had acquired new and heterodox views on a variety of subjects1 and did not hesitate to propound them even after he had returned to ,italy4 ,the ,copernican doctrine of the motion of the earth was one of his obnoxious heresies4 ,being persecuted to some extent by the ,church1 ,bruno took refuge in ,venice--a free republic almost independent of the ,papacy--where he felt himself safe4 ,galileo was at ,padua hard by3 the ,university of ,padua was under the government of the ,senate of ,venice3 the two men must in all probability have met4 ,well1 the ,inquisition at ,rome sent messengers to ,venice with a demand for the extradition of ,bruno--they wanted him at ,rome to try him for heresy4 ,in a moment of miserable weakness the ,venetian republic gave him up1 and ,bruno was taken to ,rome4 ,there he was tried1 and cast into the dungeons for six years1 and because he entirely refused to recant1 was at length delivered over to the secular arm and burned at the stake on #afth ,february1 ,anno ,domini #afjj4 ,this event could not but have cast a gloom over the mind of lovers and expounders of truth1 and the lesson probably sank deep into ,galileo's soul4 ,in dealing with these historic events will you allow me to repudiate once for all the slightest sectarian bias or meaning4 ,i have nothing to do with ,catholic or ,protestant as such4 ,i have nothing to do with the ,church of ,rome as such4 ,i am dealing with the history of science4 ,but historically at one period science and the ,church came into conflict4 ,it was not specially one ,church rather than another--it was the ,church in general1 the only one that then existed in those countries4 ,historically1 ,i say1 they came into conflict1 and historically the ,church was the conqueror4 ,it got its way2 and science1 in the persons of ,bruno1 ,galileo1 and several others1 was vanquished4 ,such being the facts1 there is no help but to mention them in dealing with the history of science4 ,doubtless now the ,church regards it as an unhappy victory1 and gladly would ignore this painful struggle4 ,this1 however1 is impossible4 ,with their creed the ,churchmen of that day could act in no other way4 ,they were bound to prosecute heresy1 and they were bound to conquer in the struggle or be themselves shattered4 ,but let me insist on the fact that no one accuses the ecclesiastical courts of crime or evil motives4 ,they attacked heresy after their manner1 as the civil courts attacked witchcraft after their manner4 ,both erred grievously1 but both acted with the best intentions4 ,we must remember1 moreover1 that his doctrines were scientifically heterodox1 and the ,university ,professors of that day were probably quite as ready to condemn them as the ,church was4 ,to realise the position we must think of some subjects which to-day are scientifically heterodox1 and of the customary attitude adopted towards them by persons of widely differing creeds4 ,if it be contended now1 as it is1 that the ecclesiastics treated ,galileo well1 ,i admit it freely3 they treated him as well as they possibly could4 ,they overcame him1 and he recanted2 but if he had not recanted1 if he had persisted in his heresy1 they would--well1 they would still have treated his soul well1 but they would have set fire to his body4 ,their mistake consisted not in cruelty1 but in supposing themselves the arbiters of eternal truth2 and by no amount of slurring and glossing over facts can they evade the responsibility assumed by them on account of this mistaken attitude4 ,i am not here attacking the dogma of ,papal ,infallibility3 it is historically1 ,i believe1 quite unaffected by the controversy respecting the motion of the earth1 no ,papal edict ex cathedr having been promulgated on the subject4 ,we left ,galileo standing at his telescope and beginning his survey of the heavens4 ,we followed him indeed through a few of his first great discoveries--the discovery of the mountains and other variety of surface in the moon1 of the nebul and a multitude of faint stars1 and lastly of the four satellites of ,jupiter4 ,this latter discovery made an immense sensation1 and contributed its share to his removal from ,padua1 which quickly followed it1 as ,i shall shortly narrate2 but first ,i think it will be best to continue our survey of his astronomical discoveries without regard to the place whence they were made4 ,before the end of the year ,galileo had made another discovery--this time on ,saturn4 ,but to guard against the host of plagiarists and impostors1 he published it in the form of an anagram1 which1 at the request of the ,emperor ,rudolph 7a request probably inspired by ,kepler71 he interpreted2 it ran thus3 ,the furthest planet is triple4 ,very soon after he found that ,venus was changing from a full moon to a half moon appearance4 ,he announced this also by an anagram1 and waited till it should become a crescent1 which it did4 ,this was a dreadful blow to the anti-,copernicans1 for it removed the last lingering difficulty to the reception of the ,copernican doctrine4 ,illustration3 ,,fig4 #df4--,old drawings of ,saturn by different observers1 with the imperfect instruments of that day4 ,the first is ,galileo's idea of what he saw4 ,copernicus had predicted1 indeed1 a hundred years before1 that1 if ever our powers of sight were sufficiently enhanced1 ,venus and ,mercury would be seen to have phases like the moon4 ,and now ,galileo with his telescope verifies the prediction to the letter4 ,here was a triumph for the grand old monk1 and a bitter morsel for his opponents4 ,castelli writes3 ,this must now convince the most obstinate4 ,but ,galileo1 with more experience1 replies3--,you almost make me laugh by saying that these clear observations are sufficient to convince the most obstinate2 it seems you have yet to learn that long ago the observations were enough to convince those who are capable of reasoning1 and those who wish to learn the truth2 but that to convince the obstinate1 and those who care for nothing beyond the vain applause of the senseless vulgar1 not even the testimony of the stars would suffice1 were they to descend on earth to speak for themselves4 ,let us1 then1 endeavour to procure some knowledge for ourselves1 and rest contented with this sole satisfaction2 but of advancing in popular opinion1 or of gaining the assent of the book-philosophers1 let us abandon both the hope and the desire4 ,illustration3 ,,fig4 #dg4--,phases of ,venus4 ,showing also its apparent variations in size by reason of its varying distance from the earth4 ,when fully illuminated it is necessarily most distant4 ,it looks brightest to us when a broad crescent4 ,what a year's work it had been6 ,in twelve months observational astronomy had made such a bound as it has never made before or since4 ,why did not others make any of these observations8 ,because no one could make telescopes like ,galileo4 ,he gathered pupils round him however1 and taught them how to work the lenses1 so that gradually these instruments penetrated ,europe1 and astronomers everywhere verified his splendid discoveries4 ,but still he worked on1 and by ,march in the very next year1 he saw something still more hateful to the ,aristotelian philosophers1 viz4 spots on the sun4 ,illustration3 ,,fig4 #dh4 ,if anything was pure and perfect it was the sun1 they said4 ,was this impostor going to blacken its face too8 ,well1 there they were4 ,they slowly formed and changed1 and by moving all together showed him that the sun rotated about once a month4 ,before taking leave of ,galileo's astronomical researches1 ,i must mention an observation made at the end of #afab1 that the apparent triplicity of ,saturn 7,fig4 #df7 had vanished4 ,illustration3 ,,fig4 #di4--;,a portion of the sun's disk as seen in a powerful modern telescope4 ,looking on ,saturn within these few days1 ,i found it solitary1 without the assistance of its accustomed stars1 and in short perfectly round and defined1 like ,jupiter1 and such it still remains4 ,now what can be said of so strange a metamorphosis8 ,are perhaps the two smaller stars consumed like spots on the sun8 ,have they suddenly vanished and fled8 ,or has ,saturn devoured his own children8 ,or was the appearance indeed fraud and illusion1 with which the glasses have so long time mocked me and so many others who have so often observed with me8 ,now perhaps the time is come to revive the withering hopes of those1 who1 guided by more profound contemplations1 have fathomed all the fallacies of the new observations and recognized their impossibility6 ,i cannot resolve what to say in a chance so strange1 so new1 so unexpected4 ,the shortness of time1 the unexampled occurrence1 the weakness of my intellect1 the terror of being mistaken1 have greatly confounded me4 ,however1 he plucked up courage1 and conjectured that the two attendants would reappear1 by revolving round the planet4 ,illustration3 ,,fig4 #ej4--,saturn and his rings1 as seen under the most favourable circumstances4 ,the real reason of their disappearance is well known to us now4 ,the plane of ,saturn's rings oscillates slowly about our line of sight1 and so we sometimes see them edgeways and sometimes with a moderate amount of obliquity4 ,the rings are so thin that1 when turned precisely edgeways1 they become invisible4 ,the two imaginary attendants were the most conspicuous portions of the ring1 subsequently called ans4 ,i have thought it better not to interrupt this catalogue of brilliant discoveries by any biographical details2 but we must now retrace our steps to the years #afji and #afaj1 the era of the invention of the telescope4 ,by this time ,galileo had been eighteen years at ,padua1 and like many another man in like case1 was getting rather tired of continual lecturing4 ,moreover1 he felt so full of ideas that he longed to have a better opportunity of following them up1 and more time for thinking them out4 ,now in the holidays he had been accustomed to return to his family home at ,pisa1 and there to come a good deal into contact with the ,grand-,ducal ,house of ,tuscany4 ,young ,cosmo di ,medici became in fact his pupil1 and arrived at man's estate with the highest opinion of the philosopher4 ,this young man had now come to the throne as ,cosmo ,,ii41 and to him ,galileo wrote saying how much he should like more time and leisure1 how full he was of discoveries if he only had the chance of a reasonable income without the necessity of consuming so large a portion of his time in elementary teaching1 and practically asking to be removed to some position in the ,court4 ,nothing was done for a time1 but negotiations proceeded1 and soon after the discovery of ,jupiter's satellites ,cosmo wrote making a generous offer1 which ,galileo gladly and enthusiastically accepted1 and at once left ,padua for ,florence4 ,all his subsequent discoveries date from ,florence4 ,thus closed his brilliant and happy career as a professor at the ,university of ,padua4 ,he had been treated well3 his pay had become larger than that of any ,professor of ,mathematics up to that time2 and1 as you know1 immediately after his invention of the telescope the ,venetian ,senate1 in a fit of enthusiasm1 had doubled it and secured it to him for life wherever he was4 ,to throw up his chair and leave the place the very next year scarcely seems a strictly honourable procedure4 ,it was legal enough no doubt1 and it is easy for small men to criticize a great one1 but nevertheless ,i think we must admit that it is a step such as a man with a keen sense of honour would hardly have taken4 ,one quite feels and sympathizes with the temptation4 ,not emolument1 but leisure2 freedom from harassing engagements and constant teaching1 and liberty to prosecute his studies day and night without interference3 this was the golden prospect before him4 ,he yielded1 but one cannot help wishing he had not4 ,as it turned out it was a false step--the first false step of his public career4 ,when made it was irretrievable1 and it led to great misery4 ,at first it seemed brilliant enough4 ,the great philosopher of the ,tuscan ,court was courted and flattered by princes and nobles1 he enjoyed a world-wide reputation1 lived as luxuriously as he cared for1 had his time all to himself1 and lectured but very seldom1 on great occasions or to a few crowned heads4 ,his position was in fact analogous to that of ,tycho ,brah in his island of ,huen4 ,misfortune overtook both4 ,in ,tycho's case it arose mainly from the death of his patron4 ,in ,galileo's it was due to a more insidious cause1 to understand which cause aright we must remember the political divisions of ,italy at that date4 ,tuscany was a ,papal ,state1 and thought there was by no means free4 ,venice was a free republic1 and was even hostile to the ,papacy4 ,in #afjf the ,pope had placed it under an interdict4 ,in reply it had ejected every ,jesuit4 ,out of this atmosphere of comparative enlightenment and freedom into that hotbed of medivalism and superstition went ,galileo with his eyes open4 ,keen was the regret of his ,paduan and ,venetian friends2 bitter were their remonstrances and exhortations4 ,but he was determined to go1 and1 not without turning some of his old friends into enemies1 he went4 ,seldom has such a man made so great a mistake3 never1 ,i suppose1 has one been so cruelly punished for it4 ,illustration3 ,,fig4 #ea4--,map of ,italy4 ,we must remember1 however1 that ,galileo1 though by no means a saint1 was yet a really religious man1 a devout ,catholic and thorough adherent of the ,church1 so that he would have no dislike to place himself under her sway4 ,moreover1 he had been born a ,tuscan1 his family had lived at ,florence or ,pisa1 and it felt like going home4 ,his theological attitude is worthy of notice1 for he was not in the least a sceptic4 ,he quite acquiesces in the authority of the ,bible1 especially in all matters concerning faith and conduct2 as to its statements in scientific matters1 he argues that we are so liable to misinterpret their meaning that it is really easier to examine ,nature for truth in scientific matters1 and that when direct observation and ,scripture seem to clash1 it is because of our fallacious interpretation of one or both of them4 ,he is1 in fact1 what one now calls a reconciler4 ,it is curious to find such a man prosecuted for heresy1 when to-day his opinions are those of the orthodox among the orthodox4 ,but so it ever is1 and the heresy of one generation becomes the commonplace of the next4 ,he accepts ,joshua's miracle1 for instance1 not as a striking poem1 but as a literal fact2 and he points out how much more simply it could be done on the ,copernican system by stopping the earth's rotation for a short time1 than by stopping the sun and moon and all the host of heaven as on the old ,ptolemaic system1 or again by stopping only the sun and not any of the other bodies1 and so throwing astronomy all wrong4 ,this reads to us like satire1 but no doubt it was his genuine opinion4 ,these ,scriptural reconciliations of his1 however1 angered the religious authorities still more4 ,they said it was bad enough for this heretic to try and upset old scientific beliefs1 and to spoil the face of ,nature with his infidel discoveries1 but at least he might leave the ,bible alone2 and they addressed an indignant remonstrance to ,rome1 to protect it from the hands of ignorant laymen4 ,thus1 wherever he turned he encountered hostility4 ,of course he had many friends--some of them powerful like ,cosmo1 all of them faithful and sincere4 ,but against the power of ,rome what could they do8 ,cosmo dared no more than remonstrate1 and ultimately his successor had to refrain from even this1 so enchained and bound was the spirit of the rulers of those days2 and so when his day of tribulation came he stood alone and helpless in the midst of his enemies4 ,you may wonder1 perhaps1 why this man should excite so much more hostility than many another man who was suffered to believe and teach much the same doctrines unmolested4 ,but no other man had made such brilliant and exciting discoveries4 ,no man stood so prominently forward in the eyes of all ,christendom as the champion of the new doctrines4 ,no other man stated them so clearly and forcibly1 nor drove them home with such brilliant and telling illustrations4 ,and again1 there was the memory of his early conflict with the ,aristotelians at ,pisa1 of his scornful and successful refutation of their absurdities4 ,all this made him specially obnoxious to the ,aristotelian ,jesuits in their double capacity both of priests and of philosophers1 and they singled him out for relentless official persecution4 ,not yet1 however1 is he much troubled by them4 ,the chief men at ,rome have not yet moved4 ,messages1 however1 keep going up from ,tuscany to ,rome respecting the teachings of this man1 and of the harm he is doing by his pertinacious preaching of the ,copernican doctrine that the earth moves4 ,at length1 in #afae1 ,pope ,paul ,v4 wrote requesting him to come to ,rome to explain his views4 ,he went1 was well received1 made a special friend of ,cardinal ,barberino--an accomplished man in high position1 who became in fact the next ,pope4 ,galileo showed cardinals and others his telescope1 and to as many as would look through it he showed ,jupiter's satellites and his other discoveries4 ,he had a most successful visit4 ,he talked1 he harangued1 he held forth in the midst of fifteen or twenty disputants at once1 confounding his opponents and putting them to shame4 ,his method was to let the opposite arguments be stated as fully and completely as possible1 himself aiding1 and often adducing the most forcible and plausible arguments against his own views2 and then1 all having been well stated1 he would proceed to utterly undermine and demolish the whole fabric1 and bring out the truth in such a way as to convince all honest minds4 ,it was this habit that made him such a formidable antagonist4 ,he never shrank from meeting an opposing argument1 never sought to ignore it1 or cloak it in a cloud of words4 ,every hostile argument he seemed to delight in1 as a foe to be crushed1 and the better and stronger they sounded the more he liked them4 ,he knew many of them well1 he invented a number more1 and had he chosen could have out-argued the stoutest ,aristotelian on his own grounds4 ,thus did he lead his adversaries on1 almost like ,socrates1 only to ultimately overwhelm them in a more hopeless rout4 ,all this in ,rome too1 in the heart of the ,catholic world4 ,had he been worldly-wise1 he would certainly have kept silent and unobtrusive till he had leave to go away again4 ,but he felt like an apostle of the new doctrines1 whose mission it was to proclaim them even in this centre of the world and of the ,church4 ,well1 he had an audience with the ,pope--a chat an hour long--and the two parted good friends1 mutually pleased with each other4 ,he writes that he is all right now1 and might return home when he liked4 ,but the question began to be agitated whether the whole system of ,copernicus ought not to be condemned as impious and heretical4 ,this view was persistently urged upon the ,pope and ,college of ,cardinals1 and it was soon to be decided upon4 ,had ,galileo been unfaithful to the ,church he could have left them to stultify themselves in any way they thought proper1 and himself have gone2 but he felt supremely interested in the result1 and he stayed4 ,he writes3-- ,so far as concerns the clearing of my own character1 ,i might return home immediately2 but although this new question regards me no more than all those who for the last eighty years have supported those opinions both in public and private1 yet1 as perhaps ,i may be of some assistance in that part of the discussion which depends on the knowledge of truths ascertained by means of the sciences which ,i profess1 ,i1 as a zealous and ,catholic ,christian1 neither can nor ought to withhold that assistance which my knowledge affords1 and this business keeps me sufficiently employed4 ,it is possible that his stay was the worst thing for the cause he had at heart4 ,anyhow1 the result was that the system was condemned1 and both the book of ,copernicus and the epitome of it by ,kepler were placed on the forbidden list1#aa and ,galileo himself was formally ordered never to teach or to believe the motion of the earth4 ,he quitted ,rome in disgust1 which before long broke out in satire4 ,the only way in which he could safely speak of these views now was as if they were hypothetical and uncertain1 and so we find him writing to the ,archduke ,leopold1 with a presentation copy of his book on the tides1 the following3-- ,this theory occurred to me when in ,rome whilst the theologians were debating on the prohibition of ,copernicus's book1 and of the opinion maintained in it of the motion of the earth1 which ,i at that time believed3 until it pleased those gentlemen to suspend the book1 and declare the opinion false and repugnant to the ,holy ,scriptures4 ,now1 as ,i know how well it becomes me to obey and believe the decisions of my superiors1 which proceed out of more knowledge than the weakness of my intellect can attain to1 this theory which ,i send you1 which is founded on the motion of the earth1 ,i now look upon as a fiction and a dream1 and beg your highness to receive it as such4 ,but as poets often learn to prize the creations of their fancy1 so in like manner do ,i set some value on this absurdity of mine4 ,it is true that when ,i sketched this little work ,i did hope that ,copernicus would not1 after eighty years1 be convicted of error2 and ,i had intended to develop and amplify it further1 but a voice from heaven suddenly awakened me1 and at once annihilated all my confused and entangled fancies4 ,this sarcasm1 if it had been in print1 would probably have been dangerous4 ,it was safe in a private letter1 but it shows us his real feelings4 ,however1 he was left comparatively quiet for a time4 ,he was getting an old man now1 and passed the time studiously enough1 partly at his house in ,florence1 partly at his villa in ,arcetri1 a mile or so out of the town4 ,here was a convent1 and in it his two daughters were nuns4 ,one of them1 who passed under the name of ,sister ,maria ,celeste1 seems to have been a woman of considerable capacity--certainly she was of a most affectionate disposition--and loved and honoured her father in the most dutiful way4 ,this was a quiet period of his life1 spoiled only by occasional fits of illness and severe rheumatic pains1 to which the old man was always liable4 ,many little circumstances are known of this peaceful time4 ,for instance1 the convent clock won't go1 and ,galileo mends it for them4 ,he is always doing little things for them1 and sending presents to the ,lady ,superior and his two daughters4 ,he was occupied now with problems in hydrostatics1 and on other matters unconnected with astronomy3 a large piece of work which ,i must pass over4 ,most interesting and acute it is1 however4 ,in #afbc1 when the old ,pope died1 there was elected to the ,papal throne1 as ,urban ,,viii41 ,cardinal ,barberino1 a man of very considerable enlightenment1 and a personal friend of ,galileo's1 so that both he and his daughters rejoice greatly1 and hope that things will come all right1 and the forbidding edict be withdrawn4 ,the year after this election he manages to make another journey to ,rome to compliment his friend on his elevation to the ,pontifical chair4 ,he had many talks with ,urban1 and made himself very agreeable4 ,urban wrote to the ,grand ,duke ,ferdinand1 son of ,cosmo3-- ,for ,we find in him not only literary distinction but also love of piety1 and he is strong in those qualities by which ,pontifical good will is easily obtainable4 ,and now1 when he has been brought to this city to congratulate ,us on ,our elevation1 ,we have very lovingly embraced him2 nor can ,we suffer him to return to the country whither your liberality recalls him without an ample provision of ,pontifical love4 ,and that you may know how dear he is to ,us1 ,we have willed to give him this honourable testimonial of virtue and piety4 ,and ,we further signify that every benefit which you shall confer upon him1 imitating or even surpassing your father's liberality1 will conduce to ,our gratification4 ,encouraged1 doubtless1 by these marks of approbation1 and reposing too much confidence in the individual good will of the ,pope1 without heeding the crowd of half-declared enemies who were seeking to undermine his reputation1 he set about1 after his return to ,florence1 his greatest literary and most popular work1 ,dialogues on the ,ptolemaic and ,copernican ,systems4 ,this purports to be a series of four conversations between three characters3 ,salviati1 a ,copernican philosopher2 ,sagredo1 a wit and scholar1 not specially learned1 but keen and critical1 and who lightens the talk with chaff2 ,simplicio1 an ,aristotelian philosopher1 who propounds the stock absurdities which served instead of arguments to the majority of men4 ,the conversations are something between ,plato's ,dialogues and ,sir ,arthur ,helps's ,friends in ,council4 ,the whole is conducted with great good temper and fairness2 and1 discreetly enough1 no definite conclusion is arrived at1 the whole being left in abeyance as if for a fifth and decisive dialogue1 which1 however1 was never written1 and perhaps was only intended in case the reception was favourable4 ,the preface also sets forth that the object of the writer is to show that the ,roman edict forbidding the ,copernican doctrine was not issued in ignorance of the facts of the case1 as had been maliciously reported1 and that he wishes to show how well and clearly it was all known beforehand4 ,so he says the dialogue on the ,copernican side takes up the question purely as a mathematical hypothesis or speculative figment1 and gives it every artificial advantage of which the theory is capable4 ,this piece of caution was insufficient to blind the eyes of the ,cardinals2 for in it the arguments in favour of the earth's motion are so cogent and unanswerable1 and are so popularly stated1 as to do more in a few years to undermine the old system than all that he had written and spoken before4 ,he could not get it printed for two years after he had written it1 and then only got consent through a piece of carelessness or laziness on the part of the ecclesiastical censor through whose hands the manuscript passed--for which he was afterwards dismissed4 ,however1 it did appear1 and was eagerly read2 the more1 perhaps1 as the ,church at once sought to suppress it4 ,the ,aristotelians were furious1 and represented to the ,pope that he himself was the character intended by ,simplicio1 the philosopher whose opinions get alternately refuted and ridiculed by the other two1 till he is reduced to an abject state of impotence4 ,the idea that ,galileo had thus cast ridicule upon his friend and patron is no doubt a gratuitous and insulting libel3 there is no telling whether or not ,urban believed it1 but certainly his countenance changed to ,galileo henceforward1 and whether overruled by his ,cardinals1 or actuated by some other motive1 his favour was completely withdrawn4 ,the infirm old man was instantly summoned to ,rome4 ,his friends pleaded his age--he was now seventy--his ill-health1 the time of year1 the state of the roads1 the quarantine existing on account of the plague4 ,it was all of no avail1 to ,rome he must go1 and on the #adth of ,february he arrived4 ,illustration3 ,,fig4 #eb4--,portrait of ,galileo4 ,his daughter at ,arcetri was in despair2 and anxiety and fastings and penances self-inflicted on his account1 dangerously reduced her health4 ,at ,rome he was not imprisoned1 but he was told to keep indoors1 and show himself as little as possible4 ,he was allowed1 however1 to stay at the house of the ,tuscan ,ambassador instead of in gaol4 ,by ,april he was removed to the chambers of the ,inquisition1 and examined several times4 ,here1 however1 the anxiety was too much1 and his health began to give way seriously2 so1 before long1 he was allowed to return to the ,ambassador's house2 and1 after application had been made1 was allowed to drive in the public garden in a half-closed carriage4 ,thus in every way the ,inquisition dealt with him as leniently as they could4 ,he was now their prisoner1 and they might have cast him into their dungeons1 as many another had been cast4 ,by whatever they were influenced--perhaps the ,pope's old friendship1 perhaps his advanced age and infirmities--he was not so cruelly used4 ,still1 they had their rules2 he must be made to recant and abjure his heresy2 and1 if necessary1 torture must be applied4 ,this he knew well enough1 and his daughter knew it1 and her distress may be imagined4 ,moreover1 it is not as if they had really been heretics1 as if they hated or despised the ,church of ,rome4 ,on the contrary1 they loved and honoured the ,church4 ,they were sincere and devout worshippers1 and only on a few scientific matters did ,galileo presume to differ from his ecclesiastical superiors3 his disagreement with them occasioned him real sorrow2 and his dearest hope was that they could be brought to his way of thinking and embrace the truth4 ,every time he was sent for by the ,inquisition he was in danger of torture unless he recanted4 ,all his friends urged him repeatedly to submit4 ,they said resistance was hopeless and fatal4 ,within the memory of men still young1 ,giordano ,bruno had been burnt alive for a similar heresy4 ,this had happened while ,galileo was at ,padua4 ,venice was full of it4 ,and since that1 only eight years ago indeed1 ,antonio de ,dominis1 ,archbishop of ,salpetria1 had been sentenced to the same fate3 to be handed over to the secular arm to be dealt with as mercifully as possible without the shedding of blood4 ,so ran the hideous formula condemning a man to the stake4 ,after his sentence1 this unfortunate man died in the dungeons in which he had been incarcerated six years--died what is called a natural death2 but the sentence was carried out1 notwithstanding1 on his lifeless body and his writings4 ,his writings for which he had been willing to die6 ,these were the tender mercies of the ,inquisition2 and this was the kind of meaning lurking behind many of their well-sounding and merciful phrases4 ,for instance1 what they call rigorous examination1 we call torture4 ,let us1 however1 remember in our horror at this mode of compelling a prisoner to say anything they wished1 that they were a legally constituted tribunal2 that they acted with well established rules1 and not in passion2 and that torture was a recognized mode of extracting evidence1 not only in ecclesiastical but in civil courts1 at that date4 ,all this1 however1 was but poor solace to the pitiable old philosopher1 thus ruthlessly haled up and down1 questioned and threatened1 threatened and questioned1 receiving agonizing letters from his daughter week by week1 and trying to keep up a little spirit to reply as happily and hopefully as he could4 ,this condition of things could not go on4 ,from ,february to ,june the suspense lasted4 ,on the #bjth of ,june he was summoned again1 and told he would be wanted all next day for a rigorous examination4 ,early in the morning of the #bast he repaired thither1 and the doors were shut4 ,out of those chambers of horror he did not reappear till the #bdth4 ,what went on all those three days no one knows4 ,he himself was bound to secrecy4 ,no outsider was present4 ,the records of the ,inquisition are jealously guarded4 ,that he was technically tortured is certain2 that he actually underwent the torment of the rack is doubtful4 ,much learning has been expended upon the question1 especially in ,germany4 ,several eminent scholars have held the fact of actual torture to be indisputable 7geometrically certain1 one says71 and they confirm it by the hernia from which he afterwards suffered1 this being a well-known and frequent consequence4 ,other equally learned commentators1 however1 deny that the last stage was reached4 ,for there are five stages all laid down in the rules of the ,inquisition1 and steadily adhered to in a rigorous examination1 at each stage an opportunity being given for recantation1 every utterance1 groan1 or sigh being strictly recorded4 ,the recantation so given has to be confirmed a day or two later1 under pain of a precisely similar ordeal4 ,the five stages are3--#ast4 ,the official threat in the court4 #bnd4 ,the taking to the door of the torture chamber and renewing the official threat4 #crd4 ,the taking inside and showing the instruments4 #dth4 ,undressing and binding upon the rack4 #eth4 ,territio realis4 ,through how many of these ghastly acts ,galileo passed ,i do not know4 ,i hope and believe not the last4 ,there are those who lament that he did not hold out1 and accept the crown of martyrdom thus offered to him4 ,had he done so we know his fate--a few years' languishing in the dungeons1 and then the flames4 ,whatever he ought to have done1 he did not hold out--he gave way4 ,at one stage or another of the dread ordeal he said3 ,i am in your hands4 ,i will say whatever you wish4 ,then was he removed to a cell while his special form of perjury was drawn up4 ,the next day1 clothed as a penitent1 the venerable old man was taken to the ,convent of ,minerva1 where the ,cardinals and prelates were assembled for the purpose of passing judgment upon him4 ,the text of the judgment ,i have here1 but it is too long to read4 ,it sentences him--#ast4 ,to the abjuration4 #bnd4 ,to formal imprisonment for life4 #crd4 ,to recite the seven penitential psalms every week4 ,ten ,cardinals were present2 but1 to their honour be it said1 three refused to sign2 and this blasphemous record of intolerance and bigoted folly goes down the ages with the names of seven ,cardinals immortalized upon it4 ,this having been read1 he next had to read word for word the abjuration which had been drawn up for him1 and then sign it4 ,,the ,,abjuration ,,of ,,galileo4 ,i1 ,galileo ,galilei1 son of the late ,vincenzo ,galilei1 of ,florence1 aged seventy years1 being brought personally to judgment1 and kneeling before you ,most ,eminent and ,most ,reverend ,lords ,cardinals1 ,general ,inquisitors of the universal ,christian republic against heretical depravity1 having before my eyes the ,holy ,gospels1 which ,i touch with my own hands1 swear that ,i have always believed1 and now believe1 and with the help of ,god will in future believe1 every article which the ,holy ,catholic and ,apostolic ,church of ,rome holds1 teaches1 and preaches4 ,but because ,i have been enjoined by this ,holy ,office altogether to abandon the false opinion which maintains that the sun is the centre and immovable1 and forbidden to hold1 defend1 or teach the said false doctrine in any manner1 and after it hath been signified to me that the said doctrine is repugnant with the ,holy ,scripture1 ,i have written and printed a book1 in which ,i treat of the same doctrine now condemned1 and adduce reasons with great force in support of the same1 without giving any solution1 and therefore have been judged grievously suspected of heresy2 that is to say1 that ,i held and believed that the sun is the centre of the universe and is immovable1 and that the earth is not the centre and is movable2 willing1 therefore1 to remove from the minds of your ,eminences1 and of every ,catholic ,christian1 this vehement suspicion rightfully entertained towards me1 with a sincere heart and unfeigned faith1 ,i abjure1 curse1 and detest the said errors and heresies1 and generally every other error and sect contrary to ,holy ,church2 and ,i swear that ,i will never more in future say or assert anything verbally1 or in writing1 which may give rise to a similar suspicion of me2 but if ,i shall know any heretic1 or any one suspected of heresy1 that ,i will denounce him to this ,holy ,office1 or to the ,inquisitor or ,ordinary of the place where ,i may be2 ,i swear1 moreover1 and promise1 that ,i will fulfil and observe fully1 all the penances which have been or shall be laid on me by this ,holy ,office4 ,but if it shall happen that ,i violate any of my said promises1 oaths1 and protestations 7which ,god avert671 ,i subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons1 and other general and particular constitutions1 against delinquents of this description4 ,so may ,god help me1 and his ,holy ,gospels which ,i touch with my own hands4 ,i1 the above-named ,galileo ,galilei1 have abjured1 sworn1 promised1 and bound myself as above1 and in witness thereof with my own hand have subscribed this present writing of my abjuration1 which ,i have recited word for word4 ,at ,rome1 in the ,convent of ,minerva1 #bbnd ,june1 #afcc4 ,i1 ,galileo ,galilei1 have abjured as above with my own hand4 ,those who believe the story about his muttering to a friend1 as he rose from his knees1 e pur si muove1 do not realize the scene4 #ast4 ,there was no friend in the place4 #bnd4 ,it would have been fatally dangerous to mutter anything before such an assemblage4 #crd4 ,he was by this time an utterly broken and disgraced old man2 wishful1 of all things1 to get away and hide himself and his miseries from the public gaze2 probably with his senses deadened and stupefied by the mental sufferings he had undergone1 and no longer able to think or care about anything--except perhaps his daughter1--certainly not about any motion of this wretched earth4 ,far and wide the news of the recantation spread4 ,copies of the abjuration were immediately sent to all ,universities1 with instructions to the professors to read it publicly4 ,at ,florence1 his home1 it was read out in the ,cathedral church1 all his friends and adherents being specially summoned to hear it4 ,for a short time more he was imprisoned in ,rome2 but at length was permitted to depart1 never more of his own will to return4 ,he was allowed to go to ,siena4 ,here his daughter wrote consolingly1 rejoicing at his escape1 and saying how joyfully she already recited the penitential psalms for him1 and so relieved him of that part of his sentence4 ,but the poor girl was herself1 by this time1 ill--thoroughly worn out with anxiety and terror2 she lay1 in fact1 on what proved to be her death-bed4 ,her one wish was to see her dearest lord and father1 so she calls him1 once more4 ,the wish was granted4 ,his prison was changed1 by orders from ,rome1 from ,siena to ,arcetri1 and once more father and daughter embraced4 ,six days after this she died4 ,the broken-hearted old man now asks for permission to go to live in ,florence1 but is met with the stern answer that he is to stay at ,arcetri1 is not to go out of the house1 is not to receive visitors1 and that if he asks for more favours1 or transgresses the commands laid upon him1 he is liable to be haled back to ,rome and cast into a dungeon4 ,these harsh measures were dictated1 not by cruelty1 but by the fear of his still spreading heresy by conversation1 and so he was to be kept isolated4 ,idle1 however1 he was not and could not be4 ,he often complains that his head is too busy for his body4 ,in the enforced solitude of ,arcetri he was composing those dialogues on motion which are now reckoned his greatest and most solid achievement4 ,in these the true laws of motion are set forth for the first time 7see page #afg74 ,one more astronomical discovery also he was to make--that of the moon's libration4 ,and then there came one more crushing blow4 ,his eyes became inflamed and painful--the sight of one of them failed1 the other soon went2 he became totally blind4 ,but this1 being a heaven-sent infliction1 he could bear with resignation1 though it must have been keenly painful to a solitary man of his activity4 ,alas6 says he1 in one of his letters1 your dear friend and servant is totally blind4 ,henceforth this heaven1 this universe1 which by wonderful observations ,i had enlarged a hundred and a thousand times beyond the conception of former ages1 is shrunk for me into the narrow space which ,i myself fill in it4 ,so it pleases ,god2 it shall therefore please me also4 ,he was now allowed an amanuensis1 and the help of his pupils ,torricelli1 ,castelli1 and ,viviani1 all devotedly attached to him1 and ,torricelli very famous after him4 ,visitors also were permitted1 after approval by a ,jesuit supervisor2 and under these circumstances many visited him1 among them a man as immortal as himself--,john ,milton1 then only twenty-nine1 travelling in ,italy4 ,surely a pathetic incident1 this meeting of these two great men--the one already blind1 the other destined to become so4 ,no wonder that1 as in his old age he dictated his masterpiece1 the thoughts of the ,english poet should run on the blind sage of ,tuscany1 and the reminiscence of their conversation should lend colour to the poem4 ,well1 it were tedious to follow the petty annoyances and troubles to which ,galileo was still subject--how his own son was set to see that no unauthorized procedure took place1 and that no heretic visitors were admitted2 how it was impossible to get his new book printed till long afterwards2 and how one form of illness after another took possession of him4 ,the merciful end came at last1 and at the age of seventy-eight he was released from the ,inquisition4 ,they wanted to deny him burial--they did deny him a monument2 they threatened to cart his bones away from ,florence if his friends attempted one4 ,and so they hoped that he and his work might be forgotten4 ,poor schemers6 ,before the year was out an infant was born in ,lincolnshire1 whose destiny it was to round and complete and carry forward the work of their victim1 so that1 until man shall cease from the planet1 neither the work nor its author shall have need of a monument4 99 99 99 99 99 ,here might ,i end1 were it not that the same kind of struggle as went on fiercely in the seventeenth century is still smouldering even now4 ,not in astronomy indeed1 as then2 nor yet in geology1 as some fifty years ago2 but in biology mainly--perhaps in other subjects4 ,i myself have heard ,charles ,darwin spoken of as an atheist and an infidel1 the theory of evolution assailed as unscriptural1 and the doctrine of the ascent of man from a lower state of being1 as opposed to the fall of man from some higher condition1 denied as impious and un-,christian4 ,men will not learn by the past2 still they brandish their feeble weapons against the truths of ,nature1 as if assertions one way or another could alter fact1 or make the thing other than it really is4 ,as ,galileo said before his spirit was broken1 ,in these and other positions certainly no man doubts but ,his ,holiness the ,pope hath always an absolute power of admitting or condemning them2 but it is not in the power of any creature to make them to be true or false1 or otherwise than of their own nature and in fact they are4 ,i know nothing of the views of any here present2 but ,i have met educated persons who1 while they might laugh at the men who refused to look through a telescope lest they should learn something they did not like1 yet also themselves commit the very same folly4 ,i have met persons who utterly refuse to listen to any view concerning the origin of man other than that of a perfect primval pair in a garden1 and ,i am constrained to say this much3 ,take heed lest some prophet1 after having excited your indignation at the follies and bigotry of a bygone generation1 does not turn upon you with the sentence1 ,thou art the man4 ,,summary ,,of ,,facts ,,for ,,lecture ,,vi ,science before ,newton ,dr4 ,gilbert1 of ,colchester1 ,physician to ,queen ,elizabeth1 was an excellent experimenter1 and made many discoveries in magnetism and electricity4 ,he was contemporary with ,tycho ,brah1 and lived from #aedj to #afjc4 ,francis ,bacon1 ,lord ,verulam1 #aefa-afbf1 though a brilliant writer1 is not specially important as regards science4 ,he was not a scientific man1 and his rules for making discoveries1 or methods of induction1 have never been consciously1 nor often indeed unconsciously1 followed by discoverers4 ,they are not in fact practical rules at all1 though they were so intended4 ,his really strong doctrines are that phenomena must be studied direct1 and that variations in the ordinary course of nature must be induced by aid of experiment2 but he lacked the scientific instinct for pursuing these great truths into detail and special cases4 ,he sneered at the work and methods of both ,gilbert and ,galileo1 and rejected the ,copernican theory as absurd4 ,his literary gifts have conferred on him an artificially high scientific reputation1 especially in ,england2 at the same time his writings undoubtedly helped to make popular the idea of there being new methods for investigating ,nature1 and1 by insisting on the necessity for freedom from preconceived ideas and opinions1 they did much to release men from the bondage of ,aristotelian authority and scholastic tradition4 ,the greatest name between ,galileo and ,newton is that of ,descartes4 ,ren ,descartes was born at ,la ,haye in ,touraine1 #aeif1 and died at ,stockholm in #afej4 ,he did important work in mathematics1 physics1 anatomy1 and philosophy4 ,was greatest as a philosopher and mathematician4 ,at the age of twenty-one he served as a volunteer under ,prince ,maurice of ,nassau1 but spent most of his later life in ,holland4 ,his famous ,discourse on ,method appeared at ,leyden in #afcg1 and his ,principia at ,amsterdam in #afdd2 great pains being taken to avoid the condemnation of the ,church4 ,descartes's main scientific achievement was the application of algebra to geometry2 his most famous speculation was the theory of vortices1 invented to account for the motion of planets4 ,he also made many discoveries in optics and physiology4 ,his best known immediate pupils were the ,princess ,elizabeth of ,bohemia1 and ,christina1 ,queen of ,sweden4 ,he founded a distinct school of thought 7the ,cartesian71 and was the precursor of the modern mathematical method of investigating science1 just as ,galileo and ,gilbert were the originators of the modern experimental method4 ,,lecture ,,vi ,,descartes ,,and ,,his ,,theory ,,of ,,vortices ,after the dramatic life we have been considering in the last two lectures1 it is well to have a breathing space1 to look round on what has been accomplished1 and to review the state of scientific thought1 before proceeding to the next great era4 ,for we are still in the early morning of scientific discovery3 the dawn of the modern period1 faintly heralded by ,copernicus1 brought nearer by the work of ,tycho and ,kepler1 and introduced by the discoveries of ,galileo--the dawn has occurred1 but the sun is not yet visible4 ,it is hidden by the clouds and mists of the long night of ignorance and prejudice4 ,the light is sufficient1 indeed1 to render these earth-born vapours more visible3 it is not sufficient to dispel them4 ,a generation of slow and doubtful progress must pass1 before the first ray of sunlight can break through the eastern clouds and the full orb of day itself appear4 ,it is this period of hesitating progress and slow leavening of men's ideas that we have to pass through in this week's lecture4 ,it always happens thus3 the assimilation of great and new ideas is always a slow and gradual process3 there is no haste either here or in any other department of ,nature4 ,die ,zeit ist unendlich lang4 ,steadily the forces work1 sometimes seeming to accomplish nothing2 sometimes even the motion appears retrograde2 but in the long run the destined end is reached1 and the course1 whether of a planet or of men's thoughts about the universe1 is permanently altered4 ,then1 the controversy was about the earth's place in the universe2 now1 if there be any controversy of the same kind1 it is about man's place in the universe2 but the process is the same3 a startling statement by a great genius or prophet1 general disbelief1 and1 it may be1 an attitude of hostility1 gradual acceptance by a few1 slow spreading among the many1 ending in universal acceptance and faith often as unquestioning and unreasoning as the old state of unfaith had been4 ,now the process is comparatively speedy3 twenty years accomplishes a great deal3 then it was tediously slow1 and a century seemed to accomplish very little4 ,periodical literature may be responsible for some waste of time1 but it certainly assists the rapid spread of ideas4 ,the rate with which ideas are assimilated by the general public cannot even now be considered excessive1 but how much faster it is than it was a few centuries ago may be illustrated by the attitude of the public to ,darwinism now1 twenty-five years after ,the ,origin of ,species1 as compared with their attitude to the ,copernican system a century after ,de ,revolutionibus4 ,by the way1 it is1 ,i know1 presumptuous for me to have an opinion1 but ,i cannot hear ,darwin compared to or mentioned along with ,newton without a shudder4 ,the stage in which he found biology seems to me far more comparable with the ,ptolemaic era in astronomy1 and he himself to be quite fairly comparable to ,copernicus4 ,let us proceed to summarize the stage at which the human race had arrived at the epoch with which we are now dealing4 ,the ,copernican view of the solar system had been stated1 restated1 fought1 and insisted on2 a chain of brilliant telescopic discoveries had made it popular and accessible to all men of any intelligence3 henceforth it must be left to slowly percolate and sink into the minds of the people4 ,for the nations were waking up now1 and were accessible to new ideas4 ,england especially was1 in some sort1 at the zenith of its glory2 or1 if not at the zenith1 was in that full flush of youth and expectation and hope which is stronger and more prolific of great deeds and thoughts than a maturer period4 ,a common cause against a common and detested enemy had roused in the hearts of ,englishmen a passion of enthusiasm and patriotism2 so that the mean elements of trade1 their cheating yard-wands1 were forgotten for a time2 the ,armada was defeated1 and the nation's true and conscious adult life began4 ,commerce was now no mere struggle for profit and hard bargains2 it was full of the spirit of adventure and discovery2 a new world had been opened up2 who could tell what more remained unexplored8 ,men awoke to the splendour of their inheritance1 and away sailed ,drake and ,frobisher and ,raleigh into the lands of the ,west4 ,for literature1 you know what a time it was4 ,the author of ,hamlet and ,othello was alive3 it is needless to say more4 ,and what about science8 ,the atmosphere of science is a more quiet and less stirring one2 it thrives best when the fever of excitement is allayed2 it is necessarily a later growth than literature4 ,already1 however1 our second great man of science was at work in a quiet country town--second in point of time1 ,i mean1 ,roger ,bacon being the first4 ,dr4 ,gilbert1 of ,colchester1 was the second in point of time1 and the age was ripening for the time when ,england was to be honoured with such a galaxy of scientific luminaries--,hooke and ,boyle and ,newton--as the world had not yet known4 ,yes1 the nations were awake4 ,in all directions1 as ,draper says1 ,nature was investigated3 in all directions new methods of examination were yielding unexpected and beautiful results4 ,on the ruins of its ivy-grown cathedrals ,ecclesiasticism or ,scholasticism1 surprised and blinded by the breaking day1 sat solemnly blinking at the light and life about it1 absorbed in the recollection of the night that had passed1 dreaming of new phantoms and delusions in its wished-for return1 and vindictively striking its talons at any derisive assailant who incautiously approached too near4 ,of the work of ,gilbert there is much to say2 so there is also of ,roger ,bacon1 whose life ,i am by no means sure ,i did right in omitting4 ,but neither of them had much to do with astronomy1 and since it is in astronomy that the most startling progress was during these centuries being made1 ,i have judged it wiser to adhere mainly to the pioneers in this particular department4 ,only for this reason do ,i pass ,gilbert with but slight mention4 ,he knew of the ,copernican theory and thoroughly accepted it 7it is convenient to speak of it as the ,copernican theory1 though you know that it had been considerably improved in detail since the first crude statement by ,copernicus71 but he made in it no changes4 ,he was a cultivated scientific man1 and an acute experimental philosopher2 his main work lay in the domain of magnetism and electricity4 ,the phenomena connected with the mariner's compass had been studied somewhat by ,roger ,bacon2 and they were now examined still more thoroughly by ,gilbert1 whose treatise ,de ,magnete1 marks the beginning of the science of magnetism4 ,as an appendix to that work he studied the phenomenon of amber1 which had been mentioned by ,thales4 ,he resuscitated this little fact after its burial of #b1bjj years1 and greatly extended it4 ,he it was who invented the name electricity--,i wish it had been a shorter one4 ,mankind invents names much better than do philosophers4 ,what can be better than heat1 light1 sound8 ,how favourably they compare with electricity1 magnetism1 galvanism1 electro-magnetism1 and magneto-electricity6 ,the only long-established monosyllabic name ,i know invented by a philosopher is gas--an excellent attempt1 which ought to be imitated4#ab ,of ,lord ,bacon1 who flourished about the same time 7a little later71 it is necessary to say something1 because many persons are under the impression that to him and his ,novum ,organon the reawakening of the world1 and the overthrow of ,aristotelian tradition1 are mainly due4 ,his influence1 however1 has been exaggerated4 ,i am not going to enter into a discussion of the ,novum ,organon1 and the mechanical methods which he propounded as certain to evolve truth if patiently pursued2 for this is what he thought he was doing--giving to the world an infallible recipe for discovering truth1 with which any ordinarily industrious man could make discoveries by means of collection and discrimination of instances4 ,you will take my statement for what it is worth1 but ,i assert this3 that many of the methods which ,bacon lays down are not those which the experience of mankind has found to be serviceable2 nor are they such as a scientific man would have thought of devising4 ,true it is that a real love and faculty for science are born in a man1 and that to the man of scientific capacity rules of procedure are unnecessary2 his own intuition is sufficient1 or he has mistaken his vocation1--but that is not my point4 ,it is not that ,bacon's methods are useless because the best men do not need them2 if they had been founded on a careful study of the methods actually employed1 though it might be unconsciously employed1 by scientific men--as the methods of induction1 stated long after by ,john ,stuart ,mill1 were founded--then1 no doubt1 their statement would have been a valuable service and a great thing to accomplish4 ,but they were not this4 ,they are the ideas of a brilliant man of letters1 writing in an age when scientific research was almost unknown1 about a subject in which he was an amateur4 ,i confess ,i do not see how he1 or ,john ,stuart ,mill1 or any one else1 writing in that age1 could have formulated the true rules of philosophizing2 because the materials and information were scarcely to hand4 ,science and its methods were only beginning to grow4 ,no doubt it was a brilliant attempt4 ,no doubt also there are many good and true points in the statement1 especially in his insistence on the attitude of free and open candour with which the investigation of ,nature should be approached4 ,no doubt there was much beauty in his allegories of the errors into which men were apt to fall--the idola of the market-place1 of the tribe1 of the theatre1 and of the den2 but all this is literature1 and on the solid progress of science may be said to have had little or no effect4 ,descartes's ,discourse on ,method was a much more solid production4 ,you will understand that ,i speak of ,bacon purely as a scientific man4 ,as a man of letters1 as a lawyer1 a man of the world1 and a statesman1 he is beyond any criticism of mine4 ,i speak only of the purely scientific aspect of the ,novum ,organon4 ,the ,essays and ,the ,advancement of ,learning are masterly productions2 and as a literary man he takes high rank4 ,the over-praise which1 in the ,british ,isles1 has been lavished upon his scientific importance is being followed abroad by what may be an unnecessary amount of detraction4 ,this is always the worst of setting up a man on too high a pinnacle2 some one has to undertake the ungrateful task of pulling him down again4 ,justus von ,liebig addressed himself to this task with some vigour in his ,reden und ,abhandlung 7,leipzig1 #ahgd71 where he quotes from ,bacon a number of suggestions for absurd experimentation4#ac ,the next paragraph ,i read1 not because ,i endorse it1 but because it is always well to hear both sides of a question4 ,you have probably been long accustomed to read over-estimates of ,bacon's importance1 and extravagant laudation of his writings as making an epoch in science2 hear what ,draper says on the opposite side3--#ad ,the more closely we examine the writings of ,lord ,bacon1 the more unworthy does he seem to have been of the great reputation which has been awarded to him4 ,the popular delusion to which he owes so much originated at a time when the history of science was unknown4 ,they who first brought him into notice knew nothing of the old school of ,alexandria4 ,this boasted founder of a new philosophy could not comprehend1 and would not accept1 the greatest of all scientific doctrines when it was plainly set before his eyes4 ,it has been represented that the invention of the true method of physical science was an amusement of ,bacon's hours of relaxation from the more laborious studies of law1 and duties of a ,court4 ,his chief admirers have been persons of a literary turn1 who have an idea that scientific discoveries are accomplished by a mechanico-mental operation4 ,bacon never produced any great practical result himself1 no great physicist has ever made any use of his method4 ,he has had the same to do with the development of modern science that the inventor of the orrery has had to do with the discovery of the mechanism of the world4 ,of all the important physical discoveries1 there is not one which shows that its author made it by the ,baconian instrument4 ,newton never seems to have been aware that he was under any obligation to ,bacon4 ,archimedes1 and the ,alexandrians1 and the ,arabians1 and ,leonardo da ,vinci did very well before he was born2 the discovery of ,america by ,columbus and the circumnavigation by ,magellan can hardly be attributed to him1 yet they were the consequences of a truly philosophical reasoning4 ,but the investigation of ,nature is an affair of genius1 not of rules4 ,no man can invent an organon for writing tragedies and epic poems4 ,bacon's system is1 in its own terms1 an idol of the theatre4 ,it would scarcely guide a man to a solution of the riddle of lia ,llia ,crispis1 or to that of the charade of ,sir ,hilary4 ,few scientific pretenders have made more mistakes than ,lord ,bacon4 ,he rejected the ,copernican system1 and spoke insolently of its great author2 he undertook to criticize adversely ,gilbert's treatise ,de ,magnete2 he was occupied in the condemnation of any investigation of final causes1 while ,harvey was deducing the circulation of the blood from ,aquapendente's discovery of the valves in the veins2 he was doubtful whether instruments were of any advantage1 while ,galileo was investigating the heavens with the telescope4 ,ignorant himself of every branch of mathematics1 he presumed that they were useless in science but a few years before ,newton achieved by their aid his immortal discoveries4 ,it is time that the sacred name of philosophy should be severed from its long connection with that of one who was a pretender in science1 a time-serving politician1 an insidious lawyer1 a corrupt judge1 a treacherous friend1 a bad man4 ,this seems to me a depreciation as excessive as are the eulogies commonly current4 ,the truth probably lies somewhere between the two extremes4 ,it is unfair to judge ,bacon's methods by thinking of physical science in its present stage4 ,to realise his position we must think of a subject still in its very early infancy1 one in which the advisability of applying experimental methods is still doubted2 one which has been studied by means of books and words and discussion of normal instances1 instead of by collection and observation of the unusual and irregular1 and by experimental production of variety4 ,if we think of a subject still in this infantile and