,,the ,,earth',s ,,beginning ---------------------------------------- -------------------------------- ,,works ,,by ,,sir ,,robert ,s4 ,,ball1 ,m4,a41 ,,ll4,d41 ,f4,r4,s4 ,,the ,,story ,,of ,,the ,,heavens4 ,with #bd ,coloured ,plates and ,numerous ,illustrations4 ,new ,edition4 #ajs4 #f;d4 ,,the ,,earth',s ,,beginning4 ,with #d ,coloured ,plates and ,numerous ,illustrations4 ,new ,edition4 #gs4 #f;d4 ,,the ,,story ,,of ,,the ,,sun4 ,with #aa ,full ,page ,coloured and other ,plates and ,numerous ,illustrations4 #gs4 #f;d4 ,,star-,,land4 ,being ,talks with ,young ,people about the ,wonders of the ,heavens ,with ,rembrandt ,frontispiece and #id ,illustrations in ,text4 #gs4 #f;d4 ,,cassell ,,company1 ,,limited1 ,london1 ,new ,york1 ,toronto ,melbourne4 ---------------------------------------- -------------------------------- ,illustration3 ,,an ,,english ,,sunset ,,tinged ,,by ,,krakatoa4 7,from a ,drawing made at ,chelsea at #d4dj p4m4 on ,nov4 #bfth1 #ahhc1 by ,mr4 ,w4 ,ascroft47 ---------------------------------------- -------------------------------- ,,the ,,earth',s ,,beginning ,,by ,,sir ,,robert ,s4 ,,ball1 ,m4,a41 ,,ll4,d41 ,f4,r4,s4 ,lowndean ,professor of ,astronomy and ,geometry in the ,university of ,cambridge1 ,author of 8,star-,land10 8,the ,story of the ,heavens10 etc4 etc4 ,,with ,,four ,,coloured ,,plates ,,and ,,numerous ,,illustrations ,,new ,,edition ,,cassell ,,and ,,company1 ,,limited ,,london1 ,,new ,,york1 ,,toronto ,,and ,,melbourne ,,mcmix ---------------------------------------- -------------------------------- ,first ,edition ,october #aija4 ,reprinted ,december #aija1 #aijc4 ,enlarged ,edition #aiji4 ,,all ,,rights ,,reserved ---------------------------------------- -------------------------------- ,,foreword ,,since these lectures were delivered in the ,royal ,institution of ,great ,britain there has been much advance in our knowledge of astronomy4 ,the simultaneous advance in other sciences allied with astronomy has been1 perhaps1 even more remarkable4 ,i am glad to avail myself of the opportunity afforded by a new issue of 8,the ,earth's ,beginning0 to draw attention to certain recent developments of science which relate in a very striking way to the subject of this volume1 namely1 the famous ,nebular ,theory of the origin of the solar system4 ,it appears to me that these recent developments tend to reduce greatly1 even if they do not altogether remove1 the chief outstanding difficulty which has hitherto retarded the acceptance of the ,nebular ,theory4 ,i have explained in ,chapter ,,vi4 those views of ,helmholtz which have for so long provided the received explanation of the maintenance of solar heat4 ,calculation shows that if the sun's heat has been maintained by the contraction of the primval nebula--and this was the supposition of ,helmholtz--the orb of day cannot have radiated with its present intensity for a period much longer than twenty million years4 ,but from the evidence of geology it must now be admitted that the existence of our earth1 indeed even that part of its existence during which it has been the abode of life1 has endured for a period far in excess of that which this calculation would allow4 ,it therefore seems to follow that the theory of ,helmholtz does not provide an adequate explanation of such an amazing phenomenon as the continuance of a sufficient supply of sunbeams throughout the vast periods demanded by geological phenomena4 ,there is another entirely different line of reasoning by which ,professor ,john ,joly has recently taught us the immense antiquity of our earth4 ,his argument is based upon an estimate of the time that must have elapsed since the waters of the ocean1 which had previously been sustained in the great vapours of the atmosphere1 were deposited in the ocean beds4 ,when the earth had become sufficiently cool to permit of the vapours now forming the ocean passing from the gaseous to the liquid form1 the oceans descended from the heavens above to the earth beneath in the form of fresh water4 ,in the lapse of subsequent ages the sea has become salt because ordinary river water1 which always contains some small quantity of salt in solution1 is continually bearing salt down to the sea4 ,no doubt water is constantly being abstracted from the sea by evaporation1 but only fresh water is thus removed1 so in this cycle of change the salt in the sea must be gradually accumulating4 ,thus1 day by day1 though no doubt extremely slowly1 the sea has been growing more and more salt4 ,professor ,joly has made an estimate of the quantity of salt daily added to the sea by all the rivers of the globe4 ,he has also made an estimate of the total quantity of salt which is at present contained in the sea4 ,he has thus the means of forming an estimate of the number of years necessary for the sea to have become converted from its primval freshness to its present saltness4 ,his result is not a little astonishing4 ,the saltness of the sea could not be accounted for unless the rivers had been running into the sea for at least a hundred million years4 ,this period is five times as long as the total period during which the sun could have been shining if the ,helmholtzian view were correct4 ,of course1 there are many elements of uncertainty in such a calculation4 ,we have assumed that the total flow of the rivers is practically constant1 and that our estimate fairly represents the average salinity of river water4 ,we have also made a large assumption in supposing that we have accurately estimated the total volume of salt in the oceans4 ,but taken in conjunction with the geological evidence already referred to1 taken in conjunction with the immense periods of time that have been required for the evolution of life on the globe by the process of natural selection1 the conclusion arrived at is inevitable4 ,it seems impossible to doubt that the sun must have been shining and that our solar system must have existed in practically the same form as it is at present for periods enormously greater than would have been possible if the heat of the sun had been sustained by the solar contraction only4 ,the difficulty here indicated has been not unjustly considered the most serious difficulty with which the development of modern physical and astronomical science has been confronted4 ,the time during which the sun must have lasted1 according to the received explanation of the source of its heat and the time during which the sun has actually lasted1 as shown by the facts of geology1 present a wide discrepancy4 ,science demands that some reconciliation must be effected1 yet how is that to be accomplished8 ,there is only one possible solution of the problem4 ,it is obvious that there must have been some vast reserve of heat in the sun in comparison with which the quantity of heat yielded by the contraction may be deemed insignificant4 ,until this new source of solar energy had been discovered1 our knowledge of the physics of the solar system lay under a reproach1 which it was the bounden duty of men of science to endeavour to remove4 ,during the last few years lines of research carried on in various directions have1 in a most unexpected manner1 thrown much light on the origin of the sun's heat1 and1 indeed1 we may now say that the great difficulty which has for so long troubled us no longer exists in a serious form4 ,recent discoveries show that matter possesses stores of energy which1 if not actually boundless1 are enormously in excess of what had been previously deemed possible4 ,these stores of energy are available for supplying the heat of the sun1 and it is easy to show that they are amply sufficient to furnish the necessary sunbeams for even the longest periods during which the claims of geology maintain that the sun must have been shining4 ,the researches of ,professor ,sir ,j4 ,j4 ,thomson have shown how corpuscles of matter are sometimes moving with velocities enormously greater than those of any celestial body with which astronomy had made us acquainted4 ,the case of high corpuscular velocity which is most generally known is that presented by radium1 the particles from which are being continually shot forth in myriads4 ,it is quite true that each of these corpuscles is excessively small1 and it may be useful to give the following illustration bearing on the subject4 ,think of a number represented by unity followed by eighteen cyphers1 or more concisely as #ajah1 and think of a line a kilometre long4 ,if that line were divided into #ajah parts1 each of those parts would represent the diameter of a corpuscle of radium4 ,if that line were multiplied by #ajah1 the result would be a line so long that a ray of light would require a period of no less than #ajj1jjj years to pass from one end to the other4 ,these corpuscles of radium are1 no doubt1 excessively small1 but the velocity with which they are moving is comparable with the velocity of light4 ,when a material object is moving with a velocity of that magnitude the energy it contains in virtue of that velocity is indeed startling4 ,a very small grain of sand would1 if moving with the velocity of light1 contain1 in virtue of that motion1 the equivalent of more heat than could be produced by the combustion of a ton of the best coal4 ,the late ,dr4 ,w4 ,e4 ,wilson showed that if an excessively minute percentage of radium should be found to exist in the sun1 it would completely account for the sustentation of the solar heat1 and the ,hon4 ,r4 ,strutt has shown that the minute quantities of radium which he has proved to exist in terrestrial rocks would enormously protract the earth's cooling4 ,these discoveries have1 in fact1 completely changed the outlook on the problem of the sun's heat1 and1 though no doubt much has yet to be done before the whole subject is cleared up1 the great difficulty may be regarded as vanquished4 ,thus1 the discovery of radium1 and the wonderful phenomena associated therewith1 has pointed out a possible escape from one of the gravest difficulties in science4 ,the most notable fact which emerges from the modern study of the structure of the heavens is the ever-increasing significance and importance of the spiral nebul4 ,the following pages will have failed in their object if they have not succeeded in emphasising the fact that the spiral nebula is1 next to a fixed star itself1 the most characteristic type of object in the material universe4 ,with every increase in the power of the telescope1 and with every development of the application of photography to celestial portraiture1 the importance of the spiral structure in nebul becomes of ever-increasing interest4 ,but ,i revert to this subject here for the purpose of taking notice of a suggestive paper by ,mr4 ,c4 ,easton in the 8,astrophysical ,journal10 ,vol4 ,,xii41 ,no4 #b1 ,september1 #aijj1 entitled 8,a ,new ,theory of the ,milky ,way40 ,this paper advances the striking view that the ,milky ,way is itself a spiral nebula1 and certainly the considerations adduced by ,mr4 ,easton seem to justify his remarkable conclusion4 ,it is first to be noticed that the ,milky ,way extends as an irregular band completely round the heavens1 and that it follows very nearly the course of a great circle4 ,the curious convolutions of the ,milky ,way1 the varying star densities of its different parts1 would1 as shown by ,mr4 ,easton1 be completely accounted for if the ,milky ,way were a mighty spiral4 ,we view the ordinary celestial spirals from the outside at an immense distance in space4 ,we view the ,milky ,way from a position within the circuit of the nebula4 ,it has1 however1 been shown by ,mr4 ,easton that the centre of the ,spiral ,nebula is not exactly at the sun4 ,the centre of the ,milky ,way is near that superb region of the galaxy which lies in ,cygnus4 ,thus1 the significance of the spiral structure in the universe becomes greatly enhanced4 ,the spirals abound in every part of the heavens2 they are placed in every conceivable position and in every possible plane2 they have every range in size from comparatively small objects1 whose destiny is to evolve into a system like our solar system1 up to stupendous objects which include a myriad of such systems4 ,there is now the further interest that as the sun and the solar system are included within the ,milky ,way1 and as the ,milky ,way is a spiral1 this earth of ours is itself at this moment a constituent part of a great spiral4 ,finally1 ,i would say that1 so far as ,i have been able to understand the subject1 it appears to me that every advance in our knowledge of the heavens tends more and more to support