,,astronomical ,,discovery ,illustration3 ,,astronomers ,,royal4 ,,astronomical ,,discovery ,,by ,,herbert ,,hall ,,turner1 ,d4,sc41 ,f4,r4,s4 ,,savilian ,,professor ,,of ,,astronomy ,,in ,,the ,,university ,,of ,,oxford ,,with ,,plates ,,london ,,edward ,,arnold #da #dc ,,maddox ,,street1 ,w4 #aijd 7,all rights reserved7 ,,to ,,edward ,,emerson ,,barnard ,,astronomical ,,discoverer ,,these ,,pages ,,are ,,inscribed ,,in ,,memory ,,of ,,never-,,to-,,be-,,forgotten ,,days ,,spent ,,with ,,him ,,at ,,the ,,yerkes ,,observatory ,,of ,,the ,,university ,,of ,,chicago ,,preface ,the aim of the following pages is to illustrate1 by the study of a few examples chosen almost at random1 the variety in character of astronomical discoveries4 ,an attempt has indeed been made to arrange the half-dozen examples1 once selected1 into a rough sequence according to the amount of chance associated with the discovery1 though from this point of view ,chapter ,,iv4 should come first2 but ,i do not lay much stress upon it4 ,there is undoubtedly an element of luck in most discoveries4 ,the biggest strokes are all luck1 writes a brother astronomer who had done me the honour to glance at a few pages1 but a man must not drop his catches4 ,have you ever read ,montaigne's essay ',of ,glory'8 ,it is worth reading4 ,change war and glory to discovery and it is exactly the same theme4 ,if you are looking for a motto you will find a score in it4 ,indeed even in cases such as those in ,chapters ,v4 and ,,vi41 where a discovery is made by turning over a heap of rubbish--declared such by experts and abandoned accordingly--we instinctively feel that the finding of something valuable was especially fortunate4 ,we should scarcely recommend such waste material as the best hunting ground for gems4 ,the chapters correspond approximately to a series of six lectures delivered at the ,university of ,chicago in ,august #aijd1 at the hospitable invitation of ,president ,harper4 ,they afforded me the opportunity of seeing something of this wonderful ,university1 only a dozen years old and yet so amazingly vigorous2 and especially of its observatory 7the ,yerkes observatory1 situated eighty miles away on ,lake ,geneva71 which is only eight years old and yet has taken its place in the foremost rank4 ,for these opportunities ,i venture here to put on record my grateful thanks4 ,in a portion of the first chapter it will be obvious that ,i am indebted to ,miss ,clerke's ,history of ,astronomy in the ,nineteenth ,century2 in the second to ,professor ,r4 ,a4 ,sampson's ,memoir on the ,adams ,,mss42 in the third to ,rigaud's ,life of ,bradley4 ,there are other debts which ,i hope are duly acknowledged in the text4 ,my grateful thanks are due to ,mr4 ,f4 ,a4 ,bellamy for the care with which he has read the proofs2 and ,i am indebted for permission to publish illustrations to the ,royal ,astronomical ,society1 the ,astronomer ,royal1 the editors of ,the ,observatory1 the ,cambridge ,university ,press1 the ,harvard ,college ,observatory1 the ,yerkes ,observatory1 and the living representatives of two portraits4 ,h4 ,h4 ,,turner4 ,,university ,,observatory1 ,,oxford1 ,november #i1 #aijd4 ,,contents ,,page ,,chapter ,i ,,uranus ,,and ,,eros #a ,,chapter ,,ii ,,the ,,discovery ,,of ,,neptune #ch ,,chapter ,,iii ,,bradley',s ,,discoveries ,,of ,,the ,,aberration ,,of ,,light ,,and ,,of ,,the ,,nutation ,,of ,,the ,,earth',s ,,axis #hf ,,chapter ,,iv ,,accidental ,,discoveries #aba ,,chapter ,v ,,schwabe ,,and ,,the ,,sun-,,spot ,,period #aee ,,chapter ,,vi ,,the ,,variation ,,of ,,latitude #agg ,,index #bba ,,list ,,of ,,plates ,,plate ,i4 ,,portrait ,,of ,j4 ,c4 ,,adams ,to face page #bb ,,ii4 ,,portrait ,,of ,a4 ,,graham #bb ,,iii4 ,,portrait ,,of ,u4 ,j4 ,,le ,,verrier #fj ,,iv4 ,,portrait ,,of ,j4 ,g4 ,,galle #fj ,v4 ,,corner ,,of ,,the ,,berlin ,,map ,,by ,,the ,,use ,,of ,,which ,,galle ,,found ,,neptune #hb ,,vi4 ,,astronomers ,,royal ,frontispiece ,,vii4 ,,great ,,comet ,,of ,,nov4 #g1 #ahhb ,to face page #abb ,,viii4 ,,the ,,oxford ,,new ,,star #adb ,,ix4 ,,nebulosity ,,round ,,nova ,,persei #adf ,x4 ,,sun-,,spots ,,at ,,greenwich1 ,,feb4 #ah ,,and #ai1 #ahid #aeh ,,xi4 ,,sun-,,spots ,,at ,,greenwich1 ,,feb4 #bj ,,and #ba1 #ahid #afb ,,xii4 ,,number ,,of ,,sun-,,spots ,,compared ,,with ,,daily ,,range ,,of ,,magnetic ,,declination ,,and ,,daily ,,range ,,of ,,magnetic ,,horizontal ,,force #afd ,,xiii4 ,,greenwich ,,magnetic ,,curves1 #ahei-fj #aff ,,xiv4 ,,greenwich ,,magnetic ,,curves1 #ahda-ahfj #aff ,,xv4 ,,sun-,,spots ,,and ,,turns ,,of ,,vane #agj ,,errata ,page #acc1 line #bg1 for #bjj stars read #bjj stars per hour4 #ade1 ,see note on page #bbj4 #adf1 bottom of page4 ,this nebulosity was first discovered by ,dr4 ,max ,wolf of ,heidelberg4 ,see ,astr4 ,nachr4 #cgcf4 #aha1 line #ag1 for observation read aberration4 ,,astronomical ,,discovery ,,chapter ,i ,,uranus ,,and ,,eros ,sidenote3 ,popular view of discovery4 ,discovery is expected from an astronomer4 ,the lay mind scarcely thinks of a naturalist nowadays discovering new animals1 or of a chemist as finding new elements save on rare occasions2 but it does think of the astronomer as making discoveries4 ,the popular imagination pictures him spending the whole night in watching the skies from a high tower through a long telescope1 occasionally rewarded by the finding of something new1 without much mental effort4 ,i propose to compare with this romantic picture some of the actual facts1 some of the ways in which discoveries are really made2 and if we find that the image and the reality differ1 ,i hope that the romance will nevertheless not be thereby destroyed1 but may adapt itself to conditions more closely resembling the facts4 ,sidenote3 ,keats' lines4 ,the popular conception finds expression in the lines of ,keats3-- ,then felt ,i like some watcher of the skies ,when a new planet swims into his ken4 ,keats was born in #agie1 published his first volume of poems in #ahag1 and died in #ahba4 ,at the time when he wrote the discovery of planets was comparatively novel in human experience4 ,uranus had been found by ,william ,herschel in #agha1 and in the years #ahjj to #ahjg followed the first four minor planets1 a number destined to remain without additions for nearly forty years4 ,it would be absurd to read any exact allusion into the words quoted1 when we remember the whole circumstances under which they were written2 but perhaps ,i may be forgiven if ,i compare them especially with the actual discovery of the planet ,uranus1 for the reason that this was by far the largest of the five--far larger than any other planet known except ,jupiter and ,saturn1 while the others were far smaller--and that ,keats is using throughout the poem metaphors drawn from the first glimpses of vast expanses of land or water4 ,perhaps ,i may reproduce the whole sonnet4 ,his friend ,c4 ,c4 ,clarke had put before him ,chapman's paraphrase of ,homer1 and they sat up till daylight to read it1 ,keats shouting with delight as some passage of especial energy struck his imagination4 ,at ten o'clock the next morning ,mr4 ,clarke found the sonnet on his breakfast-table4 ,,sonnet ,,xi ,on first looking into ,chapman's ,homer ,much have ,i travell'd in the realms of gold1 ,and many goodly states and kingdoms seen2 ,round many western islands have ,i been ,which bards in fealty to ,apollo hold4 ,oft of one wide expanse had ,i been told ,that deep-brow'd ,homer ruled as his demesne2 ,yet did ,i never breathe its pure serene ,till ,i heard ,chapman speak out loud and bold3 ,then felt ,i like some watcher of the skies ,when a new planet swims into his ken2 ,or like stout ,cortez when with eagle eyes ,he star'd at the ,pacific--and all his men ,look'd at each other with a wild surmise-- ,silent1 upon a peak in ,darien4 ,sidenote3 ,comparison with discovery of ,uranus4 ,let us then1 as our first example of the way in which astronomical discoveries are made1 turn to the discovery of the planet ,uranus1 and see how it corresponds with the popular conception as voiced by ,keats4 ,in one respect his words are true to the life or the letter4 ,if ever there was a watcher of the skies1 ,william ,herschel was entitled to the name4 ,it was his custom to watch them the whole night through1 from the earliest possible moment to daybreak2 and the fruits of his labours were many and various almost beyond belief4 ,but did the planet swim into his ken8 ,let us turn to the original announcement of his discovery as given in the ,philosophical ,transactions for #agha4 ,,philosophical ,,transactions1 #agha ,,xxxii4--,,account ,,of ,a ,,comet ,,by ,,mr4 ,,herschel1 ,f4,r4,s4 7,communicated by ,dr4 ,watson1 jun41 of ,bath1 ,f4,r4,s47 ,read ,april #bf1 #agha ,sidenote3 ,original announcement4 ,on ,tuesday the #acth of ,march1 between ten and eleven in the evening1 while ,i was examining the small stars in the neighbourhood of ,h ,geminorum1 ,i perceived one that appeared visibly larger than the rest2 being struck with its uncommon magnitude1 ,i compared it to ,h ,geminorum and the small star in the quartile between ,auriga and ,gemini1 and finding it to be so much larger than either of them1 suspected it to be a comet4 ,i was then engaged in a series of observations on the parallax of the fixed stars1 which ,i hope soon to have the honour of laying before the ,royal ,society2 and those observations requiring very high powers1 ,i had ready at hand the several magnifiers of #bbg1 #dfj1 #icb1 #aecf1 #bjaj1 c41 all which ,i have successfully used upon that occasion4 ,the power ,i had on when ,i first saw the comet was #bbg4 ,from experience ,i knew that the diameters of the fixed stars are not proportionally magnified with higher powers as the planets are2 therefore ,i now put on the powers of #dfj and #icb1 and found the diameter of the comet increased in proportion to the power1 as it ought to be1 on a supposition of its not being a fixed star1 while the diameters of the stars to which ,i compared it were not increased in the same ratio4 ,moreover1 the comet being magnified much beyond what its light would admit of1 appeared hazy and ill-defined with these great powers1 while the stars preserved that lustre and distinctness which from many thousand observations ,i knew they would retain4 ,the sequel has shown that my surmises were well founded1 this proving to be the ,comet we have lately observed4 ,i have reduced all my observations upon this comet to the following tables4 ,the first contains the measures of the gradual increase of the comet's diameter4 ,the micrometers ,i used1 when every circumstance is favourable1 will measure extremely small angles1 such as do not exceed a few seconds1 true to #f1 #h1 or #aj thirds at most2 and in the worst situations true to #bj or #cj thirds2 ,i have therefore given the measures of the comet's diameter in seconds and thirds4 ,and the parts of my micrometer being thus reduced1 ,i have also given all the rest of the measures in the same manner2 though in large distances1 such as one1 two1 or three minutes1 so great an exactness1 for several reasons1 is not pretended to4 ,sidenote3 ,called first a comet4 ,sidenote3 ,other observers would not have found it at all4 ,at first sight this seems to be the wrong reference1 for it speaks of a new comet1 not a new planet4 ,but it is indeed of ,uranus that ,herschel is speaking2 and so little did he realise the full magnitude of his discovery at once1 that he announced it as that of a comet2 and a comet the object was called for some months4 ,attempts were made to calculate its orbit as a comet1 and broke down2 and it was only after much work of this kind had been done that the real nature of the object began to be suspected4 ,but far more striking than this misconception is the display of skill necessary to detect any peculiarity in the object at all4 ,among a number of stars one seemed somewhat exceptional in size1 but the difference was only just sufficient to awaken suspicion in a keen-eyed ,herschel4 ,would any other observer have noticed the difference at all8 ,certainly several good observers had looked at the object before1 and looked at it with the care necessary to record its position1 without noting any peculiarity4 ,their observations were recovered subsequently and used to fix the orbit of the new planet more accurately4 ,i shall remind you in the next chapter that ,uranus had been observed in this way no less than seventeen times by first-rate observers without exciting their attention to anything remarkable4 ,the first occasion was in #afij1 nearly a century before ,herschel's grand discovery1 and these chance observations1 which lay so long unnoticed as in some way erroneous1 subsequently proved to be of the utmost value in fixing the orbit of the new planet4 ,but there is even more striking testimony than this to the exceptional nature of ,herschel's achievement4 ,it is a common experience in astronomy that an observer may fail to notice in a general scrutiny some phenomenon which he can see perfectly well when his attention is directed to it3 when a man has made a discovery and others are told what to look for1 they often see it so easily that they are filled with amazement and chagrin that they never saw it before4 ,not so in the case of ,uranus4 ,at least two great astronomers1 ,lalande and ,messier1 have left on record their astonishment that ,herschel could differentiate it from an ordinary star at all2 for even when instructed where to look and what to look for1 they had the greatest difficulty in finding it4 ,i give a translation of ,messier's words1 which ,herschel records in the paper already quoted announcing the discovery3-- ,nothing was more difficult than to recognise it2 and ,i cannot conceive how you have been able to return several times to this star or comet2 for absolutely it has been necessary to observe it for several consecutive days to perceive that it was in motion4 ,sidenote3 ,no swimming into ken4 ,we cannot1 therefore1 fit the facts to ,keats' version of them4 ,the planet did not majestically reveal itself to a merely passive observer3 rather did it1 assuming the disguise of an ordinary star1 evade detection to the utmost of its power2 so that the keenest eye1 the most alert attention1 the most determined following up of a mere hint1 were all needed to unmask it4 ,but is the romance necessarily gone8 ,if another ,keats could arise and know the facts1 could he not coin a newer and a truer phrase for us which would still sound as sweetly in our ears8 ,sidenote3 ,though this may happen at times4 ,sidenote3 ,name of new planet4 ,i must guard against a possible misconception4 ,i do not mean to convey that astronomical discoveries are not occasionally made somewhat in the manner so beautifully pictured by ,keats4 ,three years ago a persistent watcher of the skies1 ,dr4 ,anderson of ,edinburgh1 suddenly caught sight of a brilliant new star in ,perseus2 though here flashed into his ken would perhaps be a more suitable phrase than swam4 ,and comets have been detected by a mere glance at the heavens without sensible effort or care on the part of the discoverer4 ,but these may be fairly called exceptions2 in the vast majority of cases hard work and a keen eye are necessary to make the discovery4 ,the relative importance of these two factors of course varies in different cases2 for the detection of ,uranus perhaps the keen eye may be put in the first place1 though we must not forget the diligent watching which gave it opportunity4 ,other cases of planetary discovery may be attributed more completely to diligence alone1 as we shall presently see4 ,but before leaving ,uranus for them ,i should like to recall the circumstances attending the naming of the planet4 ,herschel proposed to call it ,georgium ,sidus in honour of his patron1 ,king ,george ,,iii41 and as the best way of making his wishes known1 wrote the following letter to the ,president of the ,royal ,society1 which is printed at the beginning of the ,philosophical ,transactions for #aghc4 ,a ,letter from ,,william ,,herschel1 ,esq41 ,f4,r4,s41 to ,sir ,,joseph ,,banks1 ,bart41 ,p4,r4,s4 ,sir1--,by the observations of the most eminent astronomers in ,europe it appears that the new star1 which ,i had the honour of pointing out to them in ,march #agha1 is a ,primary ,planet of our ,solar ,system4 ,a body so nearly related to us by its similar condition and situation in the unbounded expanse of the starry heavens1 must often be the subject of conversation1 not only of astronomers1 but of every lover of science in general4 ,this consideration then makes it necessary to give it a name whereby it may be distinguished from the rest of the planets and fixed stars4 ,sidenote3 ,georgium ,sidus4 ,in the fabulous ages of ancient times1 the appellations of ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn were given to the planets as being the names of their principal heroes and divinities4 ,in the present more philosophical era1 it would hardly be allowable to have recourse to the same method1 and call on ,juno1 ,pallas1 ,apollo1 or ,minerva for a name to our new heavenly body4 ,the first consideration in any particular event1 or remarkable incident1 seems to be its chronology3 if in any future age it should be asked1 when this last found planet was discovered8 ,it would be a very satisfactory answer to say1 ',in the reign of ,king ,george the ,third4' ,as a philosopher then1 the name ,,georgium ,,sidus presents itself to me1 as an appellation which will conveniently convey the information of the time and country where and when it was brought to view4 ,but as a subject of the best of kings1 who is the liberal protector of every art and science2 as a native of the country from whence this illustrious family was called to the ,british throne2 as a member of that ,society which flourishes by the distinguished liberality of its royal patron2 and1 last of all1 as a person now more immediately under the protection of this excellent monarch1 and owing everything to his unlimited bounty2--,i cannot but wish to take this opportunity of expressing my sense of gratitude by giving the name ,georgium ,sidus1 ,georgium ,sidus ----jam nunc assuesce vocari1 ,virg4 ,georg4 to a star which 7with respect to us7 first began to shine under his auspicious reign4 ,by addressing this letter to you1 ,sir1 as ,president of the ,royal ,society1 ,i take the most effectual method of communicating that name to the literati of ,europe1 which ,i hope they will receive with pleasure4--,i have the honour to be1 with the greatest respect1 ,sir1 your most humble and most obedient servant1 ,w4 ,,herschel4 ,sidenote3 ,herschel4 ,this letter reminds us how long it was since a new name had been required for a new planet1--to find a similar occasion ,herschel had to go to the almost prehistoric past1 when the names of heroes and divinities were given to the planets4 ,it is1 perhaps1 not unnatural that he should have considered an entirely new departure appropriate for a discovery separated by so great a length of time from the others2 but his views were not generally accepted1 especially on the ,continent4 ,lalande courteously proposed the name of ,herschel for the new planet1 in honour of the discoverer1 and this name was used in ,france2 but ,bode1 on the other hand1 was in favour of retaining the old practice simply1 and calling the new planet ,uranus4 ,all three names seem to have been used for many years4 ,only the other day ,i was interested to see an old pack of cards1 used for playing a parlour game of ,astronomy1 in which the name ,herschel is used4 ,the owner told me that they had belonged to his grandfather2 and the date of publication was #ahbi1 and the place ,london1 so that this name was in common use in ,england nearly half a century after the actual discovery2 though in the ,english ,nautical ,almanac the name the ,georgian 7apparently preferred to ,herschel's ,georgium ,sidus7 was being used officially after #agia1 and did not disappear from that work until #ahea 7published in #ahdg47 ,sidenote3 ,uranus finally adopted4 ,it would appear to have been the discovery of ,neptune1 with which we shall deal in the next chapter1 which led to this official change2 for in the volume for #ahea is included ,adams' account of his discovery with the title-- ,,on ,,the ,,perturbations ,,of ,,uranus1 and there was thus a definite reason for avoiding two names for the same planet in the same work4 ,but ,le ,verrier's paper on the same topic at the same date still uses the name ,herschel for the planet4 ,sidenote3 ,bode's law4 ,the discovery of ,neptune1 as we shall see1 was totally different in character from that of ,uranus4 ,the latter may be described as the finding of something by an observer who was looking for anything2 ,neptune was the finding of something definitely sought for1 and definitely pointed out by a most successful and brilliant piece of methodical work4 ,but before that time several planets had been found1 as the practical result of a definite search1 although the guiding principle was such as cannot command our admiration to quite the same extent as in the case of ,neptune4 ,to explain it ,i must say something of the relative sizes of the orbits in which planets move round the sun4 ,these orbits are1 as we know1 ellipses2 but they are very nearly circles1 and1 excluding refinements1 we may consider them as circles1 with the sun at the centre of each1 so that we may talk of the distance of any planet from the sun as a constant quantity without serious error4 ,now if we arrange the planetary distances in order1 we shall notice a remarkable connection between the terms of the series4 ,here is a table showing this connection4 ,,table ,,of ,,the ,,distances ,,of ,,the ,,planets ,,from ,,the ,,sun1 ,,showing ,,bode',s ,,law4 ---------------------------------------- ------------ ,name of ,distance from ,bode's ,law ,planet4 ,sun1 taking 7originally formulated that of ,earth by ,titius1 but brought as #aj4 into notice by ,bode74 ---------------------------------------- ------------ ,mercury #d #d #j #d ,venus #g #d #c #g ,the ,earth #aj #d #f #aj ,mars #ae #d #ab #af 7 7 7 7 #d #bd #bh ,jupiter #eb #d #dh #eb ,saturn #ie #d #if #ajj ,uranus #aib #d #aib #aif ---------------------------------------- ------------ ,sidenote3 ,gap in the series suggesting unknown planet4 ,sidenote3 ,search for it4 ,sidenote3 ,accidental discovery4 ,if we write down a series of #d's1 and then add the numbers #c1 #f1 #ab1 and so on1 each formed by doubling the last1 we get numbers representing very nearly the planetary distances1 which are shown approximately in the second column4 ,but three points call for notice4 ,firstly1 the number before #c should be #a-a_/b1 and not zero1 to agree with the rest4 ,secondly1 there is a gap1 or rather was a gap1 after the discovery of ,uranus1 between ,mars and ,jupiter2 and thirdly1 we see that when ,uranus was discovered1 and its distance from the sun determined1 this distance was found to fall in satisfactorily with this law1 which was first stated by ,titius of ,wittenberg4 ,this third fact naturally attracted attention4 ,no explanation of the so-called law was known at the time2 nor is any known even yet1 though we may be said to have some glimmerings of a possible cause2 and in the absence of such explanation it must be regarded as merely a curious coincidence4 ,but the chances that we are in the presence of a mere coincidence diminish very quickly with each new term added to the series1 and when it was found that ,herschel's new planet fitted in so well at the end of the arrangement1 the question arose whether the gap above noticed was real1 or whether there was perhaps another planet which had hitherto escaped notice1 revolving in an orbit represented by this blank term4 ,this question had indeed been asked even before the discovery of ,uranus1 by ,bode1 a young astronomer of ,berlin2 and for fifteen years he kept steadily in view this idea of finding a planet to fill the vacant interval4 ,the search would be a very arduous one1 involving a careful scrutiny1 not perhaps of the whole heavens1 but of a considerable portion of it along the ,zodiac2 too great for one would-be discoverer single-handed2 but in ,september #ahjj ,bode succeeded in organising a band of six ,german astronomers 7including himself7 for the purpose of conducting this search4 ,they divided the ,zodiac into twenty-four zones1 and were assigning the zones to the different observers1 when they were startled by the news that the missing planet had been accidentally found by ,piazzi in the constellation ,taurus4 ,the discovery was made somewhat dramatically on the first evening of the nineteenth century 7,january #a1 #ahja74 ,piazzi was not looking for a planet at all1 but examining an error made by another astronomer2 and in the course of this work he recorded the position of a star of the eighth magnitude4 ,returning to it on the next night1 it seemed to him that it had slightly moved westwards1 and on the following night this suspicion was confirmed4 ,remark that in this case no peculiar appearance in the star suggested that it might be a comet or planet1 as in the case of the discovery of ,uranus4 ,we are not unfair in ascribing the discovery to pure accident1 although we must not forget that a careless observer might easily have missed it4 ,piazzi was anything but careless1 and watched the new object assiduously till ,february #aath1 when he became dangerously ill2 but he had written1 on ,january #bcrd1 to ,oriani of ,milan1 and to ,bode at ,berlin on the following day4 ,these letters1 however1 did not reach the recipients 7in those days of leisurely postal service7 until ,april #eth and ,march #bjth respectively2 and we can imagine the mixed feelings with which ,bode heard that the discovery which he had contemplated for fifteen years1 and for which he was just about to organise a diligent search1 was thus curiously snatched from him4 ,sidenote3 ,hegel's forecast4 ,more curious still must have seemed the intelligence to a young philosopher of ,jena named ,hegel1 who has since become famous1 but who had just imperilled his future reputation by publishing a dissertation proving conclusively that the number of the planets could not be greater than seven1 and pouring scorn on the projected search of the half-dozen enthusiasts who were proposing to find a new planet merely to fill up a gap in a numerical series4 ,sidenote3 ,the planet lost again4 ,the sensation caused by the news of the discovery was intensified by anxiety lest the new planet should already have been lost2 for it had meanwhile travelled too close to the sun for further observation1 and the only material available for calculating its orbit1 and so predicting its place in the heavens at future dates1 was afforded by the few observations made by ,piazzi4 ,was it possible to calculate the orbit from such slender material8 ,it would take too long to explain fully the enormous difficulty of this problem1 but some notion of it may be obtained1 by those unacquainted with mathematics1 from a rough analogy4 ,if we are given a portion of a circle1 we can1 with the help of a pair of compasses1 complete the circle3 we can find the centre from which the arc is struck1 either by geometrical methods1 or by a few experimental trials1 and then fill in the rest of the circumference4 ,if the arc given is large we can do this with certainty and accuracy2 but if the arc is small it is difficult to make quite sure of the centre1 and our drawing may not be quite accurate4 ,now the arc which had been described by the tiny planet during ,piazzi's observations was only three degrees2 and if any one will kindly take out his watch and look at the minute marks round the dial1 three degrees is just half a single minute space4 ,if the rest of the dial were obliterated1 and only this small arc left1 would he feel much confidence in restoring the obliterated portion8 ,this problem gives some idea of the difficulties to be encountered1 but only even then a very imperfect one4 ,sidenote3 ,gauss shows how to find it4 ,briefly1 the solution demanded a new mathematical method in astronomy4 ,but difficulties are sometimes the opportunities of great men1 and this particular difficulty attracted to astronomy the great mathematician ,gauss1 who set himself to make the best of the observation available1 and produced his classical work1 the ,theoria ,motus1 which is the standard work for such calculations to the present day4 ,may we look for a few moments at what he himself says in the preface to his great work8 ,i venture to reproduce the following rough translation 7the book being written in ,latin1 according to the scientific usage of the time73-- ,,extract ,,from ,,the ,,preface ,,to ,,the ,theoria ,motus4 ,sidenote3 ,the ,theoria ,motus4 ,some ideas had occurred to me on this subject in ,september #ahja1 at a time when ,i was occupied on something quite different2 ideas which seemed to contribute to the solution of the great problem of which ,i have spoken4 ,in such cases it often happens that1 lest we be too much ,distracted ,from the ,attractive ,investigation ,on ,which ,we ,are ,engaged1 ,we ,allow ,associations ,of ,ideas ,which1 ,if ,more ,closely ,examined1 ,might ,prove ,extraordinarily ,fruitful1 ,to ,perish ,from ,neglect4 ,perchance ,these ,same ,idea-lets of ,mine ,would ,have ,met ,with ,this ,fate1 ,if ,they ,had ,not ,most ,fortunately ,lighted ,upon a ,time ,than ,which ,none ,could ,have ,been ,chosen ,more ,favourable ,for ,their ,preservation and ,development4 ,for ,about ,the ,same ,time a ,rumour ,began ,to ,be ,spread ,abroad ,concerning a ,new ,planet ,which ,had ,been ,detected ,on ,january #ast of ,that ,year at the ,observatory ,of ,palermo2 and ,shortly ,afterwards the ,actual ,observations ,which ,had ,been ,made ,between ,january #ast ,and ,february #aath by the ,renowned ,philosopher ,piazzi ,were ,published4 ,nowhere in ,all ,the ,annals of ,astronomy ,do ,we ,find ,such an ,important ,occasion2 and ,scarcely ,is ,it ,possible ,to ,imagine a ,more ,important ,opportunity for ,pointing ,out1 ,as ,emphatically ,as ,possible1 the ,importance ,of ,that ,problem1 ,as at the ,moment ,when ,every ,hope of ,re-discovering1 ,among the ,innumerable ,little ,stars of ,heaven1 ,that ,mite of a ,planet ,which ,had ,been ,lost ,to ,sight for ,nearly a ,year1 ,depended ,entirely on an ,approximate ,knowledge ,of ,its ,orbit1 ,which ,must ,be ,deduced ,from ,those ,scanty ,observations4 ,could ,i ,ever ,have ,had ,a ,better ,opportunity for ,trying ,whether ,those ,idea-lets ,of ,mine ,were of ,any ,practical ,value ,than ,if ,i ,then ,were ,to ,use ,them for the ,determination ,of ,the ,orbit of ,ceres1 a ,planet ,which1 in the ,course of those forty-one days1 had described around the earth an arc of no more than three degrees8 and1 after a year had passed1 required to be tracked out in a region of the sky far removed from its original position8 ,the first application of this method was made in the month of ,october #ahja1 and the first clear night1 when the planet was looked for by the help of the ephemeris ,i had made1 revealed the truant to the observer4 ,three new planets found since then have supplied fresh opportunities for examining and proving the efficacy and universality of this method4 ,now a good many astronomers1 immediately after the rediscovery of ,ceres1 desired me to publish the methods which had been used in my calculations4 ,there were1 however1 not a few objections which prevented me from gratifying at that moment these friendly solicitations1 viz4 other business1 the desire of treating the matter more fully1 and more especially the expectation that1 by continuing to devote myself to this research1 ,i should bring the different portions of the solution of the problem to a more perfect pitch of universality1 simplicity1 and elegance4 ,as my hopes have been justified1 ,i do not think there is any reason for repenting of my delay4 ,for the methods which ,i had repeatedly applied from the beginning admitted of so many and such important variations1 that scarcely a vestige of resemblance remains between the method by which formerly ,i had arrived at the orbit of ,ceres and the practice which ,i deal with in this work4 ,although indeed it would be alien to my intention to write a complete history about all these researches which ,i have gradually brought to even greater perfection1 yet on many occasions1 especially whenever ,i was confronted by some particularly serious problem1 ,i thought that the first methods which ,i employed ought not to be entirely suppressed4 ,nay1 rather1 in addition to the solutions of the principal problems1 ,i have in this work followed out many questions which presented themselves to me1 in the course of a long study of the motions of the heavenly bodies in conic sections1 as being particularly worthy of attention1 whether on account of the neatness of the analysis1 or more especially by reason of their practical utility4 ,yet ,i have always given the greater care to subjects which ,i have made my own1 merely noticing by the way well-known facts where connection of thought seemed to demand it4 ,sidenote3 ,rediscovery of ,ceres4 ,sidenote3 ,another planet found4 ,these words do not explain in any way the methods introduced by ,gauss1 but they give us some notion of the flavour of the work4 ,aided by these brilliant researches1 the little planet was found on the last day of the year by ,von ,zach at ,gotha1 and on the next night1 independently1 by ,olbers at ,bremen4 ,but1 before this success1 there had been an arduous search1 which led to a curious consequence4 ,olbers had made himself so familiar with all the small stars along the track which was being searched for the missing body1 that he was at once struck by the appearance of a stranger near the spot where he had just identified ,ceres4 ,at first he thought this must be some star which had blazed up to brightness2 but he soon found that it also was moving1 and1 to the great bewilderment of the astronomical world1 it proved to be another planet revolving round the sun at a distance nearly the same as the former4 ,this was an extraordinary and totally unforeseen occurrence4 ,the world had been prepared for one planet2 but here were two6 ,sidenote3 ,hypothesis of many fragments4 ,the thought occurred to ,olbers that they were perhaps fragments of a single body which had been blown to pieces by some explosion1 and that there might be more of the pieces2 and he therefore suggested as a guide for finding others that1 since by the known laws of gravitation1 bodies which circle round the sun return periodically to their starting-point1 therefore all these fragments would in due course return to the point in the heavens where the original planet had exploded4 ,hence the search might be most profitably conducted in the neighbourhood of the spot where the two first fragments 7which had been named ,ceres and ,pallas7 had already been found4 ,we now have good reason to believe that this view is a mistaken one1 but nevertheless it was apparently confirmed by the discovery of two more bodies of the same kind1 which were called ,juno and ,vesta2 the second of these being found by ,olbers himself after three years' patient work in #ahjg4 ,hence1 although the idea of searching for a more or less definitely imagined planet was not new1 although ,bode had conceived it as early as #aghe1 and organised a search on this plan1 three planets were actually found before the first success attending a definite search4 ,ceres1 as already remarked1 was found by a pure accident2 and the same may be said of ,pallas and ,juno1 though it may fairly be added that ,pallas was actually contrary to expectation4 ,,minor ,,planets1 #ahja ,,to #ahej4 --------------------------------------- ,number ,name4 ,discoverer4 ,date4 --------------------------------------- #a ,ceres ,piazzi #ahja #b ,pallas ,olbers #ahjb #c ,juno ,harding #ahjd #d ,vesta ,olbers #ahjg ------------------------------------ #e ,astraea ,hencke #ahde #f ,hebe ,hencke #ahdg #g ,iris ,hind #ahdg #h ,flora ,hind #ahdg #i ,metis ,graham #ahdh #aj ,hygeia ,de ,gasparis #ahdi #aa ,parthenope ,de ,gasparis #ahej #ab ,victoria ,hind #ahej #ac ,egeria ,de ,gasparis #ahej --------------------------------------- ,sidenote3 ,hencke's long search4 ,here now is a table showing how other bodies were gradually added to this first list of four1 but you will see that no addition was made for a long time4 ,not that the search was immediately abandoned2 but being rewarded by no success for some years1 it was gradually dropped1 and the belief gained ground that the number of the planets was at last complete4 ,the discoverers of ,uranus and of these first four minor planets all died before any further addition was made2 and it was not until the end of #ahde that ,astraea was found by an ex-postmaster of the ,prussian town of ,driessen1 by name ,hencke1 who1 in spite of the general disbelief in the existence of any more planets1 set himself diligently to search for them1 and toiled for fifteen long years before at length reaping his reward4 ,others then resumed the search2 ,hind1 the observer of an ,english amateur astronomer near ,london1 found ,iris a few weeks after ,hencke had been rewarded by a second discovery in #ahdg1 and in the following year ,mr4 ,graham at ,markree in ,ireland 7who is still living1 and has only just retired from active work at the ,cambridge ,observatory7 found ,metis2 and from that time new discoveries have been added year by year1 until the number of planets now known exceeds #ejj1 and is steadily increasing4 ,illustration3 ,by permission of ,messrs4 ,macmillan ,co4 ,i4--,j4 ,c4 ,,adams4 ,illustration3 ,,ii4--,a4 ,,graham4 ,,discoverer ,,of ,,the ,,ninth ,,minor ,,planet 7,,metis74 ,sidenote3 ,the photographic method4 ,you will see the great variety characterising these discoveries2 some of them are the result of deliberate search1 others have come accidentally1 and some even contrary to expectation4 ,of the great majority of the earlier ones it may be said that enormous diligence was required for each discovery2 to identify a planet it is necessary to have either a good map of the stars or to know them thoroughly1 so that the map practically exists in the brain4 ,we need only remember ,hencke's fifteen years of search before success to recognise what vast stores of patience and diligence were required in carrying out the search4 ,but of late years photography has effected a great revolution in this respect4 ,it is no longer necessary to do more than set what ,sir ,robert ,ball has called a star-trap1 or rather planet-trap4 ,if a photograph be taken of a region of the heavens1 by the methods familiar to astronomers1 so that each star makes a round dot on the photographic plate1 any sufficiently bright object moving relatively to the stars will make a small line or trail1 and thus betray its planetary character4 ,in this way most of the recent discoveries have been made1 and although diligence is still required in taking the photographs1 and again in identifying the objects thus found 7which are now very often the images of already known members of the system71 the tedious scrutiny with the eye has become a thing of the past4 ,,table ,,showing ,,the ,,number ,,of ,,minor ,,planets ,,discovered ,,in ,,each ,,decade ,,since #ahej4 #ahja to #ahej--;altogether #ac discoveries4 #ahea to #ahfj-- #di #ahfa to #ahgj-- #di #ahga to #ahhj-- #ajh #ahha to #ahij-- #hc #ahia to #aijj-- #ahj announcements ,in #aija #cf #aijb #ej #aijc #da --- ,total #fji ,n4,b4--,many of the more recent announcements turned out to refer to old discoveries4 ,sidenote3 ,scarcity of names4 ,the known number of these bodies has accordingly increased so rapidly as to become almost an embarrassment2 and in one respect the embarrassment is definite1 for it has become quite difficult to find names for the new discoveries4 ,we remember with amusement at the present time that for the early discoveries there was sometimes a controversy 7of the same kind as in the case of ,uranus7 about the exact name which a planet should have4 ,thus when it was proposed to call ,no4 #ab 7discovered in #ahej1 in ,london1 by ,mr4 ,hind7 ,victoria1 there was an outcry by foreign astronomers that by a subterfuge the name of a reigning monarch was again being proposed for a planet1 and considerable opposition was manifested1 especially in ,america4 ,but it became clear1 as other discoveries were added1 that the list of goddesses1 or even humbler mythological people1 would not be large enough to go round if we were so severely critical1 and must sooner or later be supplemented from sources hitherto considered unsuitable2 so1 ultimately1 the opposition to the name ,victoria was withdrawn4 ,later still the restriction to feminine names has been broken through2 one planet has been named ,endymion1 and another1 of which we shall presently speak more particularly1 has been called ,eros4 ,but before passing to him you may care to look at some of the names selected for others3-- ,no4 ,name4 #bdh ,lameia #bej ,bettina #bfa ,prymno #bfd ,libussa #bif ,phaetusa #cdj ,eduarda #cda ,california #cej ,ornamenta #ceg ,ninina #che ,ilmatar #chi ,industria #cia ,ingeborg #dcc ,eros #ddc ,photographica #deg ,alleghenia #dfb ,eriphyla #dge ,ocllo #dhd ,pittsburghia #ejc ,evelyn ,sidenote3 ,bettina4 ,sidenote3 ,the provisional letters4 ,in connection with ,no4 #bej there is an interesting little history4 ,in the ,observatory for #ahhe1 page #fc1 appeared the following advertisement3--,herr ,palisa being desirous to raise funds for his intended expedition to observe the ,total ,solar ,eclipse of ,august #ahhf1 will sell the right of naming the minor planet ,no4 #bdd for ,l#ej4 ,the bright idea seems to have struck ,herr ,palisa1 who had already discovered many planets and begun to find difficulties in assigning suitable names1 that he might turn his difficulty into a source of profit in a good cause4 ,the offer was not responded to immediately1 nor until ,herr ,palisa had discovered two more planets1 ,nos4 #bdh and #bej4 ,he found names for two1 leaving1 however1 the last discovered always open for a patron1 and on page #adb of the same magazine for #ahhf the following note informs us how his patience was ultimately rewarded3--,minor planet ,no4 #bej has been named ',bettina' by ,baron ,albert de ,rothschild4 ,i have not heard1 however1 that this precedent has been followed in other cases1 and the ingenuity of discoverers was so much overtaxed towards the end of last century that the naming of their planets fell into arrears4 ,recently a ,commission1 which has been established to look after these small bodies generally1 issued a notice that unless the naming was accomplished before a certain date it would be ruthlessly taken out of the hands of the negligent discoverers4 ,perhaps