almost pre-scientific stage1 ,bacon's words and formul are far from inapplicable2 they are1 within their limitations1 quite necessary and wholesome4 ,a subject in this stage1 strange to say1 exists1--psychology2 now hesitatingly beginning to assume its experimental weapons amid a stifling atmosphere of distrust and suspicion4 ,bacon's lack of the modern scientific instinct must be admitted1 but he rendered humanity a powerful service in directing it from books to nature herself1 and his genius is indubitable4 ,a judicious account of his life and work is given by ,prof4 ,adamson1 in the ,encyclopdia ,britannica1 and to this article ,i now refer you4 99 99 99 99 99 ,who1 then1 was the man of first magnitude filling up the gap in scientific history between the death of ,galileo and the maturity of ,newton8 ,unknown and mysterious are the laws regulating the appearance of genius4 ,we have passed in review a ,pole1 a ,dane1 a ,german1 and an ,italian1--the great man is now a ,frenchman1 ,ren ,descartes1 born in ,touraine1 on the #cast of ,march1 #aeif4 ,his mother died at his birth2 the father was of no importance1 save as the owner of some landed property4 ,the boy was reared luxuriously1 and inherited a fair fortune4 ,nearly all the men of first rank1 you notice1 were born well off4 ,genius born to poverty might1 indeed1 even then achieve name and fame--as we see in the case of ,kepler--but it was terribly handicapped4 ,handicapped it is still1 but far less than of old2 and we may hope it will become gradually still less so as enlightenment proceeds1 and the tremendous moment of great men to a nation is more clearly and actively perceived4 ,it is possible for genius1 when combined with strong character1 to overcome all obstacles1 and reach the highest eminence1 but the struggle must be severe2 and the absence of early training and refinement during the receptive years of youth must be a lifelong drawback4 ,descartes had none of these drawbacks2 life came easily to him1 and1 as a consequence perhaps1 he never seems to have taken it quite seriously4 ,great movements and stirring events were to him opportunities for the study of men and manners2 he was not the man to court persecution1 nor to show enthusiasm for a losing or struggling cause4 ,in this1 as in many other things1 he was imbued with a very modern spirit1 a cynical and sceptical spirit1 which1 to an outside and superficial observer like myself1 seems rather rife just now4 ,he was also imbued with a phase of scientific spirit which you sometimes still meet with1 though ,i believe it is passing away1 viz4 an uncultured absorption in his own pursuits1 and some feeling of contempt for classical and literary and sthetic studies4 ,in politics1 art1 and history he seems to have had no interest4 ,he was a spectator rather than an actor on the stage of the world2 and though he joined the army of that great military commander ,prince ,maurice of ,nassau1 he did it not as a man with a cause at heart worth fighting for1 but precisely in the spirit in which one of our own gilded youths would volunteer in a similar case1 as a good opportunity for frolic and for seeing life4 ,he soon tired of it and withdrew--at first to gay society in ,paris4 ,here he might naturally have sunk into the gutter with his companions1 but for a great mental shock which became the main epoch and turning-point of his life1 the crisis which diverted him from frivolity to seriousness4 ,it was a purely intellectual emotion1 not excited by anything in the visible or tangible world2 nor could it be called conversion in the common acceptation of that term4 ,he tells us that on the #ajth of ,november1 #afai1 at the age of twenty-four1 a brilliant idea flashed upon him--the first idea1 namely1 of his great and powerful mathematical method1 of which ,i will speak directly2 and in the flush of it he foresaw that just as geometers1 starting with a few simple and evident propositions or axioms1 ascend by a long and intricate ladder of reasoning to propositions more and more abstruse1 so it might be possible to ascend from a few data1 to all the secrets and facts of the universe1 by a process of mathematical reasoning4 ,comparing the mysteries of ,nature with the laws of mathematics1 he dared to hope that the secrets of both could be unlocked with the same key4 ,that night he lapsed gradually into a state of enthusiasm1 in which he saw three dreams or visions1 which he interpreted at the time1 even before waking1 to be revelations from the ,spirit of ,truth to direct his future course1 as well as to warn him from the sins he had already committed4 ,his account of the dreams is on record1 but is not very easy to follow2 nor is it likely that a man should be able to convey to others any adequate idea of the deepest spiritual or mental agitation which has shaken him to his foundations4 ,his associates in ,paris were now abandoned1 and he withdrew1 after some wanderings1 to ,holland1 where he abode the best part of his life and did his real work4 ,even now1 however1 he took life easily4 ,he recommends idleness as necessary to the production of good mental work4 ,he worked and meditated but a few hours a day3 and most of those in bed4 ,he used to think best in bed1 he said4 ,the afternoon he devoted to society and recreation4 ,after supper he wrote letters to various persons1 all plainly intended for publication1 and scrupulously preserved4 ,he kept himself free from care1 and was most cautious about his health1 regarding himself1 no doubt1 as a subject of experiment1 and wishful to see how long he could prolong his life4 ,at one time he writes to a friend that he shall be seriously disappointed if he does not manage to see #ajj years4 ,illustration3 ,,fig4 #ec4--;,descartes4 ,this plan of not over-working himself1 and limiting the hours devoted to serious thought1 is one that might perhaps advantageously be followed by some over-laborious students of the present day4 ,at any rate it conveys a lesson2 for the amount of ground covered by ,descartes1 in a life not very long1 is extraordinary4 ,he must1 however1 have had a singular aptitude for scientific work2 and the judicious leaven of selfishness whereby he was able to keep himself free from care and embarrassments must have been a great help to him4 ,and what did his versatile genius accomplish during his fifty-four years of life8 ,in philosophy1 using the term as meaning mental or moral philosophy and metaphysics1 as opposed to natural philosophy or physics1 he takes a very high rank1 and it is on this that perhaps his greatest fame rests4 7,he is the author1 you may remember1 of the famous aphorism1 ,cogito1 ergo sum47 ,in biology ,i believe he may be considered almost equally great3 certainly he spent a great deal of time in dissecting1 and he made out a good deal of what is now known of the structure of the body1 and of the theory of vision4 ,he eagerly accepted the doctrine of the circulation of the blood1 then being taught by ,harvey1 and was an excellent anatomist4 ,you doubtless know ,professor ,huxley's article on ,descartes in the ,lay ,sermons1 and you perceive in what high estimation he is there held4 ,he originated the hypothesis that animals are automata1 for which indeed there is much to be said from some points of view2 but he unfortunately believed that they were unconscious and non-sentient automata1 and this belief led his disciples into acts of abominable cruelty4 ,professor ,huxley lectured on this hypothesis and partially upheld it not many years since4 ,the article is included in his volume called ,science and ,culture4 ,concerning his work in mathematics and physics ,i can speak with more confidence4 ,he is the author of the ,cartesian system of algebraic or analytic geometry1 which has been so powerful an engine of research1 far easier to wield than the old synthetic geometry4 ,without it ,newton could never have written the ,principia1 or made his greatest discoveries4 ,he might indeed have invented it for himself1 but it would have consumed some of his life to have brought it to the necessary perfection4 ,the principle of it is the specification of the position of a point in a plane by two numbers1 indicating say its distance from two lines of reference in the plane2 like the latitude and longitude of a place on the globe4 ,for instance1 the two lines of reference might be the bottom edge and the left-hand vertical edge of a wall2 then a point on the wall1 stated as being for instance #f feet along and #b feet up1 is precisely determined4 ,these two distances are called co-ordinates2 horizontal ones are usually denoted by x1 and vertical ones by y4 ,if1 instead of specifying two things1 only one statement is made1 such as y #b1 it is satisfied by a whole row of points1 all the points in a horizontal line #b feet above the ground4 ,hence y #b may be said to represent that straight line1 and is called the equation to that straight line4 ,similarly x #f represents a vertical straight line #f feet 7or inches or some other unit7 from the left-hand edge4 ,if it is asserted that x #f and y #b1 only one point can be found to satisfy both conditions1 viz4 the crossing point of the above two straight lines4 ,suppose an equation such as x y to be given4 ,this also is satisfied by a row of points1 viz4 by all those that are equidistant from bottom and left-hand edges4 ,in other words1 x y represents a straight line slanting upwards at #de4 ,the equation x #by represents another straight line with a different angle of slope1 and so on4 ,the equation x#b y#b #cf represents a circle of radius #f4 ,the equation #cx#b #dy#b #be represents an ellipse2 and in general every algebraic equation that can be written down1 provided it involve only two variables1 x and y1 represents some curve in a plane2 a curve moreover that can be drawn1 or its properties completely investigated without drawing1 from the equation4 ,thus algebra is wedded to geometry1 and the investigation of geometric relations by means of algebraic equations is called analytical geometry1 as opposed to the old ,euclidian or synthetic mode of treating the subject by reasoning consciously directed to the subject by help of figures4 ,if there be three variables--x1 y1 and z1--instead of only two1 an equation among them represents not a curve in a plane but a surface in space2 the three variables corresponding to the three dimensions of space3 length1 breadth1 and thickness4 ,an equation with four variables usually requires space of four dimensions for its geometrical interpretation1 and so on4 ,thus geometry can not only be reasoned about in a more mechanical and therefore much easier1 manner1 but it can be extended into regions of which we have and can have no direct conception1 because we are deficient in sense organs for accumulating any kind of experience in connexion with such ideas4 ,illustration3 ,,fig4 #ed4--,the eye diagram4 ,from ,descartes' ,principia4 ,three external points are shown depicted on the retina3 the image being appreciated by a representation of the brain4 ,in physics proper ,descartes' tract on optics is of considerable historical interest4 ,he treats all the subjects he takes up in an able and original manner4 ,in ,astronomy he is the author of that famous and long upheld theory1 the doctrine of vortices4 ,he regarded space as a plenum full of an all-pervading fluid4 ,certain portions of this fluid were in a state of whirling motion1 as in a whirlpool or eddy of water2 and each planet had its own eddy1 in which it was whirled round and round1 as a straw is caught and whirled in a common whirlpool4 ,this idea he works out and elaborates very fully1 applying it to the system of the world1 and to the explanation of all the motions of the planets4 ,illustration3 ,,fig4 #ee4--;,descartes's diagram of vortices1 from his ,principia4 ,this system evidently supplied a void in men's minds1 left vacant by the overthrow of the ,ptolemaic system1 and it was rapidly accepted4 ,in the ,english ,universities it held for a long time almost undisputed sway2 it was in this faith that ,newton was brought up4 ,something was felt to be necessary to keep the planets moving on their endless round2 the primum mobile of ,ptolemy had been stopped2 an angel was sometimes assigned to each planet to carry it round1 but though a widely diffused belief1 this was a fantastic and not a serious scientific one4 ,descartes's vortices seemed to do exactly what was wanted4 ,it is true they had no connexion with the laws of ,kepler4 ,i doubt whether he knew about the laws of ,kepler2 he had not much opinion of other people's work2 he read very little--found it easier to think4 7,he travelled through ,florence once when ,galileo was at the height of his renown without calling upon or seeing him47 ,in so far as the motion of a planet was not circular1 it had to be accounted for by the jostling and crowding and distortion of the vortices4 ,gravitation he explained by a settling down of bodies toward the centre of each vortex2 and cohesion by an absence of relative motion tending to separate particles of matter4 ,he can imagine no stronger cement4 ,the vortices1 as ,descartes imagined them1 are not now believed in4 ,are we then to regard the system as absurd and wholly false8 ,i do not see how we can do this1 when to this day philosophers are agreed in believing space to be completely full of fluid1 which fluid is certainly capable of vortex motion1 and perhaps everywhere does possess that motion4 ,true1 the now imagined vortices are not the large whirls of planetary size1 they are rather infinitesimal whirls of less than atomic dimensions2 still a whirling fluid is believed in to this day1 and many are seeking to deduce all the properties of matter 7rigidity1 elasticity1 cohesion gravitation1 and the rest7 from it4 ,further1 although we talk glibly about gravitation and magnetism1 and so on1 we do not really know what they are4 ,progress is being made1 but we do not yet properly know4 ,much1 overwhelmingly much1 remains to be discovered1 and it ill-behoves us to reject any well-founded and long-held theory as utterly and intrinsically false and absurd4 ,the more one gets to know1 the more one perceives a kernel of truth even in the most singular statements2 and scientific men have learned by experience to be very careful how they lop off any branch of the tree of knowledge1 lest as they cut away the dead wood they lose also some green shoot1 some healthy bud of unperceived truth4 ,however1 it may be admitted that the idea of a ,cartesian vortex in connexion with the solar system applies1 if at all1 rather to an earlier--its nebulous--stage1 when the whole thing was one great whirl1 ready to split or shrink off planetary rings at their appropriate distances4 ,soon after he had written his great work1 the ,principia ,mathematica1 and before he printed it1 news reached him of the persecution and recantation of ,galileo4 ,he seems to have been quite thunderstruck at the tidings1 says ,mr4 ,mahaffy1 in his ,life of ,descartes4#ae ,he had started on his scientific journeys with the firm determination to enter into no conflict with the ,church1 and to carry out his system of pure mathematics and physics without ever meddling with matters of faith4 ,he was rudely disillusioned as to the possibility of this severance4 ,he wrote at once--apparently1 ,november #bjth1 #afcc--to ,mersenne to say he would on no account publish his work--nay1 that he had at first resolved to burn all his papers1 for that he would never prosecute philosophy at the risk of being censured by his ,church4 ',i could hardly have believed1' he says1 'that an ,italian1 and in favour with the ,pope as ,i hear1 could be considered criminal for nothing else than for seeking to establish the earth's motion2 though ,i know it has formerly been censured by some ,cardinals4 ,but ,i thought ,i had heard that since then it was constantly being taught1 even at ,rome2 and ,i confess that if the opinion of the earth's movement is false1 all the foundations of my philosophy are so also1 because it is demonstrated clearly by them4 ,it is so bound up with every part of my treatise that ,i could not sever it without making the remainder faulty2 and although ,i consider all my conclusions based on very certain and clear demonstrations1 ,i would not for all the world sustain them against the authority of the ,church4' ,ten years later1 however1 he did publish the book1 for he had by this time hit on an ingenious compromise4 ,he formally denied that the earth moved1 and only asserted that it was carried along with its water and air in one of those larger motions of the celestial ether which produce the diurnal and annual revolutions of the solar system4 ,so1 just as a passenger on the deck of a ship might be called stationary1 so was the earth4 ,he gives himself out therefore as a follower of ,tycho rather than of ,copernicus1 and says if the ,church won't accept this compromise he must return to the ,ptolemaic system2 but he hopes they won't compel him to do that1 seeing that it is manifestly untrue4 ,this elaborate deference to the powers that be did not indeed save the work from being ultimately placed upon the forbidden list by the ,church1 but it saved himself1 at any rate1 from annoying persecution4 ,he was not1 indeed1 at all willing to be persecuted1 and would no doubt have at once withdrawn anything they wished4 ,i should be sorry to call him a time-server1 but he certainly had plenty of that worldly wisdom in which some of his predecessors had been so lamentably deficient4 ,moreover1 he was really a sceptic1 and cared nothing at all about the ,church or its dogmas4 ,he knew the ,church's power1 however1 and the advisability of standing well with it3 he therefore professed himself a ,catholic1 and studiously kept his science and his ,christianity distinct4 ,in saying that he was a sceptic you must not understand that he was in the least an atheist4 ,very few men are2 certainly ,descartes never thought of being one4 ,the term is indeed ludicrously inapplicable to him1 for a great part of his philosophy is occupied with what he considers a rigorous proof of the existence of the ,deity4 ,at the age of fifty-three he was sent for to ,stockholm by ,christina1 ,queen of ,sweden1 a young lady enthusiastically devoted to study of all kinds and determined to surround her ,court with all that was most famous in literature and science4 ,thither1 after hesitation1 ,descartes went4 ,he greatly liked royalty1 but he dreaded the cold climate4 ,born in ,touraine1 a ,swedish winter was peculiarly trying to him1 especially as the energetic ,queen would have lessons given her at five o'clock in the morning4 ,she intended to treat him well1 and was immensely taken with him2 but this getting up at five o'clock on a ,november morning1 to a man accustomed all his life to lie in bed till eleven1 was a cruel hardship4 ,he was too much of a courtier1 however1 to murmur1 and the early morning audience continued4 ,his health began to break down3 he thought of retreating1 but suddenly he gave way and became delirious4 ,the ,queen's physician attended him1 and of course wanted to bleed him4 ,this1 knowing all he knew of physiology1 sent him furious1 and they could do nothing with him4 ,after some days he became quiet1 was bled twice1 and gradually sank1 discoursing with great calmness on his approaching death1 and duly fortified with all the rites of the ,catholic ,church4 ,his general method of research was as nearly as possible a purely deductive one3--i4e41 after the manner of ,euclid he starts with a few simple principles1 and then1 by a chain of reasoning1 endeavours to deduce from them their consequences1 and so to build up bit by bit an edifice of connected knowledge4 ,in this he was the precursor of ,newton4 ,this method1 when rigorously pursued1 is the most powerful and satisfactory of all1 and results in an ordered province of science far superior to the fragmentary conquests of experiment4 ,but few indeed are the men who can handle it safely and satisfactorily3 and none without continual appeals to experiment for verification4 ,it was through not perceiving the necessity for verification that he erred4 ,his importance to science lies not so much in what he actually discovered as in his anticipation of the right conditions for the solution of problems in physical science4 ,he in fact made the discovery that ,nature could after all be interrogated mathematically--a fact that was in great danger of remaining unknown4 ,for1 observe1 that the mathematical study of ,nature1 the discovery of truth with a piece of paper and a pen1 has a perilous similarity at first sight to the straw-thrashing subtleties of the ,greeks1 whose methods of investigating nature by discussing the meaning of words and the usage of language and the necessities of thought1 had proved to be so futile and unproductive4 ,a reaction had set in1 led by ,galileo1 ,gilbert1 and the whole modern school of experimental philosophers1 lasting down to the present day3--men who teach that the only right way of investigating ,nature is by experiment and observation4 ,it is indeed a very right and an absolutely necessary way2 but it is not the only way4 ,a foundation of experimental fact there must be2 but upon this a great structure of theoretical deduction can be based1 all rigidly connected together by pure reasoning1 and all necessarily as true as the premises1 provided no mistake is made4 ,to guard against the possibility of mistake and oversight1 especially oversight1 all conclusions must sooner or later be brought to the test of experiment2 and if disagreeing therewith1 the theory itself must be re-examined1 and the flaw discovered1 or else the theory must be abandoned4 ,of this grand method1 quite different from the gropings in the dark of ,kepler--this method1 which1 in combination with experiment1 has made science what it now is--this which in the hands of ,newton was to lead to such stupendous results1 we owe the beginning and early stages to ,ren ,descartes4 ,,summary ,,of ,,facts ,,for ,,lectures ,,vii ,,and ,,viii ,otto ,guericke #afjb-afhf ,hon4 ,robert ,boyle #afbf-afia ,huyghens #afbi-afie ,christopher ,wren #afcb-agbc ,robert ,hooke #afce-agjb ,,newton #afdb-agbg ,edmund ,halley #afef-agdb ,james ,bradley #afib-agfb ,chronology of ,newton's ,life4 ,isaac ,newton was born at ,woolsthorpe1 near ,grantham1 ,lincolnshire1 on ,christmas ,day1 #afdb4 ,his father1 a small freehold farmer1 also named ,isaac1 died before his birth4 ,his mother1 ne ,hannah ,ayscough1 in two years married a ,mr4 ,smith1 rector of ,north ,witham1 but was again left a widow in #afef4 ,his uncle1 ,w4 ,ayscough1 was rector of a near parish and a graduate of ,trinity ,college1 ,cambridge4 ,at the age of fifteen ,isaac was removed from school at ,grantham to be made a farmer of1 but as it seemed he would not make a good one his uncle arranged for him to return to school and thence to ,cambridge1 where he entered ,trinity ,college as a sub-sizar in #affa4 ,studied ,descartes's geometry4 ,found out a method of infinite series in #affe1 and began the invention of ,fluxions4 ,in the same year and the next he was driven from ,cambridge by the plague4 ,in #afff1 at ,woolsthorpe1 the apple fell4 ,in #affg he was elected a fellow of his college1 and in #affi was specially noted as possessing an unparalleled genius by ,dr4 ,barrow1 first ,lucasian ,professor of ,mathematics4 ,the same year ,dr4 ,barrow retired from his chair in favour of ,newton1 who was thus elected at the age of twenty-six4 ,he lectured first on optics with great success4 ,early in #afgb he was elected a ,fellow of the ,royal ,society1 and communicated his researches in optics1 his reflecting telescope1 and his discovery of the compound nature of white light4 ,annoying controversies arose2 but he nevertheless contributed a good many other most important papers in optics1 including observations in diffraction1 and colours of thin plates4 ,he also invented the modern sextant4 ,in #afgb a letter from ,paris was read at the ,royal ,society concerning a new and accurate determination of the size of the earth by ,picard4 ,when ,newton heard of it he began the ,principia1 working in silence4 ,in #afhd arose a discussion between ,wren1 ,hooke1 and ,halley concerning the law of inverse square as applied to gravity and the path it would cause the planets to describe4 ,hooke asserted that he had a solution1 but he would not produce it4 ,after waiting some time for it ,halley went to ,cambridge to consult ,newton on the subject1 and thus discovered the existence of the first part of the ,principia1 wherein all this and much more was thoroughly worked out4 ,on his representations to the ,royal ,society the manuscript was asked for1 and when complete was printed and published in #afhg at ,halley's expense4 ,while it was being completed ,newton and seven others were sent to uphold the dignity of the ,university1 before the ,court of ,high ,commission and ,judge ,jeffreys1 against a high-handed action of ,james ,,ii4 ,in #afhb he was sent to ,parliament1 and was present at the coronation of ,william and ,mary4 ,made friends with ,locke4 ,in #afid ,montague1 ,lord ,halifax1 made him ,warden1 and in #afig ,master1 of the ,mint4 ,whiston succeeded him as ,lucasian ,professor4 ,in #afic the method of fluxions was published4 ,in #agjc ,newton was made ,president of the ,royal ,society1 and held the office to the end of his life4 ,in #agje he was knighted by ,anne4 ,in #agac ,cotes helped him to bring out a new edition of the ,principia1 completed as we now have it4 ,on the #bjth of ,march #agbg1 he died3 having lived from ,charles ,i4 to ,george ,,ii4 ,,the ,,laws ,,of ,,motion1 ,,discovered ,,by ,,galileo1 ,,stated ,,by ,,newton4 ,law #a4--;,if no force acts on a body in motion1 it continues to move uniformly in a straight line4 ,law #b4--;,if force acts on a body1 it produces a change of motion proportional to the force and in the same direction4 ,law #c4--,when one body exerts force on another1 that other reacts with equal force upon the one4 ,,lecture ,,vii ,,sir ,,isaac ,,newton ,the little hamlet of ,woolsthorpe lies close to the village of ,colsterworth1 about six miles south of ,grantham1 in the county of ,lincoln4 ,in the manor house of ,woolsthorpe1 on ,christmas ,day1 #afdb1 was born to a widowed mother a sickly infant who seemed not long for this world4 ,two women who were sent to ,north ,witham to get some medicine for him scarcely expected to find him alive on their return4 ,however1 the child lived1 became fairly robust1 and was named ,isaac1 after his father4 ,what sort of a man this father was we do not know4 ,he was what we may call a yeoman1 that most wholesome and natural of all classes4 ,he owned the soil he tilled1 and his little estate had already been in the family for some hundred years4 ,he was thirty-six when he died1 and had only been married a few months4 ,of the mother1 unfortunately1 we know almost as little4 ,we hear that she was recommended by a parishioner to the ,rev4 ,barnabas ,smith1 an old bachelor in search of a wife1 as the widow ,newton--an extraordinary good woman3 and so ,i expect she was1 a thoroughly sensible1 practical1 homely1 industrious1 middle-class1 ,mill-on-the-,floss sort of woman4 ,however1 on her second marriage she went to live at ,north ,witham1 and her mother1 old ,mrs4 ,ayscough1 came to superintend the farm at ,woolsthorpe1 and take care of young ,isaac4 ,by her second marriage his mother acquired another piece of land1 which she settled on her first son2 so ,isaac found himself heir to two little properties1 bringing in a rental of about #hj a year4 ,illustration3 ,,fig4 #ef4--,manor-house of ,woolsthorpe4 ,he had been sent to a couple of village schools to acquire the ordinary accomplishments taught at those places1 and for three years to the grammar school at ,grantham1 then conducted by an old gentleman named ,mr4 ,stokes4 ,he had not been very industrious at school1 nor did he feel keenly the fascinations of the ,latin ,grammar1 for he tells us that he was the last boy in the lowest class but one4 ,he used to pay much more attention to the construction of kites and windmills and waterwheels1 all of which he made to work very well4 ,he also used to tie paper lanterns to the tail of his kite1 so as to make the country folk fancy they saw a comet1 and in general to disport himself as a boy should4 ,it so happened1 however1 that he succeeded in thrashing1 in fair fight1 a bigger boy who was higher in the school1 and who had given him a kick4 ,his success awakened a spirit of emulation in other things than boxing1 and young ,newton speedily rose to be top of the school4 ,under these circumstances1 at the age of fifteen1 his mother1 who had now returned to ,woolsthorpe1 which had been rebuilt1 thought it was time to train him for the management of his land1 and to make a farmer and grazier of him4 ,the boy was doubtless glad to get away from school1 but he did not take kindly to the farm--especially not to the marketing at ,grantham4 ,he and an old servant were sent to ,grantham every week to buy and sell produce1 but young ,isaac used to leave his old mentor to do all the business1 and himself retire to an attic in the house he had lodged in when at school1 and there bury himself in books4 ,after a time he didn't even go through the farce of visiting ,grantham at all2 but stopped on the road and sat under a hedge1 reading or making some model1 until his companion returned4 ,we hear of him now in the great storm of #afeh1 the storm on the day ,cromwell died1 measuring the force of the wind by seeing how far he could jump with it and against it4 ,he also made a water-clock and set it up in the house at ,grantham1 where it kept fairly good time so long as he was in the neighbourhood to look after it occasionally4 ,at his own home he made a couple of sundials on the side of the wall 7he began by marking the position of the sun by the shadow of a peg driven into the wall1 but this gradually developed into a regular dial7 one of which remained of use for some time2 and was still to be seen in the same place during the first half of the present century1 only with the gnomon gone4 ,in #ahdd the stone on which it was carved was carefully extracted and presented to the ,royal ,society1 who preserve it in their library4 ,the letters ,,wton roughly carved on it are barely visible4 ,all these pursuits must have been rather trying to his poor mother1 and she probably complained to her brother1 the rector of ,burton ,coggles3 at any rate this gentleman found master ,newton one morning under a hedge when he ought to have been farming4 ,but as he found him working away at mathematics1 like a wise man he persuaded his sister to send the boy back to school for a short time1 and then to ,cambridge4 ,on the day of his finally leaving school old ,mr4 ,stokes assembled the boys1 made them a speech in praise of ,newton's character and ability1 and then dismissed him to ,cambridge4 ,at ,trinity ,college a new world opened out before the country-bred lad4 ,he knew his classics passably1 but of mathematics and science he was ignorant1 except through the smatterings he had picked up for himself4 ,he devoured a book on logic1 and another on ,kepler's ,optics1 so fast that his attendance at lectures on these subjects became unnecessary4 ,he also got hold of a ,euclid and of ,descartes's ,geometry4 ,the ,euclid seemed childishly easy1 and was thrown aside1 but the ,descartes baffled him for a time4 ,however1 he set to it again and again and before long mastered it4 ,he threw himself heart and soul into mathematics1 and very soon made some remarkable discoveries4 ,first he discovered the binomial theorem3 familiar now to all who have done any algebra1 unintelligible to others1 and therefore ,i say nothing about it4 ,by the age of twenty-one or two he had begun his great mathematical discovery of infinite series and fluxions--now known by the name of the ,differential ,calculus4 ,he wrote these things out and must have been quite absorbed in them1 but it never seems to have occurred to him to publish them or tell any one about them4 ,in #affd he noticed some halos round the moon1 and1 as his manner was1 he measured their angles--the small ones #c and #e degrees each1 the larger one #bbce4 ,later he gave their theory4 ,small coloured halos round the moon are often seen1 and are said to be a sign of rain4 ,they are produced by the action of minute globules of water or cloud particles upon light1 and are brightest when the particles are nearly equal in size4 ,they are not like the rainbow1 every part of which is due to light that has entered a raindrop1 and been refracted and reflected with prismatic separation of colours2 a halo is caused by particles so small as to be almost comparable with the size of waves of light1 in a way which is explained in optics under the head diffraction4 ,it may be easily imitated by dusting an ordinary piece of window-glass over with lycopodium1 placing a candle near it1 and then looking at the candle-flame through the dusty glass from a fair distance4 ,or you may look at the image of a candle in a dusted looking-glass4 ,lycopodium dust is specially suitable1 for its granules are remarkably equal in size4 ,the large halo1 more rarely seen1 of angular radius #bbce1 is due to another cause again1 and is a prismatic effect1 although it exhibits hardly any colour4 ,the angle #bb-a_/b is characteristic of refraction in crystals with angles of #fj and refractive index about the same as water2 in other words this halo is caused by ice crystals in the higher regions of the atmosphere4 ,he also the same year observed a comet1 and sat up so late watching it that he made himself ill4 ,by the end of the year he was elected to a scholarship and took his ,b4,a4 degree4 ,the order of merit for that year never existed or has not been kept4 ,it would have been interesting1 not as a testimony to ,newton1 but to the sense or non-sense of the examiners4 ,the oldest ,professorship of ,mathematics at the ,university of ,cambridge1 the ,lucasian1 had not then been long founded1 and its first occupant was ,dr4 ,isaac ,barrow1 an eminent mathematician1 and a kind old man4 ,with him ,newton made good friends1 and was helpful in preparing a treatise on optics for the press4 ,his help is acknowledged by ,dr4 ,barrow in the preface1 which states that he had corrected several errors and made some capital additions of his own4 ,thus we see that1 although the chief part of his time was devoted to mathematics1 his attention was already directed to both optics and astronomy4 7,kepler1 ,descartes1 ,galileo1 all combined some optics with astronomy4 ,tycho and the old ones combined alchemy2 ,newton dabbled in this also47 ,newton reached the age of twenty-three in #affe1 the year of the ,great ,plague4 ,the plague broke out in ,cambridge as well as in ,london1 and the whole college was sent down4 ,newton went back to ,woolsthorpe1 his mind teeming with ideas1 and spent the rest of this year and part of the next in quiet pondering4 ,somehow or other he had got hold of the notion of centrifugal force4 ,it was six years before ,huyghens discovered and published the laws of centrifugal force1 but in some quiet way of his own ,newton knew about it and applied the idea to the motion of the planets4 ,we can almost follow the course of his thoughts as he brooded and meditated on the great problem which had taxed so many previous thinkers1--,what makes the planets move round the sun8 ,kepler had discovered how they moved1 but why did they so move1 what urged them8 ,even the how took a long time--all the time of the ,greeks1 through ,ptolemy1 the ,arabs1 ,copernicus1 ,tycho3 circular motion1 epicycles1 and excentrics had been the prevailing theory4 ,kepler1 with his marvellous industry1 had wrested from ,tycho's observations the secret of their orbits4 ,they moved in ellipses with the sun in one focus4 ,their rate of description of area1 not their speed1 was uniform and proportional to time4 ,yes1 and a third law1 a mysterious law of unintelligible import1 had also yielded itself to his penetrating industry--a law the discovery of which had given him the keenest delight1 and excited an outburst of rapture--viz4 that there was a relation between the distances and the periodic times of the several planets4 ,the cubes of the distances were proportional to the squares of the times for the whole system4 ,this law1 first found true for the six primary planets1 he had also extended1 after ,galileo's discovery1 to the four secondary planets1 or satellites of ,jupiter 7p4 #ha74 ,but all this was working in the dark--it was only the first step--this empirical discovery of facts2 the facts were so1 but how came they so8 ,what made the planets move in this particular way8 ,descartes's vortices was an attempt1 a poor and imperfect attempt1 at an explanation4 ,it had been hailed and adopted throughout ,europe for want of a better1 but it did not satisfy ,newton4 ,no1 it proceeded on a wrong tack1 and ,kepler had proceeded on a wrong tack in imagining spokes or rays sticking out from the sun and driving the planets round like a piece of mechanism or mill work4 ,for1 note that all these theories are based on a wrong idea--the idea1 viz41 that some force is necessary to maintain a body in motion4 ,but this was contrary to the laws of motion as discovered by ,galileo4 ,you know that during his last years of blind helplessness at ,arcetri1 ,galileo had pondered and written much on the laws of motion1 the foundation of mechanics4 ,in his early youth1 at ,pisa1 he had been similarly occupied2 he had discovered the pendulum1 he had refuted the ,aristotelians by dropping weights from the leaning tower 7which we must rejoice that no earthquake has yet injured71 and he had returned to mechanics at intervals all his life2 and now1 when his eyes were useless for astronomy1 when the outer world has become to him only a prison to be broken by death1 he returns once more to the laws of motion1 and produces the most solid and substantial work of his life4 ,for this is ,galileo's main glory--not his brilliant exposition of the ,copernican system1 not his flashes of wit at the expense of a moribund philosophy1 not his experiments on floating bodies1 not even his telescope and astronomical discoveries--though these are the most taking and dazzling at first sight4 ,no2 his main glory and title to immortality consists in this1 that he first laid the foundation of mechanics on a firm and secure basis of experiment1 reasoning1 and observation4 ,he first discovered the true ,laws of ,motion4 ,i said little of this achievement in my lecture on him2 for the work was written towards the end of his life1 and ,i had no time then4 ,but ,i knew ,i should have to return to it before we came to ,newton1 and here we are4 ,you may wonder how the work got published when so many of his manuscripts were destroyed4 ,horrible to say1 ,galileo's own son destroyed a great bundle of his father's manuscripts1 thinking1 no doubt1 thereby to save his own soul4 ,this book on mechanics was not burnt1 however4 ,the fact is it was rescued by one or other of his pupils1 ,toricelli or ,viviani1 who were allowed to visit him in his last two or three years2 it was kept by them for some time1 and then published surreptitiously in ,holland4 ,not that there is anything in it bearing in any visible way on any theological controversy2 but it is unlikely that the ,inquisition would have suffered it to pass notwithstanding4 ,i have appended to the summary preceding this lecture 7p4 #afj7 the three axioms or laws of motion discovered by ,galileo4 ,they are stated by ,newton with unexampled clearness and accuracy1 and are hence known as ,newton's laws1 but they are based on ,galileo's work4 ,the first is the simplest2 though ignorance of it gave the ancients a deal of trouble4 ,it is simply a statement that force is needed to change the motion of a body2 i4e4 that if no force act on a body it will continue to move uniformly both in speed and direction--in other words1 steadily1 in a straight line4 ,the old idea had been that some force was needed to maintain motion4 ,on the contrary1 the first law asserts1 some force is needed to destroy it4 ,leave a body alone1 free from all friction or other retarding forces1 and it will go on for ever4 ,the planetary motion through empty space therefore wants no keeping up2 it is not the motion that demands a force to maintain it1 it is the curvature of the path that needs a force to produce it continually4 ,the motion of a planet is approximately uniform so far as speed is concerned1 but it is not constant in direction2 it is nearly a circle4 ,the real force needed is not a propelling but a deflecting force4 ,the second law asserts that when a force acts1 the motion changes1 either in speed or in direction1 or both1 at a pace proportional to the magnitude of the force1 and in the same direction as that in which the force acts4 ,now since it is almost solely in direction that planetary motion alters1 a deflecting force only is needed2 a force at right angles to the direction of motion1 a force normal to the path4 ,considering the motion as circular1 a force along the radius1 a radial or centripetal force1 must be acting continually4 ,whirl a weight round and round by a bit of elastic1 the elastic is stretched2 whirl it faster1 it is stretched more4 ,the moving mass pulls at the elastic--that is its centrifugal force2 the hand at the centre pulls also--that is centripetal force4 ,the third law asserts that these two forces are equal1 and together constitute the tension in the elastic4 ,it is impossible to have one force alone1 there must be a pair4 ,you can't push hard against a body that offers no resistance4 ,whatever force you exert upon a body1 with that same force the body must react upon you4 ,action and reaction are always equal and opposite4 ,sometimes an absurd difficulty is felt with respect to this1 even by engineers4 ,they say1 ,if the cart pulls against the horse with precisely the same force as the horse pulls the cart1 why should the cart move8 ,why on earth not8 ,the cart moves because the horse pulls it1 and because nothing else is pulling it back4 ,yes1 they say1 the cart is pulling back4 ,but what is it pulling back8 ,not itself1 surely8 ,no1 the horse4 ,yes1 certainly the cart is pulling at the horse2 if the cart offered no resistance what would be the good of the horse8 ,that is what he is for1 to overcome the pull-back of the cart2 but nothing is pulling the cart back 7except1 of course1 a little friction71 and the horse is pulling it forward1 hence it goes forward4 ,there is no puzzle at all when once you realise that there are two bodies and two forces acting1 and that one force acts on each body4#af ,if1 indeed1 two balanced forces acted on one body that would be in equilibrium1 but the two equal forces contemplated in the third law act on two different bodies1 and neither is in equilibrium4 ,so much for the third law1 which is extremely simple1 though it has extraordinarily far-reaching consequences1 and when combined with a denial of action at a distance1 is precisely the principle of the ,conservation of ,energy4 ,attempts at perpetual motion may all be regarded as attempts to get round this third law4 ,illustration3 ,,fig4 #eg4 ,on the subject of the second law a great deal more has to be said before it can be in any proper sense even partially appreciated1 but a complete discussion of it would involve a treatise on mechanics4 ,it is the law of mechanics4 ,one aspect of it we must attend to now in order to deal with the motion of the planets1 and that is the fact that the change of motion of a body depends solely and simply on the force acting1 and not at all upon what the body happens to be doing at the time it acts4 ,it may be stationary1 or it may be moving in any direction2 that makes no difference4 ,thus1 referring back to the summary preceding ,lecture ,,iv1 it is there stated that a dropped body falls #af feet in the first second1 that in two seconds it falls #fd feet1 and so on1 in proportion to the square of the time4 ,so also will it be the case with a thrown body1 but the drop must be reckoned from its line of motion--the straight line which1 but for gravity1 it would describe4 ,thus a stone thrown from ,o with the velocity ,,oa would in one second find itself at ,a1 in two seconds at ,b1 in three seconds at ,c1 and so on1 in accordance with the first law of motion1 if no force acted4 ,but if gravity acts it will have fallen #af feet by the time it would have got to ,a1 and so will find itself at ,p4 ,in two seconds it will be at ,q1 having fallen a vertical height of #fd feet2 in three seconds it will be at ,r1 #add feet below ,c2 and so on4 ,its actual path will be a curve1 which in this case is a parabola4 7,fig4 #eg47 ,if a cannon is pointed horizontally over a level plain1 the cannon ball will be just as much affected by gravity as if it were dropped1 and so will strike the plain at the same instant as another which was simply dropped where it started4 ,one ball may have gone a mile and the other only dropped a hundred feet or so1 but the time needed by both for the vertical drop will be the same4 ,the horizontal motion of one is an extra1 and is due to the powder4 ,as a matter of fact the path of a projectile in vacuo is only approximately a parabola4 ,it is instructive to remember that it is really an ellipse with one focus very distant1 but not at infinity4 ,one of its foci is the centre of the earth4 ,a projectile is really a minute satellite of the earth's1 and in vacuo it accurately obeys all ,kepler's laws4 ,it happens not to be able to complete its orbit1 because it was started inconveniently close to the earth1 whose bulk gets in its way2 but in that respect the earth is to be reckoned as a gratuitous obstruction1 like a target1 but a target that differs from most targets in being hard to miss4 ,illustration3 ,,fig4 #eh4 ,now consider circular motion in the same way1 say a ball whirled round by a string4 7,fig4 #eh47 ,attending to the body at ,o1 it is for an instant moving towards ,a1 and if no force acted it would get to ,a in a time which for brevity we may call a second4 ,but a force1 the pull of the string1 is continually drawing it towards ,s1 and so it really finds itself at ,p1 having described the circular arc ,,op1 which may be considered to be compounded of1 and analyzable into the rectilinear motion ,,oa and the drop ,,ap4 ,at ,p it is for an instant moving towards ,b1 and the same process therefore carries it to ,q2 in the third second it gets to ,r2 and so on3 always falling1 so to speak1 from its natural rectilinear path1 towards the centre1 but never getting any nearer to the centre4 ,the force with which it has thus to be constantly pulled in towards the centre1 or1 which is the same thing1 the force with which it is tugging at whatever constraint it is that holds it in1 is mv#b_/r2 where m is the mass of the particle1 v its velocity1 and r the radius of its circle of movement4 ,this is the formula first given by ,huyghens for centrifugal force4 ,we shall find it convenient to express it in terms of the time of one revolution1 say ,t4 ,it is easily done1 since plainly ,t circumference_/speed #bpir_/v2 so the above expression for centrifugal force becomes #dpi#bmr_/,t#b4 ,as to the fall of the body towards the centre every microscopic unit of time1 it is easily reckoned4 ,for by ,euclid ,,iii4 #cf1 and ,fig4 #eh1 ,,ap4,,aa' ,,ao#b4 ,take ,a very near ,o1 then ,,oa vt1 and ,,aa' #br2 so ,,ap v#bt#b_/br #bpi#br t#b_/,t#b2 or the fall per second is #bpi#br_/,t#b1 r being its distance from the centre1 and ,t its time of going once round4 ,in the case of the moon for instance1 r is #fj earth radii2 more exactly #fjb2 and ,t is a lunar month1 or more precisely #bg days1 #g hours1 #dc minutes1 and #aa-a_/b seconds4 ,hence the moon's deflection from the tangential or rectilinear path every minute comes out as very closely #af feet 7the true size of the earth being used74 ,returning now to the case of a small body revolving round a big one1 and assuming a force directly proportional to the mass of both bodies1 and inversely proportional to the square of the distance between them3 i4e4 assuming the known force of gravity1 it is ,v ,mm_/r#b where ,v is a constant1 called the gravitation constant1 to be determined by experiment4 ,if this is the centripetal force pulling a planet or satellite in1 it must be equal to the centrifugal force of this latter1 viz4 7see above74 #dpi#bmr_/,t#b ,equate the two together1 and at once we get r#c_/,t#b ,v_/#dpi#b,m2 or1 in words1 the cube of the distance divided by the square of the periodic time for every planet or satellite of the system under consideration1 will be constant and proportional to the mass of the central body4 ,this is ,kepler's third law1 with a notable addition4 ,it is stated above for circular motion only1 so as to avoid geometrical difficulties1 but even so it is very instructive4 ,the reason of the proportion between r#c and ,t#b is at once manifest2 and as soon as the constant ,v became known1 the mass of the central body1 the sun in the case of a planet1 the earth in the case of the moon1 ,jupiter in the case of his satellites1 was at once determined4 ,newton's reasoning at this time might1 however1 be better displayed perhaps by altering the order of the steps a little1 as thus3-- ,the centrifugal force of a body is proportional to r#c_/,t#b1 but by ,kepler's third law r#c_/,t#b is constant for all the planets1 reckoning r from the sun4 ,hence the centripetal force needed to hold in all the planets will be a single force emanating from the sun and varying inversely with the square of the distance from that body4 ,such a force is at once necessary and sufficient4 ,such a force would explain the motion of the planets4 ,but then all this proceeds on a wrong assumption--that the planetary motion is circular4 ,will it hold for elliptic orbits8 ,will an inverse square law of force keep a body moving in an elliptic orbit about the sun in one focus8 ,this is a far more difficult question4 ,newton solved it1 but ,i do not believe that even he could have solved it1 except that he had at his disposal two mathematical engines of great power--the ,cartesian method of treating geometry1 and his own method of ,fluxions4 ,one can explain the elliptic motion now mathematically1 but hardly otherwise2 and ,i must be content to state that the double fact is true--viz41 that an inverse square law will move the body in an ellipse or other conic section with the sun in one focus1 and that if a body so moves it must be acted on by an inverse square law4 ,illustration3 ,,fig4 #ei4 ,this then is the meaning of the first and third laws of ,kepler4 ,what about the second8 ,what is the meaning of the equable description of areas8 ,well1 that rigorously proves that a planet is acted on by a force directed to the centre about which the rate of description of areas is equable4 ,it proves1 in fact1 that the sun is the attracting body1 and that no other force acts4 ,for first of all if the first law of motion is obeyed1 i4e4 if no force acts1 and if the path be equally subdivided to represent equal times1 and straight lines be drawn from the divisions to any point whatever1 all these areas thus enclosed will be equal1 because they are triangles on equal base and of the same height 7,euclid1 ,i74 ,see ,fig4 #ei2 ,s being any point whatever1 and ,a1 ,b1 ,c1 successive positions of a body4 ,now at each of the successive instants let the body receive a sudden blow in the direction of that same point ,s1 sufficient to carry it from ,a to ,d in the same time as it would have got to ,b if left alone4 ,the result will be that there will be a compromise1 and it will really arrive at ,p1 travelling along the diagonal of the parallelogram ,,ap4 ,the area its radius vector sweeps out is therefore ,,sap1 instead of what it would have been1 ,,sab4 ,but then these two areas are equal1 because they are triangles on the same base ,,as1 and between the same parallels ,,bp1 ,,as2 for by the parallelogram law ,,bp is parallel to ,,ad4 ,hence the area that would have been described is described1 and as all the areas were equal in the case of no force1 they remain equal when the body receives a blow at the end of every equal interval of time1 provided that every blow is actually directed to ,s1 the point to which radii vectores are drawn4 ,illustration3 ,,fig4 #fj4 ,illustration3 ,,fig4 #fa4 ,it is instructive to see that it does not hold if the blow is any otherwise directed2 for instance1 as in ,fig4 #fa1 when the blow is along ,,ae1 the body finds itself at ,p at the end of the second interval1 but the area ,,sap is by no means equal to ,,sab1 and therefore not equal to ,,soa1 the area swept out in the first interval4 ,in order to modify ,fig4 #fj so as to represent continuous motion and steady forces1 we have to take the sides of the polygon ,,oapq1 c41 very numerous and very small2 in the limit1 infinitely numerous and infinitely small4 ,the path then becomes a curve1 and the series of blows becomes a steady force directed towards ,s4 ,about whatever point therefore the rate of description of areas is uniform1 that point and no other must be the centre of all the force there is4 ,if there be no force1 as in ,fig4 #ei1 well and good1 but if there be any force however small not directed towards ,s1 then the rate of description of areas about ,s cannot be uniform4 ,kepler1 however1 says that the rate of description of areas of each planet about the sun is1 by ,tycho's observations1 uniform2 hence the sun is the centre of all the force that acts on them1 and there is no other force1 not even friction4 ,that is the moral of ,kepler's second law4 ,we may also see from it that gravity does not travel like light1 so as to take time on its journey from sun to planet2 for1 if it did1 there would be a sort of aberration1 and the force on its arrival could no longer be accurately directed to the centre of the sun4 7,see ,nature1 vol4 xlvi41 p4 #dig47 ,it is a matter for accuracy of observation1 therefore1 to decide whether the minutest trace of such deviation can be detected1 i4e4 within what limits of accuracy ,kepler's second law is now known to be obeyed4 ,i will content myself by saying that the limits are extremely narrow4 ,reference may be made also to p4 #bjh4 ,thus then it became clear to ,newton that the whole solar system depended on a central force emanating from the sun1 and varying inversely with the square of the distance from him3 for by that hypothesis all the laws of ,kepler concerning these motions were completely accounted for2 and1 in fact1 the laws necessitated the hypothesis and established it as a theory4 ,similarly the satellites of ,jupiter were controlled by a force emanating from ,jupiter and varying according to the same law4 ,and again our moon must be controlled by a force from the earth1 decreasing with the distance according to the same law4 ,grant this hypothetical attracting force pulling the planets towards the sun1 pulling the moon towards the earth1 and the whole mechanism of the solar system is beautifully explained4 ,if only one could be sure there was such a force6 ,it was one thing to calculate out what the effects of such a force would be3 it was another to be able to put one's finger upon it and say1 this is the force that actually exists and is known to exist4 ,we must picture him meditating in his garden on this want--an attractive force towards the earth4 ,if only such an attractive force pulling down bodies to the earth existed4 ,an apple falls from a tree4 ,why1 it does exist6 ,there is gravitation1 common gravity that makes bodies fall and gives them their weight4 ,wanted1 a force tending towards the centre of the earth4 ,it is to hand6 ,it is common old gravity that had been known so long1 that was perfectly familiar to ,galileo1 and probably to ,archimedes4 ,gravity that regulates the motion of projectiles4 ,why should it only pull stones and apples8 ,why should it not reach as high as the moon8 ,why should it not be the gravitation of the sun that is the central force acting on all the planets8 ,surely the secret of the universe is discovered6 ,but1 wait a bit2 is it discovered8 ,is this force of gravity sufficient for the purpose8 ,it must vary inversely with the square of the distance from the centre of the earth4 ,how far is the moon away8 ,sixty earth's radii4 ,hence the force of gravity at the moon's distance can only be #a_/cfjj of what it is on the earth's surface4 ,so1 instead of pulling it #af ft4 per second1 it should pull it #af_/cfjj ft4 per second1 or #af ft4 a minute4#ag ,how can one decide whether such a force is able to pull the moon the actual amount required8 ,to ,newton this would seem only like a sum in arithmetic4 ,out with a pencil and paper and reckon how much the moon falls toward the earth in every second of its motion4 ,is it #af_/cfjj8 ,that is what it ought to be3 but is it8 ,the size of the earth comes into the calculation4 ,sixty miles make a degree1 #cfj degrees a circumference4 ,this gives as the earth's diameter #f1hgc miles2 work it out4 ,the answer is not #af feet a minute1 it is #aci feet4 ,surely a mistake of calculation8 ,no1 it is no mistake3 there is something wrong in the theory1 gravity is too strong4 ,instead of falling toward the earth #e-a_/c hundredths of an inch every second1 as it would under gravity1 the moon only falls #d-b_/c hundredths of an inch per second4 ,with such a discovery in his grasp at the age of twenty-three he is disappointed--the figures do not agree1 and he cannot make them agree4 ,either gravity is not the force in action1 or else something interferes with it4 ,possibly1 gravity does part of the work1 and the vortices of ,descartes interfere with it4 ,he must abandon the fascinating idea for the time4 ,in his own words1 he laid aside at that time any further thought of the matter4 ,so far as is known1 he never mentioned his disappointment to a soul4 ,he might1 perhaps1 if he had been at ,cambridge1 but he was a shy and solitary youth1 and just as likely he might not4 ,up in ,lincolnshire1 in the seventeenth century1 who was there for him to consult8 ,true1 he might have rushed into premature publication1 after our nineteenth century fashion1 but that was not his method4 ,publication never seemed to have occurred to him4 ,his reticence now is noteworthy1 but later on it is perfectly astonishing4 ,he is so absorbed in making discoveries that he actually has to be reminded to tell any one about them1 and some one else always has to see to the printing and publishing for him4 ,i have entered thus fully into what ,i conjecture to be the stages of this early discovery of the law of gravitation1 as applicable to the heavenly bodies1 because it is frequently and commonly misunderstood4 ,it is sometimes thought that he discovered the force of gravity2 ,i hope ,i have made it clear that he did no such thing4 ,every educated man long before his time1 if asked why bodies fell1 would reply just as glibly as they do now1 ,because the earth attracts them1 or because of the force of gravity4 ,his discovery was that the motions of the solar system were due to the action of a central force1 directed to the body at the centre of the system1 and varying inversely with the square of the distance from it4 ,this discovery was based upon ,kepler's laws1 and was clear and certain4 ,it might have been published had he so chosen4 ,but he did not like hypothetical and unknown forces2 he tried to see whether the known force of gravity would serve4 ,this discovery at that time he failed to make1 owing to a wrong numerical datum4 ,the size of the earth he only knew from the common doctrine of sailors that #fj miles make a degree2 and that threw him out4 ,instead of falling #af feet a minute1 as it ought under gravity1 it only fell #aci feet1 so he abandoned the idea4 ,we do not find that he returned to it for sixteen years4 ,,lecture ,,viii ,,newton ,,and ,,the ,,law ,,of ,,gravitation ,we left ,newton at the age of twenty-three on the verge of discovering the mechanism of the solar system1 deterred therefrom only by an error in the then imagined size of the earth4 ,he had proved from ,kepler's laws that a centripetal force directed to the sun1 and varying as the inverse square of the distance from that body1 would account for the observed planetary motions1 and that a similar force directed to the earth would account for the lunar motion2 and it had struck him that this force might be the very same as the familiar force of gravitation which gave to bodies their weight3 but in attempting a numerical verification of this idea