the grand outlines of the ,nebular ,theory as imagined by ,kant and ,laplace4 ,r4 ,s4 ,b4 ,may #a1 #aiji4 ---------------------------------------- -------------------------------- ,,contents ,,chapter ,,page ,i4 --,,introduction #a ,,ii4 --,,the ,,problem ,,stated #ba ,,iii4 --,,the ,,fire-,,mist #ci ,,iv4 --,,nebul--,,apparent ,,and ,,real #eb ,v4 --,,the ,,heat ,,of ,,the ,,sun #ge ,,vi4 --,,how ,,the ,,sun',s ,,heat ,,is ,,maintained #ie ,,vii4 --,,the ,,history ,,of ,,the ,,sun #aab ,,viii4 --,,the ,,earth',s ,,beginning #abb ,,ix4 --,,earthquakes ,,and ,,volcanoes #aeh ,x4 --,,spiral ,,and ,,planetary ,,nebul #aia ,,xi4 --,,the ,,unerring ,,guide #bjg ,,xii4 --,,the ,,evolution ,,of ,,the ,,solar ,,system #bdf ,,xiii4 --,,the ,,unity ,,of ,,material ,,in ,,the ,,heavens #bfa ,,and ,,the ,,earth ,,xiv4 --,,the ,,first ,,concord #bid ,,xv4 --,,the ,,second ,,concord #cjh ,,xvi4 --,,the ,,third ,,concord #cbd ,,xvii4 --,,objections ,,to ,,the ,,nebular ,,theory #ccg ,,xviii4 --,,the ,,beginning ,,of ,,the ,,nebula #cdh ,,xix4 --,,concluding ,,chapter #cfa ,,appendices #cfi ,,index #chb ---------------------------------------- -------------------------------- ,,list ,,of ,,illustrations ,,fig4 ,,page ,an ,english ,sunset tinged by ,krakatoa ,frontispiece 7colour7 #a4 ,immanuel ,kant 7from an old print7 #g #b4 ,a ,faint ,diffused ,nebulosity #ag #c4 ,the ,crab ,nebula #ai #d4 ,jupiter #be #e4 ,nebulous ,region and ,star-cluster #cc #f4 ,the ,great ,nebula in ,orion #da #g4 ,the ,dumb-bell ,nebula #de #h4 ,the ,crossley ,reflector #di #i4 ,the ,cluster in ,hercules #ec #aj4 ,spectra of the ,sun and ,capella #fb #aa4 ,spectrum of ,nebula in ,orion and ,spectrum #fd of ,white ,star #ab4 ,solar ,spectra with ,bright ,lines and ,dark #fi ,lines during ,eclipse #ac4 ,the ,nebul in the ,pleiades #ga #ad4 ,the ,sun #ha #ae4 ,i4 ,spectrum of the ,sun4 ,,ii4 ,spectrum of #he ,arcturus #af4 ,brooks' ,comet and ,meteor ,trail #hi #ag4 ,argus and the surrounding ,stars and #ajc ,nebulosity #ah4 ,trifid ,nebula in ,sagittarius #aje #ai4 ,to illustrate the ,history of the ,sun #aac #bj4 ,solar ,corona #aag #ba4 ,the ,great ,comet of #ahhb #aai #bb4 ,special ,thermometer for use in ,deep #abi ,borings #bc4 ,at the ,bottom of the ,great ,bore #adj #bd4 ,three consecutive ,shells of the ,earth's #ade ,crust #be4 ,earthquake ,routes from ,japan to the ,isle #aga of ,wight ,showing ,localities of ,earthquakes #age 7colour7 #bf4 ,showing ,coasts invaded by the ,great #agi ,sea-waves from ,krakatoa ,the ,early ,stage of the ,eruption of #ahj ,krakatoa 7colour7 #bg4 ,spread of the ,air-wave from ,krakatoa to #ahc the ,antipodes #bh4 ,the great ,spiral ,nebula #aic #bi4 ,how to find the great ,spiral ,nebula #aif #cj4 ,a group of ,nebul #aii #ca4 ,a ,ray ,nebula #bja #cb4 ,portion of the ,milky ,way #bje #cc4 ,a ,spiral ,nebula seen ,edgewise #baa #cd4 ,a foreshortened ,spiral #bab #ce4 ,edge-view of a ,spiral boldly shown #bac #cf4 ,to illustrate ,moment of ,momentum #bbc #cg4 ,saturn #bcc #ch4 ,the ,ring ,nebula in ,lyra #bdi #ci4 ,lunar ,craters3 ,hyginus and ,albategnius #bee #dj4 ,a remarkable ,spiral #beg #da4 ,a clearly-cut ,spiral #bei #db4 ,the ,h and ,k ,lines in the ,photographic #bgf ,solar ,spectrum #dc4 ,spectrum of ,comet showing ,carbon ,lines #bij ,the ,solar ,spectrum 7colour7 #bij #dd4 ,spectrum of the ,sun during ,eclipse #bia #de4 ,a ,spiral presented ,edgewise #bif #df4 ,the ,plane of a ,planet's ,orbit #bih #dg4 ,a ,right ,angle divided into ,ten ,parts #cja #dh4 ,illustration of the ,second ,concord #cji #di4 ,orbits of the ,earth1 ,eros and ,mars #cac #ej4 ,i4 ,a ,natural ,system4 ,,ii4 ,an ,unnatural #cah ,system #ea4 ,an elongated irregular ,nebula #cbi #eb4 ,two-branched ,spiral #cde #ec4 ,cluster with ,stars of the #agth ,magnitude #cec #ed4 ,spectrum of ,nova ,persei 7#aija7 #cei #ee4 ,the ,apteryx3 a ,wingless ,bird of ,new #cfe ,zealand #ef4 ,skeleton of the ,apteryx1 showing #cff ,rudimentary ,wings #eg4 ,spirals in other ,departments of ,nature3 #cfg ,foraminifer #eh4 ,ditto ditto ,nautilus #cfg #ei4 ,to illustrate a ,theorem in the #cfi ,attraction of ,gravitation #fj4 ,first ,law of ,motion exemplifies ,constant #cge ,moment of ,momentum #fa4 ,a useful ,geometrical ,proposition #cgf #fb4 ,acceleration of ,moment of ,momentum #cgf equals ,moment of ,force #fc4 ,moment of ,momentum unaltered by #chj ,collision ---------------------------------------- -------------------------------- ,,the ,,earth',s ,,beginning4 ,,chapter ,i4 ,,introduction4 ,the ,earth's ,beginning--,the ,nebular ,theory--,many ,applications of the ,theory--,the ,founders of the ,doctrine--,kant1 ,laplace1 ,william ,herschel3 ,their ,different ,methods of ,work--,the ,vastness of the ,problem--,voltaire's ,fable--,the ,oak-,tree--,the ,method of ,studying the ,subject--,inadequacy of our ,time ,conceptions4 ,i ,,try in these lectures to give some account of an exceptionally great subject--a subject1 ,i ought rather to say1 of sublime magnificence4 ,it may1 ,i believe1 be affirmed without exaggeration that the theme which is to occupy our attention represents the most daring height to which the human intellect has ever ventured to soar in its efforts to understand the great operations of ,nature4 ,the earth's beginning relates to phenomena of such magnitude and importance that the temporary concerns which usually engage our thoughts must be forgotten in its presence4 ,our personal affairs1 the affairs of the nation1 and of the empire--indeed1 of all nations and of all empires--nay1 even all human affairs1 past1 present1 and to come1 shrink into utter insignificance when we are to consider the majestic subject of the evolution of that solar system of which our earth forms a part4 ,we shall obtain a glimpse of what that evolution has been in the mighty chapter of the book of ,nature on which we are now to enter4 ,the nebular theory discloses the beginning of this earth itself4 ,it points out the marvellous process by which from original chaos the firm globe on which we stand was gradually evolved4 ,it shows how the foundations of this solid earth have been laid1 and how it is that we have land to tread on and air to breathe4 ,but the subject has a scope far wider than merely in its relation to our earth4 ,the nebular theory accounts for the beginning of that great and glorious orb the sun1 which presides over the system of revolving planets1 guides them in their paths1 illuminates them with its light1 and stimulates the activities of their inhabitants with its genial warmth4 ,the nebular theory explains how it comes about that the sun still continues in these latter days to shine with the brilliance and warmth that it had throughout the past ages of human history and the vastly greater periods of geological time4 ,then1 as another supreme achievement1 it discloses the origin of the planets which accompany the sun1 and shows how they have come to run their mighty courses2 and it tells us how revolving satellites have been associated with the planets4 ,the nebular theory has1 indeed1 a remarkable relation to all objects belonging to that wonderful scheme which we call the solar system4 ,it should also be noticed that the nebular theory often brings facts of the most diverse character into striking apposition4 ,as it accounts for the continued maintenance of the solar radiation1 so it also accounts for that beneficent rotation by which each continent1 after the enjoyment of a day under the invigorating rays of the sun1 passes in due alternation into the repose of night4 ,the nebular theory is ready with an explanation of the marvellous structure revealed in the rings of ,saturn1 and it shows at the same time how the volcanoes of the moon acquired their past phenomenal activity1 and why1 after ages of activity1 they have now at last become extinct4 ,with equal versatility the nebular theory will explain why a collier experiences increasing heat as he descends the coalpit1 and why the planet ,jupiter is marked with those belts which have so much interest for the astronomer4 ,the nebular theory offers an immediate explanation of the earthquake which wrought such awful destruction at ,lisbon1 while it also points out the cause of that healing warmth of the waters at ,bath4 ,above all1 the nebular theory explains that peerless discovery of cosmical chemistry which declares that those particular elements of which the sun is composed are no other than the elements which form the earth beneath our feet4 ,when a doctrine of such transcendent importance is proposed for our acceptance1 it is fitting that we should look1 in the first instance1 to the source from which the doctrine has emanated4 ,it would already have made good its claim to most careful hearing1 though not perhaps to necessary acceptance1 if it came to us bearing credentials which prove it to be the outcome of the thought and research of one endowed with the highest order of intellect4 ,if the nebular theory had been propounded by only a single great leader of thought1 the sublimity of the subject with which it deals would have compelled the attention of those who love to study the book of ,nature4 ,if it had appeared that a second investigator1 also famous for the loftiest intellectual achievement1 had given to the nebular theory the sanction of his name1 a very much stronger claim for its consideration would at once have been established4 ,if it should further appear that yet a third philosopher1 a man who was also an intellectual giant1 had been conducted to somewhat similar conclusions1 we should admit1 ,i need hardly say1 that the argument had been presented with still further force4 ,it may also be observed that there might even be certain conditions in the work of the three philosophers which would make for additional strength in the cause advocated2 if it should be found that each of the great men of science had arrived at the same conclusion irrespective of the others1 and1 indeed1 in total ignorance of the line of thought which his illustrious compeers were pursuing1 this would1 of course1 be in itself a corroboration4 ,if1 finally1 the methods of research adopted by these investigators had been wholly different1 although converging to the establishment of the theory1 then even the most sceptical might be disposed to concede the startling claim which the theory made upon his reason and his imagination4 ,all the conditions that ,i have assumed have been fulfilled in the presentation of the nebular theory to the scientific world4 ,it would not be possible to point to three names more eminent in their respective branches of knowledge than those of ,kant1 ,laplace1 and ,william ,herschel4 ,kant occupies a unique position by the profundity and breadth of his philosophical studies2 ,laplace applied the great discoveries of ,newton to the investigation of the movements of the heavenly bodies1 publishing the results in his immortal work1 ,mcanique ,cleste2 ,herschel has been the greatest and the most original observer of the heavens since the telescope was invented4 ,it is not a little remarkable that the great philosopher from his profound meditation1 the great mathematician from a life devoted to calculations about the laws of ,nature1 the great observer from sounding the depths of the firmament1 should each in the pursuit of his own line of work have been led to believe that the grand course of ,nature is essentially expressed by the nebular theory4 ,there have been differences of detail in the three theories2 indeed1 there have been differences in points which are by no means unimportant4 ,this was unavoidable in the case of workers along lines so distinct1 and of a subject where many of the elements were still unknown1 as indeed many are still4 ,even at the present day no man can give a complete account of what has happened in the great evolution4 ,but the monumental fact remains that these three most sagacious men of science1 whose lives were devoted to the pursuit of knowledge1 each approaching the subject from his own direction1 each pursuing his course in ignorance of what the others were doing1 were substantially led to the same result4 ,the progress of knowledge since the time when these great men lived has confirmed1 in ways which we shall endeavour to set forth1 the sublime doctrine to which their genius had conducted them4 ,immanuel ,kant1 whose grandfather was a ,scotsman1 was born in #agbd at ,knigsberg1 where his life was spent as a professor in the ,university1 and where he died in #ahjd4 ,in the announcement of the application of the principle of evolution