we may notice1 before passing on1 the provisional system which was adopted to fill up the interval required for finding a suitable name1 and required also for making sure that the planet was in fact a new one1 and not merely an old one rediscovered4 ,there was a system of numbering in existence as well as of naming1 but it was unadvisable to attach even a number to a planet until it was quite certain that the discovery was new1 for otherwise there might be gaps created in what should be a continuous series by spurious discoveries being struck out4 ,accordingly it was decided to attach at first to the object merely a letter of the alphabet1 with the year of discovery1 as a provisional name4 ,the alphabet was1 however1 run through so quickly1 and confusion was so likely to ensue if it was merely repeated1 that on recommencing it the letter ,a was prefixed1 and the symbols adopted were therefore ,,aa1 ,,ab1 ,,ac1 c42 after completing the alphabet again1 the letter ,b was prefixed1 and so on2 and astronomers began to fear that they had before them a monotonous prospect of continually adding new planets1 varied by no incident more exciting than starting the alphabet over again after every score4 ,sidenote3 ,eros4 ,fortunately1 however1 on running through it for the fifth time1 an object of particular interest was discovered4 ,most of these bodies revolve at a distance from the sun intermediate between that of ,mars and that of ,jupiter1 but the little planet which took the symbol ,,dq1 and afterwards the name of ,eros1 was found to have a mean distance actually less than that of ,mars1 and this gave it an extraordinary importance with respect to the great problem of determining the sun's distance4 ,to explain this importance we must make a small digression4 ,sidenote3 ,transit of ,venus4 ,about the middle of the last century our knowledge of the sun's distance was very rough1 as may be seen from the table on p4 #cb2 but there were in prospect two transits of ,venus1 in #ahgd and #ahhb1 and it was hoped that these would give opportunities of a special kind for the measurement of this important quantity1 which lies at the root of all our knowledge of the exact masses and dimensions of not only the sun1 but of the planets as well4 ,illustration3 ,,fig4 #a4 ,sidenote3 ,the ,black ,drop4 ,the method may be briefly summarised thus3 ,an observer in one part of the earth would see ,venus cross the disc of the sun along a different path from that seen by another observer1 as will be clear from the diagram4 ,if the size of the earth1 the distance of the sun1 and the relative distance of ,venus be known1 it can be calculated what this difference in path will be4 ,now the relative distance of ,venus is known with great accuracy1 from observing the time of her revolution round the sun2 the size of the earth we can measure by a survey2 there remains1 therefore1 only one unknown quantity1 the sun's distance4 ,and since from a knowledge of this we could calculate the difference in path1 it is easy to invert the problem1 and calculate the sun's distance from the knowledge of the observed difference in path4 ,accordingly1 observers were to be scattered1 not merely to two1 but to many stations over the face of the earth1 to observe the exact path taken by ,venus in transit over the sun's disc as seen from their station2 and especially to observe the exact times of beginning and ending of the transit2 and1 by comparison of their results1 it was hoped to determine this very important quantity1 the sun's distance4 ,it was known from previous experience that there were certain difficulties in observing very exactly the beginning and end of the transit4 ,there was an appearance called the ,black ,drop1 which had caused trouble on previous occasions2 an appearance as though the round black spot which can be seen when ,venus has advanced some distance over the sun's disc was reluctant to make the entry and clung to the edge or limb of the sun as it is called1 somewhat as a drop of ink clings to a pen which is slowly withdrawn from an inkpot4 ,similarly1 at the end of the transit or egress1 instead of approaching the limb steadily the planet seems at the last moment to burst out towards it1 rendering the estimation of the exact moment when the transit is over extremely doubtful4 ,sidenote3 ,failure4 ,these difficulties1 as already stated1 were known to exist2 but there is a long interval between transits of ,venus1 or rather between every pair of such transits4 ,after those of #ahgd and #ahhb there will be no more until #bjjd and #bjab1 so that we shall never see another2 similarly1 before that pair of the last century1 there had not been any such occasion since #agfa and #agfi1 and no one was alive who remembered at first hand the trouble which was known to exist4 ,it was proposed to obviate the anticipated difficulties by careful practice beforehand2 models were prepared to resemble as nearly as possible the expected appearances1 and the times recorded by different observers were compared with the true time1 which could1 in this case of a model1 be determined4 ,in this way it was hoped that the habit of each observer1 his personal equation as it is called1 could be determined beforehand1 and allowed for as a correction when he came to observe the actual transit4 ,the result1 however1 was a great disappointment4 ,the actual appearances were found to be totally different in character from those shown by the model2 chiefly1 perhaps1 because it had been impossible to imitate with a model the effect of the atmosphere which surrounds the planet ,venus4 ,observers trained beforehand1 using similar instruments1 and standing within a few feet of each other1 were expected1 after making due allowance for personal equation1 to give the same instant for contact2 but their observations when made were found to differ by nearly a minute of time1 and after an exhaustive review of the whole material it was felt that all hope of determining accurately the sun's distance by this method must be given up4 ,the following table will show how much was learned from the transits of ,venus1 and how much remained to be settled4 ,they left the result in doubt over a range of about two million miles4 ,,sun',s ,,distance1 ,,in ,,millions ,,of ,,miles1 ,,as ,,found ,,by ,,different ,,observers ,before the ,transits of ,venus estimates varied between #if million miles 7,gilliss and ,gould1 #ahef7 and #ia million 7,winneche1 #ahfc71 a range of #e million miles4 ,the ,transits of #ahgd and #ahhb gave results lying between #ic-a_/d million 7,airy1 from ,british observations of #ahgd71 #ib-a_/b million 7,stone1 from ,british observations of #ahhb71 and #ia-a_/b million 7,puiseux1 from ,french observations71 a range of #a-c_/d millions4 ,gill's ,heliometer results all lie very near #ic millions4 ,the observations of ,mars in #ahgg give about #ajj1jjj miles over this figure3 but the observations of ,victoria1 ,iris1 and ,sappho1 which are more trustworthy1 all agree in giving about #ajj1jjj miles less than the #ic millions4 ,it became necessary1 therefore1 to look to other methods2 and before the second transit of #ahhb was observed1 an energetic astronomer1 ,dr4 ,david ,gill1 had already put into operation the method which may be now regarded as the standard one4 ,sidenote3 ,modern method for sun's distance4 ,sidenote3 ,photography4 ,sidenote3 ,dr4 ,gill's expedition to ,ascension4 ,we have said that the relative distance of ,venus from the sun is accurately known from observations of the exact time of revolution4 ,it is easy to see that these times of revolution can be measured accurately by mere accumulation4 ,we may make an error of a few seconds in noting the time of return2 but if the whole interval comprises #aj revolutions1 this error is divided by #aj1 if #ajj revolutions by #ajj1 and so on2 and by this time a great number of revolutions of all the planets 7except those just discovered7 have been recorded4 ,hence we know their relative distances with great precision2 and if we can find the distance in miles of any one of them1 we can find that of the sun itself1 or of any other planet1 by a simple rule-of-three sum4 ,by making use of this principle many of the difficulties attending the direct determination of the sun's distance can be avoided2 for instance1 since the sun's light overpowers that of the stars1 it is not easy to directly observe the place of the sun among the stars2 but this is not so for the planets4 ,we can photograph a planet and the stars surrounding it on the same plate1 and then by careful measurement determine its exact position among the stars2 and since this position differs slightly according to the situation of the observer on the earth's surface1 by comparing two photographs taken at stations a known distance apart we can find the distance of the planet from the earth2 and hence1 as above remarked1 the distance of the sun and all the other members of the solar system4 ,or1 instead of taking photographs from two different stations1 we can take from the same station two photographs at times separated by a known interval4 ,for in that interval the station will have been carried by the earth's rotation some thousands of miles away from its former position1 and becomes virtually a second station separated from the first by a distance which is known accurately when we know the elapsed time4 ,again1 instead of taking photographs1 and from them measuring the position of the planet among the stars1 we may make the measurements on the planet and stars in the sky itself2 and since in #ahgh1 when ,dr4 ,gill set out on his enterprise of determining the sun's distance1 photography was in its infancy as applied to astronomy1 he naturally made his observations on the sky with an instrument known as a heliometer4 ,he made them in the little island of ,ascension1 which is suitably situated for the purpose2 because1 being near the earth's equator1 it is carried by the earth's rotation a longer distance in a given time than places nearer the poles1 and in these observations for parallax1 as they are called1 it is important to have the displacement of the station as large as possible4 ,for a similar reason the object selected among the planets must be as near the earth as possible2 and hence the planet ,mars1 which at favourable times comes nearer to us than any other superior planet#a then known1 was selected for observation with the heliometer4 ,and now it will be seen why the discovery of the little planet ,eros was important1 for ,mars was no longer the known planet capable of coming nearest to us2 it had been replaced by this new arrival4 ,sidenote3 ,victoria1 ,iris1 and ,sappho4 ,sidenote3 ,eros4 ,further1 a small planet which is in appearance just like an ordinary star has1 irrespective of this great proximity1 some distinct advantages over a planet like ,mars1 which appears as a round disc1 and is1 moreover1 of a somewhat reddish colour4 ,when the distance of an object of this kind from a point of line such as a star is measured with the heliometer it is found that a certain bias1 somewhat difficult to allow for with certainty1 is introduced into the measures2 and our confidence in the final results suffers accordingly4 ,after his observations of ,mars in #ahgh1 ,dr4 ,david ,gill was sufficiently impressed with this source of error to make three new determinations of the sun's distance1 using three of the minor planets instead of ,mars1 in spite of the fact that they were sensibly farther away2 and his choice was justified by finding that the results from these three different sets of observations agreed well among themselves1 and differed slightly from that given by the observations of ,mars4 ,hence it seems conclusively proved that one of these bodies is a better selection than ,mars in any case1 and the discovery of ,eros1 which offered the advantage of greater proximity in addition1 was hailed as a new opportunity of a most welcome kind4 ,it was seen by a little calculation that in the winter of #aijj-aija the planet would come very near the earth2 not the nearest possible 7for it was also realised that a still better opportunity had occurred in #ahid1 though it was lost because the planet had not yet been discovered71 but still the nearest approach which would occur for some thirty years2 and extensive1 though somewhat hasty1 preparations were made to use it to the fullest advantage4 ,photography had now become established as an accurate method of making measurements of the kind required2 and all the photographic telescopes which could be spared were pressed into the service1 and diligently photographed the planet and surrounding stars every fine night during the favourable period4 ,the work of measuring and reducing these photographs involves an enormous amount of labour1 and is even yet far from completed1 but we know enough to expect a result of the greatest value4 ,more than this we have not time to say here about this great problem1 but it will have been made clear that just when astronomers were beginning to wonder whether it was worth while continuing the monotonous discovery of new minor planets by the handful1 the #dccrd discovery also turned out to be one of the greatest importance4 ,to canons for the advantageous prosecution of research1 if we care to make them1 we may therefore add this--that there is no line of research1 however apparently unimportant or monotonous1 which we can afford to neglect4 ,just when we are on the point of relinquishing it under the impression that the mine is exhausted1 we may be about to find a nugget worth all our previous and future labour4 ,this rule will not1 perhaps1 help us very much in choosing what to work at2 indeed1 it is no rule at all1 for it leaves us the whole field of choice unlimited4 ,but this negative result will recur again and again as we examine the lessons taught by discoveries3 there seem to be no rules at all4 ,whenever we seem to be able to deduce one from an experience1 some other experience will flatly contradict it4 ,thus we might think that the discovery of ,eros taught us to proceed patiently with a monotonous duty1 and not turn aside to more novel and attractive work2 yet it is often by leaving what is in hand and apparently has first claim on our attention that we shall do best1 and we shall learn in the next chapter how a failure thus to turn flexibly aside was repented4 ,,chapter ,,ii ,,the ,,discovery ,,of ,,neptune ,sidenote3 ,search for definite objects4 ,in the last chapter we saw that the circumstances under which planets were discovered varied considerably4 ,sometimes the discoveries were not previously expected1 occurring during a general examination of the heavens1 or a search for other objects2 and1 on one occasion at least1 the discovery may be said to have been even contrary to expectation1 though1 as the existence of a number of minor planets began to be realised1 there have also been many cases where the discovery has been made as the result of a definite and deliberate search4 ,but the search cannot be said to have been inspired by any very clear or certain principle3 for the law of ,bode1 successful though it has been in indicating the possible existence of new planets1 cannot1 as yet1 be said to be founded upon a formulated law of nature4 ,we now come1 however1 to a discovery made in direct interpretation of ,newton's great law of gravitation--the discovery of ,neptune from its observed disturbance of ,uranus4 ,i will first briefly recall the main facts relating to the actual discovery4 ,sidenote3 ,disturbance of ,uranus4 ,after ,uranus had been discovered and observed sufficiently long for its orbit to be calculated1 it was found that the subsequent position of the planet did not always agree with this orbit2 and1 more serious than this1 some early observations were found which could not be reconciled with the later ones at all4 ,it is a wonderful testimony to the care and sagacity of ,sir ,william ,herschel1 as was remarked in the last chapter1 that ,uranus was found to have been observed1 under the mistaken impression that it was an ordinary star1 by ,flamsteed1 ,lemonnier1 ,bradley1 and ,mayer1 all observers of considerable ability4 ,flamsteed's five observations dated as far back as #afij1 #agab1 and #agae2 observations by others were in #agdh1 #agej1 #agec1 #agef1 and so on up to #agga1 and the body of testimony was so considerable that there was no room for doubt as to the irreconcilability of the observations with the orbit1 such as might have been the case had there been only one or two1 possibly affected with some errors4 ,sidenote3 ,suspicion of perturbing planet4 ,it is difficult to mention an exact date for the conversion into certainty of the suspicion that no single orbit could be found to satisfy all the observations2 but we may certainly regard this fact as established in #ahba1 when ,alexis ,bouvard published some tables of the planet1 and showed fully in the introduction that when every correction for the disturbing action of other planets had been applied1 it was still impossible to reconcile the old observations with the orbit calculated from the new ones4 ,the idea accordingly grew up that there might be some other body or bodies attracting the planet and causing these discrepancies4 ,here again it is not easy to say exactly when this notion arose1 but it was certainly existent in #ahcd1 as the following letter to the ,astronomer ,royal will show4 ,i take it from his well-known ,account of some ,circumstances historically connected with the ,discovery of the ,planet exterior to ,uranus1 which he gave to the ,royal ,astronomical ,society at its first meeting after that famous discovery 7,monthly ,notices of the ,r4,a4,s41 vol4 iii41 and ,memoirs1 vol4 xvi474 ,,no4 #a4--,the ,,rev4 ,t4 ,j4 ,,hussey to ,g4 ,b4 ,,airy4 ,extract4 ',,hayes1 ,,kent1 #agth ,november #ahcd4 ',with ,m4 ,alexis ,bouvard ,i had some conversation upon a subject ,i had often meditated1 which will probably interest you1 and your opinion may determine mine4 ,having taken great pains last year with some observations of ,uranus1 ,i was led to examine closely ,bouvard's tables of that planet4 ,the apparently inexplicable discrepancies between the ancient and modern observations suggested to me the possibility of some disturbing body beyond ,uranus1 not taken into account because unknown4 ,my first idea was to ascertain some approximate place of this supposed body empirically1 and then with my large reflector set to work to examine all the minute stars thereabouts3 but ,i found myself totally inadequate to the former part of the task4 ,if ,i could have done it formerly1 it was beyond me now1 even supposing ,i had the time1 which was not the case4 ,i therefore relinquished the matter altogether2 but subsequently1 in conversation with ,bouvard1 ,i inquired if the above might not be the case3 his answer was1 that1 as might have been expected1 it had occurred to him1 and some correspondence had taken place between ,hansen and himself respecting it4 ,hansen's opinion was1 that one disturbing body would not satisfy the phenomena2 but that he conjectured there were two planets beyond ,uranus4 ,upon my speaking of obtaining the places empirically1 and then sweeping closely for the bodies1 he fully acquiesced in the propriety of it1 intimating that the previous calculations would be more laborious than difficult2 that if he had leisure he would undertake them and transmit the results to me1 as the basis of a very close and accurate sweep4 ,i have not heard from him since on the subject1 and have been too ill to write4 ,what is your opinion on the subject8 ,if you consider the idea as possible1 can you give me the limits1 roughly1 between which this body or those bodies may probably be found during the ensuing winter8 ,as we might expect an eccentricity inclination8 approaching rather to that of the old planets than of the new1 the breadth of the zone to be examined will be comparatively inconsiderable4 ,i may be wrong1 but ,i am disposed to think that1 such is the perfection of my equatoreal's object-glass1 ,i could distinguish1 almost at once1 the difference of light of a small planet and a star4 ,my plan of proceeding1 however1 would be very different3 ,i should accurately map the whole space within the required limits1 down to the minutest star ,i could discern2 the interval of a single week would then enable me to ascertain any change4 ,if the whole of this matter do not appear to you a chimaera1 which1 until my conversation with ,bouvard1 ,i was afraid it might1 ,i shall be very glad of any sort of hint respecting it4' ,my answer was in the following terms3-- ,sidenote3 ,airy's scepticism4 ,,no4 #b4--;,g4 ,b4 ,,airy to the ,,rev4 ,t4 ,j4 ,,hussey4 ,extract4 ',,observatory1 ,,cambridge1 #ahcd1 ,nov4 #bc4 ',i have often thought of the irregularity of ,uranus1 and since the receipt of your letter have looked more carefully to it4 ,it is a puzzling subject1 but ,i give it as my opinion1 without hesitation1 that it is not yet in such a state as to give the smallest hope of making out the nature of any external action on the planet 444 if it were certain that there were any extraneous action1 ,i doubt much the possibility of determining the place of a planet which produced it4 ,i am sure it could not be done till the nature of the irregularity was well determined from several successive revolutions4' ,sidenote3 ,le ,verrier's papers4 ,sidenote3 ,planet to be detected by disc4 ,sidenote3 ,galle's discovery of the planet4 ,although only a sentence or two have been selected from ,airy's reply 7he was not yet ,astronomer ,royal71 they are sufficient to show that the problem of finding the place of such a possible disturbing body was regarded at that time as one of extreme difficulty2 and no one appears seriously to have contemplated embarking upon its solution4 ,it was not until many years later that the solution was attempted4 ,of the first attempt we shall speak presently1 putting it aside for the moment because it had no actual bearing on the discovery of the planet1 for reasons which form an extraordinary episode of this history4 ,the attempt which led to success dates from ,november #ahde4 ,the great ,french astronomer ,le ,verrier1 on ,november #aj1 #ahde1 read to the ,french ,academy a paper on the ,orbit of ,uranus1 considering specially the disturbances produced by ,jupiter and ,saturn1 and showing clearly that with no possible orbit could the observations be satisfied4 ,on ,june #a1 #ahdf1 followed a second paper by the same author1 in which he considers all the possible explanations of the discordance1 and concludes that none is admissible except that of a disturbing planet exterior to ,uranus4 ,and assuming1 in accordance with ,bode's ,law1 that the distance of this new planet from the sun would be about double that of ,uranus 7and it is important to note this assumption71 he proceeds to investigate the orbit of such a planet1 and to calculate the place where it must be looked for in the heavens4 ,this was followed by a third paper on ,august #cast1 giving a rather completer discussion1 and arriving at the conclusion that the planet should be recognisable from its disc4 ,this again is an important point4 ,we remember that in the discovery of ,uranus it needed considerable skill on the part of ,sir ,william ,herschel to detect the disc1 to see in fact any difference between it and surrounding stars2 and that other observers1 even when their attention had been called to the planet1 found it difficult to see this difference4 ,it might be expected1 therefore1 that with a planet twice as far away 7as had been assumed for the new planet7 the disc would be practically unrecognisable1 and as we shall presently see1 this assumption was made in some searches for the planet which had been commenced even before the publication of this third paper4 ,le ,verrier's courageous announcement1 which he deduced from a consideration of the mass of the planet1 that the disc should be recognisable1 led immediately to the discovery of the suspected body4 ,he wrote to a ,german astronomer1 ,dr4 ,galle 7still1 ,i am glad to say1 alive and well1 though now a very old man71 telling him the spot in the heavens to search1 and stating that he might expect to detect the planet by its appearance in this way2 and the same night ,dr4 ,galle1 by comparing a star map with the heavens1 found the planet4 ,sidenote3 ,adams' work publicly announced4 ,to two points to which ,i have specially called attention in this brief summary--namely1 the preliminary assumption that the planet would be1 according to ,bode's ,law1 twice as far away as ,uranus2 secondly1 the confident assertion that it would have a visible disc--,i will ask you to add1 thirdly1 that it was found by the aid of a star map1 for this map played an important part in the further history to which we shall now proceed4 ,it may naturally be supposed that the announcement of the finding of a planet in this way1 the calculation of its place from a belief in the universal action of the great ,law of ,gravitation1 the direction to an eminent observer to look in that place for a particular thing1 and his immediate success1--this extraordinary combination of circumstances caused a profound sensation throughout not only the astronomical1 but the whole world2 and this sensation was greatly enhanced by the rumour which had begun to gather strength that1 but for some unfortunate circumstances1 the discovery might have been made even earlier and as a consequence of totally independent calculations made by a young ,cambridge mathematician1 ,j4 ,c4 ,adams4 ,some of you are doubtless already familiar with the story in its abridged form1 for it has been scattered broadcast through literature4 ,in ,england it generally takes the form of emphasising the wickedness or laziness of the ,astronomer ,royal who1 when told where to look for a planet1 neglected his obvious duty1 so that in consequence another astronomer who made the calculation much later and gave a more virtuous observer the same directions where to look1 obtained for ,france the glory of a discovery which ought to have been retained in ,england4 ,there is no doubt that ,airy's conduct received a large amount of what he called savage abuse4 ,when the facts are clearly stated ,i think it will be evident that many of the harsh things said of him were scarcely just1 though at the same time it is also difficult to understand his conduct at two or three points of the history1 even as explained by himself4 ,sidenote3 ,facts undoubted4 ,there is fortunately no doubt whatever about any of the facts4 ,airy himself gave a very clear and straightforward account of them at the time1 for which more credit is due to him than he commonly receives2 and since the death of the chief actors in this sensational drama they have been naturally again ransacked1 with the satisfactory result that there is practically no doubt about any of the facts4 ,as to the proper interpretations of them there certainly may be wide differences of opinion1 nor does this circumstance detract from their interest4 ,it is almost impossible to make a perfectly colourless recital of them1 nor is it perhaps necessary to do so4 ,i will therefore ask you to remember in what ,i now say that there is almost necessarily an element of personal bias1 and that another writer would probably give a different colouring4 ,having said this1 ,i hope ,i may speak quite freely as the matter appears in my personal estimation4 ,sidenote3 ,airy's ,account4 ,sidenote3 ,a movement of the age4 ,airy's account was1 as above stated1 given to the ,royal ,astronomical ,society at their first meeting 7after the startling announcement of the discovery of the new planet71 on ,november #ac1 #ahdf1 and ,i have already quoted an extract from it4 ,he opens with a tribute to the sensational character of the discovery1 and then states that although clearly due to two individuals 7namely1 ,le ,verrier and ,galle71 it might also be regarded as to some extent the consequence of a movement of the age4 ,his actual words are these3 ,the principal steps in the theoretical investigations have been made by one individual1 and the published discovery of the planet was necessarily made by one individual4 ,to these persons the public attention has been principally directed2 and well do they deserve the honours which they have received1 and which they will continue to receive4 ,yet we should do wrong if we considered that these two persons alone are to be regarded as the authors of the discovery of this planet4 ,i am confident that it will be found that the discovery is a consequence of what may properly be called a movement of the age2 that it has been urged by the feeling of the scientific world in general1 and has been nearly perfected by the collateral1 but independent labours1 of various persons possessing the talents or powers best suited to the different parts of the researches4 ,sidenote3 ,airy under-estimated ,adams' work4 ,i have quoted these words as the first point at which it is difficult to understand ,airy's conduct in excluding from them all specific mention of ,adams1 knowing as he did the special claims which entitled him to such mention2 claims indeed which he proceeded immediately to make clear4 ,it seems almost certain that ,airy entirely under-estimated the value of ,adams' work throughout4 ,but this will become clearer as we proceed4 ,the account takes the form of the publication of a series of letters with occasional comments4 ,airy was a most methodical person1 and filed all his correspondence with great regularity4 ,it was jestingly said of him once that if he wiped his pen on a piece of blotting-paper1 he would date the blotting-paper and file it for reference4 ,the letters reproduced in this account are still in the ,observatory at ,greenwich1 pinned together just as ,airy left them2 and in preparing his account it was necessary to do little else than to have them copied out and interpolate comments4 ,from two of them ,i have already quoted to show how difficult the enterprise of finding an exterior planet from its action on ,uranus was considered in #ahcd4 ,to these may be added the following sentence from ,no4 #d1 dated #ahcg4 ,if it be the effect of any unseen body1 writes ,airy to ,bouvard1 it will be nearly impossible ever to find out its place4 ,but the first letter which need concern us is ,no4 #f1 and it is only necessary to explain that ,professor ,challis was the ,professor of ,astronomy at ,cambridge1 and in charge of the ,cambridge ,observatory1 in which offices he had succeeded ,airy himself on his leaving ,cambridge for ,greenwich some eight years earlier4 ,no4 #f4--,,professor ,,challis to ,g4 ,b4 ,,airy4 ,extract4 ',,cambridge ,,observatory1 ,feb4 #ac1 #ahdd4 ,sidenote3 ,challis mentions ,adams to ,airy1 and suggests ,adams' visit to ,greenwich4 ',a young friend of mine1 ,mr4 ,adams of ,st4 ,john's ,college1 is working at the theory of ,uranus1 and is desirous of obtaining errors of the tabular geocentric longitudes of this planet1 when near opposition1 in the years #ahah-ahbf1 with the factors for reducing them to errors of heliocentric longitude4 ,are your reductions of the planetary observations so far advanced that you could furnish these data8 and is the request one which you have any objection to comply with8 ,if ,mr4 ,adams may be favoured in this respect1 he is further desirous of knowing1 whether in the calculation of the tabular errors any alterations have been made in ,bouvard's ,tables of ,uranus besides that of ,jupiter's mass4' ,my answer to him was as follows3-- ,no4 #g4--;,g4 ,b4 ,,airy to ,,professor ,,challis4 ,extract4 ',,royal ,,observatory1 ,,greenwich1 #ahdd1 ,feb4 #ae4 ',i send all the results of the observations of ,uranus made with both instruments 7that is1 the heliocentric errors of ,uranus in longitude and latitude from #aged to #ahcj1 for all those days on which there were observations1 both of right ascension and of polar distance74 ,no alteration is made in ,bouvard's ,tables of ,uranus except in increasing the two equations which depend on ,jupiter by #a_/ej part4 ,as constants have been added 7in the printed tables7 to make the equations positive1 and as #a_/ej part of the numbers in the tables has been added1 #a_/ej part of the constants has been subtracted from the final results4' ,professor ,challis in acknowledging the receipt of these1 used the following expressions3-- ,no4 #h4--,,professor ,,challis to ,g4 ,b4 ,,airy4 ,extract4 ',,cambridge ,,observatory1 ,feb4 #af1 #ahdd4 ',i am exceedingly obliged by your sending so complete a series of tabular errors of ,uranus4444 ,the list you have sent will give ,mr4 ,adams the means of carrying on in the most effective manner the inquiry in which he is engaged4' ,the next letter shows that ,mr4 ,adams has derived results from these errors4 ,no4 #i4--,,professor ,,challis to ,g4 ,b4 ,,airy4 ',,cambridge ,,observatory1 ,sept4 #bb1 #ahde4 ',my friend ,mr4 ,adams 7who will probably deliver this note to you7 has completed his calculations respecting the perturbation of the orbit of ,uranus by a supposed ulterior planet1 and has arrived at results which he would be glad to communicate to you personally1 if you could spare him a few moments of your valuable time4 ,his calculations are founded on the observations you were so good as to furnish him with some time ago2 and from his character as a mathematician1 and his practice in calculation1 ,i should consider the deductions from his premises to be made in a trustworthy manner4 ,if he should not have the good fortune to see you at ,greenwich1 he hopes to be allowed to write to you on this subject4' ,on the day on which this letter was dated1 ,i was present at a meeting of the ,french ,institute4 ,i acknowledged it by the following letter3-- ,,no4 #aj4--;,g4 ,b4 ,,airy to ,,professor ,,challis4 ',,royal ,,observatory1 ,,greenwich1 #ahde1 ,sept4 #bi4 ',i was1 ,i suppose1 on my way from ,france1 when ,mr4 ,adams called here2 at all events1 ,i had not reached home1 and therefore1 to my regret1 ,i have not seen him4 ,would you mention to ,mr4 ,adams that ,i am very much interested with the subject of his investigations1 and that ,i should be delighted to hear of them by letter from him8' ,on one of the last days of ,october #ahde1 ,mr4 ,adams called at the ,royal ,observatory1 ,greenwich1 in my absence and left the following important paper3-- ,no4 #aa4--;,j4 ,c4 ,,adams1 ,esq41 to ,g4 ,b4 ,,airy4 ,sidenote3 ,adams' announcement of the new planet4 ',according to my calculations1 the observed irregularities in the motion of ,uranus may be accounted for by supposing the existence of an exterior planet1 the mass and orbit of which are as follows3-- ,mean distance 7assumed nearly in accordance with ,bode's ,law7 #ch4d ,mean sidereal motion in #cfe4be days #a deg4#cj'4i ,mean longitude1 #ast ,october #ahde #cbc #cd ,longitude of perihelion #cae #ee ,eccentricity #j4afaj4 ,mass 7that of the sun being unity7 #j4jjjafef4 ,for the modern observations ,i have used the method of normal places1 taking the mean of the tabular errors1 as given by observations near three consecutive oppositions1 to correspond with the mean of the times2 and the ,greenwich observations have been used down to #ahcj3 since which1 the ,cambridge and ,greenwich observations1 and those given in the ,astronomische ,nachrichten1 have been made use of4 ,the following are the remaining errors of mean longitude3-- ,observation--,theory4 #aghj #j4bg #aghc -#j4bc #aghf -#j4if #aghi #a4hb #agib -#j4ia #agie #j4ji #agih -#j4ii #ahja -#j4jd #ahjd #a4gf #ahjg -#j4ba #ahaj #j4ef #ahac -#j4id #ahaf -#j4ca #ahai -#b4jj #ahbb #j4cj #ahbe #a4ib #ahbh #b4be #ahca -#a4jf #ahcd -#a4dd #ahcg -#a4fb #ahdj #a4gc ,the error for #aghj is concluded from that for #agha given by observation1 compared with those of four or five following years1 and also with ,lemonnier's observations in #agfi and #agga4 ',for the ancient observations1 the following are the remaining errors3-- ,observation--,theory4 #afij #dd4d #agab #f4g #agae - #f4h #agej - #a4f #agec #e4g #agef - #d4j #agfc - #e4a #agfi #j4f #agga #aa4h ,the errors are small1 except for ,flamsteed's observation of #afij4 ,this being an isolated observation1 very distant from the rest1 ,i thought it best not to use it in forming the equations of condition4 ,it is not improbable1 however1 that this error might be destroyed by a small change in the assumed mean motion of the planet4' ,i acknowledged the receipt of this paper in the following terms3-- ,,no4 #ab4--;,g4 ,b4 ,,airy to ,j4 ,c4 ,,adams1 ,esq4 ',,royal ,,observatory1 ,,greenwich1 #ahde1 ,nov4 #e4 ,sidenote3 ,airy's inquiry about the radius vector4 ',i am very much obliged by the paper of results which you left here a few days since1 showing the perturbations on the place of ,uranus produced by a planet with certain assumed elements4 ,the latter numbers are all extremely satisfactory3 ,i am not enough acquainted with ,flamsteed's observations about #afij to say whether they bear such an error1 but ,i think it extremely probable4 ',but ,i should be very glad to know whether this assumed perturbation will explain the error of the radius vector of ,uranus4 ,this error is now very considerable1 as you will be able to ascertain by comparing the normal equations1 given in the ,greenwich observations for each year1 for the times before opposition with the times after opposition4' ,i have before stated that ,i considered the establishment of this error of the radius vector of ,uranus to be a very important determination4 ,i therefore considered that the trial1 whether the error of radius vector would be explained by the same theory which explained the error of longitude1 would be truly an experimentum crucis4 ,and ,i waited with much anxiety for ,mr4 ,adams' answer to my query4 ,had it been in the affirmative1 ,i should at once have exerted all the influence which ,i might possess1 either directly1 or indirectly through my friend ,professor ,challis1 to procure the publication of ,mr4 ,adams' theory4 ,from some cause with which ,i am unacquainted1 probably an accidental one1 ,i received no immediate answer to this inquiry4 ,i regret this deeply1 for many reasons4 ,sidenote3 ,adams' silence4 ,here we may leave ,airy's account for a few moments to consider the reason why he received no answer4 ,adams was a very shy and retiring young man1 and very sensitive2 though capable of a great resolution1 and of enormous perseverance in carrying it out4 ,we know 7what is not indicated in the above account71 how steadily he had kept in view the idea of solving this great problem4 ,it was characteristic of him that as early as #ahda he had formed a resolution to undertake it1 although at the time he was not able to enter upon its accomplishment4 ,the following memorandum1 which is still in existence1 having been found among his papers after his death1 records these facts3 #ahda1 ,july #c4 ,formed a design1 in the beginning of this week1 of investigating1 as soon as possible after taking my degree1 the irregularities in the motion of ,uranus1 which were as yet unaccounted for3 in order to find whether they may be attributed to the action of an undiscovered planet beyond it1 and if possible thence to determine the elements of its orbit1 c41 approximately1 which would probably lead to its discovery4 ,accordingly1 as soon as possible after taking his degree he embarked upon the enterprise1 and the first solution was made in the long vacation of #ahdc1 assuming the orbit of the unknown planet to be a circle with a radius equal to twice the mean distance of ,uranus from the sun 7an assumption which1 as we have seen1 was also made by ,le ,verrier74 ,having satisfied himself that there was a good general agreement between his results and the observations1 ,adams began a more complete solution2 indeed from first to last he made no less than six separate solutions1 the one which he announced to ,airy in the above letter being the fourth4 ,hence he had already done an enormous amount of work on the problem1 and was in his own mind so justly convinced of the correctness and value of his results that he was liable to forget that others had not had the same opportunity of judging of their completeness2 and he was grievously disappointed when his announcement was not received with full confidence4 ,sidenote3 ,his disappointment at ,greenwich1 and at ,airy's question4 ,but perhaps it should first be stated that by a series of mischances ,adams had been already much disappointed at the failure of his attempts to see the ,astronomer ,royal on his visits to ,greenwich4 ,this does not seem to have been exactly ,airy's fault2 he was1 as may well be supposed1 an extremely busy man1 and was much occupied at the time on a question of great practical importance1 at the direct request of the ,government1 namely1 the settling of the proper gauge for railways throughout the country4 ,the first time ,adams called to see him1 he was actually in ,london sitting on the ,committee which dealt with this question1 and ,adams was asked to call later2 when the visit was repeated1 ,airy was unfortunately at dinner 7and it may be added that his hours for dinner were somewhat peculiar71 and the butler1 acting somewhat in the manner of his kind1 protected his master's dinner by sending away one whom he doubtless regarded as a troublesome visitor4 ,there is1 as ,i have said1 little doubt about any of the facts1 and it seems well established that ,airy himself did not learn of ,adams' visits until afterwards1 and it would scarcely be just to blame him for a servant's oversight4 ,but ,adams had left the paper above reproduced1 and ,airy with his business-like habits ultimately proceeded to deal with it2 he wrote the answer given above asking ,adams a definite question1 filed a copy of it with the original letter1 and then dismissed the matter from his thoughts until the reply from ,adams1 which he confidently expected should again bring it under notice4 ,this further disappointment was1 however1 too much for ,adams2 he regarded the question put by ,airy as having so obvious an answer that it was intended as an evasion1 though this was far from being the case4 ,airy was thoroughly in earnest about his question1 though it must be admitted that a more careful study of the problem would have shown him that it was unnecessary4 ,later1 when he learnt of ,le ,verrier's researches1 he put the same question to him1 and received a polite but very clear answer1 showing that the suggested test was not an experimentum crucis as he supposed4 ,but ,adams did not feel equal to making this reply2 he shrank into his shell and solaced himself only by commencing afresh another solution of the problem which had so engrossed his life at that time4 ,sidenote3 ,the merits of ,airy's question4 ,sidenote3 ,the range of possibilities4 ,i have heard severe or contemptuous things said about this question by those who most blame ,airy4 ,some of them have no hesitation in accusing him of intellectual incompetence3 they say that it was the question of a stupid man4 ,i think that in the first place they forget the difference between a deliberate error of judgement and a mere consequence of insufficient attention4 ,but there is even more than this to be said in defence of the question4 ,the error of radius vector came before ,airy in an entirely independent way1 and as an entirely independent phenomenon1 from the error of longitude1 and there was nothing unnatural in regarding it as requiring independent explanation4 ,it is true that1 as the event proved1 a mere readjustment of the orbit of ,uranus got rid of this error of radius vector 7this was substantially ,le ,verrier's answer to ,airy's question72 but we must not judge of what was possible before the event in the light of what we now know4 ,the original possibilities were far wider1 though we have forgotten their former extent now that they have been narrowed down by the discovery4 ,if a sentry during war time hears a noise in a certain direction1 he may be compelled to make the assumption that it is the movement of an enemy2 and if he fires in that direction and kills him1 and thus saves his own army from destruction1 he is deservedly applauded for the success which attends his action4 ,but it does not follow that the assumption on which he acted was the only possible one4 ,or1 to take a more peaceful illustration1 in playing whist it sometimes becomes apparent that the game can only be won if the cards lie in a certain way2 and a good player will thereupon assume that this is the fact1 and play accordingly4 ,adams and ,le ,verrier played to win the game on the particular assumption that the disturbance of ,uranus was due to an external planet revolving at a distance from the sun about twice that of ,uranus2 and won it2 and we applaud them for doing so4 ,but it is easy to imagine a rearrangement of the cards with which they would have lost it2 and ,airy's question simply meant that he was alive to these wider possibilities1 and did not see the need for attempting to win the game in that particular way4 ,one such alternative possibility has already been mentioned4 ,hansen's opinion was1 that one disturbing body would not satisfy the phenomena2 but he conjectured that there were two planets beyond ,uranus4 ,another conceivable alternative is that there was some change in the law of gravitation at the distance of ,uranus1 which1 it must be remembered1 is twice as great as that of any planet previously known4 ,or some wandering body might have passed close enough to ,uranus to change its orbit somewhat suddenly4 ,we now know1 for instance1 that the swarm of meteorites which gives rise to the well-known ,november meteors must have passed very close to ,uranus in ,a4,d4 #abf1 assuming that neither the planet nor the swarm have been disturbed in any unknown manner in the meantime4 ,it is to this encounter that we owe the introduction of this swarm to our solar system3 wandering through space1 they met ,uranus1 and were swept by his attraction into an orbit round the sun4 ,was there no reaction upon ,uranus himself8 ,the probabilities are that the total mass of the swarm was so small as to affect the huge planet inappreciably2 but who was to say that some other swarm of larger mass1 or other body1 might not have approached near ,uranus at some date between #afij and #ahde1 and been responsible at any rate in part for the observed errors8 ,these are two or three suppositions from our familiar experience2 and there are1 of course1 limitless possibilities beyond4 ,which is the true scientific attitude1 to be alive to them all1 or to concentrate attention upon one8 ,but we are perhaps wandering too far from the main theme4 ,it is easy to do so in reviewing this extraordinary piece of history1 for at almost every point new possibilities are suggested4 ,illustration3 ,,iii--,u4 ,j4 ,,le ,,verrier4 7,from a print in the possession of the ,royal ,astronomical ,society47 ,illustration3 ,,iv--,j4 ,g4 ,,galle4 ,,who ,,first ,,saw ,,the ,,planet ,,neptune ,sidenote3 ,airy receives ,le ,verrier's memoir4 ,we must return1 however1 to ,airy's account4 ,we reached the point where he had written to ,adams 7on ,november #e1 #ahde71 asking his question about the radius vector1 and received no reply2 and there the matter remained1 so far as he was concerned1 until the following ,june1 when ,le ,verrier's memoir reached him2 and we will let him give his own version of the result4 ,this memoir reached me about the #bcrd or #bdth of ,june4 ,i cannot sufficiently express the feeling of delight and satisfaction which ,i received from it4 ,the place which it assigned to the disturbing planet was the same1 to one degree1 as that given by ,mr4 ,adams' calculations1 which ,i had perused seven months earlier4 ,to this time ,i had considered that there was still room for doubt of the accuracy of ,mr4 ,adams' investigations2 for ,i think that the results of algebraic and numerical computations1 so long and so complicated as those of an inverse problem of perturbations1 are liable to many risks of error in the details of the process3 ,i know that there are important numerical errors in the ,mecanique ,celeste of ,laplace2 in the ,theorie de la ,lune of ,plana2 above all1 in ,bouvard's first tables of ,jupiter and ,saturn2 and to express it in a word1 ,i have always considered the correctness of a distant mathematical result to be a subject rather of moral than of mathematical evidence4 ,but now ,i felt no doubt of the accuracy of both calculations1 as applied to the perturbation in longitude4 ,i was1 however1 still desirous1 as before1 of learning whether the perturbation in radius vector was fully explained4 ,i therefore addressed to ,m4 ,le ,verrier the following letter3-- ,no4 #ac4--;,g4 ,b4 ,,airy to ,m4 ,,le ,,verrier4 ',royal ,observatory1 ,greenwich1 #ahdf1 ,june #bf4 ,sidenote3 ,he puts the radius-vector question to ,le ,verrier1 but makes no mention of ,adams4 ',i have read1 with very great interest1 the account of your investigations on the probable place of a planet disturbing the motions of ,uranus1 which is contained in the ,compte ,rendu de l',academie of ,june #a2 and ,i now beg leave to trouble you with the following question4 ,it appears1 from all the later observations of ,uranus made at ,greenwich 7which are most completely reduced in the ,greenwich ,observations of each year1 so as to exhibit the effect of an error either in the tabular heliocentric longitude1 or the tabular radius vector71 that the tabular radius vector is considerably too small4 ,and ,i wish to inquire of you whether this would be a consequence of the disturbance produced by an exterior planet1 now in the position which you have indicated8' ,there is more of the letter1 but this will suffice to show that he wrote to ,le ,verrier in the same way as to ,adams1 and1 as already stated1 received a reply dated three or four days later4 ,but the rest of the letter contains no mention of ,adams1 and thus arises a second difficulty in understanding ,airy's conduct4 ,it seems extraordinary that when he wrote to ,le ,verrier he made no mention of the computations which he had previously received from ,adams2 or that he should not have written to ,adams1 and made some attempt to understand his long silence1 now that1 as he himself states1 he felt no doubt of the accuracy of both calculations4 ,the omission may have been1 and probably was1 mere carelessness or forgetfulness2 but he could hardly be surprised if others mistook it for deliberate action4 ,sidenote3 ,airy announces the likelihood of a new planet1 and suggests a search for it at ,cambridge not having suitable telescope at ,greenwich ,however1 attention had now been thoroughly attracted to the near possibility of finding the planet4 ,on ,june #bi1 #ahdf1 there was a special meeting of the ,board of ,visitors of ,greenwich ,observatory1 and ,airy incidentally mentioned to them this possibility4 ,the impression produced must have been definite and deep2 for ,sir ,john ,herschel1 who was present1 was bold enough to say on ,september #ajth following to the ,british ,association assembled at ,southampton3 ,we see it 7the probable new planet7 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 that of ocular demonstration4 ,airy discussed the matter with ,professor ,challis 7who1 it will be remembered1 had originally written to him on behalf of ,adams71 suggesting that he should immediately commence a search for the supposed planet at ,cambridge4 ,it may be asked why ,airy did not commence this search himself at ,greenwich1 and the answer is that he had no telescope which he regarded as large enough for the purpose4 ,the ,royal ,observatory at ,greenwich has always been1 and is now1 better equipped in some respects than any other observatory1 as might be expected from its deservedly great reputation2 but to possess the largest existing telescope has never been one of its ambitions4 ,the instruments in which it takes most pride are remarkable for their steadiness and accuracy rather than for their size2 and at that time the best telescope possessed by the observatory was not1 in ,airy's opinion1 large enough to detect the planet with certainty4 ,in this opinion we now know that he was mistaken2 but1 again1 we must not judge his conduct before the event in the light of what we have since discovered4 ,it may be recalled here that it was not until ,le ,verrier's third paper1 published on ,august #ca1 that he 7,le ,verrier7 emphatically pointed out that the new planet might be of such a size as to have a sensible disc2 and it was this remark which led immediately to its discovery4 ,until this was so decisively stated1 it must have seemed exceptionally improbable2 for we saw in the last chapter how diligently the ,zodiac had been swept in the search for minor planets1--how1 for instance1 ,hencke had searched for fifteen years without success2 and it might fairly be considered that if there were a fairly bright object 7such as ,neptune has since been found to be7 it would have been discovered earlier4 ,hence ,airy not unreasonably considered it necessary to spread his net for very small objects4 ,on ,july #i he wrote to ,professor ,challis as follows3-- ,no4 #ae4--;,g4 ,b4 ,,airy to ,,professor ,,challis4 ,,the ,,deanery1 ,,ely1 #ahdf1 ,july #i4 ,you know that ,i attach importance to the examination of that part of the heavens in which there is 444 reason for suspecting the existence of a planet exterior to ,uranus4 ,i have thought about the way of making such examination1 but ,i am convinced that 7for various reasons1 of declination1 latitude of place1 feebleness of light1 and regularity of superintendence7 there is no prospect whatever of its being made with any chance of success1 except with the ,northumberland telescope4 ,now1 ,i should be glad to ask you1 in the first place1 whether you could make such an examination8 ,presuming that your answer would be in the negative1 ,i would ask1 secondly1 whether1 supposing that an assistant were supplied to you for this purpose1 you would superintend the examination8 ,you will readily perceive that all this is in a most unformed state at present1 and that ,i am asking these questions almost at a venture1 in the hope of rescuing the matter from a state which is1 without the assistance that you and your instruments can give1 almost desperate4 ,therefore ,i should be glad to have your answer1 not only responding simply to my questions1 but also entering into any other considerations which you think likely to bear on the matter4 ,the time for the said examination is approaching near4 ,sidenote3 ,challis undertakes the search4 ,sidenote3 ,he finds too late that he had observed the planet4 ,professor ,challis did not require an assistant1 but determined to undertake the work himself1 and devised his own plan of procedure2 but he also set out on the undertaking with the expectation of a long and arduous search4 ,no such idea as that of finding the planet on the first night ever entered his head4 ,for one thing1 he had no map of the region to be examined1 for although the map used by ,galle had been published1 no copy of it had as yet reached ,cambridge1 and ,professor ,challis had practically to construct a map for himself4 ,in these days of photography to make such a map is a simple matter1 but at that time the process was terribly laborious4 ,i get over the ground very slowly1 he wrote on ,september #bnd to ,airy1 thinking it right to include all stars to #aj-aa magnitude2 and ,i find that to scrutinise thoroughly in this way the proposed portion of the heavens will require many more observations than ,i can take this year4 ,with such a prospect1 it is not surprising that one night's observations were not even compared with the next2 there would be a certain economy in waiting until a large amount of material had been accumulated1 and then making the comparisons all together1 and this was the course adopted4 ,but when ,le ,verrier's third paper1 with the decided opinion that the planet would be bright enough to be seen by its disc1 ultimately reached ,professor ,challis1 it naturally gave him an entirely different view of the possibilities2 he immediately began to compare the observations already made1 and found that he had observed the planet early in ,august4 ,but it was now too late to be first in the field1 for ,galle had already made his announcement of discovery4 ,writing to ,airy on ,october #ab1 ,challis could only lament that after four days' observing the planet was in his grasp1 if only he had examined or mapped the observations1 and if he had not delayed doing so until he had more observations to reduce1 and if he had not been very busy with some comet observations4 ,oh6 these terrible ifs which come so often between a man and success6 ,the third of them is a peculiarly distressing one1 for it represents that eternal conflict between one duty and another1 which is so constantly recurring in scientific work4 ,shall we finish one piece of work now well under way1 or shall we attend to something more novel and more attractive8 ,challis thought his duty lay in steadily completing the comet observations already begun4 ,we saw in the last lecture how the steady pursuit of the discovery of minor planets1 a duty which had become tedious and apparently led nowhere1 suddenly resulted in the important discovery of ,eros4 ,but ,challis was not so fortunate in electing to plod along the beaten track2 he would have done better to leave it4 ,there is no golden rule for the answer2 we must be guided in each case by the special circumstances1 and the dilemma is consequently a new one on every occasion1 and perhaps the more trying with each repetition4 ,sidenote3 ,sensation caused by the discovery4 ,sidenote3 ,not all national jealousy4 ,such are briefly the events which led to the discovery of ,neptune1 which was made in ,germany by direction from ,france1 when it might have been made in ,cambridge alone4 ,the incidents created a great stir at the time4 ,the ,account of them1 as read by ,airy to the ,royal ,astronomical ,society on ,november #ac1 #ahdf1 straightforward and interesting though it was1 making clear where he had himself been at fault1 nevertheless stirred up angry passions in many quarters1 and chiefly directed against ,airy himself4 ,cambridge was furious at ,airy's negligence1 which it considered responsible for costing the ,university a great discovery2 and others were equally irate at his attempting to claim for ,adams some of that glory which they considered should go wholly to ,le ,verrier4 ,but it may be remarked that feeling was not purely national4 ,some foreigners were cordial in their recognition of the work of ,adams1 while some of those most eager to oppose his claims were found in this country4 ,in their anxiety to show that they were free from national jealousy1 scientific men went almost too far in the opposite direction4 ,sidenote3 ,the position of ,cambridge in the matter4 ,sidenote3 ,challis the weakest point4 ,airy's conduct was certainly strange at several points1 as has already been remarked4 ,one cannot understand his writing to ,le ,verrier in ,june #ahdf without any mention of ,adams4 ,he could not even momentarily have forgotten ,adams' work2 for he tells us himself how he noticed the close correspondence of his result with that of ,le ,verrier3 and had he even casually mentioned this fact in writing to the latter1 it would have prepared the way for his later statement4 ,but we can easily understand the unfavourable impression produced by this statement after the discovery had been made1 when there had been no previous hint on the subject at all4 ,of those who abused him ,cambridge had the least excuse2 for there is no doubt that with a reasonably competent ,professor of ,astronomy in ,cambridge1 she need not have referred to ,airy at all4 ,it would not seem to require any great amount of intelligence to undertake to look in a certain region for a strange object if one is in possession of a proper instrument4 ,we have seen that ,challis had the instrument1 and when urged to do so was equal to the task of finding the planet2 but he was a man of no initiative1 and the idea of doing so unless directed by some authority never entered his head4 ,he had been accustomed for many years to lean rather helplessly upon ,airy1 who had preceded him in office at ,cambridge4 ,for instance1 when appointed to succeed him1 and confronted with the necessity of lecturing to students1 he was so helpless that he wrote to implore ,airy to come back to ,cambridge and lecture for him2 and this was actually done1 ,airy obtaining leave from the ,government to leave his duties at ,greenwich for a time in order to return to ,cambridge1 and show ,challis how to lecture4 ,now it seems to me that this helplessness was the very root of all the mischief of which ,cambridge so bitterly complained4 ,i claimed at the outset the privilege of stating my own views1 with which others may not agree3 and of all the mistakes and omissions made in this little piece of history1 the most unpardonable and the one which had most serious consequences seems to me to be this3 that ,challis never made the most casual inquiry as to the result of the visit to ,greenwich which he himself had directed ,adams to make4 ,i am judging him to some extent by default2 because ,i assume the facts from lack of evidence to the contrary3 but it seems practically certain that after sending this young man to see ,airy on this important topic1 ,challis thereupon washed his hands of all responsibility so completely that he never even took the trouble to inquire on his return1 ,well6 how did you get on8 ,what did the ,astronomer ,royal say8 ,had he put this simple question1 which scarcely required the initiative of a machine1 and learnt in consequence1 as he must have done1 that the sensitive young man thought ,airy's question trivial1 and did not propose to answer it1 ,i think we might have trusted events to right themselves4 ,even ,challis might have been trusted to reply1 ,oh6 but you must answer the ,astronomer ,royal's question3 you may think it stupid1 but you had better answer it politely1 and show him that you know what you are about4 ,it is unprofitable to pursue speculation further2 this did not happen1 and something else did4 ,but ,i have always felt that my old ,university made a scapegoat of the wrong man in venting its fury upon ,airy1 when the real culprit was among themselves1 and was the man they had themselves chosen to represent astronomy4 ,he was presumably the best they had2 but if they had no one better than this1 they should not have been surprised1 and must not complain1 if things went wrong4 ,if a ,university is ambitious of doing great things1 it must take care to see that there are men of ability and initiative in the right places4 ,this is a most difficult task in any case1 and we require all possible incentives towards it4 ,to blink the facts when a weak spot is mercilessly exposed by the loss of a great opportunity is to lose one kind of incentive1 and perhaps not the least valuable4 ,sidenote3 ,curious difference between actual and supposed planet4 ,sidenote3 ,professor ,peirce's contention that the discovery was a mere accident4 ,sidenote3 ,the explanation4 ,let us now turn to some curious circumstances attending this remarkable discovery of a planet by mathematical investigation1 of which there are several4 ,the first is1 that although ,neptune was found so near the place where it was predicted1 its orbit1 after discovery1 proved to be very different from that which ,adams and ,le ,verrier had supposed4 ,you will remember that both calculators assumed the distance from the sun1 in accordance with ,bode's ,law1 to be nearly twice that of ,uranus4 ,the actual planet was found to have a mean distance less than this by #be per cent41 an enormous quantity in such a case4 ,for instance1 if the supposed planet and the real were started round the sun together1 the real planet would soon be a long way ahead of the other1 and the ultimate disturbing effect of the two on ,uranus would be very different4 ,to explain the difference1 we must first recall a curious property of such disturbances4 ,when two planets are revolving1 so that one takes just twice or three times1 or any exact number of times1 as long to revolve round the sun as the other1 the usual mathematical expressions for the disturbing action of one planet on the other would assign an infinite disturbance1 which1 translated into ordinary language1 means that we must start with a fresh assumption1 for this state of things cannot persist4 ,if the period of one were a little longer than this critical value1 some of the mathematical expressions would be of contrary sign from those corresponding to a period a little shorter4 ,now it is curious that the supposed planet and the real had orbits on opposite sides of a critical value of this kind1 namely1 that which would assign a period of revolution for ,neptune exactly half that of ,uranus2 and it was pointed out in ,america by ,professor ,peirce that the effect of the planet imagined by ,adams and ,le ,verrier was thus totally different from that of ,neptune4 ,he therefore declared that the mathematical work had not really led to the discovery at all2 but that it had resulted from mere coincidence1 and this opinion--somewhat paradoxical though it was--found considerable support4 ,it was not replied to by ,adams until some thirty years later1 when a short reply was printed in ,liouville's ,journal4 ,the explanation is this3 the expressions considered by ,professor ,peirce are those representing the action of the planet throughout an indefinite past1 and did not enter into the problem1 which would have been precisely the same if ,neptune had been suddenly created in #afij2 while1 on the other hand1 if ,neptune had existed up till #afij 7the time when ,uranus was first observed1 although unknowingly71 and then had been destroyed1 there would have been no means of tracing its previous existence4 ,in past ages it had no doubt been perturbing the orbit of ,uranus1 and had effected large changes in it2 but if it had then been suddenly destroyed1 we should have had no means of identifying these changes4 ,there might have been instead of ,neptune another planet1 such as that supposed by ,adams and ,le ,verrier2 and its action in all past time would have been very different from that of ,neptune1 as is properly represented in the mathematical expressions which ,professor ,peirce considered4 ,in consequence the orbit of ,uranus in #afij would have been very different from the orbit as it was actually found2 but in either case the mathematicians ,adams and ,le ,verrier would have had to take it as they found it2 and the disturbing action which they considered in their calculations was the comparatively small disturbance which began in #afij and ended in #ahdf4 ,during this limited number of years the disturbance of the planet they imagined1 although not precisely the same as that of ,neptune1 was sufficiently like it to give them the approximate place of the planet4 ,still it is somewhat bewildering to look at the mathematical expressions for the disturbances as used by ,adams and ,le ,verrier1 when we can now compare with them the actual expressions to which they ought to correspond2 and one may say frankly that there seems to be no sort of resemblance4 ,recently a memorial of ,adams' work has been published by the ,royal ,astronomical ,society2 they have reproduced in their ,memoirs a facsimile of ,adams' ,,ms4 containing the first solution1 which he made in #ahdc in the ,long ,vacation after he had taken his degree1 and which would have given the place of ,neptune at that time with an error of #ae deg44 ,in an introduction describing the whole of the ,,mss41 written by ,professor ,r4 ,a4 ,sampson of ,durham1 it is shown how different the actual expressions for ,neptune's influence are from those used by ,adams1 and it is one of the curiosities of this remarkable piece of history that some of them seem to be actually in the wrong direction2 and others are so little alike that it is only by fixing our attention resolutely on the considerations above mentioned that we can realise that the analytical work did indeed lead to the discovery of the planet4 ,sidenote3 ,suggested elementary method for finding ,neptune illusory4 ,a second curiosity is that a mistaken idea should have been held by at least one eminent man 7,sir ,j4 ,herschel71 to the effect that it would have been possible to find the place of the planet by a much simpler mathematical calculation than that actually employed by ,adams or ,le ,verrier4 ,in his famous ,outlines of ,astronomy ,sir ,john ,herschel describes a simple graphical method1 which he declares would have indicated the place of the planet without much trouble4 ,concerning it ,i will here merely quote ,professor ,sampson's words3-- ,the conclusion is drawn that ,uranus arrived at a conjunction with the disturbing planet about #ahbb2 and this was the case4 ,plausible as this argument may seem1 it is entirely baseless4 ,for the maximum of perturbations depending on the eccentricities has no relation to conjunction1 and the others which depend upon the differences of the mean motions alone are of the nature of forced oscillations1 and conjunction is not their maximum or stationary position1 but their position of most rapid change4 ,professor ,sampson goes on to show that a more elaborate discussion seems quite as unpromising2 and he concludes that the refinements employed were not superfluous1 although it seems now clear that a different mode of procedure might have led more certainly to the required conclusion4 ,sidenote3 ,the evil influence of ,bode's ,law4 ,for the third curious point is that both calculators should have adhered so closely to ,bode's ,law4 ,if they had not had this guiding principle it seems almost certain that they would have made a better approximation to the place of the planet1 for instead of helping them it really led them astray4 ,we have already remarked that if two planets are at different distances from the sun1 however slight1 and if they are started in their revolution together1 they must inevitably separate in course of time1 and the amount of separation will ultimately become serious4 ,thus by assuming a distance for the planet which was in error1 however slight1 the calculators immediately rendered it impossible for themselves to obtain a place for the planet which should be correct for more than a very brief period4 ,professor ,sampson has given the following interesting lists of the dates at which ,adams' six solutions gave the true place of the planet and the intervals during which the error was within #e deg4 either way4 ,i4 ,,ii4 ,,iii4 ,,iv4 ,v4 ,,vi4 ,correct #ahbj #ahce #ahgb #ahcj #ahfa #ahef ,within -#e deg4 #ahab #ahbg #ahfe #ahac #ahae #ahbf #ahbg #ahdb #ahgg #ahff #ahga #ahfh ,now the date at which it was most important to obtain the correct place was #ahde or thereabouts when it was proposed to look for the planet2 but no special precaution seems to have been taken by either investigator to secure any advantage for this particular date4 ,criticising the procedure after the event 7and of course this is a very unsatisfactory method of criticism71 we should say that it would have been better to make several assumptions as regards the distance instead of relying upon ,bode's ,law2 but no one1 so far as ,i know1 has ever taken the trouble to write out a satisfactory solution of the problem as it might have been conducted4 ,such a solution would be full of interest1 though it could only have a small weight in forming our estimation of the skill with which the problem was solved in the first instance4 ,sidenote3 ,le ,verrier's erroneous limits4 ,fourthly1 we may notice a very curious point4 ,le ,verrier went to some trouble not only to point out the most likely place for the planet1 but to indicate limits outside which it was not necessary to look4 ,this part of his work is specially commented upon with enthusiasm by ,airy1 and ,i will reproduce what he says4 ,it is rather technical perhaps1 but those who cannot follow the mathematics will be able to appreciate the tone of admiration4 ,sidenote3 ,the visible disc4 ,m4 ,le ,verrier then enters into a most ingenious computation of the limits between which the planet must be sought4 ,the principle is this3 assuming a time of revolution1 all the other unknown quantities may be varied in such a manner that though the observations will not be so well represented as before1 yet the errors of observation will be tolerable4 ,at last1 on continuing the variation of elements1 one error of observation will be intolerably great4 ,then1 by varying the elements in another way1 we may at length make another error of observation intolerably great2 and so on4 ,if we compute1 for all these different varieties of elements1 the place of the planet for #ahdg1 its locus will evidently be a discontinuous curve or curvilinear polygon4 ,if we do the same thing with different periodic times1 we shall get different polygons2 and the extreme periodic times that can be allowed will be indicated by the polygons becoming points4 ,these extreme periodic times are #bjg and #bcc years4 ,if now we draw one grand curve1 circumscribing all the polygons1 it is certain that the planet must be within that curve4 ,in one direction1 ,m4 ,le ,verrier found no difficulty in assigning a limit2 in the other he was obliged to restrict it1 by assuming a limit to the eccentricity4 ,thus he found that the longitude of the planet was certainly not less than #cba deg41 and not greater than #cce deg4 or #cde deg41 according as we limit the eccentricity to #j4abe or #j4b4 ,and if we adopt #j4abe as the limit1 then the mass will be included between the limits #j4jjjjg and #j4jjjba2 either of which exceeds that of ,uranus4 ,from this circumstance1 combined with a probable hypothesis as to the density1 ,m4 ,le ,verrier concluded that the planet would have a visible disk1 and sufficient light to make it conspicuous in ordinary telescopes4 ,m4 ,le ,verrier then remarks1 as one of the strong proofs of the correctness of the general theory1 that the error of radius vector is explained as accurately as the error of longitude4 ,and finally1 he gives his opinion that the latitude of the disturbing planet must be small4 ,my analysis of this paper has necessarily been exceedingly imperfect1 as regards the astronomical and mathematical parts of it2 but ,i am sensible that1 in regard to another part1 it fails totally4 ,i cannot attempt to convey to you the impression which was made on me by the author's undoubting confidence in the general truth of his theory1 by the calmness and clearness with which he limited the field of observation1 and by the firmness with which he proclaimed to observing astronomers1 ',look in the place which ,i have indicated1 and you will see the planet well4' ,since ,copernicus declared that1 when means should be discovered for improving the vision1 it would be found that ,venus had phases like the moon1 nothing 7in my opinion7 so bold1 and so justifiably bold1 has been uttered in astronomical prediction4 ,it is here1 if ,i mistake not1 that we see a character far superior to that of the able1 or enterprising1 or industrious mathematician2 it is here that we see the philosopher4 ,sidenote3 ,peirce's views of the limits4 ,but now this process of limitation was faulty and actually misleading4 ,let us compare what is said about it by ,professor ,peirce a little later4 ,guided by this principle1 well established1 and legitimate1 if confined within proper limits1 ,m4 ,le ,verrier narrowed with consummate skill the field of research1 and arrived at two fundamental propositions1 namely3-- #ast4 ,that the mean distance of the planet cannot be less than #ce or more than #cg4i4 ,the corresponding limits of the time of sidereal revolution are about #bjg and #bcc years4 #bnd4 ',that there is only one region in which the disturbing planet can be placed in order to account for the motions of ,uranus2 that the mean longitude of this planet must have been1 on ,january #a1 #ahjj1 between #bdc deg4 and #beb deg44' ',neither of these propositions is of itself necessarily opposed to the observations which have been made upon ,neptune1 but the two combined are decidedly inconsistent with observation4 ,it is impossible to find an orbit1 which1 satisfying the observed distance and motion1 is subject to them4 ,if1 for instance1 a mean longitude and time of revolution are adopted according with the first1 the corresponding mean longitude in #ahjj must have been at least #dj deg4 distant from the limits of the second proposition4 ,and again1 if the planet is assumed to have had in #ahjj a mean longitude near the limits of the second proposition1 the corresponding time of revolution with which its motions satisfy the present observations cannot exceed #agj years1 and must therefore be about #dj years less than the limits of the first proposition4' ,neptune cannot1 then1 be the planet of ,m4 ,le ,verrier's theory1 and cannot account for the observed perturbations of ,uranus under the form of the inequalities involved in his analysis--7,proc4 ,amer4 ,acad4 ,i41 #ahdf-ahdh1 p4 #ff74 ,sidenote3 ,newcomb's criticism4 ,at the time when ,professor ,peirce wrote1 the orbit of ,neptune was not sufficiently well determined to decide whether one of the two limitations might not be correct1 though he could see that they could not both be right1 and we now know that they are both wrong4 ,the mean distance of ,neptune is #cj1 which does not lie between #ce and #cg4i2 and the longitude in #ahjj was #bbe deg41 which does not lie between #bdc deg4 and #beb deg44 ,the ingenious process which ,airy admired and which ,peirce himself calls consummately skilful was wrong in principle4 ,as ,professor ,newcomb has said1 the error was the elementary one that1 instead of considering all the elements simultaneously variable1 ,le ,verrier took them one at a time1 considering the others as fixed1 and determining the limits between which each could be contained on this hypothesis4 ,no solver of least square equations at the present day ought to make such a blunder4 ,of course one trouble in ,le ,verrier's demonstration1 had he attempted a rigorous one1 would have been the impossibility of forming the simultaneous equations expressive of possible variations of all the elements4 ,sidenote3 ,element of good fortune4 ,sidenote3 ,the map used by ,galle4 ,the account of ,le ,verrier's limits by ,professor ,peirce1 though it exhibits the error with special clearness1 is a little unfair to ,le ,verrier in one point4 ,if1 instead of taking the limits for the date #ahjj1 we take them for #ahdf 7when the search for ,neptune was actually made71 we shall find that they do include the actual place of the planet1 as ,airy found4 ,the erroneous mean motion of ,le ,verrier's planet allowed of his being right at one time and wrong at another2 and ,airy examined the limits under favourable conditions1 which explains his enthusiasm4 ,but we can scarcely wonder that ,professor ,peirce came to the conclusion that the planet discovered was not the one pointed out by ,le ,verrier1 and had been found by mere accident4 ,and all these circumstances inevitably contribute to a general impression that the calculators had a large element of good fortune to thank for their success4 ,nor need we hesitate to make this admission1 for there is an element of good fortune in all discoveries4 ,to look no further than this--if a man had not been doing a particular thing at a particular time1 as he might easily not have been1 most discoveries would never have been made4 ,if ,sir ,william ,herschel had not been looking at certain small stars for a totally different purpose he would never have found ,uranus2 and no one need hesitate to admit the element of chance in the finding of ,neptune4 ,it is well illustrated by a glance at the map which1 as has been remarked1 ,galle used to compare with the sky on the night when he made the actual discovery4 ,the planet was found down near the bottom corner of the map1 and since the limits assigned for its place might easily have varied a few degrees one way or the other1 it might easily have been off the map2 in which case1 it is probable that the search would not have been successful1 or at any rate that success would have been delayed4 ,illustration3 ,v4--,,corner ,,of ,,the ,,berlin ,,map1 ,,by ,,the ,,use ,,of ,,which ,,galle ,,found ,,neptune4 ,sidenote3 ,every one made mistakes4 ,thus1 it is a most remarkable feature of the discovery of ,neptune that mistakes were made by almost every one concerned1 however eminent4 ,airy made a mistake in regarding the question of the ,radius ,vector as of fundamental importance2 ,sir ,j4 ,herschel was wrong in describing an elementary method which he considered might have found the planet2 ,professor ,peirce was wrong in supposing that the actual and the supposed planet were essentially different in their action on ,uranus2 ,le ,verrier was wrong in assigning limits outside which it was not necessary to look when the actual planet was outside them2 ,adams was more or less wrong in thinking that the eccentricity of the new planet could be found from the material already at disposal of man4 ,both ,adams and ,le ,verrier gave far too much importance to ,bode's ,law4 ,to review a piece of history of this kind and note the mistakes of such men is certainly comforting1 and need not in any way lessen our admiration4 ,in the case of the investigators themselves1 much may be set down to excitement in the presence of a possible discovery4 ,professor ,sampson has provided us with a small but typical instance of this fact4 ,when ,adams had carried through all his computations for finding ,neptune1 and was approaching the actual place of the planet1 he1 who could carry through fabulous computations without error1 for the first time wrote down a wrong figure4 ,the mistake was corrected upon the ,,ms41 probably as soon as made1 but no doubt betrays the excitement which the great worker could not repress at this critical moment4 ,there is a tradition that1 similarly1 when the mighty ,newton was approaching the completion of his calculations to verify the ,law of ,gravitation1 his excitement was so great that he was compelled to assign to a friend the task of finishing them4 ,finally1 we may remark how the history of the discovery of ,neptune again illustrates the difficulty of formulating any general principles for guiding scientific work4 ,sometimes it is well to follow the slightest clue1 however imperfectly understood2 at other times we shall do better to refuse such guidance4 ,bode's ,law pointed to the existence of minor planets1 and might conceivably have helped in finding ,uranus3 but by trusting to it in the case of ,neptune1 the investigators were perilously near going astray4 ,sometimes it is better to follow resolutely the work in hand whatever it may be1 shutting one's ears to other calls2 but ,airy and ,challis lost their opportunities by just this course of action4 ,the history of science is full of such contradictory experiences2 and the only safe conclusion seems to be that there are no general rules of conduct for discovery4 ,,chapter ,,iii ,,bradley',s ,,discoveries ,,of ,,the ,,aberration ,,of ,,light ,,and ,,of ,,the ,,nutation ,,of ,,the ,,earth',s ,,axis ,sidenote3 ,biographical method adopted4 ,in examining different types of astronomical discovery1 we shall find certain advantages in varying to some extent the method of presentation4 ,in the two previous chapters our opportunities for learning anything of the life and character of those who made the discoveries have been slight2 but ,i propose to adopt a more directly biographical method in dealing with ,bradley's discoveries1 which are so bound up with the simple earnestness of his character that we could scarcely appreciate their essential features properly without some biographical study4 ,but the record of his life apart from his astronomical work is not in any way sensational2 indeed it is singularly devoid of incident4 ,he had not even a scientific quarrel4 ,there was scarcely a man of science of that period who had not at least one violent quarrel with some one1 save only ,bradley1 whose gentle nature seems to have kept him clear of them all4 ,judged by ordinary standards his life was uneventful3 and yet it may be doubted whether1 to him who lived it1 that life contained one dull moment4 ,incident came for him in his scientific work3 in the preparation of apparatus1 the making of observations1 above all in the hard-thinking which he did to get at the clue which would explain them2 and after reviewing his biography1#b ,i think we shall be inclined to admit that if ever there was a happy life1 albeit one of unremitting toil1 it was that of ,james ,bradley4 ,sidenote3 ,bradley's birth and early life4 ,sidenote3 ,brief clerical career4 ,he was born at ,sherbourn1 in ,gloucestershire1 in #afic4 ,we know little of his boyhood except that he went to the ,grammar ,school at ,northleach1 and that the memory of this fact was preserved at the school in #ahcb when ,rigaud was writing his memoir4 ,the school is at present shut up for want of funds to carry it on2 and all inquiries ,i have made have failed to elicit any trace of this memory4 ,similarly we know little of his undergraduate days at ,oxford1 except that he entered as a commoner at ,balliol in #agaj1 took his ,b4,a4 in the regular course in #agad1 and his ,m4,a4 in #agag4 ,as a career he chose the ,church1 