in the case of the moon he was led by the then received notion that sixty miles made a degree on the earth's surface into an erroneous estimate of the size of the moon's orbit4 ,being thus baffled in obtaining such verification1 he laid the matter aside for a time4 ,the anecdote of the apple we learn from ,voltaire1 who had it from ,newton's favourite niece1 who with her husband lived and kept house for him all his later life4 ,it is very like one of those anecdotes which are easily invented and believed in1 and very often turn out on scrutiny to have no foundation4 ,fortunately this anecdote is well authenticated1 and moreover is intrinsically probable2 ,i say fortunately1 because it is always painful to have to give up these child-learnt anecdotes1 like ,alfred and the cakes and so on4 ,this anecdote of the apple we need not resign4 ,the tree was blown down in #ahbj and part of its wood is preserved4 ,i have mentioned ,voltaire in connection with ,newton's philosophy4 ,this acute critic at a later stage did a good deal to popularise it throughout ,europe and to overturn that of his own countryman ,descartes4 ,cambridge rapidly became ,newtonian1 but ,oxford remained ,cartesian for fifty years or more4 ,it is curious what little hold science and mathematics have ever secured in the older and more ecclesiastical ,university4 ,the pride of possessing ,newton has however no doubt been the main stimulus to the special pursuits of ,cambridge4 ,he now began to turn his attention to optics1 and1 as was usual with him1 his whole mind became absorbed in this subject as if nothing else had ever occupied him4 ,his cash-book for this time has been discovered1 and the entries show that he is buying prisms and lenses and polishing powder at the beginning of #affg4 ,he was anxious to improve telescopes by making more perfect lenses than had ever been used before4 ,accordingly he calculated out their proper curves1 just as ,descartes had also done1 and then proceeded to grind them as near as he could to those figures4 ,but the images did not please him2 they were always blurred and rather indistinct4 ,at length1 it struck him that perhaps it was not the lenses but the light which was at fault4 ,perhaps light was so composed that it could not be focused accurately to a sharp and definite point4 ,perhaps the law of refraction was not quite accurate1 but only an approximation4 ,so he bought a prism to try the law4 ,he let in sunlight through a small round hole in a window shutter1 inserted the prism in the light1 and received the deflected beam on a white screen2 turning the prism about till it was deviated as little as possible4 ,the patch on the screen was not a round disk1 as it would have been without the prism1 but was an elongated oval and was coloured at its extremities4 ,evidently refraction was not a simple geometrical deflection of a ray1 there was a spreading out as well4 ,illustration3 ,,fig4 #fc4--;,a prism not only deviates a beam of sunlight1 but also spreads it out or disperses it4 ,why did the image thus spread out8 ,if it were due to irregularities in the glass a second prism should rather increase them1 but a second prism when held in appropriate position was able to neutralise the dispersion and to reproduce the simple round white spot without deviation4 ,evidently the spreading out of the beam was connected in some definite way with its refraction4 ,could it be that the light particles after passing through the prism travelled in variously curved lines1 as spinning racquet balls do8 ,to examine this he measured the length of the oval patch when the screen was at different distances from the prism1 and found that the two things were directly proportional to each other4 ,doubling the distance of the screen doubled the length of the patch4 ,hence the rays travelled in straight lines from the prism1 and the spreading out was due to something that occurred within its substance4 ,could it be that white light was compound1 was a mixture of several constituents1 and that its different constituents were differently bent8 ,no sooner thought than tried4 ,pierce the screen to let one of the constituents through and interpose a second prism in its path4 ,if the spreading out depended on the prism only it should spread out just as much as before1 but if it depended on the complex character of white light1 this isolated simple constituent should be able to spread out no more4 ,it did not spread out any more3 a prism had no more dispersive power over it2 it was deflected by the appropriate amount1 but it was not analysed into constituents4 ,it differed from sunlight in being simple4 ,with many ingenious and beautifully simple experiments1 which are quoted in full in several books on optics1 he clinched the argument and established his discovery4 ,white light was not simple but compound4 ,it could be sorted out by a prism into an infinite number of constituent parts which were differently refracted1 and the most striking of which ,newton named violet1 indigo1 blue1 green1 yellow1 orange1 and red4 ,illustration3 ,,fig4 #fd4--;,a single constituent of white light1 obtained by the use of perforated screens is capable of no more dispersion4 ,at once the true nature of colour became manifest4 ,colour resided not in the coloured object as had till now been thought1 but in the light which illuminated it4 ,red glass for instance adds nothing to sunlight4 ,the light does not get dyed red by passing through the glass2 all that the red glass does is to stop and absorb a large part of the sunlight2 it is opaque to the larger portion1 but it is transparent to that particular portion which affects our eyes with the sensation of red4 ,the prism acts like a sieve sorting out the different kinds of light4 ,coloured media act like filters1 stopping certain kinds but allowing the rest to go through4 ,leonardo's and all the ancient doctrines of colour had been singularly wrong2 colour is not in the object but in the light4 ,goethe1 in his ,farbenlehre1 endeavoured to controvert ,newton1 and to reinstate something more like the old views2 but his failure was complete4 ,refraction analysed out the various constituents of white light and displayed them in the form of a series of overlapping images of the aperture1 each of a different colour2 this series of images we call a spectrum1 and the operation we now call spectrum analysis4 ,the reason of the defect of lenses was now plain3 it was not so much a defect of the lens as a defect of light4 ,a lens acts by refraction and brings rays to a focus4 ,if light be simple it acts well1 but if ordinary white light fall upon a lens1 its different constituents have different foci2 every bright object is fringed with colour1 and nothing like a clear image can be obtained4 ,illustration3 ,,fig4 #fe4--,showing the boundary rays of a parallel beam passing through a lens4 ,a parallel beam passing through a lens becomes conical2 but instead of a single cone it is a sheaf or nest of cones1 all having the edge of the lens as base1 but each having a different vertex4 ,the violet cone is innermost1 near the lens1 the red cone outermost1 while the others lie between4 ,beyond the crossing point or focus the order of cones is reversed1 as the above figure shows4 ,only the two marginal rays of the beam are depicted4 ,if a screen be held anywhere nearer the lens than the place marked #a there will be a whitish centre to the patch of light and a red and orange fringe or border4 ,held anywhere beyond the region #b1 the border of the patch will be blue and violet4 ,held about #c the colour will be less marked than elsewhere1 but nowhere can it be got rid of4 ,each point of an object will be represented in the image not by a point but by a coloured patch3 a fact which amply explains the observed blurring and indistinctness4 ,newton measured and calculated the distance between the violet and red foci--,,vr in the diagram--and showed that it was #a_/ejth the diameter of the lens4 ,to overcome this difficulty 7called chromatic aberration7 telescope glasses were made small and of very long focus3 some of them so long that they had no tube1 all of them egregiously cumbrous4 ,yet it was with such instruments that all the early discoveries were made4 ,with such an instrument1 for instance1 ,huyghens discovered the real shape of ,saturn's ring4 ,the defects of refractors seemed irremediable1 being founded in the nature of light itself4 ,so he gave up his glass works2 and proceeded to think of reflexion from metal specula4 ,a concave mirror forms an image just as a lens does1 but since it does so without refraction or transmission through any substance1 there is no accompanying dispersion or chromatic aberration4 ,the first reflecting telescope he made was #a in4 diameter and #f in4 long1 and magnified forty times4 ,it acted as well as a three or four feet refractor of that day1 and showed ,jupiter's moons4 ,so he made a larger one1 now in the library of the ,royal ,society1 ,london1 with an inscription3 ,the first reflecting telescope1 invented by ,sir ,isaac ,newton1 and made with his own hands4 ,this has been the parent of most of the gigantic telescopes of the present day4 ,fifty years elapsed before it was much improved on1 and then1 first by ,hadley and afterwards by ,herschel and others1 large and good reflectors were constructed4 ,the largest telescope ever made1 that of ,lord ,rosse1 is a ,newtonian reflector1 fifty feet long1 six feet diameter1 with a mirror weighing four tons4 ,the sextant1 as used by navigators1 was also invented by ,newton4 ,the year after the plague1 in #affg1 ,newton returned to ,trinity ,college1 and there continued his experiments on optics4 ,it is specially to be noted that at this time1 at the age of twenty-four1 ,newton had laid the foundations of all his greatest discoveries3-- ,illustration3 ,,fig4 #ff4--,newton's telescope4 ,the ,theory of ,fluxions2 or1 the ,differential ,calculus4 ,the ,law of ,gravitation2 or1 the complete theory of astronomy4 ,the compound nature of white light2 or1 the beginning of ,spectrum ,analysis4 ,illustration3 ,,fig4 #fg4--,the sextant1 as now made4 ,his later life was to be occupied in working these incipient discoveries out4 ,but the most remarkable thing is that no one knew about any one of them4 ,however1 he was known as an accomplished young mathematician1 and was made a fellow of his college4 ,you remember that he had a friend there in the person of ,dr4 ,isaac ,barrow1 first ,lucasian ,professor of ,mathematics in the ,university4 ,it happened1 about #affi1 that a mathematical discovery of some interest was being much discussed1 and ,dr4 ,barrow happened to mention it to ,newton1 who said yes1 he had worked out that and a few other similar things some time ago4 ,he accordingly went and fetched some papers to ,dr4 ,barrow1 who forwarded them to other distinguished mathematicians1 and it thus appeared that ,newton had discovered theorems much more general than this special case that was exciting so much interest4 ,dr4 ,barrow1 being anxious to devote his time more particularly to theology1 resigned his chair the same year in favour of ,newton1 who was accordingly elected to the ,lucasian ,professorship1 which he held for thirty years4 ,this chair is now the most famous in the ,university1 and it is commonly referred to as the chair of ,newton4 ,still1 however1 his method of fluxions was unknown1 and still he did not publish it4 ,he lectured first on optics1 giving an account of his experiments4 ,his lectures were afterwards published both in ,latin and ,english1 and are highly valued to this day4 ,the fame of his mathematical genius came to the ears of the ,royal ,society1 and a motion was made to get him elected a fellow of that body4 ,the ,royal ,society1 the oldest and most famous of all scientific societies with a continuous existence1 took its origin in some private meetings1 got up in ,london by the ,hon4 ,robert ,boyle and a few scientific friends1 during all the trouble of the ,commonwealth4 ,after the restoration1 ,charles ,,ii4 in #affb incorporated it under ,royal ,charter2 among the original members being ,boyle1 ,hooke1 ,christopher ,wren1 and other less famous names4 ,boyle was a great experimenter1 a worthy follower of ,dr4 ,gilbert4 ,hooke began as his assistant1 but being of a most extraordinary ingenuity he rapidly rose so as to exceed his master in importance4 ,fate has been a little unkind to ,hooke in placing him so near to ,newton2 had he lived in an ordinary age he would undoubtedly have shone as a star of the first magnitude4 ,with great ingenuity1 remarkable scientific insight1 and consummate experimental skill1 he stands in many respects almost on a level with ,galileo4 ,but it is difficult to see stars even of the first magnitude when the sun is up1 and thus it happens that the name and fame of this brilliant man are almost lost in the blaze of ,newton4 ,of ,christopher ,wren ,i need not say much4 ,he is well known as an architect1 but he was a most accomplished all-round man1 and had a considerable taste and faculty for science4 ,these then were the luminaries of the ,royal ,society at the time we are speaking of1 and to them ,newton's first scientific publication was submitted4 ,he communicated to them an account of his reflecting telescope1 and presented them with the instrument4 ,their reception of it surprised him2 they were greatly delighted with it1 and wrote specially thanking him for the communication1 and assuring him that all right should be done him in the matter of the invention4 ,the ,bishop of ,salisbury 7,bishop ,burnet7 proposed him for election as a fellow1 and elected he was4 ,in reply1 he expressed his surprise at the value they set on the telescope1 and offered1 if they cared for it1 to send them an account of a discovery which he doubts not will prove much more grateful than the communication of that instrument1 being in my judgment the oddest1 if not the most considerable detection that has recently been made into the operations of ,nature4 ,so he tells them about his optical researches and his discovery of the nature of white light1 writing them a series of papers which were long afterwards incorporated and published as his ,optics4 ,a magnificent work1 which of itself suffices to place its author in the first rank of the world's men of science4 ,the nature of white light1 the true doctrine of colour1 and the differential calculus6 besides a good number of minor results--binomial theorem1 reflecting telescope1 sextant1 and the like2 one would think it enough for one man's life-work1 but the masterpiece remains still to be mentioned4 ,it is as when one is considering ,shakspeare3 ,king ,lear1 ,macbeth1 ,othello1--surely a sufficient achievement1--but the masterpiece remains4 ,comparisons in different departments are but little help perhaps1 nevertheless it seems to me that in his own department1 and considered simply as a man of science1 ,newton towers head and shoulders over1 not only his contemporaries--that is a small matter--but over every other scientific man who has ever lived1 in a way that we can find no parallel for in other departments4 ,other nations admit his scientific pre-eminence with as much alacrity as we do4 ,well1 we have arrived at the year #afgb and his election to the ,royal ,society4 ,during the first year of his membership there was read at one of the meetings a paper giving an account of a very careful determination of the length of a degree 7i4e4 of the size of the earth71 which had been made by ,picard near ,paris4 ,the length of the degree turned out to be not sixty miles1 but nearly seventy miles4 ,how soon ,newton heard of this we do not learn--probably not for some years1--,cambridge was not so near ,london then as it is now1 but ultimately it was brought to his notice4 ,armed with this new datum1 his old speculation concerning gravity occurred to him4 ,he had worked out the mechanics of the solar system on a certain hypothesis1 but it had remained a hypothesis somewhat out of harmony with apparent fact4 ,what if it should turn out to be true after all6 ,he took out his old papers and began again the calculation4 ,if gravity were the force keeping the moon in its orbit1 it would fall toward the earth sixteen feet every minute4 ,how far did it fall8 ,the newly known size of the earth would modify the figures3 with intense excitement he runs through the working1 his mind leaps before his hand1 and as he perceives the answer to be coming out right1 all the infinite meaning and scope of his mighty discovery flashes upon him1 and he can no longer see the paper4 ,he throws down the pen2 and the secret of the universe is1 to one man1 known4 ,but of course it had to be worked out4 ,the meaning might flash upon him1 but its full detail required years of elaboration2 and deeper and deeper consequences revealed themselves to him as he proceeded4 ,for two years he devoted himself solely to this one object4 ,during those years he lived but to calculate and think1 and the most ludicrous stories are told concerning his entire absorption and inattention to ordinary affairs of life4 ,thus1 for instance1 when getting up in a morning he would sit on the side of the bed half-dressed1 and remain like that till dinner time4 ,often he would stay at home for days together1 eating what was taken to him1 but without apparently noticing what he was doing4 ,one day an intimate friend1 ,dr4 ,stukely1 called on him and found on the table a cover laid for his solitary dinner4 ,after waiting a long time1 ,dr4 ,stukely removed the cover and ate the chicken underneath it1 replacing and covering up the bones again4 ,at length ,newton appeared1 and after greeting his friend1 sat down to dinner1 but on lifting the cover he said in surprise1 ,dear me1 ,i thought ,i had not dined1 but ,i see ,i have4 ,it was by this continuous application that the ,principia was accomplished4 ,probably nothing of the first magnitude can be accomplished without something of the same absorbed unconsciousness and freedom from interruption4 ,but though desirable and essential for the work1 it was a severe tax upon the powers of the man4 ,there is1 in fact1 no doubt that ,newton's brain suffered temporary aberration after this effort for a short time4 ,the attack was slight1 and it has been denied2 but there are letters extant which are inexplicable otherwise1 and moreover after a year or two he writes to his friends apologizing for strange and disjointed epistles1 which he believed he had written without understanding clearly what he wrote4 ,the derangement was1 however1 both slight and temporary3 and it is only instructive to us as showing at what cost such a work as the ,principia must be produced1 even by so mighty a mind as that of ,newton4 ,the first part of the work having been done1 any ordinary mortal would have proceeded to publish it2 but the fact is that after he had sent to the ,royal ,society his papers on optics1 there had arisen controversies and objections2 most of them rather paltry1 to which he felt compelled to find answers4 ,many men would have enjoyed this part of the work1 and taken it as evidence of interest and success4 ,but to ,newton's shy and retiring disposition these discussions were merely painful4 ,he writes1 indeed1 his answers with great patience and ability1 and ultimately converts the more reasonable of his opponents1 but he relieves his mind in the following letter to the secretary of the ,royal ,society3 ,i see ,i have made myself a slave to philosophy1 but if ,i get free of this present business ,i will resolutely bid adieu to it eternally1 except what ,i do for my private satisfaction or leave to come out after me2 for ,i see a man must either resolve to put out nothing new1 or to become a slave to defend it4 ,and again in a letter to ,leibnitz3 ,i have been so persecuted with discussions arising out of my theory of light that ,i blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow4 ,this shows how much he cared for contemporary fame4 ,so he locked up the first part of the ,principia in his desk1 doubtless intending it to be published after his death4 ,but fortunately this was not so to be4 ,in #afhc1 among the leading lights of the ,royal ,society1 the same sort of notions about gravity and the solar system began independently to be bruited4 ,the theory of gravitation seemed to be in the air1 and ,wren1 ,hooke1 and ,halley had many a talk about it4 ,hooke showed an experiment with a pendulum1 which he likened to a planet going round the sun4 ,the analogy is more superficial than real4 ,it does not obey ,kepler's laws2 still it was a striking experiment4 ,they had guessed at a law of inverse squares1 and their difficulty was to prove what curve a body subject to it would describe4 ,they knew it ought to be an ellipse if it was to serve to explain the planetary motion1 and ,hooke said he could prove that an ellipse it was2 but he was nothing of a mathematician1 and the others scarcely believed him4 ,undoubtedly he had shrewd inklings of the truth1 though his guesses were based on little else than a most sagacious intuition4 ,he surmised also that gravity was the force concerned1 and asserted that the path of an ordinary projectile was an ellipse1 like the path of a planet--which is quite right4 ,in fact the beginnings of the discovery were beginning to dawn upon him in the well-known way in which things do dawn upon ordinary men of genius3 and had ,newton not lived we should doubtless1 by the labours of a long chain of distinguished men1 beginning with ,hooke1 ,wren1 and ,halley1 have been now in possession of all the truths revealed by the ,principia4 ,we should never have had them stated in the same form1 nor proved with the same marvellous lucidity and simplicity1 but the facts themselves we should by this time have arrived at4 ,their developments and completions1 due to such men as ,clairaut1 ,euler1 ,d',alembert1 ,lagrange1 ,laplace1 ,airy1 ,leverrier1 ,adams1 we should of course not have had to the same extent2 because the lives and energies of these great men would have been partially consumed in obtaining the main facts themselves4 ,the youngest of the three questioners at the time we are speaking of was ,edmund ,halley1 an able and remarkable man4 ,he had been at ,cambridge1 doubtless had heard ,newton lecture1 and had acquired a great veneration for him4 ,in ,january1 #afhd1 we find ,wren offering ,hooke and ,halley a prize1 in the shape of a book worth forty shillings1 if they would either of them bring him within two months a demonstration that the path of a planet subject to an inverse square law would be an ellipse4 ,not in two months1 nor yet in seven1 was there any proof forthcoming4 ,so at last1 in ,august1 ,halley went over to ,cambridge to speak to ,newton about the difficult problem and secure his aid4 ,arriving at his rooms he went straight to the point4 ,he said1 ,what path will a body describe if it be attracted by a centre with a force varying as the inverse square of the distance4 ,to which ,newton at once replied1 ,an ellipse4 ,how on earth do you know8 said ,halley in amazement4 ,why1 ,i have calculated it1 and began hunting about for the paper4 ,he actually couldn't find it just then1 but sent it him shortly by post1 and with it much more--in fact1 what appeared to be a complete treatise on motion in general4 ,with his valuable burden ,halley hastened to the ,royal ,society and told them what he had discovered4 ,the ,society at his representation wrote to ,mr4 ,newton asking leave that it might be printed4 ,to this he consented2 but the ,royal ,society wisely appointed ,mr4 ,halley to see after him and jog his memory1 in case he forgot about it4 ,however1 he set to work to polish it up and finish it1 and added to it a great number of later developments and embellishments1 especially the part concerning the lunar theory1 which gave him a deal of trouble--and no wonder2 for in the way he has put it there never was a man yet living who could have done the same thing4 ,mathematicians regard the achievement now as men might stare at the work of some demigod of a bygone age1 wondering what manner of man this was1 able to wield such ponderous implements with such apparent ease4 ,to ,halley the world owes a great debt of gratitude--first1 for discovering the ,principia2 second1 for seeing it through the press2 and third1 for defraying the cost of its publication out of his own scanty purse4 ,for though he ultimately suffered no pecuniary loss1 rather the contrary1 yet there was considerable risk in bringing out a book which not a dozen men living could at the time comprehend4 ,it is no small part of the merit of ,halley that he recognized the transcendent value of the yet unfinished work1 that he brought it to light1 and assisted in its becoming understood to the best of his ability4 ,though ,halley afterwards became ,astronomer-,royal1 lived to the ripe old age of eighty-six1 and made many striking observations1 yet he would be the first to admit that nothing he ever did was at all comparable in importance with his discovery of the ,principia2 and he always used to regard his part in it with peculiar pride and pleasure4 ,and how was the ,principia received8 ,considering the abstruse nature of its subject1 it was received with great interest and enthusiasm4 ,in less than twenty years the edition was sold out1 and copies fetched large sums4 ,we hear of poor students copying out the whole in manuscript in order to possess a copy--not by any means a bad thing to do1 however many copies one may possess4 ,the only useful way really to read a book like that is to pore over every sentence3 it is no book to be skimmed4 ,while the ,principia was preparing for the press a curious incident of contact between ,english history and the ,university occurred4 ,it seems that ,james ,,ii41 in his policy of ,catholicising the country1 ordered both ,universities to elect certain priests to degrees without the ordinary oaths4 ,oxford had given way1 and the ,dean of ,christ ,church was a creature of ,james's choosing4 ,cambridge rebelled1 and sent eight of its members1 among them ,mr4 ,newton1 to plead their cause before the ,court of ,high ,commission4 ,judge ,jeffreys presided over the ,court1 and threatened and bullied with his usual insolence4 ,the ,vice-,chancellor of ,cambridge was deprived of office1 the other deputies were silenced and ordered away4 ,from the precincts of this court of justice ,newton returned to ,trinity ,college to complete the ,principia4 ,by this time ,newton was only forty-five years old1 but his main work was done4 ,his method of fluxions was still unpublished2 his optics was published only imperfectly2 a second edition of the ,principia1 with additions and improvements1 had yet to appear2 but fame had now come upon him1 and with fame worries of all kinds4 ,by some fatality1 principally no doubt because of the interest they excited1 every discovery he published was the signal for an outburst of criticism and sometimes of attack4 ,i shall not go into these matters3 they are now trivial enough1 but it is necessary to mention them1 because to ,newton they evidently loomed large and terrible1 and occasioned him acute torment4 ,illustration3 ,,fig4 #fh4--,newton when young4 7,from an engraving by ,b4 ,reading after ,sir ,peter ,lely47 ,no sooner was the ,principia put than ,hooke put in his claims for priority4 ,and indeed his claims were not altogether negligible2 for vague ideas of the same sort had been floating in his comprehensive mind1 and he doubtless felt indistinctly conscious of a great deal more than he could really state or prove4 ,by indiscreet friends these two great men were set somewhat at loggerheads1 and worse might have happened had they not managed to come to close quarters1 and correspond privately in a quite friendly manner1 instead of acting through the mischievous medium of third parties4 ,in the next edition ,newton liberally recognizes the claims of both ,hooke and ,wren4 ,however1 he takes warning betimes of what he has to expect1 and writes to ,halley that he will only publish the first two books1 those containing general theorems on motion4 ,the third book--concerning the system of the world1 i4e4 the application to the solar system--he says ,i now design to suppress4 ,philosophy is such an impertinently litigious lady that a man had as good be engaged in law-suits as have to do with her4 ,i found it so formerly1 and now ,i am no sooner come near her again but she gives me warning4 ,the two books without the third will not so well bear the title ',mathematical ,principles of ,natural ,philosophy1' and therefore ,i had altered it to this1 ',on the ,free ,motion of ,two ,bodies'2 but on second thoughts ,i retain the former title3 'twill help the sale of the book--which ,i ought not to diminish now 'tis yours4 ,however1 fortunately1 ,halley was able to prevail upon him to publish the third book also4 ,it is1 indeed1 the most interesting and popular of the three1 as it contains all the direct applications to astronomy of the truths established in the other two4 ,some years later1 when his method of fluxions was published1 another and a worse controversy arose--this time with ,leibnitz1 who had also independently invented the differential calculus4 ,it was not so well recognized then how frequently it happens that two men independently and unknowingly work at the very same thing at the same time4 ,the history of science is now full of such instances2 but then the friends of each accused the other of plagiarism4 ,i will not go into the controversy3 it is painful and useless4 ,it only served to embitter the later years of two great men1 and it continued long after ,newton's death--long after both their deaths4 ,it can hardly be called ancient history even now4 ,but fame brought other and less unpleasant distractions than controversies4 ,we are a curious1 practical1 and rather stupid people1 and our one idea of honouring a man is to vote for him in some way or other2 so they sent ,newton to ,parliament4 ,he went1 ,i believe1 as a ,whig1 but it is not recorded that he spoke4 ,it is1 in fact1 recorded that he was once expected to speak when on a ,royal ,commission about some question of chronometers1 but that he would not4 ,however1 ,i dare say he made a good average member4 ,then a little later it was realized that ,newton was poor1 that he still had to teach for his livelihood1 and that though the ,crown had continued his fellowship to him as ,lucasian ,professor without the necessity of taking orders1 yet it was rather disgraceful that he should not be better off4 ,so an appeal was made to the ,government on his behalf1 and ,lord ,halifax1 who exerted himself strongly in the matter1 succeeding to office on the accession of ,william ,,iii41 was able to make him ultimately ,master of the ,mint1 with a salary of some #a1bjj a year4 ,i believe he made rather a good ,master1 and turned out excellent coins3 certainly he devoted his attention to his work there in a most exemplary manner4 ,but what a pitiful business it all is6 ,here is a man sent by ,heaven to do certain things which no man else could do1 and so long as he is comparatively unknown he does them2 but so soon as he is found out1 he is clapped into a routine office with a big salary3 and there is1 comparatively speaking1 an end of him4 ,it is not to be supposed that he had lost his power1 for he frequently solved problems very quickly which had been given out by great ,continental mathematicians as a challenge to the world4 ,we may ask why ,newton allowed himself to be thus bandied about instead of settling himself down to the work in which he was so pre-eminently great4 ,well1 ,i expect your truly great man never realizes how great he is1 and seldom knows where his real strength lies4 ,certainly ,newton did not know it4 ,he several times talks of giving up philosophy altogether2 and though he never really does it1 and perhaps the feeling is one only born of some temporary overwork1 yet he does not sacrifice everything else to it as he surely must had he been conscious of his own greatness4 ,no2 self-consciousness was the last thing that affected him4 ,it is for a great man's contemporaries to discover him1 to make much of him1 and to put him in surroundings where he may flourish luxuriantly in his own heaven-intended way4 ,however1 it is difficult for us to judge of these things4 ,perhaps if he had been maintained at the national expense to do that for which he was preternaturally fitted1 he might have worn himself out prematurely2 whereas by giving him routine work the scientific world got the benefit of his matured wisdom and experience4 ,it was no small matter to the young ,royal ,society to be able to have him as their ,president for twenty-four years4 ,his portrait has hung over the ,president's chair ever since1 and there ,i suppose it will continue to hang until the ,royal ,society becomes extinct4 ,the events of his later life ,i shall pass over lightly4 ,he lived a calm1 benevolent life1 universally respected and beloved4 ,his silver-white hair when he removed his peruke was a venerable spectacle4 ,a lock of it is still preserved1 with many other relics1 in the library of ,trinity ,college4 ,he died quietly1 after a painful illness1 at the ripe age of eighty-five4 ,his body lay in state in the ,jerusalem ,chamber1 and he was buried in ,westminster ,abbey1 six peers bearing the pall4 ,these things are to be mentioned to the credit of the time and the country2 for after we have seen the calamitous spectacle of the way ,tycho and ,kepler and ,galileo were treated by their ungrateful and unworthy countries1 it is pleasant to reflect that ,england1 with all its mistakes1 yet recognized her great man when she received him1 and honoured him with the best she knew how to give4 ,illustration3 ,,fig4 #fi4--,sir ,isaac ,newton4 ,concerning his character1 one need only say that it was what one would expect and wish4 ,it was characterized by a modest1 calm1 dignified simplicity4 ,he lived frugally with his niece and her husband1 ,mr4 ,conduit1 who succeeded him as ,master of the ,mint4 ,he never married1 nor apparently did he ever think of so doing4 ,the idea1 perhaps1 did not naturally occur to him1 any more than the idea of publishing his work did4 ,he was always a deeply religious man and a sincere ,christian1 though somewhat of the ,arian or ,unitarian persuasion--so1 at least1 it is asserted by orthodox divines who understand these matters4 ,he studied theology more or less all his life1 and towards the end was greatly interested in questions of ,biblical criticism and chronology4 ,by some ancient eclipse or other he altered the recognized system of dates a few hundred years2 and his book on the prophecies of ,daniel and the ,revelation of ,st4 ,john1 wherein he identifies the beast with the ,church of ,rome in quite the orthodox way1 is still by some admired4 ,but in all these matters it is probable that he was a merely ordinary man1 with natural acumen and ability doubtless1 but nothing in the least superhuman4 ,in science1 the impression he makes upon me is only expressible by the words inspired1 superhuman4 ,and yet if one realizes his method of work1 and the calm1 uninterrupted flow of all his earlier life1 perhaps his achievements become more intelligible4 ,when asked how he made his discoveries1 he replied3 ,by always thinking unto them4 ,i keep the subject constantly before me1 and wait till the first dawnings open slowly by little and little into a full and clear light4 ,that is the way--quiet1 steady1 continuous thinking1 uninterrupted and unharassed brooding4 ,much may be done under those conditions4 ,much ought to be sacrificed to obtain those conditions4 ,all the best thinking work of the world has been thus done4#ah ,buffon said3 ,genius is patience4 ,so says ,newton3 ,if ,i have done the public any service this way1 it is due to nothing but industry and patient thought4 ,genius patience8 ,no1 it is not quite that1 or1 rather1 it is much more than that2 but genius without patience is like fire without fuel--it will soon burn itself out4 ,,notes ,,for ,,lecture ,,ix ,the ,principia published #afhg4 ,newton died #agbg4 ,,the ,,law ,,of ,,gravitation4--,every particle of matter attracts every other particle of matter with a force proportional to the mass of each and to the inverse square of the distance between them4 ,,some ,,of ,,newton',s ,,deductions4 #a4 ,kepler's second law 7equable description of areas7 proves that each planet is acted on by a force directed towards the sun as a centre of force4 #b4 ,kepler's first law proves that this central force diminishes in the same proportion as the square of the distance increases4 #c4 ,kepler's third law proves that all the planets are acted on by the same kind of force2 of an intensity depending on the mass of the sun4#ai #d4 ,so by knowing the length of year and distance of any planet from the sun1 the sun's mass can be calculated1 in terms of that of the earth4 #e4 ,for the satellites1 the force acting depends on the mass of their central body1 a planet4 ,hence the mass of any planet possessing a satellite becomes known4 #f4 ,the force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles4 ,because1 while a stone drops #af feet in a second1 the moon1 which is #fj times as far from the centre of the earth1 drops #af feet in a minute4 99 99 99 99 99 #g4 ,the moon is attracted not only by the earth1 but by the sun also2 hence its orbit is perturbed1 and ,newton calculated out the chief of these perturbations1 viz43-- 7,the equation of the centre1 discovered by ,hipparchus47 7a7 ,the evection1 discovered by ,hipparchus and ,ptolemy4 7b7 ,the variation1 discovered by ,tycho ,brah4 7c7 ,the annual equation1 discovered by ,tycho ,brah4 7d7 ,the retrogression of the nodes1 then being observed at ,greenwich by ,flamsteed4 7e7 ,the variation of inclination1 then being observed at ,greenwich by ,flamsteed4 7f7 ,the progression of the apses 7with an error of one-half74 7g7 ,the inequality of apogee1 previously unknown4 7h7 ,the inequality of nodes1 previously unknown4 #h4 ,each planet is attracted not only by the sun but by the other planets1 hence their orbits are slightly affected by each other4 ,newton began the theory of planetary perturbations4 #i4 ,he recognized the comets as members of the solar system1 obedient to the same law of gravity and moving in very elongated ellipses2 so their return could be predicted 7e4g4 ,halley's comet74 #aj4 ,applying the idea of centrifugal force to the earth considered as a rotating body1 he perceived that it could not be a true sphere1 and calculated its oblateness1 obtaining #bh miles greater equatorial than polar diameter4 #aa4 ,conversely1 from the observed shape of ,jupiter1 or any planet1 the length of its day could be estimated4 #ab4 ,the so-calculated shape of the earth1 in combination with centrifugal force1 causes the weight of bodies to vary with latitude2 and ,newton calculated the amount of this variation4 #aid lbs4 at pole balance #aie lbs4 at equator4 #ac4 ,a homogeneous sphere attracts as if its mass were concentrated at its centre4 ,for any other figure1 such as an oblate spheroid1 this is not exactly true4 ,a hollow concentric spherical shell exerts no force on small bodies inside it4 #ad4 ,the earth's equatorial protuberance1 being acted on by the attraction of the sun and moon1 must disturb its axis of rotation in a calculated manner2 and thus is produced the precession of the equinoxes4 ,the attraction of the planets on the same protuberance causes a smaller and rather different kind of precession4 #ae4 ,the waters of the ocean are attracted towards the sun and moon on one side1 and whirled a little further away than the solid earth on the other side3 hence ,newton explained all the main phenomena of the tides4 #af4 ,the sun's mass being known1 he calculated the height of the solar tide4 #ag4 ,from the observed heights of spring and neap tides he determined the lunar tide1 and thence made an estimate of the mass of the moon4 ,,reference ,,table ,,of ,,numerical ,,data4 ---------------------------------------- ----------------------- ,masses in ,solar ,height dropped by a ,length of ,day or ,system4 stone in first second4time of rotation4 ---------------------------------------- ----------------------- ,mercury #jfe #gj feet #bd hours ,venus #hhe #aeh #bc-a_/b ,earth #ajjj #afa #bd ,mars #ajh #fb #bd-a_/b ,jupiter #cjjh #dej #aj ,saturn #hig #ahd #aj-a_/b ,the ,sun #cafjjj #dcfj #fjh ,the ,moon about #jab #cg #gjb ---------------------------------------- ----------------------- ,the mass of the earth1 taken above as unity1 is #f1jjj trillion tons4 ,observatories4--,uraniburg flourished from #aegf to #aeig2 the ,observatory of ,paris was founded in #affg2 ,greenwich ,observatory in #afge4 ,astronomers-,royal4--,flamsteed1 ,halley1 ,bradley1 ,bliss1 ,maskelyne1 ,pond1 ,airy1 ,christie4 ,,lecture ,,ix ,,newton',s ,,principia ,the law of gravitation1 above enunciated1 in conjunction with the laws of motion rehearsed at the end of the preliminary notes of ,lecture ,,vii41 now supersedes the laws of ,kepler and includes them as special cases4 ,the more comprehensive law enables us to criticize ,kepler's laws from a higher standpoint1 to see how far they are exact and how far they are only approximations4 ,they are1 in fact1 not precisely accurate1 but the reason for every discrepancy now becomes abundantly clear1 and can be worked out by the theory of gravitation4 ,we may treat ,kepler's laws either as immediate consequences of the law of gravitation1 or as the known facts upon which that law was founded4 ,historically1 the latter is the more natural plan1 and it is thus that they are treated in the first three statements of the above notes2 but each proposition may be worked inversely1 and we might state them thus3-- #a4 ,the fact that the force acting on each planet is directed to the sun1 necessitates the equable description of areas4 #b4 ,the fact that the force varies as the inverse square of the distance1 necessitates motion in an ellipse1 or some other conic section1 with the sun in one focus4 #c4 ,the fact that one attracting body acts on all the planets with an inverse square law1 causes the cubes of their mean distances to be proportional to the squares of their periodic times4 ,not only these but a multitude of other deductions follow rigorously from the simple datum that every particle of matter attracts every other particle with a force directly proportional to the mass of each and to the inverse square of their mutual distance4 ,those dealt with in the ,principia are summarized above1 and it will be convenient to run over them in order1 with the object of giving some idea of the general meaning of each1 without attempting anything too intricate to be readily intelligible4 ,illustration3 ,,fig4 #gj4 ,no4 #a4 ,kepler's second law 7equable description of areas7 proves that each planet is acted on by a force directed towards the sun as a centre of force4 ,the equable description of areas about a centre of force has already been fully1 though briefly1 established4 7p4 #age47 ,it is undoubtedly of fundamental importance1 and is the earliest instance of the serious discussion of central forces1 i4e4 of forces directed always to a fixed centre4 ,we may put it afresh thus3--,,oa has been the motion of a particle in a unit of time2 at ,a it receives a knock towards ,c1 whereby in the next unit it travels along ,,ad instead of ,,ab4 ,now the area of the triangle ,,cad1 swept out by the radius vector in unit time1 is #a_/b;bh2 h being the perpendicular height of the triangle from the base ,,ac4 7,fig4 #gj47 ,now the blow at ,a1 being along the base1 has no effect upon h2 and consequently the area remains just what it would have been without the blow4 ,a blow directed to any point other than ,c would at once alter the area of the triangle4 ,one interesting deduction may at once be drawn4 ,if gravity were a radiant force emitted from the sun with a velocity like that of light1 the moving planet would encounter it at a certain apparent angle 7aberration71 and the force experienced would come from a point a little in advance of the sun4 ,the rate of description of areas would thus tend to increase2 whereas in reality it is constant4 ,hence the force of gravity1 if it travel at all1 does so with a speed far greater than that of light4 ,it appears to be practically instantaneous4 7,cf4 ,modern ,views of ,electricity1 #abf1 end of chap4 xii47 ,again1 anything like a retarding effect of the medium through which the planets move would constitute a tangential force1 entirely un-directed towards the sun4 ,hence no such frictional or retarding force can appreciably exist4 ,it is1 however1 conceivable that both these effects might occur and just neutralize each other4 ,the neutralization is unlikely to be exact for all the planets2 and the fact is1 that no trace of either effect has as yet been discovered4 7,see also p4 #agf47 ,the planets are1 however1 subject to forces not directed towards the sun1 viz4 their attractions for each other2 and these perturbing forces do produce a slight discrepancy from ,kepler's second law1 but a discrepancy which is completely subject to calculation4 ,no4 #b4 ,kepler's first law proves that this central force diminishes in the same proportion as the square of the distance increases4 ,to prove the connection between the inverse-square law of distance1 and the travelling in a conic section with the centre of force in one focus 7the other focus being empty71 is not so simple4 ,it obviously involves some geometry1 and must therefore be left to properly armed students4 ,but it may be useful to state that the inverse-square law of distance1 although the simplest possible law for force emanating from a point or sphere1 is not to be regarded as self-evident or as needing no demonstration4 ,the force of a magnetic pole on a magnetized steel scrap1 for instance1 varies as the inverse cube of the distance2 and the curve described by such a particle would be quite different from a conic section--it would be a definite class of spiral 7called ,cotes's spiral74 ,again1 on an iron filing the force of a single pole might vary more nearly as the inverse fifth power2 and so on4 ,even when the thing concerned is radiant in straight lines1 like light1 the law of inverse squares is not universally true4 ,its truth assumes1 first1 that the source is a point or sphere2 next1 that there is no reflection or refraction of any kind2 and lastly1 that the medium is perfectly transparent4 ,the law of inverse squares by no means holds from a prairie fire for instance1 or from a lighthouse1 or from a street lamp in a fog4 ,mutual perturbations1 especially the pull of ,jupiter1 prevent the path of a planet from being really and truly an ellipse1 or indeed from being any simple re-entrant curve4 ,moreover1 when a planet possesses a satellite1 it is not the centre of the planet which ever attempts to describe the ,keplerian ellipse1 but it is the common centre of gravity of the two bodies4 ,thus1 in the case of the earth and moon1 the point which really does describe a close attempt at an ellipse is a point displaced about #cjjj miles from the centre of the earth towards the moon1 and is therefore only #ajjj miles beneath the surface4 ,no4 #c4 ,kepler's third law proves that all the planets are acted on by the same kind of force2 of an intensity depending on the mass of the sun4 ,the third law of ,kepler1 although it requires geometry to state and establish it for elliptic motion 7for which it holds just as well as it does for circular motion71 is very easy to establish for circular motion1 by any one who knows about centrifugal force4 ,if m is the mass of a planet1 v its velocity1 r the radius of its orbit1 and ,t the time of describing it2 #bpir v,t1 and the centripetal force needed to hold it in its orbit is mv#b #dpi#bmr -------- or ----------- r ,t#b ,now the force of gravitative attraction between the planet and the sun is ,vm,s -----1 r#b where v is a fixed quantity called the gravitation-constant1 to be determined if possible by experiment once for all4 ,now1 expressing the fact that the force of gravitation is the force holding the planet in1 we write1 #dpi#bmr ,vm,s ----------- ---------1 ,t#b r#b whence1 by the simplest algebra1 r#c ,,vs ------ ---------4 ,t#b #dpi#b ,the mass of the planet has been cancelled out2 the mass of the sun remains1 multiplied by the gravitation-constant1 and is seen to be proportional to the cube of the distance divided by the square of the periodic time3 a ratio1 which is therefore the same for all planets controlled by the sun4 ,hence1 knowing r and ,t for any single planet1 the value of ,,vs is known4 ,no4 #d4 ,so by knowing the length of year and distance of any planet from the sun1 the sun's mass can be calculated1 in terms of that of the earth4 ,no4 #e4 ,for the satellites1 the force acting depends on the mass of their central body1 a planet4 ,hence the mass of any planet possessing a satellite becomes known4 ,the same argument holds for any other system controlled by a central body--for instance1 for the satellites of ,jupiter2 only instead of ,s it will be natural to write ,j1 as meaning the mass of ,jupiter4 ,hence1 knowing r and ,t for any one satellite of ,jupiter1 the value of ,,vj is known4 ,apply the argument also to the case of moon and earth4 ,knowing the distance and time of revolution of our moon1 the value of ,,ve is at once determined2 ,e being the mass of the earth4 ,hence1 ,s and ,j1 and in fact the mass of any central body possessing a visible satellite1 are now known in terms of ,e1 the mass of the earth 7or1 what is practically the same thing1 in terms of ,v1 the gravitation-constant74 ,observe that so far none of these quantities are known absolutely4 ,their relative values are known1 and are tabulated at the end of the ,notes above1 but the finding of their absolute values is another matter1 which we must defer4 ,but1 it may be asked1 if ,kepler's third law only gives us the mass of a central body1 how is the mass of a satellite to be known8 ,well1 it is not easy2 the mass of no satellite is known with much accuracy4 ,their mutual perturbations give us some data in the case of the satellites of ,jupiter2 but to our own moon this method is of course inapplicable4 ,our moon perturbs at first sight nothing1 and accordingly its mass is not even yet known with exactness4 ,the mass of comets1 again1 is quite unknown4 ,all that we can be sure of is that they are smaller than a certain limit1 else they would perturb the planets they pass near4 ,nothing of this sort has ever been detected4 ,they are themselves perturbed plentifully1 but they perturb nothing2 hence we learn that their mass is small4 ,the mass of a comet may1 indeed1 be a few million or even billion tons2 but that is quite small in astronomy4 ,but now it may be asked1 surely the moon perturbs the earth1 swinging it round their common centre of gravity1 and really describing its own orbit about this point instead of about the earth's centre8 ,yes1 that is so2 and a more precise consideration of ,kepler's third law enables us to make a fair approximation to the position of this common centre of gravity1 and thus practically to weigh the moon1 i4e4 to compare its mass with that of the earth2 for their masses will be inversely as their respective distances from the common centre of gravity or balancing point--on the simple steel-yard principle4 ,hitherto we have not troubled ourselves about the precise point about which the revolution occurs1 but ,kepler's third law is not precisely accurate unless it is attended to4 ,the bigger the revolving body the greater is the discrepancy3 and we see in the table preceding ,lecture ,,iii41 on page #eg1 that ,jupiter exhibits an error which1 though very slight1 is greater than that of any of the other planets1 when the sun is considered the fixed centre4 ,let the common centre of gravity of earth and moon be displaced a distance x from the centre of the earth1 then the moon's distance from the real centre of revolution is not r1 but r-x2 and the equation of centrifugal force to gravitative-attraction is strictly #dpi#b ,,ve --------- 7r-x7 ------1 ,t#b r#b instead of what is in the text above2 and this gives a slightly modified third law4 ,from this equation1 if we have any distinct method of determining ,,ve 7and the next section gives such a method71 we can calculate x and thus roughly weigh the moon1 since r-x ,e ----- -----1 r ,e,m but to get anything like a reasonable result the data must be very precise4 ,no4 #f4 ,the force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles4 ,here we come to the ,newtonian verification already several times mentioned2 but because of its importance ,i will repeat it in other words4 ,the hypothesis to be verified is that the force acting on the moon is the same kind of force as acts on bodies we can handle and weigh1 and which gives them their weight4 ,now the weight of a mass m is commonly written mg1 where g is the intensity of terrestrial gravity1 a thing easily measured2 being1 indeed1 numerically equal to twice the distance a stone drops in the first second of free fall4 ,see table p4 #bje4 ,hence1 expressing that the weight of a body is due to gravity1 and remembering that the centre of the earth's attraction is distant from us by one earth's radius 7,r71 we can write ,vm,e mg ------1 ,r#b or ,v,e g,r#b #ie1ebb cubic miles-per-second per second4 ,but we already know v,e1 in terms of the moon's motion1 as #dpi#br#c ----------- ,t#b approximately1 more accurately1 see preceding note1 this quantity is ,v7,e ,m72 hence we can easily see if the two determinations of this quantity agree4#bj ,all these deductions are fundamental1 and may be considered as the foundation of the ,principia4 ,it was these that flashed upon ,newton during that moment of excitement when he learned the real size of the earth1 and discovered his speculations to be true4 ,the next are elaborations and amplifications of the theory1 such as in ordinary times are left for subsequent generations of theorists to discover and work out4 ,newton did not work out these remoter consequences of his theory completely by any means3 the astronomical and mathematical world has been working them out ever since2 but he carried the theory a great way1 and here it is that his marvellous power is most conspicuous4 ,it is his treatment of ,no4 #g1 the perturbations of the moon1 that perhaps most especially has struck all future mathematicians with amazement4 ,no4 #g1 ,no4 #ad1 ,no4 #ae1 these are the most inspired of the whole4 ,no4 #g4 ,the moon is attracted not only by the earth1 but by the sun also2 hence its orbit is perturbed1 and ,newton calculated out the chief of these perturbations4 ,now running through the perturbations 7p4 #bjc7 in order3--,the first is in parenthesis1 because it is mere excentricity4 ,it is not a true perturbation at all1 and more properly belongs to ,kepler4 7a7 ,the first true perturbation is what ,ptolemy called the evection1 the principal part of which is a periodic change in the ellipticity or excentricity of the moon's orbit1 owing to the pull of the sun4 ,it is a complicated matter1 and ,newton only partially solved it4 ,i shall not attempt to give an account of it4 7b7 ,the next1 the variation1 is a much simpler affair4 ,it is caused by the fact that as the moon revolves round the earth it is half the time nearer to the sun than the earth is1 and so gets pulled more than the average1 while for the other fortnight it is further from the sun than the earth is1 and so gets pulled less4 ,for the week during which it is changing from a decreasing half to a new moon it is moving in the direction of the extra pull1 and hence becomes new sooner than would have been expected4 ,all next week it is moving against the same extra pull1 and so arrives at quadrature 7half moon7 somewhat late4 ,for the next fortnight it is in the region of too little pull1 the earth gets pulled more than it does2 the effect of this is to hurry it up for the third week1 so that the full moon occurs a little early1 and to retard it for the fourth week1 so that the decreasing half moon like the increasing half occurs behind time again4 ,thus each syzygy 7as new and full are technically called7 is too early2 each quadrature is too late2 the maximum hurrying and slackening force being felt at the octants1 or intermediate #de points4 7c7 ,the annual equation is a fluctuation introduced into the other perturbations by reason of the varying distance of the disturbing body1 the sun1 at different seasons of the year4 ,its magnitude plainly depends simply on the excentricity of the earth's orbit4 ,both these perturbations1 7b7 and 7c71 ,newton worked out completely4 7d7 and 7e7 ,next come the retrogression of the nodes and the variation of the inclination1 which at the time were being observed at ,greenwich by ,flamsteed1 from whom ,newton frequently1 but vainly1 begged for data that he might complete their theory while he had his mind upon it4 ,fortunately1 ,halley succeeded ,flamsteed as ,astronomer-,royal see list at end of notes above1 and then ,newton would have no difficulty in gaining such information as the national ,observatory could give4 ,the inclination meant is the angle between the plane of the moon's orbit and that of the earth4 ,the plane of the earth's orbit round the sun is called the ecliptic2 the plane of the moon's orbit round the earth is inclined to it at a certain angle1 which is slowly changing1 though in a periodic manner4 ,imagine a curtain ring bisected by a sheet of paper1 and tilted to a certain angle2 it may be likened to the moon's orbit1 cutting the plane of the ecliptic4 ,the two points at which the plane is cut by the ring are called nodes2 and these nodes are not stationary1 but are slowly regressing1 i4e4 travelling in a direction opposite to that of the moon itself4 ,also the angle of tilt is varying slowly1 oscillating up and down in the course of centuries4 7f7 ,the two points in the moon's elliptic orbit where it comes nearest to or farthest from the earth1 i4e4 the points at the extremity of the long axis of the ellipse1 are called separately perigee and apogee1 or together the apses4 ,now the pull of the sun causes the whole orbit to slowly revolve in its own plane1 and consequently these apses progress1 so that the true path is not quite a closed curve1 but a sort of spiral with elliptic loops4 ,but here comes in a striking circumstance4 ,newton states with reference to this perturbation that theory only accounts for #a-a_/b per annum1 whereas observation gives #c1 or just twice as much4 ,this is published in the ,principia as a fact1 without comment4 ,it was for long regarded as a very curious thing1 and many great mathematicians afterwards tried to find an error in the working4 ,d',alembert1 ,clairaut1 and others attacked the problem1 but were led to just the same result4 ,it constituted the great outstanding difficulty in the way of accepting the theory of gravitation4 ,it was suggested that perhaps the inverse square law was only a first approximation2 that perhaps a more complete expression1 such as ,a ,b ---- -----1 r#b r#d must be given for it2 and so on4 ,ultimately1 ,clairaut took into account a whole series of neglected terms1 and it came out correct2 thus verifying the theory4 ,but the strangest part of this tale is to come4 ,for only a few years ago1 ,prof4 ,adams1 of ,cambridge 7,neptune ,adams1 as he is called71 was editing various old papers of ,newton's1 now in the possession of the ,duke of ,portland1 and he found manuscripts bearing on this very point1 and discovered that ,newton had reworked out the calculations himself1 had found the cause of the error1 had taken into account the terms hitherto neglected1 and so1 fifty years before ,clairaut1 had completely1 though not publicly1 solved this long outstanding problem of the progression of the apses4 7g7 and 7h7 ,two other inequalities he calculated out and predicted1 viz4 variation in the motions of the apses and the nodes4 ,neither of these had then been observed1 but they were afterwards detected and verified4 ,a good many other minor irregularities are now known--some thirty1 ,i believe2 and altogether the lunar theory1 or problem of the moon's exact motion1 is one of the most complicated and difficult in astronomy2 the perturbations being so numerous and large1 because of the enormous mass of the perturbing body4 ,the disturbances experienced by the planets are much smaller1 because they are controlled by the sun and perturbed by each other4 ,the moon is controlled only by the earth1 and perturbed by the sun4 ,planetary perturbations can be treated as a series of disturbances