to the solar system1 ,laplace was preceded by this great ,german philosopher4 ,the profound thinker who expounded the famous doctrine of time and space did not disdain to allow his attention to be also occupied with things more material than the subtleties of metaphysical investigation4 ,as a natural philosopher ,kant was much in advance of his time4 ,his speculations on questions relating to the operations in progress in the material universe are in remarkable conformity with what is now accepted as the result of modern investigation4 ,kant outlined with a firmness inspired by genius that nebular theory to which ,laplace subsequently and independently gave a more definite form1 and which now bears his name4 ,kant's famous work with which we are now concerned appeared in #agee4a ,in it he laid down the immortal principle of the nebular theory4 ,the greatness of this book is acknowledged by all who have read it1 and notwithstanding that the progress of knowledge has made it obvious that many of the statements it contains must now receive modification1 ,kant's work contains the essential principle affirming that the earth1 the sun1 the planets1 and all the bodies now forming the solar system did really originate from a vast contracting nebula4 ,in later years ,kant's attention was diverted from these physical questions to that profound system of philosophy with which his name is chiefly associated4 ,the nebular theory is therefore to be regarded as incidental to ,kant's great lifework rather than as forming a very large and important part of it4 ,footnote #a3 ,we are now fortunately able to refer the ,english reader to the work of ,professor ,w4 ,hastie1 ,d4,d41 entitled 8,kant's ,cosmogony10 ,glasgow1 #aijj4 ,kant's most interesting career is charmingly described in ,de ,quincey's 8,last ,days of ,immanuel ,kant40 ,illustration3 ,,immanuel ,,kant4 7,from an old ,print47 ,at the close of the last century1 while ,france was in the throes of the ,revolution1 a school of ,french mathematicians was engaged in the accomplishment of a task which marked an epoch in the history of human thought4 ,foremost among the mathematicians who devoted their energies to the discussion of the great problems of the universe was the illustrious ,laplace4 ,as a personal friend of ,napoleon1 ,laplace received marked distinction from the ,emperor1 who was himself enough of a mathematician to be able to estimate at their true value the magnificent results to which ,laplace was conducted4 ,it was at the commencement of ,kant's career1 and before his great lifework in metaphysics was undertaken1 that he was led to his nebular theory of the solar system4 ,in the case of ,laplace1 on the other hand1 the nebular theory was not advanced until the close of the great work of his life4 ,the ,mcanique ,cleste had been written1 and the fame of its author had been established for all time2 and then in a few pages of a subsequent volume1 called the ,systme du ,monde1 he laid down his famous nebular theory4 ,in that small space he gave a wonderful outline of the history of the solar system4 ,he had not read that history in any books or manuscripts2 he had not learned it from any ancient inscriptions2 he had taken it direct from the great book of ,nature4 ,influenced by the caution so characteristic of one whose life had been devoted entirely to the pursuit of the most accurate of all the sciences1 ,laplace accompanied his announcement of the nebular theory with becoming words of warning4 ,the great philosopher pointed out that there are two methods of discovering the truths of astronomy4 ,some truths may be discovered by observing the heavenly bodies with telescopes1 by measuring with every care their dimensions and their positions1 and by following their movements with assiduous watchfulness4 ,but there is another totally different method which has enabled many remarkable discoveries to be made in astronomy2 for discoveries may be made by mathematical calculations which have as their basis the numerical facts obtained by actual observation4 ,this mathematical method often yields results far more profound than any which can be obtained by the astronomer's telescope4 ,the pen of the mathematician is indeed an instrument which sometimes anticipates revelations that are subsequently confirmed by actual observation4 ,it is an instrument which frequently performs the highly useful task of checking the deductions that might too hastily be drawn from telescopic observations4 ,it is an instrument the scope of whose discoveries embraces regions immeasurably beyond the reach of the greatest telescope4 ,the pen of the mathematician can give us information as to events which took place long before telescopes came into existence--nay1 even unnumbered ages prior to the advent of man on this earth4 ,laplace was careful to say that the nebular theory which he sketched must necessarily be judged by a standard different from that which we apply to astronomical truths revealed by telescopic observation or ascertained by actual calculation4 ,the nebular theory1 said the great ,french mathematician1 has to be received with caution1 inasmuch as from the nature of the case it cannot be verified by observation1 nor does it admit of proof possessing mathematical certainty4 ,a large part of these lectures will be devoted to the evidence bearing upon this famous doctrine4 ,let it suffice here to remark that the quantity of evidence now available is vastly greater than it was a hundred years ago1 and furthermore1 that there are lines of evidence which can now be followed which were wholly undreamt of in the days of ,kant and ,laplace4 ,the particular canons laid down by ,laplace1 to which we have just referred1 are perhaps not regarded as so absolutely binding in modern days4 ,if we were to reject belief in everything which cannot be proved either by the testimony of actual eye-witnesses or by strict mathematical deductions1 it would1 ,i fear1 fare badly with not a few great departments of modern science4 ,it will not be necessary to do more at present than just to mention1 in illustration of this1 the great doctrine of the evolution of life1 which accounts for the existing races of plants and animals1 including even man himself4 ,i need hardly say that the ,darwinian theory1 which claims that man has come by lineal descent from animals of a lower type1 admits of no proof by mathematics2 it receives assuredly no direct testimony from eye witnesses2 and yet the fact that man has so descended is1 ,i suppose1 now almost universally admitted4 ,in the case of the great ,german philosopher1 as well as in the case of the great ,french mathematician1 the enunciation and the promulgation of their nebular theories were merely incidental to the important scientific undertakings with which their respective lives were mainly occupied4 ,the relation of the nebular theory to the main lifework of the third philosopher ,i have named1 has been somewhat different4 ,when ,william ,herschel constructed the telescopes with which1 in conjunction with his illustrious sister1 he conducted his long night-watches1 he discovered thousands of new nebul2 he may1 in fact1 be said to have created nebular astronomy as we now know it4 ,ever meditating on the objects which his telescopes brought to light1 ever striving to sound the mysteries of the universe1 ,herschel perceived that between a nebula which was merely a diffused stain of light on the sky1 and an object which was hardly distinguishable from a star with a slight haze around it1 every intermediate grade could be found4 ,in this way he was led to the splendid discovery which announced the gradual transformation of nebul into stars4 ,we have already noted how the profound mathematician was conducted to a view of the origin of the solar system which was substantially identical with that which had been arrived at by the consummate metaphysician4 ,the interest is greatly increased when we find that similar conclusions were drawn independently from the telescopic work of the most diligent and most famous astronomical observer who has ever lived4 ,not from abstract speculation like ,kant1 not from mathematical suggestion like ,laplace1 but from accurate and laborious study of the heavens was the great ,william ,herschel led to the conception of the nebular theory of evolution4 ,that three different men of science1 approaching the study of perhaps the greatest problem which ,nature offers us from points of view so fundamentally different1 should have been led substantially to the same result1 is a remarkable incident in the history of knowledge4 ,surely the theory introduced under such auspices and sustained by such a weight of testimony has the very strongest claim on our attention and respect4 ,in the discussion on which we are about to enter in these lectures we must often be prepared to make a special effort of the imagination to help us to realise how greatly the scale of the operations on which the attention is fixed transcends that of the phenomena with which our ordinary affairs are concerned4 ,our eyes can explore a region of space which1 however vast1 must still be only infinitesimal in comparison with the extent of space itself4 ,notwithstanding all that telescopes can do for us1 our knowledge of the universe must be necessarily restricted to a mere speck in space1 a speck which bears to the whole of space a ratio less--we might perhaps say infinitely less--than that which the area of a single daisy bears to the area of the continent where that daisy blooms4 ,but we need not repine at this limitation2 a whole life devoted to the study of a daisy would not be long enough to explore all the mysteries of its life4 ,in like manner the duration of the human race would not be long enough to explore adequately even that small part of space which is submitted for our examination4 ,but it is not merely the necessary limits of our senses which restrict our opportunities for the study of the great phenomena of the universe4 ,man's life is too short for the purpose4 ,that our days are but a span is the commonplace of the preacher4 ,but it is a commonplace specially brought home to us in the study of the nebular theory4 ,a man of fourscore will allude to his life as a long one1 and no doubt it may be considered long in relation to the ordinary affairs of our abode on earth2 but what is a period of eighty years in the history of the formation of a solar system in the great laboratory of the universe8 ,such a period then seems to be but a trifle--it is nothing4 ,eighty years may be long enough to witness the growth of children and grandchildren2 but it is too short for a single heartbeat in the great life of ,nature4 ,even the longest lifetime is far too brief to witness a perceptible advance in the grand transformation4 ,the periods of time demanded in the great evolution shadowed forth by the nebular theory utterly transcend our ordinary notions of chronology4 ,the dates at which supreme events occurred in the celestial evolution are immeasurably more remote than any other dates which we are ever called upon to consider in other departments of science4 ,the time of the story on which we are to be engaged is earlier1 far earlier1 than any date we have ever learned at school1 or have ever forgotten since4 ,the incidents of that period took place long before any date was written in figures--earlier than any of those very ancient dates which the geologists indicate not by figures indeed1 but by creatures whose remains imbedded in the rocks suffice to give a character to the period referred to4 ,the geologist will specify one epoch as that in which the fossilized bone of some huge extinct reptile was part of a living animal2 he may specify another by the statement that the shell of some beautiful ammonite was then inhabited by a living form which swam in the warm primval seas4 ,the date of our story has at least this much certainty3 that it is prior--immeasurably prior--to the time when that marvellous thing which we call life first came into being4 ,voltaire has an instructive fable which ,i cannot resist repeating4 ,it will serve1 at all events1 to bring before us the way in which the lapse of time ought to be regarded by one who desires to view the great operations of ,nature in their proper proportions4 ,he tells how an inhabitant of the star ,sirius went forth on a voyage of exploration through the remote depths of space4 ,in the course of his travels he visited many other worlds1 and at length reached ,saturn1 that majestic orb1 which revolved upon the