being ordained in #agai1 and presented to the vicarage of ,bridstow in ,monmouthshire2 but he only discharged the duties of vicar for a couple of years1 for in #agba he returned to ,oxford as ,professor of ,astronomy1 an appointment which involved the resignation of his livings2 and so slight was this interruption to his career as an astronomer that we may almost disregard it1 and consider him as an astronomer from the first4 ,but to guard against a possible misconception1 let me say that ,bradley entered on a clerical career in a thoroughly earnest spirit2 to do otherwise would have been quite foreign to his nature4 ,when vicar of ,bridstow he discharged his duties faithfully towards that tiny parish1 and moreover was so active in his uncle's parish of ,wansted that he left the reputation of having been curate there1 although he held no actual appointment4 ,and thirty years later1 when he was ,astronomer ,royal and resident at ,greenwich1 and when the valuable vicarage of ,greenwich was offered to him by the ,chancellor of the ,exchequer1 he honourably refused the preferment1 because the duty of a pastor was incompatible with his other studies and necessary engagements4 ,sidenote3 ,learnt astronomy not at ,oxford1 but from his uncle1 ,james ,pound4 ,sidenote3 ,pound a first-rate observer4 ,but now let us turn to ,bradley's astronomical education4 ,i must admit1 with deep regret1 that we cannot allow any of the credit of it to ,oxford4 ,there was a great astronomer in ,oxford when ,bradley was an undergraduate1 for ,edmund ,halley had been appointed ,savilian ,professor of ,geometry in #agjc1 and had immediately set to work to compute the orbits of comets1 which led to his immortal discovery that some of these bodies return to us again and again1 especially the one which bears his name--,halley's ,comet--and returns every seventy-five years1 being next expected about #aiaj4 ,but there is no record that ,bradley came under ,halley's teaching or influence as an undergraduate4 ,in later years the two men knew each other well1 and it was ,halley's one desire towards the close of his life that ,bradley should succeed him as ,astronomer ,royal at ,greenwich2 a desire which was fulfilled in rather melancholy fashion1 for ,halley died without any assurance that his wish would be gratified4 ,but ,bradley got no astronomical teaching at ,oxford either from ,halley or others4 ,the art of astronomical observation he learnt from his maternal uncle1 the ,rev4 ,james ,pound1 ,rector of ,wansted1 in ,essex4 ,he is the man to whom we owe ,bradley's training and the great discoveries which came out of it4 ,he was1 ,i am glad to say1 an ,oxford man too2 very much an ,oxford man2 for he seems to have spent some thirteen years there migrating from one ,hall to another4 ,his record indeed was such as good tutors of colleges frown upon2 for it was seven years before he managed to take a degree at all2 and he could not settle to anything4 ,after ten years at ,oxford he thought he would try medicine2 after three years more he gave it up and went out in #agjj as chaplain to the ,east ,indies4 ,but he seems to have been a thoroughly lovable man1 for news was brought of him four years later that he had a mind to come home1 but was dissuaded by the ,governor saying that if ,dr4 ,pound goes1 ,i and the rest of the ,company will not stay behind4 ,soon afterwards the settlement was attacked in an insurrection1 and ,pound was one of the few who escaped with his life1 losing however all the property he had gradually acquired4 ,he returned to ,england in #agjf1 and was presented to the living of ,wansted2 married twice1 and ended his days in peace and fair prosperity in #agbd4 ,such are briefly the facts about ,bradley's uncle1 ,james ,pound2 but the most important of all remains to be told--that somehow or other he had learnt to make first-rate astronomical observations1 how or when is not recorded2 but in #agai he was already so skilled that ,sir ,isaac ,newton made him a present of fifty guineas for some observations2 and repeated the gift in the following year2 and even three years before this we find ,halley writing to ask for certain observations from ,mr4 ,pound4 ,sidenote3 ,bradley worked with him4 ,with this excellent man ,bradley used frequently to stay4 ,to his nephew he seems to have been more like a father than an uncle4 ,when his nephew had smallpox in #agag1 he nursed him through it2 and he supplemented from his own pocket the scanty allowance which was all that ,bradley's own father could afford4 ,but what concerns us most is that he fostered1 if he did not actually implant1 a love of astronomical observation in his nephew4 ,the two worked together1 entering their observations one after the other on the same paper2 and it was to the pair of them together1 rather than to the uncle alone1 that ,newton made his princely presents1 and ,halley wrote for help in his observations4 ,there seems to be no doubt that the uncle and nephew were about this time the best astronomical observers in the world4 ,there was no rivalry between them1 and therefore there is no need to discuss whether the partnership was one of equal merit on both sides2 but it is interesting to note that it probably was4 ,the ability of ,pound was undoubted2 many were keenly desirous that he1 and not his nephew1 should be elected to the ,oxford ,chair in #agba1 but he felt unequal to the duties at his advanced age4 ,on the other hand1 when ,bradley lost his uncle's help1 there was no trace of faltering in his steps to betray previous dependence on a supporting or guiding hand4 ,he walked erect and firm1 and trod paths where even his uncle might not have been able to follow4 ,sidenote3 ,the work done by ,pound and ,bradley4 ,sidenote3 ,use of very long telescopes4 ,sidenote3 ,reason for great length4 ,a few instances will suffice to show the kind of observations made by this notable firm of ,pound and ,bradley4 ,they observed the positions of the fixed stars and nebulae3 these being generally the results required by ,halley and ,newton4 ,they also observed the places of the planets among the stars1 and especially the planet ,mars1 and determined its distance from the ,earth by the method of parallax1 thus anticipating the modern standard method of finding the ,sun's distance2 and though with their imperfect instruments they did not obtain a greater accuracy than #a in #aj1 still this was a great advance on what had been done before1 and excited the wonder and admiration of ,halley4 ,they also paid some attention to double stars1 and did a great deal of work on ,jupiter's satellites4 ,we might profitably linger over the records of these early years1 which are full of interest1 but we must press on to the time of the great discoveries1 and we will dismiss them with brief illustrations of three points3 ,bradley's assiduity1 his skill in calculation1 and his wonderful skill in the management of instruments4 ,of his assiduity an example is afforded by his calculations of the orbits of two comets which are still extant4 ,one of them fills thirty-two pages of foolscap1 and the other sixty2 and it must be remembered that the calculations themselves were quite novel at that time4 ,of his skill in calculation1 apart from his assiduity1 we have a proof in a paper communicated to the ,royal ,society rather later 7#agbf71 where he determines the longitudes of ,lisbon and ,new ,york from the eclipses of ,jupiter's satellites1 using observations which were not simultaneous1 and had therefore to be corrected by an ingenious process which ,bradley devised expressly for this purpose4 ,and finally1 his skill in the management of instruments is shown by his measuring the diameter of the planet ,venus with a telescope actually #bab-a_/d feet in length4 ,it is difficult for us to realise in these days what this means2 even the longest telescope of modern times does not exceed #ajj feet in length1 and it is mounted so conveniently with all the resources of modern engineering1 in the shape of rising floors1 c41 that the management of it is no more difficult than that of a #aj-;foot telescope4 ,but ,bradley had no engineering appliances beyond a pole to hold up one end of the telescope and his own clever fingers to work the other2 and he managed to point the unwieldy weapon accurately to the planet1 and measure the diameter with an exactness which would do credit to modern times4 ,a few words of explanation may be given why such long telescopes were used at all4 ,the reason lay in the difficulty of getting rid of coloured images1 due to the composite character of white light4 ,whenever we use a single lens to form an image1 coloured fringes appear4 ,nowadays we know that by making two lenses of different kinds of glass and putting them together1 we can practically get rid of these coloured fringes2 but this discovery had not been made in ,bradley's time4 ,the only known ways of dealing with the evil then were to use a reflecting telescope like ,newton and ,gregory1 or if a lens was used1 to make one of very great focal length2 and hence the primary necessity for these very long telescopes4 ,they had another advantage in producing a large image1 or they would probably have given way to the reflector4 ,this advantage is gradually bringing them back into use1 and perhaps in the eclipse of #aije we may use a telescope as long as ,bradley's2 but we shall not use it as he did in any case4 ,it will be laid comfortably flat on the ground1 and the rays of light reflected into it by a coelostat4 ,sidenote3 ,bradley appointed at ,oxford1 but continues to work at ,wansted4 ,in #agba ,bradley was appointed to the ,savilian ,professorship of ,astronomy at ,oxford1 vacant by the death of ,dr4 ,john ,keill4 ,once it became clear that there was no chance of securing his uncle for this position1 ,bradley himself was supported enthusiastically by all those whose support was worth having1 especially by the ,earl of ,macclesfield1 who was then ,lord ,chancellor2 by ,martin ,foulkes1 who was afterwards the ,president of the ,royal ,society2 and by ,sir ,isaac ,newton himself4 ,he was accordingly elected on ,october #ca1 #agba1 and forthwith resigned his livings4 ,his resignation of the livings was necessitated by a definite statute of the ,university relating to the ,professorship1 and not by the existence of any very onerous duties attaching to it2 indeed such duties seem to have been conspicuously absent1 and after ,bradley's election he passed more time than ever with his uncle in ,wansted1 making the astronomical observations which both loved2 for there was not the vestige of an observatory in ,oxford4 ,his uncle's death in #agbd interrupted the continuity of these joint observations1 and by an odd accident prepared the way for ,bradley's great discovery4 ,he was fain to seek elsewhere that companionship in his work which had become so essential to him1 and his new friend gave a new bent to his observations4 ,sidenote3 ,samuel ,molyneux4 ,sidenote3 ,attempts to find stellar parallax4 ,samuel ,molyneux was a gentleman of fortune much attached to science1 and particularly to astronomy1 who was living about this time at ,kew4 ,he was one of the few1 moreover1 who are not content merely to amuse themselves with a telescope1 but had the ambition to do some real earnest work1 and the courage to choose a problem which had baffled the human race for more than a century4 ,the theory of ,copernicus1 that the earth moved round the sun1 necessitated a corresponding apparent change in the places of the stars1 one relatively to another2 and it was a standing difficulty in the way of accepting this theory that no such change could be detected4 ,in the old days before the telescope it was perhaps easy to understand that the change might be too small to be noticed1 but the telescope had made it possible to measure changes of position at least a hundred times as small as before1 and still no parallax1 as the astronomical term goes1 could be found for the stars4 ,the observations of ,galileo1 and the measures of ,tycho ,brahe1 as reduced to systematic laws by ,kepler1 and finally by the great ,newton1 made it clear that the ,copernican theory was true3 but no one had succeeded in proving its truth in this particular way4 ,samuel ,molyneux must have been a man of great courage to set himself to try to crack this hard nut2 and we can understand the attraction which his enterprise must have had for ,bradley1 who had just lost the beloved colleague of many courageous astronomical undertakings4 ,his co-operation seems to have been welcomed from the first2 his help was invited and freely given in setting up the instrument1 and he fortunately had the leisure to spend considerable time at ,kew making the observations with ,molyneux1 just as he had been wont to observe with his uncle4 ,i must now briefly explain what these observations were4 ,there is a bright star gamma ,draconis1 which passes almost directly overhead in the latitude of ,london4 ,its position is slowly changing owing to the precession of the equinoxes1 but for two centuries it has been1 and is still1 under constant observation by ,london astronomers owing to this circumstance1 that it passes directly overhead1 and so its position is practically undisturbed by the refraction of our atmosphere4 ,sidenote3 ,the instrument4 ,sidenote3 ,expected results4 ,it was therefore thought at the time that1 there being no disturbance from refraction1 the disturbance from precession being accurately known1 and there being nothing else to disturb the position but parallax 7the apparent shift due to the earth's motion which it was desirable to find71 this star ought to be a specially favourable object for the determination of parallax4 ,indeed it had been announced many years before by ,hooke that its parallax had been found2 but his observations were not altogether satisfactory1 and it was with a view of either confirming them or seeing what was wrong with them that ,molyneux and ,bradley started their search4 ,they set up a much more delicate piece of apparatus than ,hooke had employed4 ,it was a telescope #bd feet long pointed upwards to the star1 and firmly attached to a large stack of brick chimneys within the house4 ,the telescope was not absolutely fixed1 for the lower end could be moved by a screw so as to make it point accurately to the star1 and a plumb-line showed how far it was from the vertical when so pointing4 ,hence if the star changed its position1 however slightly1 the reading of this screw would show the change4 ,now1 before setting out on the observations1 the observers knew what to expect if the star had a real parallax2 that is to say1 they knew that the star would seem to be farthest south in ,december1 farthest north in ,june1 and at intermediate positions in ,march and ,september2 though they did not know how much farther south it would appear in ,december than in ,june--this was exactly the point to be decided4 ,illustration3 ,,fig4 #b4 ,sidenote3 ,unexpected results4 ,the reason of this will be clear from ,fig4 #b4 ,remark1 however1 that this figure and the corresponding figure #d do not represent the case of ,bradley's star1 gamma ,draconis3 another star has been chosen which simplifies the diagram1 though the principle is essentially the same4 ,let ,a ,b ,c ,d represent the earth's orbit1 the earth being at ,a in ,june1 at ,b in ,september1 and so on1 and let ,k represent the position of the star on the line ,d ,b4 ,then in ,march and ,september it will be seen from the earth in the same direction1 namely1 ,d ,b ,k2 but the directions in which it is seen in ,june and ,december1 viz4 ,a ,k and ,c ,k1 are inclined in opposite ways to this line4 ,the farther away the star is1 the less will this inclination or parallax be2 and the star is actually so far away that the inclination can only be detected with the utmost difficulty3 the lines ,c ,k and ,a ,k are sensibly parallel to ,d ,b ,k4 ,but ,bradley did not know this2 it was just this point which he was to examine1 and he expected the greatest inclination in one direction to be in ,december4 ,accordingly when a few observations had been made on ,december #c1 #e1 #aa1 and #ab it was thought that the star had been caught at its most southerly apparent position1 and might be expected thereafter to move northwards1 if at all4 ,but when ,bradley repeated the observation on ,december #ag1 he found to his great surprise that the star was still moving southwards4 ,here was something quite new and unexpected1 and such a keen observer as ,bradley was at once on the alert4 ,he soon found that the changes in the position of the star were of a totally unexpected character4 ,instead of the extreme positions being occupied in ,june and ,december1 they were occupied in ,march and ,september1 just midway between these4 ,and the range in position was quite large1 about #dj--not a quantity which could have been detected in the days before telescopes1 but one which was unmistakable with an instrument of the most moderate measuring capacity4 ,sidenote3 ,tentative explanations4 ,what1 then1 was the cause of this quite unforeseen behaviour on the part of the star8 ,the first thought of the observers was that something might be wrong with their instrument1 and it was carefully examined1 but without result4 ,the next was that the apparent movement was in the plumb-line1 the line of reference4 ,if the whole earth1 instead of carrying its axis round the sun in a constant direction1 were to be executing an oscillation1 then all our plumb-lines would oscillate1 and when the direction of a star like gamma ,draconis was compared with that of the plumb-line it would seem to vary1 owing actually to the variation in the plumb-line4 ,the earth might have a motion of this kind in two ways1 which it will be necessary for us to distinguish1 and the adopted names for them are nutation of the axis and variation of latitude respectively4 ,in the case of nutation the ,north ,pole remains in the same geographical position1 but points to a different part of the heavens4 ,the variation of latitude1 on the other hand1 means that the ,north ,pole wanders about on the earth itself4 ,we shall refer to the second phenomenon more particularly in the sixth chapter4 ,sidenote3 ,nutation8 ,sidenote3 ,anomalous refraction4 ,but it was the first kind of change1 the nutation1 which ,bradley suspected2 and very early in the series of observations he had already begun to test this hypothesis4 ,if it was not the star1 but the earth and the plumb-line1 which were in motion1 then other stars ought to be affected4 ,the telescope had been deliberately restricted in its position to suit gamma ,draconis2 but since the stars circle round the ,pole1 if we draw a narrow belt in the heavens with the ,pole as centre1 and including gamma ,draconis1 the other stars included would make the same circuit1 preceding or following gamma ,draconis by a constant interval4 ,most of them would be too faint for observation with ,bradley's telescope2 but there was one bright enough to be observed1 which also came within its limited range1 and it was promptly put under surveillance when a nutation of the earth's axis was suspected4 ,careful watching showed that it was not affected in the same way as gamma ,draconis1 and hence the movement could not be in the plumb-line4 ,was there1 then1 after all1 some effect of the earth's atmosphere which had been overlooked8 ,we have already remarked that since the star passes directly overhead there should be practically no refraction2 and this assumption was made by ,molyneux and ,bradley in choosing this particular star for observation4 ,it follows at once1 if we assume that the atmosphere surrounds the earth in spherical layers4 ,but perhaps this was not so8 ,perhaps1 on the contrary1 the atmosphere was deformed by the motion of the earth1 streaming out behind her like the smoke of a moving engine8 ,no possibility must be overlooked if the explanation of this puzzling fact was to be got at4 ,illustration3 ,,fig4 #c4 ,the way in which a deformation of the atmosphere might explain the phenomenon is best seen by a diagram4 ,first1 it must be remarked that rays of light are only bent by the earth's atmosphere1 or refracted1 if they enter it obliquely4 ,if the atmosphere were of the same density throughout1 like a piece of glass1 then a vertical ray of light1 ,a ,b 7see ,fig4 #c71 entering the atmosphere at ,b would suffer no bending or refraction1 and a star shining from the direction ,a ,b would be seen truly in that direction from ,c4 ,but an oblique ray1 ,d ,e1 would be bent on entering the atmosphere at ,e along the path ,,ef1 and a star shining along ,d ,e would appear from ,f to be shining along the dotted line ,g ,e ,f4 ,the atmosphere is not of the same density throughout1 but thins out as we go upwards from the earth2 and in consequence there is no clear-cut surface1 ,b ,e1 and no sudden bending of the rays as at ,e3 they are gradually bent at an infinite succession of imaginary surfaces4 ,but it still remains true that there is no bending at all for vertical rays2 and of oblique rays those most oblique are most bent4 ,illustration3 ,,fig4 #d4 ,now1 suppose the atmosphere of the earth took up1 owing to its revolution round the sun1 an elongated shape like that indicated in diagram #d1 and suppose the star to be at a great distance away to the right of the diagram4 ,when the earth is in the position labelled ,june1 the light would fall vertically on the nose of the atmosphere at ,a1 and there would be no refraction4 ,similarly in ,december the light would fall at ,c on the stern1 also vertically1 and there would be no refraction4 ,the rays from the distant star in ,december are to be taken as sensibly parallel to those received in ,june1 notwithstanding that the earth is on the opposite side of the sun1 as was remarked on p4 #ih4 ,but in ,march and ,september the rays would strike obliquely on the sides of the supposed figure1 and thus be bent in opposite directions1 as indicated by the dotted lines2 and the extreme positions would thus occur in ,march and ,september1 as had been observed4 ,the explanation thus far seems satisfactory enough4 ,but we have assumed the star to lie in the plane of the earth's orbit2 and the stars under observation by ,bradley did not lie in this plane1 nor did they lie in directions equally inclined to it4 ,making the proper allowance for their directions1 it was found impossible to fit in the facts with this hypothesis1 which had ultimately to be abandoned4 ,sidenote3 ,delay in finding real explanation4 ,sidenote3 ,bradley sets up another instrument at ,wansted4 ,sidenote3 ,finds the right clue4 ,sidenote3 ,a wind-vane on a boat4 ,it is remarkable to find that two or three years went by before the real explanation of this new phenomenon occurred to ,bradley1 and during this time he must have done some hard thinking4 ,we have all had experience of the kind of thinking if only in the guessing of conundrums4 ,we know the apparent hopelessness of the quest at the outset3 the racking of our brains for a clue1 the too frequent despair and giving it up1 and the simplicity of the answer when once it is declared4 ,but with scientific conundrums the expedient of giving it up is not available4 ,we must find the answer for ourselves or remain in ignorance2 and though we may feel sure that the answer when found will be as simple as that to the best conundrum1 this expected simplicity does not seem to aid us in the search4 ,bradley was not content with sitting down to think3 he set to work to accumulate more facts4 ,molyneux's instrument only allowed of the observation of two stars1 gamma ,draconis and the small star above mentioned4 ,bradley determined to have an instrument of his own which should command a wider range of stars2 and by this time he was able to return to his uncle's house at ,wansted for this purpose4 ,his uncle had been dead for two or three years1 and the memory of the loss was becoming mellowed with time4 ,his uncle's widow was only too glad to welcome back her nephew1 though no longer to the old rectory1 and she allowed him to set up a long telescope1 even though he cut holes in her floor to pass it through4 ,the object-glass end was out on the roof and the eye end down in the coal cellar2 and accordingly in this coal cellar ,bradley made the observations which led to his immortal discovery4 ,he had a list of seventy stars to observe1 fifty of which he observed pretty regularly4 ,it may seem odd that he did not set up this new instrument at ,oxford1 but we find from an old memorandum that his professorship was not bringing him in quite ,l#adj a year1 and probably he was glad to accept his aunt's hospitality for reasons of economy4 ,by watching these different stars he gradually got a clear conception of the laws of aberration4 ,the real solution of the problem1 according to a well-authenticated account1 occurred to him almost accidentally4 ,we all know the story of the apple falling and setting ,newton to think about the causes of gravitation4 ,it was a similarly trivial circumstance which suggested to ,bradley the explanation which he had been seeking for two or three years in vain4 ,in his own words1 at last1 when he despaired of being able to account for the phenomena which he had observed1 a satisfactory explanation of them occurred to him all at once when he was not in search of it4 ,he accompanied a pleasure party in a sail upon the river ,thames4 ,the boat in which they were was provided with a mast which had a vane at the top of it4 ,it blew a moderate wind1 and the party sailed up and down the river for a considerable time4 ,dr4 ,bradley remarked that every time the boat put about the vane at the top of the boat's mast shifted a little1 as if there had been a slight change in the direction of the wind4 ,he observed this three or four times without speaking2 at last he mentioned it to the sailors1 and expressed his surprise that the wind should shift so regularly every time they put about4 ,the sailors told him that the wind had not shifted1 but that the apparent change was owing to the change in the direction of the boat1 and assured him that the same thing invariably happened in all cases4 ,this accidental observation led him to conclude that the phenomenon which had puzzled him so much was owing to the combined motion of light and of the earth4 ,to explain exactly what is meant we must again have recourse to a diagram2 and we may also make use of an illustration which has become classical4 ,illustration3 ,,fig4 #e4 ,sidenote3 ,analogy of rain4 ,if rain is falling vertically1 as represented by the direction ,a ,b2 and if a pedestrian is walking horizontally in the direction ,c ,d1 the rain will appear to him to be coming in an inclined direction1 ,e ,f1 and he will find it better to tilt his umbrella forwards4 ,the quicker his pace the more he will find it advisable to tilt the umbrella4 ,this analogy was stated by ,lalande before the days of umbrellas in the following words3 ,je suppose que1 dans un temps calme1 la pluie tombe perpendiculairement1 et qu'on soit dans une voiture ouverte sur le devant2 si la voiture est en repos1 on ne recoit pas la moindre goutte de pluie2 si la voiture avance avec rapidite1 la pluie entre sensiblement1 comme si elle avoit pris une direction oblique4 ,lalande's example1 modified to suit modern conditions1 has been generally adopted by teachers1 and in examinations candidates produce graphic pictures of the stationary1 the moderate-paced1 and the flying1 possessors of umbrellas4 ,sidenote3 ,aberration4 ,applying it to the phenomenon which it is intended to illustrate1 if light is being received from a star by an earth1 travelling across the direction of the ray1 the telescope 7which in this case represents the umbrella7 must be tilted forward to catch the light4 ,now on reference to ,fig4 #d it will be seen that the earth is travelling across the direction of rays from the star in ,march and ,september2 and in opposite directions in the two cases4 ,hence the telescope must be tilted a little1 in opposite directions1 to catch the light2 or1 in other words1 the star will appear to be farthest south in ,march1 farthest north in ,september4 ,and so at last the puzzle was solved1 and the solution was found1 as so often happens1 to be of the simplest kind2 so simple when once we know1 and so terribly hard to imagine when we don't6 ,it may comfort us in our struggles with minor problems to reflect that ,bradley manfully stuck to his problem for two or three years4 ,it was probably never out of his thoughts1 waking or sleeping2 when at work it was the chief object of his labours1 and when on a pleasure party he was ready to catch at the slightest clue1 in the motion of a wind-vane on a boat1 which might help him to the solution4 ,sidenote3 ,results of discovery4 ,the discovery of aberration made ,bradley famous at a bound4 ,oxford might well be proud of her two ,savilian ,professors at this time1 for they had both made world-famous discoveries--,halley that of the periodicity of comets1 and ,bradley of the aberration of light4 ,how different their tastes were and how difficult it would have been for either to do the work of the other6 ,bradley was no great mathematician1 and though he was quite able to calculate the orbit of a comet1 and carried on such work when ,halley left it1 it was probably not congenial to him4 ,halley1 on the other hand1 almost despised accurate observations as finicking4 ,be sure you are correct to a minute1 he was wont to say1 and the fractions do not so much matter4 ,with such a precept ,bradley would never have made his discoveries4 ,no quantity was too small in his eyes1 and no sooner was the explanation of aberration satisfactorily established than he perceived that though it would account for the main facts1 it would not explain all4 ,there was something left4 ,this is often the case in the history of science4 ,a few years ago it was thought that we knew the constitution of our air completely--oxygen1 nitrogen1 water vapour1 and carbonic acid gas2 but a great physicist1 ,lord ,rayleigh1 found that after extracting all the water and carbonic acid gas1 all the oxygen and all the nitrogen1 there was something left--a very minute residuum1 which a careless experimenter would have overlooked or neglected1 but which a true investigator like ,lord ,rayleigh saw the immense importance of4 ,he kept his eye on that something left1 and presently discovered a new gas which we now know as argon4 ,had he repeated the process1 extracting all the argon after the nitrogen1 he might have found by a scrutiny much more accurate still yet another gas1 helium1 which we now know to exist in extremely minute quantities in the air4 ,but meantime this discovery was made in another way4 ,sidenote3 ,still something to be explained4 ,sidenote3 ,probably nutation4 ,sidenote3 ,his nineteen years' campaign4 ,when ,bradley had extracted all the aberration from his observations he found that there was something left1 another problem to be solved and some more thinking to be done to solve it4 ,but he was now able to profit by his previous labours1 and the second step was made more easily than the first4 ,the residuum was not the parallax of which he had originally been in search1 for it did not complete a cycle within the year2 it was rather a progressive change from year to year4 ,but there was an important clue of another kind4 ,he saw that the apparent movements of all stars were in this case the same2 and he knew that a movement of this kind can be referred1 not to the stars themselves1 but to the plumb-line from which their directions are measured4 ,he had thought out the possible causes of such a movement of the plumb-line or of the earth itself1 and had realised that there might be a nutation which would go through a cycle in about nineteen years1 the period in which the moon's nodes revolve4 ,he was not mathematician enough to work out the cause completely1 but he saw clearly that to trace the whole effect he must continue the observations for nineteen years2 and accordingly he entered on this long campaign without any hesitation4 ,his instrument was still that in his aunt's house at ,wansted1 where he continued to live and make the observations for a few years1 but in #agcb he removed to ,oxford1 as we shall see1 and he must have made many journeys between ,wansted and ,oxford in the course of the remaining fifteen years during which he continued to trace out the effects of nutation4 ,his aunt too left ,wansted to accompany ,bradley to ,oxford1 and the house passed into other hands4 ,it is to the lasting credit of the new occupant1 ,mrs4 ,elizabeth ,williams1 that the great astronomer was allowed to go on and complete the valuable series of observations which he had commenced4 ,bradley was not lodged in her house2 he stayed with a friend close by on his visits to ,wansted1 but came freely in and out of his aunt's old home to make his observations4 ,how many of us are there who would cheerfully allow an astronomer to enter our house at any hour of the night to make observations in the coal-cellar6 ,it says much1 not only for ,bradley's fame1 but for his personal attractiveness1 that he should have secured this permission1 and that there should be no record of any friction during these fifteen years4 ,at the end of the whole series of nineteen years his conclusions were abundantly verified1 and his second great discovery of nutation was established4 ,honours were showered upon him1 and no doubt the gentle heart of ,mrs4 ,elizabeth ,williams was uplifted at the glorious outcome of her long forbearance4 ,sidenote3 ,residence at ,oxford4 ,but we may now turn for a few moments from ,bradley's scientific work to his daily life4 ,we have said that in #agcb1 after holding his professorship for eleven years1 he first went definitely to reside in ,oxford4 ,he actually had not been able to afford it previously4 ,his income was only ,l#adj a year1 and the statutes prevented him from holding a living3 so that he was fain to accept ,mrs4 ,pound's hospitable shelter4 ,but in #agbi an opportunity of adding to his income presented itself1 by giving lectures in experimental philosophy4 ,the observations on nutation were not like those on aberration3 he was not occupied day and night trying to find the solution3 he had practically made up his mind about the solution1 and the actual observations were to go on in a quiet methodical manner for nineteen years1 so that he now had leisure to look about him for other employment4 ,dr4 ,keill1 who had been ,professor of ,astronomy before ,bradley1 had attracted large classes to lectures1 not on astronomy1 but on experimental philosophy3 but had sold his apparatus and goodwill to ,mr4 ,whiteside1 of ,christ ,church1 one of the candidates who were disappointed by ,bradley's election4 ,in #agbi ,bradley purchased the apparatus from ,whiteside1 and began to give lectures in experimental philosophy4 ,his discovery of aberration had made him famous1 so that his classes were large from the first1 and paid him considerable fees4 ,suddenly therefore he changed his poverty for a comfortable income1 and he was able to live in ,oxford in one of two red brick houses in ,new ,college ,lane1 which were in those days assigned to the ,savilian ,professors 7now inhabited by ,new ,college undergraduates74 ,his aunt1 ,mrs4 ,pound1 to whom he was devotedly attached1 came with him1 and two of her nephews4 ,in his time of prosperity ,bradley was thus able to return the hospitality which had been so generously afforded him in times of stress4 ,sidenote3 ,astronomer ,royal at ,greenwich4 ,sidenote3 ,letter from ,earl of ,macclesfield4 ,before he completed his observations for nutation another great change in his fortunes took place4 ,in #agdb he was elected to succeed ,halley as ,astronomer ,royal4 ,it was ,halley's dying wish that ,bradley should succeed him1 and it is said that he was even willing to resign in his favour1 for his right hand had been attacked by paralysis1 and the disease was gradually spreading4 ,but he died without any positive assurance that his wish would be fulfilled4 ,the chief difficulty in securing the appointment of ,bradley seems to have been that he was the obvious man for the post in universal opinion4 ,it is not only my friendship for ,mr4 ,bradley that makes me so ardently wish to see him possessed of the position1 wrote the ,earl of ,macclesfield to the ,lord ,chancellor2 it is my real concern for the honour of the nation with regard to science4 ,for as our credit and reputation have hitherto not been inconsiderable amongst the astronomical part of the world1 ,i should be extremely sorry we should forfeit it all at once by bestowing upon a man of inferior skill and abilities the most honourable1 though not the most lucrative1 post in the profession 7a post so well filled by ,dr4 ,halley and his predecessor71 when at the same time we have amongst us a man known by all the foreign1 as well as our own astronomers1 not to be inferior to either of them1 and one whom ,sir ,isaac ,newton was pleased to call the best astronomer in ,europe4 ,and again1 ,as ,mr4 ,bradley's abilities in astronomical learning are allowed and confessed by all1 so his character in every respect is so well established1 and so unblemished1 that ,i may defy the worst of his enemies 7if so good and worthy a man have any7 to make even the lowest or most trifling objection to it4 ,after all1 the letter goes on1 it may be said if ,mr4 ,bradley's skill is so universally acknowledged1 and his character so established1 there is little danger of opposition1 since no competitor can entertain the least hope of success against him4 ,but1 my lord1 we live in an age when most men how little soever their merit may be1 seem to think themselves fit for whatever they can get1 and often meet with some people1 who by their recommendations of them appear to entertain the same opinion of them1 and it is for this reason that ,i am so pressing with your lordship not to lose any time4 ,such recommendations had1 however1 their effect3 the dreaded possibility of a miscarriage of justice was averted1 and ,bradley became the third ,astronomer ,royal1 though he did not resign his professorship at ,oxford4 ,halley1 ,bradley1 and ,bliss1 who were ,astronomers ,royal in succession1 all held the appointment along with one of the ,savilian professorships at ,oxford2 but since the death of ,bliss in #agfa1 the appointment has always gone to a ,cambridge man4 ,sidenote3 ,instruments very defective4 ,when ,bradley went to ,greenwich1 in ,june #agdb1 he was at first unable to do much from the wretched state in which he found the instruments4 ,halley was not a good observer3 his heart was not in the work1 and he had not taken the trouble to set the instruments right when they went wrong4 ,the counterpoises of that instrument which ought to have been the best in the world at the time rubbed against the roof so that the telescope could scarcely be moved in some positions3 and some of the screws were broken4 ,there was no proper means of illuminating the cross-wires1 and so on4 ,with care and patience ,bradley set all this right1 and began observations4 ,he had the good fortune to secure the help of his nephew1 ,john ,bradley1 as assistant1 and the companionship seems to have been as happy as that previous one of ,james ,bradley and his uncle ,pound4 ,john ,bradley was able to carry on the observations when his uncle was absent in ,oxford1 and the work the two got through together in the first year is 7in the words of ,bradley's biographer ,rigaud7 scarcely to be credited4 ,the transit observations occupy #agg folio pages1 and no less than #bee observations were taken on one night4 ,and at the same time1 it must be remembered1 ,bradley was still carrying on his nutation observations at ,wansted1 still lecturing at ,oxford1 and not content with all this1 began a course of experiments on the length of the seconds' pendulum4 ,truly a giant for hard work6 ,sidenote3 ,new instruments4 ,but1 in spite of his care in setting them right1 the instruments in the ,observatory were found to be hopelessly defective4 ,the history of the instruments at the ,royal ,observatory is a curious one4 ,when ,flamsteed was appointed the first ,astronomer ,royal he was given the magnificent salary of ,l#ajj a year1 and no instruments to observe with4 ,he purchased some instruments with his own money1 and at his death they were claimed by his executors4 ,hence ,halley1 the second ,astronomer ,royal1 found the ,observatory totally unprovided in this respect4 ,he managed to persuade the nation to furnish the funds for an equipment2 but ,halley1 though a man of great ability in other ways1 did not know a good instrument from a bad one2 so that ,bradley's first few years at the ,observatory were wasted owing to the imperfection of the equipment4 ,when this was fully realised he asked for funds to buy new instruments1 and such was the confidence felt in him that he got what he asked for without much difficulty4 ,more than ,l#ajjj1 a large sum for those days1 was spent under his direction1 the principal purchases being two quadrants for observation of the position of the stars1 one to the north and the other to the south4 ,with these quadrants1 which represented the perfection of such apparatus at that time1 ,bradley made that long and wonderful series of observations which is the starting-point of our knowledge of the movements of the stars4 ,the instruments are still in the ,royal ,observatory1 the more important of the two in its original position as ,bradley mounted it and left it4 ,sidenote3 ,work at ,greenwich4 ,it seems needless to mention his work as ,astronomer ,royal1 but ,i will give quite briefly a summary of what he accomplished1 and then recall a particular incident1 which shows how far ahead of his generation his genius for observation placed him4 ,the summary may be given as follows4 ,we owe to ,bradley-- #a4 ,a better knowledge of the movements of ,jupiter's satellites4 #b4 ,the orbits of several comets calculated directly from his own observations1 when such work was new and difficult4 #c4 ,experiments on the length of the pendulum4 #d4 ,the foundation of our knowledge of the refraction of our atmosphere4 #e4 ,considerable improvements in the tables of the moon1 and the promotion of the method for finding the longitude by lunar distances4 #f4 ,the proper equipment of our national ,observatory with instruments1 and the use of these to form the basis of our present knowledge of the positions and motions of the stars4 ,many men would consider any one of these six achievements by itself a sufficient title to fame4 ,bradley accomplished them all in addition to his great discoveries of aberration and nutation4 ,sidenote3 ,might have found variation