with some satisfaction3 not so those of the moon4 ,and yet it is the only way at present known of dealing with the lunar theory4 ,to deal with it satisfactorily would demand the solution of such a problem as this3--,given three rigid spherical masses thrown into empty space with any initial motions whatever1 and abandoned to gravity3 to determine their subsequent motions4 ,with two masses the problem is simple enough1 being pretty well summed up in ,kepler's laws2 but with three masses1 strange to say1 it is so complicated as to be beyond the reach of even modern mathematics4 ,it is a famous problem1 known as that of the three bodies1 but it has not yet been solved4 ,even when it is solved it will be only a close approximation to the case of earth1 moon1 and sun1 for these bodies are not spherical1 and are not rigid4 ,one may imagine how absurdly and hopelessly complicated a complete treatment of the motions of the entire solar system would be4 ,no4 #h4 ,each planet is attracted not only by the sun but by the other planets1 hence their orbits are slightly affected by each other4 ,the subject of planetary perturbation was only just begun by ,newton4 ,gradually 7by ,laplace and others7 the theory became highly developed2 and1 as everybody knows1 in #ahdf ,neptune was discovered by means of it4 ,no4 #i4 ,he recognized the comets as members of the solar system1 obedient to the same law of gravity and moving in very elongated ellipses2 so their return could be predicted4 ,it was a long time before ,newton recognized the comets as real members of the solar system1 and subject to gravity like the rest4 ,he at first thought they moved in straight lines4 ,it was only in the second edition of the ,principia that the theory of comets was introduced4 ,halley observed a fine comet in #afhb1 and calculated its orbit on ,newtonian principles4 ,he also calculated when it ought to have been seen in past times2 and he found the year #afjg1 when one was seen by ,kepler2 also the year #aeca1 when one was seen by ,appian2 again1 he reckoned #adef1 #achj1 #acje4 ,all these appearances were the same comet1 in all probability1 returning every seventy-five or seventy-six years4 ,the period was easily allowed to be not exact1 because of perturbing planets4 ,he then predicted its return for #ageh1 or perhaps #agei1 a date he could not himself hope to see4 ,he lived to a great age1 but he died sixteen years before this date4 ,as the time drew nigh1 three-quarters of a century afterwards1 astronomers were greatly interested in this first cometary prediction1 and kept an eager look-out for ,halley's comet4 ,clairaut1 a most eminent mathematician and student of ,newton1 proceeded to calculate out more exactly the perturbing influence of ,jupiter1 near which it had passed4 ,after immense labour 7for the difficulty of the calculation was extreme1 and the mass of mere figures something portentous71 he predicted its return on the #acth of ,april1 #agei1 but he considered that he might have made a possible error of a month4 ,it returned on the #acth of ,march1 #agei1 and established beyond all doubt the rule of the ,newtonian theory over comets4 ,illustration3 ,,fig4 #ga4--,well-known model exhibiting the oblate spheroidal form as a consequence of spinning about a central axis4 ,the brass strip a looks like a transparent globe when whirled1 and bulges out equatorially4 ,no4 #aj4 ,applying the idea of centrifugal force to the earth considered as a rotating body1 he perceived that it could not be a true sphere1 and calculated its oblateness1 obtaining #bh miles greater equatorial than polar diameter4 ,here we return to one of the more simple deductions4 ,a spinning body of any kind tends to swell at its circumference 7or equator71 and shrink along its axis 7or poles74 ,if the body is of yielding material1 its shape must alter under the influence of centrifugal force2 and if a globe of yielding substance subject to known forces rotates at a definite pace1 its shape can be calculated4 ,thus a plastic sphere the size of the earth1 held together by its own gravity1 and rotating once a day1 can be shown to have its equatorial diameter twenty-eight miles greater than its polar diameter3 the two diameters being #h1jjj and #h1jbh respectively4 ,now we have no guarantee that the earth is of yielding material3 for all ,newton could tell it might be extremely rigid4 ,as a matter of fact it is now very nearly rigid4 ,but he argued thus4 ,the water on it is certainly yielding1 and although the solid earth might decline to bulge at the equator in deference to the diurnal rotation1 that would not prevent the ocean from flowing from the poles to the equator and piling itself up as an equatorial ocean fourteen miles deep1 leaving dry land everywhere near either pole4 ,nothing of this sort is observed3 the distribution of land and water is not thus regulated4 ,hence1 whatever the earth may be now1 it must once have been plastic enough to accommodate itself perfectly to the centrifugal forces1 and to take the shape appropriate to a perfectly plastic body4 ,in all probability it was once molten1 and for long afterwards pasty4 ,thus1 then1 the shape of the earth can be calculated from the length of its day and the intensity of its gravity4 ,the calculation is not difficult3 it consists in imagining a couple of holes bored to the centre of the earth1 one from a pole and one from the equator2 filling these both with water1 and calculating how much higher the water will stand in one leg of the gigantic ,v tube so formed than in the other4 ,the answer comes out about fourteen miles4 ,the shape of the earth can now be observed geodetically1 and it accords with calculation1 but the observations are extremely delicate2 in ,newton's time the size was only barely known1 the shape was not observed till long after2 but on the principles of mechanics1 combined with a little common-sense reasoning1 it could be calculated with certainty and accuracy4 ,no4 #aa4 ,from the observed shape of ,jupiter or any planet the length of its day could be estimated4 ,jupiter is much more oblate than the earth4 ,its two diameters are to one another as #ag is to #af2 the ellipticity of its disk is manifest to simple inspection4 ,hence we perceive that its whirling action must be more violent--it must rotate quicker4 ,as a matter of fact its day is ten ,illustration3 ,,fig4 #gb4--;,jupiter4 hours long--five hours daylight and five hours night4 ,the times of rotation of other bodies in the solar system are recorded in a table above4 ,no4 #ab4 ,the so-calculated shape of the earth1 in combination with centrifugal force1 causes the weight of bodies to vary with latitude2 and ,newton calculated the amount of this variation4 #aid lbs4 at pole balance #aie lbs4 at equator4 ,but following from the calculated shape of the earth follow several interesting consequences4 ,first of all1 the intensity of gravity will not be the same everywhere2 for at the equator a stone is further from the average bulk of the earth 7say the centre7 than it is at the poles1 and owing to this fact a mass of #eij pounds at the pole2 would suffice to balance #eia pounds at the equator1 if the two could be placed in the pans of a gigantic balance whose beam straddled along an earth's quadrant4 ,this is a true variation of gravity due to the shape of the earth4 ,but besides this there is a still larger apparent variation due to centrifugal force1 which affects all bodies at the equator but not those at the poles4 ,from this cause1 even if the earth were a true sphere1 yet if it were spinning at its actual pace1 #bhh pounds at the pole could balance #bhi pounds at the equator2 because at the equator the true weight of the mass would not be fully appreciated1 centrifugal force would virtually diminish it by #a_/bhith of its amount4 ,in actual fact both causes co-exist1 and accordingly the total variation of gravity observed is compounded of the real and the apparent effects2 the result is that #aid pounds at a pole weighs as much as #aie pounds at the equator4 ,no4 #ac4 ,a homogeneous sphere attracts as if its mass were concentrated at its centre4 ,for any other figure1 such as an oblate spheroid1 this is not exactly true4 ,a hollow concentric spherical shell exerts no force on small bodies inside it4 ,a sphere composed of uniform material1 or of materials arranged in concentric strata1 can be shown to attract external bodies as if its mass were concentrated at its centre4 ,a hollow sphere1 similarly composed1 does the same1 but on internal bodies it exerts no force at all4 ,hence1 at all distances above the surface of the earth1 gravity decreases in inverse proportion as the square of the distance from the centre of the earth increases2 but1 if you descend a mine1 gravity decreases in this case also as you leave the surface1 though not at the same rate as when you went up4 ,for as you penetrate the crust you get inside a concentric shell1 which is thus powerless to act upon you1 and the earth you are now outside is a smaller one4 ,at what rate the force decreases depends on the distribution of density2 if the density were uniform all through1 the law of variation would be the direct distance1 otherwise it would be more complicated4 ,anyhow1 the intensity of gravity is a maximum at the surface of the earth1 and decreases as you travel from the surface either up or down4 ,no4 #ad4 ,the earth's equatorial protuberance1 being acted on by the attraction of the sun and moon1 must disturb its axis of rotation in a calculated manner2 and thus is produced the precession of the equinoxes4 ,here we come to a truly awful piece of reasoning4 ,a sphere attracts as if its mass were concentrated at its centre 7,no4 #ab71 but a spheroid does not4 ,the earth is a spheroid1 and hence it pulls and is pulled by the moon with a slightly uncentric attraction4 ,in other words1 the line of pull does not pass through its precise centre4 ,now when we have a spinning body1 say a top1 overloaded on one side so that gravity acts on it unsymmetrically1 what happens8 ,the axis of rotation begins to rotate cone-wise1 at a pace which depends on the rate of spin1 and on the shape and mass of the top1 as well as on the amount and leverage of the overloading4 ,newton calculated out the rapidity of this conical motion of the axis of the earth1 produced by the slightly unsymmetrical pull of the moon1 and found that it would complete a revolution in #bf1jjj years--precisely what was wanted to explain the precession of the equinoxes4 ,in fact he had discovered the physical cause of that precession4 ,observe that there were three stages in this discovery of precession3-- ,first1 the observation by ,hipparchus1 that the nodes1 or intersections of the earth's orbit 7the sun's apparent orbit7 with the plane of the equator1 were not stationary1 but slowly moved4 ,second1 the description of this motion by ,copernicus1 by the statement that it was due to a conical motion of the earth's axis of rotation about its centre as a fixed point4 ,third1 the explanation of this motion by ,newton as due to the pull of the moon on the equatorial protuberance of the earth4 ,the explanation could not have been previously suspected1 for the shape of the earth1 on which the whole theory depends1 was entirely unknown till ,newton calculated it4 ,another and smaller motion of a somewhat similar kind has been worked out since3 it is due to the unsymmetrical attraction of the other planets for this same equatorial protuberance4 ,it shows itself as a periodic change in the obliquity of the ecliptic1 or so-called recession of the apses1 rather than as a motion of the nodes4#ba ,no4 #ae4 ,the waters of the ocean are attracted towards the sun and moon on one side1 and whirled a little farther away than the solid earth on the other side3 hence ,newton explained all the main phenomena of the tides4 ,and now comes another tremendous generalization4 ,the tides had long been an utter mystery4 ,kepler likens the earth to an animal1 and the tides to his breathings and inbreathings1 and says they follow the moon4 ,galileo chaffs him for this1 and says that it is mere superstition to connect the moon with the tides4 ,descartes said the moon pressed down upon the waters by the centrifugal force of its vortex1 and so produced a low tide under it4 ,everything was fog and darkness on the subject4 ,the legend goes that an astronomer threw himself into the sea in despair of ever being able to explain the flux and reflux of its waters4 ,newton now with consummate skill applied his theory to the effect of the moon upon the ocean1 and all the main details of tidal action gradually revealed themselves to him4 ,he treated the water1 rotating with the earth once a day1 somewhat as if it were a satellite acted on by perturbing forces4 ,the moon as it revolves round the earth is perturbed by the sun4 ,the ocean as it revolves round the earth 7being held on by gravitation just as the moon is7 is perturbed by both sun and moon4 ,the perturbing effect of a body varies directly as its mass1 and inversely as the cube of its distance4 7,the simple law of inverse square does not apply1 because a perturbation is a differential effect3 the satellite or ocean when nearer to the perturbing body than the rest of the earth1 is attracted more1 and when further off it is attracted less than is the main body of the earth2 and it is these differences alone which constitute the perturbation47 ,the moon is the more powerful of the two perturbing bodies1 hence the main tides are due to the moon2 and its chief action is to cause a pair of low waves or oceanic humps1 of gigantic area1 to travel round the earth once in a lunar day1 i4e4 in about #bd hours and #ej minutes4 ,the sun makes a similar but still lower pair of low elevations to travel round once in a solar day of #bd hours4 ,and the combination of the two pairs of humps1 thus periodically overtaking each other1 accounts for the well-known spring and neap tides1--spring tides when their maxima agree1 neap tides when the maximum of one coincides with the minimum of the other3 each of which events happens regularly once a fortnight4 ,these are the main effects1 but besides these there are the effects of varying distances and obliquity to be taken into account2 and so we have a whole series of minor disturbances1 very like those discussed in ,no4 #g1 under the lunar theory1 but more complex still1 because there are two perturbing bodies instead of only one4 ,the subject of the tides is1 therefore1 very recondite2 and though one may give some elementary account of its main features1 it will be best to defer this to a separate lecture 7,lecture ,,xvii74 ,i had better1 however1 here say that ,newton did not limit himself to the consideration of the primary oceanic humps3 he pursued the subject into geographical detail4 ,he pointed out that1 although the rise and fall of the tide at mid-ocean islands would be but small1 yet on stretches of coast the wave would fling itself1 and by its momentum would propel the waters1 to a much greater height--for instance1 #bj or #cj feet2 especially in some funnel-shaped openings like the ,bristol ,channel and the ,bay of ,fundy1 where the concentrated impetus of the water is enormous4 ,he also showed how the tidal waves reached different stations in successive regular order each day2 and how some places might be fed with tide by two distinct channels2 and that if the time of these channels happened to differ by six hours1 a high tide might be arriving by one channel and a low tide by the other1 so that the place would only feel the difference1 and so have a very small observed rise and fall2 instancing a port in ,china 7in the ,gulf of ,tonquin7 where that approximately occurs4 ,in fact1 although his theory was not1 as we now know1 complete or final1 yet it satisfactorily explained a mass of intricate detail as well as the main features of the tides4 ,no4 #af4 ,the sun's mass being known1 he calculated the height of the solar tide4 ,no4 #ag4 ,from the observed heights of spring and neap tides he determined the lunar tide1 and thence made an estimate of the mass of the moon4 ,knowing the sun's mass and distance1 it was not difficult for ,newton to calculate the height of the protuberance caused by it in a pasty ocean covering the whole earth4 ,i say pasty1 because1 if there was any tendency for impulses to accumulate1 as timely pushes given to a pendulum accumulate1 the amount of disturbance might become excessive1 and its calculation would involve a multitude of data4 ,the ,newtonian tide ignored this1 thus practically treating the motion as either dead-beat1 or else the impulses as very inadequately timed4 ,with this reservation the mid-ocean tide due to the action of the sun alone comes out about one foot1 or let us say one foot for simplicity4 ,now the actual tide observed in mid-,atlantic is at the springs about four feet1 at the neaps about two4 ,the spring tide is lunar plus solar2 the neap tide is lunar minus solar4 ,hence it appears that the tide caused by the moon alone must be about three feet1 when unaffected by momentum4 ,from this datum ,newton made the first attempt to approximately estimate the mass of the moon4 ,i said that the masses of satellites must be estimated1 if at all1 by the perturbation they are able to cause4 ,the lunar tide is a perturbation in the diurnal motion of the sea1 and its amount is therefore a legitimate mode of calculating the moon's mass4 ,the available data were not at all good1 however2 nor are they even now very perfect2 and so the estimate was a good way out4 ,it is now considered that the mass of the moon is about one-eightieth that of the earth4 99 99 99 99 99 ,such are some of the gems extracted from their setting in the ,principia1 and presented as clearly as ,i am able before you4 ,do you realize the tremendous stride in knowledge--not a stride1 as ,whewell says1 nor yet a leap1 but a flight--which has occurred between the dim gropings of ,kepler1 the elementary truths of ,galileo1 the fascinating but wild speculations of ,descartes1 and this magnificent and comprehensive system of ordered knowledge4 ,to some his genius seemed almost divine4 ,does ,mr4 ,newton eat1 drink1 sleep1 like other men8 said the ,marquis de l',hpital1 a ,french mathematician of no mean eminence2 ,i picture him to myself as a celestial genius1 entirely removed from the restrictions of ordinary matter4 ,to many it seemed as if there was nothing more to be discovered1 as if the universe were now explored1 and only a few fragments of truth remained for the gleaner4 ,this is the attitude of mind expressed in ,pope's famous epigram3-- ,nature and ,nature's laws lay hid in ,night1 ,god said1 ,let ,newton be1 and all was light4 ,this feeling of hopelessness and impotence was very natural after the advent of so overpowering a genius1 and it prevailed in ,england for fully a century4 ,it was very natural1 but it was very mischievous2 for1 as a consequence1 nothing of great moment was done by ,england in science1 and no ,englishman of the first magnitude appeared1 till some who are either living now or who have lived within the present century4 ,it appeared to his contemporaries as if he had almost exhausted the possibility of discovery2 but did it so appear to ,newton8 ,did it seem to him as if he had seen far and deep into the truths of this great and infinite universe8 ,it did not4 ,when quite an old man1 full of honour and renown1 venerated1 almost worshipped1 by his contemporaries1 these were his words3-- ,i know not what the world will think of my labours1 but to myself it seems that ,i have been but as a child playing on the sea-shore2 now finding some pebble rather more polished1 and now some shell rather more agreeably variegated than another1 while the immense ocean of truth extended itself unexplored before me4 ,and so it must ever seem to the wisest and greatest of men when brought into contact with the great things of ,god--that which they know is as nothing1 and less than nothing1 to the infinitude of which they are ignorant4 ,newton's words sound like a simple and pleasing echo of the words of that great unknown poet1 the writer of the book of ,job3-- ,lo1 these are parts of ,his ways1 ,but how little a portion is heard of ,him2 ,the thunder of ,his power1 who can understand8 ,,end ,,of ,,part ,i4 ,,part ,,ii ,a ,,couple ,,of ,,centuries' ,,progress4 ,,notes ,,to ,,lecture ,x ,science during the century after ,newton ,the ,principia published1 #afhg ,roemer #afdd-agaj ,james ,bradley #afib-agfb ,clairaut #agac-agfe ,euler #agjg-aghc ,d',alembert #agag-aghc ,lagrange #agcf-ahac ,laplace #agdi-ahbg ,william ,herschel #agch-ahbb ,olaus ,roemer was born in ,jutland1 and studied at ,copenhagen4 ,assisted ,picard in #afga to determine the exact position of ,tycho's observatory on ,huen4 ,accompanied ,picard to ,paris1 and in #afge read before the ,academy his paper ,on ,successive ,propagation of ,light as revealed by a certain inequality in the motion of ,jupiter's ,first ,satellite4 ,in #afha he returned to ,copenhagen as ,professor of ,mathematics and ,astronomy1 and died in #agaj4 ,he invented the transit instrument1 mural circle1 equatorial mounting for telescopes1 and most of the other principal instruments now in use in observatories4 ,he made as many observations as ,tycho ,brah1 but the records of all but the work of three days were destroyed by a great fire in #agbh4 ,bradley1 ,professor of ,astronomy at ,oxford1 discovered the aberration of light in #agbi1 while examining stars for parallax1 and the nutation of the earth's axis in #agdh4 ,was appointed ,astronomer-,royal in #agdb4 ,,lecture ,x ,,roemer ,,and ,,bradley ,,and ,,the ,,velocity ,,of ,,light ,at ,newton's death ,england stood pre-eminent among the nations of ,europe in the sphere of science4 ,but the pre-eminence did not last long4 ,two great discoveries were made very soon after his decease1 both by ,professor ,bradley1 of ,oxford1 and then there came a gap4 ,a moderately great man often leaves behind him a school of disciples able to work according to their master's methods1 and with a healthy spirit of rivalry which stimulates and encourages them4 ,newton left1 indeed1 a school of disciples1 but his methods of work were largely unknown to them1 and such as were known were too ponderous to be used by ordinary men4 ,only one fresh result1 and that a small one1 has ever been attained by other men working according to the methods of the ,principia4 ,the methods were studied and commented on in ,england to the exclusion of all others for nigh a century1 and as a consequence no really important work was done4 ,on the ,continent1 however1 no such system of slavish imitation prevailed4 ,those methods of ,newton's which had been simultaneously discovered by ,leibnitz were more thoroughly grasped1 modified1 extended1 and improved4 ,there arose a great school of ,french and ,german mathematicians1 and the laurels of scientific discovery passed to ,france and ,germany--more especially1 perhaps1 at this time to ,france4 ,england has never wholly recovered them4 ,during the present century this country has been favoured with some giants who1 as they become distant enough for their true magnitude to be perceived1 may possibly stand out as great as any who have ever lived2 but for the mass and bulk of scientific work at the present day we have to look to ,germany1 with its enlightened ,government and extensive intellectual development4 ,england1 however1 is waking up1 and what its ,government does not do1 private enterprise is beginning to accomplish4 ,the establishment of centres of scientific and literary activity in the great towns of ,england1 though at present they are partially encumbered with the supply of education of an exceedingly rudimentary type1 is a movement that in the course of another century or so will be seen to be one of the most important and fruitful steps ever taken by this country4 ,on the ,continent such centres have long existed2 almost every large town is the seat of a ,university1 and they are now liberally endowed4 ,the ,university of ,bologna 7where1 you may remember1 ,copernicus learnt mathematics7 has recently celebrated its #hjjth anniversary4 ,the scientific history of the century after ,newton1 summarized in the above table of dates1 embraces the labours of the great mathematicians ,clairaut1 ,euler1 ,d',alembert1 and especially of ,lagrange and ,laplace4 ,but the main work of all these men was hardly pioneering work4 ,it was rather the surveying1 and mapping out1 and bringing into cultivation1 of lands already discovered4 ,probably ,herschel may be justly regarded as the next true pioneer4 ,we shall not1 however1 properly appreciate the stages through which astronomy has passed1 nor shall we be prepared adequately to welcome the discoveries of modern times unless we pay some attention to the intervening age4 ,moreover1 during this era several facts of great moment gradually came into recognition2 and the importance of the discovery we have now to speak of can hardly be over-estimated4 ,our whole direct knowledge of the planetary and stellar universe1 from the early observations of the ancients down to the magnificent discoveries of a ,herschel1 depends entirely upon our happening to possess a sense of sight4 ,to no other of our senses do any other worlds than our own in the slightest degree appeal4 ,we touch them or hear them never4 ,consequently1 if the human race had happened to be blind1 no other world but the one it groped its way upon could ever have been known or imagined by it4 ,the outside universe would have existed1 but man would have been entirely and hopelessly ignorant of it4 ,the bare idea of an outside universe beyond the world would have been inconceivable1 and might have been scouted as absurd4 ,we do possess the sense of sight2 but is it to be supposed that we possess every sense that can be possessed by finite beings8 ,there is not the least ground for such an assumption4 ,it is easy to imagine a deaf race or a blind race3 it is not so easy to imagine a race more highly endowed with senses than our own2 and yet the sense of smell in animals may give us some aid in thinking of powers of perception which transcend our own in particular directions4 ,if there were a race with higher or other senses than our own1 or if the human race should ever in the process of development acquire such extra sense-organs1 a whole universe of existent fact might become for the first time perceived by us1 and we should look back upon our past state as upon a blind chrysalid form of existence in which we had been unconscious of all this new wealth of perception4 ,it cannot be too clearly and strongly insisted on and brought home to every mind1 that the mode in which the universe strikes us1 our view of the universe1 our whole idea of matter1 and force1 and other worlds1 and even of consciousness1 depends upon the particular set of sense-organs with which we1 as men1 happen to be endowed4 ,the senses of force1 of motion1 of sound1 of light1 of touch1 of heat1 of taste1 and of smell--these we have1 and these are the things we primarily know4 ,all else is inference founded upon these sensations4 ,so the world appears to us4 ,but given other sense-organs1 and it might appear quite otherwise4 ,what it is actually and truly like1 therefore1 is quite and for ever beyond us--so long as we are finite beings4 ,without eyes1 astronomy would be non-existent4 ,light it is which conveys all the information we possess1 or1 as it would seem1 ever can possess1 concerning the outer and greater universe in which this small world forms a speck4 ,light is the channel1 the messenger of information2 our eyes1 aided by telescopes1 spectroscopes1 and many other scopes that may yet be invented1 are the means by which we read the information that light brings4 ,light travels from the stars to our eyes3 does it come instantaneously8 or does it loiter by the way8 for if it lingers it is not bringing us information properly up to date--it is only telling us what the state of affairs was when it started on its long journey4 ,now1 it is evidently a matter of interest to us whether we see the sun as he is now1 or only as he was some three hundred years ago4 ,if the information came by express train it would be three hundred years behind date1 and the sun might have gone out in the reign of ,queen ,anne without our being as yet any the wiser4 ,the question1 therefore1 ,at what rate does our messenger travel8 is evidently one of great interest for astronomers1 and many have been the attempts made to solve it4 ,very likely the ancient ,greeks pondered over this question1 but the earliest writer known to me who seriously discussed the question is ,galileo4 ,he suggests a rough experimental means of attacking it4 ,first of all1 it plainly comes quicker than sound4 ,this can be perceived by merely watching distant hammering1 or by noticing that the flash of a pistol is seen before its report is heard1 or by listening to the noise of a flash of lightning4 ,sound takes five seconds to travel a mile--it has about the same speed as a rifle bullet2 but light is much quicker than that4 ,the rude experiment suggested by ,galileo was to send two men with lanterns and screens to two distant watch-towers or neighbouring mountain tops1 and to arrange that each was to watch alternate displays and obscurations of the light made by the other1 and to imitate them as promptly as possible4 ,either man1 therefore1 on obscuring or showing his own light would see the distant glimmer do the same1 and would be able to judge if there was any appreciable interval between his own action and the response of the distant light4 ,the experiment was actually tried by the ,florentine ,academicians1#bb with the result that1 as practice improved1 the interval became shorter and shorter1 so that there was no reason to suppose that there was any real interval at all4 ,light1 in fact1 seemed to travel instantaneously4 ,well might they have arrived at this result4 ,even if they had made far more perfect arrangements--for instance1 by arranging a looking-glass at one of the stations in which a distant observer might see the reflection of his own lantern1 and watch the obscurations and flashings made by himself1 without having to depend on the response of human mechanism--even then no interval whatever could have been detected4 ,if1 by some impossibly perfect optical arrangement1 a lighthouse here were made visible to us after reflection in a mirror erected at ,new ,york1 so that the light would have to travel across the ,atlantic and back before it could be seen1 even then the appearance of the light on removing a shutter1 or the eclipse on interposing it1 would seem to happen quite instantaneously4 ,there would certainly be an interval3 the interval would be the fiftieth part of a second 7the time a stone takes to drop #a_/acth of an inch71 but that is too short to be securely detected without mechanism4 ,with mechanism the thing might be managed1 for a series of shutters might be arranged like the teeth of a large wheel2 so that1 when the wheel rotates1 eclipses follow one another very rapidly2 if then an eye looked through the same opening as that by which the light goes on its way to the distant mirror1 a tooth might have moved sufficiently to cover up this space by the time the light returned2 in which case the whole would appear dark1 for the light would be stopped by a tooth1 either at starting or at returning1 continually4 ,at higher speeds of rotation some light would reappear1 and at lower speeds it would also reappear2 by noticing1 therefore1 the precise speed at which there was constant eclipse the velocity of light could be determined4 ,illustration3 ,,fig4 #gc4--;,diagram of eye looking at a light reflected in a distant mirror through the teeth of a revolving wheel4 ,this experiment has now been made in a highly refined form by ,fizeau1 and repeated by ,m4 ,cornu with prodigious care and accuracy4 ,but with these recent matters we have no concern at present4 ,it may be instructive to say1 however1 that if the light had to travel two miles altogether1 the wheel would have to possess #dej teeth and to spin #ajj times a second 7at the risk of flying to pieces7 in order that the ray starting through any one of the gaps might be stopped on returning by the adjacent tooth4 ,well might the velocity of light be called instantaneous by the early observers4 ,an ordinary experiment seemed 7and was7 hopeless1 and light was supposed to travel at an infinite speed4 ,but a phenomenon was noticed in the heavens by a quick-witted and ingenious ,danish astronomer1 which was not susceptible of any ordinary explanation1 and which he perceived could at once be explained if light had a certain rate of travel--great1 indeed1 but something short of infinite4 ,this phenomenon was connected with the satellites of ,jupiter1 and the astronomer's name was ,roemer4 ,i will speak first of the observation and then of the man4 ,illustration3 ,,fig4 #gd4--;,fizeau's wheel1 shewing the appearance of distant image seen through its teeth4 #ast1 when stationary1 next when revolving at a moderate speed1 last when revolving at the high speed just sufficient to cause eclipse4 ,jupiter's satellites are visible1 precisely as our own moon is1 by reason of the shimmer of sunlight which they reflect4 ,but as they revolve round their great planet they plunge into his shadow at one part of their course1 and so become eclipsed from sunshine and invisible to us4 ,the moment of disappearance can be sharply observed4 ,take the first satellite as an example4 ,the interval between successive eclipses ought to be its period of revolution round ,jupiter4 ,observe this period4 ,it was not uniform4 ,on the average it was #db hours #dg minutes1 but it seemed to depend on the time of year4 ,when ,roemer observed in spring it was less1 and in autumn it was more than usual4 ,this was evidently a puzzling fact3 what on earth can our year have to do with the motion of a moon of ,jupiter's8 ,it was probably1 therefore1 only an apparent change1 caused either by our greater or less distance from ,jupiter1 or else by our greater or less speed of travelling to or from him4 ,considering it thus1 he was led to see that1 when the time of revolution seemed longest1 we were receding fastest from ,jupiter1 and when shortest1 approaching fastest4 ,if1 then1 light took time on its journey1 if it travelled progressively1 the whole anomaly would be explained4 ,in a second the earth goes nineteen miles2 therefore in #db-c_/d hours 7the time of revolution of ,jupiter's first satellite7 it goes #bi million 7say three million7 miles4 ,the eclipse happens punctually1 but we do not see it till the light conveying the information has travelled the extra three million miles and caught up the earth4 ,evidently1 therefore1 by observing how much the apparent time of revolution is lengthened in one part of the earth's orbit and shortened in another1 getting all the data accurately1 and assuming the truth of our hypothetical explanation1 we can calculate the velocity of light4 ,this is what ,roemer did4 ,now the maximum amount of retardation is just about fifteen seconds4 ,hence light takes this time to travel three million miles2 therefore its velocity is three million divided by fifteen1 say #bjj1jjj1 or1 as we now know more exactly1 #ahf1jjj miles every second4 ,note that the delay does not depend on our distance1 but on our speed4 ,one can tell this by common-sense as soon as we grasp the general idea of the explanation4 ,a velocity cannot possibly depend on a distance only4 ,illustration3 ,,fig4 #ge4--;,eclipses of one of ,jupiter's satellites4 ,a diagram intended to illustrate the dependence of its apparent time of revolution 7from eclipse to eclipse7 on the motion of the earth2 but not illustrating the matter at all well4 ,,tt' ,t'' are successive positions of the earth1 while ,,jj' ,j'' are corresponding positions of ,jupiter4 ,roemer's explanation of the anomaly was not accepted by astronomers4 ,it excited some attention1 and was discussed1 but it was found not obviously applicable to any of the satellites except the first1 and not very simply and satisfactorily even to that4 ,i have1 of course1 given you the theory in its most elementary and simple form4 ,in actual fact a host of disturbing and complicated considerations come in--not so violently disturbing for the first satellite as for the others1 because it moves so quickly1 but still complicated enough4 ,the fact is1 the real motion of ,jupiter's satellites is a most difficult problem4 ,the motion even of our own moon 7the lunar theory7 is difficult enough3 perturbed as its motion is by the sun4 ,you know that ,newton said it cost him more labour than all the rest of the ,principia4 ,but the motion of ,jupiter's satellites is far worse4 ,no one1 in fact1 has yet worked their theory completely out4 ,they are perturbed by the sun1 of course1 but they also perturb each other1 and ,jupiter is far from spherical4 ,the shape of ,jupiter1 and their mutual attractions1 combine to make their motions most peculiar and distracting4 ,hence an error in the time of revolution of a satellite was not certainly due to the cause ,roemer suggested1 unless one could be sure that the inequality was not a real one1 unless it could be shown that the theory of gravitation was insufficient to account for it4 ,this had not then been done2 so the half-made discovery was shelved1 and properly shelved1 as a brilliant but unverified speculation4 ,it remained on the shelf for half a century1 and was no doubt almost forgotten4 ,illustration3 ,,fig4 #gf4--;,a ,transit-instrument for the ,british astronomical expedition1 #ahgd4 ,shewing in its essential features the simplest form of such an instrument4 ,now a word or two about the man4 ,he was a ,dane1 educated at ,copenhagen1 and learned in the mathematics4 ,we first hear of him as appointed to assist ,picard1 the eminent ,french geodetic surveyor 7whose admirable work in determining the length of a degree you remember in connection with ,newton71 who had come over to ,denmark with the object of fixing the exact site of the old and extinct ,tychonic observatory in the island of ,huen4 ,for of course the knowledge of the exact latitude and longitude of every place whence numerous observations have been taken must be an essential to the full interpretation of those observations4 ,the measurements being finished1 young ,roemer accompanied ,picard to ,paris1 and here it was1 a few years after1 that he read his famous paper concerning ,an ,inequality in the ,motion of ,jupiter's ,first ,satellite1 and its explanation by means of an hypothesis of the successive propagation of light4 ,the later years of his life he spent in ,copenhagen as a professor in the ,university and an enthusiastic observer of the heavens1--not a descriptive observer like ,herschel1 but a measuring observer like ,sir ,george ,airy or ,tycho ,brah4 ,he was1 in fact1 a worthy follower of ,tycho1 and the main work of his life is the development and devising of new and more accurate astronomical instruments4 ,many of the large and accurate instruments with which a modern observatory is furnished are the invention of this ,dane4 ,one of the finest observatories in the world is the ,russian one at ,pulkowa1 and a list of the instruments there reads like an extended catalogue of ,roemer's inventions4 ,he not only invented the instruments1 he had them made1 being allowed money for the purpose2 and he used them vigorously1 so that at his death he left great piles of manuscript stored in the national observatory4 ,unfortunately this observatory was in the heart of the city1 and was thus exposed to a danger from which such places ought to be as far as possible exempt4 ,some eighteen years after ,roemer's death a great conflagration broke out in ,copenhagen1 and ruined large portions of the city4 ,the successor to ,roemer1 ,horrebow by name1 fled from his house1 with such valuables as he possessed1 to the observatory1 and there went on with his work4 ,but before long the wind shifted1 and to his horror he saw the flames coming his way4 ,he packed up his own and his predecessor's manuscript observations in two cases1 and prepared to escape with them1 but the neighbours had resorted to the observatory as a place of safety1 and so choked up the staircase with their property that he was barely able to escape himself1 let alone the luggage1 and everything was lost4 ,illustration3 ,,fig4 #gg4--;,diagram of equatorially mounted telescope2 ,,ce is the polar axis parallel to the axis of the earth2 ,,ab the declination axis4 ,the diurnal motion is compensated by motion about the polar axis only1 the other being clamped4 ,of all the observations1 only three days' work remains1 and these were carefully discussed by ,dr4 ,galle1 of ,berlin1 in #ahde1 and their nutriment extracted4 ,these ancient observations are of great use for purposes of comparison with the present state of the heavens1 and throw light upon possible changes that are going on4 ,of course nowadays such a series of observations would be printed and distributed in many libraries1 and so made practically indestructible4 ,sad as the disaster was to the posthumous fame of the great observer1 a considerable compensation was preparing4 ,the very year that the fire occurred in ,denmark a quiet philosopher in ,england was speculating and brooding on a remarkable observation that he had made concerning the apparent motion of certain stars1 and he was led thereby to a discovery of the first magnitude concerning the speed of light--a discovery which resuscitated the old theory of ,roemer about ,jupiter's satellites1 and made both it and him immortal4 ,james ,bradley lived a quiet1 uneventful1 studious life1 mainly at ,oxford but afterwards at the ,national ,observatory at ,greenwich1 of which he was third ,astronomer-,royal1 ,flamsteed and ,halley having preceded him in that office4 ,he had taken orders1 and lectured at ,oxford as ,savilian ,professor4 ,it is said that he pondered his great discovery while pacing the ,long ,walk at ,magdalen ,college--and a beautiful place it is to meditate in4 ,bradley was engaged in making observations to determine if possible the parallax of some of the fixed stars4 ,parallax means the apparent relative shift of bodies due to a change in the observer's position4 ,it is parallax which we observe when travelling by rail and looking out of window at the distant landscape4 ,things at different distances are left behind at different apparent rates1 and accordingly they seem to move relatively to each other4 ,the most distant objects are least affected2 and anything enormously distant1 like the moon1 is not subject to this effect1 but would retain its position however far we travelled1 unless we had some extraordinarily precise means of observation4 ,so with the fixed stars3 they were being observed from a moving carriage--viz4 the earth--and one moving at the rate of nineteen miles a second4 ,unless they were infinitely distant1 or unless they were all at the same distance1 they must show relative apparent motions among themselves4 ,seen from one point of the earth's orbit1 and then in six months from an opposite point1 nearly #ahd million miles away1 surely they must show some difference of aspect4 ,remember that the old ,copernican difficulty had never been removed4 ,if the earth revolved round the sun1 how came it that the fixed stars showed no parallax8 ,the fact still remained a surprise1 and the question a challenge4 ,picard1 like other astronomers1 supposed that it was only because the methods of observation had not been delicate enough2 but now that1 since the invention of the telescope and the founding of ,national ,observatories1 accuracy hitherto undreamt of was possible1 why not attack the problem anew8 ,this1 then1 he did1 watching the stars with great care to see if in six months they showed any change in absolute position with reference to the pole of the heavens2 any known secular motion of the pole1 such as precession1 being allowed for4 ,already he thought he detected a slight parallax for several stars near the pole1 and the subject was exciting much interest4 ,bradley determined to attempt the same investigation4 ,he was not destined to succeed in it4 ,not till the present century was success in that most difficult observation achieved2 and even now it cannot be done by the absolute methods then attempted2 but1 as so often happens1 ,bradley1 in attempting one thing1 hit upon another1 and1 as it happened1 one of still greater brilliance and importance4 ,let us trace the stages of his discovery4 ,atmospheric refraction made horizon observations useless for the delicacy of his purpose1 so he chose stars near the zenith1 particularly one--gamma ,draconis4 ,this he observed very carefully at different seasons of the year by means of an instrument specially adapted for zenith observations1 viz4 a zenith sector4 ,the observations were made in conjunction with a friend of his1 an amateur astronomer named ,molyneux1 and they were made at ,kew4 ,molyneux was shortly made ,first ,lord of the ,admiralty1 or something important of that sort1 and gave up frivolous pursuits4 ,so ,bradley observed alone4 ,they observed the star accurately early in the month of ,december1 and then intended to wait six months4 ,but from curiosity ,bradley observed it again only about a week later4 ,to his surprise1 he found that it had already changed its position4 ,he recorded his observation on the back of an old envelope3 it was his wont thus to use up odd scraps of paper--he was not1 ,i regret to say1 a tidy or methodical person--and this odd piece of paper turned up long afterwards among his manuscripts4 ,it has been photographed and preserved as an historical relic4 ,again and again he repeated the observation of the star1 and continually found it moving still a little further and further south1 an excessively small motion1 but still an appreciable one--not to be set down to errors of observation4 ,so it went on till ,march4 ,it then waited1 and after a bit longer began to return1 until ,june4 ,by ,september it was displaced as much to the north as it had been to the south1 and by ,december it had got back to its original position4 ,it had described1 in fact1 a small oscillation in the course of the year4 ,the motion affected neighbouring stars in a similar way1 and was called an aberration1 or wandering from their true place4 ,for a long time ,bradley pondered over this observation1 and over others like them which he also made4 ,he found one group of stars describing small circles1 while others at a distance from them were oscillating in straight lines1 and all the others were describing ellipses4 ,unless this state of things were cleared up1 accurate astronomy was impossible4 ,the fixed stars6--they were not fixed a bit4 ,to refined and accurate observation1 such as was now possible1 they were all careering about in little orbits having a reference to the earth's year1 besides any proper motion which they might really have of their own1 though no such motion was at present known4 ,not till ,herschel was that discovered2 not till this extraordinary aberration was allowed for could it be discovered4 ,the effect observed by ,bradley and ,molyneux must manifestly be only an apparent motion3 it was absurd to suppose a real stellar motion regulating itself according to the position of the earth4 ,parallax could not do it1 for that would displace stars relatively among each other--it would not move similarly a set of neighbouring stars4 ,at length1 four years after the observation1 the explanation struck him1 while in a boat upon the ,thames4 ,he noticed the apparent direction of the wind changed whenever the boat started4 ,the wind veered when the boat's motion changed4 ,of course the cause of this was obvious enough--the speed of the wind and the speed of the boat were compounded1 and gave an apparent direction of the wind other than the true direction4 ,but this immediately suggested a cause for what he had observed in the heavens4 ,he had been observing an apparent direction of the stars other than the true direction1 because he was observing from a moving vehicle4 ,the real direction was doubtless fixed3 the apparent direction veered about with the motion of the earth4 ,it must be that light did not travel instantaneously1 but gradually1 as ,roemer had surmised fifty years ago2 and that the motion of the light was compounded with the motion of the earth4 ,think of a stream of light or anything else falling on a moving carriage4 ,the carriage will run athwart the stream1 the occupants of the carriage will mistake its true direction4 ,a rifle fired through the windows of a railway carriage by a man at rest outside would make its perforations not in the true line of fire unless the train is stationary4 ,if the train is moving1 the line joining the holes will point to a place in advance of where the rifle is really located4 ,so it is with the two glasses of a telescope1 the object-glass and eye-piece1 which are pierced by the light2 an astronomer1 applying his eye to the tube and looking for the origin of the disturbance1 sees it apparently1 but not in its real position--its apparent direction is displaced in the direction of the telescope's motion2 by an amount depending on the ratio of the velocity of the earth to the velocity of light1 and on the angle between those two directions4 ,illustration3 ,,fig4 #gh4--;,aberration diagram4 ,the light-ray ,l penetrates the object-glass of the moving telescope at ,o1 but does not reach the eye-piece until the telescope has travelled to the second position4 ,consequently a moving telescope does not point out the true direction of the light1 but aims at a point a little in advance4 ,but how minute is the displacement6 ,the greatest effect is obtained when the two motions are at right angles to each other1 i4e4 when the star seen is at right angles to the direction of the earth's motion1 but even then it is only #bj1 or #a_/ahjth part of a degree2 one-ninetieth of the moon's apparent diameter4 ,it could not be detected without a cross-wire in the telescope1 and would only appear as a slight displacement from the centre of the field1 supposing the telescope accurately pointed to the true direction4 ,but if this explanation be true1 it at once gives a method of determining the velocity of light4 ,the maximum angle of deviation1 represented as a ratio of arc radius1 amounts to #a #a ------------ - #jjja ------ #ahj #eg-a_/c #aj1jjj 7a gradient of #a foot in two miles74 ,in other words1 the velocity of light must be #aj1jjj times as great as the velocity of the earth in its orbit4 ,this amounts to a speed of #aij1jjj miles a second--not so very different from what ,roemer had reckoned it in order to explain the anomalies of ,jupiter's first satellite4 ,stars in the direction in which the earth was moving would not be thus affected2 there would be nothing in mere approach or recession to alter direction or to make itself in any way visible4 ,stars at right angles to the earth's line of motion would be most affected1 and these would be all displaced by the full amount of #bj seconds of arc4 ,stars in intermediate directions would be displaced by intermediate amounts4 ,but the line of the earth's motion is approximately a circle round the sun1 hence the direction of its advance is constantly though slowly changing1 and in one year it goes through all the points of the compass4 ,the stars1 being displaced always in the line of advance1 must similarly appear to describe little closed curves1 always a quadrant in advance of the earth1 completing their orbits once a year4 ,those near the pole of the ecliptic will describe circles1 being always at right angles to the motion4 ,those in the plane of the ecliptic 7near the zodiac7 will be sometimes at right angles to the motion1 but at other times will be approached or receded from2 hence these will oscillate like pendulums once a year2 and intermediate stars will have intermediate motions--that is to say1 will describe ellipses of varying excentricity1 but all completed in a year1 and all with the major axis #bj4 ,this agreed very closely with what was observed4 ,the main details were thus clearly and simply explained by the hypothesis of a finite velocity for light1 the successive propagation of light in time4 ,this time there was no room for hesitation1 and astronomers hailed the discovery with enthusiasm4 ,not yet1 however1 did ,bradley rest4 ,the finite velocity of light explained the major part of the irregularities he had observed1 but not the whole4 ,the more carefully he measured the amount of the deviation1 the less completely accurate became its explanation4 ,there clearly was a small outstanding error or discrepancy2 the stars were still subject to an unexplained displacement--not1 indeed1 a displacement that repeated itself every year1 but one that went through a cycle of changes in a longer period4 ,the displacement was only about half that of aberration1 and having a longer period was rather more difficult to detect securely4 ,but the major difficulty was the fact that the two sorts of disturbances were co-existent1 and the skill of disentangling them1 and exhibiting the true and complete cause of each inequality1 was very brilliant4 ,for nineteen years did ,bradley observe this minor displacement1 and in that time he saw it go through a complete cycle4 ,its cause was now clear to him2 the nineteen-year period suggested the explanation4 ,it is the period in which the moon goes through all her changes--a period known to the ancients as the lunar cycle1 or ,metonic cycle1 and used by them to predict eclipses4 ,it is still used for the first rough approximation to the prediction of eclipses1 and to calculate ,easter4 ,the ,golden ,number of the ,prayer-book is the number of the year in this cycle4 ,the cause of the second inequality1 or apparent periodic motion of the stars1 ,bradley made out to be a nodding motion of the earth's axis4 ,the axis of the earth describes its precessional orbit or conical motion every #bf1jjj years1 as had long been known2 but superposed upon this great movement have now been detected minute nods1 each with a period of nineteen years4 ,the cause of the nodding is completely accounted for by the theory of gravitation1 just as the precession of the equinoxes was4 ,both disturbances result from the attraction of the moon on the non-spherical earth--on its protuberant equator4 ,nutation is1 in fact1 a small perturbation of precession4 ,the motion may be observed in a non-sleeping top4 ,the slow conical motion of the top's slanting axis represents the course of precession4 ,sometimes this path is loopy1 and its little nods correspond to nutation4 ,the probable existence of some such perturbation had not escaped the sagacity of ,newton1 and he mentions something about it in the ,principia1 but thinks it too small to be detected by observation4 ,he was thinking1 however1 of a solar disturbance rather than a lunar one1 and this is certainly very small1 though it1 too1 has now been observed4 ,newton was dead before ,bradley made these great discoveries1 else he would have been greatly pleased to hear of them4 ,these discoveries of aberration and nutation1 says ,delambre1 the great ,french historian of science1 secure to their author a distinguished place after ,hipparchus and ,kepler among the astronomers of all ages and all countries4 ,,notes ,,to ,,lecture ,,xi ,lagrange and ,laplace1 both tremendous mathematicians1 worked very much in alliance1 and completed ,newton's work4 ,the ,mcanique ,cleste contains the higher intricacies of astronomy mathematically worked out according to the theory of gravitation4 ,they proved the solar system to be stable2 all its inequalities being periodic1 not cumulative4 ,and ,laplace suggested the nebular hypothesis concerning the origin of sun and planets3 a hypothesis previously suggested1 and to some extent1 elaborated1 by ,kant4 ,a list of some of the principal astronomical researches of ,lagrange and ,laplace3--,libration of the moon4 ,long inequality of ,jupiter and ,saturn4 ,perturbations of ,jupiter's satellites4 ,perturbations of comets4 ,acceleration of the moon's mean motion4 ,improved lunar theory4 ,improvements in the theory of the tides4 ,periodic changes in the form and obliquity of the earth's orbit4 ,stability of the solar system considered as an assemblage of rigid bodies subject to gravity4 ,the two equations which establish the stability of the solar system are3-- ,sum 7me#bsquare rootd7 constant1 and ,sum 7m tan#bthetasquare rootd7 constant2 where m is the mass of each planet1 d its mean distance from the sun1 e the excentricity of its orbit1 and theta the inclination of its plane4 ,however the expressions above formulated may change for individual planets1 the sum of them for all the planets remains invariable4 ,the period of the variations in excentricity of the earth's orbit is #hf1jjj years2 the period of conical revolution of the earth's axis is #be1hjj years4 ,about #ah1jjj years ago the excentricity was at a maximum4 ,,lecture ,,xi ,,lagrange ,,and ,,laplace--,,the ,,stability ,,of ,,the ,,solar ,,system1 ,,and ,,the ,,nebular ,,hypothesis ,laplace was the son of a small farmer or peasant of ,normandy4 ,his extraordinary ability was noticed by some wealthy neighbours1 and by them he was sent to a good school4 ,from that time his career was one brilliant success1 until in the later years of his life his prominence brought him tangibly into contact with the deteriorating influence of politics4 ,perhaps one ought rather to say trying than deteriorating2 for they seem trying to a strong character1 deteriorating to a weak one--and unfortunately1 ,laplace must be classed in this latter category4 ,it has always been the custom in ,france for its high scientific men to be conspicuous also in politics4 ,it seems to be now becoming the fashion in this country also1 ,i regret to say4 ,the life of ,laplace is not specially interesting1 and ,i shall not go into it4 ,his brilliant mathematical genius is unquestionable1 and almost unrivalled4 ,he is1 in fact1 generally considered to come in this respect next after ,newton4 ,his talents were of a more popular order than those of ,lagrange1 and accordingly he acquired fame and rank1 and rose to the highest dignities4 ,nevertheless1 as a man and a politician he hardly commands our respect1 and in time-serving adjustability he is comparable to the redoubtable ,vicar of ,bray4 ,his scientific insight and genius were however unquestionably of the very highest order1 and his work has been invaluable to astronomy4 ,i will give a short sketch of some of his investigations1 so far as they can be made intelligible without overmuch labour4 ,he worked very much in conjunction with ,lagrange1 a more solid though a less brilliant man1 and it is both impossible and unnecessary for us to attempt to apportion respective shares of credit between these two scientific giants1 the greatest scientific men that ,france ever produced4 ,first comes a research into the libration of the moon4 ,this was discovered by ,galileo in his old age at ,arcetri1 just before his blindness4 ,the moon1 as every one knows1 keeps the same face to the earth as it revolves round it4 ,in other words1 it does not rotate with reference to the earth1 though it does rotate with respect to outside bodies4 ,its libration consists in a sort of oscillation1 whereby it shows us now a little more on one side1 now a little more on the other1 so that altogether we are cognizant of more than one-half of its surface--in fact1 altogether of about three-fifths4 ,it is a simple and unimportant matter1 easily explained4 ,the motion of the moon may be analyzed into a rotation about its own axis combined with a revolution about the earth4 ,the speed of the rotation is quite uniform1 the speed of the revolution is not quite uniform1 because the orbit is not circular but elliptical1 and the moon has to travel faster in perigee than in apogee 7in accordance with ,kepler's second law74 ,the consequence of this is that we see a little too far round the body of the moon1 first on one side1 then on the other4 ,hence it appears to oscillate slightly1 like a lop-sided fly-wheel whose revolutions have been allowed to die away so that they end in oscillations of small amplitude4#bc ,its axis of rotation1 too1 is not precisely perpendicular to its plane of revolution1 and therefore we sometimes see a few hundred miles beyond its north pole1 sometimes a similar amount beyond its south4 ,lastly1 there is a sort of parallax effect1 owing to the fact that we see the rising moon from one point of view1 and the setting