frontier of the solar system1 as then known4 ,alighting on the ringed globe for rest and investigation1 the ,sirian wanderer1 in quest of knowledge1 was successful in obtaining an interview with a stately inhabitant of ,saturn who enjoyed the reputation of exceptional learning and wisdom4 ,the ,sirian hoped to have some improving conversation with this sage who dwelt on a globe so utterly unlike his own1 and who had such opportunities of studying the majestic processes of ,nature in remote parts of the universe4 ,he thought perhaps they might be able to compare instructive notes about the constitution of the suns and systems in their respective neighbourhoods4 ,the visitor accordingly prattled away gaily4 ,he opened all his little store of knowledge about the ,milky ,way1 about the ,great ,bear1 and about the great ,nebula in ,orion2 and then pausing1 he asked what the ,saturnian had to communicate in reply4 ,but the philosopher remained silent4 ,eagerly pressed to make some response1 the grave student who dwelt on the frontier globe at last said in effect3 8,sirian1 ,i can tell you but little of ,nature4 ,i can tell you indeed nothing that is really worthy of the great theme which ,nature proposes2 for the grand operations of ,nature are very slow2 they are so slow that the great transformations in progress around us would have to be watched for a very long time before they could be properly understood4 ,to observe ,nature so as to perceive what is really happening1 it would be necessary to have a long life2 but the lives of the inhabitants of ,saturn are not long2 none of us ever lives more than fifteen thousand years40 ,change is the order of ,nature4 ,many changes no doubt take place rapidly1 but the great changes by which the system has been wrought into its present form1 those profound changes which have produced results of the greatest magnificence in celestial architecture are extremely slow4 ,we should make a huge mistake if we imagined that changes--even immense changes--are not in progress1 merely because our brief day is too short a period wherein to perceive them4 ,on the village green stands an oak-tree1 a veteran which some say dates from the time of ,william the ,conqueror1 but which all agree must certainly have been a magnificent piece of timber in the days of ,queen ,elizabeth4 ,the children play under that tree just as their parents and their grandparents did before them4 ,a year1 a few years1 even a lifetime1 may show no appreciable changes in a tree of such age and stature4 ,its girth does not perceptibly increase in such a period4 ,but suppose that a butterfly whose life lasts but a day or two were to pass his little span in and about this venerable oak4 ,he would not be able to perceive any changes in the tree during the insignificant period over which his little life extended4 ,not alone the mighty trunk and the branches1 but even the very foliage itself would seem essentially the same in the minutes of the butterfly's extreme old age as they did in the time of his life's meridian or at the earliest moment of his youth4 ,to the observations of a spectator who viewed it under such ephemeral conditions the oak-tree would appear steadfast1 and might incautiously be deemed eternal4 ,if the butterfly could reflect on the subject1 he might perhaps argue that there could not be any change in progress in the oak-tree1 because although he had observed it carefully all his life he could not detect any certain alteration4 ,he might therefore not improbably draw the preposterous conclusion that the oak-tree must always have been just as large and just as green as he had invariably known it2 and he might also infer that just as the oak-tree is now1 so will it remain for all time4 ,illustration3 ,fig4 #b4--;,a ,,faint ,,diffused ,,nebulosity 7n4g4c4 #adii2 in ,perseus74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,in our study of the heavens we must strive to avoid inferences so utterly fallacious as these which ,i have here tried to illustrate4 ,let it be granted that to our superficial view the sun and the moon1 the stars and the constellations present features which appear to us as eternal as the bole of the oak seemed to the butterfly4 ,but though the sun may seem to us always of the same size and always of the same lustre1 it would be quite wrong to infer that the lustre and size of the sun are in truth unchanging4 ,the sun is no more unchanging than the oak-tree is eternal4 ,the sun and the earth1 no less than the other bodies of the universe1 are in process of a transformation no less astonishing than that wonderful transformation which in the course of centuries develops an acorn into the giant of the forest4 ,we could not indeed with propriety apply to the great transformation of the sun the particular word growth2 the character of the solar transformation cannot be so described4 ,the oak-tree1 of course1 enlarges with its years1 while the sun1 on the other hand1 is becoming smaller4 ,the resemblance between the sun and the oak-tree extends no further than that a transformation is taking place in each4 ,the rate at which each transformation is effected is but slow2 the growth of the oak is too slow to be perceived in a day or two2 the contraction of the sun is too slow to be appreciable within the centuries of human history4 ,whatever the butterfly's observation might have suggested with regard to the eternity of the oak1 we know there was a time when that oak-tree was not1 and we know that a time will come when that oak-tree will no longer be4 ,in like manner we know there was a time when the solar system was utterly different from the solar system as we see it now2 and we know that a time will come when the solar system will be utterly different from that which we see at present4 ,the mightiest changes are most certainly in progress around us4 ,we must not deem them non-existent1 merely because they elude our scrutiny1 for our senses may not be quick enough to perceive the small extent of some of these changes within our limited period of observation4 ,the intellect in such a case confers on man a power of surveying ,nature with a penetration immeasurably beyond that afforded by his organs of sense4 ,illustration3 ,fig4 #c4--,,the ,,crab ,,nebula 7n4g4c4 #aieb2 in ,taurus74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s7 ,that the great oak-tree which has lived for centuries sprang from an acorn no one can doubt2 but what is the evidence on which we believe this to have been the origin of a veteran of the forest when history and tradition are both silent8 ,in the absence of authentic documents to trace the growth of that oak-tree from the beginning1 how do we know that it sprouted from an acorn8 ,the only reason we have for believing that the oak-tree has gone through this remarkable development is deduced from the observation of other oak-trees4 ,we know the acorn that has just sprouted2 we know the young sapling as thick as a walking stick2 we know the vigorous young tree as stout as a man's arm or as his body2 we know the tree when it first approaches the dignity of being called timber2 we can therefore observe different trees grade by grade in a continuous succession from the acorn to the monarch of five centuries4 ,no one doubts for a moment that the growth as witnessed in the stages exhibited by several different trees1 gives a substantially accurate picture of the development of any individual tree4 ,such is the nature of one of the arguments which we apply to the great problem before us4 ,we are to study what the solar system has been in the course of its history by the stages which we witness at the present moment in the evolution of other systems throughout the universe4 ,we cannot indeed read the history in time1 but we can read it in space4 ,the mighty transformation through which the solar system has passed1 and is even now at this moment passing1 cannot be actually beheld by us poor creatures of a day4 ,it might perhaps be surveyed by beings whose pulses counted centuries1 as our pulses count seconds1 by beings whose minutes lasted longer than the dynasties of human history1 by beings to whom a year was comparable with the period since the earth was young1 and since life began to move in the waters4 ,may ,i1 with all reverence1 try to attune our thoughts to the time conceptions required in this mighty theme by quoting those noble lines of the hymn-- 8,a thousand ages in ,thy sight ,are like an evening gone1 ,short as the watch that ends the night1 ,before the rising sun40 ---------------------------------------- -------------------------------- ,,chapter ,,ii4 ,,the ,,problem ,,stated4 ,the ,great ,diurnal ,motion--,the ,distinction between ,stars and ,planets--,the ,earth no more than a ,planet--,relation of the ,stars to the ,solar ,system--,contrast between ,aldebaran and ,mars--,illustration of ,star-distances--,the ,celestial ,perspective--,illustration of an ,attractive ,force--,instructive ,experiments--,the ,globe and the ,tennis ,ball--,the ,law of ,gravitation--,the ,focal ,ellipse--,the ,solar ,system as it is now ,known--,statement of the ,great ,problem before us4 ,,when we raise our eyes to the heavens on a clear night1 thousands of bright objects claim our attention4 ,we observe that all these objects move as if they were fastened to the inside of an invisible sphere4 ,they are seen gradually ascending from the east1 passing across the south1 and in due course sinking towards the west4 ,the sun and the moon1 as well as all the other bodies1 alike participate in this great diurnal movement4 ,the whole scheme of celestial objects seems to turn around the two points in the heavens that we call the ,poles1 and so far as the pole in the northern hemisphere is concerned1 its position is most conveniently indicated by the proximity of the well-known ,pole ,star4 ,except this great diurnal motion1 the vast majority of the bodies on the celestial sphere have no other movement easily recognisable1 and certainly none which it is necessary for us to consider at present4 ,the groups in which the stars have been arranged by the poetical imagination of the ancients exist to-day1 as they have existed during all the ages since they were first recognised1 without any noticeable alteration in their lineaments4 ,the stately belt of ,orion is seen to-night as ,job beheld it thousands of years ago2 the stars in the ,pleiades have not altered their positions1 relatively to the adjacent stars nor their arrangement among themselves1 since the time when astronomers in early ,greece observed them4 ,all the bodies which form these groups are therefore known as fixed stars4 ,but besides the fixed stars1 which exist in many thousands1 and1 of course1 the sun and the moon1 there are other celestial objects1 so few in number as to be counted on the fingers of one hand1 which are in no sense fixed stars4 ,it is quite true that these wandering bodies1 or planets1 as they are generally designated1 bear a certain resemblance to the fixed stars4 ,in each case the star or the planet appears as a bright point1 like many other bright points in the heavens1 and star and planet both participate in the general diurnal motion4 ,but a little attention will show that while the stars1 properly so called1 retain their relative places for months and years and centuries1 the planets change their places so rapidly that in the course of a few nights it is quite easy to see1 even without the aid of any instrument1 that they have independent motion4 ,we may compare the movements of these bodies to the movement of the moon1 which nightly shifts her place over a long track in the sky2 and although we are not able to see the stars in the vicinity of the sun1 inasmuch as the brilliant light of the orb quenches the feeble radiance from such stars1 there is no doubt that1 did we see them1 the sun itself would seem to move relatively to the stars1 just as does the moon and just as do the planets4 ,the fundamental distinction between stars and planets was noticed by acute observers of ,nature in the very earliest times4 ,the names of the planets come to us as survivals from the time when the sun1 the moon1 and the stars were objects of worship1 and they come to us bearing the names of the deities of which these moving globes were regarded as the symbols4 ,but it was not the movements of the planets alone which called for the notice of the early observers of the skies4 ,the brightness and certain other features peculiar to them also attracted the attention of the primitive astronomers4 ,they could not