of latitude4 ,and with a little more opportunity he might have added another great discovery which has shed lustre on the work of the last decade4 ,we said earlier in this chapter that the axis of the earth may move in one or two ways4 ,either it may point to a different star1 remaining fixed relatively to the earth1 as in the nutation which ,bradley discovered2 or it may actually change its position in the earth4 ,this second kind of movement was believed until twenty years ago not to exist appreciably2 but the work of ,kuestner and ,chandler led to the discovery that it did exist1 and its complexities have been unravelled1 and will be considered in the sixth chapter4 ,now a century and a half ago ,bradley was on the track of this variation of latitude4 ,his careful observations actually showed the motion of the pole1 as ,mr4 ,chandler has recently demonstrated2 and1 moreover1 ,bradley himself noticed that there was something unexplained4 ,once again there was a residuum after 7first7 aberration and 7next7 nutation had been extracted from the observations2 and with longer life he might have explained this residuum1 and added a third great discovery to the previous two4 ,or another coming after him might have found it2 but after the giant came men who could not tread in his footsteps1 and the world waited #aej years before the discrepancy was explained4 ,sidenote3 ,oxford's tardy recognition of ,bradley4 ,the attitude of our leading universities towards science and scientific men is of sufficient importance to justify another glance at the relations between ,bradley and ,oxford4 ,we have seen that ,oxford's treatment of ,bradley was not altogether satisfactory4 ,she left him to learn astronomy as he best could1 and he owes no teaching to her4 ,she made him ,professor of ,astronomy1 but gave him no observatory and a beggarly income which he had to supplement by giving lectures on a different subject4 ,but when he had disregarded these discouragements and made a name for himself1 ,oxford took her share in recognition4 ,he was created ,d4,d4 by diploma in #agdb2 and when his discovery of nutation was announced in #agdh1 and produced distinctions and honours of all kinds from over the world1 we are told that amidst all these distinctions1 wide as the range of modern science1 and permanent as its history1 there was one which probably came nearer his heart1 and was still more gratifying to his feeling than all4 ,lowth 7afterwards ,bishop of ,london71 a popular man1 an elegant scholar1 and possessed of considerable eloquence1 had in #agea to make his last speech in the ,sheldonian ,theatre at ,oxford as ,professor of ,poetry4 ,in recording the benefits for which the ,university was indebted to its benefactors1 he mentioned the names of those whom ,sir ,henry ,savile's foundation had established there3 ',what men of learning6 what mathematicians6 we owe to ,savile1 ,briggs1 ,wallis1 ,halley2 to ,savile we owe ,greaves1 ,ward1 ,wren1 ,gregory1 ,keill1 and one whom ,i will not name1 for posterity will ever have his name on its lips4' ,bradley was himself present2 there was no one in the crowded assembly on whom the allusion was lost1 or who did not feel the truth and justice of it2 all eyes were turned to him1 while the walls rung with shouts of heartfelt affection and admiration2 it was like the triumph of ,themistocles at the ,olympic games4 ,sidenote3 ,the study of residual phenomena4 ,these words of ,rigaud indicate the fame deservedly acquired by an earnest and simple-minded devotion to science3 but can we learn anything from the study of ,bradley's work to guide us in further research8 ,the chief lessons would seem to be that if we make a series of careful observations1 we shall probably find some deviation from expectation3 that we must follow up this clue until we have found some explanation which fits the facts1 not being discouraged if we cannot hit upon the explanation at once1 since ,bradley himself was puzzled for several years3 that after finding one vera causa1 and allowing for the effect of it1 the observations may show traces of another which must again be patiently hunted1 even though we spend nineteen years in the chase3 and that again we may have to leave the complete rectification of the observations to posterity4 ,but though we may admit the general helpfulness of these directions1 and that this patient dealing with residual phenomena seems to be a method capable of frequent application1 we cannot deduce any universal principle of procedure from them3 witness the difficulty of dealing with meteorological observations1 for instance4 ,it is not always possible to find any orderly arrangement of the residuals which will give us a clue to start with4 ,when such an arrangement is manifested1 we must certainly follow up the clue2 it would almost seem that no expense should be prohibitive1 since it is impossible to foresee the importance of the result4 ,,chapter ,,iv ,,accidental ,,discoveries ,sidenote3 ,the ,oxford new star found during work on ,astrographic ,chart4 ,in reviewing various types of astronomical discovery ,i have laid some stress upon the fact that they are1 generally speaking1 far from being accidental in character4 ,a new planet does not swim into our ken1 at any rate not usually1 but is found only after diligent search1 and then only by an investigator of acute vision1 or other special qualifications4 ,but this is1 of course1 not always the case4 ,some discoveries are made by the merest accident1 as we have had occasion to remark incidentally in the case of the minor planets2 and for the sake of completeness it is desirable to include among our types at least one case of such accidental discovery4 ,as1 however1 the selection is a little invidious1 ,i may perhaps be pardoned for taking the instance from my own experience1 which happens to include a case where one of those remarkable objects called new stars walked deliberately into a net spread for totally different objects4 ,there is the further reason for choosing this instance3 that it will afford me the opportunity of saying something about the special research in which we were actually engaged1 the work of mapping out the heavens by photography1 or1 as it has been called1 the ,astrographic ,chart--a great scheme of international co-operation by which it is hoped to leave as a legacy for future centuries a record of the state of the sky in our age4 ,such a record cannot be complete2 for however faint the stars included1 we know that there are fainter stars which might have been included had we given longer exposures to the plates4 ,nor can it be in other ways final or perfect2 however large the scale1 for instance1 on which the map is made1 we can imagine the scale doubled or increased many-fold4 ,but the map will be a great advance on anything that has hitherto been made1 and some account of it will therefore no doubt be of interest4 ,sidenote3 ,origin of the chart4 ,we may perhaps begin with a brief historical account of the enterprise4 ,photographs of the stars were taken many years ago1 but only by a few enthusiasts1 and with no serious hope of competing with eye observations of the sky4 ,the old wet-plate photography was1 in fact1 somewhat unsuited to astronomical purposes2 to photograph faint objects a long exposure is necessary1 and the wet plate may dry up before the exposure is concluded--nay1 even before it is commenced1 if the observer has to wait for passing clouds--and therefore it may be said that the successful application of photography to astronomy dates from the time when the dry plate was invented2 when it became possible to expose a plate in the telescope for hours1 or by accumulation even for days4 ,the dry plate remains sensitive for a long period1 and if it is desired to extend an exposure beyond the limits of one night1 it is quite easy to close up the telescope and return to the operations again on the next fine night2 and so on1 if not perhaps indefinitely1 at any rate so long as to transcend the limits of human patience up to the present4 ,illustration3 ,,vii4--,,great ,,comet ,,of ,,nov4 #g,,th1 #ahhb 7,from a photograph taken at the ,royal ,observatory1 ,cape of ,good ,hope47 ,sidenote3 ,comet of #ahhb4 ,sidenote3 ,stars shown on the pictures4 ,but to consider our particular project4 ,we may assign1 perhaps1 the date #ahhb as that in which it first began to take shape4 ,in that year there was a magnificent bright comet1 the last really large comet which we1 in the ,northern ,hemisphere1 have had the good fortune to see4 ,some of us1 of course1 were not born at that time1 and perhaps others who were alive may nevertheless not have seen that comet2 for it kept somewhat uncomfortably early morning hours1 and ,i can well remember myself feeling rather more resentment than gratitude to the man who waked me up about four o'clock to see it4 ,many observations were of course made of this interesting visitor1 and what specially concerns us is that at the ,cape of ,good ,hope some enterprising photographers tried to photograph it4 ,they tried in the first instance with ordinary cameras1 and soon found--what any astronomer could have told them--that the movement of the earth1 causing an apparent movement of the comet and the stars in the opposite direction1 frustrated their efforts4 ,the difficulties of obtaining pictures of moving objects are familiar to all photographers4 ,a snap-shot might have met the difficulty1 but the comet was scarcely bright enough to affect the plate with a short exposure4 ,ultimately ,dr4 ,david ,gill1 the astronomer at the ,cape ,observatory1 invited one of the photographers to strap his camera to one of the telescopes at the ,observatory1 a telescope which could be carried round by clockwork in the usual way1 so as to counteract the earth's motion1 and in effect to keep the comet steadily in view1 as though it were at rest4 ,as a consequence1 some very beautiful and successful pictures of the comet were obtained1 and on them a large number of stars were also shown4 ,they were1 as ,i have said1 not by any means the first pictures of stars obtained by photography1 but they represented in facility and in success so great an advance upon what had been formerly obtained that they attracted considerable attention4 ,they were sent to ,europe and stimulated various workers to further experiments4 ,sidenote3 ,the brothers ,henry begin work4 ,sidenote3 ,conference of #ahhg4 ,the late ,dr4 ,common in ,england1 an amateur astronomer1 began that magnificent pioneer work in astronomical photography which soon brought him the ,gold ,medal of the ,royal ,astronomical ,society for his photographs of nebulae4 ,but the most important result for our purpose was produced in ,france4 ,there had been started many years before by the ,french astronomer ,chacornac a series of star maps round the ,zodiac similar in intention to the ,berlin maps which figured in the history of the discovery of ,neptune4 ,chacornac died before his enterprise was very far advanced1 and the work was taken up by two brothers1 ,paul and ,prosper ,henry1 who followed ,chacornac in adopting for the work the laborious method of eye observation of each individual star4 ,they proceeded patiently with the work on these lines2 but when they came to the region where the ,zodiac is crossed by the ,milky ,way1 and the number of stars in a given area increases enormously1 they found the labour so great as to be practically prohibitive1 and were in doubt how to deal with the difficulty4 ,it was at this critical moment that these comet photographs1 showing the stars so beautifully1 suggested the alternative of mapping the stars photographically4 ,they immediately set to work with a trial lens1 and obtained such encouraging results that they proceeded themselves to make a larger lens of the same type2 this again was satisfactory1 and the idea naturally arose of extending to the whole heavens the scheme which they had hitherto intended only for the ,zodiac1 a mere belt of the heavens4 ,but this rendered the enterprise too large for a single observatory4 ,it became necessary to obtain the co-operation of other observatories1 and with this end in view an ,international ,conference was summoned to meet in ,paris in #ahhg to consider the whole project4 ,there were delegates from1 if not all nations1 at any rate a considerable number3-- ,france #bj ,british ,empire #h ,germany #f ,russia #c ,holland #c ,u4,s4 ,america #c ,austria #b ,sweden #b ,denmark #b ,belgium #a ,italy #a ,spain #a ,switzerland #a ,portugal #a ,brazil #a ,argentine ,republic #a ,sidenote3 ,choice of instrument4 ,sidenote3 ,expense of doublet4 ,sidenote3 ,advantages of reflector4 ,sidenote3 ,refractor chosen4 ,the ,conference had a number of very important questions to discuss1 for knowledge of the photographic method and its possibilities was at that time in its infancy4 ,there was1 for instance1 the question whether all the instruments need be of the same pattern1 and if so what that pattern should be4 ,the first of these questions was settled in the affirmative1 as we might expect2 in the interests of uniformity it was desirable that the maps should be as nearly similar as possible4 ,the second question was not so easy2 there were at least three different types of instruments which might be used4 ,first of all1 there was the photographic lens1 such as is familiar to all who have used an ordinary camera1 consisting of two lenses with a space between2 though since each of these lenses is itself made up of two1 we should more correctly say four lenses in all4 ,it was with a lens of this kind that the comet pictures had been taken at the ,cape of ,good ,hope1 and it might seem the safest plan to adopt what had been shown to be capable of such good work4 ,but there was this difficulty2 the pictures of the comet were on a very small scale1 and taken with a small lens2 a much larger lens was required for the scheme now under contemplation1 and when there are four separate lenses to be made1 each with two surfaces to polish1 and each requiring a perfectly sound clear piece of glass1 it will be obvious that the difficulties of making a large compound lens of this kind are much greater1 and the expense much more serious than in the case of a single lens1 or even a pair4 ,it was this question of expense which had led the brothers ,henry to experiment with a different kind of instrument1 in which only one pair of lenses was used instead of two4 ,their instrument was1 in fact1 very similar to the ordinary telescope1 excepting that they were bound to make their lenses somewhat different in shape in order to bring to focus the rays of light suitable for photography1 which are not the same as those suitable for eye observation with the ordinary telescope4 ,dr4 ,common1 again1 had used a third kind of instrument1 mainly with the view of reducing the necessary expense still further1 or1 perhaps1 of increasing the size of the instrument for the same expense4 ,his telescope had no lens at all1 but a curved mirror instead1 the mirror being made of glass silvered on the face 7not on the back as in the ordinary looking-glass74 ,in this case there is only one surface to polish instead of four1 as in the ,henrys' telescope1 or eight1 as in the case of the photographic doublet2 and1 moreover1 since the rays of light are reflected from the surface of the glass1 and do not pass through it at all1 the internal structure of the glass is not so strictly important as in the other cases4 ,hence the reflector is a very cheap instrument1 and it is1 moreover1 quite free from some difficulties attached to the other instruments4 ,no correction for rays of light of different colours is required1 since all rays of whatever colour come to the same focus automatically4 ,these advantages of the reflector were so considerable as to almost outweigh one well-known disadvantage1 which is1 however1 not very easily expressed in words4 ,the reflector might be described as an instrument with a temper2 sometimes it gives excellent results1 but at others something seems to be wrong1 though the worried observer does not exactly know what4 ,long experience and patience are requisite to humour the instrument and get the best results from it1 and it was felt that this uncertainty was sufficient to disqualify the instrument for the serious piece of routine work contemplated in mapping the heavens4 ,accordingly the handier and more amiable instrument with which the brothers ,henry had done such good work was selected as the pattern to be adopted4 ,sidenote3 ,doublet would have been better4 ,it is curious that at the ,conference of #ahhg nothing at all was said about the type of instrument first mentioned 7the doublet lens71 although a letter was written in its favour by ,professor ,pickering of ,harvard ,college ,observatory4 ,since that time we have learnt much of its advantages1 and it is probable that if the ,conference were to meet now they might arrive at a different decision2 but at that time they were1 to put it briefly1 somewhat afraid of an instrument which seemed to promise1 if anything1 too well1 especially in one respect4 ,with the reflector and the refractor it had been found that the field of good images was strictly limited4 ,the ,henrys' telescope would not photograph an area of the sky greater in extent than #b deg4 in diameter at any one time1 and the reflector was more limited still2 within this area the images of the stars were good1 and it had been found that their places were accurately represented4 ,now the doublet seemed to be able to show much larger areas than this with accuracy1 but no one had been able to test the accuracy to see whether it was sufficient for astronomical purposes2 and although no such feeling was openly expressed or is on record1 ,i think there is no doubt that a feeling existed of general mistrust of an instrument which seemed to offer such specious promises4 ,whatever the reason1 its claims were passed over in silence at the ,conference1 and the safer line 7as it was then thought7 of adopting as the type the ,henrys' instrument1 was taken4 ,sidenote3 ,the eighteen observatories4 ,this was perhaps the most important question settled at the ,conference1 and the answers to many of the others naturally followed4 ,the size of the plates1 for instance1 was settled automatically4 ,the question down to what degree of faintness should stars be included1 resolved itself into the equivalent question1 ,what should be the length of time during which the plates were exposed8 ,then1 again1 the question1 ,what observatories should take part in the work8 became simply this3 ,what observatories could afford to acquire the instruments of this new pattern and get other funds for carrying out the work specified8 ,it was ultimately found that eighteen observatories were able to obtain the apparatus and funds1 though unfortunately three of the eighteen have since found it impossible to proceed4 ,the following is the original list1 and in brackets are added the names of three other observatories which in #aijj undertook to fill the places of the defaulters4 ,,observatories ,,co-,,operating ,,for ,,the ,,astrographic ,,chart4 ---------------------------------------- ---- ,observatory4 ,zones of ,number ,declination4of ,plates4 ---------------------------------------- ---- ,greenwich #ij deg4 to #fe deg4 #aadi ,rome #fd deg4 #ee deg4 #aadj ,catania #ed deg4 #dg deg4 #ajjh ,helsingfors #df deg4 #dj deg4 #ajjh ,potsdam #ci deg4 #cb deg4 #abcb ,oxford #ca deg4 #be deg4 #aahj ,paris #bd deg4 #ah deg4 #abfj ,bordeaux #ag deg4 #aa deg4 #abfj ,toulouse #aj deg4 #e deg4 #ajhj ,algiers #d deg4 - #b deg4 #abfj ,san ,fernando - #c deg4 - #i deg4 #abfj ,tacubaya -#aj deg4 -#af deg4 #abfj ,santiago 7,monte ,video7-#ag deg4 -#bc deg4 #abfj ,la ,plata 7,cordoba7 -#bd deg4 -#ca deg4 #acfj ,rio 7,perth1 ,australia7-#cb deg4 -#dj deg4 #acgf ,cape of ,good ,hope -#da deg4 -#ea deg4 #aeab ,sydney -#eb deg4 -#fd deg4 #adjj ,melbourne -#fe deg4 -#ij deg4 #aadi ---------------------------------------- ---- ,sidenote3 ,sky covered twice4 ,in the list is also shown the total number of plates that were to be taken by each observatory4 ,when once the size of the plates had been settled1 it was a straightforward matter to divide up the sky into the proper number of regions necessary to cover it completely1 not only without gaps between the plates1 but with actually a small overlap of contiguous plates4 ,and more than this1 it was decided that the whole sky should be completely covered twice over4 ,it was conceivable that a question might arise whether an apparent star image on a plate was1 on the one hand1 a dust speck1 or1 on the other hand1 a planet1 or perhaps a variable or new star4 ,by taking two different plates at slightly different times1 questions of this kind could be settled2 and to make the check more independent it was decided that the plates should not be exactly repeated on the same portion of sky1 but that in the second series the centre of a plate should occupy the point assigned to the corner of a plate in the first series4 ,sidenote3 ,times of exposure4 ,then there came the important question of time of exposure1 which involved a long debate between those who desired the most modest programme possible consistent with efficiency1 and those enthusiasts who were anxious to strain the programme to the utmost limits attainable4 ,ultimately it was resolved to take two series of plates2 one series of long exposure which was set in the first instance at #aj minutes1 then became #ae1 then #cj1 then #dj1 and has by some enterprising observers been extended to #a-a_/b hours2 the other a series of short exposures which have been generally fixed at #f minutes4 ,thus instead of covering the sky twice1 it was decided to cover it in all four times1 and the number of plates assigned to each observatory in the above list must be regarded as doubled by this new decision4 ,and further still1 on the series of short-exposure plates it was decided to add to the exposure of six minutes another one of three minutes1 having slightly shifted the telescope between the two so that they should not be superimposed2 and later still1 a third exposure of twenty seconds was added to these4 ,it would take too long to explain here the reasons for these details1 but it will be clear that the general result of the discussion was to extend the original programme considerably1 and render the work even more laborious than it had appeared at the outset4 ,sidenote3 ,measurement of plates4 ,sidenote3 ,the reseau4 ,sidenote3 ,the microscope4 ,sidenote3 ,reversal of plates4 ,sidenote3 ,personal equation4 ,when all these plates have been taken1 the work is by no means finished2 indeed1 it is only just commencing4 ,there remains the task of measuring accurately on each of the short-exposure plates the positions of the stars which it represents1 numbering on the average some #cjj or #djj2 so that for instance at ,oxford the total number of stars measured on the twelve hundred plates is nearly half a million4 ,these are not all separate stars2 for the sky is represented twice over1 and there is also the slight overlap of contiguous plates2 but the number of actual separate stars measured at this one observatory is not far short of a quarter of a million1 and it has taken nearly ten years to make the measurements1 with the help of three or four measurers trained for the purpose4 ,to render the measures easy1 a network or reseau of cross lines is photographed on each plate by artificial light after it has been exposed to the stars1 so that on development these cross lines and the stars both appear4 ,we can see at a glance the approximate position of a star by counting the number of the space from left to right and from top to bottom in which it occurs2 and we can also estimate the fraction of a space in addition to the whole number2 but it is necessary for astronomical purposes to estimate this fraction with the greatest exactness4 ,the whole numbers are already given with great exactness by the careful ruling of the cross lines1 which can be spaced with extraordinary perfection4 ,to measure the fraction1 we place the plate under a microscope in the eye-piece of which there is a finally divided cross scale2 the centre of the cross is placed over a star image1 and then it is noted where the lines of the reseau cut the cross scale4 ,in this way the position of the image of a star is read off with accuracy1 and after a little practice with considerable rapidity4 ,it has been found at ,oxford that under favourable conditions the places of nearly #bjj stars per hour can be recorded in this way by a single measurer1 if he has some one to write down for him the numbers he calls out4 ,this is only one form of measuring apparatus2 there are others in which1 instead of a scale in the eye-piece1 micrometer screws are used to measure the fractions2 but the general principle in all these instruments is much the same1 and the rate of work is not very different2 while to the minor advantages and disadvantages of the different types there seems no need here to refer4 ,one particular point1 however1 is worth noting4 ,after a plate has been measured1 it is turned round completely1 so that left is now right1 and top is now bottom1 and the measurements are repeated4 ,this repetition has the advantage first of all of checking any mistakes4 ,when a long piece of measuring or numerical work of any kind is undertaken there are invariably moments when the attention seems to wander1 and some small error is the result4 ,but there are also certain errors of a systematic character similar to those denoted by the term personal equation1 which has found its way into other walks of life4 ,in the operation of placing a cross exactly over the image of a star1 different observers would show slight differences of habit2 one might place it a little more to the right than another4 ,but when the plate is turned round the effect of this habit on the measure is exactly reversed1 and hence if we take the mean of the two measures any personal habit of this kind is eliminated4 ,it has been found by experience that such personal habits are much smaller for measures of this kind than for those to which we have long been accustomed in observations made by eye on the stars themselves4 ,the troubles from personal equation have been much diminished by the photographic method1 and certain peculiarities of the former method have been clearly exhibited by the comparison4 ,for instance1 it has gradually become clear that with eye observations personal equation is not a constant quantity1 but is different for stars of different brightness4 ,when observing the transit of a bright star the observer apparently records an instant definitely earlier than in recording the transit of a faint one2 and this peculiarity seems to be common to the large majority of observers1 which is perhaps the reason why it was not noticed earlier4 ,but when positions of the stars determined in this way are compared with their positions measured on the photographic plates1 the peculiarity is made clearly manifest4 ,for example1 at ,oxford1 our first business after making measurements is to compare them with visual observations on a limited number of the brighter stars made at ,cambridge about twenty years ago4 7,about #ad1jjj stars were observed at ,cambridge1 and we are dealing with ten times that number47 ,the comparison shows that the ,cambridge observations are affected with the following systematic errors3-- ,if stars of magnitude #aj are observed correctly1 then #i #j4aj secs4 too early #h #j4af #g #j4ai #f #j4ba #e #j4bc ,sidenote3 ,main object of the work4 ,this may serve as an illustration of various incidental results which are already flowing from the enormous and laborious piece of work which1 as far as the ,university ,observatory at ,oxford is concerned1 we have just completed1 though some of the other colleagues are not so far advanced4 ,but the main results will not appear just yet4 ,the work must be repeated1 and the positions of the stars just obtained must be compared with those which they will be found to occupy at some future date1 in order to see what kind of changes are going on in the heavens4 ,whether this future date shall be one hundred years hence1 or fifty1 or ten1 or whether we should begin immediately to repeat what has been done1 is a matter not yet decided1 and one which requires some little consideration4 ,sidenote3 ,the concluding year4 ,i have said perhaps enough to give you a general idea of the work on which we have been engaged at ,oxford for the last ten years4 ,ten years ago it seemed to stretch out in front of us rather hopelessly2 the pace we were able to make seemed so slow in view of the distance to be covered4 ,we felt rather like the schoolboy who has just returned to school and sees the next holidays as a very remote prospect1 and we solaced ourselves much in the same way as he does1 by making a diagram representing the total number of plates to be dealt with and crossing off each one as it was finished1 just as he sometimes crosses off the days still remaining between him and the prospective holidays4 ,it was pleasant to watch the growth of the number of crosses on this diagram1 and by the end of the year #aijb we had the satisfaction of seeing very little blank space remaining4 ,now1 up to this point it had not much mattered whether any particular plate was secured in any particular year1 or in a subsequent year1 so long as there were always sufficient plates to keep us occupied in measuring them4 ,but it then became a matter of importance to secure each plate at the proper time of year2 for the sun1 as we know1 travels round the ,zodiac among the stars1 obliterating by his radiance a large section of the sky for a period of some months1 and in this way a particular region of the heavens is apt to run into daylight1 as the observatory phrase goes1 and ceases to be available for photography during several months1 until the sun is again far enough away to allow of the particular region being seen at night4 ,sidenote3 ,a disappointment4 ,sidenote3 ,a curious plate4 ,sidenote3 ,a strange object4 ,sidenote3 ,a new star8 ,roughly speaking then1 if a plate which should be taken in ,february is not secured in this month owing to bad weather1 the proper time for taking it will not occur again until the following ,february2 and when there was a fair prospect of finishing our work in #aijc1 it became important to secure each plate at the proper time in that year4 ,hence we were making special efforts to utilise to the full any fine night that ,providence sent in our way1 and on such occasions it is clearly an economy1 if not exactly to make hay while the sun shines1 at any rate to take plates vigorously while the sun is not shining and the night is fine2 leaving the development of them until the daytime4 ,there is1 of course1 the risk that the whole night's work may in this way be lost owing to some fault in the plates1 which might have been detected if some of them were immediately developed4 ,perhaps in the early days of our work it would have been reckless or foolish to neglect this little precaution2 but we had for years been accustomed to rely upon the excellence of the plates without finding our trust betrayed2 and the sensitiveness of the plates had increased rather than diminished as time went on4 ,hence it will be readily understood that when one fatal morning we developed a series of some thirty plates1 and found that owing to some unexplained lack of sensitiveness they were all unsuitable for our purpose1 it came as a most unwelcome and startling surprise4 ,it was1 of course1 necessary to make certain that there was no oversight1 that the developer was not at fault1 and that the weather had not been treacherous4 ,all such possibilities were carefully considered before communication with the makers of the plates1 but it ultimately became clear that there had been some unfortunate failure in sensitiveness1 and that it would be necessary to repeat the work with opportunities restricted by the intervening lapse of time4 ,however1 disappointments from this or similar causes are not unknown in astronomical work2 and we set about this repetition with as little loss of time and cheerfulness as was possible4 ,under the circumstances1 however1 it seemed desirable to examine carefully whether anything could be saved from the wreck--whether any of the plates could be admitted as just coming up to the minimum requirements4 ,and ,i devoted a morning to this inquiry4 ,in the course of it ,i came across one plate which certainly seemed worth an inclusion among our series from the point of view of the number of stars shown upon it4 ,it seemed quite rich in stars1 perhaps even a little richer than might have been expected4 ,on inquiry ,i was told that this was not one of the originally condemned plates1 but one which had been taken since the failure in sensitiveness of the plates had been detected2 was from a new and specially sensitive batch with which the courteous makers had supplied us2 but though there were certainly a sufficient number of stars upon the plate1 owing to some unexplained cause the telescope had been erroneously pointed1 and the region taken did not correspond to the region required4 ,to investigate the cause of the discrepancy ,i thereupon took down from our store of plates the other one of the same region which had been rejected for insufficiency of stars1 and on comparing the two it was at once evident that there was a strange object on the plate taken later of the two1 a bright star or other heavenly body1 which was not on the former plate4 ,i have explained that by repeating the exposure more than once1 it is easily possible to recognise whether a mark upon the plate is really a celestial body or is an accidental blot or dust speck1 and there was no doubt that this was the image of some strange celestial body4 ,it might1 of course1 be a new planet1 or even an old one which had wandered into the region2 but a few measures soon showed that it was not in movement4 ,the measures consisted in comparing the separation of the three exposures with the separation of the corresponding exposures of obvious stars1 for the exposures were not1 of course1 simultaneous1 and if the body were a planet and had moved in the interval between them1 this would be made manifest on measuring the separations4 ,no such movements could be detected2 and the possibilities were thus restricted to two4 ,so far as we knew the object was a star1 but might be either a star of the class known as variable or of that known as new4 ,in the former case it would become bright and faint at more or less regular intervals1 and might possibly have been already catalogued2 for the number of these bodies already known amounts to some hundreds4 ,search being made in the catalogues1 no entry of it was found1 though it still might be one of this class which had hitherto escaped detection4 ,or it might be a new star1 one of those curious bodies which blaze up quite suddenly to brightness and then die away gradually until they become practically invisible4 ,the most famous perhaps of these is the star which appeared in #aegb1 and was so carefully observed by ,tycho ,brahe2 but such apparitions are rare1 and altogether we have not records as yet of a score altogether2 so that in this latter case the discovery would be of much greater interest than in the former4 ,in either event it was desirable to inform other observers as soon as possible of the existence of a strange body2 already some time had elapsed since the plate had been taken1 ,march #afth1 for the examination of which ,i have spoken was not made until ,march #bdth4 ,accordingly1 a telegram was at once despatched to the ,central ,office at ,kiel1 which undertakes to distribute such information all over the world1 and a few post-cards were sent to observers close at hand who might be able to observe the star the same night4 ,certain observations with the spectroscope soon made it clear that the object was really a new star4 ,sidenote3 ,the discovery accidental4 ,sidenote3 ,mrs4 ,fleming's discoveries4 ,this1 therefore1 is the discovery which we made at ,oxford3 as you will see1 in an entirely accidental manner1 during the course of a piece of work in which it was certainly never contemplated4 ,its purely accidental nature is sufficiently illustrated by the fact that if the plates originally supplied by the makers had been of the proper quality1 the plate which led to the discovery would never have been taken4 ,if the plates exposed in ,february had been satisfactory1 we should have been content1 and should not have repeated the exposure on ,march #afth4 ,again ,i can testify personally how purely accidental it was that the examination was made on ,march #bdth to see whether anything could be saved1 as ,i have said1 from the wreck4 ,the idea came casually into my mind as ,i was walking through the room and saw the neat pile of rejected plates2 and one may fairly call it an accidental impulse4 ,this new star is not1 however1 the first of such objects to have been discovered accidentally2 many of the others were found just as much by chance1 though a notable exception must be made of those discovered at the ,harvard ,observatory1 which are the result of a deliberate search for such bodies by the careful examination of photographic plates4 ,mrs4 ,fleming1 who spends her life in such work1 has had the good fortune to detect no less than six of these wonderful objects as the reward of her laborious scrutiny2 and she is the only person who has thus found new stars by photography until this accidental discovery at ,oxford4 ,the following is a complete list of new stars discovered to date3-- ,,list ,,of ,,new ,,stars4 ---------------------------------------- ------ ,ref4 ,no4 ,constellation4 ,year4 ,discoverer4 ---------------------------------------- ------ #a ,cassiopeia #aegb ,tycho ,brahe4 #b ,cygnus #afjj ,janson4 #c ,ophiuchus #afjd ,kepler4 #d ,vulpecula #afgj ,anthelm4 #e ,ophiuchus #ahdh ,hind4 #f ,scorpio #ahfj ,auwers4 #g ,corona ,borealis #ahff ,birmingham4 #h ,cygnus #ahgf ,schmidt4 #i ,andromeda #ahhe ,hartwig4 #aj ,perseus #ahhg ,fleming4 #aa ,auriga #ahia ,anderson4 #ab ,norma #ahic ,fleming4 #ac ,carina #ahie ,fleming4 #ad ,centaurus #ahie ,fleming4 #ae ,sagittarius #ahih ,fleming4 #af ,aquila #ahii ,fleming4 #ag ,perseus #aija ,anderson4 #ah ,gemini #aijc ,at ,oxford4 ---------------------------------------- ------ ,illustration3 ,,march #a1 #aijc ,,march #ad1 #aijc ,,viii4--,,the ,,oxford ,,new ,,star4 ,a ,,pair ,,of ,,photographs ,,taken ,,at ,,the ,,harvard ,,college ,,observatory ,,before ,,and ,,after ,,its ,,appearance 7,the arrow indicates the place of the new star4 ,it will be seen that the left-hand picture though it shews fainter stars than the other1 has not a trace of the new star47 ,sidenote3 ,dr4 ,anderson4 ,sidenote3 ,nova ,persei4 ,generally these stars have been noted by eye observation1 as in the case of the two found by ,dr4 ,anderson of ,edinburgh4 ,in these cases also we may say that deliberate search was rewarded2 for ,dr4 ,anderson is probably the most assiduous watcher of the skies living1 though he seldom uses a telescope2 sometimes he uses an opera-glass1 but usually the naked eye4 ,he describes himself as an ,astrophil rather than as an astronomer4 ,i love the stars1 he says2 and whenever they are shining1 ,i must be looking4 ,and so on every fine night he stands or sits at his open study window gazing at the heavens4 ,i believe he was just about to leave them for his bed1 near #c ,a4,m4 on the night of ,february #ba1 #aija1 when1 throwing a last glance upward1 he suddenly saw a brilliant star in the constellation ,perseus4 ,his first feeling was actually one of disappointment1 for he felt sure that this object must have been there for some time past without his knowing of it1 and he grudged the time lost when he might have been regarding it4 ,more in a spirit of complaint than of inquiry1 he made his way to the ,royal ,observatory at ,edinburgh next day to hear what they had to say about it1 though he found it difficult to approach the subject4 ,he first talked about the weather1 and the crops1 and similar topics of general interest2 and only after some time dared he venture a casual reference to the new portent in the heavens4 ,seeing his interlocutor look somewhat blank1 he ventured a little farther1 and made a direct reference to the new star in ,perseus2 and then found to his astonishment1 as also to his great delight1 that he was the first to bring news of it4 ,the news was soon communicated to other observers2 all the telescopes of the world were soon trained upon it2 and this wonderful new star of the new century has taught us more of the nature of these extraordinary bodies than all we knew before4 ,sidenote3 ,records previous to discovery4 ,sidenote3 ,was ,nova ,geminorum previously shining faintly8 ,sidenote3 ,the suspicion negatived4 ,perhaps ,i may add a few remarks on one or two features of these bodies4 ,firstly1 let us note that ,professor ,pickering of ,harvard is now able to make a most important contribution to the former history of these objects--that is to say1 their history preceding their actual detection4 ,we remember that1 after ,uranus had been discovered1 it was found that several observers had long before recorded its place unknowingly2 and similarly ,professor ,pickering and his staff have usually photographed other new objects unknowingly4 ,there are on the shelves at ,harvard vast stores of photographs1 so many that they are unable to examine them when they have been taken2 but once any object of interest has been discovered1 it is easy to turn over the store and examine the particular plates which may possibly show it at an earlier date4 ,in this way it was found that ,dr4 ,anderson's new star had been visible only for a few days before its discovery1 there being no trace of it on earlier plates4 ,similarly1 in the case of the new star found at ,oxford1 plates taken on ,march #ast and #fth1 fifteen days and ten days respectively before the discovery-plate of ,march #afth1 showed the star4 ,but1 in this particular instance1 greater interest attaches to two still earlier plates taken elsewhere1 and with exposures much longer than any available at ,harvard4 ,one had been obtained at ,heidelberg by ,dr4 ,max ,wolf1 and another at the ,yerkes ,observatory of ,chicago ,university1 by ,mr4 ,parkhurst2 and on both there appeared to be a faint star of about the fourteenth or fifteenth magnitude1 in the place subsequently occupied by the ,nova2 and the question naturally arose1 ,was this the object which ultimately blazed up and became the new star8 ,to settle this point1 it was necessary to measure its position1 with reference to neighbouring stars1 