moon from a point #h1jjj miles distant2 and this base-line of the earth's diameter gives us again some extra glimpses4 ,this diurnal or parallactic libration is really more effective than the other two in extending our vision into the space-facing hemisphere of the moon4 ,these simple matters may as well be understood1 but there is nothing in them to dwell upon4 ,the far side of the moon is probably but little worth seeing4 ,its features are likely to be more blurred with accumulations of meteoric dust than are those of our side1 but otherwise they are likely to be of the same general character4 ,the thing of real interest is the fact that the moon does turn the same face towards us2 i4e4 has ceased to rotate with respect to the earth 7if ever it did so74 ,the stability of this state of things was shown by ,lagrange to depend on the shape of the moon4 ,it must be slightly egg-shape1 or prolate--extended in the direction of the earth2 its earth-pointing diameter being a few hundred feet longer than its visible diameter2 a cause slight enough1 but nevertheless sufficient to maintain stability1 except under the action of a distinct disturbing cause4 ,the prolate or lemon-like shape is caused by the gravitative pull of the earth1 balanced by the centrifugal whirl4 ,the two forces balance each other as regards motion1 but between them they have strained the moon a trifle out of shape4 ,the moon has yielded as if it were perfectly plastic2 in all probability it once was so4 ,it may be interesting to note for a moment the correlative effect of this aspect of the moon1 if we transfer ourselves to its surface in imagination1 and look at the earth 7cf4 ,fig4 #da74 ,the earth would be like a gigantic moon of four times our moon's diameter1 and would go through its phases in regular order4 ,but it would not rise or set3 it would be fixed in the sky1 and subject only to a minute oscillation to and fro once a month1 by reason of the libration we have been speaking of4 ,its aspect1 as seen by markings on its surface1 would rapidly change1 going through a cycle in twenty-four hours2 but its permanent features would be usually masked by lawless accumulations of cloud1 mainly aggregated in rude belts parallel to the equator4 ,and these cloudy patches would be the most luminous1 the whitest portions2 for of course it would be their silver lining that we would then be looking on4#bd ,next among the investigations of ,lagrange and ,laplace we will mention the long inequality of ,jupiter and ,saturn4 ,halley had found that ,jupiter was continually lagging behind its true place as given by the theory of gravitation2 and1 on the other hand1 that ,saturn was being accelerated4 ,the lag on the part of ,jupiter amounted to about #cd-a_/b minutes in a century4 ,overhauling ancient observations1 however1 ,halley found signs of the opposite state of things1 for when he got far enough back ,jupiter was accelerated and ,saturn was being retarded4 ,here was evidently a case of planetary perturbation1 and ,laplace and ,lagrange undertook the working of it out4 ,they attacked it as a case of the problem of three bodies1 viz4 the sun1 ,jupiter1 and ,saturn2 which are so enormously the biggest of the known bodies in the system that insignificant masses like the ,earth1 ,mars1 and the rest1 may be wholly neglected4 ,they succeeded brilliantly1 after a long and complex investigation3 succeeded1 not in solving the problem of the three bodies1 but1 by considering their mutual action as perturbations superposed on each other1 in explaining the most conspicuous of the observed anomalies of their motion1 and in laying the foundation of a general planetary theory4 ,illustration3 ,,fig4 #gi4--,shewing the three conjunction places in the orbits of ,jupiter and ,saturn4 ,the two planets are represented as leaving one of the conjunctions where ,jupiter was being pulled back and ,saturn being pulled forward by their mutual attraction4 ,one of the facts that plays a large part in the result was known to the old astrologers1 viz4 that ,jupiter and ,saturn come into conjunction with a certain triangular symmetry2 the whole scheme being called a trigon1 and being mentioned several times by ,kepler4 ,it happens that five of ,jupiter's years very nearly equal two of ,saturn's1#be so that they get very nearly into conjunction three times in every five ,jupiter years1 but not exactly4 ,the result of this close approach is that periodically one pulls the other on and is itself pulled back2 but since the three points progress1 it is not always the same planet which gets pulled back4 ,the complete theory shows that in the year #aefj there was no marked perturbation3 before that it was in one direction1 while afterwards it was in the other direction1 and the period of the whole cycle of disturbances is #ibi of our years4 ,the solution of this long outstanding puzzle by the theory of gravitation was hailed with the greatest enthusiasm by astronomers1 and it established the fame of the two ,french mathematicians4 ,next they attacked the complicated problem of the motions of ,jupiter's satellites4 ,they succeeded in obtaining a theory of their motions which represented fact very nearly indeed1 and they detected the following curious relationship between the satellites3--,the speed of the first satellite twice the speed of the second is equal to the speed of the third4 ,they found this1 not empirically1 after the manner of ,kepler1 but as a deduction from the law of gravitation2 for they go on to show that even if the satellites had not started with this relation they would sooner or later1 by mutual perturbation1 get themselves into it4 ,one singular consequence of this1 and of another quite similar connection between their positions1 is that all three satellites can never be eclipsed at once4 ,the motion of the fourth satellite is less tractable2 it does not so readily form an easy system with the others4 ,after these great successes the two astronomers naturally proceeded to study the mutual perturbations of all other bodies in the solar system4 ,and one very remarkable discovery they made concerning the earth and moon1 an account of which will be interesting1 though the details and processes of calculation are quite beyond us in a course like this4 ,astronomical theory had become so nearly perfect by this time1 and observations so accurate1 that it was possible to calculate many astronomical events forwards or backwards1 over even a thousand years or more1 with admirable precision4 ,now1 ,halley had studied some records of ancient eclipses1 and had calculated back by means of the lunar theory to see whether the calculation of the time they ought to occur would agree with the record of the time they did occur4 ,to his surprise he found a discrepancy1 not a large one1 but still one quite noticeable4 ,to state it as we know it now3--,an eclipse a century ago happened twelve seconds later than it ought to have happened by theory2 two centuries back the error amounted to forty-eight seconds1 in three centuries it would be #ajh seconds1 and so on2 the lag depending on the square of the time4 ,by research1 and help from scholars1 he succeeded in obtaining the records of some very ancient eclipses indeed4 ,one in ,egypt towards the end of the tenth century ,a4,d42 another in #bja ,a4,d42 another a little before ,christ2 and one1 the oldest of all of which any authentic record has been preserved1 observed by the ,chaldan astronomers in ,babylon in the reign of ,hezekiah4 ,calculating back to this splendid old record of a solar eclipse1 over the intervening #b1djj years1 the calculated and the observed times were found to disagree by nearly two hours4 ,pondering over an explanation of the discrepancy1 ,halley guessed that it must be because the moon's motion was not uniform1 it must be going quicker and quicker1 gaining twelve seconds each century on its previous gain--a discovery announced by him as the acceleration of the moon's mean motion4 ,the month was constantly getting shorter4 ,what was the physical cause of this acceleration according to the theory of gravitation8 ,many attacked the question1 but all failed4 ,this was the problem ,laplace set himself to work out4 ,a singular and beautiful result rewarded his efforts4 ,you know that the earth describes an elliptic orbit round the sun3 and that an ellipse is a circle with a certain amount of flattening or excentricity4#bf ,well1 ,laplace found that the excentricity of the earth's orbit must be changing1 getting slightly less2 and that this change of excentricity would have an effect upon the length of the month4 ,it would make the moon go quicker4 ,one can almost see how it comes about4 ,a decrease in excentricity means an increase in mean distance of the earth from the sun4 ,this means to the moon a less solar perturbation4 ,now one effect of the solar perturbation is to keep the moon's orbit extra large3 if the size of its orbit diminishes1 its velocity must increase1 according to ,kepler's third law4 ,laplace calculated the amount of acceleration so resulting1 and found it ten seconds a century2 very nearly what observation required2 for1 though ,i have quoted observation as demanding twelve seconds per century1 the facts were not then so distinctly and definitely ascertained4 ,this calculation for a long time seemed thoroughly satisfactory1 but it is not the last word on the subject4 ,quite lately an error has been found in the working1 which diminishes the theoretical gravitation-acceleration to six seconds a century instead of ten1 thus making it insufficient to agree exactly with fact4 ,the theory of gravitation leaves an outstanding error4 7,the point is now almost thoroughly understood1 and we shall return to it in ,lecture ,,xviii74 ,but another question arises out of this discussion4 ,i have spoken of the excentricity of the earth's orbit as decreasing4 ,was it always decreasing8 and if so1 how far back was it so excentric that at perihelion the earth passed quite near the sun8 ,if it ever did thus pass near the sun1 the inference is manifest--the earth must at one time have been thrown off1 or been separated off1 from the sun4 ,if a projectile could be fired so fast that it described an orbit round the earth--and the speed of fire to attain this lies between five and seven miles a second 7not less than the one1 nor more than the other7--it would ever afterwards pass through its point of projection as one point of its elliptic orbit2 and its periodic return through that point would be the sign of its origin4 ,similarly1 if a satellite does not come near its central orb1 and can be shown never to have been near it1 the natural inference is that it has not been born from it1 but has originated in some other way4 ,the question which presented itself in connexion with the variable ellipticity of the earth's orbit was the following3--,had it always been decreasing1 so that once it was excentric enough just to graze the sun at perihelion as a projected body would do8 ,into the problem thus presented ,lagrange threw himself1 and he succeeded in showing that no such explanation of the origin of the earth is possible4 ,the excentricity of the orbit1 though now decreasing1 was not always decreasing2 ages ago it was increasing3 it passes through periodic changes4 ,eighteen thousand years ago its excentricity was a maximum2 since then it has been diminishing1 and will continue to diminish for #be1jjj years more1 when it will be an almost perfect circle2 it will then begin to increase again1 and so on4 ,the obliquity of the ecliptic is also changing periodically1 but not greatly3 the change is less than three degrees4 ,this research has1 or ought to have1 the most transcendent interest for geologists and geographers4 ,you know that geologists find traces of extraordinary variations of temperature on the surface of the earth4 ,england was at one time tropical1 at another time glacial4 ,far away north1 in ,spitzbergen1 evidence of the luxuriant vegetation of past ages has been found2 and the explanation of these great climatic changes has long been a puzzle4 ,does not the secular variation in excentricity of the earth's orbit1 combined with the precession of the equinoxes1 afford a key8 ,and if a key at all1 it will be an accurate key1 and enable us to calculate back with some precision to the date of the glacial epoch2 and again to the time when a tropical flora flourished in what is now northern ,europe1 i4e4 to the date of the ,carboniferous era4 ,this aspect of the subject has recently been taught with vigour and success by ,dr4 ,croll in his book ,climate and ,time4 ,a brief and partial explanation of the matter may be given1 because it is a point of some interest and is also one of fair simplicity4 ,every one knows that the climatic conditions of winter and summer are inverted in the two hemispheres1 and that at present the sun is nearest to us in our 7northern7 winter4 ,in other words1 the earth's axis is inclined so as to tilt its north pole away from the sun at perihelion1 or when the earth is at the part of its elliptic orbit nearest the sun's focus2 and to tilt it towards the sun at aphelion4 ,the result of this present state of things is to diminish the intensity of the average northern winter and of the average northern summer1 and on the other hand to aggravate the extremes of temperature in the southern hemisphere2 all other things being equal4 ,of course other things are not equal1 and the distribution of land and sea is a still more powerful climatic agent than is the three million miles or so extra nearness of the sun4 ,but it is supposed that the ,antarctic ice-cap is larger than the northern1 and increased summer radiation with increased winter cold would account for this4 ,but the present state of things did not always obtain4 ,the conical movement of the earth's axis 7now known by a curious perversion of phrase as precession7 will in the course of #ac1jjj years or so cause the tilt to be precisely opposite1 and then we shall have the more extreme winters and summers instead of the southern hemisphere4 ,if the change were to occur now1 it might not be overpowering1 because now the excentricity is moderate4 ,but if it happened some time back1 when the excentricity was much greater1 a decidedly different arrangement of climate may have resulted4 ,there is no need to say if it happened some time back3 it did happen1 and accordingly an agent for affecting the distribution of mean temperature on the earth is to hand2 though whether it is sufficient to achieve all that has been observed by geologists is a matter of opinion4 ,once more1 the whole diversity of the seasons depends on the tilt of the earth's axis1 the #bc by which it is inclined to a perpendicular to the orbital plane2 and this obliquity or tilt is subject to slow fluctuations4 ,hence there will come eras when all causes combine to produce a maximum extremity of seasons in the northern hemisphere1 and other eras when it is the southern hemisphere which is subject to extremes4 ,but a grander problem still awaited solution--nothing less than the fate of the whole solar system4 ,here are a number of bodies of various sizes circulating at various rates round one central body1 all attracted by it1 and all attracting each other1 the whole abandoned to the free play of the force of gravitation3 what will be the end of it all8 ,will they ultimately approach and fall into the sun1 or will they recede further and further from him1 into the cold of space8 ,there is a third possible alternative3 may they not alternately approach and recede from him1 so as on the whole to maintain a fair approximation to their present distances1 without great and violent extremes of temperature either way8 ,if any one planet of the system were to fall into the sun1 more especially if it were a big one like ,jupiter or ,saturn1 the heat produced would be so terrific that life on this earth would be destroyed1 even at its present distance2 so that we are personally interested in the behaviour of the other planets as well as in the behaviour of our own4 ,the result of the portentously difficult and profoundly interesting investigation1 here sketched in barest outline1 is that the solar system is stable3 that is to say1 that if disturbed a little it will oscillate and return to its old state2 whereas if it were unstable the slightest disturbance would tend to accumulate1 and would sooner or later bring about a catastrophe4 ,a hanging pendulum is stable1 and oscillates about a mean position2 its motion is periodic4 ,a top-heavy load balanced on a point is unstable4 ,all the changes of the solar system are periodic1 i4e4 they repeat themselves at regular intervals1 and they never exceed a certain moderate amount4 ,the period is something enormous4 ,they will not have gone through all their changes until a period of #b1jjj1jjj years has elapsed4 ,this is the period of the planetary oscillation3 a great pendulum of eternity which beats ages as our pendulums beat seconds4 ,enormous it seems2 and yet we have reason to believe that the earth has existed through many such periods4 ,the two laws of stability discovered and stated by ,lagrange and ,laplace ,i can state1 though they may be difficult to understand3-- ,represent the masses of the several planets by m#a1 m#b1 c42 their mean distances from the sun 7or radii vectores7 by r#a1 r#b1 c42 the excentricities of their orbits by e#a1 e#b1 c42 and the obliquity of the planes of these orbits1 reckoned from a single plane of reference or invariable plane1 by theta#a1 theta#b1 c42 then all these quantities 7except m7 are liable to fluctuate2 but1 however much they change1 an increase for one planet will be accompanied by a decrease for some others2 so that1 taking all the planets into account1 the sum of a set of terms like these1 m#a;e#ab square rootr#a m#b;e#bb square rootr#b c41 will remain always the same4 ,this is summed up briefly in the following statement3 ,sigma7me#b square rootr7 constant4 ,that is one law1 and the other is like it1 but with inclination of orbit instead of excentricity1 viz43 ,sigma7mtheta#b square rootr7 constant4 ,the value of each of these two constants can at any time be calculated4 ,at present their values are small4 ,hence they always were and always will be small2 being1 in fact1 invariable4 ,hence neither e nor r nor theta can ever become infinite1 nor can their average value for the system ever become zero4 ,the planets may share the given amount of total excentricity and obliquity in various proportions between themselves2 but even if it were all piled on to one planet it would not be very excessive1 unless the planet were so small a one as ,mercury2 and it would be most improbable that one planet should ever have all the excentricity of the solar system heaped upon itself4 ,the earth1 therefore1 never has been1 nor ever will be1 enormously nearer the sun than it is at present3 nor can it ever get very much further off4 ,its changes are small and are periodic--an increase is followed by a decrease1 like the swing of a pendulum4 ,the above two laws have been called the ,magna ,charta of the solar system1 and were long supposed to guarantee its absolute permanence4 ,so far as the theory of gravitation carries us1 they do guarantee its permanence2 but something more remains to be said on the subject in a future lecture 7,,xviii74 ,and now1 finally1 we come to a sublime speculation1 thrown out by ,laplace1 not as the result of profound calculation1 like the results hitherto mentioned1 not following certainly from the theory of gravitation1 or from any other known theory1 and therefore not to be accepted as more than a brilliant hypothesis1 to be confirmed or rejected as our knowledge extends4 ,this speculation is the ,nebular hypothesis4 ,since the time of ,laplace the nebular hypothesis has had ups and downs of credence1 sometimes being largely believed in1 sometimes being almost ignored4 ,at the present time it holds the field with perhaps greater probability of ultimate triumph than has ever before seemed to belong to it--far greater than belonged to it when first propounded4 ,it had been previously stated clearly and well by the philosopher ,kant1 who was intensely interested in the starry heavens as well as in the mind of man1 and who shewed in connexion with astronomy also a most surprising genius4 ,the hypothesis ought by rights perhaps to be known rather by his name than by that of ,laplace4 ,the data on which it was founded are these3--,every motion in the solar system known at that time took place in one direction1 and in one direction only4 ,thus the planets revolve round the sun1 all going the same way round2 moons revolve round the planets1 still maintaining the same direction of rotation1 and all the bodies that were known to rotate on their own axis did so with still the same kind of spin4 ,moreover1 all these motions take place in or near a single plane4 ,the ancients knew that sun moon and planets all keep near to the ecliptic1 within a belt known as the zodiac3 none strays away into other parts of the sky4 ,satellites also1 and rings1 are arranged in or near the same plane2 and the plane of diurnal spin1 or equator of the different bodies1 is but slightly tilted4 ,now all this could not be the result of chance4 ,what could have caused it8 ,is there any connection or common ancestry possible1 to account for this strange family likeness8 ,there is no connection now1 but there may have been once4 ,must have been1 we may almost say4 ,it is as though they had once been parts of one great mass rotating as a whole2 for if such a rotating mass broke up1 its parts would retain its direction of rotation4 ,but such a mass1 filling all space as far as or beyond ,saturn1 although containing the materials of the whole solar system in itself1 must have been of very rare consistency4 ,occupying so much bulk it could not have been solid1 nor yet liquid1 but it might have been gaseous4 ,are there any such gigantic rotating masses of gas in the heaven now8 ,certainly there are2 there are the nebul4 ,some of the nebul are now known to be gaseous1 and some of them at least are in a state of rotation4 ,laplace could not have known this for certain1 but he suspected it4 ,the first distinctly spiral nebula was discovered by the telescope of ,lord ,rosse2 and quite recently a splendid photograph of the great ,andromeda nebula1 by our townsman1 ,mr4 ,isaac ,roberts1 reveals what was quite unsuspected--and makes it clear that this prodigious mass also is in a state of extensive and majestic whirl4 ,very well1 then1 put this problem3--,a vast mass of rotating gas is left to itself to cool for ages and to condense as it cools3 how will it behave8 ,a difficult mathematical problem1 worthy of being attacked to-day2 not yet at all adequately treated4 ,there are those who believe that by the complete treatment of such a problem all the history of the solar system could be evolved4 ,illustration3 ,,fig4 #hj4--,lord ,rosse's drawing of the spiral nebula in ,canes ,venatici1 with the stub marks of the draughtsman unduly emphasised into features by the engraver4 ,laplace pictured to himself this mass shrinking and thereby whirling more and more rapidly4 ,a spinning body shrinking in size and retaining its original amount of rotation1 as it will unless a brake is applied1 must spin more and more rapidly as it shrinks4 ,it has what mathematicians call a constant moment of momentum2 and what it loses in leverage1 as it shrinks1 it gains in speed4 ,the mass is held together by gravitation1 every particle attracting every other particle2 but since all the particles are describing curved paths1 they will tend to fly off tangentially1 and only a small excess of the gravitation force over the centrifugal is left to pull the particles in1 and slowly to concentrate the nebula4 ,the mutual gravitation of the parts is opposed by the centrifugal force of the whirl4 ,at length a point is reached where the two forces balance4 ,a portion outside a certain line will be in equilibrium2 it will be left behind1 and the rest must contract without it4 ,a ring is formed1 and away goes the inner nucleus contracting further and further towards a centre4 ,after a time another ring will be left behind in the same way1 and so on4 ,what happens to these rings8 ,they rotate with the motion they possess when thrown or shrunk off2 but will they remain rings8 ,if perfectly regular they may2 if there be any irregularity they are liable to break up4 ,they will break into one or two or more large masses1 which are ultimately very likely to collide and become one4 ,the revolving body so formed is still a rotating gaseous mass2 and it will go on shrinking and cooling and throwing off rings1 like the larger nucleus by which it has been abandoned4 ,as any nucleus gets smaller1 its rate of rotation increases1 and so the rings last thrown off will be spinning faster than those thrown off earliest4 ,the final nucleus or residual central body will be rotating fastest of all4 ,the nucleus of the whole original mass we now see shrunk up into what we call the sun1 which is spinning on its axis once every twenty-five days4 ,the rings successively thrown off by it are now the planets--some large1 some small--those last thrown off rotating round him comparatively quickly1 those outside much more slowly4 ,the rings thrown off by the planetary gaseous masses as they contracted have now become satellites2 except one ring which has remained without breaking up1 and is to be seen rotating round ,saturn still4 ,one other similar ring1 an abortive attempt at a planet1 is also left round the sun 7the zone of asteroids74 ,such1 crudely and baldly1 is the famous nebular hypothesis of ,laplace4 ,it was first stated1 as has been said above1 by the philosopher ,kant1 but it was elaborated into much fuller detail by the greatest of ,french mathematicians and astronomers4 ,the contracting masses will condense and generate great quantities of heat by their own shrinkage2 they will at a certain stage condense to liquid1 and after a time will begin to cool and congeal with a superficial crust1 which will get thicker and thicker2 but for ages they will remain hot1 even after they have become thoroughly solid4 ,the small ones will cool fastest2 the big ones will retain their heat for an immense time4 ,bullets cool quickly1 cannon-balls take hours or days to cool1 planets take millions of years4 ,our moon may be nearly cold1 but the earth is still warm--indeed1 very hot inside4 ,jupiter is believed by some observers still to glow with a dull red heat2 and the high temperature of the much larger and still liquid mass of the sun is apparent to everybody4 ,not till it begins to scum over will it be perceptibly cooler4 ,illustration3 ,,fig4 #ha4--,saturn4 ,many things are now known concerning heat which were not known to ,laplace 7in the above paragraph they are only hinted at71 and these confirm and strengthen the general features of his hypothesis in a striking way2 so do the most recent telescopic discoveries4 ,but fresh possibilities have now occurred to us1 tidal phenomena are seen to have an influence then wholly unsuspected1 and it will be in a modified and amplified form that the philosopher of next century will still hold to the main features of this famous old ,nebular ,hypothesis respecting the origin of the sun and planets--the ,evolution of the solar system4 ,,notes ,,to ,,lecture ,,xii ,the subject of stellar astronomy was first opened up by ,sir ,william ,herschel1 the greatest observing astronomer4 ,frederick ,william ,herschel was born in ,hanover in #agch1 and brought up as a musician4 ,came to ,england in #agef4 ,first saw a telescope in #aggc4 ,made a great many himself1 and began a survey of the heavens4 ,his sister ,caroline1 born in #agej1 came to ,england in #aggb1 and became his devoted assistant to the end of his life4 ,uranus discovered in #agha4 ,music finally abandoned next year1 and the #dj-;foot telescope begun4 ,discovered two moons of ,saturn and two of ,uranus4 ,reviewed1 described1 and gauged all the visible heavens4 ,discovered and catalogued #b1ejj nebul and #hjf double stars4 ,speculated concerning the ,milky ,way1 the nebulosity of stars1 the origin and growth of solar systems4 ,discovered that the stars were in motion1 not fixed1 and that the sun as one of them was journeying towards a point in the constellation ,hercules4 ,died in #ahbb1 eighty-four years old4 ,caroline ,herschel discovered eight comets1 and lived on to the age of ninety-eight4 ,,lecture ,,xii ,,herschel ,,and ,,the ,,motion ,,of ,,the ,,fixed ,,stars ,we may admit1 ,i think1 that1 with a few notable exceptions1 the work of the great men we have been recently considering was rather to complete and round off the work of ,newton1 than to strike out new and original lines4 ,this was the whole tendency of eighteenth century astronomy4 ,it appeared to be getting into an adult and uninteresting stage1 wherein everything could be calculated and predicted4 ,labour and ingenuity1 and a severe mathematical training1 were necessary to work out the remote consequences of known laws1 but nothing fresh seemed likely to turn up4 ,consequently men's minds began turning in other directions1 and we find chemistry and optics largely studied by some of the greatest minds1 instead of astronomy4 ,but before the century closed there was destined to arise one remarkable exception--a man who was comparatively ignorant of that which had been done before--a man unversed in mathematics and the intricacies of science1 but who possessed such a real and genuine enthusiasm and love of ,nature that he overcame the force of adverse circumstances1 and entering the territory of astronomy by a by-path1 struck out a new line for himself1 and infused into the science a healthy spirit of fresh life and activity4 ,this man was ,william ,herschel4 ,the rise of ,herschel1 says ,miss ,clerke1 is the one conspicuous anomaly in the otherwise somewhat quiet and prosy eighteenth century4 ,it proved decisive of the course of events in the nineteenth4 ,it was unexplained by anything that had gone before1 yet all that came after hinged upon it4 ,it gave a new direction to effort2 it lent a fresh impulse to thought4 ,it opened a channel for the widespread public interest which was gathering towards astronomical subjects to flow in4 ,herschel was born at ,hanover in #agch1 the son of an oboe player in a military regiment4 ,the father was a good musician1 and a cultivated man4 ,the mother was a ,german ,frau of the period1 a strong1 active1 business-like woman1 of strong character and profound ignorance4 ,herself unable to write1 she set her face against learning and all new-fangled notions4 ,the education of the sons she could not altogether control1 though she lamented over it1 but the education of her two daughters she strictly limited to cooking1 sewing1 and household management4 ,these1 however1 she taught them well4 ,it was a large family1 and ,william was the fourth child4 ,we need only remember the names of his younger brother ,alexander1 and of his much younger sister ,caroline4 ,they were all very musical--the youngest boy was once raised upon a table to play the violin at a public performance4 ,the girls were forbidden to learn music by their mother1 but their father sometimes taught them a little on the sly4 ,alexander was besides an ingenious mechanician4 ,at the age of seventeen1 ,william became oboist to the ,hanoverian ,guards1 shortly before the regiment was ordered to ,england4 ,two years later he removed himself from the regiment1 with the approval of his parents1 though probably without the approbation or consent of the commanding officer1 by whom such removal would be regarded as simple desertion1 which indeed it was2 and ,george ,,iii4 long afterwards handed him an official pardon for it4 ,at the age of nineteen1 he was thus launched in ,england with an outfit of some ,french1 ,latin1 and ,english1 picked up by himself2 some skill in playing the hautboy1 the violin1 and the organ1 as taught by his father2 and some good linen and clothing1 and an immense stock of energy1 provided by his mother4 ,he lived as musical instructor to one or two militia bands in ,yorkshire1 and for three years we hear no more than this of him4 ,but1 at the end of that time1 a noted organist1 ,dr4 ,miller1 of ,durham1 who had heard his playing1 proposed that he should come and live with him and play at concerts1 which he was very glad to do4 ,he next obtained the post of organist at ,halifax2 and some four or five years later he was invited to become organist at the ,octagon ,chapel in ,bath1 and soon led the musical life of that then very fashionable place4 ,about this time he went on a short visit to his family at ,hanover1 by all of whom he was very much beloved1 especially by his young sister ,caroline1 who always regarded him as specially her own brother4 ,it is rather pitiful1 however1 to find that her domestic occupations still unfairly repressed and blighted her life4 ,she says3-- ,of the joys and pleasures which all felt at this long-wished-for meeting with my--let me say my dearest--brother1 but a small portion could fall to my share2 for with my constant attendance at church and school1 besides the time ,i was employed in doing the drudgery of the scullery1 it was but seldom ,i could make one in the group when the family were assembled together4 ,while at ,bath he wrote many musical pieces--glees1 anthems1 chants1 pieces for the harp1 and an orchestral symphony4 ,he taught a large number of pupils1 and lived a hard and successful life4 ,after fourteen hours or so spent in teaching and playing1 he would retire at night to instruct his mind with a study of mathematics1 optics1 ,italian1 or ,greek1 in all of which he managed to make some progress4 ,he also about this time fell in with some book on astronomy4 ,in #agfc his father was struck with paralysis1 and two years later he died4 ,william then proposed that ,alexander should come over from ,hanover and join him at ,bath1 which was done4 ,next they wanted to rescue their sister ,caroline from her humdrum existence1 but this was a more difficult matter4 ,caroline's journal gives an account of her life at this time that is instructive4 ,here are a few extracts from it3-- ,my father wished to give me something like a polished education1 but my mother was particularly determined that it should be a rough1 but at the same time a useful one2 and nothing further she thought was necessary but to send me two or three months to a sempstress to be taught to make household linen4444 ,my mother would not consent to my being taught ,french1 444 so all my father could do for me was to indulge me 7and please himself7 sometimes with a short lesson on the violin1 when my mother was either in good humour or out of the way4444 ,she had cause for wishing me not to know more than was necessary for being useful in the family2 for it was her certain belief that my brother ,william would have returned to his country1 and my eldest brother not have looked so high1 if they had had a little less learning4 ,however1 seven years after the death of their father1 ,william went over to ,germany and returned to ,england in triumph1 bringing ,caroline with him3 she being then twenty-two4 ,so now began a busy life in ,bath4 ,for ,caroline the work must have been tremendous4 ,for1 besides having to learn singing1 she had to learn ,english4 ,she had1 moreover1 to keep accounts and do the marketing4 ,when the season at ,bath was over1 she hoped to get rather more of her brother ,william's society2 but he was deep in optics and astronomy1 used to sleep with the books under his pillow1 read them during meals1 and scarcely ever thought of anything else4 ,he was determined to see for himself all the astronomical wonders2 and there being a small ,gregorian reflector in one of the shops1 he hired it4 ,but he was not satisfied with this1 and contemplated making a telescope #bj feet long4 ,he wrote to opticians inquiring the price of a mirror suitable1 but found there were none so large1 and that even the smaller ones were beyond his means4 ,nothing daunted1 he determined to make some for himself4 ,alexander entered into his plans3 tools1 hones1 polishers1 and all sorts of rubbish were imported into the house1 to the sister's dismay1 who says3-- ,illustration3 ,,fig4 #hb4--,principle of ,newtonian reflector4 ,and then1 to my sorrow1 ,i saw almost every room turned into a workshop4 ,a cabinet-maker making a tube and stands of all descriptions in a handsomely furnished drawing-room2 ,alex4 putting up a huge turning-machine 7which he had brought in the autumn from ,bristol1 where he used to spend the summer7 in a bed-room1 for turning patterns1 grinding glasses1 and turning eye-pieces1 c4 ,at the same time music durst not lie entirely dormant during the summer1 and my brother had frequent rehearsals at home4 ,finally1 in #aggd1 at the age of thirty-six1 he had made himself a #e-a_/b-;foot telescope1 and began to view the heavens4 ,so attached was he to the instrument that he would run from the concert-room between the parts1 and take a look at the stars4 ,he soon began another telescope1 and then another4 ,he must have made some dozen different telescopes1 always trying to get them bigger and bigger2 at last he got a #g-;foot and then a #aj-;foot instrument1 and began a systematic survey of the heavens2 he also began to communicate his results to the ,royal ,society4 ,he now took a larger house1 with more room for workshops1 and a grass plot for a #bj-;foot telescope1 and still he went on grinding mirrors--literally hundreds of them4 ,i read another extract from the diary of his sister1 who waited on him and obeyed him like a spaniel3-- ,my time was taken up with copying music and practising1 besides attendance on my brother when polishing1 since by way of keeping him alive ,i was constantly obliged to feed him by putting the victuals by bits into his mouth4 ,this was once the case when1 in order to finish a #g-;foot mirror1 he had not taken his hands from it for sixteen hours together4 ,in general he was never unemployed at meals1 but was always at those times contriving or making drawings of whatever came in his mind4 ,generally ,i was obliged to read to him whilst he was at the turning-lathe1 or polishing mirrors--,don ,quixote1 ,arabian ,nights' ,entertainments1 the novels of ,sterne1 ,fielding1 c42 serving tea and supper without interrupting the work with which he was engaged1 444 and sometimes lending a hand4 ,i became1 in time1 as useful a member of the workshop as a boy might be to his master in the first year of his apprenticeship4444 ,but as ,i was to take a part the next year in the oratorios1 ,i had1 for a whole twelvemonth1 two lessons per week from ,miss ,fleming1 the celebrated dancing-mistress1 to drill me for a gentlewoman 7,god knows how she succeeded74 ,so we lived on without interruption4 ,my brother ,alex4 was absent from ,bath for some months every summer1 but when at home he took much pleasure in executing some turning or clockmaker's work for his brother4 ,the music1 and the astronomy1 and the making of telescopes1 all went on together1 each at high pressure1 and enough done in each to satisfy any ordinary activity4 ,but the ,herschels knew no rest4 ,grinding mirrors by day1 concerts and oratorios in the evening1 star-gazing at night4 ,it is strange his health could stand it4 ,the star-gazing1 moreover1 was no dilettante work2 it was based on a serious system--a well thought out plan of observation4 ,it was nothing less than this--to pass the whole heavens steadily and in order through the telescope1 noting and describing and recording every object that should be visible1 whether previously known or unknown4 ,the operation is called sweeping2 but it is not a rapid passage from one object to another1 as the term might suggest2 it is a most tedious business1 and consists in following with the telescope a certain field of view for some minutes1 so as to be sure that nothing is missed1 then shifting it to the next overlapping field1 and watching again4 ,and whatever object appears must be scrutinized anxiously to see what there is peculiar about it4 ,if a star1 it may be double1 or it may be coloured1 or it may be nebulous2 or again it may be variable1 and so its brightness must be estimated in order to compare with a subsequent observation4 ,four distinct times in his life did ,herschel thus pass the whole visible heavens under review2 and each survey occupied him several years4 ,he discovered double stars1 variable stars1 nebul1 and comets2 and ,mr4 ,william ,herschel1 of ,bath1 the amateur astronomer1 was gradually emerging from his obscurity1 and becoming a known man4 ,tuesday1 the #acth of ,march1 #agha1 is a date memorable in the annals of astronomy4 ,on this night1 he writes to the ,royal ,society1 in examining the small stars near eta ,geminorum1 ,i perceived one visibly larger than the rest4 ,struck with its uncommon appearance1 ,i compared it to eta ,geminorum and another star1 and finding it so much larger than either1 ,i suspected it to be a comet4 ,the comet was immediately observed by professional astronomers1 and its orbit was computed by some of them4 ,it was thus found to move in nearly a circle instead of an elongated ellipse1 and to be nearly twice as far from the sun as ,saturn4 ,it was no comet1 it was a new planet2 more than #ajj times as big as the earth1 and nearly twice as far away as ,saturn4 ,it was presently christened ,uranus4 ,this was a most striking discovery1 and the news sped over ,europe4 ,to understand the interest it excited we must remember that such a discovery was unique4 ,since the most ancient times of which men had any knowledge1 the planets ,mercury1 ,venus1 ,mars1 ,jupiter1 ,saturn1 had been known1 and there had been no addition to their number4 ,galileo and others had discovered satellites indeed1 but a new primary planet was an entire and utterly unsuspected novelty4 ,one of the most immediate consequences of the event was the discovery of ,herschel himself4 ,the ,royal ,society made him a ,fellow the same year4 ,the ,university of ,oxford dubbed him a doctor2 and the ,king sent for him to bring his telescope and show it at ,court4 ,so to ,london and ,windsor he went1 taking with him his best telescope4 ,maskelyne1 the then ,astronomer-,royal1 compared it with the ,national one at ,greenwich1 and found ,herschel's home-made instrument far the better of the two4 ,he had a stand made after ,herschel's pattern1 but was so disgusted with his own instrument now that he scarcely thought it worthy of the stand when it was made4 ,at ,windsor1 ,george ,,iii4 was very civil1 and ,mr4 ,herschel was in great request to show the ladies of the ,court ,saturn and other objects of interest4 ,mr4 ,herschel exhibited a piece of worldly wisdom under these circumstances1 that recalls faintly the behaviour of ,tycho ,brah under similar circumstances4 ,the evening when the exhibition was to take place threatened to become cloudy and wet1 so ,herschel rigged up an artificial ,saturn1 constructed of card and tissue paper1 with a lamp behind it1 in the distant wall of a garden2 and1 when the time came1 his new titled friends were regaled with a view of this imitation ,saturn through the telescope--the real one not being visible4 ,they went away much pleased4 ,he stayed hovering between ,windsor and ,greenwich1 and uncertain what was to be the outcome of all this regal patronizing4 ,he writes to his sister that he would much rather be back grinding mirrors at ,bath4 ,and she writes begging him to come1 for his musical pupils were getting impatient4 ,they had to get the better of their impatience1 however1 for the ,king ultimately appointed him astronomer or rather telescope-maker to himself1 and so ,caroline and the whole household were sent for1 and established in a small house at ,datchet4 ,from being a star-gazing musician1 ,herschel thus became a practical astronomer4 ,henceforth he lived in his observatory2 only on wet and moonlight nights could he be torn away from it4 ,the day-time he devoted to making his long-contemplated #bj-;foot telescope4 ,not yet1 however1 were all their difficulties removed4 ,the house at ,datchet was a tumble-down barn of a place1 chosen rather as a workshop and observatory than as a dwelling-house4 ,and the salary allowed him by ,george ,,iii4 was scarcely a princely one4 ,it was1 as a matter of fact1 #bjj a year4 ,the idea was that he would earn his living by making telescopes1 and so indeed he did4 ,he made altogether some hundreds4 ,among others1 four for the ,king4 ,but this eternal making of telescopes for other people to use or play with was a weariness to the flesh4 ,what he wanted was to observe1 observe1 observe4 ,sir ,william ,watson1 an old friend of his1 and of some influence at ,court1 expressed his mind pretty plainly concerning ,herschel's position2 and as soon as the ,king got to understand that there was anything the matter1 he immediately offered #b1jjj for a gigantic telescope to be made for ,herschel's own use4 ,nothing better did he want in life4 ,the whole army of carpenters and craftsmen resident in ,datchet were pressed into the service4 ,furnaces for the speculum metal were built1 stands erected1 and the #dj-;foot telescope fairly begun4 ,it cost #d1jjj before it was finished1 but the ,king paid the whole4 ,illustration3 ,,fig4 #hc4--;,herschel's #dj-;foot telescope4 ,with it he discovered two more satellites to ,saturn 7five hitherto had been known71 and two moons to his own planet ,uranus4 ,these two are now known as ,oberon and ,titania4 ,they were not seen again till some forty years after1 when his son1 ,sir ,john ,herschel1 reobserved them4 ,and in #ahdg1 ,mr4 ,lassell1 at his house1 ,starfield1 near ,liverpool1 discovered two more1 called ,ariel and ,umbriel1 making the number four1 as now known4 ,mr4 ,lassell also discovered1 with a telescope of his own making1 an eighth satellite of ,saturn--,hyperion--and a satellite to ,neptune4 ,a letter from a foreign astronomer about this period describes ,herschel and his sister's method of work3-- ,i spent the night of the #fth of ,january at ,herschel's1 in ,datchet1 near ,windsor1 and had the good luck to hit on a fine evening4 ,he has his #bj-;foot ,newtonian telescope in the open air1 and mounted in his garden very simply and conveniently4 ,it is moved by an assistant1 who stands below it4444 ,near the instrument is a clock regulated to sidereal time4444 ,in the room near it sits ,herschel's sister1 and she has ,flamsteed's atlas open before her4 ,as he gives her the word1 she writes down the declination and right ascension1 and the other circumstances of the observation4 ,in this way ,herschel examines the whole sky without omitting the least part4 ,he commonly observes with a magnifying power of one hundred and fifty1 and is sure that after four or five years he will have passed in review every object above our horizon4 ,he showed me the book in which his observations up to this time are written1 and ,i am astonished at the great number of them4 ,each sweep covers #b #ae' in declination1 and he lets each star pass at least three times through the field of his telescope1 so that it is impossible that anything can escape him4 ,he has already found about #ijj double stars1 and almost as many nebul4 ,i went to bed about one o'clock1 and up to that time he had found that night four or five new nebul4 ,the thermometer in the garden stood at #ac ,fahrenheit2 but1 in spite of this1 ,herschel observes the whole night through1 except that he stops every three or four hours and goes into the room for a few moments4 ,for some years ,herschel has observed the heavens every hour when the weather is clear1 and this always in the open air1 because he says that the telescope only performs well when it is at the same temperature as the air4 ,he protects himself against the weather by putting on more clothing4 ,he has an excellent constitution1 and thinks about nothing else in the world but the celestial bodies4 ,he has promised me in the most cordial way1 entirely in the service of astronomy1 and without thinking of his own interest1 to see to the telescopes ,i have ordered for ,european observatories1 and he will himself attend to the preparation of the mirrors4 ,illustration3 ,painted by ,abbott4 ,engraved by ,ryder4 ,,fig4 #hd4--,,william ,,herschel4 ,from an ,original ,picture in the ,possession of ,,wm4 ,,watson1 ,m4,d41 ,f4,r4,s4 ,in #aghc1 ,herschel married an estimable lady who sympathized with his pursuits4 ,she was the only daughter of a ,city magnate1 so his pecuniary difficulties1 such as they were 7they were never very troublesome to him71 came to an end4 ,they moved now into a more commodious house at ,slough4 ,their one son1 afterwards the famous ,sir ,john ,herschel1 was born some nine years later4 ,but the marriage was rather a blow to his devoted sister3 henceforth she lived in lodgings1 and went over at night-time to help him observe4 ,for it must be remarked that this family literally turned night into day4 ,whatever sleep they got was in the day-time4 ,every fine night without exception was spent in observing3 and the quite incredible fierceness of the pursuit is illustrated1 as strongly as it can be1 by the following sentence out of ,caroline's diary1 at the time of the move from ,datchet to ,slough3 ,the last night at ,datchet was spent in sweeping till daylight1 and by the next evening the telescope stood ready for observation at ,slough4 ,caroline was now often allowed to sweep with a small telescope on her own account4 ,in this way she picked up a good many nebul in the course of her life1 and eight comets1 four of which were quite new1 and one of which1 known since as ,encke's comet1 has become very famous4 ,the work they got through between them is something astonishing4 ,he made with his own hands #dcj parabolic mirrors for reflecting telescopes1 besides a great number of complete instruments4 ,he was forty-two when he began contributing to the ,royal ,society2 yet before he died he had sent them sixty-nine long and elaborate treatises4 ,one of these memoirs is a catalogue of #ajjj nebul4 ,fifteen years after he sends in another #ajjj2 and some years later another #ejj4 ,he also discovered #hjf double stars1 which he proved were really corrected from the fact that they revolved round each other 7p4 #cji74 ,he lived to see some of them perform half a revolution4 ,for him the stars were not fixed3 they moved slowly among themselves4 ,he detected their proper motions4 ,he passed the whole northern firmament in review four distinct times2 counted the stars in #c1djj gauge-fields1 and estimated the brightness of hundreds of stars4 ,he also measured as accurately as he could their proper motions1 devising for this purpose the method which still to this day remains in use4 ,and what is the outcome of it all8 ,it is not ,uranus1 nor the satellites1 nor even the double stars and the nebul considered as mere objects3 it is the beginning of a science of the stars4 ,illustration3 ,,fig4 #he4--;,,caroline ,,herschel4 ,from a ,drawing from ,life1 by ,,george ,m,,ller1 #ahdg4 ,hitherto the stars had only been observed for nautical and practical purposes4 ,their times of rising and southing and setting had been noted2 they had been treated as a clock or piece of dead mechanism1 and as fixed points of reference4 ,all the energies of astronomers had gone out towards the solar system4 ,it was the planets that had been observed4 ,tycho had observed and tabulated their positions4 ,kepler had found out some laws of their motion4 ,galileo had discovered their peculiarities and attendants4 ,newton and ,laplace had perceived every detail of their laws4 ,but for the stars--the old ,ptolemaic system might still have been true4 ,they might still be mere dots in a vast crystalline sphere1 all set at about one distance1 and subservient to the uses of the earth4 ,herschel changed all this4 ,instead of sameness1 he found variety2 instead of uniformity of distance1 limitless and utterly limitless fields and boundless distances2 instead of rest and quiescence1 motion and activity2 instead of stagnation1 life4 ,illustration3 ,,fig4 #hf4--,the double-double star epsilon ,lyr as seen under three different powers4 ,yes1 that is what ,herschel discovered--the life and activity of the whole visible universe4 ,no longer was our little solar system to be the one object of regard1 no longer were its phenomena to be alone interesting to man4 ,with ,herschel every star was a solar system4 ,and more than that3 he found suns revolving round suns1 at distances such as the mind reels at1 still obeying the same law of gravitation as pulls an apple from a tree4 ,he tried hard to estimate the distance of the stars from the earth1 but there he failed3 it was too hopeless a problem4 ,it was solved some time after his death by ,bessel1 and the distances of many stars are now known but these distances are awful and unspeakable4 ,our distance from the sun shrinks up into a mere speck--the whole solar system into a mere unit of measurement1 to be repeated hundreds of thousands of times before we reach the stars4 ,yet their motion is visible--yes1 to very accurate measurement quite plain4 ,one star1 known as #fa ,cygni1 was then and is now rushing along at the rate of #ajj miles every second4 ,not that you must imagine that this makes any obvious and apparent change in its position4 ,no1 for all ordinary and practical purposes they are still fixed stars2 thousands of years will show us no obvious change2 ,adam saw precisely the same constellations as we do3 it is only by refined micrometric measurement with high magnifying power that their flight can be detected4 ,but the sun is one of the stars--not by any means a specially large or bright one2 ,sirius we now know to be twenty times as big as the sun4 ,the sun is one of the stars3 then is it at rest8 ,herschel asked this question and endeavoured to answer it4 ,he succeeded in the most astonishing manner4 ,it is1 perhaps1 his most remarkable discovery1 and savours of intuition4 ,this is how it happened4 ,with imperfect optical means and his own eyesight to guide him1 he considered and pondered over the proper motion of the stars as he had observed it1 till he discovered a kind of uniformity running through it all4 ,mixed up with irregularities and individualities1 he found that in a certain part of the heavens the stars were on the whole opening out--separating slowly from each other2 on the opposite side of the heavens they were on the average closing up--getting slightly nearer to each other2 while in directions at right angles to this they were fairly preserving their customary distances asunder4 ,now1 what is the moral to be drawn from such uniformity of behaviour among unconnected bodies8 ,surely that this part of their motion is only apparent--that it is we who are moving4 ,travelling over a prairie bounded by a belt of trees1 we should see the trees in our line of advance opening out1 and those behind closing up2 we should see in fact the same kind of apparent motion as ,herschel was able to detect among the stars3 the opening out being most marked near the constellation ,hercules4 ,the conclusion is obvious3 the sun1 with all its planets1 must be steadily moving towards a point in the constellation ,hercules4 ,the most accurate modern research has been hardly able to improve upon this statement of ,herschel's4 ,possibly the solar system may ultimately be found to revolve round some other body1 but what that is no one knows4 ,all one can tell is the present direction of the majestic motion3 since it was discovered it has continued unchanged1 and will probably so continue for thousands of years4 ,illustration3 ,,fig4 #hg4--,old drawing of the cluster in ,hercules4 ,and1 finally1 concerning the nebul4 ,these mysterious objects exercised a strong fascination for ,herschel1 and many are the speculations he indulges in concerning them4 ,at one time he regards them all as clusters of stars1 and the ,milky ,way as our cluster2 the others he regards as other universes almost infinitely distant2 and he proceeds to gauge and estimate the shape of our own universe or galaxy of suns1 the ,milky ,way4 ,later on1 however1 he pictures to himself the nebul as nascent suns3 solar systems before they are formed4 ,some he thinks have begun to aggregate1 while some are still glowing gas4 ,illustration3 ,,fig4 #hh4--,old drawing of the ,andromeda nebula4 ,he likens the heavens to a garden in which there are plants growing in all manner of different stages3 some shooting1 some in leaf1 some in flower1 some bearing seed1 some decaying2 and thus at one inspection we have before us the whole life-history of the plant4 ,just so he thinks the heavens contain worlds1 some old1 some dead1 some young and vigorous1 and some in the act of being formed4 ,the nebul are these latter1 and the nebulous stars are a further stage in the condensation towards a sun4 ,and thus1 by simple observation1 he is led towards something very like the nebular hypothesis of ,laplace2 and his position1 whether it be true or false1 is substantially the same as is held to-day4 ,illustration3 ,,fig4 #hi4--,the great nebula in ,orion4 ,we know now that many of the nebul consist of innumerable isolated particles and may be spoken of as gas4 ,we know that some are in a state of whirling motion4 ,we know also that such gas left to itself will slowly as it cools condense and shrink1 so as to form a central solid nucleus2 and also1 if it were in whirling motion1 that it would send off rings from itself1 and that these rings could break up into planets4 ,in two familiar cases the ring has not yet thus aggregated into planet or satellite--the zone of asteroids1 and ,saturn's ring4 ,the whole of this could not have been asserted in ,herschel's time3 for further information the world had to wait4 ,these are the problems of modern astronomy--these and many others1 which are the growth of this century1 aye1 and the growth of the last thirty or forty1 and indeed of the last ten years4 ,even as ,i write1 new and very confirmatory discoveries are being announced4 ,the ,milky ,way does seem to have some affinity with our sun4 ,and the chief stars of the constellation of ,orion constitute another family1 and are enveloped in the great nebula1 now by photography perceived to be far greater than had ever been imagined4 ,what is to be the outcome of it all ,i know not2 but sure ,i am of this1 that the largest views of the universe that we are able to frame1 and the grandest manner of its construction that we can conceive1 are certain to pale and shrink and become inadequate when confronted with the truth4 ,,notes ,,to ,,lecture ,,xiii ,,bode',s ,,law4--,write down the series #j1 #c1 #f1 #ab1 #bd1 #dh1 c42 add #d to each1 and divide by #aj2 you get the series3 #d #g #aj #af #bh #eb #ajj #aif #chh ,mercury ,venus ,earth ,mars ---- ,jupiter ,saturn ,uranus ---- numbers which very fairly represent the distances of the then known planets from the sun in the order specified4 ,ceres was discovered on the #ast of ,january1 #ahja1 by ,piazzi2 ,pallas in ,march1 #ahjb1 by ,olbers2 ,juno in #ahjd1 by ,harding2 and ,vesta in #ahjg1 by ,olbers4 ,no more asteroids were discovered till #ahde1 but there are now several hundreds known4 ,their diameters range from #ejj to #bj miles4 ,neptune was discovered from the perturbations of ,uranus by sheer calculation1 carried on simultaneously and independently by ,leverrier in ,paris1 and ,adams in ,cambridge4 ,it was first knowingly seen by ,galle1 of ,berlin1 on the #bcrd of ,september1 #ahdf4 ,,lecture ,,xiii ,,the ,,discovery ,,of ,,the ,,asteroids ,up to the time of ,herschel1 astronomical interest centred on the solar system4 ,since that time it has been divided1 and a great part of our attention has been given to the more distant celestial bodies4 ,the solar system has by no means lost its interest--it has indeed gained in interest continually1 as we gain in knowledge concerning it2 but in order to follow the course of science it will be necessary for us to oscillate to and fro1 sometimes attending to the solar system--the planets and their satellites--sometimes extending our vision to the enormously more distant stellar spaces4 ,those who have read the third lecture in ,part ,i4 will remember the speculation in which ,kepler indulged respecting the arrangements of the planets1 the order in which they succeeded one another in space1 and the law of their respective distances from the sun2 and his fanciful guess about the five regular solids inscribed and circumscribed about their orbits4 ,the rude coincidences were1 however1 accidental1 and he failed