fail to observe that when the beautiful planet ,venus was placed so as to be seen to the greatest advantage1 her orb was far brighter than any other object in the host of heaven1 the sun and the moon both of course excepted4 ,it was also obvious that ,jupiter at its best exceeded the stars in lustre1 and sometimes approached even to that of ,venus itself4 ,though ,mercury was generally so close to the sun as to be invisible among its beams1 yet on the rare occasions when that planet was seen1 just after sunset or just before sunrise1 its lustre was such as to mark it out as one of the remarkable bodies in the heavens4 ,thus the astronomers of the earliest ages pointed to the five planets and the sun and the moon as the seven wandering stars4 ,the diligent attention of the learned of every subsequent period was given to the discovery of the character of their movements4 ,the problems that these motions presented were1 however1 so difficult that not until after the lapse of thousands of years did their nature become understood4 ,the supreme importance of the earth appeared so obvious to the early astronomers that it did not at first occur to them to assign to our earth a position which would reduce it to the same class as any of the celestial bodies4 ,the obviously great size of our globe1 the fact that to the uninstructed senses the earth seemed to be at rest1 while the other bodies seemed to be in motion1 and many other analogous circumstances1 appeared to show that the earth must be a body totally different from the other objects distributed around us in space4 ,it was only by slow degrees1 and after much observation and reflection1 and not a little controversy1 that at last the true nature of our system was detected4 ,those who have been brought up from childhood in full knowledge of the rotation of the earth and of the other fundamental facts relating to the celestial sphere1 will often find it difficult to realise the way such problems must have presented themselves to the observers of old1 who believed1 as for centuries men did believe1 that the earth was a plane of indefinite extent fixed in space1 and that the sun and the planets1 the moon and the stars1 were relatively small bodies whose movements must be accounted for as best they could be1 consistently with the fixity and flatness of the earth4 ,illustration3 ,fig4 #d4--;,,jupiter 7,may #cjth1 #ahii1 #aj;h4 #i4em42 g4m4t474 7,e4 ,m4 ,antoniadi47 ,but at last it began to be seen that the earth must be relegated to a position infinitely less important than that which the untutored imagination assigned to it4 ,it was found that the earth was not an indefinite plane2 it was rather a globe poised in space1 without direct material support from any other body4 ,it was found that the earth was turning round on its axis3 while instead of the sun revolving around the earth1 it was much more correct to say that the earth revolved around the sun4 ,the astonishing truth was then disclosed that the five planets1 ,jupiter and ,saturn1 ,mercury1 ,venus and ,mars1 stood in a remarkable relation to the earth4 ,for as each of these planets was found to revolve round the sun1 and as the earth also revolved round the sun1 the assumed difference in character between the earth and the planets tended to vanish altogether4 ,there was in fact no essential difference4 ,if indeed the earth was smaller than ,jupiter and ,saturn1 yet it was considerably greater and heavier than ,mars or ,mercury1 and it was almost exactly the same size and weight as ,venus4 ,there was clearly nothing in the question of bulk to indicate any marked difference between our earth and the planets4 ,it was also observed that there was no distinction to be drawn between the way in which the earth revolved round the sun and the movements of the planets4 ,no doubt the earth is not so near the sun as ,mercury2 it is not so near the sun as even ,venus2 on the other hand the sun is nearer the earth than ,mars1 while ,jupiter is a long way further off than ,mars1 and ,saturn is even beyond ,jupiter again4 ,it is these considerations which justify us in regarding our earth as one of the planets4 ,we have also to note the overwhelming magnitude of the sun in comparison with any one of the planets4 ,it will suffice to give a single illustration4 ,the sun is more than a thousand times as massive as ,jupiter1 and ,jupiter is the greatest of the planets4 ,this latter noble globe is in fact greater than all the rest of the planets put together4 ,but before we can fully realise the circumstances of the solar system1 it will be necessary to see how the stars1 properly so called1 enter into the scheme of things celestial4 ,the stars look so like the planets that it has not infrequently happened that even an experienced astronomer has mistaken one for the other4 ,the planet ,mars is often very like the star ,aldebaran1 and there are not a few first-magnitude stars which on a superficial view closely resemble ,saturn4 ,but how great is the intrinsic difference between a star and a planet6 ,in the first place we have to note that every planet is a dark object like this earth of ours1 possessing no light of its own1 and dependent entirely on the sun for the supply of light by which it is illumined4 ,but a star is totally different4 ,the star is not a dark object1 but is really an object which is in itself intensely luminous and brilliant2 the star is in fact a sun-like body4 ,how then1 it may well be asked1 does a star like ,aldebaran1 which is indeed a sun-like body1 and in all probability is quite as large and quite as brilliant as the sun itself1 bear even a superficial resemblance to an object like ,mars1 which would not be visible at all were it not for the illumination with which the beams from the sun endow it8 ,the explanation of this striking resemblance is to be sought in the relative distances of the two objects4 ,a light which is near to the eye may produce an effect quite as great as a very much stronger light which is further away4 ,the intensity of a light varies inversely as the square of the distance4 ,if the distance of a light from the eye be doubled1 then the intensity of that light is reduced to one-fourth4 ,now ,aldebaran as a sun-like body emits light which is literally millions of times as great as the gleam of sunshine which starts back to us after reflection from ,mars2 but ,aldebaran is1 let us say1 a million times as far away from us as ,mars1 and this being so1 the light from ,aldebaran would come to us with only a million-millionth part of the intensity that it would have if the star were at the same distance as the planet4 ,there can be no doubt that if ,aldebaran were merely at the same distance from the earth as ,mars1 then ,aldebaran would dispense lustre like a splendid sun4 ,by moving ,aldebaran further off its light1 or rather the light that arrives at the earth1 will gradually decrease until by the time that the star is a million times as far as ,mars1 the light that it sends us is about equal to that of ,mars4 ,if it were removed further still1 the light that it would send us would become less than that which we receive from ,mars1 and if still more remote1 ,aldebaran might cease to be visible altogether4 ,this illustration will suffice to explain the fundamental difference between planets and stars1 notwithstanding the fact that the two classes of bodies bear to each other a resemblance which is extremely remarkable1 even if it must be described as being in a sense accidental4 ,but we now know that all of the thousands of stars are to be regarded as brilliant suns1 some of which may not be so far off as ,aldebaran1 though doubtless some are very much further4 ,the actual distances are immaterial1 for the essential point to notice is that the five planets are distinguished from the stars1 not merely by the fact that they are moving1 while the stars are at rest1 but by the circumstance that the planets are comparatively close to each other and close to the sun1 while the stars are at distances millions of times as great as the distances which the planets are from each other and from the sun4 ,we are now enabled to place the scheme of things celestial in its proper perspective4 ,i shall suppose that at a point in a field in the centre of ,england1 somewhere near ,leamington1 let us say1 we drive in a peg to represent the sun4 ,let us draw a circle with that peg as centre1 a yard being the radius1 and let that circle represent the track in which the earth goes round the sun4 ,i do not indeed say that the orbit of the earth is exactly a circle1 and the actual shape of that orbit we may have to refer to later4 ,as1 however1 the apparent size of the sun does not greatly alter with the seasons1 it is evident that the track which our earth pursues cannot be very different from a circular path4 ,inside this circle which we have drawn with a yard radius1 we shall put two smaller circles which are to represent the path in which ,venus moves1 and the path in which ,mercury moves4 ,outside the path of the earth we shall draw another circle with a radius of five yards2 this will be the highway along which the majestic ,jupiter wends his way4 ,inside the path of ,jupiter we shall put a circle which will represent the track of ,mars1 and outside the path of ,jupiter a circle with ten yards as radius will represent the track of ,saturn4 ,in each of these circles we shall suppose the corresponding planet to revolve1 and the time of revolution will of course be greater the further the planet is from the sun4 ,to complete one of its circuits the earth will require a year1 ,jupiter twelve years1 while ,saturn1 which in the ancient astronomy moved on the frontier of the solar system1 will need thirty years to accomplish its mighty journey4 ,we have thus obtained a plan of the solar system2 but now we should like to indicate the positions which some of the stars are to occupy on the same scale4 ,let us1 to begin with1 see where the very nearest fixed star is to be placed4 ,we may suppose that the field at the centre of ,england1 in which our little diagram has been constructed1 is a large one1 so that we can represent the places of objects which are ten or twenty times as far from the sun as ,saturn4 ,it is1 however1 certain that no actual field would be large enough to contain within its bounds the points which would faithfully represent the positions of even the nearest fixed stars4 ,the whole county of ,warwick would not be nearly big enough for this purpose2 indeed we may say that the whole of ,england1 or indeed of the ,united ,kingdom1 would not be sufficiently extensive4 ,if we represented the star at its true relative distance1 it could not be put down anywhere within the bounds of the ,united ,kingdom2 the nearest object of this kind would have to be far away out on the continent of ,europe1 or far away out on the ,atlantic ,ocean1 far away down near the equator1 or far away up near the pole4 ,this illustration will at all events give some notion of the isolated position of the sun1 with the planets revolving around it1 in relation to the rest of the host of heaven4 ,we thus learn that the real scheme of the universe is widely different from that which a superficial glance at the heavens would lead us to expect4 ,we are now able to put our system into its proper perspective4 ,we are to think of the universe as consisting of a myriad suns1 each sun1 however1 being so far from the other suns that viewed from any one of its neighbours it appears only of star-like insignificance4 ,let us fix our attention on one of these suns in space1 and imagine that around it1 and comparatively close to it1 there are a number of small particles in revolution1 the particles being illumined by the light and warmed by the heat of the central body to which they are attached4 ,viewed from one of those particles1 the sun to which they belong would doubtless appear as a great and glorious orb1 while a glance from one of these particles to any of the other myriad suns in space will show these orbs reduced to mere points of stellar light by reason of their enormous distance4 ,this sun and the particles around it1 by which of course we shall understand the planets1 constitute what we know as the solar system4 ,this illustration may suffice to show the isolation of our system in space1 and that isolation is due to the vast distances by which the sun and its attendant worlds are separated from the myriads of other bodies which form the sidereal heavens4 ,we must next1 so far as our present subject requires it1 consider