with extreme precision2 and here it was unfortunate that the photographs did not help us as much as they might1 for they were scarcely capable of being measured with the requisite precision4 ,the point was an important one1 because if the identity of the ,nova with this faint star could be established1 it would be the second instance of the kind2 but so far as they went1 measurements of the photographs were distinctly against the identity4 ,such was the conclusion of ,mr4 ,parkhurst from his photograph alone2 and it was confirmed by measures made at ,oxford on copies of both plates1 which were kindly sent there for the purpose4 ,the conclusion seemed to be that there was a faint star very near1 but not at1 the place of the new star2 and it was therefore probable that1 although this faint star was temporarily invisible from the brightness of the adjacent ,nova1 as the latter became fainter 7in the way with which we have become familiar in the case of new stars71 it might be possible to see the two stars alongside each other4 ,this critical observation was ultimately made by the sharp eyes of ,professor ,barnard1 aided by the giant telescope of the ,yerkes ,observatory2 and it seems clear therefore that the object which blazed up to become the ,nova of #aijc could not have previously been so bright as a faint star of the fourteenth magnitude4 ,although this is merely a negative conclusion1 it is an important one in the history of these bodies4 ,sidenote3 ,nebula round ,nova ,persei4 ,sidenote3 ,its changes4 ,sidenote3 ,due to travelling illumination4 ,the second point to which ,i will draw your attention is from the history of the other ,nova just mentioned--,dr4 ,anderson's ,new ,star of #aija4 ,in this instance it is not the history previous to discovery1 but what followed many months after discovery1 that was of engrossing interest2 and again ,yerkes ,observatory1 with its magnificent equipment1 played an important part in the drama4 ,when1 with its giant reflecting telescope1 photographs were taken of the region of ,nova ,persei after it had become comparatively faint1 it was found that there was an extraordinarily faint nebulosity surrounding the star4 ,repeating the photographs at intervals1 it was found that this nebulosity was rapidly changing in shape4 ,rapidly is1 of course1 a relative term1 and a casual inspection of two of the photographs might not convey any impression of rapidity2 it is only when we come to consider the enormous distance at which the movements1 or apparent movements1 of the nebulae must be taking place that it becomes clear how rapid the changes must be4 ,it was not possible to determine this distance with any exactness1 but limits to it could be set1 and it seemed probable that the velocity of the movement was comparable with that of light4 ,the conclusion suggested itself that the velocity might actually be identical with that of light1 in which case what we saw was not the movement of actual matter1 but merely that of illumination1 travelling from point to point of matter already existing4 ,illustration3 ,,sept4 #bj1 #aija ,,nov4 #ac1 #aija ,,ix--,,nebulosity ,,round ,,nova ,,persei 7,from photographs taken at the ,yerkes ,observatory by ,g4 ,w4 ,ritchey47 ,sidenote3 ,when did it all happen8 ,an analogy from the familiar case of sound may make clearer what is meant4 ,if a loud noise is made in a large hall1 we hear echoes from the walls4 ,the sound travels with a velocity of about #aajj feet per second1 reaches the walls1 is reflected back from them1 and returns to us with the same velocity4 ,from the interval occupied in going and returning we could calculate the distance of the walls4 ,the velocity of light is so enormous compared with that of sound that we are usually quite unable to observe any similar phenomenon in the case of light4 ,if we strike a match in the largest hall1 all parts of it are illuminated so immediately that we cannot possibly realise that there was really an interval between the striking of the match1 the travelling of the light to the walls1 and its return to our eyes4 ,the scale of our terrestrial phenomenon is far too small to render this interval perceptible4 ,but those who accept the theory above mentioned regarding the appearances round ,nova ,persei 7although there are some who discredit it7 believe that we have in this case an illustration of just this phenomenon of light echoes1 on a scale large enough to be easily visible4 ,they think that1 surrounding the central star which blazed up so brightly in ,february #aija1 there was a vast dark nebula1 of which we had no previous knowledge1 because it was not shining with any light of its own4 ,when the star blazed up1 the illumination travelled from point to point of this dark nebula and lighted it up2 but the size of the nebula was so vast that1 although the light was travelling with the enormous velocity of #bjj1jjj miles per second1 it was not until months afterwards that it reached different portions of this nebula2 and we accordingly got news of the existence of this nebula some months after the news reached us of the central conflagration1 whatever it was4 ,remark that all we can say is that the news of the nebula reached us some months later than that of the outburst4 ,the actual date when either of the actual things happened1 we have as yet no means of knowing2 it may have been hundreds or even thousands of years ago that the conflagration actually occurred of which we got news in ,february #aija1 the light having taken all that time to reach us from that distant part of space2 and the light reflected from the nebula was following it on its way to us all these years at that same interval of a few months4 ,sidenote3 ,an objection4 ,now1 let me refer before leaving this point to the chief objection which has been urged against this theory4 ,it has been maintained that the illumination would necessarily appear to travel outwards from the centre with an approach to uniformity1 whereas the observed rate of travel is not uniform1 and has been even towards the centre instead of away from it2 which would seem as though portions of the nebula more distant from the centre were lighted up sooner than those closer to it4 ,by a simple illustration from our solar system1 we shall see that these curious anomalies may easily be explained4 ,let us consider for simplicity two planets only1 say the ,earth and ,saturn4 ,we know that ,saturn travels round the sun in an orbit which is ten times larger than the orbit of the earth4 ,suppose now that the sun were suddenly to be extinguished2 light takes about eight minutes to travel from the sun to the earth1 and consequently we should not get news of the extinction for some eight minutes2 the sun would appear to us to still go on shining for eight minutes after he had really been extinguished4 ,saturn being about ten times as far away from the sun1 the news would take eighty minutes to reach ,saturn2 and from the earth we should see ,saturn shining more#c than eighty minutes after the sun had been extinguished1 although we ourselves should have lost the sun's light after eight minutes4 ,i think we already begin to see possibilities of curious anomalies2 but they can be made clearer than this4 ,instead of imagining an observer on the earth1 let us suppose him removed to a great distance away in the plane of the two orbits2 and let us suppose that the sun is now lighted up again as suddenly as the new star blazed up in ,february #aija4 ,then such an observer would first see this blaze in the centre2 eight minutes afterwards the illumination would reach the earth1 a little speck of light near the sun would be illuminated1 just as we saw a portion of the dark nebula round ,nova ,persei illuminated2 eighty minutes later another speck1 namely1 ,saturn1 would begin to shine4 ,but now1 would ,saturn necessarily appear to the distant observer to be farther away from the sun than the earth was8 ,looking at the diagram1 we can see that if ,saturn were at ,s#a then it would present this natural appearance of being farther away from the sun than the earth2 but it might be at ,s#b or ,s#c1 in which case it would seem to be nearer the sun1 and the illumination would seem to travel inwards towards the central body instead of outwards4 ,without considering other cases in detail1 it will be tolerably clear that almost any anomalous appearance might be explained by choosing a suitable arrangement of the nebulous matter which we suppose lighted up by the explosion of ,nova ,persei4 ,another objection urged against the theory ,i have sketched is that the light reflected from such a nebula would be so feeble that it would not affect our photographic plates4 ,this depends upon various assumptions which we have no time to notice here2 but ,i think we may say that there is certainly room for the acceptance of the theory4 ,illustration3 ,,fig4 #f4 ,sidenote3 ,did the nebula cause the outburst8 ,now1 if this dark nebula was previously existing in this way all round the star which blazed up1 the question naturally arises whether the nebula had anything to do with the conflagration4 ,was there previously a star1 either so cold or so distant as not to be shining with appreciable light1 which1 travelling through space1 encountered this vast nebula1 and by the friction of the encounter was suddenly rendered so luminous as to outshine a star of the first magnitude8 ,the case of meteoric stones striking our own atmosphere seems to suggest such a possibility4 ,these little stones are previously quite cold and invisible1 and are travelling in some way through space1 many of them probably circling round our sun4 ,if they happen in their journey to encounter our earth1 even the extremely tenuous atmosphere1 so thin that it will scarcely bend the rays of light appreciably1 even this is sufficient by its friction to raise the stones to a white heat1 so that they blaze up into the falling stars with which we are familiar4 ,this analogy is suggested1 but we must be cautious in accepting it2 for we know so very little of the nature of nebulae such as that of which we have been speaking4 ,but in any case1 a totally new series of phenomena have been laid open to our study by those wonderful photographs taken at the ,yerkes ,observatory and the ,lick ,observatory in the few years which the present century has as yet run4 ,sidenote3 ,importance of new stars ,one thing is quite certain3 we must lose no opportunity of studying such stars as may appear1 and no diligence spent in discovering them at the earliest possible moment is thrown away4 ,we have only known up to the present1 as already stated1 less than a score of them1 and of these many have told us but little2 partly because they were only discovered too late 7after they had become faint71 and partly because the earlier ones could not be observed with the spectroscope1 which had not then been invented4 ,it seems clear that in the future we must not allow accident to play so large a part in the discovery of these objects2 more must be done in the way of deliberate search4 ,although we know beforehand that this will involve a vast amount of apparently useless labour1 that months and years must be spent in comparing photographic plates1 or portions of the sky itself1 with one another without detecting anything remarkable1 it will not be the first time that years have been cheerfully spent in such searches without result4 ,we need only recall ,hencke's fifteen years of fruitless search1 before finding a minor planet1 to realise this fact4 ,sidenote3 ,superposition of plates4 ,sidenote3 ,the stereo-comparator4 ,one thing of importance may be done2 we may improve our methods of making the search1 so as to economise labour1 and several successful attempts have already been made in this direction4 ,the simplest plan is to superpose two photographs taken at different dates1 so that the stars on one lie very close to those on the other2 then if an image is seen to be unpaired we may have found a new star1 though of course the object may be merely a planet or a variable4 ,the superposition of the plates may be either actual or virtual4 ,a beautiful instrument has been devised on the principle of the stereoscope for examining two plates placed side by side1 one with each eye4 ,we know that in this way two photographs of the same object from different points of view will appear to coalesce1 and at the same time to give an appearance of solidity to the object or landscape1 portions of which will seem to stand out in front of the background4 ,applying this principle to two photographs of stars1 what happens is this3 if the stars have all remained in the same positions exactly1 the two pictures will seem to us to coalesce1 and the images all to lie on a flat background2 but if in the interval between the exposures of the two plates one of the stars has appreciably moved or disappeared1 it will seem1 when looked at with this instrument1 to stand out in front of this background1 and is accordingly detected with comparatively little trouble4 ,this new instrument1 to which the name ,stereo-comparator has been given1 promises to be of immense value in dredging the sky for strange bodies in the future4 ,i am glad to say that a generous friend has kindly presented the ,university ,observatory at ,oxford with one of these beautiful instruments1 which have been constructed by ,messrs4 ,zeiss of ,jena after the skilful designs of ,dr4 ,pulfrich4 ,whether we shall be able to repeat by deliberate search the success which mere accident threw in our way remains to be seen4 ,,chapter ,v ,,schwabe ,,and ,,the ,,sun-,,spot ,,period ,sidenote3 ,discoveries contrary to expectation4 ,in preceding chapters we have reviewed discoveries1 some of which have been made as a result of a deliberate search1 and others accidentally in the course of work directed to a totally different end2 but so far we have not considered a case in which the discoverer entered upon an enterprise from which he was positively dissuaded4 ,sidenote3 ,nothing expected from spots4 ,in the next chapter we shall come across a very striking instance of this type2 but even in the discovery that there was a periodicity in the solar spots1 with which ,i propose to deal now1 ,herr ,schwabe began his work in the face of deterrent opinions from eminent men4 ,his definite announcement was first made in #ahdc1 though he had himself been convinced some years earlier4 ,in #aheg the ,royal ,astronomical ,society awarded him their gold medal for the discovery2 and in the address delivered on the occasion the ,president commenced by drawing attention to this very fact1 that astronomers who had expressed any opinions on the subject had been uniformly and decidedly against the likelihood of there being anything profitable in the study of the solar spots4 ,i will quote the exact words of the ,president1 ,mr4 ,manuel ,johnson1 then ,radcliffe ,observer at ,oxford4 ,it was in #ahbf that ,heinrich ,schwabe1 a gentleman resident in ,dessau1 entered upon those researches which are now to engage our attention4 ,i am not aware of the motive that induced him--whether any particular views had suggested themselves to his own mind--or whether it was a general desire of investigating1 more thoroughly than his predecessors had done1 the laws of a remarkable phenomenon1 which it had long been the fashion to neglect4 ,he could hardly have anticipated the kind of result at which he has arrived2 at the same time we cannot imagine a course of proceeding better calculated for its detection1 even if his mind had been prepared for it1 than that which he has pursued from the very commencement of his career4 ,assuredly if he entertained such an idea1 it was not borrowed from the authorities of the last century1 to whom the solar spots were objects of more attention than they have been of late years4 ',nulla constanti temporum lege apparent aut evanescunt1' says ,keill in #agci4--;,introduct4 ad ,physic4 ,astronom41 p4 #bec4 ',il est manifest par ce que nous venons de rapporter qu'il n'y a point de regle certaine de leur formation1 ni de leur nombre et de leur figure1' says ,cassini ,,ii4 in #agdj4--;,elem d',astron41 vol4 i4 p4 #hb4 ',il semble qu'elles ne suivent aucune loi dans leur apparitions1' says ,le ,monnier in #agdf4--;,instit4 ,astron41 p4 #hc4 ',solar spots observe no regularity in their shape1 magnitude1 number1 or in the time of their appearance or continuance1' says ,long in #agfd4--;,astron41 vol4 ii4 p4 #dgb4 ',les apparitions des taches du soleil n'ont rien de regulier1' says ,lalande in #agga4--;,astron41 vol4 iii4 ,sec4 #caca1 #bnd edit4 ,and ,delambre's opinion may be inferred from a well-known passage in the third volume of his ',astronomy' 7p4 #bj71 published in #ahad1 where treating of the solar spots he says1 ',il est vrai qu'elles sont plus curieuses que vraiment utiles4'#d ,it will thus be evident that ,herr ,schwabe had the courage to enter upon a line of investigation which others had practically condemned as likely to lead nowhere1 and that his discovery was quite contrary to expectation4 ,it is a lesson to us that not even the most unlikely line of work is to be despised2 for the outcome of ,schwabe's work was the first step in the whole series of discoveries which have gradually built up the modern science of ,solar ,physics1 which occupies so deservedly large a part of the energies of1 for instance1 the great observatory attached to the ,university of ,chicago4 ,sidenote3 ,schwabe's announcement4 ,it has been our practice to recall the actual words in which the discoverer himself stated his discovery1 and ,i will give the original modest announcement of ,schwabe1 though for convenience of those who do not read ,german ,i will attempt a rough translation4 ,he had communicated year by year the results of his daily counting of the solar spots to the ,astronomische ,nachrichten1 and after he had given ten years' results in this way he collected them together1 but he made no remark on the curious sequence which they undoubtedly showed at that time4 ,waiting patiently six years for further material1 in #ahdc he ventured to make his definite announcement as follows3--,from my earlier observations1 which ,i have communicated annually to this journal1 there was manifest already a certain periodicity of sun-spots2 and the probability of this being really the case is confirmed by this year's results4 ,although ,i gave in volume #ae the total numbers of groups for the years #ahbf-ahcg1 nevertheless ,i will repeat here a complete series of all my observations of sun-spots1 giving not only the number of groups1 but also the number of days of observation1 and further the days when the sun was free from spots4 ,the number of groups alone will not in itself give sufficient accuracy for determination of a period1 since ,i have convinced myself that when there are a large number of sun-spots the number will be reckoned somewhat too small1 and when few sun-spots1 the number somewhat too large2 in the first case several groups are often counted together in one1 and in the second it is easy to divide a group made up of two component parts into two separate groups4 ,this must be my excuse for repeating the early catalogue1 as follows3-- ---------------------------------------- ----- ,year4 ,number of ,days free ,days of ,groups4 from ,spots4 ,observation4 ---------------------------------------- ----- #ahbf #aah #bb #bgg #ahbg #afa #b #bgc #ahbh #bbe #j #bhb #ahbi #aii #j #bdd #ahcj #aij #a #bag ---------------------------------------- ----- #ahca #adi #c #bci #ahcb #hd #di #bgj #ahcc #cc #aci #bfg #ahcd #ea #abj #bgc #ahce #agc #ah #bdd ---------------------------------------- ----- #ahcf #bgb #j #bjj #ahcg #ccc #j #afh #ahch #bhb #j #bjb #ahci #afb #j #bje #ahdj #aeb #c #bfc ---------------------------------------- ----- #ahda #ajb #ae #bhc #ahdb #fh #fd #cjg #ahdc #cd #adi #cbd 7#ahdd7 7#eb7 7#aaa7 7#cbj7 ---------------------------------------- ----- ,if we now compare together the number of groups1 and the days free from spots1 we find that the sun-spots have a period of about ten years1 and that for about five years they are so numerous that during this period few days1 if any1 are free from spots4 ,the sequel must show whether this period is constant1 whether the minimum activity of the sun in producing spots lasts for one or two years1 and whether this activity increases more quickly than it decreases4 ,illustration3 ,,feb4 #ah1 #ahid4 ,,feb4 #ai1 #ahid4 ,x4--,,photographs ,,of ,,the ,,sun ,,taken ,,at ,,the ,,royal ,,observatory1 ,,greenwich1 ,,shewing ,,sunspots4 ,sidenote3 ,attracted little attention1 until eight years later4 ,this brief announcement is all that the discoverer says upon the subject2 and it is perhaps not remarkable that it attracted very little attention1 especially when we remember that it related to a matter which the astronomical world had agreed to put aside as unprofitable and not worth attention4 ,next year1 in giving his usual paper on the spots for #ahdd he recurs to the subject in the following sentence3 ,the periodicity of spots of about ten years which was indicated in my summary published last year1 is confirmed by this year's observations4 ,i have added in brackets to the table above reproduced the numbers for #ahdd subsequently given1 and it will be seen how nearly they might have been predicted4 ,sidenote3 ,other phenomena sympathetic and others not4 ,still the subject attracted little attention4 ,turning over the leaves of the journal at random1 ,i came across the annual report of the ,astronomer ,royal of ,england1 printed at length4 ,but in it there is no reference to this discovery1 which opened up a line of work now strongly represented in the annual programme of the ,royal ,observatory at ,greenwich4 ,mr4 ,johnson remarks that the only person who had taken it up was ,julius ,schmidt1 who then resided near ,hamburg4 ,but ,schwabe went on patiently accumulating facts2 and in #ahea the great ,von ,humboldt in the third volume of his ,cosmos1 drew attention to the discovery1 which was accordingly for the first time brought into general notice4 ,it will be seen that there are not many facts of general interest relating to the actual discovery beyond the courage with which the work was commenced in a totally unpromising direction1 and the scant attention it received after being made for us4 ,we may admit that interest centres chiefly in the tremendous consequences which flowed from it4 ,we now recognise that many other phenomena are bound up with this waxing and waning of the solar spots4 ,we might be prepared for a sympathy in phenomena obviously connected with the sun itself2 but it was an unexpected and startling discovery that magnetic phenomena on the earth had also a sympathetic relation with the changes in sun-spots1 and it is perhaps not surprising that when once this connection of solar and terrestrial phenomena was realised1 various attempts have been made to extend it into regions where we cannot as yet allow that it has earned a legitimate right of entry4 ,we have heard of the weather and of ,indian famines occurring in cycles identical with the sun-spot cycle2 and it is obvious how tremendously important it would be for us if this were found to be actually the case4 ,for we might in this way predict years of possible famine and guard against them2 or if we could even partially foretell the kind of weather likely to occur some years hence1 we might take agricultural measures accordingly4 ,the importance of the connection1 if only it could be established1 is no doubt the reason which has misled investigators into laying undue stress on evidence which will not bear close scrutiny4 ,for the present we must say decidedly that no case has been made out for paying serious attention to the influence of sun-spots on weather4 ,nevertheless1 putting all this aside1 there is quite enough of first-rate importance in the sequel to ,schwabe's discovery4 ,sidenote3 ,greenwich sun records4 ,sidenote3 ,the sun's rotation4 ,let us review the facts in order4 ,most of us1 though we may not have had the advantage of seeing an actual sun-spot through a telescope1 have seen drawings or photographs of spots4 ,there is a famous drawing made by ,james ,nasmyth 7of steam-hammer fame71 in ,july1 #ahfd1 which is of particular interest1 because at that time ,nasmyth was convinced--and he convinced many others with him--that the solar surface was made up of a miscellaneous heap of solid bodies in shape like willow leaves1 or grains of rice1 thrown together almost at random1 and the drawing was made by him to illustrate this idea4 ,comparing a modern photograph with it1 we see that there is something to be said for ,nasmyth's view1 which attracted much attention at the time and occasioned a somewhat heated controversy4 ,but since the invention of the spectroscope it has become quite obsolete2 it probably does not correspond in any way to the real facts4 ,but instead of looking at pictures which have been enlarged to show the detailed structure in and near a spot1 we will look at a series of pictures of the whole sun taken on successive days at ,greenwich in which the spots are necessarily much smaller1 but which show the behaviour of the spots from day to day4 7,see ,plates ,x4 and ,,xi47 ,from the date at the foot of each it will be seen that they gradually cross the disc of the sun 7a fact first discovered by ,galileo in #afaj71 showing that the sun rotates on an axis once in about every twenty-five days4 ,there are many interesting facts connected with this rotation2 especially that the sun does not rotate as a solid body1 the parts near the 7,sun's7 ,equator flowing quicker than those nearer the ,poles2 but for the present we cannot stop to dwell upon them4 ,what interests us particularly is the history1 not from day to day1 but from year to year1 as ,schwabe has already given it for a series of years4 ,illustration3 ,,feb4 #bj1 #ahid4 ,,feb4 #ba1 #ahid4 ,,xi4--,,photographs ,,of ,,the ,,sun ,,taken ,,at ,,the ,,royal ,,observatory1 ,,greenwich1 ,,shewing ,,sunspots ,sidenote3 ,wolf's numbers4 ,sidenote3 ,greenwich areas4 ,sidenote3 ,magnetic fluctuations4 ,when it became generally established that this periodicity existed1 ,rudolf ,wolf of ,zurich collected the facts about sun-spots from the earliest possible date1 and represented this history by a series of numbers which are still called ,wolf's ,sun-,spot ,numbers4 ,you will see from the diagram the obvious rise and fall for eleven years1--not ten years1 as ,schwabe thought1 but just a little over eleven years4 ,the facts are1 however1 given more completely by the work done at the ,royal ,observatory at ,greenwich4 ,it is part of the regular daily work of that ,observatory to photograph the sun at least twice4 ,many days are of course cloudy or wet1 so that photographs cannot be obtained2 but there are available photographs similarly taken in ,india or in ,mauritius1 where the weather is more favourable1 and from these the gaps are so well filled up that very few days1 if any1 during the whole year are left without some photograph of the sun's surface4 ,on these photographs the positions and the areas of the spots are carefully measured under a microscope1 and the results when submitted to certain necessary calculations are published year by year4 ,it is clearly a more accurate estimate of the spottedness of the sun to take the total area of all the spots rather than their mere number1 for in the latter case a large spot and a small one count equally4 ,hence the ,greenwich records will perhaps give us an even better idea of the periodicity than ,wolf's numbers4 ,now1 at the same observatory magnetic observations are also made continuously4 ,if a magnet be suspended freely we are accustomed to say that it will point to the ,north ,pole2 but this is only very roughly true4 ,in the first place1 it is probably well known to you that there is a considerable deviation from due north owing to the fact that the magnetic ,north ,pole is not the same as the geographical ,north ,pole2 but this for the present need not concern us4 ,what does concern us is1 that if the needle is hung up and left long enough to come to rest1 it does not then remain steadily at rest1 but executes slow and small oscillations backwards and forwards1 up and down1 throughout the day2 repeating nearly the same oscillations on the following day1 but at the same time gradually changing its behaviour so as to oscillate differently in summer and winter4 ,these changes are very small1 and would pass unnoticed by the naked eye2 but when carefully watched through a telescope1 or better still1 when photographed by some apparatus which will at the same time magnify them1 they can be rendered easily visible4 ,when the history of these changes is traced it is seen at once that there is a manifest connection with the cycle of sun-spot changes2 for instance1 if we measure the range of swing backwards and forwards during the day and take the average for all the days in the year1 and then compare this with the average number of sun-spots1 we shall see that the averages rise and fall together4 ,similarly we may take the up and down swing1 find the average amount of it throughout the year1 and again we shall find that this corresponds very closely with the average number of sun-spots4 ,illustration3 ,,plate ,,xii4 ,,number ,,of ,,sunspots 7,wolf7 ,compared with ,,daily ,,range of ,,magnetic ,,declination ,,daily ,,range of ,,magnetic ,,horzl4 ,,force 7as observed at ,greenwich47 ,sidenote3 ,daily curves4 ,sidenote3 ,difference between summer and winter1 and between sun-spot maximum and minimum4 ,sidenote3 ,cause unknown4 ,but perhaps the most striking way to exhibit the sympathy is to combine different variations of the needle into one picture4 ,and first we must remark that there is another important variation of the earth's magnetic action which we have not yet considered4 ,we have mentioned the swing of the needle to and fro1 and the swing up and down1 and these correspond to changes in the direction of the force of attraction on the needle4 ,but there may be also changes in intensity of this action2 the pull may be a little stronger or a little weaker than before1 and these variations are not represented by any actual movement of the needle1 though they can be measured by proper experiments4 ,we can1 however1 imagine them represented by a movement of the end of the needle if we suppose it made of elastic material1 so that it would lengthen when the force was greater and contract slightly when the force was less4 ,if a pencil were attached to the end of such an elastic needle so as to make a mark on a sheet of paper1 and if for a moment we exclude the up and down movements1 the pencil would describe during the day a curve on the paper1 as the end of the needle swung backwards and forwards with the change in direction1 and moved across the direction of swing with the change in intensity4 ,now when curves of this kind are described for a day in each month of the year1 there is a striking difference between the forms of them4 ,during the summer months they are1 generally speaking1 comparatively large and open1 and during the winter months they are small and close4 ,this change in form is seen by a glance at ,plate ,,xiii41 which gives the curves throughout the whole of one year4 ,let us now1 instead of forming a curve of this kind for each month1 form a single average curve for the whole year2 and let us further do this for a series of years4 7,plate ,,xiv47 ,we see that the curves change from year to year in a manner very similar to that in which they change from month to month in any particular year1 and the law of change is such that in years when there are many sun-spots we get a large open curve similar to those found in the summer1 while for years when there are few sun-spots we get small close curves very like those in the winter4 ,hence we have two definite conclusions suggested3 firstly1 that the changes of force are sympathetic with the changes in the sun-spots2 and secondly1 that times of maximum sun-spots correspond to summer1 and times of minimum to winter4 ,and here ,i must admit that this is about as far as we have got at present in the investigation of this relationship4 ,why the needle behaves in this way we have as yet only the very vaguest ideas2 suggestions of different kinds have certainly been put forward1 but none of them as yet can be said to have much evidence in favour of its being the true one4 ,for our present purpose1 however1 it is sufficient to note that there is this very real connection1 and that consequently ,schwabe's sun-spot period may have a very real importance with regard to changes in our earth itself4 ,illustration3 ,,greenwich ,,magnetic ,,curves #ahei-fj ,,plate ,,xiii4 ,,greenwich ,,magnetic ,,curves ,,for ,,april #ahda-ahfj ,sidenote3 ,illustration of spurious connection4 ,but ,i may perhaps repeat the word of caution already uttered against extending without sufficient evidence this notion of the influence of sun-spots to other phenomena1 such as weather4 ,a simple illustration will perhaps serve better than a long argument to show both the way in which mistakes have been made and the way in which they can be seen to be mistakes4 ,there is at the ,royal ,observatory at ,greenwich an instrument for noting the direction of the wind1 the essential part being an ordinary wind-vane1 the movements of which are automatically recorded on a sheet of paper4 ,as the wind shifts from north to east the pencil moves in one direction1 and when it shifts back again towards the north the pencil moves in the reverse way4 ,but sometimes the wind shifts continuously from north to east1 south1 west1 and back to north again1 the vane making a complete revolution2 and this causes the pencil to move continuously in one direction1 until when the vane has come to north again1 the pencil is far away from the convenient place of record2 on such occasions it is often necessary to replace it by hand4 ,then again1 the vane may turn in the opposite direction1 sending the pencil inconveniently to the other side of the record4 ,during the year it is easy to count the number of complete changes of wind in either direction1 and subtracting one number from the other1 we get the excess of complete revolutions of the vane in one direction over that in the other4 ,now if these rather arbitrary numbers are set down year by year1 or plotted in the shape of a diagram1 we get a curve which may be compared with the sun-spot curve1 and during a period of no less than sixteen years--from #aheh to #ahgd--there was a remarkable similarity between the two diagrams4 ,from this evidence alone it might fairly be inferred that the sun-spots had some curious effect upon the weather at ,greenwich1 traceable in this extraordinary way in the changes of the wind4 ,but the particular way in which these changes are recorded is so arbitrary that we should naturally feel surprise if there was a real connection between the two phenomena2 and fortunately there were other records preceding these years and following them which enabled us to test the connection further1 and it was found1 as we might naturally expect1 that it was not confirmed4 ,on looking at diagrams 7,plate ,,xv47 for the periods before and after1 no similarity can be traced between the sun-spot curve and the wind-vane curve1 and we infer that the similarity during the period first mentioned was entirely accidental4 ,this shows that we must be cautious in accepting1 from a limited amount of evidence1 a connection between two phenomena as real and established2 for it may be purely fortuitous4 ,we may particularly remark that it is desirable to have repetitions through several complete periods instead of one alone4 ,it is possible to reduce to mathematical laws the rules for caution in this matter2 and much useful work has already been done in this direction by ,professor ,schuster of ,manchester and others1 though as yet too little attention has been paid to their rules by investigators naturally eager to discover some hitherto unthought-of connection between phenomena4 ,sidenote3 ,faculae follow spots and the chromosphere4 ,with this example of the need for caution1 we may return to phenomena of which we can certainly say that they vary sympathetically with the sun-spots4 ,roughly speaking1 the whole history of the sun seems to be bound up with them4 ,besides these dark patches which we call spots 7which1 by the way1 are not really dark but only less bright than the surrounding part of the disc71 there are patches brighter than the rest which have been called faculae4 ,with ordinary telescopes1 either visual or photographic1 these can generally only be detected near the edge of the sun's disc2 but even with this limitation it can easily be established that the faculae vary in number and size from year to year much in the same way as the spots1 and this conclusion is amply confirmed by the beautiful method of observing the faculae with the new instrument designed by ,professor ,hale of the ,yerkes ,observatory4 ,with this instrument1 called a spectroheliograph1 it is possible to photograph the faculae in all parts of the sun's disc1 and thus to obtain a much more complete history of them1 and there is no doubt whatever of their variation sympathetically with the spots4 ,nor is there any doubt about similar variations in other parts of the sun which we cannot see at all with ordinary telescopes1 except on the occasions when the sun is totally eclipsed4 ,roughly speaking1 these outlying portions of the sun consist of two kinds1 the chromosphere and the corona1 the former looking like an irregular close coating of the ordinary sun1 and the latter like a pearly halo of light extending to many diameters of the sun's disc1 but not with any very regular form4 ,illustration3 ,,plate ,,xv4 ,,smoothed ,,sunspot ,,curve 7,,wolf7 ,,compared ,,with ,,the ,,number ,,of ,,turns ,,made ,,in ,,each ,,year ,,by ,,the ,,osler ,,anemometer ,,vane ,,of ,,the ,,royal ,,observatory1 ,,greenwich 7,,the ,,excess ,,of ,,the ,,direct ,,turns 7,d7 ,,over ,,the ,,retrograde ,,turns 7,r7 ,,or ,,vice ,,versa47 ,,the ,,upper ,,curve ,,is ,,in ,,each ,,case ,,the ,,sunspot ,,curve1 ,,the ,,lower ,,the ,,vane ,,curve4 ,,the ,,break ,,in #ahhb ,,in ,,the ,,vane ,,curve ,,is ,,due ,,to ,,the ,,omission ,,of ,,evidently ,,accidental ,,turns ,,from ,,that ,,date4 ,the chromosphere1 from which shoot out the prominences or red flames1 can now be observed without an eclipse if we employ the beautiful instrument above-mentioned1 the spectroheliograph2 and ,professor ,hale has succeeded in photographing spots1 faculae1 and prominences all on the same plate4 ,but although many have made the attempt 7and ,professor ,hale1 perhaps1 a more determined attempt than any man living71 no one has yet succeeded in obtaining any picture or evidence of the existence of the corona excepting on the occasion of a total solar eclipse4 ,sidenote3 ,eclipses of sun4 ,sidenote3 ,total eclipses rare4 ,now these occasions are very rare4 ,there are two or three eclipses of the sun every year1 but they are generally of the kind known as partial2 when the moon does indeed come between us and the sun to some extent1 but only cuts off a portion of his light--a clean-cut black disc is seen to encroach more or less on the surface of the sun4 ,most of us have had an opportunity of seeing a partial eclipse1 probably more than once2 but few have seen a total eclipse4 ,for this the moon must come with great exactness centrally between us and the sun2 and the spot where this condition is fulfilled completely only covers a few hundred miles of the earth's surface at one moment4 ,as the earth turns round1 and as the moon revolves in its orbit1 this patch from which the sun is totally eclipsed travels over the earth's surface1 marking out a track some thousands of miles in length possibly1 but still not more than #bjj miles wide2 and in order to see the sun totally eclipsed even on the rare occasions when it is possible at all 7for1 as already remarked1 in the majority of cases the eclipse is only partial71 we must occupy some station in this narrow belt or track1 which often tantalisingly passes over either the ocean or some regions not easily accessible to civilised man4 ,moreover1 if we travel to such favoured spots the whole time during which the sun is totally eclipsed cannot exceed a few minutes1 and hence observations are made under rather hurried and trying conditions4 ,in these modern days of photography it is easier to take advantage of these precious moments than it used to be when there was only the eye and memory of an excited observer to rely upon4 ,it is perhaps not surprising that some of the evidence collected on these earlier occasions was conflicting2 but nowadays the observers1 generally speaking1 direct their energies in the first place to mounting accurately in position photographic apparatus of different kinds1 each item of it specially designed to settle some particular problem in the most feasible way2 secondly1 to rehearsing very carefully the exact programme of exposures necessary during the critical few minutes2 and finally1 to securing these photographs with as few mistakes as possible when the precious moments actually arrive4 ,even then the whole of their efforts are quite likely to be rendered unavailing by a passing cloud2 and bitter is the disappointment when1 after travelling thousands of miles1 and spending months in preparation1 the whole enterprise ends in nothing owing to some caprice of the weather4 ,sidenote3 ,corona follows spots4 ,hence it will easily be imagined that our knowledge of the corona1 the part of the sun which we can still only study on occasions of a total solar eclipse1 advances but slowly4 ,during the last twenty years there has been altogether scarcely half-an-hour available for this research1 though it may fairly be said that the very best possible use has been made of that half-hour4 ,and1 what is of importance for our immediate purpose1 it has gradually been established by comparing the photographs of one eclipse with those of another1 that the corona itself undergoes distinct changes in form in the same period which governs the changes of sun-spots4 ,when there are many sun-spots the corona spreads out in all directions from the edge of the sun's disc2 when there are few sun-spots the corona extends very much further in the direction of the sun's equator1 so that at sun-spot minimum there is an appearance of two huge wings4 ,although the evidence is necessarily collected in a scrappy manner1 by this time there is sufficient to remove this relationship out of the region of mere suspicion1 and to give it a well-established place in our knowledge of the sun's surroundings4 ,sidenote3 ,corona may influence magnets4 ,now the corona of the sun may be compared to some rare animal which we only see by paying a visit to some distant land1 and may consider ourselves even then fortunate to get a glimpse of2 and it might be thought that the habits of such an animal are not likely to be of any great importance in our everyday life4 ,but so far from this being the case in regard to the corona1 it is more than possible that the knowledge of its changes may be of vital interest to us4 ,i have already said that1 as yet1 we have no satisfactory account of the reason why changes in sun-spots seem to influence changes in our magnets on the earth2 but one of the theories put forward in explanation1 and one by no means the least plausible1 is that this influence may come1 not from the sun-spots themselves1 but from some other solar phenomenon which varies in sympathy with them2 and in particular that it may come from the corona4 ,these wings which reach out at sun-spot minimum can be seen to extend a considerable distance1 and there is no reason to suppose that they actually cease at the point where they become too faint for us to detect them further2 they may extend quite as far as the earth itself and even beyond2 and they may be of such a nature as to influence our magnets4 ,as the earth revolves round the sun it may sometime plunge into them1 to emerge later and pass above or below them2 as again the wings spread themselves at sun-spot minimum and seem to shrink at maximum1 so our magnets may respond by sympathetic though very small vibrations4 ,hence it is quite possible that the corona is directly influencing the magnetic changes on the earth4 ,sidenote3 ,possible importance of corona4 ,but it may be urged that these changes are so slight as to be merely of scientific interest4 ,that may be true to-day1 but who will be bold enough to say that it will be true to-morrow8 ,if we are thinking of practical utility alone1 we may remember that two great forces of ,nature which we have chained into the service of man1 steam and electricity1 put forth originally the most feeble manifestations1 which might readily have been despised as valueless2 but by careful attention to proper conditions results of overwhelming practical importance have been obtained from these forces1 which might have been1 and for many centuries were1 neglected as too trivial to be worth attention4 ,recently the world has been startled by the discovery of new elements1 such as radium1 whose very existence was only detected by a triumph of scientific acuteness in investigation1 and yet which promise to yield influences on our lives which may overwhelm in importance all that has gone before4 ,and similarly it may be that these magnetic changes1 when properly interpreted or developed1 may become of an importance in the future out of all proportion to the attention which they have hitherto attracted4 ,hence1 although perhaps sufficient has already been established to show the immense consequences which flow from ,schwabe's remarkable discovery of the periodicity in solar spots1 we may be as yet only on the threshold of its real value4 ,from what little causes great events spring6 ,how little can ,schwabe have realised1 when he began to point his modest little telescope at the sun1 and to count the number of spots--the despised spots which he had been assured were of no interest and exhibited no laws1 and were generally unprofitable--that he was taking the first step in the invention of the great science of ,solar ,physics6--a science which is1 ,i am glad to say1 occupying at the present moment so much of the attention1 not only of the great ,yerkes ,observatory1 but of many other observatories scattered over the globe4 ,,chapter ,,vi ,,the ,,variation ,,of ,,latitude ,if we should desire to classify discoveries in order of merit1 we must undoubtedly give a high place to those which are made under direct discouragements4 ,in the last chapter we saw that ,schwabe entered upon his work under conditions of this kind1 it being the opinion of experienced astronomers who had looked at the facts that there was nothing of interest to be got by watching sun-spots4 ,in the present chapter ,i propose to deal with a discovery made in the very teeth of the unanimous opinion of the astronomical world by an ,american amateur1 ,mr4 ,s4 ,c4 ,chandler of ,cambridge 7,massachusetts74 ,it is my purpose to allow him to himself explain the steps of this discovery by giving extracts from the magnificent series of papers which he contributed to the ,astronomical ,journal on the subject in the years #ahia-id1 but it may help in the understanding of these extracts if ,i give a brief summary of the facts4 ,and ,i will first explain what is meant by the ,variation of ,latitude4 ,sidenote3 ,latitude4 ,sidenote3 ,precession4 ,we are all familiar with the existence of a certain star in the heavens called the ,pole ,star1 and we know that at any particular place it is seen constantly in the north at a definite height above the horizon1 which is the latitude of the place4 ,when watched carefully with a telescope it is found to be not absolutely stationary1 but to describe a small circle in the heavens day by day1 or rather night by night4 ,these simple facts are bound up with the phenomenon of the earth's rotation in this way3 the axis about which it is rotating points to the centre of that little circle1 and any change in the position of the axis can therefore be determined by observing these motions of the ,pole ,star4 ,such changes may be of two kinds3 firstly1 we might find that the size of the circle increased or diminished1 and this would mean that the earth's axis was pointing farther away from the ,pole ,star or nearer to it--pointing1 that is to say1 in a different direction in space4 ,this actually happens 7as has been known for some thousands of years7 owing to the phenomenon called precession2 the circle described by our ,pole ,star is at present getting a little smaller1 but it will ultimately increase in size1 and after thousands of years become so large that the ,pole ,star will entirely lose its character as a steady guide to the ,north4 ,sidenote3 ,change of latitude4 ,sidenote3 ,twenty years ago disbelieved4 ,secondly 7and this is what more immediately concerns us71 the centre of the circle may alter its position and be no longer at the same height above the horizon of any given place4 ,this would mean that the earth's axis was shifting in the earth itself--that the ,north ,pole which our explorers go to seek is not remaining in the same place4 ,that it does not change appreciably in position we know from familiar experience2 our climates1 for instance1 would suffer considerably if there were any large changes4 ,but astronomers are concerned with minute changes which would not have any appreciable effect on climate1 and the question has long been before them whether1 putting aside large movements1 there were any minute variations in position of the ,north ,pole4 ,twenty years ago the answer to this question would have been given decidedly in the negative2 it was considered as certain that the ,north ,pole did not move at all within the limits of our most refined astronomical observations4 ,accepted theory seemed to indicate that any movements must in any case recur after a period of ten months1 and careful discussion of the observations showed that there was no oscillation in such a period4 ,now we know that the theory itself was wrong1 or rather was founded upon a mistaken assumption2 and that the facts when properly examined show clearly a distinct movement of the ,north ,pole1 not a very large one1 for all its movements take place within the area occupied by a moderate-sized room1 but still a movement easily measurable by astronomical observations1 and ,mr4 ,chandler was the first to point out the law of these movements1 and very possibly the first to suspect them4 ,sidenote3 ,chandler's papers4 ,with these few words of explanation ,i will let ,mr4 ,chandler tell his own story4 ,his first paper appeared in the ,astronomical ,journal in ,november #ahia1 and is courageously headed1 ,on the ,variation of ,latitude--,i say courageously1 because at that time it was believed that the latitude did not vary1 and ,mr4 ,chandler himself was only in possession of a small portion of the facts4 ,they unravelled themselves as he went forward2 but he felt that he had firm hold of the end of the thread1 and he faced the world confidently in that belief4 ,he begins thus3-- ,sidenote3 ,first signs of change4 ,in the determination of the latitude of ,cambridge#e with the ,almucantar1 about six years and a half ago1 it was shown that the observed values1 arranged according to nights of observation1 exhibited a decided and curious progression throughout the series1 the earlier values being small1 the later ones large1 and the range from ,november #ahhd to ,april #ahhe being about four-tenths of a second4 ,there was no known or imaginable instrumental or personal cause for this phenomenon1 yet the only alternative seemed to be an inference that the latitude had actually changed4 ,this seemed at the time too bold an inference to place upon record1 and ,i therefore left the results to speak for themselves4 ,the subsequent continuation of the series of observations to the end of ,june #ahhe gave a maximum about ,may #a1 while the discussion of the previous observations from ,may to ,november #ahhd gave a minimum about ,september #a1 indicating a range of #j4g within a half-period of about seven months4 ,mr4 ,chandler then gives some figures in support of these statements1 presenting them with the clearness which is so well marked a feature of the whole series of papers1 and concludes this introductory paper as follows3-- ,it thus appears that the apparent change in the latitude of ,cambridge is verified by this discussion of more abundant material4 ,the presumption that it is real1 on this determination alone1 would justify further inquiry4 ,sidenote3 ,confirmed in ,europe4 ,curiously enough ,dr4 ,kuestner1 in his determination of the aberration from a series of observations coincident in time with those of the ,almucantar1 came upon similar anomalies1 and his results1 published in #ahhh1 furnish a counterpart to those which ,i had pointed out in #ahhe4 ,the verification afforded by the recent parallel determinations at ,berlin1 ,prague1 ,potsdam1 and ,pulkowa1 which show a most surprising and satisfactory accordance1 as to the character of the change1 in range and periodicity1 with the ,almucantar results1 has led me to make further investigations on the subject4 ,they seem to establish the nature of the law of those changes1 and ,i will proceed to present them in due order4 ,the second paper appeared on ,november #bc1 and opens with the following brief statement of his general results at that time3-- ,sidenote3 #dbg days' period4 ,before entering upon the details of the investigations spoken of in the preceding number1 it is convenient to say that the general result of a preliminary discussion is to show a revolution of the earth's pole in a period of #dbg days1 from west to east1 with a radius of thirty feet1 measured at the earth's surface4 ,assuming provisionally1 for the purpose of statement1 that this is a motion of the north pole of the principal axis of inertia about that of the axis of rotation1 the direction of the former from the latter lay towards the ,greenwich meridian about the beginning of the year #ahij4 ,this1 with the period of #dbg days1 will serve to fix approximately the relative positions of these axes at any other time1 for any given meridian4 ,it is not possible at this stage of the investigation to be more precise1 as there are facts which appear to show that the rotation is not a perfectly uniform one1 but is subject to secular change1 and perhaps irregularities within brief spaces of time4 ,sidenote3 ,contrary to received views4 ,it is almost impossible1 now that we have become familiar with the ideas conveyed in this paragraph1 to understand1 or even fully to remember1 the impression produced by them at the time2 the sensation caused in some quarters1 and the ridicule excited in others4 ,they were in flat contradiction to all accepted views2 and it was believed that these views were not only theoretically sound1 but had been matured by a thorough examination of observational evidence4 ,the only period in which the earth's pole could revolve was believed to be ten mouths2 and here was ,mr4 ,chandler proclaiming1 apparently without any idea that he was contradicting the laws of dynamics1 that it was revolving in fourteen months6 ,the radius of its path had been found to be insensible by careful discussion of observations1 and now he proclaimed a sensible radius o,l thirty feet4 ,finally1 he had the audacity to announce a variable period1 to which there was nothing at all corresponding in the mathematical possibilities4 ,this was the bitterest pill of all4 ,even after ,professor ,newcomb had shown us how to swallow the other two1 he could not recommend any attempt at the third1 as we shall presently see2 and ,mr4 ,chandler was fain ultimately to gild it a little before it could be gulped4 ,sidenote3 ,pulkowa puzzle solved1 also ,washington4 ,but this is anticipating1 and it is our intention to follow patiently the evidence adduced in support of the above statements1 made with such splendid confidence to a totally disbelieving world4 ,mr4 ,chandler first examines the observations of ,dr4 ,kuestner of ,berlin1 quoted at the end of his last paper1 and shows how well they are suited by the existence of a variation in the latitude of #dbg days2 and that this new fact is added--when the ,cambridge 7,u4,s4,a47 latitudes were the smallest those of ,berlin were the largest1 and vice versa1 as would clearly be the case if the phenomenon was due to a motion of the earth's pole2 for if it moved nearer ,america it must move further from ,europe4 ,he then examines a long series of observations made in the years #ahfd-ahgc at ,pulkowa1 near ,st4 ,petersburg1 and again finds satisfactory confirmation of his law of variation4 ,now it had long been known that there was something curious about these observations1 but no one could tell what it was4 ,the key offered by ,mr4 ,chandler fitted the lock exactly1 and the anomalies which had been a puzzle were removed4 ,this was in itself a great triumph2 but there was another to come1 which we may let ,mr4 ,chandler describe in his own words3-- ,in #ahfb ,professor ,hubbard began a series of observations of a ,lyrae at the ,washington ,observatory with the prime vertical transit instrument1 for the purpose of determining the constants of aberration and nutation and the parallax of the star4 ,the methods of observation and reduction were conformed to those used with such success by ,w4 ,struve4 ,after ,hubbard's death the series was continued by ,professors ,newcomb1 ,hall1 and ,harkness until the beginning of #ahfg4 ,professor ,hall describes these observations as the most accurate determinations of declination ever made at the ,naval ,observatory4 ,the probable error of a declination from a single transit was -#j4ada1 and judging from the accidental errors1 the series ought to give trustworthy results4 ,upon reducing them1 however1 it was found that some abnormal source of error existed1 which resulted in anomalous values of the aberration-constant in the different years1 and a negative parallax in all4 ,a careful verification of the processes of reduction failed to discover the cause of the trouble1 and ,professor ,hall says that the results must stand as printed1 and that probably some annual disturbance in the observations or the instrument occurred1 which will never be explained1 and which renders all deductions from them uncertain4 ,the trouble could not be connected with personal equation1 the anomalies remaining when the observations of the four observers who took part were separately treated4 ,nor1 as ,professor ,hall points out1 will the theoretical ten-month period in the latitude furnish the explanation4 ,it is manifest1 however1 that if the #dbg-;day period exists1 its effect ought to appear distinctly in declination-measurements of such high degree of excellence as these presumably were1 and1 as ,i hope satisfactorily to show1 actually are4 ,when this variation is taken into account the observations will unquestionably vindicate the high expectations entertained with regard to them by the accomplished and skilful astronomers who designed and carried them out4 ,sidenote3 ,direction of revolution of ,pole4 ,sidenote3 ,example of results4 ,from this general account ,i am excluding technical details and figures1 and unfortunately a great deal is thereby lost4 ,we lose the sense of conviction which the long rows of accordant figures force upon us1 and we lose the opportunities of admiring both the astonishing amount of work done and the beautiful way in which the material is handled by a master4 ,but ,i am tempted to give one very small illustration of the numerical results from near the end of the paper4 ,after discussing the ,washington results1 and amply fulfilling the promise made in the preceding extract1 ,mr4 ,chandler compares them with the ,pulkowa results1 and shows that the ,earth's ,pole must be revolving from west to east1 and not from east to west4 ,and then he writes down a simple formula representing this motion1 and compares his formula with the observations4 ,he gives the results in seconds of arc1 but for the benefit of those not familiar with astronomical measurements we may readily convert these into feet2 and in the following tables are shown the distances of the ,earth's ,pole in feet from its average position1#f as observed at ,washington and at ,pulkowa1 and the same distances calculated according to the formula which ,mr4 ,chandler was able to write down at this early stage4 ,the signs and - of course indicate opposite directions of displacement3-- ,,washington4 ,deviation of ,pole4 ------------------------------------- ,date4 ,observed4 ,formula4 ------------------------------------- #ahfd1 ,dec4 #bh -#bh feet -#bc feet #ahfe1 ,mar4 #ai - #a -#ab ,june #a #ae #ab ,aug4 #aa #bb #bc ,oct4 #i #aa #ae ,dec4 #ac -#ag - #f ------------------------------------- ,,pulkowa4 ,deviation of ,pole4 ------------------------------------- ,date4 ,observed4 ,formula4 ------------------------------------- #ahfe1 ,july #be -#ah feet -#ab feet ,sept4 #i #c #c ,nov4 #bb #bf #bb #ahff1 ,feb4 #bb #ah #ac ,june #d -#aa -#ah ,july #ag -#af -#bc ------------------------------------- ,of course the figures are not exact in every case1 but they are never many feet wrong2 and it may well be imagined that it is a difficult thing to deduce1 even from the most refined observations1 the position of the earth's pole to within a foot4 ,the difficulty is exactly the same as that of measuring the length of an object #cjj miles away to within an inch6 ,mr4 ,chandler winds up his second paper thus3-- ,we thus find that the comparison of the simultaneous series at ,pulkowa and ,washington1 #ahfc-ahfg1 leads to the same conclusion as that already drawn from the simultaneous series at ,berlin and ,cambridge1 #ahhd-ahhe4 ,the direction of the polar motion may therefore be looked upon as established with a large degree of probability4 ,in the next paper ,i will present the results derived from ,,peters1 ,,struve1 ,,bradley1 and various other series of observations1 after which the results of all will be brought to bear upon the determination of the best numerical values of the constants involved4 ,sidenote3 ,bradley's observations4 ,sidenote3 ,latitude varied in twelve months then4 ,the results were not1 however1 presented in this order4 ,in the next paper1 which appeared on ,december #bc1 #ahia1 ,mr4 ,chandler begins1 with the work of ,bradley1 the very series of observations at ,kew and ,wansted which led to the discoveries of aberration and nutation1 and which we considered in the third chapter4 ,he first shows that1 notwithstanding the obvious accuracy of the observations1 there is some unexplained discordance4 ,the very constant of aberration which ,bradley discovered from them differs by half-a-second of arc from our best modern determinations4 ,attempts have been made to ascribe the discordance to changes in the instrument1 but ,mr4 ,chandler shows that such changes1 setting aside the fact that ,bradley would almost certainly have discovered them1 will not fit in with the facts4 ,the facts1 when analysed with the skill to which we have become accustomed1 are that there is a periodic swing in the results with a period of about a year1 and not fourteen months1 as before1 a result so curious1 as he admits1 that if we found no further support1 it might lead us to distrust the above reasoning1 and throw us back to the possibility that1 after all1 ,,bradley',s observations may have been vitiated by some kind of annual instrumental error4 ,but it will abundantly appear1 when ,i have had the opportunity to print the deductions from all the other series of observations down to the present time1 that the inference of an increase in the period of polar revolution is firmly established by their concurrent testimony4 ,we shall presently return to this curious result1 which might well have dismayed a less determined researcher than ,mr4 ,chandler1 but which only led him on to renewed exertions4 ,the results obtained from ,bradley's observations may be put in the form of a diagram thus3-- ,illustration3 ,,fig4 #g4 ,it will be seen that the maxima and minima fall in the spring and autumn1 and this fact alone seemed to show that the effect could not be due to temperature1 for we should expect the greatest effect in that case in winter and summer4 ,it could not be due to the parallax of the stars for which ,bradley began his search1 for stars in different quarters of the heavens would then be differently affected1 and this was not the case4 ,there remains1 concluded ,mr4 ,chandler after full discussion1 the only natural conclusion of an actual displacement of the zenith1 in other words1 a change of latitude4 ,and he concludes this paper with the following fine passage3-- ,so far1 then1 as the results of this incomparable series of observations at ,kew and ,wansted1 considered by themselves alone1 can now be stated1 the period of the polar rotation at that epoch appears to have been probably somewhat over a year1 and certainly shorter by about two months than it is at the present time4 ,the range of the variation was apparently in the neighbourhood of a second of arc1 or considerably larger than that shown by the best modern observations4 ,sidenote3 ,bradley's greatness4 ,before taking leave of these observations for the present ,i cannot forbear to speak of the profound impression which a study of them leaves upon the mind1 and the satisfaction which all astronomers must feel in recognising that1 besides its first fruits of the phenomena of aberration and nutation1 we now owe also our first knowledge of the polar motion to this same immortal work of ,bradley4 ,its excellence1 highly appreciated as it has been1 has still been hitherto obscured by the presence of this unsuspected phenomenon4 ,when divested of its effects1 the wonderful accuracy of this work must appear in a finer light1 and our admiration must be raised to higher pitch4 ,going back to it after one hundred and sixty years seems indeed like advancing into an era of practical astronomy more refined than that from which we pass4 ,and this leads to a suggestion worthy of serious practical consideration--whether we can do better in the future study of the polar rotation1 than again to avail ourselves of ,bradley's method1 without endangering its elegant simplicity and effectiveness by attempts at improvement1 other than supplying certain means of instrumental control which would without doubt commend themselves to his sagacious mind4 ,sidenote3 ,other puzzles explained4 ,in the next article ,bradley's later observations at ,greenwich1 the results of which are not so distinct1 will be discussed2 and also those of ,brinkley at ,dublin1 #ahjh-ac and #ahah-bb4 ,this will bring again to the surface one of the most interesting episodes in astronomical history1 the spirited and almost acrimonious dispute between ,brinkley and ,pond with regard to stellar parallaxes4 ,i hope to show that the hitherto unsolved enigma of ,brinkley's singular results finds its easy solution in the fact of the polar motion4 ,the period of his epoch appears to have been about a year1 and its range more than a second4 ,afterwards will follow various discussions already more or less advanced towards completion4 ,these include ,bessel's observations at ,koenigsberg1 #ahbj-bd1 with the ,reichenbach circle1 and in #ahdb-dd with the ,repsold circle2 the latitudes derived from the polar-point determinations of ,struve and ,maedler with the ,dorpat circle1 #ahbb-ch2 ,struve's observations for the determination of the aberration2 ,peters' observations of ,polaris1 #ahda-dc1 with the vertical-circle2 the results obtained from the reflex zenith-tube at ,greenwich1 #ahcg-ge1 whose singular anomalies can be referred in large part to our present phenomenon1 complicated with instrumental error1 to which until now they have been exclusively attributed2 the ,greenwich transit-circle results1 #ahea-fe1 in which case1 however1 a similar complication and the large accidental errors of observation seem to frustrate efforts to get any pertinent results2 the ,berlin prime-vertical observations of ,weyer and ,bruennow1 #ahde-df1 in which ,i hope to show that the parallax of beta ,draconis derived from them is simply a record of the change of latitude2 the conflicting latitude determinations at ,cambridge1 ,england2 the ,washington observation of ,polaris and other close ,polars1 #ahff-hg1 with the transit-circle2 also those at ,melbourne1 #ahfc-hd1 a portion of which have already been drawn upon in the last number of the ,journal1 and some others4 ,while the list is a considerable one1 ,i shall be able to compress the statement of results for many of the series into a short space4 ,sidenote3 ,provisional nature of results4 ,in connection with this synopsis of the scope of the investigations1 one or two particulars may be of interest1 which at the present writing seem to foreshadow the probable outcome4 ,i beg1 however1 that the statement will be regarded merely as a provisional one4 ,first1 while the period is manifestly subject to change1 as has already once or twice been intimated1 ,i have hitherto failed in tracing the variations to any regular law1 expressible in a numerical formula4 ,indeed1 the general impression produced by a study of these changes in the length of the period is that the cause which produces them operates capriciously to a certain degree1 although the average effect for a century has been to diminish the velocity of the revolution of the pole4 ,how far this impression is due to the uncertainty of the observations1 and to the complication of the phenomenon with other periodical changes of a purely instrumental kind1 ,i cannot say4 ,almost all of the series of any extent which have been examined1 have the peculiarity that they manifest the periodicity quite uniformly and distinctly for a number of years1 then for a while obscurely4 ,in some cases1 however1 what at first appears to be an objective irregularity proves not to be so by comparison with overlapping series at other observatories4 ,another characteristic which has struck my attention1 although somewhat vaguely1 is that the variations in the length of the period seem to go hand in hand with simultaneous alterations in the amplitude of the rotation2 the shorter periods being apparently associated with the larger coefficients for the latter4 ,the verification of these surmises awaits a closer comparative scrutiny1 the opportunity for which will come when the computations are in a more forward state4 ,if confirmed1 these observations will afford a valuable touchstone1 in seeking for the cause of a phenomenon which now seems to be at variance with the accepted laws of terrestrial rotation4 ,sidenote3 ,reception of discovery4 ,let us now for a few moments turn aside from the actual research to see how the announcement was received4 ,it would be ungracious to reprint here any of the early statements of incredulity which found their way into print1 especially in ,germany4 ,but the first note of welcome came from ,simon ,newcomb1 in the same number of the ,astronomical ,journal as the paper just dealt with1 and the following extract will indicate both the difficulties felt in receiving ,mr4 ,chandler's results and the way in which ,newcomb struck at the root of them4 ,sidenote3 ,newcomb's explanation4 ,mr4 ,chandler's remarkable discovery1 that the apparent variations in terrestrial latitudes may be accounted for by supposing a revolution of the axis of rotation of the earth around that of figure1 in a period of #dbg days1 is in such disaccord with the received theory of the earth's rotation that at first ,i was disposed to doubt its possibility4 ,but ,i am now able to point out a vera causa which affords a complete explanation of this period4 ,up to the present time the treatment of this subject has been this3 ,the ratio of the moment of inertia of the earth around its principal axis to the mean of the other two principal moments1 admits of very accurate determination from the amount of precession and nutation4 ,this ratio involves what we might call1 in a general way1 the solid ellipticity of the earth1 or the ellipticity of a homogeneous spheroid having the same moments of inertia as the earth4 ,when the differential equations of the earth's rotation are integrated1 there appear two arbitrary constants1 representing the position of any assigned epoch of the axis of rotation relative to that of figure4 ,theory then shows that the axis of rotation will revolve round that of figure1 in a period of #cjf days1 and in a direction from west toward east4 ,the attempts to determine the value of these constants have seemed to show that both are zero1 or that the axes of rotation and figure are coincident4 ,several years since1 ,sir ,william ,thomson published the result of a brief computation from the ,washington ,prime-,vertical observations of alpha ,lyrae which ,i made at his request and which showed a coefficient #j4je4 ,this coefficient did not exceed the possible error of the result2 ,i therefore regarded it as unreal4 ,sidenote3 ,the forgotten assumption4 ,the question now arises whether ,mr4 ,chandler's result can be reconciled with dynamic theory4 ,i answer that it can1 because the theory which assigns #cjf days as the time of revolution is based on the hypothesis that the earth is an absolutely rigid body4 ,but1 as a matter of fact1 the fluidity of the ocean plays an important part in the phenomenon1 as does also the elasticity of the earth4 ,the combined effect of this fluidity and elasticity is that if the axis of rotation is displaced by a certain amount1 the axis of figure will1 by the changed action of the centrifugal force1 be moved toward coincidence with the new axis of rotation4 ,the result is1 that the motion of the latter will be diminished in a corresponding ratio1 and thus the time of revolution will be lengthened4 ,an exact computation of the effect is not possible without a knowledge of the earth's modulus of elasticity4 ,but ,i think the result of investigation will be that the rigidity derived from ,mr4 ,chandler's period is as great as that claimed by ,sir ,william ,thomson from the phenomena of the tides4 ,sidenote3 ,but ,chandler's work still mistrusted4 ,this was very satisfactory4 ,professor ,newcomb put his finger on the assumption which had been made so long ago that it had been forgotten3 and the lesson is well worth taking to heart1 for it is not the first time that mistaken confidence in a supposed fact has been traced to some forgotten preliminary assumption3 and we must be ever ready to cast our eyes backward over all our assumptions1 when some new fact seems to challenge our conclusions4 ,it might further be expected that this discovery of the way in which theory had been defective would as a secondary consequence inspire confidence in the other conclusions which ,mr4 ,chandler had arrived at in apparent contradiction to theory2 or at least suggest the suspension of judgment4 ,but ,professor ,newcomb did not feel that this was possible in respect of the change of period1 from about twelve months in ,bradley's time to fourteen months in ours4 ,we have seen that ,mr4 ,chandler himself regarded this as a curious result requiring confirmation3 but since the confirmation was forthcoming1 he stated it with full confidence1 and drew the following remarks from ,professor ,newcomb in ,july #bb1 #ahib3-- ,the fact of a periodic variation of terrestrial latitudes1 and the general law of that variation1 have been established beyond reasonable doubt by the observations collected by ,mr4 ,chandler4 ,but two of his minor conclusions1 as enumerated in ,no4 #c of this volume1 do not seem to me well founded4 ,they are-- #a4 ,that the period of the inequality is a variable quantity4 #b4 ,that the amplitude of the inequality has remained constant for the last half century4 ,professor ,newcomb proceeds to give his reasons for scepticism1 which are too technical in character to reproduce here4 ,but ,i will quote the following further sentence from his paper3-- ,the question now arises how far we are entitled to assume that the period must be invariable4 ,i reply that1 perturbations aside1 any variation of the period is in such direct conflict with the laws of dynamics that we are entitled to pronounce it impossible4 ,but we know that there are perturbations1 and ,i do not see how one can doubt that they have so acted as to increase the amplitude of the variation since #ahdj4 ,sidenote3 ,chandler's reply4 ,in other words1 while recognising that there may be a way of reconciling one of the minor conclusions with theory1 ,professor ,newcomb considers that in this case the other must go4 ,mr4 ,chandler's answer will speak for itself4 ,it was delayed a little in order that he might present an immense mass of evidence in support of his conclusions1 and was ultimately printed on ,august #bc1 #ahib4 ,the material utilised in the foregoing forty-five series aggregates more than thirty-three thousand observations4 ,of these more than one-third were made in the southern hemisphere1 a fact which we owe principally to ,cordoba4 ,it comprises the work of seventeen observatories 7four of them in the southern hemisphere7 with twenty-one different instruments1 and by nine distinct methods of observation4 ,only three of the series 7,,xxi41 ,,xxv41 and ,,xxxv471 and these among the least precise intrinsically1 give results contradictory of the general law developed in ,no4 #bfg4 ,this degree of general harmony is indeed surprising when the evanescent character of the phenomenon under investigation is considered4 ,the reader has now before him the means for independent scrutiny of the material on which the conclusions already drawn1 and those which are to follow1 are based4 ,the space taken in the printing may seem unconscionable1 but ,i hope this will be charged to the extent of the evidence collected1 and not to diffuseness or the presentation of needless detail2 for ,i have studiously sought to compress the form of statement without omitting anything essential for searching criticism4 ,that it was important to do this is manifest1 since the conclusions1 if established1 overthrow the existing theory of the earth's rotation1 as ,i have pointed out on p4 #ba4 ,i am neither surprised nor disconcerted1 therefore1 that ,professor ,newcomb should hesitate to accept some of these conclusions on the ground 7,a4 ,j41 ,no4 #bga7 that they are in such conflict with the laws of dynamics that we are entitled to pronounce them impossible4 ,he has been so considerate and courteous in his treatment of my work thus far1 that ,i am sure he will not deem presumptuous the following argument in rebuttal4 ,sidenote3 ,he put aside all teachings of theory1 and is not dismayed4 ,it should be said1 first1 that in beginning these investigations last year1 ,i deliberately put aside all teachings of theory1 because it seemed to me high time that the facts should be examined by a purely inductive process2 that the nugatory results of all attempts to detect the existence of the ,eulerian period probably arose from a defect of the theory itself2 and that the entangled condition of the whole subject required that it should be examined afresh by processes unfettered by any preconceived notions whatever4 ,the problem which ,i therefore proposed to myself was to see whether it would not be possible to lay the numerous ghosts--in the shape of numerous discordant residual phenomena pertaining to determinations of aberration1 parallaxes1 latitudes1 and the like--which had heretofore flitted elusively about the astronomy of precision during the century2 or to reduce them to tangible form by some simple consistent hypothesis4 ,it was thought that if this could be done1 a study of the nature of the forces1 as thus indicated1 by which the earth's rotation is influenced1 might lead to a physical explanation of them4 ,naturally1 then1 ,i am not much dismayed by the argument of conflict with dynamic laws1 since all that such a phrase means must refer merely to the existent state of the theory at any given time4 ,when the #dbg-;day period was propounded1 it was as inconsistent with known dynamic law as the variation of it now appears to be4 ,professor ,newcomb's own happy explanation has already set aside the first difficulty1 as it would appear1 and advanced the theory by an important step4 ,are we so sure yet of a complete knowledge of all the forces at work as to exclude the chance of a vera causa for the second8 ,sidenote3 ,faraday's words4 ,there is a splendid ring of resolution about these words4 ,let us compare them with a notable utterance of ,faraday3-- ,the philosopher should be a man willing to listen to every suggestion1 but determined to judge for himself4 ,he should not be biassed by appearances2 have no favourite hypothesis2 be of no school2 and in doctrine have no master4 ,he should not be a respecter of persons1 but of things4 ,truth should be his primary object4 ,if to these qualities be added industry1 he may indeed hope to walk within the veil of the temple of ,nature4 ,sidenote3 ,chandler's other work at this time4 ,sidenote3 ,his ultimate satisfactory solution4 ,sidenote3 ,interference of two waves4 ,tested by this severe standard1 ,mr4 ,chandler fails in no particular1 least of all in that of industry4 ,the amount of work he got through about this time was enormous1 for besides the main line of investigation1 of which we have only had after all a mere glimpse1 he had been able to turn aside to discuss a subsidiary question with ,professor ,comstock2 he had examined with great care some puzzling characteristics in the variability of stars2 he computed some comet ephemerides2 and he was preparing a new catalogue of variable stars--a piece of work involving the collection and arrangement of great masses of miscellaneous material4 ,yet within a few months after replying as above to ,professor ,newcomb's criticism1 he was able to announce that he had found the key to the new puzzle1 and that theory and observation were again brought into complete accord4 ,we will as before listen to the account of this new step in his own words1 but a slight preliminary explanation may help those unaccustomed to the terminology4 ,the polar motion was found to be compounded of two independent motions1 both periodic1 but having different periods4 ,now1 the general results of such a composition are well known in several different branches of physics1 especially in the theory of sound4 ,if two notes of nearly the same pitch be struck at the same time1 we hear the resultant sound alternately swell and die away1 because the vibrations caused by the two notes are sometimes going in the same direction1 and after an interval are going exactly in opposite directions4 ,diagrammatically we should represent the vibrations by two waves1 as below2 the upper wave goes through its period seven and a half times between ,a and ,d1 the lower only six times2 and it is easily seen that at ,a and ,c the waves are sympathetic1 at ,b and ,d antipathetic4 ,at ,a and ,c the compound vibration would be doubled2 at ,b and ,d reduced to insensibility4 ,the point is so important that perhaps a numerical illustration of it will not be superfluous4 ,the waves are now represented by rows of figures as below4 ,the first series recurs after every #f1 the second after every #g4 ,illustration3 ,,fig4 #h4 ,first ,wave #a #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a ,second ,wave #a #b #c #d #d #c #b #a #b #c #d #d #c #b #a #b #c #d #d #c #b #a #b #c #d #d #c #b #a #b #c ---------------------------------------- --------------------- ,combined ,effect #b #d #f #h #g #e #c #c #e #g #g #f #d #d #d #f #f #f #e #e #e #e #e #e #e #f #f #f #d #d #d ,great disturbance4 ,calm4 ---------------------------------------- ------------------------------------- ,first ,wave #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a #b #c #d #c #b #a #b ,second ,wave #d #d #c #b #a #b #c #d #d #c #b #a #b #c #d #d #c #b #a #b #c #d #d #c #b #a #b #c #d #d #c ---------------------------------------- --------------------- ,combined ,effect #f #g #g #e #c #c #e #g #h #f #d #b #d #f #h #g #e #c #c #e #g #g #f #d #d #d #f #f #f #e #e ,great disturbance4 ,sidenote3 ,illustration from ocean travel4 ,adding the two rows together1 the oscillations at first reinforce one another and we get numbers ranging from #b to #h instead of from #a to #d2 but one wave gains on the other1 until it is rising when the other is falling1 and the numbers add up to a steady series of #e's4 ,it will be seen that there are no less than seven consecutive #e's1 and all the variation seems to have disappeared4 ,but presently the waves separate again1 and the period of great disturbance recurs2 it will be seen that in the combined effect the numbers repeat exactly after the #dbnd term4 ,now those unfamiliar with the subject may not be prepared for the addition of one physical wave to another1 as though they were numbers1 but the analogy is perfect4 ,travellers by some of the fast twin-screw steamers have had unpleasant occasion to notice this phenomenon1 when the engineer does not run the two screws precisely at the same speed2 there come times when the ship vibrates violently1 separated by periods of comparative stillness4 ,instances from other walks of life may recur to the memory when once attention is called to the general facts2 but enough