to discover any true law4 ,no thoroughly satisfactory law is known at the present day4 ,and yet1 if the nebular hypothesis or anything like it be true1 there must be some law to be discovered hereafter1 though it may be a very complicated one4 ,an empirical relation is1 however1 known3 it was suggested by ,tatius1 and published by ,bode1 of ,berlin1 in #aggb4 ,it is always known as ,bode's law4 ,bode's law asserts that the distance of each planet is approximately double the distance of the inner adjacent planet from the sun1 but that the rate of increase is distinctly slower than this for the inner ones2 consequently a better approximation will be obtained by adding a constant to each term of an appropriate geometrical progression4 ,thus1 form a doubling series like this1 #a-a_/b1 #c1 #f1 #ab1 #bd1 c4 doubling each time2 then add #d to each1 and you get a series which expresses very fairly the relative distances of the successive planets from the sun1 except that the number for ,mercury is rather erroneous1 and we now know that at the other extreme the number for ,neptune is erroneous too4 ,i have stated it in the notes above in a form calculated to give the law every chance1 and a form that was probably fashionable after the discovery of ,uranus2 but to call the first term of the doubling series #j is evidently not quite fair1 though it puts ,mercury's distance right4 ,neptune's distance1 however1 turns out to be more nearly #cj times the earth's distance than #chh4 ,the others are very nearly right3 compare column ,d of the table preceding ,lecture ,,iii4 on p4 #eg1 with the numbers in the notes on p4 #bid4 ,the discovery of ,uranus a few years afterwards1 in #agha1 at #aib times the earth's distance from the sun1 lent great clt to the law1 and seemed to establish its right to be regarded as at least a close approximation to the truth4 ,the gap between ,mars and ,jupiter1 which had often been noticed1 and which ,kepler filled with a hypothetical planet too small to see1 comes into great prominence by this law of ,bode4 ,so much so1 that towards the end of last century an enthusiastic ,german1 von ,zach1 after some search himself for the expected planet1 arranged a committee of observing astronomers1 or1 as he termed it1 a body of astronomical detective police1 to begin a systematic search for this missing subject of the sun4 ,illustration3 ,,fig4 #ij4--,planetary orbits to scale2 showing the ,asteroidal region between ,jupiter and ,mars4 7,the orbits of satellites are exaggerated47 ,in #ahjj the preliminaries were settled3 the heavens near the zodiac were divided into twenty-four regions1 each of which was intrusted to one observer to be swept4 ,meanwhile1 however1 quite independently of these arrangements in ,germany1 and entirely unknown to this committee1 a quiet astronomer in ,sicily1 ,piazzi1 was engaged in making a catalogue of the stars4 ,his attention was directed to a certain region in ,taurus by an error in a previous catalogue1 which contained a star really non-existent4 ,in the course of his scrutiny1 on the #ast of ,january1 #ahja1 he noticed a small star which next evening appeared to have shifted4 ,he watched it anxiously for successive evenings1 and by the #bdth of ,january he was quite sure he had got hold of some moving body1 not a star3 probably1 he thought1 a comet4 ,it was very small1 only of the eighth magnitude2 and he wrote to two astronomers 7one of them ,bode himself7 saying what he had observed4 ,he continued to observe till the #aath of ,february1 when he was attacked by illness and compelled to cease4 ,his letters did not reach their destination till the end of ,march4 ,directly ,bode opened his letter he jumped to the conclusion that this must be the missing planet4 ,but unfortunately he was unable to verify the guess1 for the object1 whatever it was1 had now got too near the sun to be seen4 ,it would not be likely to be out again before ,september1 and by that time it would be hopelessly lost again1 and have just as much to be rediscovered as if it had never been seen4 ,mathematical astronomers tried to calculate a possible orbit for the body from the observations of ,piazzi1 but the observed places were so desperately few and close together4 ,it was like having to determine a curve from three points close together4 ,three observations ought to serve1#bg but if they are taken with insufficient interval between them it is extremely difficult to construct the whole circumstances of the orbit from them4 ,all the calculations gave different results1 and none were of the slightest use4 ,the difficulty as it turned out was most fortunate4 ,it resulted in the discovery of one of the greatest mathematicians1 perhaps the greatest1 that ,germany has ever produced--,gauss4 ,he was then a young man of twenty-five1 eking out a living by tuition4 ,he had invented but not published several powerful mathematical methods 7one of them now known as the method of least squares71 and he applied them to ,piazzi's observations4 ,he was thus able to calculate an orbit1 and to predict a place where1 by the end of the year1 the planet should be visible4 ,on the #cast of ,december of that same year1 very near the place predicted by ,gauss1 von ,zach rediscovered it1 and ,olbers discovered it also the next evening4 ,piazzi called it ,ceres1 after the tutelary goddess of ,sicily4 ,its distance from the sun as determined by ,gauss was #bgfg times the earth's distance4 ,bode's law made it #bh4 ,it was undoubtedly the missing planet4 ,but it was only one hundred and fifty or two hundred miles in diameter--the smallest heavenly body known at the time of its discovery4 ,it revolves the same way as other planets1 but the plane of its orbit is tilted #aj to the plane of the ecliptic1 which was an exceptionally large amount4 ,very soon1 a more surprising discovery followed4 ,olbers1 while searching for ,ceres1 had carefully mapped the part of the heavens where it was expected2 and in ,march1 #ahjb1 he saw in this place a star he had not previously noticed4 ,in two hours he detected its motion1 and in a month he sent his observations to ,gauss1 who returned as answer the calculated orbit4 ,it was distant #bfg1 like ,ceres1 and was a little smaller1 but it had a very excentric orbit3 its plane being tilted #cd-a_/b1 an extraordinary inclination4 ,this was called ,pallas4 ,olbers at once surmised that these two planets were fragments of a larger one1 and kept an eager look out for other fragments4 ,in two years another was seen1 in the course of charting the region of the heavens traversed by ,ceres and ,pallas4 ,it was smaller than either1 and was called ,juno4 ,in #ahjg the persevering search of ,olbers resulted in the discovery of another1 with a very oblique orbit1 which ,gauss named ,vesta4 ,vesta is bigger than any of the others1 being five hundred miles in diameter1 and shines like a star of the sixth magnitude4 ,gauss by this time had become so practised in the difficult computations that he worked out the complete orbit of ,vesta within ten hours of receiving the observational data from ,olbers4 ,for many weary years ,olbers kept up a patient and unremitting search for more of these small bodies1 or fragments of the large planet as he thought them2 but his patience went unrewarded1 and he died in #ahdj without seeing or knowing of any more4 ,in #ahde another was found1 however1 in ,germany1 and a few weeks later two others by ,mr4 ,hind in ,england4 ,since then there seems no end to them2 numbers have been discovered in ,america1 where ,professors ,peters and ,watson have made a specialty of them1 and have themselves found something like a hundred4 ,vesta is the largest--its area being about the same as that of ,central ,europe1 without ,russia or ,spain--and the smallest known is about twenty miles in diameter1 or with a surface about the size of ,kent4 ,the whole of them together do not nearly equal the earth in bulk4 ,the main interest of these bodies to us lies in the question1 ,what is their history8 ,can they have been once a single planet broken up8 or are they rather an abortive attempt at a planet never yet formed into one8 ,the question is not entirely settled1 but ,i can tell you which way opinion strongly tends at the present time4 ,imagine a shell travelling in an elliptic orbit round the earth to suddenly explode3 the centre of gravity of all its fragments would continue moving along precisely the same path as had been traversed by the centre of the shell before explosion1 and would complete its orbit quite undisturbed4 ,each fragment would describe an orbit of its own1 because it would be affected by a different initial velocity2 but every orbit would be a simple ellipse1 and consequently every piece would in time return through its starting-point--viz4 the place at which the explosion occurred4 ,if the zone of asteroids had a common point through which they all successively passed1 they could be unhesitatingly asserted to be the remains of an exploded planet4 ,but they have nothing of the kind2 their orbits are scattered within a certain broad zone--a zone everywhere as broad as the earth's distance from the sun1 #ib1jjj1jjj miles--with no sort of law indicating an origin of this kind4 ,it must be admitted1 however1 that the fragments of our supposed shell might in the course of ages1 if left to themselves1 mutually perturb each other into a different arrangement of orbits from that with which they began4 ,but their perturbations would be very minute1 and moreover1 on ,laplace's theory1 would only result in periodic changes1 provided each mass were rigid4 ,it is probable that the asteroids were at one time not rigid1 and hence it is difficult to say what may have happened to them2 but there is not the least reason to believe that their present arrangement is derivable in any way from an explosion1 and it is certain that an enormous time must have elapsed since such an event if it ever occurred4 ,it is far more probable that they never constituted one body at all1 but are the remains of a cloudy ring thrown off by the solar system in shrinking past that point3 a small ring after the immense effort which produced ,jupiter and his satellites3 a ring which has aggregated into a multitude of little lumps instead of a few big ones4 ,such an event is not unique in the solar system2 there is a similar ring round ,saturn4 ,at first sight1 and to ordinary careful inspection1 this differs from the zone of asteroids in being a solid lump of matter1 like a quoit4 ,but it is easy to show from the theory of gravitation1 that a solid ring could not possibly be stable1 but would before long get precipitated excentrically upon the body of the planet4 ,devices have been invented1 such as artfully distributed irregularities calculated to act as satellites and maintain stability2 but none of these things really work4 ,nor will it do to imagine the rings fluid2 they too would destroy each other4 ,the mechanical behaviour of a system of rings1 on different hypotheses as to their constitution1 has been worked out with consummate skill by ,clerk ,maxwell2 who finds that the only possible constitution for ,saturn's assemblage of rings is a multitude of discrete particles each pursuing its independent orbit4 ,saturn's ring is1 in fact1 a very concentrated zone of minor asteroids1 and there is every reason to conclude that the origin of the solar asteroids cannot be very unlike the origin of the ,saturnian ones4 ,the nebular hypothesis lends itself readily to both4 ,the interlockings and motions of the particles in ,saturn's rings are most beautiful1 and have been worked out and stated by ,maxwell with marvellous completeness4 ,his paper constituted what is called ,the ,adams ,prize ,essay for #ahef4 ,sir ,george ,airy1 one of the adjudicators 7recently ,astronomer-,royal71 characterized it as one of the most remarkable applications of mathematics to physics that ,i have ever seen4 ,there are several distinct constituent rings in the entire ,saturnian zone1 and each perturbs the other1 with the result that they ripple and pulse in concord4 ,the waves thus formed absorb the effect of the mutual perturbations1 and prevent an accumulation which would be dangerous to the persistence of the whole4 ,the only effect of gravitational perturbation and of collisions is gradually to broaden out the whole ring1 enlarging its outer and diminishing its inner diameter4 ,but if there were any frictional resistance in the medium through which the rings spin1 then other effects would slowly occur1 which ought to be looked for with interest4 ,so complete and intimate is the way ,maxwell works out and describes the whole circumstances of the motion of such an assemblage of particles1 and so cogent his argument as to the necessity that they must move precisely so1 and no otherwise1 else the rings would not be stable1 that it was a ,cambridge joke concerning him that he paid a visit to ,saturn one evening1 and made his observations on the spot4 ,,notes ,,to ,,lecture ,,xiv ,the total number of stars in the heavens visible to a good eye is about #e1jjj4 ,the total number at present seen by telescope is about #ej1jjj1jjj4 ,the number able to impress a photographic plate has not yet been estimated2 but it is enormously greater still4 ,of those which we can see in these latitudes1 about #ad are of the first magnitude1 #dh of the second1 #aeb of the third1 #cac of the fourth1 #hed of the fifth1 and #b1jaj of the sixth2 total1 #c1cia4 ,the quickest-moving stars known are a double star of the sixth magnitude1 called #fa ,cygni1 and one of the seventh magnitude1 called ,groombridge #ahcj4 ,the velocity of the latter is #bjj miles a second4 ,the nearest known stars are #fa ,cygni and alpha ,centauri4 ,the distance of these from us is about #djj1jjj times the distance of the sun4 ,their parallax is accordingly half a second of arc4 ,sirius is more than a million times further from us than our sun is1 and twenty times as big2 many of the brightest stars are at more than double this distance4 ,the distance of ,arcturus is too great to measure even now4 ,stellar parallax was first securely detected in #ahch1 by ,bessel1 for #fa ,cygni4 ,bessel was born in #aghd1 and died in #ahdf1 shortly before the discovery of ,neptune4 ,the stars are suns1 and are most likely surrounded by planets4 ,one planet belonging to ,sirius has been discovered4 ,it was predicted by ,bessel1 its position calculated by ,peters1 and seen by ,alvan ,clark in #ahfb4 ,another predicted one1 belonging to ,procyon1 has not yet been seen4 ,a velocity of #e miles a second could carry a projectile right round the earth4 ,a velocity of #g miles a second would carry it away from the earth1 and round the sun4 ,a velocity of #bg miles a second would carry a projectile right out of the solar system never to return4 ,,lecture ,,xiv ,,bessel--,,the ,,distances ,,of ,,the ,,stars1 ,,and ,,the ,,discovery ,,of ,,stellar ,,planets ,we will now leave the solar system for a time1 and hastily sketch the history of stellar astronomy from the time of ,sir ,william ,herschel4 ,you remember how greatly ,herschel had changed the aspect of the heavens for man1--how he had found that none of the stars were really fixed1 but were moving in all manner of ways3 some of this motion only apparent1 much of it real4 ,nevertheless1 so enormously distant are they1 that if we could be transported back to the days of the old ,chaldan astronomers1 or to the days of ,noah1 we should still see the heavens with precisely the same aspect as they wear now4 ,only by refined apparatus could any change be discoverable in all those centuries4 ,for all practical purposes1 therefore1 the stars may still be well called fixed4 ,another thing one may notice1 as showing their enormous distances1 is that from every planet of the solar system the aspect of the heavens will be precisely the same4 ,inhabitants of ,mars1 or ,jupiter1 or ,saturn1 or ,uranus1 will see exactly the same constellations as we do4 ,the whole dimensions of the solar system shrink up into a speck when so contemplated4 ,and from the stars none of the planetary orbs of our system are visible at all2 nothing but the sun is visible1 and that merely as a twinkling star1 brighter than some1 but fainter than many others4 ,the sun and the stars are one4 ,try to realize this distinctly1 and keep it in mind4 ,i find it often difficult to drive this idea home4 ,after some talk on the subject a friendly auditor will report1 the lecturer then described the stars1 including that greatest and most magnificent of all stars1 the sun4 ,it would be difficult more completely to misapprehend the entire statement4 ,when ,i say the sun is one of the stars1 ,i mean one among the others2 we are a long way from them1 they are a long way from each other4 ,they need be no more closely packed among each other than we are closely packed among them2 except that some of them are double or multiple1 and we are not double4 ,it is highly desirable to acquire an intimate knowledge of the constellations and a nodding acquaintance with their principal stars4 ,a description of their peculiarities is dull and uninteresting unless they are at least familiar by name4 ,a little viv voce help to begin with1 supplemented by patient night scrutiny with a celestial globe or star maps under a tent or shed1 is perhaps the easiest way3 a very convenient instrument for the purpose of learning the constellations is the form of map called a planisphere1 because it can be made to show all the constellations visible at a given time at a given date1 and no others4 ,the ,greek alphabet also is a thing that should be learnt by everybody4 ,the increased difficulty in teaching science owing to the modern ignorance of even a smattering of ,greek is becoming grotesque4 ,the stars are named from their ancient grouping into constellations1 and by the prefix of a ,greek letter to the larger ones1 and of numerals to the smaller ones4 ,the biggest of all have special ,arabic names as well4 ,the brightest stars are called of the first magnitude1 the next are of the second magnitude1 and so on4 ,but this arrangement into magnitudes has become technical and precise1 and intermediate or fractional magnitudes are inserted4 ,those brighter than the ordinary first magnitude are therefore now spoken of as of magnitude #a_/b1 for instance1 or #f1 which is rather confusing4 ,small telescopic stars are often only named by their numbers in some specified catalogue--a dull but sufficient method4 ,here is a list of the stars visible from these latitudes1 which are popularly considered as of the first magnitude4 ,all of them should be familiarly recognized in the heavens1 whenever seen4 ,star4 ,constellation4 ,sirius ,canis major ,procyon ,canis minor ,rigel ,orion ,betelgeux ,orion ,castor ,gemini ,pollux ,gemini ,aldebaran ,taurus ,arcturus ,botes ,vega ,lyra ,capella ,auriga ,regulus ,leo ,altair ,aquila ,fomalhaut ,southern ,fish ,spica ,virgo alpha ,cygni is a little below the first magnitude4 ,so1 perhaps1 is ,castor4 ,in the southern heavens1 ,canopus and alpha ,centauri rank next after ,sirius in brightness4 ,illustration3 ,,fig4 #ia4--;,diagram illustrating ,parallax4 ,the distances of the fixed stars had1 we know1 been a perennial problem1 and many had been the attempts to solve it4 ,all the methods of any precision have depended on the ,copernican fact that the earth in ,june was #ahd million miles away from its position in ,december1 and that accordingly the grouping and aspect of the heavens should be somewhat different when seen from so different a point of view4 ,an apparent change of this sort is called generally parallax2 the parallax of a star being technically defined as the angle subtended at the star by the radius of the earth's orbit3 that is to say1 the angle ,esigma,s2 where ,e is the earth1 ,s the sun1 and sigma a star 7,fig4 #ia74 ,plainly1 the further off sigma is1 the more nearly parallel will the two lines to it become4 ,and the difficulty of determining the parallax was just this1 that the more accurately the observations were made1 the more nearly parallel did those lines become4 ,the angle was1 in fact1 just as likely to turn out negative as positive--an absurd result1 of course1 to be attributed to unavoidable very minute inaccuracies4 ,for a long time absolute methods of determining parallax were attempted2 for instance1 by observing the position of the star with respect to the zenith at different seasons of the year4 ,and many of these determinations appeared to result in success4 ,hooke fancied he had measured a parallax for ,vega in this way1 amounting to #cj of arc4 ,flamsteed obtained #dj for gamma ,draconis4 ,roemer made a serious attempt by comparing observations of ,vega and ,sirius1 stars almost the antipodes of each other in the celestial vault2 hoping to detect some effect due to the size of the earth's orbit1 which should apparently displace them with the season of the year4 ,all these fancied results however1 were shown to be spurious1 and their real cause assigned1 by the great discovery of the aberration of light by ,bradley4 ,after this discovery it was possible to watch for still outstanding very minute discrepancies2 and so the problem of stellar parallax was attacked with fresh vigour by ,piazzi1 by ,brinkley1 and by ,struve4 ,but when results were obtained1 they were traced after long discussion to age and gradual wear of the instrument1 or to some other minute inaccuracy4 ,the more carefully the observation was made1 the more nearly zero became the parallax--the more nearly infinite the distance of the stars4 ,the brightest stars were the ones commonly chosen for the investigation1 and ,vega was a favourite1 because1 going near the zenith1 it was far removed from the fluctuating and tiresome disturbances of atmospheric refraction4 ,the reason bright stars were chosen was because they were presumably nearer than the others2 and indeed a rough guess at their probable distance was made by supposing them to be of the same size as the sun1 and estimating their light in comparison with sunlight4 ,by this confessedly unsatisfactory method it had been estimated that ,sirius must be #adj1jjj times further away than the sun is1 if he be equally big4 ,we now know that ,sirius is much further off than this2 and accordingly that he is much brighter1 perhaps sixty times as bright1 though not necessarily sixty times as big1 as our sun4 ,but even supposing him of the same light-giving power as the sun1 his parallax was estimated as #ah1 a quantity very difficult to be sure of in any absolute determination4 ,relative methods were1 however1 also employed1 and the advantages of one of these 7which seems to have been suggested by ,galileo7 so impressed themselves upon ,william ,herschel that he made a serious attempt to compass the problem by its means4 ,the method was to take two stars in the same telescopic field and carefully to estimate their apparent angular distance from each other at different seasons of the year4 ,all such disturbances as precession1 aberration1 nutation1 refraction1 and the like1 would affect them both equally1 and could thus be eliminated4 ,if they were at the same distance from the solar system1 relative parallax would1 indeed1 also be eliminated2 but if1 as was probable1 they were at different distances1 then they would apparently shift relatively to one another1 and the amount of shift1 if it could be observed1 would measure1 not indeed the distance of either from the earth1 but their distance from each other4 ,and this at any rate would be a step4 ,it might be completed by similarly treating other stars in the same field1 taking them in pairs together4 ,a bright and a faint star would naturally be suitable1 because their distances were likely to be unequal2 and so ,herschel fixed upon a number of doublets which he knew of1 containing one bright and one faint component4 ,for up to that time it had been supposed that such grouping in occasional pairs or triplets was chance coincidence1 the two being optically foreshortened together1 but having no real connection or proximity4 ,herschel failed in what he was looking for1 but instead of that he discovered the real connection of a number of these doublets1 for he found that they were slowly revolving round each other4 ,there are a certain number of merely optical or accidental doublets1 but the majority of them are real pairs of suns revolving round each other4 ,this relative method of mapping micrometrically a field of neighbouring stars1 and comparing their configuration now and six months hence1 was1 however1 the method ultimately destined to succeed2 and it is1 ,i believe1 the only method which has succeeded down to the present day4 ,certainly it is the method regularly employed1 at ,dunsink1 at the ,cape of ,good ,hope1 and everywhere else where stellar parallax is part of the work4 ,between #ahcj and #ahdj the question was ripe for settlement1 and1 as frequently happens with a long-matured difficulty1 it gave way in three places at once4 ,bessel1 ,henderson1 and ,struve almost simultaneously announced a stellar parallax which could reasonably be accepted4 ,bessel was a little the earliest1 and by far the most accurate4 ,his1 indeed1 was the result which commanded confidence1 and to him the palm must be awarded4 ,he was largely a self-taught student1 having begun life in a counting-house1 and having abandoned business for astronomy4 ,but notwithstanding these disadvantages1 he became a highly competent mathematician as well as a skilful practical astronomer4 ,he was appointed to superintend the construction of ,germany's first great astronomical observatory1 that of ,knigsberg1 which1 by his system1 zeal1 and genius1 he rapidly made a place of the first importance4 ,struve at ,dorpat1 ,bessel at ,knigsberg1 and ,henderson at the ,cape of ,good ,hope--all of them at newly-equipped observatories--were severally engaged at the same problem4 ,but the ,russian and ,german observers had the advantage of the work of one of the most brilliant opticians--,i suppose the most brilliant--that has yet appeared3 ,fraunhofer1 of ,munich4 ,an orphan lad1 apprenticed to a maker of looking-glasses1 and subject to hard struggles and privations in early life1 he struggled upwards1 and ultimately became head of the optical department of a ,munich firm of telescope-makers4 ,here he constructed the famous ,dorpat refractor for ,struve1 which is still at work2 and designed the ,knigsberg heliometer for ,bessel4 ,he also made a long and most skilful research into the solar spectrum1 which has immortalized his name4 ,but his health was broken by early trials1 and he died at the age of thirty-nine1 while planning new and still more important optical achievements4 ,a heliometer is the most accurate astronomical instrument for relative measurements of position1 as a transit circle is the most accurate for absolute determinations4 ,it consists of an equatorial telescope with object-glass cut right across1 and each half movable by a sliding movement one past the other1 the amount by which the two halves are dislocated being read off by a refined method1 and the whole instrument having a multitude of appendages conducive to convenience and accuracy4 ,its use is to act as a micrometer or measurer of small distances4#bh ,each half of the object-glass gives a distinct image1 which may be allowed to coincide or may be separated as occasion requires4 ,if it be the components of a double star that are being examined1 each component will in general be seen double1 so that four images will be seen altogether2 but by careful adjustment it will be possible to arrange that one image of each pair shall be superposed on or coincide with each other1 in which case only three images are visible2 the amount of dislocation of the halves of the object-glass necessary to accomplish this is what is read off4 ,the adjustment is one that can be performed with extreme accuracy1 and by performing it again and again with all possible modifications1 an extremely accurate determination of the angular distance between the two components is obtained4 ,illustration3 ,,fig4 #ib4--;,heliometer4 ,bessel determined to apply this beautiful instrument to the problem of stellar parallax2 and he began by considering carefully the kind of star for which success was most likely4 ,hitherto the brightest had been most attended to1 but ,bessel thought that quickness of proper motion would be a still better test of nearness4 ,not that either criterion is conclusive as to distance1 but there was a presumption in favour of either a very bright or an obviously moving star being nearer than a faint or a stationary one2 and as the bright criterion had already been often applied without result1 he decided to try the other4 ,he had already called attention to a record by ,piazzi in #agib of a double star in ,cygnus whose proper motion was five seconds of arc every year--a motion which caused this telescopic object1 #fa ,cygni1 to be known as the flying star4 ,its motion is not really very perceptible1 for it will only have traversed one-third of a lunar diameter in the course of a century2 still it was the quickest moving star then known4 ,the position of this interesting double he compared with two other stars which were seen simultaneously in the field of the heliometer1 by the method ,i have described1 throughout the whole year #ahch2 and in the last month of that year he was able to announce with confidence a distinct though very small parallax2 substantiating it with a mass of detailed evidence which commanded the assent of astronomers4 ,the amount of it he gave as one-third of a second4 ,we know now that he was very nearly right1 though modern research makes it more like half a second4#bi ,soon afterwards1 ,struve announced a quarter of a second as the parallax of ,vega1 but that is distinctly too great2 and ,henderson announced for alpha ,centauri 7then thought to be a double7 a parallax of one second1 which1 if correct1 would make it quite the nearest of all the stars1 but the result is now believed to be about twice too big4 ,knowing the distance of #fa ,cygni1 we can at once tell its real rate of travel--at least1 its rate across our line of sight3 it is rather over three million miles a day4 ,now just consider the smallness of the half second of arc1 thus triumphantly though only approximately measured4 ,it is the angle subtended by twenty-six feet at a distance of #b1jjj miles4 ,if a telescope planted at ,new ,york could be directed to a house in ,england1 and be then turned so as to set its cross-wire first on one end of an ordinary room and then on the other end of the same room1 it would have turned through half a second1 the angle of greatest stellar parallax4 ,or1 putting it another way4 ,if the star were as near us as ,new ,york is1 the sun1 on the same scale1 would be nine paces off4 ,as twenty-six feet is to the distance of ,new ,york1 so is ninety-two million miles to the distance of the nearest fixed star4 ,suppose you could arrange some sort of telegraphic vehicle able to carry you from here to ,new ,york in the tenth part of a second--i4e4 in the time required to drop two inches--such a vehicle would carry you to the moon in twelve seconds1 to the sun in an hour and a quarter4 ,travelling thus continually1 in twenty-four hours you would leave the last member of the solar system behind you1 and begin your plunge into the depths of space4 ,how long would it be before you encountered another object8 ,a month1 should you guess8 ,twenty years you must journey with that prodigious speed before you reach the nearest star1 and then another twenty years before you reach another4 ,at these awful distances from one another the stars are scattered in space1 and were they not brilliantly self-luminous and glowing like our sun1 they would be hopelessly invisible4 ,i have spoken of #fa ,cygni as a flying star1 but there is another which goes still quicker1 a faint star1 #ahcj in ,groombridge's ,catalogue4 ,its distance is far greater than that of #fa ,cygni1 and yet it is seen to move almost as quickly4 ,its actual speed is about #bjj miles a second--greater than the whole visible firmament of fifty million stars can control2 and unless the universe is immensely larger than anything we can see with the most powerful telescopes1 or unless there are crowds of invisible non-luminous stars mixed up with the others1 it can only be a temporary visitor to this frame of things2 it is rushing from an infinite distance to an infinite distance2 it is passing through our visible universe for the first and only time--it will never return4 ,but so gigantic is the extent of visible space1 that even with its amazing speed of #bjj miles every second1 this star will take two or three million years to get out of sight of our present telescopes1 and several thousand years before it gets perceptibly fainter than it is now4 ,have we any reason for supposing that the stars we see are all there are8 ,in other words1 have we any reason for supposing all celestial objects to be sufficiently luminous to be visible8 ,we have every ground for believing the contrary4 ,every body in the solar system is dull and dark except the sun1 though probably ,jupiter is still red-hot4 ,why may not some of the stars be dark too8 ,the genius of ,bessel surmised this1 and consistently upheld the doctrine that the astronomy of the future would have to concern itself with dark and invisible bodies2 he preached an astronomy of the invisible4 ,moreover he predicted the presence of two such dark bodies--one a companion of ,sirius1 the other of ,procyon4 ,he noticed certain irregularities in the motions of these stars which he asserted must be caused by their revolving round other bodies in a period of half a century4 ,he announced in #ahdd that both ,sirius and ,procyon were double stars1 but that their companions1 though large1 were dark1 and therefore invisible4 ,no one accepted this view1 till ,peters1 in ,america1 found in #ahea that the hypothesis accurately explained the anomalous motion of ,sirius1 and1 in fact1 indicated an exact place where the companion ought to be4 ,the obscure companion of ,sirius became now a recognized celestial object1 although it had never been seen1 and it was held to revolve round ,sirius in fifty years1 and to be about half as big4 ,in #ahfb1 the firm of ,alvan ,clark and ,sons1 of ,new ,york1 were completing a magnificent #ah-;inch refractor1 and the younger ,clark was trying it on ,sirius1 when he said3 ,why1 father1 the star has a companion6 ,the elder ,clark also looked1 and sure enough there was a faint companion due east of the bright star1 and in just the position required by theory4 ,not that the ,clarks knew anything about the theory4 ,they were keen-sighted and most skilful instrument-makers1 and they made the discovery by accident4 ,after it had once been seen1 it was found that several of the large telescopes of the world were able to show it4 ,it is half as big1 but it only gives #a_/ajjjjth part of the light that ,sirius gives4 ,no doubt it shines partly with a borrowed light and partly with a dull heat of its own4 ,it is a real planet1 but as yet too hot to live on4 ,it will cool down in time1 as our earth has cooled and as ,jupiter is cooling1 and no doubt become habitable enough4 ,it does revolve round ,sirius in a period of #did years--almost exactly what ,bessel assigned to it4 ,but ,bessel also assigned a dark companion to ,procyon4 ,it and its luminous neighbour are considered to revolve round each other in a period of forty years1 and astronomers feel perfectly assured of its existence1 though at present it has not been seen by man4 ,,lecture ,,xv ,,the ,,discovery ,,of ,,neptune ,we approach to-night perhaps the greatest1 certainly the most conspicuous1 triumphs of the theory of gravitation4 ,the explanation by ,newton of the observed facts of the motion of the moon1 the way he accounted for precession and nutation and for the tides1 the way in which ,laplace explained every detail of the planetary motions--these achievements may seem to the professional astronomer equally1 if not more1 striking and wonderful2 but of the facts to be explained in these cases the general public are necessarily more or less ignorant1 and so no beauty or thoroughness of treatment appeals to them1 nor can excite their imaginations4 ,but to predict in the solitude of the study1 with no weapons other than pen1 ink1 and paper1 an unknown and enormously distant world1 to calculate its orbit when as yet it had never been seen1 and to be able to say to a practical astronomer1 ,point your telescope in such a direction at such a time1 and you will see a new planet hitherto unknown to man--this must always appeal to the imagination with dramatic intensity1 and must awaken some interest in almost the dullest4 ,prediction is no novelty in science2 and in astronomy least of all is it a novelty4 ,thousands of years ago1 ,thales1 and others whose very names we have forgotten1 could predict eclipses with some certainty1 though with only rough accuracy4 ,and many other phenomena were capable of prediction by accumulated experience4 ,we have seen1 for instance 7coming to later times71 how a gap between ,mars and ,jupiter caused a missing planet to be suspected and looked for1 and to be found in a hundred pieces4 ,we have seen1 also1 how the abnormal proper-motion of ,sirius suggested to ,bessel the existence of an unseen companion4 ,and these last instances seem to approach very near the same class of prediction as that of the discovery of ,neptune4 ,wherein1 then1 lies the difference8 ,how comes it that some classes of prediction--such as that if you put your finger in fire it will get burnt--are childishly easy and commonplace1 while others excite in the keenest intellects the highest feelings of admiration8 ,mainly1 the difference lies1 first1 in the grounds on which the prediction is based2 second1 on the difficulty of the investigation whereby it is accomplished2 third1 in the completeness and the accuracy with which it can be verified4 ,in all these points1 the discovery of ,neptune stands out pre-eminently among the verified predictions of science1 and the circumstances surrounding it are of singular interest4 99 99 99 99 99 ,in #agha1 ,sir ,william ,herschel discovered the planet ,uranus4 ,now you know that three distinct observations suffice to determine the orbit of a planet completely1 and that it is well to have the three observations as far apart as possible so as to minimize the effects of minute but necessary errors of observation4 7,see p4 #bih47 ,directly ,uranus was found1 therefore1 old records of stellar observations were ransacked1 with the object of discovering whether it had ever been unwittingly seen before4 ,if seen1 it had been thought of course to be a star 7for it shines like a star of the sixth magnitude1 and can therefore be just seen without a telescope if one knows precisely where to look for it1 and if one has good sight71 but if it had been seen and catalogued as a star it would have moved from its place1 and the catalogue would by that entry be wrong4 ,the thing to detect1 therefore1 was errors in the catalogues3 to examine all entries1 and see if the stars entered actually existed1 or were any of them missing4 ,if a wrong entry were discovered1 it might of course have been due to some clerical error1 though that is hardly probable considering the care taken over these things1 or it might have been some tailless comet or other1 or it might have been the newly found planet4 ,so the next thing was to calculate backwards1 and see if by any possibility the planet could have been in that place at that time4 ,examined in this way the tabulated observations of ,flamsteed showed that he had unwittingly observed ,uranus five distinct times1 the first time in #afij1 nearly a century before ,herschel discovered its true nature4 ,but more remarkable still1 ,le ,monnier1 of ,paris1 had observed it eight times in one month1 cataloguing it each time as a different star4 ,if only he had reduced and compared his observations1 he would have anticipated ,herschel by twelve years4 ,as it was1 he missed it altogether4 ,it was seen once by ,bradley also4 ,altogether it had been seen twenty times4 ,these old observations of ,flamsteed and those of ,le ,monnier1 combined with those made after ,herschel's discovery1 were very useful in determining an exact orbit for the new planet1 and its motion was considered thoroughly known4 ,it was not an exact ellipse1 of course3 none of the planets describe exact ellipses--each perturbs all the rest1 and these small perturbations must be taken into account1 those of ,jupiter and ,saturn being by far the most important4 ,for a time ,uranus seemed to travel regularly and as expected1 in the orbit which had been calculated for it2 but early in the present century it began to be slightly refractory1 and by #ahbj its actual place showed quite a distinct discrepancy from its position as calculated with the aid of the old observations4 ,it was at first thought that this discrepancy must be due to inaccuracies in the older observations1 and they were accordingly rejected1 and tables prepared for the planet based on the newer and more accurate observations only4 ,but by #ahcj it became apparent that it would not accurately obey even these4 ,the error amounted to some #bj4 ,by #ahdj it was as much as #ij'1 or a minute and a half4 ,this discrepancy is quite distinct1 but still it is very small1 and had two objects been in the heavens at once1 the actual ,uranus and the theoretical ,uranus1 no unaided eye could possibly have distinguished them or detected that they were other than a single star4 ,illustration3 ,,fig4 #ic4--,perturbations of ,uranus4 ,the chance observations by ,flamsteed1 by ,le ,monnier1 and others1 are plotted in this diagram1 as well as the modern determinations made after ,herschel had discovered the nature of the planet4 ,the decades are laid off horizontally4 ,vertical distance represents the difference between observed and subsequently calculated longitudes--in other words1 the principal perturbations caused by ,neptune4 ,to show the scale1 a number of standard things are represented too by lengths measured upwards from the line of time1 viz3 the smallest quantity perceptible to the naked eye1--the maximum angle of aberration1 of nutation1 and of stellar parallax2 though this last is too small to be properly indicated4 ,the perturbations are much bigger than these2 but compared with what can be seen without a telescope they are small--the distance between the component pairs of epsilon ,lyr 7#baj7 7see fig4 #hf1 page #bhh71 which a few keen-eyed persons can see as a simple double star1 being about twice the greatest perturbation4 ,the diagram shows all the irregularities plotted in the light of our present knowledge2 and1 to compare with their amounts1 a few standard things are placed on the same scale1 such as the smallest interval capable of being detected with the unaided eye1 the distance of the component stars in epsilon ,lyr1 the constants of aberration1 of nutation1 and of stellar parallax4 ,the errors of ,uranus therefore1 though small1 were enormously greater than things which had certainly been observed2 there was an unmistakable discrepancy between theory and observation4 ,some cause was evidently at work on this distant planet1 causing it to disagree with its motion as calculated according to the law of gravitation4 ,some thought that the exact law of gravitation did not apply to so distant a body4 ,others surmised the presence of some foreign and unknown body1 some comet1 or some still more distant planet perhaps1 whose gravitative attraction for ,uranus was the cause of the whole difficulty--some perturbations1 in fact1 which had not been taken into account because of our ignorance of the existence of the body which caused them4 ,but though such an idea was mentioned among astronomers1 it was not regarded with any special favour1 and was considered merely as one among a number of hypotheses which could be suggested as fairly probable4 ,it is perfectly right not to attach much importance to unelaborated guesses4 ,not until the consequences of an hypothesis have been laboriously worked out--not until it can be shown capable of producing the effect quantitatively as well as qualitatively--does its statement rise above the level of a guess1 and attain the dignity of a theory4 ,a later stage still occurs when the theory has been actually and completely verified by agreement with observation4 ,now the errors in the motion of ,uranus1 i4e4 the discrepancy between its observed and calculated longitudes--all known disturbing causes1 such as ,jupiter and ,saturn1 being allowed for--are as follows 7as quoted by ,dr4 ,haughton7 in seconds of arc3-- ,,ancient ,,observations 7casually made1 as of a star74 ,flamsteed #afij #fab #agab #ibg #agae #gch ,le ,monnier #agej -#dgf ,bradley #agec -#cie ,mayer #agef -#deg ,le ,monnier #agfd -#cdi #agfi -#aic #agga -#bc ,,modern ,,observations4 #aghj #cdf #aghc #hde #aghf #abcf #aghi #aijb #ahja #bbba #ahaj #bcaf #ahbb #bjig #ahbe #ahaf #ahbh #ajhb #ahca -#cih #ahcd -#bjhj #ahcg -#dbff #ahdj -#fffd ,these are the numbers plotted in the above diagram 7,fig4 #ib71 where ,h marks the discovery of the planet and the beginning of its regular observation4 ,something was evidently the matter with the planet4 ,if the law of gravitation held exactly at so great a distance from the sun1 there must be some perturbing force acting on it besides all those known ones which had been fully taken into account4 ,could it be an outer planet8 ,the question occurred to several1 and one or two tried if they could solve the problem1 but were soon stopped by the tremendous difficulties of calculation4 ,the ordinary problem of perturbation is difficult enough3 ,given a disturbing planet in such and such a position1 to find the perturbations it produces4 ,this problem it was that ,laplace worked out in the ,mcanique ,cleste4 ,but the inverse problem3 ,given the perturbations1 to find the planet which causes them--such a problem had never yet been attacked1 and by only a few had its possibility been conceived4 ,bessel made preparations for trying what he could do at it in #ahdj1 but he was prevented by fatal illness4 ,in #ahda the difficulties of the problem presented by these residual perturbations of ,uranus excited the imagination of a young student1 an undergraduate of ,st4 ,john's ,college1 ,cambridge--,john ,couch ,adams by name--and he determined to have a try at it as soon as he was through his ,tripos4 ,in ,january1 #ahdc1 he graduated as ,senior ,wrangler1 and shortly afterwards he set to work4 ,in less than two years he reached a definite conclusion2 and in ,october1 #ahde1 he wrote to the ,astronomer-,royal1 at ,greenwich1 ,professor ,airy1 saying that the perturbations of ,uranus would be explained by assuming the existence of an outer planet1 which he reckoned was now situated in a specified latitude and longitude4 ,we know now that had the ,astronomer-,royal put sufficient faith in this result to point his big telescope to the spot indicated and commence sweeping for a planet1 he would have detected it within #a-c_/d of the place assigned to it by ,mr4 ,adams4 ,but any one in the position of the ,astronomer-,royal knows that almost every post brings an absurd letter from some ambitious correspondent or other1 some of them having just discovered perpetual motion1 or squared the circle1 or proved the earth flat1 or discovered the constitution of the moon1 or of ether1 or of electricity2 and out of this mass of rubbish it requires great skill and patience to detect such gems of value as there may be4 ,now this letter of ,mr4 ,adams's was indeed a jewel of the first water1 and no doubt bore on its face a very different appearance from the chaff of which ,i have spoken2 but still ,mr4 ,adams was an unknown man3 he had graduated as ,senior ,wrangler it is true1 but somebody must graduate as ,senior ,wrangler every year1 and every year by no means produces a first-rate mathematician4 ,those behind the scenes1 as ,professor ,airy of course was1 having been a ,senior ,wrangler himself1 knew perfectly well that the labelling of a young man on taking his degree is much more worthless as a testimony to his genius and ability than the general public are apt to suppose4 ,was it likely that a young and unknown man should have successfully solved so extremely difficult a problem8 ,it was altogether unlikely4 ,still1 he would test him3 he would ask for further explanations concerning some of the perturbations which he himself had specially noticed1 and see if ,mr4 ,adams could explain these also by his hypothesis4 ,if he could1 there might be something in his theory4 ,if he failed--well1 there was an end of it4 ,the questions were not difficult4 ,they concerned the error of the radius vector4 ,mr4 ,adams could have answered them with perfect ease2 but sad to say1 though a brilliant mathematician1 he was not a man of business4 ,he did not answer ,professor ,airy's letter4 ,it may to many seem a pity that the ,greenwich ,equatoreal was not pointed to the place1 just to see whether any foreign object did happen to be in that neighbourhood2 but it is no light matter to derange the work of an ,observatory1 and alter the work mapped out for the staff into a sudden sweep for a new planet1 on the strength of a mathematical investigation just received by post4 ,if observatories were conducted on these unsystematic and spasmodic principles1 they would not be the calm1 accurate1 satisfactory places they are4 ,of course1 if any one could have known that a new planet was to be had for the looking1 any course would have been justified2 but no one could know this4 ,i do not suppose that ,mr4 ,adams himself could feel all that confidence in his attempted prediction4 ,so there the matter dropped4 ,mr4 ,adams's communication was pigeon-holed1 and remained in seclusion for eight or nine months4 ,meanwhile1 and quite independently1 something of the same sort was going on in ,france4 ,a brilliant young mathematician1 born in ,normandy in #ahaa1 had accepted the post of ,astronomical ,professor at the cole ,polytechnique1 then recently founded by ,napoleon4 ,his first published papers directed attention to his wonderful powers2 and the official head of astronomy in ,france1 the famous ,arago1 suggested to him the unexplained perturbations of ,uranus as a worthy object for his fresh and well-armed vigour4 ,at once he set to work in a thorough and systematic way4 ,he first considered whether the discrepancies could be due to errors in the tables or errors in the old observations4 ,he discussed them with minute care1 and came to the conclusion that they were not thus to be explained away4 ,this part of the work he published in ,november1 #ahde4 ,he then set to work to consider the perturbations produced by ,jupiter and ,saturn1 to see if they had been with perfect accuracy allowed for1 or whether some minute improvements could be made sufficient to destroy the irregularities4 ,he introduced several fresh terms into these perturbations1 but none of them of sufficient magnitude to do more than slightly lessen the unexplained perturbations4 ,he next examined the various hypotheses that had been suggested to account for them3--,was it a failure in the law of gravitation8 ,was it due to the presence of a resisting medium8 ,was it due to some unseen but large satellite8 ,or was it due to a collision with some comet8 ,all these he examined and dismissed for various reasons one after the other4 ,it was due to some steady continuous cause--for instance1 some unknown planet4 ,could this planet be inside the orbit of ,uranus8 ,no1 for then it would perturb ,saturn and ,jupiter also1 and they were not perturbed by it4 ,it must1 therefore1 be some planet outside the orbit of ,uranus1 and in all probability1 according to ,bode's empirical law1 at nearly double the distance from the sun that ,uranus is4 ,lastly he proceeded to examine where this planet was1 and what its orbit must be to produce the observed disturbances4 ,illustration3 ,,fig4 #id4--,uranus's and ,neptune's relative positions4 ,the above diagram1 drawn to scale by ,dr4 ,haughton1 shows the paths of ,uranus and ,neptune1 and their positions from #agha to #ahdj1 and illustrates the direction of their mutual perturbing force4 ,in #ahbb the planets were in conjunction1 and the force would then perturb the radius vector 7or distance from the sun71 but not the longitude 7or place in orbit74 ,before that date ,uranus had been hurried along1 and after that date it had been retarded1 by the pull of ,neptune1 and thus the observed discrepancies from its computed place were produced4 ,the problem was first to disentangle the outstanding perturbations from those which would be caused by ,jupiter and ,saturn and all other known causes1 and then to assign the place of an outer planet able to produce precisely those perturbations in ,uranus4 ,not without failures and disheartening complications was this part of the process completed4 ,this was1 after all1 the real tug of war4 ,so many unknown quantities3 its mass1 its distance1 its excentricity1 the obliquity of its orbit1 its position at any time--nothing known1 in fact1 about the planet except the microscopic disturbance it caused in ,uranus1 some thousand million miles away from it4 ,without going into further detail1 suffice it to say that in ,june1 #ahdf1 he published his last paper1 and in it announced to the world his theoretical position for the planet4 ,professor ,airy received a copy of this paper before the end of the month1 and was astonished to find that ,leverrier's theoretical place for the planet was within #a of the place ,mr4 ,adams had assigned to it eight months before4 ,so striking a coincidence seemed sufficient to justify a ,herschelian sweep for a week or two4 ,but a sweep for so distant a planet would be no easy matter4 ,when seen in a large telescope it would still only look like a star1 and it would require considerable labour and watching to sift it out from the other stars surrounding it4 ,we know that ,uranus had been seen twenty times1 and thought to be a star1 before its true nature was by ,herschel discovered2 and ,uranus is only about half as far away as ,neptune is4 ,neither in ,paris nor yet at ,greenwich was any optical search undertaken2 but ,professor ,airy wrote to ask ,m4 ,leverrier the same old question as he had fruitlessly put to ,mr4 ,adams3 ,did the new theory explain the errors of the radius vector or not8 ,the reply of ,leverrier was both prompt and satisfactory--these errors were explained1 as well as all the others4 ,the existence of the object was then for the first time officially believed in4 ,the ,british ,association met that year at ,southampton1 and ,sir ,john ,herschel was one of its ,sectional ,presidents4 ,in his inaugural address1 on ,september #ajth1 #ahdf1 he called attention to the researches of ,leverrier and ,adams in these memorable words3-- ,the past year has given to us the new minor planet ,astra2 it has done more--it has given us the probable prospect of another4 ,we see it as ,columbus saw ,america from the shores of ,spain4 ,its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to ocular demonstration4 ,it was about time to begin to look for it4 ,so the ,astronomer-,royal thought on reading ,leverrier's paper4 ,but as the national telescope at ,greenwich was otherwise occupied1 he wrote to ,professor ,challis1 at ,cambridge1 to know if he would permit a search to be made for it with the ,northumberland ,equatoreal1 the large telescope of ,cambridge ,university1 presented to it by one of the ,dukes of ,northumberland4 ,professor ,challis said he would conduct the search himself2 and shortly commenced a leisurely and dignified series of sweeps round about the place assigned by theory1 cataloguing all the stars which he observed1 intending afterwards to sort out his observations1 compare one with another1 and find out whether any one star had changed its position2 because if it had it must be the planet4 ,he thus1 without giving an excessive time to the business1 accumulated a host of observations1 which he intended afterwards to reduce and sift at his leisure4 ,the wretched man thus actually saw the planet twice--on ,august #dth and ,august #abth1 #ahdf--without knowing it4 ,if only he had had a map of the heavens containing telescopic stars down to the tenth magnitude1 and if he had compared his observations with this map as they were made1 the process would have been easy1 and the discovery quick4 ,but he had no such map4 ,nevertheless one was in existence3 it had just been completed in that country of enlightened method and industry--,germany4 ,dr4 ,bremiker had not1 indeed1 completed his great work--a chart of the whole zodiac down to stars of the tenth magnitude--but portions of it were completed1 and the special region where the new planet was expected happened to be among the portions already just done4 ,but in ,england this was not known4 ,meanwhile1 ,mr4 ,adams wrote to the ,astronomer-,royal several additional communications1 making improvements in his theory1 and giving what he considered nearer and nearer approximations for the place of the planet4 ,he also now answered quite satisfactorily1 but too late1 the question about the radius vector sent to him months before4 ,let us return to ,leverrier4 ,this great man was likewise engaged in improving his theory and in considering how best the optical search could be conducted4 ,actuated1 probably1 by the knowledge that in such matters as cataloguing and mapping ,germany was then1 as now1 far ahead of all the other nations of the world1 he wrote in ,september 7the same ,september as ,sir ,john ,herschel delivered his eloquent address at ,southampton7 to ,berlin4 ,leverrier wrote1 ,i say1 to ,dr4 ,galle1 head of the ,observatory at ,berlin1 saying to him1 clearly and decidedly1 that the new planet was now in or close to such and such a position1 and that if he would point his telescope to that part of the heavens he would see it2 and1 moreover1 that he would be able to tell it from a star by its having a sensible magnitude1 or disk1 instead of being a mere point4 ,galle got the letter on the #bcrd of ,september1 #ahdf4 ,that same evening he did point his telescope to the place ,leverrier told him1 and he saw the planet that very night4 ,he recognized it first by its appearance4 ,to his practised eye it did seem to have a small disk1 and not quite the same aspect as an ordinary star4 ,he then consulted ,bremiker's great star chart1 the part just engraved and finished1 and sure enough on that chart there was no such star there4 ,undoubtedly it was the planet4 ,the news flashed over ,europe at the maximum speed with which news could travel at that date 7which was not very fast72 and by the #ast of ,october ,professor ,challis and ,mr4 ,adams heard it at ,cambridge1 and had the pleasure of knowing that they were forestalled1 and that ,england was out of the race4 ,it was an unconscious race to all concerned1 however4 ,those in ,france knew nothing of the search going on in ,england4 ,mr4 ,adams's papers had never been published2 and very annoyed the ,french were when a claim was set up on his behalf to a share in this magnificent discovery4 ,controversies and recriminations1 excuses and justifications1 followed2 but the discussion has now settled down4 ,all the world honours the bright genius and mathematical skill of ,mr4 ,adams1 and recognizes that he first solved the problem by calculation4 ,all the world1 too1 perceives clearly the no less eminent mathematical talents of ,m4 ,leverrier1 but it recognizes in him something more than the mere mathematician--the man of energy1 decision1 and character4 ,,lecture ,,xvi ,,comets ,,and ,,meteors ,we have now considered the solar system in several aspects1 and we have passed in review something of what is known about the stars4 ,we have seen how each star is itself1 in all probability1 the centre of another and distinct solar system1 the constituents of which are too dark and far off to be visible to us2 nothing visible here but the central sun alone1 and that only as a twinkling speck4 ,but between our solar system and these other suns--between each of these suns and all the rest--there exist vast empty spaces1 apparently devoid of matter4 ,we have now to ask1 ,are these spaces really empty8 ,is there really nothing in space but the nebul1 the suns1 their planets1 and their satellites8 ,are all the bodies in space of this gigantic size8 ,may there not be an infinitude of small bodies as well8 ,the answer to this question is in the affirmative4 ,there appears to be