the laws according to which the planets belonging to that system revolve around the sun4 ,let us think first of a single one of these bodies which1 as is most natural1 we shall take to be the earth itself1 and now let us consider by what agency the movement of the earth around the sun is guided along the path which so closely resembles a circle4 ,it must1 of course1 be borne in mind that there can be no direct material connection between the two bodies2 there is no physical bond uniting the earth to the sun4 ,it is1 however1 certain that some influence proceeding from the sun does really control the motion4 ,we may perhaps illustrate what takes place in the following manner4 ,here is a globe1 and here in my hand ,i hold a tennis ball1 which is attached to a silken thread1 the other end of the thread being attached to the ceiling4 ,the tennis ball is to hang so that both globe and ball are about the same height from the floor4 ,we put the globe directly underneath the point on the ceiling from which the silken thread hangs4 ,if ,i draw the tennis ball aside and simply release it1 then of course everybody knows what happens--it is hardly necessary to try the experiment--the tennis ball falls at once towards the globe and strikes it4 ,we may1 if we please1 regard that tendency of the tennis ball towards the globe as a sort of attraction which the globe exercises upon the ball4 ,i must1 however1 say that this is not a strictly accurate version of what actually takes place4 ,the attraction of the earth for the tennis ball is of course largely neutralised by the support given by the silk thread4 ,there is thus only a slight outstanding component of gravitation acting on the ball1 and this component1 which is virtually the effective force on the ball1 tends to draw the ball directly towards the globe4 ,for the purpose of our illustration we may neglect the direct attraction of the earth altogether2 we may omit all thought of the tension of the silken thread4 ,if there were indeed no attraction from the earth1 the tennis ball might remain poised in space without falling2 and if it were then attracted by the globe it would fly towards the globe just as we actually see it do4 ,we are therefore justified in regarding the movement of the tennis ball as equivalent to that which would be produced if an attractive virtue resided in the globe by which it pulled the tennis ball4 ,we may also imagine that the globe attracts the tennis ball in all its positions2 for whatever be the point at which the ball is released it starts off straight towards the globe4 ,this is our first experiment in which1 having withdrawn the ball1 it is merely released without receiving an initial impulse to one side4 ,illustration3 ,fig4 #e4--,,nebulous ,,region ,,and ,,star-,,cluster 7n4g4c4 #bbcg-i in ,monoceros74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,let us now try a different experiment4 ,we withdraw the ball1 and1 instead of merely releasing it quietly and allowing it to drop directly to the globe1 we give it a little throw sideways1 perpendicular to the line joining it to the centre of the globe4 ,if we start it with the proper speed1 which a few trials will indicate1 the ball can be made actually to move in a circle round the globe4 ,if the initial speed be somewhat different1 the path in which the tennis ball moves will not be a circle2 it will rather be an ellipse of some form4 ,even if the speed be correct the orbit will always be an ellipse if the direction of the initial throw be not perpendicular to the line joining the ball to the centre of the globe4 ,we can make the ball describe a very long ellipse or an ellipse which differs but little from a circle4 ,but ,i would ask you to note particularly that1 no matter how we may start the tennis ball into motion1 it will1 so long as it passes clear of the globe1 move in an ellipse of some kind2 but in making this statement we assume that a circle is a particular form of the ellipse4 ,and now for the lesson which we are to learn from this experiment1 which1 as it is so easily performed1 ,i would wish everyone to try for himself4 ,we have in this simple device an illustration of the movement of a planet around the sun4 ,we see that this tennis ball can be made to move in a circle round the globe1 and that as it performs this circular movement the globe is all the time attracting the ball towards it4 ,thus we illustrate the important law that when one body moves round another in a circular path this movement takes place in consequence of a force of attraction constantly exerted between the large body in the centre and the body revolving round it4 ,the principle here involved will provide the explanation of the movements of the planets round the sun4 ,each of the planets revolves round the sun in an orbit which is approximately circular1 and each of the planets performs that movement because it is continually attracted by the sun4 ,it is1 however1 necessary to add that there is a fundamental difference between the attraction of the sun for the planets and the attraction which the globe appeared to exert on the tennis ball in our experiment4 ,the difference relates to the character of the forces in the two cases4 ,if the tennis ball be drawn but a very small distance from the globe1 the attraction between the two bodies is very slight4 ,if the tennis ball be drawn to a greater distance from the globe1 the attraction is increased correspondingly2 and1 indeed1 in this experiment the attraction between the two bodies increases with the distance1 and is said to be proportional to the distance4 ,but the case is very different in that particular kind of attraction by which the sun controls the movements of the planets4 ,this attraction of gravitation1 as it is called1 also depends on the distance between the two bodies4 ,but the attraction does not increase when the distance of the two bodies increases1 for the change lies the other way4 ,the attraction1 in fact1 diminishes more rapidly than the distance increases4 ,if the distance between the sun and a planet be doubled1 then the attraction between the two bodies is only a fourth of what the attraction was between the two bodies in the former case4 ,this difference between the law of attraction as it exists in the solar system and the law of attraction which is exemplified in our little experiment produces a remarkable contrast in the resulting movements4 ,the orbit in each case is1 no doubt1 an ellipse1 but in the case of the tennis ball revolving round the globe the ellipse is so circumstanced that the fixed attracting body stood at its centre1 while in the case of a planet revolving round the sun the conditions are not so simple4 ,the sun does not stand in the centre of the ellipse4 ,the sun is placed at that remarkable point of the ellipse so dear to the heart of the geometer1 which he calls the focus4 ,the solar system consists1 first1 of the great regulating orb1 the sun2 then of the planets1 each of which revolves in its own track round the sun2 each of these tracks is an ellipse1 and all these ellipses have this in common1 that a focus in each is identical with the centre of the sun4 ,in other respects the ellipses may be quite different4 ,to begin with1 they are not in the same plane1 though it is most important to notice1 as we shall have to discuss more fully hereafter1 that these planes are not very much separated4 ,the dimensions of the ellipses vary1 of course1 for the different planets1 and the periods that the planets require for their several revolutions are also widely different in the cases of the different bodies2 for the greater the diameter of a planet's orbit1 the longer is the time required for that planet to complete a single journey round the sun4 ,the sun presiding at the common focus of the orbits while governing the planets by its attraction1 at the same time that it illumines them with its light and warms them by its rays1 gives the conception of the solar system4 ,but the planetary system ,i have here indicated is merely that system as known to the ancients4 ,it is very imperfect from the standpoint of our present knowledge4 ,the solar system as we now know it1 when telescopes have been applied with such marvellous diligence and success to the discovery of new bodies1 is a system of much greater complexity4 ,to the five old planets have been added two new and majestic planets--,uranus and ,neptune--which revolve outside the track of ,saturn4 ,hundreds of smaller planets1 invisible to the unaided eye1 the asteroids as they are called1 also describe their ellipses round the presiding luminary4 ,and then just as the sun controls the planets revolving round it1 so do many of the planets themselves preside over subordinate systems of revolving globes4 ,our earth has a single attendant1 the moon1 which1 under the guidance of the earth's attraction1 performs its monthly journey2 ,jupiter has its five moons1 while ,mars has two1 and ,saturn eight or nine1 besides his incomparable system of rings1 and we must also add that ,uranus has four satellites and ,neptune one4 ,to complete the tale of bodies in the solar system1 we should add many thousands of comets1 not to mention their more humble associates the meteors1 which swarm in countless myriads4 ,finally1 we are to remember that this elaborate system associated with the sun is an isolated object in the universe2 it is but as a grain of sand in the extent of infinite space4 ,as we contemplate a system so wonderful1 the question naturally arises1 ,how came that system into being8 ,we have to consider whether the laws of nature as we know them afford any rational explanation of the manner in which this system came into existence1 any rational explanation of how the sun came to shine1 how the earth had its beginning1 how the planets came to revolve round the sun1 and to rotate on their own axes4 ,we have to seek for a rational explanation of the rings of ,saturn1 and of the satellites by which so many planets are attended4 ,we have to show that a satisfactory explanation of these remarkable phenomena is forthcoming1 and that it is provided by the famous doctrine of evolution1 which it is the object of these lectures to discuss4 ---------------------------------------- -------------------------------- ,,chapter ,,iii4 ,,the ,,fire-,,mist4 ,evolution of other ,bodies in the ,universe--,the ,nebul--,estimate of the ,size of the ,great ,nebula in ,orion--,photograph of that ,nebula taken at ,lick ,observatory--,the ,dumb-bell ,nebula--,the ,crossley ,reflector--,the late ,professor ,keeler--,astonishing ,discovery of ,new ,nebul--#abj1jjj ,nebul--,the ,continuous ,chain from a ,fluid ,haze of ,light to a ,star--,the ,celestial ,evolution4 ,,we commence this chapter with a scrutiny of the heavens1 to see whether1 among the bodies which it contains1 we can discover any which appear at this moment to be in the condition through which our system has passed in some of its earlier stages4 ,so far as our unaided vision is concerned1 we can see little or nothing in the skies which will render us assistance in our present endeavour4 ,the objects that we do see in thousands are1 of course1 the stars1 and1 as we have already pointed out1 the stars are sun-like objects1 and as such have advanced many stages beyond the elementary condition4 ,the stars are therefore not immediately available for the illustration we require4 ,but when we come to look at the heavens through our telescopes we presently find that there are objects which were not visible to the eye1 and which are neither stars nor planets4 ,closer examination of these objects with the powerful instruments of modern observatories1 and especially with the help of those marvellous appliances which have enabled us to learn the actual chemistry of the heavenly bodies1 supplies the suggestions that are required4 ,for not only does the telescope reveal myriads of stars which the naked eye cannot detect2 not only does it reveal wonderful clusters in which thousands of stars are grouped closely together so as to form spectacles of indescribable magnificence1 when we take into account the intrinsic splendour of each star-like point1 but it also reveals totally different objects1 known as nebul4 ,these objects are not stars and are not composed of stars1 but are vast extensions of matter existing in a far more elementary condition4 ,it is to these curious bodies that we invite special attention at present4 ,it is believed that they offer a remarkable illustration of the origin of the solar system4 ,we shall first consider the best