has been said to explain the point numbered 7#b7 in the subjoined statement4 ,to understand the rest1 we must remember that if the two waves are not equal in amplitude1 i4e4 if the backward and forward motion is not the same in both1 they cannot annul one another1 but the greater will always predominate4 ,those interested in following the matter further should have no difficulty in constructing simple examples to illustrate such points4 ,we will proceed to give ,mr4 ,chandler's statements3-- ,sidenote3 ,chandler's final formulae4 ,we now come upon a new line of investigation4 ,heretofore1 as has been seen1 the method has been to condense the results of each series of observations into the interval comprised by a single period1 then to determine the mean epoch of minimum and the mean range for each series1 and1 finally1 by a discussion of these quantities1 to establish the general character of the law of the rotation of the pole4 ,it is now requisite to analyse the observations in a different way1 and discover whether the deviations from the general provisional law1 in the last column of ,table ,,ii41 are real1 and also in what manner the variation of the period is brought about4 ,the outcome of this discussion1 which is to be presented in the present paper1 is extremely satisfactory4 ,the real nature of the phenomenon is most distinctly revealed1 and may be described as follows3-- #a4 ,the observed variation of the latitude is the resultant curve arising from two periodic fluctuations superposed upon each other4 ,the first of these1 and in general the more considerable1 has a period of about #dbg days1 and a semi-amplitude of about #j4ab4 ,the second has an annual period with a range variable between #j4jd and #j4bj during the last half-century4 ,during the middle portion of this interval1 roughly characterised as between #ahfj and #ahhj1 the value represented by the lower limit has prevailed1 but before and after those dates1 the higher one4 ,the minimum and maximum of this annual component of the variation occur at the meridian of ,greenwich1 about ten days before the vernal and autumnal equinoxes respectively1 and it becomes zero just before the solstices4 #b4 ,as the resultant of these two motions1 the effective variation of the latitude is subject to a systematic alternation in a cycle of seven years' duration1 resulting from the commensurability of the two terms4 ,according as they conspire or interfere1 the total range varies between two-thirds of a second as a maximum1 to but a few hundredths of a second1 generally speaking1 as a minimum4 #c4 ,in consequence of the variability of the coefficient of the annual term above mentioned1 the apparent average period between #ahdj and #ahee approximated to #chj or #cij days2 widely fluctuated from #ahee to #ahfe2 from #ahfe to about #ahhe was very nearly #dbg days1 with minor fluctuations2 afterwards increased to near #ddj days1 and very recently fell to somewhat below #djj days4 ,the general course of these fluctuations is quite faithfully represented by the law of eq4 7#c71 7,no4 #bfg71 and accurately1 even down to the minor oscillations of individual periods1 by the law of eq4 7#ae71 hereafter given1 and verbally interpreted above4 ,this law also gives a similarly accurate account of the corresponding oscillations in the amplitude4 ,the closeness of the accordance between observation and the numerical theory1 in both particulars1 places the reality of the law beyond reasonable doubt4 ,those who cannot follow the details of the above statement will nevertheless catch the general purport--that the difficulties felt by ,professor ,newcomb have been surmounted2 and this is made clearer by a later extract3-- ,a very important conclusion necessarily follows from the agreement of the values of the #dbg-;day term1 deduced from the intervals between the consecutive values of ,t in ,table ,,xii41 namely1 that there has been no discontinuity in the revolution1 such as ,professor ,newcomb regarded as so probable that he doubted the possibility of drawing any conclusions from the comparison of observations before and after #ahfj 7,a4 ,j41 #bga1 p4 #ej74 ,sidenote3 ,theory must go1 if it will not fit observation4 ,the present investigation demonstrates that the way out of the apparently irreconcilable contradiction of theory and observation in this matter does not lie in the direction of discrediting the observations1 as he is inclined to do4 ,on the contrary1 the result is a beautiful vindication of the trustworthiness of the latter1 and1 at the same time1 of the theory that demands an invariable rate of motion2 providing a perfectly fitting key to the riddle by showing that another cause has intervened to produce the variability of the period4 ,i feel confident that ,professor ,newcomb will agree with the reality of the explanation here set forth1 and will reconsider his view that the perturbations in the position of the ,pole must be of the nature of chance accumulations of motion1 a view which he then considered necessary to the maintenance of the constancy in the period of latitude-variation4 ,sidenote3 ,the final paper4 ,the paper from which these words are taken appeared on ,november #d1 #ahib4 ,the next paper on the main theme did not appear till a year later1 though much work was being done in the meantime on the constant of aberration and other matters arising immediately after the discovery4 ,on ,november #ad1 #ahic1 ,mr4 ,chandler winds up the series of eight papers ,on the ,variation of ,latitude1 which he had commenced just two years before4 ,his work was by no means done2 rather was it only beginning1 for the torch he had lit illuminated many dark corners4 ,but he rightly regarded his discovery as now so firmly established that the series of papers dealing with it as still under consideration might be terminated4 ,in this final paper he first devotes the most careful attention to one point of detail4 ,he had shown earlier in the series that the ,north ,pole must be revolving from ,west to ,east1 and not from ,east to ,west2 but this was when the motion was supposed to be simple and not complex1 and it was necessary to re-examine the question of direction for each of the components4 ,after establishing conclusively that the original direction holds for each of the components1 he almost apologises for the trouble he has taken1 thus3-- ,it is therefore proved beyond reasonable doubt that the directions of the rotations is from ,west to ,east in both elements2 whence the general form of the equation for the variation of latitude adopted in ,a4 ,j41 #bhd1 p4 #aed1 eq4 7#ai74 ,it may be thought that too much pains have been here bestowed upon a point which might be trusted to theory to decide4 ,i cannot think so4 ,one of the most salient results of these articles has been the proof of the fact that theory has been a blind guide with regard to the velocity of the ,polar rotation1 obscuring truth and misleading investigators for a half a century4 ,and even if we were certain1 which we are not1 that the fourteen months' term is the ,eulerian period in a modified form4 ,it would still be necessary to settle by observation the direction of the annual motion1 with regard to which theory is powerless to inform us4 ,to save repetition of argument1 ,i must refer to the statement in ,a4 ,j41 #bgc1 pp4 #fh1 #gj1 of the principles adopted in beginning these inquiries in #ahia4 ,finally1 he answers one of the few objectors of eminence who still lingered1 the great ,french physicist ,cornu3-- ,sidenote3 ,cornu answered4 ,the ground is now cleared for examination of the only topic remaining to be covered1 to establish1 upon the foundation of fact1 every point in the present theory of these remarkable movements of the earth's axis4 ,this is the question of the possibility that these movements are not real1 but merely misinterpretations of the observed phenomena2 being in whole or in part an illusory effect of instrumental error due to the influence of temperature4 ,such a possibility has been a nightmare in practical astronomy from the first1 frightening us in every series of unexplained residuals1 brought to light continually in nearly all attempts at delicate instrumental research4 ,a source of danger so subtile could not fail to be ever present in the mind of every astronomer and physicist who has given even a superficial attention to the question of the latitude variations1 and there is no doubt that some are even now thus deterred from accepting these variations as proved facts4 ,perhaps the most explicit and forcible statement of the doubts that may arise on this subject has been given very recently by ,mr4 ,cornu4 ,the views of so distinguished a physicist1 and of others who are inclined to agree with him1 call for careful attention1 and cannot be neglected in the present closing argument upon the theory presented in these articles4 ,it is unnecessary1 for the purpose of disposing of objections of the sort raised by ,cornu1 to insist that it is not sufficient to show that the observed variations1 attributed to the unsteadiness of the ,earth's ,pole1 are near the limit of precision attainable in linear differential measures1 and in the indication of the direction of gravity by means of the air bubble of the level2 or to show that there are known variations in divided circles and in levels1 dependent on temperature and seasons4 ,nor need we require of objectors the difficult1 although essential1 task--which they have not distinctly attempted--of showing that these errors are not eliminated1 as they appear to be1 by the modes in which astronomers use their instruments4 ,neither need we even urge the fact that a large portion of the data which have been utilised in the present researches on the latitude were derived by methods which dispense with levels1 or with circles1 a part of them indeed with both1 and yet that the results of all are harmonious4 ,on the contrary1 let us admit1 although merely for argument's sake1 that all the known means of determining the direction of gravity--including the plumb-line1 the level1 and a fluid at rest1 whether used for a reflecting surface or as a support for a floating instrument--are subject to a common law of periodical error which vitiates the result of astronomical observation1 obtained by whatever methods1 and in precisely the same manner4 ,now1 the observed law of latitude variation includes two terms1 with periods of fourteen and twelve months respectively4 ,since the phases of the first term are repeated at intervals of two months in successive years1 and hence in a series of years come into all possible relations to conditions of temperature dependent on season1 the argument against the reality of this term1 on this ground1 absolutely fails1 and needs no further notice4 ,as to the second1 or annual term1 while the phases1 as observed in any given longitude1 are indeed synchronical with the seasons1 they are not so as regards different longitudes4 ,if1 therefore1 the times of any given phase1 as observed in the same latitude1 but in successively increasing longitudes1 occurred at the same date in all of them1 there would be a fatal presumption against the existence of an annual period in the polar motion4 ,if1 on the contrary1 they occur at times successively corresponding to the differences of longitude1 the presumption is equally fatal to the hypothesis that they can possibly be due to temperature variation as affecting instrumental measurement4 ,but the facts given in the foregoing section correspond most distinctly to the latter condition4 ,therefore1 unless additional facts can be brought to disprove successively these observed results1 we may dismiss for ever the bugbear which has undoubtedly led many to distrust the reality of the annual component of the latitude-variation1 while they admit the existence of the #dbg-;day term4 ,sidenote3 ,consequences of the discovery4 ,sidenote3 ,suspected observers acquitted4 ,at this point we must leave the fascinating account of the manner in which this great discovery was established1 in the teeth of opposition such as might have dismayed and dissuaded a less clear-sighted or courageous man4 ,it is my purpose to lay more stress upon the method of making the discovery than upon its results2 but we may afford a brief glance at some of the consequences which have already begun to flow from this step in advance4 ,some of them have indeed already come before us1 especially that large class represented by the explanation of anomalies in series of observations which had been put aside as inexplicable4 ,we have seen how the observations made in ,russia1 or in ,washington1 or at ,greenwich1 in all of which there was some puzzling error1 were immediately straightened out when ,chandler applied his new rule to them4 ,we in ,england have special cause to be grateful to ,chandler2 not only has he demonstrated more clearly than ever the greatness of ,bradley1 but he has rehabilitated ,pond1 the ,astronomer ,royal of the beginning of the nineteenth century2 showing that his observations1 which had been condemned as in some way erroneous1 were really far more accurate than might have been expected2 and further he has shown that the beautiful instrument designed by ,airy1 and called the ,reflex ,zenith ,tube1 which seemed to have unaccountably failed in the purpose for which it was designed1 was really all the time accumulating observations of this new phenomenon1 the ,variation of ,latitude4 ,instead of ,airy having failed in his design1 he had in ,chandler's words builded better than he knew4 ,sidenote3 ,constant of ,aberration improved4 ,secondly1 there is the modifying influence of this new phenomenon on other phenomena already known1 such1 for instance1 as that of aberration4 ,we saw in the third chapter how ,bradley discovered this effect of the velocity of light1 and how the measure of it is obtained by comparing the velocity of light with that of the earth4 ,this comparison can be effected in a variety of ways1 and we should expect all the results to agree within certain limits2 but this agreement was not obtained1 and ,chandler has been able to show one reason why1 and to remove some of the more troublesome differences4 ,it is impossible to give here an idea of the far-reaching consequences which such work as this may have2 so long as there are differences of this kind we cannot trust any part of the chain of evidence1 and there is in prospect the enormous labour of examining each separate link until the error is found4 ,the velocity of light1 for instance1 may be measured by a terrestrial experiment2 was there anything wrong in the apparatus8 ,the velocity of the earth in its journey round the sun depends directly upon the distance of the sun3 have we measured this distance wrongly1 and if so what was the error in the observations made8 ,these are some of the questions which may arise so long as the values for the ,constant of ,aberration are still conflicting2 but it requires considerable knowledge of astronomy to appreciate them fully4 ,sidenote3 ,latitude ,variation ,tide4 ,sidenote3 ,earthquakes4 ,another example will1 perhaps1 be of more general interest4 ,if the axis of the earth is executing small oscillations of this kind1 there should be an effect upon the tides2 the liquid ocean should feel the wobble of the earth's axis in some way2 and an examination of tidal registers showed that there was in fact a distinct effect4 ,it may cause some amusement when ,i say that the rise and fall are only a few inches in any case2 but they are unmistakable evidences that the earth is not spinning smoothly1 but has this kind of unbalanced vibration1 which ,i have compared to the vibrations felt by passengers on an imperfectly engineered twin-screw steamer4 ,a more sensational effect is that apparently earthquakes are more numerous at the time when the vibration is greatest4 ,we remarked that the vibration waxes and wanes1 much as that of the steamer waxes and wanes if the twin-screws are not running quite together4 ,now the passengers on the steamer would be prepared to find that breakages would be more numerous during the times of vigorous oscillation2 and it seems probable that in a similar way the little cracks of the earth's skin which we call great earthquakes are more numerous when these unbalanced vibrations are at their maximum2 that is to say1 about once every seven years4 ,this result is scarcely yet worthy of complete confidence1 for our observations of earthquakes have only very recently been reduced to proper order2 but if it should turn out to be true1 it is scarcely necessary to add any words of mine to demonstrate the importance of this rather unexpected result of the ,latitude ,variation4 ,sidenote3 ,the ,kimura phenomenon4 ,finally ,i will mention another phenomenon which seems to be at present more of a curiosity than anything else1 but which may lead to some future great discovery4 ,it is the outcome of observations which have been recently made to watch these motions of the ,pole2 for although there seems good reason to accept ,mr4 ,chandler's laws of variation as accurate1 it is necessary to establish their accuracy and complete the details by making observations for some time yet to come2 and there could be no better proof of this necessity than the discovery recently made by ,mr4 ,kimura1 one of those engaged in this watch of the ,pole in ,japan4 ,perhaps ,i can give the best idea of it by mentioning one possible explanation1 which1 however1 ,i must caution you may not be by any means the right one4 ,we are accustomed to think of this great earth as being sufficiently constant in shape2 if asked1 for instance1 whether its centre of gravity remains constantly in the same place inside it1 we should almost certainly answer in the affirmative1 just as only twenty years ago we thought that the ,north ,pole remained in the same place4 ,but it seems possible that the centre of gravity moves a few feet backwards and forwards each year--this would at any rate explain certain curious features in the observations to which ,mr4 ,kimura has drawn attention4 ,whatever the explanation of them may be1 or to settle whether this explanation is correct1 we want more observations1 especially observations in the ,southern ,hemisphere2 and it is a project under consideration by astronomers at the present moment whether three stations can be established in the ,southern ,hemisphere for the further observation of this curious phenomenon4 ,the question resolves itself chiefly into a question of money2 indeed1 most astronomical projects do ultimately resolve themselves into questions of money2 and ,i fear the world looks upon scientific men as insatiable in this respect4 ,one can only hope that on the whole the money is expended so as to give a satisfactory return4 ,in this instance ,i have no hesitation in saying that an immediate return of value for a comparatively modest expenditure is practically certain1 if only in some way we can get the means of making the observations4 ,it would be natural1 at the conclusion of this brief review of some types of astronomical discovery1 to summarise the lessons indicated3 but there is the important difficulty that there appear to be none4 ,it has been pointed out as we proceeded that what seemed to be a safe deduction from one piece of history has been flatly contradicted by another2 no sooner have we learnt that important results may be obtained by pursuing steadily a line of work in spite of the fact that it seems to have become tedious and unprofitable 7as in the search for minor planets7 than we are confronted with the possibility that by such simple devotion to the day's work we may be losing a great opportunity1 as ,challis did4 ,we can scarcely go wrong in following up the study of residual phenomena in the wake of ,bradley2 but there is the important difficulty that we may be wholly unable to find a clue for the arrangement of our residuals1 as is at present largely the case in meteorology4 ,and1 in general1 human expectations are likely to be quite misleading1 as has been shown in the last two chapters2 the discoveries we desire may lie in the direction precisely opposite to that indicated by the best opinion at present available4 ,there is no royal road to discovery1 and though this statement may meet with such ready acceptance that it seems scarcely worth making1 it is hoped that there may be sufficient of interest in the illustrations of its truth4 ,the one positive conclusion which we may derive from the examples studied is that discoveries are seldom made without both hard work and conspicuous ability4 ,a new planet1 even as large as ,uranus1 does not reveal itself to a passive observer3 thirteen times it may appear to such a one without fear of detection1 until at last it encounters an alert ,herschel1 who suspects1 tests1 and verifies1 and even then announces a comet--so little did he realise the whole truth4 ,fifteen years of unrequited labour before ,astraea was found1 nineteen years of observation before the discovery of nutation could be announced3 how seldom do these years of toil present themselves to our imaginations when we glibly say that ,bradley discovered nutation1 or ,hencke discovered ,astraea6 ,that the necessary labour is so often forgotten must be my excuse for recalling attention to it somewhat persistently in these examples4 ,but beyond the fact that he must work hard1 it would seem as though there were little of value to tell the would-be discoverer4 ,the situation has been well summarised by ,jevons in his chapter on ,induction in the ,principles of ,science2 and his words will form a fitting conclusion to these chapters3-- ,it would seem as if the mind of the great discoverer must combine contradictory attributes4 ,he must be fertile in theories and hypotheses1 and yet full of facts and precise results of experience4 ,he must entertain the feeblest analogies1 and the merest guesses at truth1 and yet he must hold them as worthless till they are verified in experiment4 ,when there are any grounds of probability he must hold tenaciously to an old opinion1 and yet he must be prepared at any moment to relinquish it when a clearly contradictory fact is encountered4 ,,index ,aberration1 #aje-aji1 #aaa1 #aab1 #aag1 #aah1 #ahe1 #ahh1 #aib1 #bad1 #bae ,accidental discovery1 #ae1 #gc1 #aba-aed ,adams1 #ab1 #de-he2 resolution1 #ee ,airy1 #cb1 #dj-he1 #bad ,algiers1 #acj ,alleghenia1 #bf ,almucantar1 #ahj1 #aha ,alphabet used for planets1 #bg ,anderson1 ,dr4 ,t4 ,c41 #h1 #adb1 #adc1 #add1 #adf ,anthelm1 #adb ,apollo1 #i ,argon1 #aji ,ascension1 #cd ,assumption1 forgotten1 #aif ,astraea1 #bb1 #bc1 #bai ,astrographic chart1 #abb1 #abe1 #acj ,astronomical ,journal1 #agg-bag ,astronomische ,nachrichten1 #eb1 #aeh ,astrophil1 #adc ,auwers1 #adb ,ball1 ,sir ,r41 #bd ,balliol ,college1 #hg ,banks1 ,sir ,j41 #i ,barnard1 ,e4 ,e41 #adf1 #bbj ,berlin1 #aha1 #ahc1 #ahd1 #ahh1 #aic ,berlin star-map1 #de1 #ff1 #hc1 #abd ,bessel1 #aib ,bettina1 #bf1 #bg ,birmingham1 #adb ,black ,drop 7in transit of ,venus71 #cj ,bliss1 #aad ,board of ,visitors of ,greenwich ,observatory1 #fc ,bode1 #aa1 #ad1 #ae1 #bb ,bode's ,law1 #ab1 #ac1 #ch1 #dc1 #de1 #eb1 #gb1 #gf1 #gg1 #hd ,bourdeaux1 #acj ,bouvard1 #ci1 #dj1 #db1 #dh1 #di1 #ej1 #fa ,bradley1 #ci1 #hf-abj1 #ahh-aib1 #bac1 #bad1 #bah1 #bai ,bradley1 ,john1 #aae ,bremen1 #bj ,bridstow1 #hg1 #hh1 #id ,briggs1 #aai ,brinkley1 #aib ,british ,association1 #fc ,bruennow1 #aic ,california1 #bf ,cambridge 7,mass471 #ahj1 #ahd1 #ahh ,cambridge ,observatory1 #bc1 #db1 #di1 #eb1 #fc1 #fe1 #ff1 #ace1 #aic ,cambridge ,university1 #fh-ga1 #aad ,cape ,observatory1 #abc1 #abd1 #acj ,cards1 #aa ,cassini ,,ii41 #aef ,catania1 #acj ,ceres1 #ad-bb 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,faraday1 #bja ,flamsteed1 #ci1 #ec1 #aae ,fleming1 ,mrs41 #adb ,flora1 #bb ,foulkes1 ,martin1 #id ,french ,academy1 #dc1 #ea1 #fb ,galileo1 #ie1 #afc ,galle1 #dd1 #de1 #dg1 #ff1 #fg1 #hc ,gasparis1 #bb ,gauge 7railways71 #ef ,gauss1 #ag-bj ,geminorum1 ,h41 #d ,george ,,iii41 #h1 #aj ,georgian1 #aa ,georgium ,sidus1 #h1 #aj1 #aa ,gill1 ,sir ,d41 #cb1 #cd1 #ce1 #abc ,gilliss1 #cb ,gotha1 #bj ,gould1 #cb ,graham1 #bb1 #bc ,gravitation1 law of1 #ch1 #de1 #ei1 #hd1 #aje ,greaves1 #aai ,greenwich ,observatory1 #dh-fd1 #hh1 #hi1 #aad-aag1 #acj1 #afj-afi1 #ahb1 #aib1 #aic1 #bjf1 #bac ,gregory1 #ic1 #aai ,hale1 ,g4 ,e41 #agj1 #aga ,hall1 ,a41 #ahd1 #ahe ,halley1 #hh-ib1 #ajh1 #aab-aaf1 #aai ,hansen1 #da1 #ei ,harkness1 #ahd ,hartwig1 #adb ,harvard ,college ,observatory1 #abh1 #adb1 #add1 #ade ,hebe1 #bb ,hegel1 #ae ,heidelberg1 #ade ,heliometer1 #cb1 #cd ,helium1 #aji ,helsingfors1 #acj ,hencke1 #bb1 #bc1 #fd1 #aec1 #bai ,henry brothers1 #abd-abi ,herschel1 ,sir ,john1 #fc1 #ge1 #hc ,herschel1 ,sir ,william1 #b-aa1 #ci1 #dd1 #hb1 #bai ,herschel 7,uranus71 #aa1 #ab ,hind1 #bb1 #bc1 #be1 #adb ,hooke1 #if1 #ig ,hubbard1 #ahd ,humboldt1 #afj ,hussey1 ,rev4 ,t4 ,j41 #dj1 #db ,hygeia1 #bb ,ilmata1 #bf ,industria1 #bf ,ingeborg1 #bf ,instruments at ,greenwich1 #aad-aaf ,iris1 #bb1 #bc1 #cb1 #ce ,janson1 #adb ,jevons1 #bai ,johnson1 ,m41 #aef1 #afj ,juno1 #i1 #ba1 #bb ,jupiter1 #i1 #bh1 #dc1 #di1 #ej1 #fa2 satellites1 #ib1 #aag ,keats1 #a-c1 #g1 #h ,keill1 #id1 #aab1 #aai1 #aef ,kelvin1 ,lord1 #aif1 #aig ,kepler1 #ie1 #adb ,kew1 #ie1 #if1 #ahh1 #aij ,kiel1 #ada ,kimura1 #baf ,koenigsberg1 #aib ,kuestner1 #aah1 #aha1 #ahc ,lalande1 #g1 #aa1 #ajg1 #aeg ,lameia1 #bf ,laplace1 #fa ,la ,plata1 #acj ,latitude variation1 #ii1 #ajj1 #aag1 #aah1 #agg-bag ,lemonnier1 #ci1 #ec1 #aeg ,le ,verrier1 #ab1 #dc-he ,libussa1 #bf ,lick ,observatory1 #aeb ,liouville's ,journal1 #gc ,lisbon1 longitude of1 #ib ,london1 #bc1 #be1 #if ,long1 #aeg ,longitude1 #ib1 #aag ,lowth1 ,bishop1 #aai ,lyrae1 alpha1 #ahd1 #aif ,macclesfield1 ,earl of1 #id1 #aac ,maedler1 #aib ,magnetic observations1 #afa1 #afd1 #agd ,magnitude equation1 #ace ,markree1 #bc ,mars1 #i1 #bh1 #cb1 #cd1 #ce1 #ia ,mayer1 #ci ,measurement of plates1 #acb-ace ,mecanique ,celeste1 #fa ,melbourne1 #acj1 #aic ,memorandum 7,adams71 #ee ,mercury1 #i ,messier1 #g ,meteorites1 #ei ,meteors 7,november71 #fj ,metis1 #bb1 #bc ,micrometer1 #e1 #acc ,milky ,way1 #abe ,minerva1 #i ,minor planets1 #ac-bh ,minor planets tables1 #bb1 #bd1 #bf ,mistakes1 #ga-hc ,molyneux1 ,samuel1 #id-if1 #aja1 #ajd ,monte ,video1 #acj ,moon1 tables of1 #aag ,names of minor planets1 #bb-bh ,nasmyth1 #afb ,nautical ,almanac1 #aa ,nebula1 #abd1 #adf-aeb ,neptune1 #aa1 #ab1 #ch-he1 #abd ,new ,college ,lane1 #aab ,newcomb1 ,simon1 #ha1 #ahc1 #ahd1 #aie-bjb1 #bjg1 #bjh ,new stars1 #aba1 #adj-aed ,newton1 #ch1 #hd1 #ij-ie1 #aje1 #aac ,new ,york1 longitude1 #ib ,ninina1 #bf ,northleach1 #hg ,northumberland1 #fe ,nova ,geminorum1 #ada1 #ade1 #adf ,nova ,persei1 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,planets by photography1 #bd ,pole ,star 7,polaris71 #agg1 #agh1 #aib1 #aic ,pond1 #aib1 #bac ,potsdam1 #acj1 #aha ,pound1 ,mrs41 #ajd1 #aaj-aab ,pound1 ,rev4 ,james1 #hi-id1 #ajd1 #aae ,prague1 #aha ,precession1 #if1 #agh ,prymno1 #bf ,puiseux1 #cb ,pulfrich1 #aed ,pulkowa1 #aha-ahh1 #bac ,quadrants at ,greenwich1 #aaf ,radium1 #age ,radius vector1 #eb-eh1 #fj-fb1 #gi1 #hc ,rayleigh1 ,lord1 #aji ,records before discovery1 #add ,reflector1 #ic1 #abg1 #abh ,reflex zenith tube1 #aib1 #bad ,refraction1 #if1 #aja-ajc1 #aag ,refractor1 #ic1 #abh ,reseau1 #acc ,residual phenomena1 #ajh-aaj1 #aah1 #abj1 #bah ,rigaud1 ,s4 ,p41 #hg1 #aae1 #aai ,rome1 #acj ,rothschild1 #bg ,royal ,astronomical ,society1 #dj1 #dg1 #fh1 #gd1 #abd1 #aee1 #aeg ,royal ,society1 #d1 #i1 #aj1 #ib1 #id ,sampson1 ,r4 ,a41 #gd-gf1 #hd ,san ,fernando1 #acj ,santiago1 #acj ,sappho1 #cb1 #ce ,saturn1 #i1 #dc1 #fa1 #adi1 #aej ,savile1 ,sir ,h41 #aai ,savilian professorship1 #hg-id1 #ajh-aai ,schmidt1 ,julius1 #adb1 #afj ,schuster1 ,a41 #afi ,schwabe1 #aee-afc1 #agf1 #agg ,sheldonian ,theatre1 #aai ,sherbourn1 #hg ,solar eclipse1 #bf1 #agj-agf ,spectro-heliograph1 #agj1 #aga ,star-maps1 #de1 #fe1 #hc1 #abd ,star-trap1 #bd ,stereo-comparator1 #aed ,stone1 ,e4 ,j41 #cb ,struve1 #ahd1 #ahh1 #aib ,sun's distance1 #bh-cg ,sun-spots1 #aee-agf ,sydney ,observatory1 #acj ,tacubaya ,observatory1 #acj ,telescopes1 #ib1 #abd-abi ,thames ,river1 #aje ,themistocles1 #aai ,theoria ,motus1 #ag ,theory and observation1 #bjh ,thomson1 ,sir ,w41 #aif1 #aig ,tides1 #bae ,titius1 #ac ,toulouse ,observatory1 #acj ,tycho ,brahe1 #ie1 #adj1 #adb ,uranus1 #b-ad1 #be1 #ch-he1 #add1 #bai ,variable stars1 #adj ,variation of latitude1 #ii1 #ajj1 #aag1 #aah1 #agg-bag ,venus1 #i1 #gi2 diameter of1 #ib2 transit of1 #bh-cb1 #cd ,vesta1 #ba1 #bb ,victoria1 #bb1 #be1 #cb1 #ce ,von ,zach1 #bj ,wallace1 #aai ,wansted1 #hh-id1 #ajd1 #aaj1 #aae1 #ahh1 #aij ,ward1 #aai ,washington ,observatory1 #ahd-ahh1 #aic1 #aif1 #bac ,weather and sun-spots1 #afa1 #afg-afi ,weyer1 #aic ,whiteside1 #aab ,williams1 ,mrs4 ,e41 #aaj1 #aaa ,wind-vane1 revolutions1 #afg-afi ,winnecke1 #cb ,wolf1 ,dr4 ,max1 #ade ,wolf1 ,rudolf1 #afc ,wren1 ,sir ,c41 #aai ,yerkes ,observatory1 #ade1 #adf1 #aeb1 #aeg1 #agj1 #agf ,zeiss1 #aed ,zodiac1 #fd1 #abd1 #acg ,,the ,,end ,printed by ,,ballantyne1 ,,hanson ,,co4 ,edinburgh ,london ,,mr4 ,,edward ,,arnold',s ,,list ,,of ,scientific and ,technical ,books4 ,,lectures ,,on ,,diseases ,,of ,,children4 ,by ,,robert ,,hutchison1 ,m4,d4 7,edin471 ,f4,r4,c4,p41 ,assistant ,physician to the ,london ,hospital and to the ,hospital for ,sick ,children1 ,great ,ormond ,street1 ,london4 ,with numerous ,illustrations4 ,crown #hvo41 #hs4 #f;d4 net4 ,,practical ,,physiology4 ,by ,a4 ,p4 ,,beddard1 ,m4,a41 ,m4,d41 ,demonstrator of ,physiology1 ,guy's ,hospital2 ,j4 ,s4 ,,edkins1 ,m4,a41 ,m4,b41 ,lecturer in ,physiology and ,demonstrator of ,physiology1 ,st4 ,bartholomew's ,hospital2 ,,leonard ,,hill1 ,m4,b41 ,f4,r4,s41 ,lecturer on ,physiology1 ,london ,hospital ,medical ,school2 ,j4 ,j4 ,r4 ,,macleod1 ,m4,b42 and ,m4 ,s4 ,,pembrey1 ,m4,a41 ,m4,d41 ,lecturer on ,physiology in ,guy's ,hospital ,medical ,school4 ,copiously ,illustrated4 ,demy #hvo41 #aes4 net4 ,,human ,,embryology ,,and ,,morphology4 ,by ,a4 ,,keith1 ,m4,d41 ,f4,r4,c4,s4 ,eng41 ,lecturer on ,anatomy at the ,london ,hospital ,medical ,college4 ,with #cjj ,illustrations4 ,new1 ,revised1 and ,enlarged ,edition4 ,demy #hvo41 #abs4 #f;d4 net4 ,,food ,,and ,,the ,,principles ,,of ,,dietetics4 ,by ,,robert ,,hutchison1 ,m4,d4 ,edin41 ,f4,r4,c4,p41 ,assistant ,physician to the ,london ,hospital4 ,fifth ,impression4 ,illustrated4 ,demy #hvo41 #afs4 net4 ,,the ,,physiological ,,action ,,of ,,drugs4 ,an ,introduction to ,practical ,pharmacology4 ,by ,m4 ,s4 ,,pembrey1 ,m4,a41 ,m4,d41 ,lecturer on ,physiology in ,guy's ,hospital ,medical ,school2 and ,c4 ,d4 ,f4 ,,phillips1 ,m4,d41 ,,ll4,d4 ,fully ,illustrated4 ,demy #hvo41 #ds4 #f;d4 net4 ,,phototherapy4 ,by ,n4 ,r4 ,,finsen4 ,translated by ,j4 ,h4 ,,sequeira1 ,m4,d4 ,with ,illustrations4 ,demy #hvo41 #ds4 #f;d4 net4 ,,contents4--,i4 ,the ,chemical ,rays of ,light and ,small-pox--,,ii4 ,light as an ,irritant--,,iii4 ,treatment of ,lupus ,vulgaris by concentrated ,chemical ,rays4 ,a ,,manual ,,of ,,human ,,physiology4 ,by ,,leonard ,,hill1 ,m4,b41 ,f4,r4,s4 ,with #agc ,illustrations1 xii #dhd pages4 ,crown #hvo41 cloth1 #fs4 ,a ,,primer ,,of ,,physiology4 ,by ,,leonard ,,hill1 ,m4,b4 #as4 ,,lectures ,,on ,,theoretical ,,and ,,physical ,,chemistry4 ,by ,dr4 ,j4 ,h4 ,,van ',t ,,hoff1 ,professor of ,chemistry at the ,university of ,berlin4 ,translated by ,dr4 ,r4 ,a4 ,,lehfeldt4 ,in three volumes4 ,illustrated4 ,demy #hvo41 #bhs4 net2 or obtainable separately1 as follows3 ,vol4 ,i4--,chemical ,dynamics4 #abs4 net4 ,vol4 ,,ii4--,chemical ,statics4 #hs4 #f;d4 net4 ,vol4 ,,iii4--,relations between ,properties and ,composition4 #gs4 #f;d4 net4 ,,the ,,elements ,,of ,,inorganic ,,chemistry4 ,for use in ,schools and ,colleges4 ,by ,w4 ,a4 ,,shenstone1 ,lecturer in ,chemistry at ,clifton ,college1 xii #ejf pages4 ,with nearly #aej ,illustrations4 #ds4 #f;d4 ,a ,,course ,,of ,,practical ,,chemistry4 ,being a ,revised ,edition of ',a ,laboratory ,companion for ,use with ,shenstone's ,inorganic ,chemistry4' ,by ,w4 ,a4 ,,shenstone4 #add pages4 ,crown #hvo41 #as4 #f;d4 ,a ,,text-,,book ,,of ,,physical ,,chemistry4 ,by ,dr4 ,r4 ,a4 ,,lehfeldt1 ,professor of ,physics at the ,east ,london ,technical ,college4 ,with #dj ,illustrations4 ,crown #hvo41 cloth1 #gs4 #f;d4 ,,the ,,chemical ,,synthesis ,,of ,,vital ,,products ,,and ,,the ,,inter-,,relations ,,between ,,organic ,,compounds4 ,by ,professor ,,raphael ,,meldola1 ,f4,r4,s41 of the ,city and ,guilds of ,london ,technical ,college1 ,finsbury4 ,two vols4 ,vol4 ,i4 now ready4 ,super ,royal #hvo41 #bas4 net4 ,a ,,text-,,book ,,of ,,physics4 ,with ,sections on the ,applications of ,physics to ,physiology and ,medicine4 ,by ,dr4 ,r4 ,a4 ,,lehfeldt4 ,fully ,illustrated4 ,crown #hvo41 cloth1 #fs4 ,,physical ,,chemistry ,,for ,,beginners4 ,by ,dr4 ,ch4 ,m4 ,,van ,,deventer4 ,with a ,preface by ,j4 ,h4 ,,van ',t ,,hoff4 ,translated by ,dr4 ,r4 ,a4 ,,lehfeldt1 ,professor of ,physics at the ,east ,london ,technical ,college1 #bs4 #f;d4 ,a ,,first ,,year',s ,,course ,,of ,,experimental ,,work ,,in ,,chemistry4 ,by ,,ernest ,h4 ,,cook1 ,d4,sc41 ,f4,i4,c41 ,principal of the ,clifton ,laboratory1 ,bristol4 ,with #bf ,illustrations4 ,crown #hvo41 cloth1 #as4 #f;d4 ,,an ,,experimental ,,course ,,of ,,chemistry ,,for ,,agricultural ,,students4 ,by ,t4 ,s4 ,,dymond1 ,f4,i4,c41 ,lecturer on ,agricultural ,chemistry in the ,county ,technical ,laboratories1 ,chelmsford4 ,with #ej ,illustrations4 #aib pages4 ,crown #hvo41 cloth1 #bs4 #f;d4 ,,the ,,standard ,,course ,,of ,,elementary ,,chemistry4 ,by ,e4 ,j4 ,,cox1 ,f4,c4,s4 ,with #ij ,illustrations4 #cej pages4 ,crown #hvo41 cloth1 #cs4 ,also obtainable in five parts1 limp cloth4 ,parts ,i4-,,iv41 #g;d4 each2 ,part ,v41 #as4 ,a ,,preliminary ,,course ,,of ,,practical ,,physics4 ,by ,c4 ,e4 ,,ashford1 ,m4,a41 ,headmaster of the ,royal ,naval ,college1 ,osborne4 ,fcap4 #dto41 #as4 #f;d4 ,,physical ,,determinations4 ,a ,manual of ,laboratory ,instructions for the ,determination of ,physical ,quantities4 ,by ,w4 ,r4 ,,kelsey1 ,b4,sc41 ,a4,i4,e4,e41 ,lecturer in ,physics to the ,bradford ,municipal ,technical ,college4 #ds4 #f;d4 ,,electrolytic ,,preparations4 ,exercises for use in the laboratory by chemists and electro-chemists4 ,by ,dr4 ,,karl ,,elbs1 ,professor of ,chemistry at the ,university of ,giessen4 ,translated by ,r4 ,s4 ,,hutton1 ,m4,sc4 ,demy #hvo41 #ds4 #f;d4 net4 ,,the ,,electric ,,furnace4 ,by ,,henri ,,moissan1 ,professor of ,chemistry at the ,sorbonne4 ,authorized ,english ,edition4 ,translated by ,a4 ,t4 ,,de ,,mouilpied1 ,m4,sc41 ,ph4,d4 ,with ,illustrations4 ,demy #hvo41 #ajs4 #f;d4 net4 ,,electrical ,,traction4 ,by ,,ernest ,,wilson1 ,wh4,sc41 ,m4,i4,e4,e41 ,professor of ,electrical ,engineering in the ,siemens ,laboratory1 ,king's ,college1 ,london4 ,crown #hvo41 #es4 ,,electricity ,,and ,,magnetism4 ,by ,c4 ,e4 ,,ashford1 ,m4,a41 ,headmaster of the ,osborne ,royal ,naval ,college1 late ,senior ,science ,master at ,harrow ,school4 ,with over #bjj ,diagrams4 ,crown #hvo41 #cs4 #f;d4 ,,magnetism ,,and ,,electricity4 ,an ,elementary ,treatise for ,junior ,students1 ,descriptive and ,experimental4 ,by ,j4 ,,paley ,,yorke1 of the ,northern ,polytechnic ,institute1 ,london4 ,with nearly #aej ,illustrations4 #cs4 #f;d4 ,,the ,,balancing ,,of ,,engines4 ,by ,w4 ,e4 ,,daley1 ,m4,a41 ,b4,sc41 ,m4,inst4,c4,e41 ,m4,i4,m4,e41 ,professor of ,mechanical ,engineering and ,applied ,mathematics in the ,city and ,guilds of ,london ,technical ,college1 ,finsbury4 ,with #agc ,illustrations4 ,demy #hvo41 #ajs4 #f;d4 net4 ,,the ,,strength ,,and ,,elasticity ,,of ,,structural ,,members4 ,by ,r4 ,j4 ,,woods1 ,master of ,engineering1 ,royal ,university of ,ireland1 ,fellow of the ,royal ,indian ,engineering ,college1 and ,assistant ,professor of ,engineering ,cooper's ,hill ,college4 ,demy #hvo4 #ajs4 #f;d4 net4 ,,traverse ,,tables4 ,with an ,introductory ,chapter on ,coordinate ,surveying4 ,by ,,henry ,,louis1 ,m4,a41 ,a4,r4,s4,m41 ,f4,i4,c41 ,f4,g4,s41 etc41 ,professor of ,mining and ,lecturer on ,surveying1 ,durham ,college of ,science1 ,newcastle-on-,tyne2 and ,g4 ,w4 ,,caunt1 ,m4,a4 ,demy #hvo41 #ds4 #f;d4 net4 ,,the ,,calculus ,,for ,,engineers4 ,by ,,john ,,perry1 ,m4,e41 ,d4,sc41 ,f4,r4,s41 ,professor of ,mechanics and ,mathematics in the ,royal ,college of ,science1 etc4 ,crown #hvo41 cloth1 #gs4 #f;d4 ,,electric ,,and ,,magnetic ,,circuits4 ,by ,,ellis ,h4 ,,crapper1 ,m4,i4,e4,e41 ,head of the ,electrical ,engineering ,department in the ,university ,college1 ,sheffield1 viii #chj pages4 ,demy #hvo41 #ajs4 #f;d4 net4 ,,an ,,introduction ,,to ,,the ,,theory ,,of ,,optics4 ,by ,professor ,,arthur ,,schuster1 ,ph4,d41 ,f4,r4,s41 ,professor of ,physics at the ,university of ,manchester4 ,with numerous ,diagrams4 ,demy #hvo41 #aes4 net4 ,,astronomical ,,discovery4 ,by ,h4 ,h4 ,,turner1 ,savilian ,professor of ,astronomy in the ,university of ,oxford4 ,with ,diagrams4 ,demy #hvo41 #ajs4 #f;d4 net4 ,,vectors ,,and ,,rotors4 ,with ,applications4 ,being ,lectures delivered at the ,central ,technical ,college ,by ,professor ,o4 ,,henrici1 ,f4,r4,s4 ,edited by ,g4 ,c4 ,,turner1 ,goldsmith ,institute4 ,crown #hvo41 cloth4 #ds4 #f;d4 ,,the ,,principles ,,of ,,mechanism4 ,by ,h4 ,a4 ,,garratt1 ,a4,m4,i4,c4,e41 ,head of the ,engineering ,department of the ,northern ,polytechnic ,institute1 ,holloway4 ,crown #hvo41 cloth1 #cs4 #f;d4 ,,elementary ,,plane ,,and ,,solid ,,mensuration4 ,by ,r4 ,w4 ,k4 ,,edwards1 ,m4,a41 ,lecturer on ,mathematics at ,king's ,college1 ,london4 ,for use in ,schools1 ,colleges1 and ,technical ,classes4 #cjd pages1 ,crown #hvo41 #cs4 #f;d4 ,,five-,,figure ,,tables ,,of ,,mathematical ,,functions4 ,by ,j4 ,b4 ,,dale1 ,m4,a4 ,camb41 ,b4,a4 ,lond41 late ,scholar ,st4 ,john's ,college1 ,cambridge1 ,lecturer on ,pure and ,applied ,mathematics1 ,king's ,college1 ,university of ,london4 ,demy #hvo41 #cs4 #f;d4 net4 ,,an ,,elementary ,,treatise ,,on ,,practical ,,mathematics4 ,by ,,john ,,graham1 ,b4,a41 ,demonstrator of ,mechanical ,engineering and ,applied ,mathematics in the ,technical ,college1 ,finsbury4 ,crown #hvo41 cloth1 #cs4 #f;d4 ,,preliminary ,,practical ,,mathematics4 ,,by ,s4 ,g4 ,,starling1 ,a4,r4,c4,sc41 ,b4,sc41 ,head of the ,mathematics and ,physics ,department of the ,west ,ham ,municipal ,technical ,institute2 and ,f4 ,c4 ,,clarke1 ,a4,r4,c4,sc41 ,b4,sc4 ,,the ,,evolution ,,theory4 ,by ,,august ,,weismann1 ,professor of ,zoology in the ,university of ,freiburg-im-,breisgau4 ,translated by ,professor ,j4 ,,arthur ,,thomson4 ,with numerous ,illustrations and ,coloured ,plates4 ,two ,vols4 ,royal #hvo41 #cbs4 net4 ,the importance of this work is twofold4 ,in the first place1 it sums up the teaching of one of ,darwin's greatest successors1 who has been for many years a leader in biological progress4 ,as ,professor ,weismann has from time to time during the last quarter of a century frankly altered some of his positions1 this deliberate summing up of his mature conclusions is very valuable4 ,in the second place1 as the volumes discuss all the chief problems of organic evolution1 they form a reliable guide to the whole subject1 and may be regarded as furnishing--what is much needed--a ,text-book of ,evolution ,theory4 ,,animal ,,behaviour4 ,by ,c4 ,,lloyd ,,morgan1 ,,ll4,d41 ,f4,r4,s41 ,principal of ,university ,college ,bristol1 author of ',animal ,life and ,intelligence1' etc4 ,with numerous ,illustrations4 ,large crown #hvo41 #ajs4 #f;d4 ,,habit ,,and ,,instinct4 ,by ,c4 ,,lloyd ,,morgan1 ,,ll4,d41 ,f4,r4,s4 ,with ,photogravure ,frontispiece4 viii #ceb pages4 ,demy #hvo41 cloth1 #afs4 ,a ,,text-,,book ,,of ,,zoology4 ,by ,g4 ,p4 ,,mudge1 ,a4,r4,c4,sc4 ,lond41 ,lecturer on ,biology at the ,london ,school of ,medicine for ,women1 and the ,polytechnic ,institute1 ,regent ,street4 ,with about #bjj original ,illustrations4 ,crown #hvo41 cloth1 #gs4 #f;d4 ,,elementary ,,natural ,,philosophy4 ,by ,,alfred ,,earl1 ,m4,a41 ,assistant ,master at ,tonbridge ,school4 ,with numerous ,illustrations and ,diagrams4 ,crown #hvo41 cloth1 #ds4 #f;d4 ,a ,,class-,,book ,,of ,,botany4 ,by ,g4 ,p4 ,,mudge1 ,a4,r4,c4,sc4 ,lond41 ,f4,z4,s41 and ,a4 ,j4 ,,maslen1 ,f4,l4,s41 ,lecturer on ,botany at the ,woolwich ,polytechnic4 ,with over #bjj ,illustrations4 ,crown #hvo41 #gs4 #f;d4 ,,the ,,becquerel ,,rays ,,and ,,the ,,properties ,,of ,,radium4 ,by the ,hon4 ,r4 ,j4 ,,strutt1 ,fellow of ,trinity ,college1 ,cambridge4 ,with ,diagrams4 ,demy #hvo4 #hs4 #f;d4 net4 ,a ,,manual ,,of ,,alcoholic ,,fermentation ,,and ,,the ,,allied ,,industries4 ,by ,,charles ,g4 ,,matthews1 ,f4,i4,c41 ,f4,c4,s41 etc4 ,fully ,illustrated4 ,crown #hvo41 cloth1 #gs4 #f;d4 net4 ,,wood4 ,a ,manual of the ,natural ,history and ,industrial ,applications of the ,timbers of ,commerce4 ,by ,g4 ,s4 ,,boulger1 ,f4,l4,s41 ,f4,g4,s4 ,fully ,illustrated4 ,crown #hvo41 #gs4 #f;d4 net4 ,,psychology ,,for ,,teachers4 ,by ,c4 ,,lloyd ,,morgan1 ,,ll4,d41 ,f4,r4,s4 xii #bea pages4 ,crown #hvo41 #cs4 #f;d4 ,,animal ,,sketches4 ,by ,c4 ,,lloyd ,,morgan1 ,,ll4,d41 ,f4,r4,s4 viii #cab pages1 with #eb ,illustrations 7many of them full-page74 ,crown #hvo41 cloth1 #cs4 #f;d4 ,,london3 ,,edward ,,arnold1 #da #dc ,,maddox ,,street1 ,w4 ,footnotes3 #a ,the inferior planet ,venus comes closer1 but is not visible throughout the night4 #b ,the facts were collected with great care and ability by ,s4 ,p4 ,rigaud1 and published by the ,oxford ,university ,press in #ahcb as ,miscellaneous ,works and ,correspondence of the ,rev4 ,james ,bradley4 #c ,since the light must travel from the sun to ,saturn and back again to the earth1 the interval would be more nearly #aej minutes4 #d ,monthly ,notices of the ,royal ,astronomical ,society1 vol4 xvii4 p4 #abf4 #e ,this should be ,cambridge1 ,mass4 #f ,the distances do not represent the total displacement1 but only the displacement towards ,washington in one case and towards ,pulkowa in the other4 ,transcriber's ,notes3 ,passages in italics are indicated by italics4 ,passages in bold are indicated by bold4 ,subscripted letters are indicated by subscript4 ,the original text includes the ,greek a1 b1 and g4 ,for this text version these letters are presented as alpha1 beta1 and gamma4 ,all side notes belonging to a single paragraph have been moved to the beginning of the paragraph4 ,sidenotes split across pages have been joined together4 ,punctuation has been corrected without note4 ,corrections in the ,errata have been made in this text version4 ,the following misprints have been corrected3 ,hencke' corrected to ,hencke's 7page #bc sidenote7 annouced corrected to announced 7page #de sidenote7 are are corrected to are 7page #aai7 ,konigsberg corrected to ,koenigsberg 7,index7 ,other than the corrections listed above1 inconsistencies in spelling and hyphenation have been retained from the original4