no special size suited to the vastness of space2 we find1 as a matter of fact1 bodies of all manner of sizes1 ranging by gradations from the most tremendous suns1 like ,sirius1 down through ordinary suns to smaller ones1 then to planets of all sizes1 satellites still smaller1 then the asteroids1 till we come to the smallest satellite of ,mars1 only about ten miles in diameter1 and weighing only some billion tons--the smallest of the regular bodies belonging to the solar system known4 ,but1 besides all these1 there are found to occur other masses1 not much bigger and some probably smaller1 and these we call comets when we see them4 ,below these1 again1 we find masses varying from a few tons in weight down to only a few pounds or ounces1 and these when we see them1 which is not often1 we call meteors or shooting-stars2 and to the size of these meteorites there would appear to be no limit3 some may be literal grains of dust4 ,there seems to be a regular gradation of size1 therefore1 ranging from ,sirius to dust2 and apparently we must regard all space as full of these cosmic particles--stray fragments1 as it were1 perhaps of some older world1 perhaps going to help to form a new one some day4 ,as ,kepler said1 there are more comets in the sky than fish in the sea4 ,not that they are at all crowded together1 else they would make a cosmic haze4 ,the transparency of space shows that there must be an enormous proportion of clear space between each1 and they are probably much more concentrated near one of the big bodies than they are in interstellar space4#cj ,even during the furious hail of meteors in ,november #ahff it was estimated that their average distance apart in the thickest of the shower was #ce miles4 ,consider the nature of a meteor or shooting-star4 ,we ordinarily see them as a mere streak of light2 sometimes they leave a luminous tail behind them2 occasionally they appear as an actual fire-ball1 accompanied by an explosion2 sometimes1 but very seldom1 they are seen to drop1 and may subsequently be dug up as a lump of iron or rock1 showing signs of rough treatment by excoriation and heat4 ,these last are the meteorites1 or siderites1 or arolites1 or bolides1 of our museums4 ,they are popularly spoken of as thunderbolts1 though they have nothing whatever to do with atmospheric electricity4 ,illustration3 ,,fig4 #ie4--,meteorite4 ,they appear to be travelling rocky or metallic fragments which in their journey through space are caught in the earth's atmosphere and instantaneously ignited by the friction4 ,far away in the depths of space one of these bodies felt the attracting power of the sun1 and began moving towards him4 ,as it approached1 its speed grew gradually quicker and quicker continually1 until by the time it has approached to within the distance of the earth1 it whizzes past with the velocity of twenty-six miles a second4 ,the earth is moving on its own account nineteen miles every second4 ,if the two bodies happened to be moving in opposite directions1 the combined speed would be terrific2 and the faintest trace of atmosphere1 miles above the earth's surface1 would exert a furious grinding action on the stone4 ,a stream of particles would be torn off2 if of iron1 they would burn like a shower of filings from a firework1 thus forming a trail2 and the mass itself would be dissipated1 shattered to fragments in an instant4 ,illustration3 ,,fig4 #if4--,meteor stream crossing field of telescope4 ,illustration3 ,,fig4 #ig4--;,diagram of direction of earth's orbital motion1 showing that after midnight1 i4e4 between midnight and noon1 more asteroids are likely to be swept up by any locality than between noon and midnight4 ,from ,sir ,r4,s4 ,ball4 ,even if the earth were moving laterally1 the same thing would occur4 ,but if earth and stone happened to be moving in the same direction1 there would be only the differential velocity of seven miles a second2 and though this is in all conscience great enough1 yet there might be a chance for a residue of the nucleus to escape entire destruction1 though it would be scraped1 heated1 and superficially molten by the friction2 but so much of its speed would be rubbed out of it1 that on striking the earth it might bury itself only a few feet or yards in the soil1 so that it could be dug out4 ,the number of those which thus reach the earth is comparatively infinitesimal4 ,nearly all get ground up and dissipated by the atmosphere2 and fortunate it is for us that they are so4 ,this bombardment of the exposed face of the moon must be something terrible4#ca ,thus1 then1 every shooting-star we see1 and all the myriads that we do not and cannot see because they occur in the day-time1 all these bright flashes or streaks1 represent the death and burial of one of these flying stones4 ,it had been careering on its own account through space for untold ages1 till it meets a planet4 ,it cannot strike the actual body of the planet--the atmosphere is a sufficient screen2 the tremendous friction reduces it to dust in an instant1 and this dust then quietly and leisurely settles down on to the surface4 ,evidence of the settlement of meteoric dust is not easy to obtain in such a place as ,england1 where the dust which accumulates is seldom of a celestial character2 but on the snow-fields of ,greenland or the ,himalayas dust can be found2 and by a ,committee of the ,british ,association distinct evidence of molten globules of iron and other materials appropriate to arolites has been obtained1 by the simple process of collecting1 melting1 and filtering long exposed snow4 ,volcanic ash may be mingled with it1 but under the microscope the volcanic and the meteoric constituents have each a distinctive character4 ,the quantity of meteoric material which reaches the earth as dust must be immensely in excess of the minute quantity which arrives in the form of lumps4 ,hundreds or thousands of tons per annum must be received2 and the accretion must1 one would think1 in the course of ages be able to exert some influence on the period of the earth's rotation--the length of the day4 ,it is too small1 however1 to have been yet certainly detected4 ,possibly1 it is altogether negligible4 ,it has been suggested that those stones which actually fall are not the true cosmic wanderers1 but are merely fragments of our own earth1 cast up by powerful volcanoes long ago when the igneous power of the earth was more vigorous than now--cast up with a speed of close upon seven miles a second2 and now in these quiet times gradually being swept up by the earth1 and so returning whence they came4 ,i confess ,i am unable to draw a clear distinction between one set and the other4 ,some falling stars may have had an origin of this sort1 but certainly others have not2 and it would seem very unlikely that one set only should fall bodily upon the earth1 while the others should always be rubbed to powder4 ,still1 it is a possibility to be borne in mind4 ,we have spoken of these cosmic visitors as wandering masses of stone or iron2 but we should be wrong if we associated with the term wandering any ideas of lawlessness and irregularity of path4 ,these small lumps of matter are as obedient to the law of gravity as any large ones can be4 ,they must all1 therefore1 have definite orbits1 and these orbits will have reference to the main attracting power of our system--they will1 in fact1 be nearly all careering round the sun4 ,each planet may1 in truth1 have a certain following of its own4 ,within the limited sphere of the earth's predominant attraction1 for instance1 extending some way beyond the moon1 we may have a number of satellites that we never see1 all revolving regularly in elliptic orbits round the earth4 ,but1 comparatively speaking1 these satellite meteorites are few4 ,the great bulk of them will be of a planetary character--they will be attendant upon the sun4 ,it may seem strange that such minute bodies should have regular orbits and obey ,kepler's laws1 but they must4 ,all three laws must be as rigorously obeyed by them as by the planets themselves4 ,there is nothing in the smallness of a particle to excuse it from implicit obedience to law4 ,the only consequence of their smallness is their inability to perturb others4 ,they cannot appreciably perturb either the planets they approach or each other4 ,the attracting power of a lump one million tons in weight is very minute4 ,a pound1 on the surface of such a body of the same density as the earth1 would be only pulled to it with a force equal to that with which the earth pulls a grain4 ,so the perturbing power of such a mass on distant bodies is imperceptible4 ,it is a good thing it is so3 accurate astronomy would be impossible if we had to take into account the perturbations caused by a crowd of invisible bodies4 ,astronomy would then approach in complexity some of the problems of physics4 ,but though we may be convinced from the facts of gravitation that these meteoric stones1 and all other bodies flying through space near our solar system1 must be constrained by the sun to obey ,kepler's laws1 and fly round it in some regular elliptic or hyperbolic orbit1 what chance have we of determining that orbit8 ,at first sight1 a very poor chance1 for we never see them except for the instant when they splash into our atmosphere2 and for them that instant is instant death4 ,it is unlikely that any escape that ordeal1 and even if they do1 their career and orbit are effectually changed4 ,henceforward they must become attendants on the earth4 ,they may drop on to its surface1 or they may duck out of our atmosphere again1 and revolve round us unseen in the clear space between earth and moon4 ,nevertheless1 although the problem of determining the original orbit of any given set of shooting-stars before it struck us would seem nearly insoluble1 it has been solved1 and solved with some approach to accuracy2 being done by the help of observations of certain other bodies4 ,the bodies by whose help this difficult problem has been attacked and resolved are comets4 ,what are comets8 ,i must tell you that the scientific world is not entirely and completely decided on the structure of comets4 ,there are many floating ideas on the subject1 and some certain knowledge4 ,but the subject is still1 in many respects1 an open one1 and the ideas ,i propose to advocate you will accept for no more than they are worth1 viz4 as worthy to be compared with other and different views4 ,up to the time of ,newton1 the nature of comets was entirely unknown4 ,they were regarded with superstitious awe as fiery portents1 and were supposed to be connected with the death of some king1 or with some national catastrophe4 ,even so late as the first edition of the ,principia the problem of comets was unsolved1 and their theory is not given2 but between the first and the second editions a large comet appeared1 in #afhj1 and ,newton speculated on its appearance and behaviour4 ,it rushed down very close to the sun1 spun half round him very quickly1 and then receded from him again4 ,if it were a material substance1 to which the law of gravitation applied1 it must be moving in a conic section with the sun in one focus1 and its radius vector must sweep out equal areas in equal times4 ,examining the record of its positions made at observatories1 he found its observed path quite accordant with theory2 and the motion of comets was from that time understood4 ,up to that time no one had attempted to calculate an orbit for a comet4 ,they had been thought irregular and lawless bodies4 ,now they were recognized as perfectly obedient to the law of gravitation1 and revolving round the sun like everything else--as members1 in fact1 of our solar system1 though not necessarily permanent members4 ,but the orbit of a comet is very different from a planetary one4 ,the excentricity of its orbit is enormous--in other words1 it is either a very elongated ellipse or a parabola4 ,the comet of #afhj1 ,newton found to move in an orbit so nearly a parabola that the time of describing it must be reckoned in hundreds of years at the least4 ,it is now thought possible that it may not be quite a parabola1 but an ellipse so elongated that it will not return till #bbee4 ,until that date arrives1 however1 uncertainty will prevail as to whether it is a periodic comet1 or one of those that only visit our system once4 ,if it be periodic1 as suspected1 it is the same as appeared when ,julius ,csar was killed1 and which likewise appeared in the years #eca and #aajf ,a4,d4 ,should it appear in #bbee1 our posterity will probably regard it as a memorial of ,newton4 ,illustration3 ,,fig4 #ih4--,parabolic and elliptic orbits4 ,the a b 7visible7 portions are indistinguishable4 ,the next comet discussed in the light of the theory of gravitation was the famous one of ,halley4 ,you know something of the history of this4 ,its period is #ge-a_/b years4 ,halley saw it in #afhb1 and predicted its return in #ageh or #agei--the first cometary prediction4 ,clairaut calculated its return right within a month 7p4 #bai74 ,it has been back once more1 in #ahce2 and this time its date was correctly predicted within three days1 because ,uranus was now known4 ,it was away at its furthest point in #ahgc4 ,it will be back again in #aiaa4 ,illustration3 ,,fig4 #ii4--,orbit of ,halley's comet4 ,coming to recent times1 we have the great comets of #ahdc and of #aheh1 the history of neither being known4 ,quite possibly they arrived then for the first time4 ,possibly the second will appear again in #chjh4 ,but besides these great comets1 there are a multitude of telescopic ones1 which do not show these striking features1 and have no gigantic tail4 ,some have no tail at all1 others have at best a few insignificant streamers1 and others show a faint haze looking like a microscopic nebula4 ,all these comets are of considerable extent--some millions of miles thick usually1 and yet stars are clearly visible through them4 ,hence they must be matter of very small density2 their tails can be nothing more dense than a filmy mist1 but their nucleus must be something more solid and substantial4 ,illustration3 ,,fig4 #ajj4--,various appearances of ,halley's comet when last seen4 ,i have said that comets arrive from the depths of space1 rush towards and round the sun1 whizzing past the earth with a speed of twenty-six miles a second1 on round the sun with a far greater velocity than that1 and then rush off again4 ,now1 all the time they are away from the sun they are invisible4 ,it is only as they get near him that they begin to expand and throw off tails and other appendages4 ,the sun's heat is evidently evaporating them1 and driving away a cloud of mist and volatile matter4 ,this is when they can be seen4 ,the comet is most gorgeous when it is near the sun1 and as soon as it gets a reasonable distance away from him it is perfectly invisible4 ,the matter evaporated from the comet by the sun's heat does not return--it is lost to the comet2 and hence1 after a few such journeys1 its volatile matter gets appreciably diminished1 and so old-established periodic comets have no tails to speak of4 ,but the new visitants1 coming from the depths of space for the first time--these have great supplies of volatile matter1 and these are they which show the most magnificent tails4 ,illustration3 ,,fig4 #aja4--;,head of ,donati's comet of #aheh4 ,the tail of a comet is always directed away from the sun as if it were repelled4 ,to this rule there is no exception4 ,it is suggested1 and held as most probable1 that the tail and sun are similarly electrified1 and that the repulsion of the tail is electrical repulsion4 ,some great force is obviously at work to account for the enormous distance to which the tail is shot in a few hours4 ,the pressure of the sun's light can do something1 and is a force that must not be ignored when small particles are being dealt with4 7,cf4 ,modern ,views of ,electricity1 #bnd edition1 p4 #cfc47 ,now just think what analogies there are between comets and meteors4 ,both are bodies travelling in orbits round the sun1 and both are mostly invisible1 but both become visible to us under certain circumstances4 ,meteors become visible when they plunge into the extreme limits of our atmosphere4 ,comets become visible when they approach the sun4 ,is it possible that comets are large meteors which dip into the solar atmosphere1 and are thus rendered conspicuously luminous8 ,certainly they do not dip into the actual main atmosphere of the sun1 else they would be utterly destroyed2 but it is possible that the sun has a faint trace of atmosphere extending far beyond this1 and into this perhaps these meteors dip1 and glow with the friction4 ,the particles thrown off might be1 also by friction1 electrified2 and the vaporous tail might be thus accounted for4 ,illustration3 ,,fig4 #ajb4--;,halley's ,comet4 ,let us make this hypothesis provisionally--that comets are large meteors1 or a compact swarm of meteors1 which1 coming near the sun1 find a highly rarefied sort of atmosphere1 in which they get heated and partly vaporized1 just as ordinary meteorites do when they dip into the atmosphere of the earth4 ,and let us see whether any facts bear out the analogy and justify the hypothesis4 ,i must tell you now the history of three bodies1 and you will see that some intimate connection between comets and meteors is proved4 ,the three bodies are known as1 first1 ,encke's comet2 second1 ,biela's comet2 third1 the ,november swarm of meteors4 ,encke's comet 7one of those discovered by ,miss ,herschel7 is an insignificant-looking telescopic comet of small period1 the orbit of which was well known1 and which was carefully observed at each reappearance after ,encke had calculated its orbit4 ,it was the quickest of the comets1 returning every #c-a_/b years4 ,illustration3 ,,fig4 #ajc4--;,encke's comet4 ,it was found1 however1 that its period was not quite constant2 it kept on getting slightly shorter4 ,the comet1 in fact1 returned to the sun slightly before its time4 ,now this effect is exactly what friction against a solar atmosphere would bring about4 ,every time it passed near the sun a little velocity would be rubbed out of it4 ,but the velocity is that which carries it away1 hence it would not go quite so far1 and therefore would return a little sooner4 ,any revolving body subject to friction must revolve quicker and quicker1 and get nearer and nearer its central body1 until1 if the process goes on long enough1 it must drop upon its surface4 ,this seems the kind of thing happening to ,encke's comet4 ,the effect is very small1 and not thoroughly proved2 but1 so far as it goes1 the evidence points to a greatly extended rare solar atmosphere1 which rubs some energy out of it at every perihelion passage4 ,illustration3 ,,fig4 #ajd4--;,biela's comet as last seen1 in two portions4 ,next1 ,biela's comet4 ,this also was a well known and carefully observed telescopic comet1 with a period of six years4 ,in one of its distant excursions1 it was calculated that it must pass very near ,jupiter1 and much curiosity was excited as to what would happen to it in consequence of the perturbation it must experience4 ,as ,i have said1 comets are only visible as they approach the sun1 and a watch was kept for it about its appointed time4 ,it was late1 but it did ultimately arrive4 ,the singular thing about it1 however1 was that it was now double4 ,it had apparently separated into two4 ,this was in #ahdf4 ,it was looked for again in #aheb1 and this time the components were further separated4 ,sometimes one was brighter1 sometimes the other4 ,next time it ought to have come round no one could find either portion4 ,the comet seemed to have wholly disappeared4 ,it has never been seen since4 ,it was then recorded and advertised as the missing comet4 ,but now comes the interesting part of the story4 ,the orbit of this ,biela comet was well known1 and it was found that on a certain night in #ahgb the earth would cross the orbit1 and had some chance of encountering the comet4 ,not a very likely chance1 because it need not be in that part of its orbit at the time2 but it was suspected not to be far off--if still existent4 ,well1 the night arrived1 the earth did cross the orbit1 and there was seen1 not the comet1 but a number of shooting-stars4 ,not one body1 nor yet two1 but a multitude of bodies--in fact1 a swarm of meteors4 ,not a very great swarm1 such as sometimes occurs1 but still a quite noticeable one2 and this shower of meteors is definitely recognized as flying along the track of ,biela's comet4 ,they are known as the ,andromedes4 ,this observation has been generalized4 ,every cometary orbit is marked by a ring of meteoric stones travelling round it1 and whenever a number of shooting-stars are seen quickly one after the other1 it is an evidence that we are crossing the track of some comet4 ,but suppose instead of only crossing the track of a comet we were to pass close to the comet itself1 we should then expect to see an extraordinary swarm--a multitude of shooting-stars4 ,such phenomena have occurred4 ,the most famous are those known as the ,november meteors1 or ,leonids4 ,this is the third of those bodies whose history ,i had to tell you4 ,professor ,h4,a4 ,newton1 of ,america1 by examining ancient records arrived at the conclusion that the earth passed through a certain definite meteor shoal every thirty-three years4 ,he found1 in fact1 that every thirty-three years an unusual flight of shooting-stars was witnessed in ,november1 the earliest record being #eii ,a4,d4 ,their last appearance had been in #ahcc1 and he therefore predicted their return in #ahff or #ahfg4 ,sure enough1 in ,november1 #ahff1 they appeared2 and many must remember seeing that glorious display4 ,although their hail was almost continuous1 it is estimated that their average distance apart was thirty-five miles6 ,their radiant point was and always is in the constellation ,leo1 and hence their name ,leonids4 ,illustration3 ,,fig4 #aje4--,radiant point perspective4 ,the arrows represent a number of approximately parallel meteor-streaks foreshortened from a common vanishing-point4 ,a parallel stream fixed in space necessarily exhibits a definite aspect with reference to the fixed stars4 ,its aspect with respect to the earth will be very changeable1 because of the rotation and revolution of that body1 but its position with respect to constellations will be steady4 ,hence each meteor swarm1 being a steady parallel stream of rushing masses1 always strikes us from the same point in stellar space1 and by this point 7or radiant7 it is identified and named4 ,the paths do not appear to us to be parallel1 because of perspective3 they seem to radiate and spread in all directions from a fixed centre like spokes1 but all these diverging streaks are really parallel lines optically foreshortened by different amounts so as to produce the radiant impression4 ,the annexed diagram 7,fig4 #aje7 clearly illustrates the fact that the radiant is the vanishing point of a number of parallel lines4 ,illustration3 ,,fig4 #ajf4--,orbit of ,november meteors4 ,this swarm is specially interesting to us from the fact that we cross its orbit every year4 ,its orbit and the earth's intersect4 ,every ,november we go through it1 and hence every ,november we see a few stragglers of this immense swarm4 ,the swarm itself takes thirty-three years on its revolution round the sun1 and hence we only encounter it every thirty-three years4 ,the swarm is of immense size4 ,in breadth it is such that the earth1 flying nineteen miles a second1 takes four or five hours to cross it1 and this is therefore the time the display lasts4 ,but in length it is far more enormous4 ,the speed with which it travels is twenty-five miles a second1 7for its orbit extends as far as ,uranus1 although by no means parabolic71 and yet it takes more than a year to pass4 ,imagine a procession #bjj1jjj miles broad1 every individual rushing along at the rate of twenty-five miles every second1 and the whole procession so long that it takes more than a year to pass4 ,it is like a gigantic shoal of herrings swimming round and round the sun every thirty-three years1 and travelling past the earth with that tremendous velocity of twenty-five miles a second4 ,the earth dashes through the swarm and sweeps up myriads4 ,think of the countless numbers swept up by the whole earth in crossing such a shoal as that6 ,but heaps more remain1 and probably the millions which are destroyed every thirty-three years have not yet made any very important difference to the numbers still remaining4 ,the earth never misses this swarm4 ,every thirty-three years it is bound to pass through some part of them1 for the shoal is so long that if the head is just missed one ,november the tail will be encountered next ,november4 ,this is a plain and obvious result of its enormous length4 ,it may be likened to a two-foot length of sewing silk swimming round and round an oval sixty feet in circumference4 ,but1 you will say1 although the numbers are so great that destroying a few millions or so every thirty-three years makes but little difference to them1 yet1 if this process has been going on from all eternity1 they ought to be all swept up4 ,granted2 and no doubt the most ancient swarms have already all or nearly all been swept up4 ,illustration3 ,,fig4 #ajg4--,orbit of ,november meteors2 showing their probable parabolic orbit previous to #abf ,a4,d41 and its sudden conversion into an elliptic orbit by the violent perturbation caused by ,uranus1 which at that date occupied the position shown4 ,the ,august meteors1 or ,perseids1 are an example4 ,every ,august we cross their path1 and we have a small meteoric display radiating from the sword-hand of ,perseus1 but never specially more in one ,august than another4 ,it would seem as if the main shoal has disappeared1 and nothing is now left but the stragglers2 or perhaps it is that the shoal has gradually become uniformly distributed all along the path4 ,anyhow1 these ,august meteors are reckoned much more ancient members of the solar system than are the ,november meteors4 ,the ,november meteors are believed to have entered the solar system in the year #abf ,a4,d4 ,this may seem an extraordinary statement4 ,it is not final1 but it is based on the calculations of ,leverrier--confirmed recently by ,mr4 ,adams4 ,a few moments will suffice to make the grounds of it clear4 ,leverrier calculated the orbit of the ,november meteors1 and found them to be an oval extending beyond ,uranus4 ,it was perturbed by the outer planets near which it went1 so that in past times it must have moved in a slightly different orbit4 ,calculating back to their past positions1 it was found that in a certain year it must have gone very near to ,uranus1 and that by the perturbation of this planet its path had been completely changed4 ,originally it had in all probability been a comet1 flying in a parabolic orbit towards the sun like many others4 ,this one1 encountering ,uranus1 was pulled to pieces as it were1 and its orbit made elliptical as shown in ,fig4 #ajg4 ,it was no longer free to escape and go away into the depths of space3 it was enchained and made a member of the solar system4 ,it also ceased to be a comet2 it was degraded into a shoal of meteors4 ,this is believed to be the past history of this splendid swarm4 ,since its introduction to the solar system it has made #eb revolutions3 its next return is due in ,november1 #ahii1 and ,i hope that it may occur in the ,english dusk1 and 7see ,fig4 #ig7 in a cloudless after-midnight sky1 as it did in #ahff4 ,,notes ,,for ,,lecture ,,xvii ,the tide-generating force of one body on another is directly as the mass of the one body and inversely as the cube of the distance between them4 ,hence the moon is more effective in producing terrestrial tides than the sun4 ,the tidal wave directly produced by the moon in the open ocean is about #e feet high1 that produced by the sun is about #b feet4 ,hence the average spring tide is to the average neap as about #g to #c4 ,the lunar tide varies between apogee and perigee from #dc to #ei4 ,the solar tide varies between aphelion and perihelion from #ai to #ba4 ,hence the highest spring tide is to the lowest neap as #ei #ba is to #dc -#ba1 or as #h to #bb4 ,the semi-synchronous oscillation of the ,southern ,ocean raises the magnitude of oceanic tides somewhat above these directly generated values4 ,oceanic tides are true waves1 not currents4 ,coast tides are currents4 ,the momentum of the water1 when the tidal wave breaks upon a continent and rushes up channels1 raises coast tides to a much greater height--in some places up to #ej or #fj feet1 or even more4 ,early observed connections between moon and tides would be these3-- #ast4 ,spring tides at new and full moon4 #bnd4 ,average interval between tide and tide is half a lunar1 not a solar1 day--a lunar day being the interval between two successive returns of the moon to the meridian3 #bd hours and #ej minutes4 #crd4 ,the tides of a given place at new and full moon occur always at the same time of day whatever the season of the year4 ,,lecture ,,xvii ,,the ,,tides ,persons accustomed to make use of the ,mersey landing-stages can hardly fail to have been struck with two obvious phenomena4 ,one is that the gangways thereto are sometimes almost level1 and at other times very steep2 another is that the water often rushes past the stage rather violently1 sometimes south towards ,garston1 sometimes north towards the sea4 ,they observe1 in fact1 that the water has two periodic motions--one up and down1 the other to and fro--a vertical and a horizontal motion4 ,they may further observe1 if they take the trouble1 that a complete swing of the water1 up and down1 or to and fro1 takes place about every twelve and a half hours2 moreover1 that soon after high and low water there is no current--the water is stationary1 whereas about half-way between high and low it is rushing with maximum speed either up or down the river4 ,to both these motions of the water the name tide is given1 and both are extremely important4 ,sailors usually pay most attention to the horizontal motion1 and on charts you find the tide-races marked2 and the places where there is but a small horizontal rush of the water are labelled very little tide here4 ,landsmen1 or1 at any rate1 such of the more philosophic sort as pay any attention to the matter at all1 think most of the vertical motion of the water--its amount of rise and fall4 ,dwellers in some low-lying districts in ,london are compelled to pay attention to the extra high tides of the ,thames1 because it is1 or was1 very liable to overflow its banks and inundate their basements4 ,sailors1 however1 on nearing a port are also greatly affected by the time and amount of high water there1 especially when they are in a big ship2 and we know well enough how frequently ,atlantic liners1 after having accomplished their voyage with good speed1 have to hang around for hours waiting till there is enough water to lift them over the ,bar--that standing obstruction1 one feels inclined to say disgrace1 to the ,liverpool harbour4 ,illustration3 ,,fig4 #ajh4--,the ,mersey ,to us in ,liverpool the tides are of supreme importance--upon them the very existence of the city depends--for without them ,liverpool would not be a port4 ,it may be familiar to many of you how this is1 and yet it is a matter that cannot be passed over in silence4 ,i will therefore call your attention to the ,ordnance ,survey of the estuaries of the ,mersey and the ,dee4 ,you see first that there is a great tendency for sand-banks to accumulate all about this coast1 from ,north ,wales right away round to ,southport4 ,you see next that the port of ,chester has been practically silted up by the deposits of sand in the wide-mouthed ,dee1 while the port of ,liverpool remains open owing to the scouring action of the tide in its peculiarly shaped channel4 ,without the tides the ,mersey would be a wretched dribble not much bigger than it is at ,warrington4 ,with them1 this splendid basin is kept open1 and a channel is cut of such depth that the ,great ,eastern easily rode in it in all states of the water4 ,the basin is filled with water every twelve hours through its narrow neck4 ,the amount of water stored up in this basin at high tide ,i estimate as #fjj million tons4 ,all this quantity flows through the neck in six hours1 and flows out again in the next six1 scouring and cleansing and carrying mud and sand far out to sea4 ,just at present the currents set strongest on the ,birkenhead side of the river1 and accordingly a ,pluckington bank unfortunately grows under the ,liverpool stage4 ,should this tendency to silt up the gates of our docks increase1 land can be reclaimed on the other side of the river between ,tranmere and ,rock ,ferry1 and an embankment made so as to deflect the water over ,liverpool way1 and give us a fairer proportion of the current4 ,after passing ,new ,brighton the water spreads out again to the left2 its velocity forward diminishes2 and after a few miles it has no power to cut away that sandbank known as the ,bar4 ,should it be thought desirable to make it accomplish this1 and sweep the ,bar further out to sea into deeper water1 it is probable that a rude training wall 7say of old hulks1 or other removable partial obstruction7 on the west of ,queen's ,channel1 arranged so as to check the spreading out over all this useless area1 may be quite sufficient to retain the needed extra impetus in the water1 perhaps even without choking up the useful old ,rock ,channel1 through which smaller ships still find convenient exit4 ,now1 although the horizontal rush of the tide is necessary to our existence as a port1 it does not follow that the accompanying rise and fall of the water is an unmixed blessing4 ,to it is due the need for all the expensive arrangements of docks and gates wherewith to store up the high-level water4 ,quebec and ,new ,york are cities on such magnificent rivers that the current required to keep open channel is supplied without any tidal action1 although ,quebec is nearly #a1jjj miles from the open ocean2 and accordingly1 ,atlantic liners do not hover in mid-river and discharge passengers by tender1 but they proceed straight to the side of the quays lining the river1 or1 as at ,new ,york1 they dive into one of the pockets belonging to the company running the ship1 and there discharge passengers and cargo without further trouble1 and with no need for docks or gates4 ,however1 rivers like the ,st4 ,lawrence and the ,hudson are the natural property of a gigantic continent2 and we in ,england may be well contented with the possession of such tidal estuaries as the ,mersey1 the ,thames1 and the ,humber4 ,that by pertinacious dredging the citizens of ,glasgow manage to get large ships right up their small river1 the ,clyde1 to the quays of the town1 is a remarkable fact1 and redounds very highly to their credit4 ,we will now proceed to consider the connection existing between the horizontal rush of water and its vertical elevation1 and ask1 ,which is cause and which is effect8 ,does the elevation of the ocean cause the tidal flow1 or does the tidal flow cause the elevation8 ,the answer is twofold3 both statements are in some sense true4 ,the prime cause of the tide is undoubtedly a vertical elevation of the ocean1 a tidal wave or hump produced by the attraction of the moon4 ,this hump as it passes the various channels opening into the ocean raises their level1 and causes water to flow up them4 ,but this simple oceanic tide1 although the cause of all tide1 is itself but a small affair4 ,it seldom rises above six or seven feet1 and tides on islands in mid-ocean have about this value or less4 ,but the tides on our coasts are far greater than this--they rise twenty or thirty feet1 or even fifty feet occasionally1 at some places1 as at ,bristol4 ,why is this8 ,the horizontal motion of the water gives it such an impetus or momentum that its motion far transcends that of the original impulse given to it1 just as a push given to a pendulum may cause it to swing over a much greater arc than that through which the force acts4 ,the inrushing water flowing up the ,english ,channel or the ,bristol ,channel or ,st4 ,george's ,channel has such an impetus that it propels itself some twenty or thirty feet high before it has exhausted its momentum and begins to descend4 ,in the ,bristol ,channel the gradual narrowing of the opening so much assists this action that the tides often rise forty feet1 occasionally fifty feet1 and rush still further up the ,severn in a precipitous and extraordinary hill of water called the bore4 ,some places are subject to considerable rise and fall of water with very little horizontal flow2 others possess strong tidal races1 but very little elevation and depression4 ,the effect observed at any given place entirely depends on whether the place has the general character of a terminus1 or whether it lies en route to some great basin4 ,you must understand1 then1 that all tide takes its rise in the free and open ocean under the action of the moon4 ,no ordinary-sized sea like the ,north ,sea1 or even the ,mediterranean1 is big enough for more than a just appreciable tide to be generated in it4 ,the ,pacific1 the ,atlantic1 and the ,southern ,oceans are the great tidal reservoirs1 and in them the tides of the earth are generated as low flat humps of gigantic area1 though only a few feet high1 oscillating up and down in the period of approximately twelve hours4 ,the tides we1 and other coast-possessing nations1 experience are the overflow or back-wash of these oceanic humps1 and ,i will now show you in what manner the great ,atlantic tide-wave reaches the ,british ,isles twice a day4 ,illustration3 ,,fig4 #aji4--;,co-tidal lines4 ,fig4 #aji shows the contour lines of the great wave as it rolls in east from the ,atlantic1 getting split by the ,land's ,end and by ,ireland into three portions2 one of which rushes up the ,english ,channel and through the ,straits of ,dover4 ,another rolls up the ,irish ,sea1 with a minor offshoot up the ,bristol ,channel1 and1 curling round ,anglesey1 flows along the ,north ,wales coast and fills ,liverpool ,bay and the ,mersey4 ,the third branch streams round the north coast of ,ireland1 past the ,mull of ,cantyre and ,rathlin ,island2 part fills up the ,firth of ,clyde1 while the rest flows south1 and1 swirling round the west side of the ,isle of ,man1 helps the southern current to fill the ,bay of ,liverpool4 ,the rest of the great wave impinges on the coast of ,scotland1 and1 curling round it1 fills up the ,north ,sea right away to the ,norway coast1 and then flows down below ,denmark1 joining the southern and earlier arriving stream4 ,the diagram ,i show you is a rough chart of cotidal lines1 which ,i made out of the information contained in ,whitaker's ,almanac4 ,a place may thus be fed with tide by two distinct channels1 and many curious phenomena occur in certain places from this cause4 ,thus it may happen that one channel is six hours longer than the other1 in which case a flow will arrive by one at the same time as an ebb arrives by the other2 and the result will be that the place will have hardly any tide at all1 one tide interfering with and neutralizing the other4 ,this is more markedly observed at other parts of the world than in the ,british ,isles4 ,whenever a place is reached by two channels of different length1 its tides are sure to be peculiar1 and probably small4 ,another cause of small tide is the way the wave surges to and fro in a channel4 ,the tidal wave surging up the ,english ,channel1 for instance1 gets largely reflected by the constriction at ,dover1 and so a crest surges back again1 as we may see waves reflected in a long trough or tilted bath4 ,the result is that ,southampton has two high tides rapidly succeeding one another1 and for three hours the high-water level varies but slightly--a fact of evident convenience to the port4 ,places on a nodal line1 so to speak1 about the middle of the length of the channel1 have a minimum of rise and fall1 though the water rushes past them first violently up towards ,dover1 where the rise is considerable1 and then back again towards the ocean4 ,at ,portland1 for instance1 the total rise and fall is very small3 it is practically on a node4 ,yarmouth1 again1 is near a less marked node in the ,north ,sea1 where stationary waves likewise surge to and fro1 and accordingly the tidal rise and fall at ,yarmouth is only about five feet 7varying from four and a half to six71 whereas at ,london it is twenty or thirty feet1 and at ,flamborough ,head or ,leith it is from twelve to sixteen feet4 ,it is generally supposed that water never flows up-hill1 but in these cases of oscillation it flows up-hill for three hours together4 ,the water is rushing up the ,english ,channel towards ,dover long after it is highest at the ,dover end2 it goes on piling itself up1 until its momentum is checked by the pressure1 and then it surges back4 ,it behaves1 in fact1 very like the bob of a pendulum1 which rises against gravity at every quarter swing4 ,to get a very large tide1 the place ought to be directly accessible by a long sweep of a channel to the open ocean1 and if it is situate on a gradually converging opening1 the ebb and flow may be enormous4 ,the ,severn is the best example of this on the ,british ,isles2 but the largest tides in the world are found1 ,i believe1 in the ,bay of ,fundy1 on the coast of ,north ,america1 where they sometimes rise one hundred and twenty feet4 ,excessive or extra tides may be produced occasionally in any place by the propelling force of a high wind driving the water towards the shore2 also by a low barometer1 i4e4 by a local decrease in the pressure of the air4 ,well1 now1 leaving these topographical details concerning tides1 which we see to be due to great oceanic humps 7great in area that is1 though small in height71 let us proceed to ask what causes these humps2 and if it be the moon that does it1 how does it do it8 ,the statement that the moon causes the tides sounds at first rather an absurdity1 and a mere popular superstition4 ,galileo chaffed ,kepler for believing it4 ,who it was that discovered the connection between moon and tides we know not--probably it is a thing which has been several times rediscovered by observant sailors or coast-dwellers--and it is certainly a very ancient piece of information4 ,probably the first connection observed was that about full moon and about new moon the tides are extra high1 being called spring tides1 whereas about half-moon the tides are much less1 and are called neap tides4 ,the word spring in this connection has no reference to the season of the year2 except that both words probably represent the same idea of energetic uprising or upspringing1 while the word neap comes from nip1 and means pinched1 scanty1 nipped tide4 ,the next connection likely to be observed would be that the interval between two day tides was not exactly a solar day of twenty-four hours1 but a lunar day of fifty minutes longer4 ,for by reason of the moon's monthly motion it lags behind the sun about fifty minutes a day1 and the tides do the same1 and so perpetually occur later and later1 about fifty minutes a day later1 or #ab hours and #be minutes on the average between tide and tide4 ,a third and still more striking connection was also discovered by some of the ancient great navigators and philosophers--viz4 that the time of high water at a given place at full moon is always the same1 or very nearly so4 ,in other words1 the highest or spring tides always occur nearly at the same time of day at a given place4 ,for instance1 at ,liverpool this time is noon and midnight4 ,london is about two hours and a half later4 ,each port has its own time for receiving a given tide1 and the time is called the establishment of the port4 ,look out a day when the moon is full1 and you will find the ,liverpool high tide occurs at half-past eleven1 or close upon it4 ,the same happens when the moon is new4 ,a day after full or new moon the spring tides rise to their highest1 and these extra high tides always occur in ,liverpool at noon and at midnight1 whatever the season of the year4 ,about the equinoxes they are liable to be extraordinarily high4 ,the extra low tides here are therefore at #f a4m4 and #f p4m41 and the #f p4m4 low tide is a nuisance to the river steamers4 ,the spring tides at ,london are highest about half-past two4 99 99 99 99 99 ,it is1 therefore1 quite clear that the moon has to do with the tides4 ,it and the sun together are1 in fact1 the whole cause of them2 and the mode in which these bodies act by gravitative attraction was first made out and explained in remarkably full detail by ,sir ,isaac ,newton4 ,you will find his account of the tides in the second and third books of the ,principia2 and though the theory does not occupy more than a few pages of that immortal work1 he succeeds not only in explaining the local tidal peculiarities1 much as ,i have done to-night1 but also in calculating the approximate height of mid-ocean solar tide2 and from the observed lunar tide he shows how to determine the then quite unknown mass of the moon4 ,this was a quite extraordinary achievement1 the difficulty of which it is not easy for a person unused to similar discussions fully to appreciate4 ,it is1 indeed1 but a small part of what ,newton accomplished1 but by itself it is sufficient to confer immortality upon any ordinary philosopher1 and to place him in a front rank4 ,illustration3 ,,fig4 #aaj4--,whirling earth model4 ,to make intelligible ,newton's theory of the tides1 ,i must not attempt to go into too great detail4 ,i will consider only the salient points4 ,first1 you know that every mass of matter attracts every other piece of matter2 second1 that the moon revolves round the earth1 or rather that the earth and moon revolve round their common centre of gravity once a month2 third1 that the earth spins on its own axis once a day2 fourth1 that when a thing is whirled round1 it tends to fly out from the centre and requires a force to hold it in4 ,these are the principles involved4 ,you can whirl a bucket full of water vertically round without spilling it4 ,make an elastic globe rotate1 and it bulges out into an oblate or orange shape2 as illustrated by the model shown in ,fig4 #aaj4 ,this is exactly what the earth does1 and ,newton calculated the bulging of it as fourteen miles all round the equator4 ,make an elastic globe revolve round a fixed centre outside itself1 and it gets pulled into a prolate or lemon shape2 the simplest illustrative experiment is to attach a string to an elastic bag or football full of water1 and whirl it round and round4 ,its prolateness is readily visible4 ,now consider the earth and moon revolving round each other like a man whirling a child round4 ,the child travels furthest1 but the man cannot merely rotate1 he leans back and thus also describes a small circle3 so does the earth2 it revolves round the common centre of gravity of earth and moon 7cf4 p4 #bab74 ,this is a vital point in the comprehension of the tides3 the earth's centre is not at rest1 but is being whirled round by the moon1 in a circle about #a_/hj as big as the circle which the moon describes1 because the earth weighs eighty times as much as the moon4 ,the effect of the revolution is to make both bodies slightly protrude in the direction of the line joining them2 they become slightly prolate as it is called--that is1 lemon-shaped4 ,illustrating still by the man and child1 the child's legs fly outwards so that he is elongated in the direction of a radius2 the man's coat-tails fly out too1 so that he too is similarly though less elongated4 ,these elongations or protuberances constitute the tides4 ,illustration3 ,,fig4 #aaa4--;,earth and moon model1 illustrating the production of statical or equilibrium tides when the whole is whirled about the point ,g4 ,fig4 #aaa shows a model to illustrate the mechanism4 ,a couple of cardboard disks 7to represent globes of course71 one four times the diameter of the other1 and each loaded so as to have about the correct earth-moon ratio of weights1 are fixed at either end of a long stick1 and they balance about a certain point1 which is their common centre of gravity4 ,for convenience this point is taken a trifle too far out from the centre of the earth--that is1 just beyond its surface4 ,through the balancing point ,g a bradawl is stuck1 and on that as pivot the whole readily revolves4 ,now1 behind the circular disks1 you see1 are four pieces of card of appropriate shape1 which are able to slide out under proper forces4 ,they are shown dotted in the figure1 and are lettered ,a1 ,b1 ,c1 ,d4 ,the inner pair1 ,b and ,c1 are attached to each other by a bit of string1 which has to typify the attraction of gravitation2 the outer pair1 ,a and ,d1 are not attached to anything1 but have a certain amount of play against friction in slots parallel to the length of the stick4 ,the moon-disk is also slotted1 so a small amount of motion is possible to it along the stick or bar4 ,these things being so arranged1 and the protuberant pieces of card being all pushed home1 so that they are hidden behind their respective disks1 the whole is spun rapidly round the centre of gravity1 ,g4 ,the result of a brief spin is to make ,a and ,d fly out by centrifugal force and show1 as in the figure2 while the moon1 flying out too in its slot1 tightens up the string1 which causes ,b and ,c to be pulled out too4 ,thus all four high tides are produced1 two on the earth and two on the moon1 ,a and ,d being caused by centrifugal force1 ,b and ,c by the attraction of gravitation4 ,each disk has become prolate in the same sort of fashion as yielding globes do4 ,of course the fluid ocean takes this shape more easily and more completely than the solid earth can1 and so here are the very oceanic humps we have been talking about1 and about three feet high 7,fig4 #aab74 ,if there were a sea on the moon1 its humps would be a good deal bigger2 but there probably is no sea there1 and if there were1 the earth's tides are more interesting to us1 at any rate to begin with4 ,illustration3 ,,fig4 #aab4--;,earth and moon 7earth's rotation neglected74 ,the humps as so far treated are always protruding in the earth-moon line1 and are stationary4 ,but now we have to remember that the earth is spinning inside them4 ,it is not easy to see what precise effect this spin will have upon the humps1 even if the world were covered with a uniform ocean2 but we can see at any rate that however much they may get displaced1 and they do get displaced a good deal1 they cannot possibly be carried round and round4 ,the whole explanation we have given of their causes shows that they must maintain some steady aspect with respect to the moon--in other words1 they must remain stationary as the earth spins round4 ,not that the same identical water remains stationary1 for in that case it would have to be dragged over the earth's equator at the rate of #a1jjj miles an hour1 but the hump or wave-crest remains stationary4 ,it is a true wave1 or form only1 and consists of continuously changing individual particles4 ,the same is true of all waves1 except breaking ones4 ,given1 then1 these stationary humps and the earth spinning on its axis1 we see that a given place on the earth will be carried round and round1 now past a hump1 and six hours later past a depression3 another six hours and it will be at the antipodal hump1 and so on4 ,thus every six hours we shall travel from the region in space where the water is high to the region where it is low2 and ignoring our own motion we shall say that the sea first rises and then falls2 and so1 with respect to the place1 it does4 ,thus the succession of high and low water1 and the two high tides every twenty-four hours1 are easily understood in their easiest and most elementary aspect4 ,a more complete account of the matter it will be wisest not to attempt3 suffice it to say that the difficulties soon become formidable when the inertia of the water1 its natural time of oscillation1 the varying obliquity of the moon to the ecliptic1 its varying distance1 and the disturbing action of the sun are taken into consideration4 ,when all these things are included1 the problem becomes to ordinary minds overwhelming4 ,a great many of these difficulties were successfully attacked by ,laplace4 ,others remained for modern philosophers1 among whom are ,sir ,george ,airy1 ,sir ,william ,thomson1 and ,professor ,george ,darwin4 ,i may just mention that the main and simplest effect of including the inertia or momentum of the water is to dislocate the obvious and simple connexion between high water and high moon2 inertia always tends to make an effect differ in phase by a quarter period from the cause producing it1 as may be illustrated by a swinging pendulum4 ,hence high water is not to be expected when the tide-raising force is a maximum1 but six hours later2 so that1 considering inertia and neglecting friction1 there would be low water under the moon4 ,including friction1 something nearer the equilibrium state of things occurs4 ,with sufficient friction the motion becomes dead-beat again1 i4e4 follows closely the force that causes it4 ,returning to the elementary discussion1 we see that the rotation of the earth with respect to the humps will not be performed in exactly twenty-four hours1 because the humps are travelling slowly after the moon1 and will complete a revolution in a month in the same direction as the earth is rotating4 ,hence a place on the earth has to catch them up1 and so each high tide arrives later and later each day--roughly speaking1 an hour later for each day tide2 not by any means a constant interval1 because of superposed disturbances not here mentioned1 but on the average about fifty minutes4 ,we see1 then1 that as a result of all this we get a pair of humps travelling all over the surface of the earth1 about once a day4 ,if the earth were all ocean 7and in the southern hemisphere it is nearly all ocean71 then they would go travelling across the earth1 tidal waves three feet high1 and constituting the mid-ocean tides4 ,but in the northern hemisphere they can only thus journey a little way without striking land4 ,as the moon rises at a place on the east shores of the ,atlantic1 for instance1 the waters begin to flow in towards this place1 or the tide begins to rise4 ,this goes on till the moon is overhead and for some time afterwards1 when the tide is at its highest4 ,the hump then follows the moon in its apparent journey across to ,america1 and there precipitates itself upon the coast1 rushing up all the channels1 and constituting the land tide4 ,at the same time1 the water is dragged away from the east shores1 and so our tide is at its lowest4 ,the same thing repeats itself in a little more than twelve hours again1 when the other hump passes over the ,atlantic1 as the moon journeys beneath the earth1 and so on every day4 ,in the free ,southern ,ocean1 where land obstruction is comparatively absent1 the water gets up a considerable swing by reason of its accumulated momentum1 and this modifies and increases the open ocean tides there4 ,also for some reason1 ,i suppose because of the natural time of swing of the water1 one of the humps is there usually much larger than the other2 and so places in the ,indian and other offshoots of the ,southern ,ocean get their really high tide only once every twenty-four hours4 ,these southern tides are in fact much more complicated than those the ,british ,isles receive4 ,ours are singularly simple4 ,no doubt some trace of the influence of the ,southern ,ocean is felt in the ,north ,atlantic1 but any ocean extending over #ij of longitude is big enough to have its own tides generated2 and ,i imagine that the main tides we feel are thus produced on the spot1 and that they are simple because the damping-out being vigorous1 and accumulated effects small1 we feel the tide-producing forces more directly4 ,but for authoritative statements on tides1 other books must be read4 ,i have thought1 and still think1 it best in an elementary exposition to begin by a consideration of the tide-generating forces as if they acted on a non-rotating earth4 ,it is the tide generating forces1 and not the tides themselves1 that are really represented in ,figs4 #aab and #aad4 ,the rotation of the earth then comes in as a disturbing cause4 ,a more complete exposition would begin with the rotating earth1 and would superpose the attraction of the moon as a disturbing cause1 treating it as a problem in planetary perturbation1 the ocean being a sort of satellite of the earth4 ,this treatment1 introducing inertia but ignoring friction and land obstruction1 gives low water in the line of pull1 and high water at right angles1 or where the pull is zero2 in the same sort of way as a pendulum bob is highest where most force is pulling it down1 and lowest where no force is acting on it4 ,for a clear treatment of the tides as due to the perturbing forces of sun and moon1 see a little book by ,mr4 ,t4,k4 ,abbott of ,trinity ,college1 ,dublin4 7,longman47 ,illustration3 ,,fig4 #aac4--,maps showing how comparatively free from land obstruction the ocean in the ,southern ,hemisphere is4 ,if the moon were the only body that swung the earth round1 this is all that need be said in an elementary treatment2 but it is not the only one4 ,the moon swings the earth round once a month1 the sun swings it round once a year4 ,the circle of swing is bigger1 but the speed is so much slower that the protuberance produced is only one-third of that caused by the monthly whirl2 i4e4 the simple solar tide in the open sea1 without taking momentum into account1 is but a little more than a foot high1 while the simple lunar tide is about three feet4 ,when the two agree1 we get a spring tide of four feet2 when they oppose each other1 we get a neap tide of only two feet4 ,they assist each other at full moon and at new moon4 ,at half-moon they oppose each other4 ,so we have spring tides regularly once a fortnight1 with neap tides in between4 ,illustration3 ,,fig4 #aad4--,spring and neap tides4 ,fig4 #aad gives the customary diagrams to illustrate these simple things4 ,you see that when the moon and sun act at right angles 7i4e4 at every half-moon71 the high tides of one coincide with the low tides of the other2 and so1 as a place is carried round by the earth's rotation1 it always finds either solar or else lunar high water1 and only experiences the difference of their two effects4 ,whereas1 when the sun and moon act in the same line 7as they do at new and full moon71 their high and low tides coincide1 and a place feels their effects added together4 ,the tide then rises extra high and falls extra low4 ,illustration3 ,,fig4 #aae4--,tidal clock4 ,the position of the disk ,b shows the height of the tide4 ,the tide represented is a nearly high tide eight feet above mean level4 ,utilizing these principles1 a very elementary form of tidal-clock1 or tide-predicter1 can be made1 and for an open coast station it really would not give the tides so very badly4 ,it consists of a sort of clock face with two hands1 one nearly three times as long as the other4 ,the short hand1 ,,ca1 should revolve round ,c once in twelve hours1 and the vertical height of its end ,a represents the height of the solar tide on the scale of horizontal lines ruled across the face of the clock4 ,the long hand1 ,,ab1 should revolve round ,a once in twelve hours and twenty-five minutes1 and the height of its end ,b 7if ,a were fixed on the zero line7 would represent the lunar tide4 ,the two revolutions are made to occur together1 either by means of a link-work parallelogram1 or1 what is better in practice1 by a string and pulleys1 as shown2 and the height of the end point1 ,b1 of the third side or resultant1 ,,cb1 read off on a scale of horizontal parallel lines behind1 represents the combination or actual tide at the place4 ,every fortnight the two will agree1 and you will get spring tides of maximum height ,,ca ,,ab2 every other fortnight the two will oppose1 and you will get neap tides of maximum height ,,ca-,,ab4 ,such a clock1 if set properly and driven in the ordinary way1 would then roughly indicate the state of the tide whenever you chose to look at it and read the height of its indicating point4 ,it would not indeed be very accurate1 especially for such an inclosed station as ,liverpool is1 and that is probably why they are not made4 ,a great number of disturbances1 some astronomical1 some terrestrial1 have to be taken into account in the complete theory4 ,it is not an easy matter to do this1 but it can be1 and has been1 done2 and a tide-predicter has not only been constructed1 but two of them are in regular work1 predicting the