known object of this class4 ,it is the ,great ,nebula in ,orion4 ,illustration3 ,fig4 #f4--,,the ,,great ,,nebula ,,in ,,orion 7,lick ,observatory1 ,california74 7,from the ,royal ,astronomical ,society ,series47 ,and here it may be well to give an estimate which will enable us to form some notion of the size of this object4 ,we are accustomed to recognise the stars as presenting the appearance of mere points of light2 but an object like the ,great ,nebula stretches over a wide area of the sky4 ,as to the actual extent of the space which it occupies we cannot speak with confidence4 ,the fact is that with every increase in the power of the telescope the nebula appears to encroach more and more on the darkness of space around4 ,we give in ,fig4 #f a representation of the ,great ,nebula as it appears on a photographic plate obtained at the ,lick ,observatory in ,california4 ,but no picture can adequately represent the extraordinary delicacy of the object and the softness and tenderness with which the blue nebulous light fades into the black sky around4 ,and it must not be imagined that the nebula1 as seen on this picture1 represents the utmost limits of the object itself4 ,every prolongation of the exposure1 every increase in the sensitiveness of the plate1 show more and more the extent of the nebula4 ,we shall1 ,i doubt not1 still be within the bounds of truth if we say that the nebula extends over an area ten times as great as that represented in this photograph4 ,but we will take only the area of the object as shown in the photograph for the purpose of our calculation4 ,let us say that the nebula1 as it is here represented1 covers about two degrees square4 ,i shall not attempt to express in miles the dimensions of an object so vast4 ,i will try to give a conception of the size of the ,great ,nebula in a different manner4 ,let us employ the dimensions of our solar system for the purpose of comparison4 ,let us suppose that we draw1 upon the scale of this celestial photograph1 a map which shall represent the sun in the centre1 the earth at her proper distance from the sun1 and ,jupiter in his orbit1 which is five times the diameter of the earth's orbit2 and then let us mark the other planets at their respective distances1 even to ,neptune1 revolving in his great ellipse1 with a diameter thirty times that of the earth's orbit4 ,let us then take the area of the orbit described by ,neptune as a unit with which to measure the size of the ,great ,nebula in ,orion4 ,we shall certainly be well within the actual truth if we say that a million circles as big as that described by ,neptune would not suffice to cover the area that is represented on this photograph4 ,this will give some idea of the imposing dimensions of the ,great ,nebula in ,orion4 ,but ,i would not have it to be supposed that the ,great ,nebula in ,orion is unique1 unless in respect to its convenient position4 ,the circumstances of its situation in space happen to make it a comparatively easy object for observation by dwellers on the earth4 ,there are1 however1 very many other nebul1 although1 with one exception--namely1 the ,great ,nebula in ,andromeda1 to which we shall have to refer in a later chapter--they do not from our point of observation appear to be so brilliant as the nebula in ,orion4 ,the fact is that by large and powerful telescopes multitudes of these nebul are revealed1 and the number ever tends to increase as greater depths in space are sounded4 ,many of the nebul are objects which possess sufficient detail to merit the particular attention which they receive from astronomers4 ,it must1 however1 be confessed that by far the greater number of these objects are so dimly discerned that it is impossible to study their individual characteristics4 ,among the nebul which possess sufficient individuality to merit study for our present purpose1 ,i must mention the so-called ,dumb-bell4 ,this most interesting object can be seen in any good telescope4 ,it requires1 however1 as indeed do all such objects1 an instrument of the highest power to do it justice2 in these modern days1 however1 the eye observation of nebul through great telescopes has been superseded by the employment of the photographic plate4 ,i may take this opportunity of mentioning that a photograph really shows more details in the nebula than can be perceived even by the most experienced eye when applied to the most powerful telescope placed in the most favoured situation as to climate4 ,those lovers of nature who desire to observe celestial objects through a great telescope1 and have not the opportunity of gratifying their wishes1 may perhaps derive consolation from the fact that a good photograph actually represents the object much better than any eye can see it4 ,more of the nebula is to be seen by looking at the photograph than has actually been directly observed by any astronomer4 ,we have chosen the ,dumb-bell 7,fig4 #g7 and the ,great ,nebula in ,orion as characteristic examples of this remarkable class of celestial objects2 but there are many others to which ,i might refer1 some of which we represent in these pages4 ,the ,crab ,nebula 7,fig4 #c7 and others have been distinguished by special names2 but ,i must forbear to dwell further on them1 and rather hasten to give the results of recent observations which have enormously extended our knowledge of the nebulous bodies in the universe4 ,let me first explain the source whence this extraordinary accession to our knowledge has arisen4 ,we owe it to the astronomers at the ,lick ,observatory1 that remarkable institution placed on the summit of ,mount ,hamilton in ,california4 ,many important discoveries had already been made with the noble instruments with which the famous ,lick ,observatory had originally been endowed by its founder2 it is1 however1 by a recent addition to its magnificent apparatus that the discoveries have been made which are specially significant for our present purpose4 ,many years ago ,dr4 ,a4 ,a4 ,common1 the distinguished ,english astronomer1 constructed an exquisite reflecting telescope of three feet aperture 7,fig4 #h74 ,with this telescope ,dr4 ,common himself obtained notable results in photographing the heavens1 and his success earned the award of the ,gold ,medal of the ,royal ,astronomical ,society4 ,this telescope passed into the possession of ,mr4 ,e4 ,crossley1 of ,halifax1 and some time later ,mr4 ,crossley presented it to the ,lick ,observatory4 ,the great mirror1 after its voyage across the ,atlantic1 was duly erected on the top of ,mount ,hamilton1 and fortunately for science ,professor ,keeler1 whose early death astronomers of both continents greatly deplore1 devoted himself to the study of the heavens with its aid4 ,he encountered many difficulties1 as might perhaps be expected in such a task as he proposed4 ,his patience and skill1 however1 overcame them1 and though death terminated his labours when his great programme had but little more than commenced1 the work he had already accomplished has led to results of the most striking character4 ,of the skill that he obtained in photographing celestial nebul we have given illustrations in ,figs4 #f and #g4 ,illustration3 ,fig4 #g4--,,the ,,dumb-,,bell ,,nebula 7,lick ,observatory1 ,california74 7,from the ,royal ,astronomical ,society ,series47 ,it is not to the individual portraits of notable nebul that we are now about to refer4 ,the most striking characteristic of the sidereal heavens is not to be found in the fact that in one part of the sky we have a brilliant ,sirius1 in another a ,capella1 and in a third a ,canopus1 but in the fact that the heavens wherever we may test them are strewn with incalculable myriads of stars1 many of which appear faint only on account of their distance and not because they are intrinsically small4 ,in like manner the remarkable fact with regard to the nebul which has been disclosed by ,keeler's memorable researches with the ,crossley ,reflector is the existence not alone of the great nebul1 but of unexpected scores of thousands of small nebul1 or rather1 ,i should say1 of nebul which appear small1 though doubtless in many cases these objects are intrinsically quite as splendid as the ,dumb-bell ,nebula or the ,nebula in ,orion4 ,they only seem small in consequence of being many times further from us than are the more famous objects4 ,professor ,keeler's experience was a remarkable one4 ,he was photographing a well-known nebula with the ,crossley ,reflector1 and he was a little surprised to find that on the same plate which gave him the nebula at which he was aiming there were no fewer than seven other small nebulous objects previously unknown to astronomers4 ,it at first appeared to him that this must be an unusual number of nebul to find crowded together on one plate which covered no more than one square degree of the heavens1 an area about five or six times as large as the area of the full moon4 ,subsequent experience1 however1 showed him that this fact1 however astonishing1 was not at all unusual4 ,in fact1 he found to his amazement that1 expose the plate where he pleased1 he generally obtained new nebul upon it1 and sometimes even a much larger number than the seven which so greatly surprised him at first4 ,i may mention just one or two instances4 ,there is a well-known and interesting nebula in ,pegasus which ,professor ,keeler photographed4 ,when he developed the plate1 which1 of course1 included a considerable region of the heavens in the vicinity of the particular nebula1 he found to his astonishment that1 besides the nebula he wanted1 there were not less than twenty other nebul on the plate4 ,but there is a more striking instance even than this4 ,a plate directed to a part of the constellation of ,andromeda1 with the object of taking a portrait of a particular nebula of considerable interest1 was found to contain not only the desired nebula1 but no fewer than thirty-one other new nebul and nebulous stars4 ,nor have we in these statements exhausted the nebulous contents of these wonderful plates1 if indeed we have rightly interpreted their nature4 ,professor ,keeler tells us that he finds upon them a considerable number of objects which in all probability are also nebul1 though they are so small that the telescope is unable to reveal them in their true character4 ,examination does little more than show these objects as points of light which1 however1 are apparently not stars4 ,in the remarkable paper from which ,i have taken these facts ,professor ,keeler makes an estimate which is founded on the examination of his plates4 ,if the heavens were to be divided into panels1 each one square degree in area1 there would be about forty thousand panels4 ,it follows that if we desired to photograph the whole heavens1 and if each of the plates was to cover one square degree1 forty thousand pictures would be needed for the representation of the whole celestial sphere4 ,keeler's work convinced him that such plates taken by the ,crossley ,reflector would1 on an average1 each show at least three new nebul4 ,he admitted it is quite possible that there may be regions of the sky in which no new nebul are to be found4 ,but in the regions which he had so far tested he invariably found more than three nebul on each square degree2 indeed1 as we have seen1 on some of his plates he found a much larger number of these remarkable objects4 ,he therefore said that he makes but a very moderate estimate when he gives a hundred and twenty thousand as the probable number of the new nebul within the reach of the photographic plates of the ,crossley ,reflector4 ,the enormous extension which these investigations have given to our knowledge demands the serious attention of all interested in the heavens4 ,the discoveries of the earlier astronomers had led to the knowledge of about six thousand nebul2 the ,crossley ,reflector at the ,lick ,observatory has now rendered it practically certain that the number of nebul in the heavens must be at least twenty-fold as great as had been hitherto supposed4 ,illustration3 ,fig4 #h4--,,the ,,crossley ,,reflector 7,,constructed ,,by ,,dr4 ,a4 ,a4 ,,common ,f4,r4,s4 ,,and ,,now ,,at ,,the ,,lick ,,observatory74 ,in subsequent chapters we are to present the evidence for the belief that this earth of ours1 as well as the sun and all the other bodies which form the solar system1 did once originate in a nebula4 ,according to this view the materials which at present are found in the globes of the solar system were once distributed over a vast extent of space as a fire-mist1 or nebula4 ,it is surely