tides for years hence--one1 the property of the ,indian ,government1 for coast stations of ,india2 the other for various ,british and foreign stations1 wherever the necessary preliminary observations have been made4 ,these machines are the invention of ,sir ,william ,thomson4 ,the tide-tables for ,indian ports are now always made by means of them4 ,illustration3 ,,fig4 #aaf4--,sir ,william ,thomson 7,lord ,kelvin74 ,illustration3 ,,fig4 #aag4--,tide-gauge for recording local tides1 a pencil moved up and down by a float writes on a drum driven by clockwork4 ,the first thing to be done by any port which wishes its tides to be predicted is to set up a tide-gauge1 or automatic recorder1 and keep it working for a year or two4 ,the tide-gauge is easy enough to understand3 it marks the height of the tide at every instant by an irregular curved line like a barometer chart 7,fig4 #aag74 ,these observational curves so obtained have next to be fed into a fearfully complex machine1 which it would take a whole lecture to make even partially intelligible1 but ,fig4 #aah shows its aspect4 ,it consists of ten integrating machines in a row1 coupled up and working together4 ,this is the harmonic analyzer1 and the result of passing the curve through this machine is to give you all the constituents of which it is built up1 viz4 the lunar tide1 the solar tide1 and eight of the sub-tides or disturbances4 ,these ten values are then set off into a third machine1 the tide-predicter proper4 ,the general mode of action of this machine is not difficult to understand4 ,it consists of a string wound over and under a set of pulleys1 which are each set on an excentric1 so as to have an up-and-down motion4 ,these up-and-down motions are all different1 and there are ten of these movable pulleys1 which by their respective excursions represent the lunar tide1 the solar tide1 and the eight disturbances already analyzed out of the tide-gauge curve by the harmonic analyzer4 ,one end of the string is fixed1 the other carries a pencil which writes a trace on a revolving drum of paper--a trace which represents the combined motion of all the pulleys1 and so predicts the exact height of the tide at the place1 at any future time you like4 ,the machine can be turned quite quickly1 so that a year's tides can be run off with every detail in about half-an-hour4 ,this is the easiest part of the operation4 ,nothing has to be done but to keep it supplied with paper and pencil1 and turn a handle as if it were a coffee-mill instead of a tide-mill4 7,figs4 #aai and #abj47 ,illustration3 ,,fig4 #aah4--;,harmonic analyzer2 for analyzing out the constituents from a set of observational curves4 ,my subject is not half exhausted4 ,i might go on to discuss the question of tidal energy--whether it can be ever utilized for industrial purposes2 and also the very interesting question whence it comes4 ,tidal energy is almost the only terrestrial form of energy that does not directly or indirectly come from the sun4 ,the energy of tides is now known to be obtained at the expense of the earth's rotation2 and accordingly our day must be slowly1 very slowly1 lengthening4 ,the tides of past ages have destroyed the moon's rotation1 and so it always turns the same face to us4 ,there is every reason to believe that in geologic ages the moon was nearer to us than it is now1 and that accordingly our tides were then far more violent1 rising some hundreds of feet instead of twenty or thirty1 and sweeping every six hours right over the face of a country1 ploughing down hills1 denuding rocks1 and producing a copious sedimentary deposit4 ,illustration3 ,,fig4 #aai4--,tide-predicter1 for combining the ascertained constituents into a tidal curve for the future4 ,in thus discovering the probable violent tides of past ages1 astronomy has1 within the last few years1 presented geology with the most powerful denuding agent known2 and the study of the earth's past history cannot fail to be greatly affected by the modern study of the intricate and refined conditions attending prolonged tidal action on incompletely rigid bodies4 ,read on this point the last chapter of ,sir ,r4 ,ball's ,story of the ,heavens4 ,illustration3 ,fig4 #abj4--,weekly sheet of curves4 ,tides for successive days are predicted on the same sheet of paper1 to economise space4 ,i might also point out that the magnitude of our terrestrial tides enables us to answer the question as to the internal fluidity of the earth4 ,it used to be thought that the earth's crust was comparatively thin1 and that it contained a molten interior4 ,we now know that this is not the case4 ,the interior of the earth is hot indeed1 but it is not fluid4 ,or at least1 if it be fluid1 the amount of fluid is but very small compared with the thickness of the unyielding crust4 ,all these1 and a number of other most interesting questions1 fringe the subject of the tides2 the theoretical study of which1 started by ,newton1 has developed1 and is destined in the future to further develop1 into one of the most gigantic and absorbing investigations--having to do with the stability or instability of solar systems1 and with the construction and decay of universes4 ,these theories are the work of pioneers now living1 whose biographies it is therefore unsuitable for us to discuss1 nor shall ,i constantly mention their names4 ,but ,helmholtz1 and ,thomson1 are household words1 and you well know that in them and their disciples the race of ,pioneers maintains its ancient glory4 ,,notes ,,for ,,lecture ,,xviii ,tides are due to incomplete rigidity of bodies revolving round each other under the action of gravitation1 and at the same time spinning on their axes4 ,two spheres revolving round each other can only remain spherical if rigid2 if at all plastic they become prolate4 ,if either rotate on its axis1 in the same or nearly the same plane as it revolves1 that one is necessarily subject to tides4 ,the axial rotation tends to carry the humps with it1 but the pull of the other body keeps them from moving much4 ,hence the rotation takes place against a pull1 and is therefore more or less checked and retarded4 ,this is the theory of ,von ,helmholtz4 ,the attracting force between two such bodies is no longer exactly towards the centre of revolution1 and therefore ,kepler's second law is no longer precisely obeyed3 the rate of description of areas is subject to slight acceleration4 ,the effect of this tangential force acting on the tide-compelling body is gradually to increase its distance from the other body4 ,applying these statements to the earth and moon1 we see that tidal energy is produced at the expense of the earth's rotation1 and that the length of the day is thereby slowly increasing4 ,also that the moon's rotation relative to the earth has been destroyed by past tidal action in it 7the only residue of ancient lunar rotation now being a scarcely perceptible libration71 so that it turns always the same face towards us4 ,moreover1 that its distance from the earth is steadily increasing4 ,this last is the theory of ,professor ,g4,h4 ,darwin4 ,long ago the moon must therefore have been much nearer the earth1 and the day was much shorter4 ,the tides were then far more violent4 ,halving the distance would make them eight times as high2 quartering it would increase them sixty-four-fold4 ,a most powerful geological denuding agent4 ,trade winds and storms were also more violent4 ,if ever the moon were close to the earth1 it would have to revolve round it in about three hours4 ,if the earth rotated on its axis in three hours1 when fluid or pasty1 it would be unstable1 and begin to separate a portion of itself as a kind of bud1 which might then get detached and gradually pushed away by the violent tidal action4 ,hence it is possible that this is the history of the moon4 ,if so1 it is probably an exceptional history4 ,the planets were not formed from the sun in this way4 ,mars' moons revolve round him more quickly than the planet rotates3 hence with them the process is inverted1 and they must be approaching him and may some day crash along his surface4 ,the inner moon is now about #d1jjj miles away1 and revolves in #g-a_/b hours4 ,it appears to be about #bj miles in diameter1 and weighs therefore1 if composed of rock1 #dj billion tons4 ,mars rotates in #bd-a_/b hours4 ,a similar fate may possibly await our moon ages hence--by reason of the action of terrestrial tides produced by the sun4 ,,lecture ,,xviii ,,the ,,tides1 ,,and ,,planetary ,,evolution ,in the last lecture we considered the local peculiarities of the tides1 the way in which they were formed in open ocean under the action of the moon and the sun1 and also the means by which their heights and times could be calculated and predicted years beforehand4 ,towards the end ,i stated that the subject was very far from being exhausted1 and enumerated some of the large and interesting questions which had been left untouched4 ,it is with some of these questions that ,i propose now to deal4 ,i must begin by reminding you of certain well-known facts1 a knowledge of which ,i may safely assume4 ,and first we must remind ourselves of the fact that almost all the rocks which form the accessible crust of the earth were deposited by the agency of water4 ,nearly all are arranged in regular strata1 and are composed of pulverized materials--materials ground down from pre-existing rocks by some denuding and grinding action4 ,they nearly all contain vestiges of ancient life embedded in them1 and these vestiges are mainly of marine origin4 ,the strata which were once horizontal are now so no longer--they have been tilted and upheaved1 bent and distorted1 in many places4 ,some of them again have been metamorphosed by fire1 so that their organic remains have been destroyed1 and the traces of their aqueous origin almost obliterated4 ,but still1 to the eye of the geologist1 all are of aqueous or sedimentary origin3 roughly speaking1 one may say they were all deposited at the bottom of some ancient sea4 ,the date of their formation no man yet can tell1 but that it was vastly distant is certain4 ,for the geological era is not over4 ,aqueous action still goes on3 still does frost chip the rocks into fragments2 still do mountain torrents sweep stone and mud and dbris down the gulleys and watercourses2 still do rivers erode their channels1 and carry mud and silt far out to sea4 ,and1 more powerful than any of these agents of denudation1 the waves and the tides are still at work along every coast-line1 eating away into the cliffs1 undermining gradually and submerging acre after acre1 and making with the refuse a shingly1 or a sandy1 or a muddy beach--the nucleus of a new geological formation4 ,of all denuding agents1 there can be no doubt that1 to the land exposed to them1 the waves of the sea are by far the most powerful4 ,think how they beat and tear1 and drive and drag1 until even the hardest rock1 like basalt1 becomes honeycombed into strange galleries and passages--,fingal's ,cave1 for instance--and the softer parts are crumbled away4 ,but the area now exposed to the teeth of the waves is not great4 ,the fury of a winter storm may dash them a little higher than usual1 but they cannot reach cliffs #ajj feet high4 ,they can undermine such cliffs indeed1 and then grind the fragments to powder1 but their direct action is limited4 ,not so limited1 however1 as they would be without the tides4 ,consider for a moment the denudation import of the tides3 how does the existence of tidal rise and fall affect the geological problem8 ,the scouring action of the tidal currents themselves is not to be despised4 ,it is the tidal ebb and flow which keeps open channel in the ,mersey1 for instance4 ,but few places are so favourably situated as ,liverpool in this respect1 and the direct scouring action of the tides in general is not very great4 ,their geological import mainly consists in this--that they raise and lower the surface waves at regular intervals1 so as to apply them to a considerable stretch of coast4 ,the waves are a great planing machine attacking the land1 and the tides raise and lower this planing machine1 so that its denuding tooth is applied1 now twenty feet vertically above mean level1 now twenty feet below4 ,making all allowance for the power of winds and waves1 currents1 tides1 and watercourses1 assisted by glacial ice and frost1 it must be apparent how slowly the work of forming the rocks is being carried on4 ,it goes on steadily1 but so slowly that it is estimated to take #fjjj years to wear away one foot of the ,american continent by all the denuding causes combined4 ,to erode a stratum #ejjj feet thick will require at this rate thirty million years4 ,the age of the earth is not at all accurately known1 but there are many grounds for believing it not to be much older than some thirty million years4 ,that is to say1 not greatly more than this period of time has elapsed since it was in a molten condition4 ,it may be as old as a hundred million years1 but its age is believed by those most competent to judge to be more likely within this limit than beyond it4 ,but if we ask what is the thickness of the rocks which in past times have been formed1 and denuded1 and re-formed1 over and over again1 we get an answer1 not in feet1 but in miles4 ,the ,laurentian and ,huronian rocks of ,canada constitute a stratum ten miles thick2 and everywhere the rocks at the base of our stratified system are of the most stupendous volume and thickness4 ,it has always been a puzzle how known agents could have formed these mighty masses1 and the only solution offered by geologists was1 unlimited time4 ,given unlimited time1 they could1 of course1 be formed1 no matter how slowly the process went on4 ,but inasmuch as the time allowable since the earth was cool enough for water to exist on it except as steam is not by any means unlimited1 it becomes necessary to look for a far more powerful engine than any now existing2 there must have been some denuding agent in those remote ages--ages far more distant from us than the ,carboniferous period1 far older than any forms of life1 fossil or otherwise1 ages among the oldest known to geology--a denuding agent must have then existed1 far more powerful than any we now know4 ,such an agent it has been the privilege of astronomy and physics1 within the last ten years1 to discover4 ,to this discovery ,i now proceed to lead up4 ,our fundamental standard of time is the period of the earth's rotation--the length of the day4 ,the earth is our one standard clock3 all time is expressed in terms of it1 and if it began to go wrong1 or if it did not go with perfect uniformity1 it would seem a most difficult thing to discover its error1 and a most puzzling piece of knowledge to utilize when found4 ,that it does not go much wrong is proved by the fact that we can calculate back to past astronomical events--ancient eclipses and the like--and we find that the record of their occurrence1 as made by the old magi of ,chalda1 is in very close accordance with the result of calculation4 ,one of these famous old eclipses was observed in ,babylon about thirty-six centuries ago1 and the ,chaldan astronomers have put on record the time of its occurrence4 ,modern astronomers have calculated back when it should have occurred1 and the observed time agrees very closely with the actual1 but not exactly4 ,why not exactly8 ,partly because of the acceleration of the moon's mean motion1 as explained in the lecture on ,laplace 7p4 #bfb74 ,the orbit of the earth was at that time getting rounder1 and so1 as a secondary result1 the speed of the moon was slightly increasing4 ,it is of the nature of a perturbation1 and is therefore a periodic not a progressive or continuous change1 and in a sufficiently long time it will be reversed4 ,still1 for the last few thousand years the moon's motion has been1 on the whole1 accelerated 7though there seems to be a very slight retarding force in action too74 ,laplace thought that this fact accounted for the whole of the discrepancy2 but recently1 in #ahec1 ,professor ,adams re-examined the matter1 and made a correction in the details of the theory which diminishes its effect by about one-half1 leaving the other half to be accounted for in some other way4 ,his calculations have been confirmed by ,professor ,cayley4 ,this residual discrepancy1 when every known cause has been allowed for1 amounts to about one hour4 ,the eclipse occurred later than calculation warrants4 ,now this would have happened from either of two causes1 either an acceleration of the moon in her orbit1 or a retardation of the earth in her diurnal rotation--a shortening of the month or a lengthening of the day1 or both4 ,the total discrepancy being1 say1 two hours1 an acceleration of six seconds-per-century per century will in thirty-six centuries amount to one hour2 and this1 according to the corrected ,laplacian theory1 is what has occurred4 ,but to account for the other hour some other cause must be sought1 and at present it is considered most probably due to a steady retardation of the earth's rotation--a slow1 very slow1 lengthening of the day4 ,the statement that a solar eclipse thirty-six centuries ago was an hour late1 means that a place on the earth's surface came into the shadow one hour behind time--that is1 had lagged one twenty-fourth part of a revolution4 ,the earth1 therefore1 had lost this amount in the course of #cfjj #cfe-a_/d revolutions4 ,the loss per revolution is exceedingly small1 but it accumulates1 and at any era the total loss is the sum of all the losses preceding it4 ,it may be worth while just to explain this point further4 ,suppose the earth loses a small piece of time1 which ,i will call an instant1 per day2 a locality on the earth will come up to a given position one instant late on the first day after an event4 ,on the next day it would come up two instants late by reason of the previous loss2 but it also loses another instant during the course of the second day1 and so the total lateness by the end of that day amounts to three instants4 ,the day after1 it will be going slower from the beginning at the rate of two instants a day1 it will lose another instant on the fresh day's own account1 and it started three instants late2 hence the aggregate loss by the end of the third day is #a #b #c #f4 ,by the end of the fourth day the whole loss will be #a #b #c #d1 and so on4 ,wherefore by merely losing one instant every day the total loss in n days is 7#a #b #c 444 n7 instants1 which amounts to #a_/bn 7n #a7 instants2 or practically1 when n is big1 to #a_/bn#b4 ,now in thirty-six centuries there have been #cfjj #cfe-a_/d days1 and the total loss has amounted to an hour2 hence the length of an instant1 the loss per diem1 can be found from the equation #a_/b7cfjj #cfe7b instants #a hour2 whence one instant equals the #bdj millionth part of a second4 ,this minute quantity represents the retardation of the earth per day4 ,in a year the aggregate loss mounts up to #a_/cfjjth part of a second1 in a century to about three seconds1 and in thirty-six centuries to an hour4 ,but even at the end of the thirty-six centuries the day is barely any longer2 it is only #cfjj #cfe instants1 that is #a_/ahjth of a second1 longer than it was at the beginning4 ,and even a million years ago1 unless the rate of loss was different 7as it probably was71 the day would only be thirty-five minutes shorter1 though by that time the aggregate loss1 as measured by the apparent lateness of any perfectly punctual event reckoned now1 would have amounted to nine years4 7,these numbers are to be taken as illustrative1 not as precisely representing terrestrial fact47 ,what can have caused the slowing down8 ,swelling of the earth by reason of accumulation of meteoric dust might do something1 but probably very little4 ,contraction of the earth as it goes on cooling would act in the opposite direction1 and probably more than counterbalance the dust effect4 ,the problem is thus not a simple one1 for there are several disturbing causes1 and for none of them are the data enough to base a quantitative estimate upon2 but one certain agent in lengthening the day1 and almost certainly the main agent1 is to be found in the tides4 ,remember that the tidal humps were produced as the prolateness of a sphere whirled round and round a fixed centre1 like a football whirled by a string4 ,these humps are pulled at by the moon1 and the earth rotates on its axis against this pull4 ,hence it tends to be constantly1 though very slightly1 dragged back4 ,in so far as the tidal wave is allowed to oscillate freely1 it will swing with barely any maintaining force1 giving back at one quarter-swing what it has received at the previous quarter2 but in so far as it encounters friction1 which it does in all channels where there is an actual ebb and flow of the water1 it has to receive more than it gives back1 and the balance of energy has to be made up to it1 or the tides would cease4 ,the energy of the tides is1 in fact1 continually being dissipated by friction1 and all the energy so dissipated is taken from the rotation of the earth4 ,if tidal energy were utilized by engineers1 the machines driven would be really driven at the expense of the earth's rotation3 it would be a mode of harnessing the earth and using the moon as fixed point or fulcrum2 the moon pulling at the tidal protuberance1 and holding it still as the earth rotates1 is the mechanism whereby the energy is extracted1 the handle whereby the friction brake is applied4 ,winds and ocean currents have no such effect 7as ,mr4 ,fronde in ,oceania supposes they have71 because they are all accompanied by a precisely equal counter-current somewhere else1 and no internal rearrangement of fluid can affect the motion of a mass as a whole2 but the tides are in different case1 being produced1 not by internal inequalities of temperature1 but by a straightforward pull from an external body4 ,the ultimate effect of tidal friction and dissipation of energy will1 therefore1 be to gradually retard the earth till it does not rotate with reference to the moon1 i4e4 till it rotates once while the moon revolves once2 in other words1 to make the day and the month equal4 ,the same cause must have been in operation1 but with eighty-fold greater intensity1 on the moon4 ,it has ceased now1 because the rotation has stopped1 but if ever the moon rotated on its axis with respect to the earth1 and if it were either fluid itself or possessed any liquid ocean1 then the tides caused by the pull of the earth must have been prodigious1 and would tend to stop its rotation4 ,have they not succeeded8 ,is it not probable that this is why the moon always now turns the same face towards us8 ,it is believed to be almost certainly the cause4 ,if so1 there was a time when the moon behaved differently--when it rotated more quickly than it revolved1 and exhibited to us its whole surface4 ,and at this era1 too1 the earth itself must have rotated a little faster1 for it has been losing speed ever since4 ,we have thus arrived at this fact1 that a thousand years ago the day was a trifle shorter than it is now4 ,a million years ago it was1 perhaps1 an hour shorter4 ,twenty million years ago it must have been much shorter4 ,fifty million years ago it may have been only a few hours long4 ,the earth may have spun round then quite quickly4 ,but there is a limit4 ,if it spun too fast it would fly to pieces4 ,attach shot by means of wax to the whirling earth model1 ,fig4 #aaj1 and at a certain speed the cohesion of the wax cannot hold them1 so they fly off4 ,the earth is held together not by cohesion but by gravitation2 it is not difficult to reckon how fast the earth must spin for gravity at its surface to be annulled1 and for portions to fly off4 ,we find it about one revolution in three hours4 ,this is a critical speed4 ,if ever the day was three hours long1 something must have happened4 ,the day can never have been shorter than that2 for if it were1 the earth would have a tendency to fly in pieces1 or1 at least1 to separate into two pieces4 ,remember this1 as a natural result of a three-hour day1 which corresponds to an unstable state of things2 remember also that in some past epoch a three-hour day is a probability4 ,if we think of the state of things going on in the earth's atmosphere1 if it had an atmosphere at that remote date1 we shall recognize the existence of the most fearful tornadoes4 ,the trade winds1 which are now peaceful agents of commerce1 would then be perpetual hurricanes1 and all the denudation agents of the geologist would be in a state of feverish activity4 ,so1 too1 would the tides3 instead of waiting six hours between low and high tide1 we should have to wait only three-quarters of an hour4 ,every hour-and-a-half the water would execute a complete swing from high tide to high again4 ,very well1 now leave the earth1 and think what has been happening to the moon all this while4 ,we have seen that the moon pulls the tidal hump nearest to it back2 but action and reaction are always equal and opposite--it cannot do that without itself getting pulled forward4 ,the pull of the earth on the moon will therefore not be quite central1 but will be a little in advance of its centre2 hence1 by ,kepler's second law1 the rate of description of areas by its radius vector cannot be constant1 but must increase 7p4 #bjh74 ,and the way it increases will be for the radius vector to lengthen1 so as to sweep out a bigger area4 ,or1 to put it another way1 the extra speed tending to be gained by the moon will fling it further away by extra centrifugal force4 ,this last is not so good a way of regarding the matter2 though it serves well enough for the case of a ball whirled at the end of an elastic string4 ,after having got up the whirl1 the hand holding the string may remain almost fixed at the centre of the circle1 and the motion will continue steadily2 but if the hand be moved so as always to pull the string a little in advance of the centre1 the speed of whirl will increase1 the elastic will be more and more stretched1 until the whirling ball is describing a much larger circle4 ,but in this case it will likewise be going faster--distance and speed increase together4 ,this is because it obeys a different law from gravitation--the force is not inversely as the square1 or any other single power1 of the distance4 ,it does not obey any of ,kepler's laws1 and so it does not obey the one which now concerns us1 viz4 the third2 which practically states that the further a planet is from the centre the slower it goes2 its velocity varies inversely with the square root of its distance 7p4 #gd74 ,if1 instead of a ball held by elastic1 it were a satellite held by gravity1 an increase in distance must be accompanied by a diminution in speed4 ,the time of revolution varies as the square of the cube root of the distance 7,kepler's third law74 ,hence1 the tidal reaction on the moon1 having as its primary effect1 as we have seen1 the pulling the moon a little forward1 has also the secondary or indirect effect of making it move slower and go further off4 ,it may seem strange that an accelerating pull1 directed in front of the centre1 and therefore always pulling the moon the way it is going1 should retard it2 and that a retarding force like friction1 if such a force acted1 should hasten it1 and make it complete its orbit sooner2 but so it precisely is4 ,gradually1 but very slowly1 the moon is receding from us1 and the month is becoming longer4 ,the tides of the earth are pushing it away4 ,this is not a periodic disturbance1 like the temporary acceleration of its motion discovered by ,laplace1 which in a few centuries1 more or less1 will be reversed2 it is a disturbance which always acts one way1 and which is therefore cumulative4 ,it is superposed upon all periodic changes1 and1 though it seems smaller than they1 it is more inexorable4 ,in a thousand years it makes scarcely an appreciable change1 but in a million years its persistence tells very distinctly2 and so1 in the long run1 the month is getting longer and the moon further off4 ,working backwards also1 we see that in past ages the moon must have been nearer to us than it is now1 and the month shorter4 ,now just note what the effect of the increased nearness of the moon was upon our tides4 ,remember that the tide-generating force varies inversely as the cube of distance1 wherefore a small change of distance will produce a great difference in the tide-force4 ,the moon's present distance is #bdj thousand miles4 ,at a time when it was only #aij thousand miles1 the earth's tides would have been twice as high as they are now4 ,the pushing away action was then a good deal more violent1 and so the process went on quicker4 ,the moon must at some time have been just half its present distance1 and the tides would then have risen1 not #bj or #cj feet1 but #afj or #bjj feet4 ,a little further back still1 we have the moon at one-third of its present distance from the earth1 and the tides #fjj feet high4 ,now just contemplate the effect of a #fjj-;foot tide4 ,we are here only about #aej feet above the level of the sea2 hence1 the tide would sweep right over us and rush far away inland4 ,at high tide we should have some #bjj feet of blue water over our heads4 ,there would be nothing to stop such a tide as that in this neighbourhood till it reached the high lands of ,derbyshire4 ,manchester would be a seaport then with a vengeance6 ,the day was shorter then1 and so the interval between tide and tide was more like ten than twelve hours4 ,accordingly1 in about five hours1 all that mass of water would have swept back again1 and great tracts of sand between here and ,ireland would be left dry4 ,another five hours1 and the water would come tearing and driving over the country1 applying its furious waves and currents to the work of denudation1 which would proceed apace4 ,these high tides of enormously distant past ages constitute the denuding agent which the geologist required4 ,they are very ancient--more ancient than the ,carboniferous period1 for instance1 for no trees could stand the furious storms that must have been prevalent at this time4 ,it is doubtful whether any but the very lowest forms of life then existed4 ,it is the strata at the bottom of the geological scale that are of the most portentous thickness1 and the only organism suspected in them is the doubtful ,eozoon ,canadense4 ,sir ,robert ,ball believes1 and several geologists agree with him1 that the mighty tides we are contemplating may have been coval with this ancient ,laurentian formation1 and others of like nature with it4 ,but let us leave geology now1 and trace the inverted progress of events as we recede in imagination back through the geological era1 beyond1 into the dim vista of the past1 when the moon was still closer and closer to the earth1 and was revolving round it quicker and quicker1 before life or water existed on it1 and when the rocks were still molten4 ,suppose the moon once touched the earth's surface1 it is easy to calculate1 according to the principles of gravitation1 and with a reasonable estimate of its size as then expanded by heat1 how fast it must then have revolved round the earth1 so as just to save itself from falling in4 ,it must have gone round once every three hours4 ,the month was only three hours long at this initial epoch4 ,remember1 however1 the initial length of the day4 ,we found that it was just possible for the earth to rotate on its axis in three hours1 and that when it did so1 something was liable to separate from it4 ,here we find the moon in contact with it1 and going round it in this same three-hour period4 ,surely the two are connected4 ,surely the moon was a part of the earth1 and was separating from it4 ,that is the great discovery--the origin of the moon4 ,once1 long ages back1 at date unknown1 but believed to be certainly as much as fifty million years ago1 and quite possibly one hundred million1 there was no moon1 only the earth as a molten globe1 rapidly spinning on its axis--spinning in about three hours4 ,gradually1 by reason of some disturbing causes1 a protuberance1 a sort of bud1 forms at one side1 and the great inchoate mass separates into two--one about eighty times as big as the other4 ,the bigger one we now call earth1 the smaller we now call moon4 ,round and round the two bodies went1 pulling each other into tremendously elongated or prolate shapes1 and so they might have gone on for a long time4 ,but they are unstable1 and cannot go on thus3 they must either separate or collapse4 ,some disturbing cause acts again1 and the smaller mass begins to revolve less rapidly4 ,tides at once begin--gigantic tides of molten lava hundreds of miles high2 tides not in free ocean1 for there was none then1 but in the pasty mass of the entire earth4 ,immediately the series of changes ,i have described begins1 the speed of rotation gets slackened1 the moon's mass gets pushed further and further away1 and its time of revolution grows rapidly longer4 ,the changes went on rapidly at first1 because the tides were so gigantic2 but gradually1 and by slow degrees1 the bodies get more distant1 and the rate of change more moderate4 ,until1 after the lapse of ages1 we find the day twenty-four hours long1 the moon #bdj1jjj miles distant1 revolving in #bg-a_/c days1 and the tides only existing in the water of the ocean1 and only a few feet high4 ,this is the era we call to-day4 ,the process does not stop here3 still the stately march of events goes on2 and the eye of ,science strives to penetrate into the events of the future with the same clearness as it has been able to descry the events of the past4 ,and what does it see8 ,it will take too long to go into full detail3 but ,i will shortly summarize the results4 ,it sees this first--the day and the month both again equal1 but both now about #a1djj hours long4 ,neither of these bodies rotating with respect to each other--the two as if joined by a bar--and total cessation of tide-generating action between them4 ,the date of this period is one hundred and fifty millions of years hence1 but unless some unforeseen catastrophe intervenes1 it must assuredly come4 ,yet neither will even this be the final stage2 for the system is disturbed by the tide-generating force of the sun4 ,it is a small effect1 but it is cumulative2 and gradually1 by much slower degrees than anything we have yet contemplated1 we are presented with a picture of the month getting gradually shorter than the day1 the moon gradually approaching instead of receding1 and so1 incalculable myriads of ages hence1 precipitating itself upon the surface of the earth whence it arose4 ,such a catastrophe is already imminent in a neighbouring planet--,mars4 ,mars' principal moon circulates round him at an absurd pace1 completing a revolution in #g-a_/b hours1 and it is now only #d1jjj miles from his surface4 ,the planet rotates in twenty-four hours as we do2 but its tides are following its moon more quickly than it rotates after them2 they are therefore tending to increase its rate of spin1 and to retard the revolution of the moon4 ,mars is therefore slowly but surely pulling its moon down on to itself1 by a reverse action to that which separated our moon4 ,the day shorter than the month forces a moon further away2 the month shorter than the day tends to draw a satellite nearer4 ,this moon of ,mars is not a large body3 it is only twenty or thirty miles in diameter1 but it weighs some forty billion tons1 and will ultimately crash along the surface with a velocity of #h1jjj miles an hour4 ,such a blow must produce the most astounding effects when it occurs1 but ,i am unable to tell you its probable date4 ,so far we have dealt mainly with the earth and its moon2 but is the existence of tides limited to these bodies8 ,by no means4 ,no body in the solar system is rigid1 no body in the stellar universe is rigid4 ,all must be susceptible of some tidal deformation1 and hence1 in all of them1 agents like those we have traced in the history of the earth and moon must be at work3 the motion of all must be complicated by the phenomena of tides4 ,it is ,prof4 ,george ,darwin who has worked out the astronomical influence of the tides1 on the principles of ,sir ,william ,thomson3 it is ,sir ,robert ,ball who has extended ,mr4 ,darwin's results to the past history of our own and other worlds4#cb ,tides are of course produced in the sun by the action of the planets1 for the sun rotates in twenty-five days or thereabouts1 while the planets revolve in much longer periods than that4 ,the principal tide-generating bodies will be ,venus and ,jupiter2 the greater nearness of one rather more than compensating for the greater mass of the other4 ,it may be interesting to tabulate the relative tide-producing powers of the planets on the sun4 ,they are as follows1 calling that of the earth #a1jjj3-- ,,relative ,,tide-,,producing ,,powers ,,of ,,the ,,planets ,,on ,,the ,,sun4 ,mercury #a1aba ,venus #b1cci ,earth #a1jjj ,mars #cjd ,jupiter #b1acf ,saturn #a1jcc ,uranus #ba ,neptune #i ,the power of all of them is very feeble1 and by acting on different sides they usually partly neutralize each other's action2 but occasionally they get all on one side1 and in that case some perceptible effect may be produced2 the probable effect seems likely to be a gentle heaving tide in the solar surface1 with breaking up of any incipient crust2 and such an effect may be considered as evidenced periodically by the great increase in the number of solar spots which then break out4 ,the solar tides are1 however1 much too small to appreciably push any planet away1 hence we are not to suppose that the planets originated by budding from the sun1 in contradiction of the nebular hypothesis4 ,nor is it necessary to assume that the satellites1 as a class1 originated in the way ours did2 though they may have done so4 ,they were more probably secondary rings4 ,our moon differs from other satellites in being exceptionally large compared with the size of its primary2 it is as big as some of the moons of ,jupiter and ,saturn4 ,the earth is the only one of the small planets that has an appreciable moon1 and hence there is nothing forced or unnatural in supposing that it may have had an exceptional history4 ,evidently1 however1 tidal phenomena must be taken into consideration in any treatment of the solar system through enormous length of time1 and it will probably play a large part in determining its future4 ,when ,laplace and ,lagrange investigated the question of the stability or instability of the solar system1 they did so on the hypothesis that the bodies composing it were rigid4 ,they reached a grand conclusion--that all the mutual perturbations of the solar system were periodic--that whatever changes were going on would reach a maximum and then begin to diminish2 then increase again1 then diminish1 and so on4 ,the system was stable1 and its changes were merely like those of a swinging pendulum4 ,but this conclusion is not final4 ,the hypothesis that the bodies are rigid is not strictly true3 and directly tidal deformation is taken into consideration it is perceived to be a potent factor1 able in the long run to upset all their calculations4 ,but it is so utterly and inconceivably minute--it only produces an appreciable effect after millions of years--whereas the ordinary perturbations go through their swings in some hundred thousand years or so at the most4 ,granted it is small1 but it is terribly persistent2 and it always acts in one direction4 ,never does it cease3 never does it begin to act oppositely and undo what it has done4 ,it is like the perpetual dropping of water4 ,there may be only one drop in a twelvemonth1 but leave it long enough1 and the hardest stone must be worn away at last4 99 99 99 99 99 ,we have been speaking of millions of years somewhat familiarly2 but what1 after all1 is a million years that we should not speak familiarly of it8 ,it is longer than our lifetime1 it is true4 ,to the ephemeral insects whose lifetime is an hour1 a year might seem an awful period1 the mid-day sun might seem an almost stationary body1 the changes of the seasons would be unknown1 everything but the most fleeting and rapid changes would appear permanent and at rest4 ,conversely1 if our life-period embraced myriads of ons1 things which now seem permanent would then appear as in a perpetual state of flux4 ,a continent would be sometimes dry1 sometimes covered with ocean2 the stars we now call fixed would be moving visibly before our eyes2 the earth would be humming on its axis like a top1 and the whole of human history might seem as fleeting as a cloud of breath on a mirror4 ,evolution is always a slow process4 ,to evolve such an animal as a greyhound from its remote ancestors1 according to ,mr4 ,darwin1 needs immense tracts of time2 and if the evolution of some feeble animal crawling on the surface of this planet is slow1 shall the stately evolution of the planetary orbs themselves be hurried8 ,it may be that we are able to trace the history of the solar system for some thousand million years or so2 but for how much longer time must it not have a history--a history1 and also a future--entirely beyond our ken8 ,those who study the stars have impressed upon them the existence of the most immeasurable distances1 which yet are swallowed up as nothing in the infinitude of space4 ,no less are we compelled to recognize the existence of incalculable ons of time1 and yet to perceive that these are but as drops in the ocean of eternity4 ,,footnotes3 #a ,the following account of ,mars's motion is from the excellent small manual of astronomy by ,dr4 ,haughton of ,trinity ,college1 ,dublin3--7,p4 #aea7 ,mars's motion is very unequal2 when he first appears in the morning emerging from the rays of the sun1 his motion is direct and rapid2 it afterwards becomes slower1 and he becomes stationary when at an elongation of #acg from the sun2 then his motion becomes retrograde1 and its velocity increases until he is in opposition to the sun at #ahj2 at this time the retrograde motion is most rapid1 and afterwards diminishes until he is #acg distant from the sun on the other side1 when ,mars again becomes stationary2 his motion then becomes direct1 and increases in velocity until it reaches a maximum1 when the planet is again in conjunction with the sun4 ,the retrograde motion of this planet lasts for #gc days3 and its arc of retrogradation is #af4 #b ,it is not so easy to plot the path of the sun among the stars by direct observation1 as it is to plot the path of a planet2 because sun and stars are not visible together4 ,hipparchus used the moon as an intermediary2 since sun and moon are visible together1 and also moon and stars4 #c ,this is1 however1 by no means the whole of the matter4 ,the motion is not a simple circle nor has it a readily specifiable period4 ,there are several disturbing causes4 ,all that is given here is a first rough approximation4 #d ,the proof is easy1 and ought to occur in books on solid geometry4 ,by a regular solid is meant one with all its faces1 edges1 angles1 c41 absolutely alike3 it is of these perfectly symmetrical bodies that there are only five4 ,crystalline forms are practically infinite in number4 #e ,best known to us by his ,christian name1 as so many others of that time are known1 e4g4 ,raphael ,sanzio1 ,dante ,alighieri1 ,michael ,angelo ,buonarotti4 ,the rule is not universal4 ,tasso and ,ariosto are surnames4 #f ,it would seem that the fact that all bodies of every material tend to fall at the same rate is still not clearly known4 ,confusion is introduced by the resistance of the air4 ,but a little thought should make it clear that the effect of the air is a mere disturbance1 to be eliminated as far as possible1 since the atmosphere has nothing to do with gravitation4 ,the old fashioned guinea and feather experiment illustrates that in a vacuum things entirely different in specific gravity or surface drop at the same pace4 #g ,karl von ,gebler 7,galileo71 p4 #ac4 #h ,it is of course the silver lining of clouds that outside observers see4 #i ,l4,u4,k41 ,life of ,galileo1 p4 #bf4 #aj ,note added ,september1 #ahib4 ,news from the ,lick ,observatory makes a very small fifth satellite not improbable4 #aa ,they remained there till this century4 ,in #ahce they were quietly dropped4 #ab ,it was invented by van ,helmont1 a ,belgian chemist1 who died in #afdd4 ,he suggested two names gas and blas1 and the first has survived4 ,blas was1 ,i suppose1 from blasen1 to blow1 and gas seems to be an attempt to get at the ,sanskrit root underlying all such words as geist4 #ac ,such as this1 among many others3--,the duration of a flame under different conditions is well worth determining4 ,a spoonful of warm spirits of wine burnt #aaf pulsations4 ,the same spoonful of spirits of wine with addition of one-sixth saltpetre burnt #id pulsations4 ,with one-sixth common salt1 #hc2 with one-sixth gunpowder1 #aaj2 a piece of wax in the middle of the spirit1 #hg2 a piece of ,kieselstein1 #id2 one-sixth water1 #hf2 and with equal parts water1 only #d pulse-beats4 ,this1 says ,liebig1 is given as an example of a licht-bringende ,versuch4 #ad ,draper1 ,history of ,civilization in ,europe1 vol4 ii4 p4 #bei4 #ae ,professor ,knight's series of ,philosophical ,classics4 #af ,to explain why the entire system1 horse and cart together1 move forward1 the forces acting on the ground must be attended to4 #ag ,the distance being proportional to the square of the time1 see p4 #hb4 #ah ,the following letter1 recently unearthed and published in ,nature1 ,may #ab1 #ahha1 seems to me well worth preserving4 ,the feeling of a respiratory interval which it describes is familiar to students during the too few periods of really satisfactory occupation4 ,the early guess concerning atmospheric electricity is typical of his extraordinary instinct for guessing right4 ,,london1 ,dec4 #ae1 #agaf4 ,,dear ,,doctor1--,he that in ye mine of knowledge deepest diggeth1 hath1 like every other miner1 ye least breathing time1 and must sometimes at least come to terr4 alt4 for air4 ,in one of these respiratory intervals ,i now sit down to write to you1 my friend4 ,you ask me how1 with so much study1 ,i manage to retene my health4 ,ah1 my dear doctor1 you have a better opinion of your lazy friend than he hath of himself4 ,morpheous is my last companion2 without #h or #i hours of him yr correspondent is not worth one scavenger's peruke4 ,my practices did at ye first hurt my stomach1 but now ,i eat heartily enou' as y' will see when ,i come down beside you4 ,i have been much amused at ye singular ,greek3 phenomena resulting from bringing of a needle into contact with a piece of amber or resin fricated on silke clothe4 ,ye flame putteth me in mind of sheet lightning on a small--how very small--scale4 ,but ,i shall in my epistles abjure ,philosophy whereof when ,i come down to ,sakly ,i'll give you enou'4 ,i began to scrawl at #e mins4 from #i of ye clk4 and have in writing consmd4 #aj mins4 ,my ,ld4 ,somerset is announced4 ,farewell1 ,gd4 bless you and help yr sincere friend4 ,,isaac ,,newton4 ,to ,,dr4 ,,law1 ,suffolk4 #ai ,kepler's laws may be called respectively1 the law of path1 the law of speed1 and the relationship law4 ,by the mass of a body is meant the number of pounds or tons in it3 the amount of matter it contains4 ,the idea is involved in the popular word massive4 #bj ,the equation we have to verify is #dpi#br#c g,r#b -----------1 ,t#b with the data that r1 the moon's distance1 is #fj times ,r1 the earth's radius1 which is #c1ifc miles2 while ,t1 the time taken to complete the moon's orbit1 is #bg days1 #ac hours1 #ah minutes1 #cg seconds4 ,hence1 suppose we calculate out g1 the intensity of terrestrial gravity1 from the above equation1 we get #dpi#b #ciib #bafjjj #cifc miles g ---------- 7#fj7c,r ----------------------------- ,t 7#bg days1 #ac hours1 c47#b #cbeg feet-per-second per second1 which is not far wrong4 #ba ,the two motions may be roughly compounded into a single motion1 which for a few centuries may without much error be regarded as a conical revolution about a different axis with a different period2 and ,lieutenant-,colonel ,drayson writes books emphasizing this simple fact1 under the impression that it is a discovery4 #bb ,members of the ,accademia dei ,lyncei1 the famous old scientific ,society established in the time of ,cosmo de ,medici--older than our own ,royal ,society4 #bc ,newton suspected that the moon really did so oscillate1 and so it may have done once2 but any real or physical libration1 if existing at all1 is now extremely minute4 #bd ,an interesting picture in the ,new ,gallery this year 7#ahia71 attempting to depict ,earth-rise in ,moon-land1 unfortunately errs in several particulars4 ,first of all1 the earth does not rise1 but is fixed relatively to each place on the moon2 and two-fifths of the moon never sees it4 ,next1 the earth would not look like a map of the world with a haze on its edge4 ,lastly1 whatever animal remains the moon may contain would probably be rather in the form of fossils than of skeletons4 ,the skeleton is of course intended as an image of death and desolation4 ,it is a matter of taste3 but a skeleton1 it seems to me1 speaks too recently of life to be as appallingly weird and desolate as a blank stone or ice landscape1 unshaded by atmosphere or by any trace of animal or plant life1 could be made4 #be ,five of ,jupiter's revolutions occupy #ba1ffc days2 two of ,saturn's revolutions occupy #ba1ebf days4 #bf ,excircularity is what is meant by this term4 ,it is called excentricity because the foci 7not the centre7 of an ellipse are regarded as the representatives of the centre of a circle4 ,their distance from the centre1 compared with the radius of the unflattened circle1 is called the excentricity4 #bg ,a curve of the nth degree has #a_/bn7n#c7 arbitrary constants in its equation1 hence this number of points specifically determine it4 ,but special points1 like focus or vertex1 count as two ordinary ones4 ,hence three points plus the focus act as five points1 and determine a conic or curve of the second degree4 ,three observations therefore fix an orbit round the sun4 #bh ,its name suggests a measure of the diameter of the sun's disk1 and this is one of its functions2 but it can likewise measure planetary and other disks2 and in general behaves as the most elaborate and expensive form of micrometer4 ,the ,knigsberg instrument is shewn in fig4 #ib4 #bi ,it may be supposed that the terms minute and second have some necessary connection with time1 but they are mere abbreviations for partes minut and partes minut secund1 and consequently may be applied to the subdivision of degrees just as properly as to the subdivision of hours4 ,a second of arc means the #cfjjth part of a degree1 just as a second of time means the #cfjjth part of an hour4 #cj ,a group of flying particles1 each one invisible1 obstructs light singularly little1 even when they are close together1 as one can tell by the transparency of showers and snowstorms4 ,the opacity of haze may be due not merely to dust particles1 but to little eddies set up by radiation above each particle1 so that the air becomes turbulent and of varying density4 7,see a similar suggestion by ,mr4 ,poynting in ,nature1 vol4 #ci1 p4 #cbc47 #ca ,the moon ought to be watched during the next great shower1 if the line of fire happens to take effect on a visible part of the dark portion4 #cb ,address to ,birmingham ,midland ,institute1 ,a ,glimpse through the ,corridors of ,time4 ,,index ,,index ,a ,abbott1 ,t4,k41 on tides1 #cfi ,adams1 ,john ,couch1 #aic1 #bag1 #cjb1 #cbc1 #cbd1 #cbe1 #cbg1 #cbi1 #ccj1 #ceb1 #che ,airy1 ,sir ,george1 #aic1 #bdd1 #cjb1 #cbc1 #cbd1 #cbg1 #cfg ,anaxagoras1 #ae ,appian1 #bah ,arabs1 the1 form a link between the old and new science1 #i ,archimedes1 #g1 #h1 #hd1 #hg1 #add1 #agg ,aristarchus1 #cd ,aristotle1 #ff1 #fi1 #hh1 #id1 #ii1 #afg4 ,he taught that the earth was a sphere1 #af2 his theories did not allow of the earth's motion1 #cd2 he was regarded as inspired1 #hi ,b ,bacon1 ,francis1 #adb1 #adc1 #add1 #ade4 ,his ,novum ,organum1 #ada ,bacon1 ,roger1 #if1 #aci1 #adj4 ,the herald of the dawn of science1 #i ,brah1 ,george1 uncle of ,tycho ,brah1 #ci ,brah1 ,steno1 brother of ,tycho ,brah1 #ci ,brah1 ,tycho1 #cg1 #ci1 #dj1 #dd1 #de1 #di1 #ea1 #ec1 #ed1 #ee1 #eh1 #fc1 #fd1 #fe1 #ff1 #fh1 #ga1 #gb1 #gd1 #ge1 #gg1 #gh1 #hf1 #id1 #aag1 #acg1 #aee1 #afe1 #aff1 #bjj1 #bdd1 #bha1 #bhh4 ,he tried to adopt the main features of the ,copernican theory without admitting the motion of the earth1 #cg2 he was a poor theorist but a great observer1 #ch2 his medicine1 #dd2 his personal history1 #ci1 seq42 his observatory1 ,uraniburg1 #dg2 his greatest invention1 #ej1 note2 his maniac ,lep1 #eb2 his kindness to ,kepler1 #fc ,ball1 ,sir ,r41 #cia1 #cid2 his ,story of the ,heavens1 #cgg ,barrow1 ,dr41 #afe1 #ahg ,bessel1 #bhh1 #caj1 #caa1 #cac1 #cae1 #caf1 #cah1 #cbc ,biela1 #cde1 #cdf1 #cdg ,bode's ,law1 #fj1 #bif1 #bih1 #bii1 #cbf ,boyle1 #aci1 #ahh ,bradley1 ,prof4 ,james1 #bcc1 #bdf1 #bdg1 #bdi1 #beb1 #bec1 #cjh1 #cai ,bremiker1 #cbh1 #cbi ,brewster1 on ,kepler1 #gh ,brinkley1 #cjh ,bruno1 ,giordano1 #ajh1 #abg ,c ,castelli1 #aab1 #acc ,cayley1 ,prof41 #che ,challis1 ,prof41 #cbh1 #cbi ,clairut1 #aic1 #baf1 #bag1 #bai1 #bcd1 #cda ,clark1 ,alvan and ,sons1 #caf ,columbus1 #i1 #add ,copernicus1 #g1 #aj1 seq41 #ad1 #bf1 #bg1 #bi1 #cj1 #ca1 #cc1 #cd1 #ce1 #cg1 #ch1 #fb1 #ff1 #fh1 #gj1 #gh1 #ic1 #ie1 #ajj1 #ajh1 #aaa1 #aba1 #abb1 #acg1 #aee1 #aff1 #bbc1 #bcd1 #bdg1 #cjg2 his ,de ,revolutionibus ,orbium ,coelestium1 #aa1 #ge1 #ach2 he proved that the earth went round the sun1 #ac2 the influence of his theory on the ,church1 #ac1 seq42 his life-work summarised1 #cj2 his ,life by ,mr4 ,e4,j4,c4 ,morton1 #ca ,copernican tables1 #dj2 ,copernican theory1 #ei1 #fj1 #abe1 #add1 #afg ,copernik1 ,nicolas2 see ,copernicus ,cornu1 #bch ,croll1 ,dr41 his ,climate and ,time1 #bfd ,d ,d',alembert1 #aic1 #bcd ,darwin1 ,charles1 #acd1 #ach1 #cig ,darwin1 ,prof4 ,george1 #cfg1 #cid ,delambre1 #bec ,descartes1 #ade1 #adf1 #adh1 #aea1 #aec1 #aef1 #aeh1 #afd1 #afe1 #afg1 #agh1 #aha1 #bbd1 #bbg2 his ,discourse on ,method1 #adb2 his dream1 #adg2 his system of algebraic geometry1 #adi1 seq42 his doctrine of vortices1 #aea1 seq42 his ,principia ,mathematica1 #aed2 his ,life by ,mr4 ,mahaffy1 #aed ,e ,earth1 the difficulties in the way of believing that it moved1 #cd1 seq4 ,earth-rise in ,moon-land1 #beh1 note ,encke1 #cde1 #cdf ,epicyclic orbits explained1 #bc1 seq4 ,equinoxes1 their precession discovered by ,hipparchus1 #bg ,eudoxus1 #ai ,euler1 #aic1 #bcd ,f ,faraday1 #hd ,fizeau1 #bch1 #bci ,flamsteed1 #bae1 #bdf1 #bhd1 #cjh1 #cai ,fraunhofer1 #caa ,froude1 ,prof42 his ,oceania1 #chg ,g ,galen1 #hg ,galileo1 ,galilei1 #fc1 #ge1 #hd1 #hh1 #ij1 #ib1 #ic1 #ig1 #ih1 #aja1 #ajd1 #ajf1 #ajg1 #ajh1 #aji1 #aaj1 #aab1 #aad1 #aaf1 #aag1 #aah1 #abj1 #aba1 #abb1 #abc1 #abe1 #abg1 #acc1 #acd1 #acg1 #add1 #ade1 #aec1 #aed1 #aeg1 #afe1 #aff1 #afg1 #afh1 #agg1 #ahh1 #bjj1 #bbd1 #bbg1 #bef1 #bha1 #bhh1 #cji1 #cfa2 his youth1 #he2 his discovery of the pendulum1 #hf2 his first observations about falling bodies1 #hh1 seq42 he invents a telescope1 #ie2 he adopts the ,copernican theory1 #id2 he conceives earth-shine1 #ajj2 he discovers ,jupiter's moons1 #ajc2 he studies ,saturn1 #aad1 seq42 his ,dialogues on the ,ptolemaic and ,copernican ,systems1 #abd2 his abjuration1 #acj2 he becomes blind1 #acb2 he discovered the ,laws of ,motion1 #afg1 seq42 he guessed that sight was not instantaneous1 #bcf1 #bcg ,galle1 ,dr41 #bde1 #cbi ,gauss1 #bii1 #cjj ,gilbert1 ,dr41 #aci1 #adj1 #aeg1 #ahh2 his ,de ,magnete1 #adj1 #add ,greeks1 their scientific methods1 #g ,groombridge's ,catalogue1 #cae ,h ,hadley1 #ahe ,halley1 #aib1 #aic1 #aid1 #aie1 #aig1 #bae1 #bah1 #bai1 #bdf1 #beh1 #bfj1 #bfa1 #cdj1 #cda2 he discovered the ,principia1 #aid ,harvey1 #add1 #adi ,haughton1 ,dr41 #cba2 his manual on ,astronomy1 #ba1 note ,heliometer1 described1 #caa ,helmholtz1 #cgh ,helmont1 ,van1 invented the word gas1 #ada ,henderson1 #caj1 #cad ,herschel1 ,alexander1 #bge1 #bgg1 #bgh1 #bgi ,herschel1 ,caroline1 #bge1 #bgf1 #bgi1 #bhf1 #cde2 her journal quoted1 #bgg1 seq42 her work with ,william ,h4 described1 #bhd ,herschel1 ,sir ,john1 #bhc1 #bhe1 #cbg1 #cbi ,herschel1 ,william1 #ahe1 #bcd1 #bce1 #bdd1 #bdi1 #bgd1 #bge1 #bhj1 #bha1 #bhb1 #bhd1 #bhh1 #bhi1 #bij1 #bic1 #bie1 #cje1 #cji1 #caj1 #cah1 #cai1 #cbg2 he sweeps the heavens1 #bhj2 his discovery of ,uranus1 #bha1 #bhg2 his artificial ,saturn1 #bha1 #bhb2 his methods of work with his sister1 described1 #bhd2 he founded the science of ,astronomy1 #bhg ,hind1 #cjj ,hipparchus1 #g1 #ah1 #bj1 #bg1 #bh1 and note1 #cj1 #dj1 #ff1 #bbc1 #bec2 an explanation of his discovery of the precession of the equinoxes1 #bg1 seq4 ,hippocrates1 #hg ,homeric ,cosmogony1 #ae1 seq4 ,hooke1 #aci1 #ahh1 #aib1 #aic1 #aif1 #aig1 #cjh ,hpital1 ,marquis de l'1 #bbh ,horkey1 ,martin1 #ajf ,horrebow1 #bdd ,huxley1 ,prof41 #adi ,huyghens1 #hf1 #aff1 #ahe ,k ,kant1 #bfg1 #bgj ,kelvin1 ,lord1 see ,thomson1 ,sir ,w4 ,kepler1 ,john1 #ei1 #fj1 #fc1 #fd1 #fe1 #ff1 #gj1 #gb1 #gc1 #ge1 #gg1 #gi1 #hd1 #ic1 #id1 #ie1 #ajd1 #ajf1 #ajg1 #aaj1 #abb1 #acg1 #ade1 #aec1 #aeh1 #afd1 #afe1 #aff1 #afg1 #aib1 #bjj1 #bjh1 #bji1 #baj1 #baa1 #bab1 #bad1 #bah1 #bbd1 #bbg1 #bec1 #bef1 #bei1 #bfj1 #bfb1 #bhh1 #bie1 #bif1 #ccb1 #cch1 #cfa1 #chi2 he replaced epicycles by an ellipse1 #bg2 he was a pupil of ,tycho ,brah1 #ed2 he was a speculator more than an observer1 #eh2 his personal life1 #eh1 seq42 his theories about the numbers and distances of the planets1 #fj1 #fb2 he was helped by ,tycho1 #fc2 his main work1 #fe1 seq42 he gave up circular motion1 #fi2 his ,mysterium ,cosmographicon1 #aje2 his ,laws1 #ga1 #gd1 #agc1 #agd1 #agf1 #agi1 #ahj1 #bjf1 seq4 ,l ,lagrange1 #aic1 #bcd1 #bee1 #bef1 #beg1 #beh1 #bfc ,lagrange and ,laplace1 #beh1 #bff1 #cie2 they laid the foundations of the planetary theory1 #bei ,laplace1 #fh1 #aic1 #bah1 #bcd1 #bee1 #bfa1 #bfb1 #bfg1 #bfh1 #bfi1 #bgj1 #bgb1 #bhh1 #cja1 #cag1 #chd1 #che1 #cij2 his nebular hypothesis1 #bfg1 #bib2 his ,mcanique ,cleste1 #cbc ,lassell1 ,mr41 #bhc1 #bhd ,leibnitz1 #aib1 #aig1 #bcc ,le ,monnier1 #cai ,leonardo1 see ,vinci1 ,leonardo da ,leverrier1 #aic1 #cbg1 #cbh1 #cbi1 #ccj1 #ceb ,lippershey1 ,hans1 #ie ,m ,maskelyne1 #bha ,maxwell1 ,clerk1 #cjb1 #cjc ,molyneux1 #bdh1 #bdi ,morton1 ,mr4 ,e4,j4 ,c1 his ,life of ,copernicus1 #ca ,n ,newton1 ,prof4 ,h4,a41 #cdg ,newton1 ,sir ,isaac1 #g1 #cj1 #gi1 #ach1 #aci1 #add1 #ade1 #adi1 #aec1 #aeg1 #aeh1 #afe1 #aff1 #afg1 #agd1 #agf1 #ahd1 #ahg1 #ahh1 #ahi1 #aia1 #aib1 #aid1 #aif1 #aih1 #aii1 #bja1 #bac1 #baf1 #bai1 #bbj1 #bba1 #bbd1 #bbf1 #bbg1 #bbh1 #bcc1 #bdb1 #bec1 #bee1 #bef1 #bgd1 #bhh1 #cag1 #cdj1 #cgh2 his ,principia1 #aia1 #aib1 #aic1 #aid1 #aie1 #aif1 #aig1 #bjg1 #bad1 #baf1 #bah1 #bbh1 #bcc1 #bdb1 #bec2 his early life1 #afa1 seq42 his first experiments1 #afc2 his work at ,cambridge1 #afd2 his ,laws1 #afh2 his application of the ,laws of ,gravity to ,astronomy1 #agg1 #agh1 #agi1 #ahe1 #aij2 his reticence1 #agh2 his discoveries in ,optics1 #aha1 seq42 his work summarised1 #ahf2 his ,optics1 #ahi2 anecdotes of him1 #aia2 his appearance in a ,court of ,justice1 #aie2 some of his manuscripts very recently discovered1 #bag2 his theories of the ,equinoxes and tides1 #bbc1 seq41 #bbe1 #cfc1 seq4 ,o ,olbers1 #bii1 #cjj ,p ,peters1 ,prof41 #cjj1 #caf ,piazzi1 #bih1 #bii1 #cjh1 #cac ,picard1 #aij1 #bdb1 #bdd1 #bdg ,pioneers1 genuine1 #g ,planets and days of the week1 #ah ,poynting1 #ccb ,printing1 #i ,ptolemy1 #ah1 #bj1 #bg1 #ch1 #aec1 #aee1 #aff1 #bad2 his system of the ,heavens simplified by ,copernicus1 #aa1 #cj2 his system described1 #ai1 seq42 his system taught1 #cd2 his harmonies1 #gd ,pythagoras1 #ai1 #bj1 #cd ,q ,quadrant1 an early1 #db1 #dc ,r ,rheiter1 #ajg ,ricci1 ,ostillio1 #hf1 #hg ,roberts1 ,isaac1 #bfh ,roemer1 #bci1 #bdj1 #bdb1 #bdd1 #bdi1 #bea1 #cjh ,rosse1 ,lord1 his telescope1 #ahf1 #bfh ,rudolphine tables1 #fe ,s ,scheiner1 #ajg ,sizzi1 ,francesca1 an orthodox astronomer1 #ajf ,snell1 ,willebrod1 and the law of refraction1 #fe ,solar system1 its fate1 #bfe ,stars1 a list of1 #cjg ,struve1 #cjh1 #caj1 #caa1 #cac ,stuart1 ,prof41 quoted1 #eb ,t ,tatius1 #bif ,telescopes1 early1 #if ,thales1 #g1 #adj1 #cag ,thomson1 ,sir ,william1 #cfg1 #cgb1 #cgc1 #cgh1 #cid ,tide-gauge1 described1 #cgc1 seq4 ,tides1 #ced1 seq4 ,time1 is not exactly uniform1 #chd ,torricelli1 #acc1 #afh ,tycho1 see ,brah1 ,tycho ,v ,vinci1 ,leonardo da1 #i1 #ajj1 #add1 #ahd ,viviani1 #acc1 #afh ,voltaire1 #aha ,w ,watson1 ,prof41 #cjj ,whewell1 #bbg ,wren1 ,sir ,christopher1 #ahh1 #aib1 #aic1 #aig ,z ,zach1 ,von1 #bif1 #bii ,zone of ,asteroids1 #cjj1 seq4 ,,the ,,end4 ,,richard ,,clay ,,and ,,sons1 ,,limited1 ,,london ,,and ,,bungay4