very pertinent to be able to show that a nebula1 such as we suppose to have been the origin of our system1 is not a mere figment of the imagination4 ,no doubt it is impossible for us now to show the original nebula from which the solar system has been evolved4 ,it is nevertheless possible1 as we have seen1 to show that a hundred and twenty thousand nebul are now actually existing of every grade of magnitude4 ,they range from such magnificent objects as the ,great ,nebula in ,orion and the ,dumb-bell ,nebula1 down to objects wholly invisible1 not merely to the unaided eye1 but even in the most powerful telescope1 and only to be discerned as hazy spots of light on the photographic plates of an instrument such as the ,crossley ,reflector4 ,though no eye has seen the actual stages in the grand evolution of our solar system1 we may at least witness parallel stages in the evolution through which some of the myriads of other nebul are now passing4 ,we find some of these nebul in that excessively diffused condition in which they are devoid of visible structure4 ,material in this form may be regarded as the primval nebula4 ,there is at least one of these extraordinary objects which is larger a great deal than even the ,great ,nebula in ,orion1 but altogether too faint to be seen except by the photographic plate4 ,here we find1 as it were1 the mother-substance in its most elementary stage of widest possible diffusion1 from which worlds and systems1 it may be1 are yet to be evolved4 ,from diffused objects such as shown in ,fig4 #e we can pass to other nebul in which we see a certain advance being made in the process by which the nebula is transformed from the primitive condition4 ,we can point to yet other nebul in which the advance to a further stage of development is more and more pronounced4 ,thus the various stages in the evolution of a system are to be witnessed1 not indeed in the transformation of a single nebula1 but by observing a properly arranged series of nebul in all gradations1 from the diffused luminous haze to a star with a faint nebulous surrounding4 ,such was ,herschel's original argument1 and its cogency has steadily increased from the time he first stated it down to the present hour4 ---------------------------------------- -------------------------------- ,,chapter ,,iv4 ,,nebul--,,apparent ,,and ,,real4 ,the ,globular ,star-clusters--,structure of these ,objects--,variability of ,stars in the ,cluster--,telescopic ,resemblance of a ,cluster to a ,nebula--,resolution of a ,nebula--,supposition that all ,nebul may be ,clusters--,a ,criterion for distinguishing a ,nebula and a ,cluster--,dark ,lines on a bright ,background characterise the ,structure of a ,star--,bright ,lines on a dark ,background characterise the ,structure of a ,nebula--,characteristics of the ,spectrum of a true ,nebula and of a ,resolvable ,nebula--,spectra of the ,sun and ,capella--,spectra of the ,nebula in ,orion and of a ,white ,star compared--,number of ,lines in a ,nebular ,spectrum--,criterion of a ,nebular ,spectrum--,spiral ,nebula not ,gaseous--,solar ,spectra during an ,eclipse--,bearing on the ,nebular ,theory--,herschel's ,work--,the ,objection to the ,theory--,the ,objection ,removed in #ahfd4 ,,there is perhaps hardly any telescopic object more pleasing or more instructive than a globular cluster of stars when viewed through an instrument sufficiently powerful to do justice to the spectacle4 ,there are several star-clusters of the class designated as 8globular40 ,the most famous of these1 or1 at all events1 the one best known to northern astronomers1 is found in the constellation of ,hercules1 and is for most purposes sufficiently described by the expression1 8,the ,cluster in ,hercules40 ,the genuine lover of ,nature finds it hard to withhold an exclamation of wonder and admiration when for the first time1 or even for the hundredth time1 the ,cluster in ,hercules is adequately displayed in the field of a first-class telescope4 ,illustration3 ,fig4 #i4--,,the ,,cluster ,,in ,,hercules4 7,photographed by ,dr4 ,w4 ,e4 ,wilson1 ,f4,r4,s47 ,in ,fig4 #i is a photograph of this celebrated object1 which was taken by ,dr4 ,w4 ,e4 ,wilson1 ,f4,r4,s41 at his observatory at ,daramona1 in ,ireland4 ,the picture has been obtained from an enlargement of the original photograph taken with the telescope in ,mr4 ,wilson's observatory4 ,it is1 however1 precisely as ,nature has given it1 except for this enlargement4 ,you will note that towards the margin of the cluster the several stars are seen separately1 and in many cases with admirable distinctness4 ,we do1 however1 occasionally find two or more stars so close together that their images overlap2 and1 indeed1 in the centre of the cluster the stars are so close together that it is impossible to differentiate them1 so as to see them as individual points of light4 ,we need have no doubt1 however1 that the cluster is mainly composed of separate stars1 although the difficulties interposed by our atmosphere1 added to the necessary imperfections of our appliances1 make it impossible for us to discriminate the individual stars4 ,in looking at a star group of this particular kind the observer may perhaps be reminded of a swarm of bees in flight from the hive1 for the stars in the cluster are1 on a vast scale1 apparently associated in the same way as the bees1 on a small scale1 are associated in the swarm4 ,we may also compare the stars in the cluster to the bees in the swarm in another respect4 ,each bee in the swarm is in incessant movement4 ,there can be no doubt that each star in a globular cluster is unceasingly changing its position with reference to the others4 ,the distance by which the cluster is separated from the earth renders it impossible for us to see those movements1 at all events within those narrow limits of time over which our observations have as yet extended2 but the laws of mechanics assure us that the mutual attraction of the stars in this cluster must give rise to incessant movements1 and that this must be the case notwithstanding the fact that the relative places of the stars in the cluster show no alteration that can be recognised from one year's end to another4 ,i may1 however1 mention that though there may be no movements in these stars great enough to be observed1 yet the brightness of some of them shows most remarkable fluctuations4 ,the investigations of ,professor ,bailey and other astronomers have1 indeed1 disclosed such curious variability in the brightness of some of these stars that if it were not for the exceedingly high authority by which this phenomenon has been guaranteed we should1 perhaps1 almost hesitate to believe so startling a fact4 ,it has1 however1 been most certainly proved that many of the stars in certain globular clusters pass through a series of periodical changes of lustre4 ,the period is a very short one as compared with the periods of better known variable stars1 for in this case twenty-four hours are more than sufficient for a complete cycle of changes1 and it not infrequently happens that in the course of a single quarter of an hour a star will lose or gain brightness to the extent of a whole magnitude4 ,the phenomenon referred to is at the present moment engaging the careful attention of astronomers2 but it offers a problem of which1 indeed1 it is not at present easy to see the solution4 ,our immediate concern1 however1 with the globular star-clusters relates to a point hardly of such refinement as that to which ,i have just referred2 it is one of a much more elementary nature4 ,the photograph in the figure may be considered to represent the ,cluster in ,hercules as it would be seen with a telescope of very considerable visual power1 for the object would assume a different appearance in a telescope which was not first class4 ,the perfection of a really powerful instrument is tested by its capability of exhibiting as two separate points a pair of stars which are excessively close together1 and which in an instrument of inferior power cannot be distinguished1 but seem fused into a single object4 ,the defining power of a telescope--that is to say1 its capability for separating close double stars--is increased with the size of the instrument1 always granting1 of course1 that there is equal optical perfection in both cases4 ,it follows that the more powerful the telescope the more numerous are the stars which can be seen separately in a globular cluster4 ,if1 however1 a small telescope be used1 or a telescope which1 though of considerable size1 has not the high optical perfection that is demanded in the best modern instruments1 then adjacent stars are not always to be seen separately4 ,it may be that the telescope1 on account of its small size1 cannot separate the objects sufficiently1 or it may be that the imperfections of the telescope do not present the star as a point of light1 but rather as a more or less diffused1 luminous disc4 ,in either case it may happen that a star overlaps other stars in its immediate neighbourhood1 and consequently an object which is really a cluster of separate stars may fail altogether to present the appearance of a cluster4 ,i have been alluding to something which1 as every astronomer knows1 is of practical importance in the observatory4 ,like every one else who has ever used a telescope1 ,i have myself seen the ,cluster of ,hercules with just the same misty appearance in a small telescope that an undoubted nebula possesses in the very finest instrument4 ,it is1 accordingly1 sometimes impossible1 merely by observation with a small instrument1 to distinguish between what is certainly a cluster of stars and what is certainly a nebula4 ,it has indeed not infrequently happened that an observer with a small telescope has discovered what appeared to him to be a nebula1 and he has recorded it as such2 and yet when the same object was subsequently examined with an instrument of greater defining power the nebulous character has been seen to have been wrongly attributed4 ,the object in such a case is proved to be nothing more than a cluster of stars1 of which the individual members are either intrinsically faint or exceedingly remote2 it certainly is not a mass of that fire-mist or gaseous material which alone is entitled to be called a nebula4 ,it is therefore a question of importance in practical astronomy to decide whether objects which appear to be nebul are really entitled to the name1 or whether the nebulous appearance may not be an optical illusion4 ,the operation by which an object previously deemed to be a nebula is shown by the application of increased telescopic power to be a cluster of stars is commonly known as the resolution of a nebula4 ,about fifty years ago the mighty six-foot reflecting telescope of ,lord ,rosse1 and other great instruments1 were largely employed on this work4 ,it was1 indeed1 at that time held to be one of the special tasks which came most legitimately within the province of the big telescopes1 to show that the so-called nebul of earlier observers were resolvable into star-clusters under the superior powers now brought to bear upon them4 ,the success with which this process was applied to many reputed nebul1 which were thereby shown to be not entitled to the name1 led not unnaturally to a certain conjecture4 ,it was admitted that certain objects which had successfully resisted the resolving powers of inferior instruments were forced to confess themselves as mere star-clusters when greatly increased telescopic power was brought to bear on them2 and it was conjectured that similar success would attend the attempts to resolve still other nebul4 ,it was even supposed that every object described as a nebula could only be entitled to bear that designation provisionally1 only indeed until some telescope of sufficient power should have been brought to bear on it4 ,it seemed not unreasonable to surmise that every one of the so-called nebul is a cluster of stars1 even though a telescope sufficiently powerful to effect its resolution might never be actually forthcoming4 ,i do not1 indeed1 believe that this opinion as to the ultimate resolvability of all nebul could have been shared by those who had much practical experience in the actual observation of these objects with the great telescopes1 for the particular classes of nebul which in telescopes of superior powers resolved themselves into groups of stars had a characteristic appearance4 ,after a little experience the observer soon learned to recognise those nebul which promised to be resolvable4 ,the object might not indeed be resolvable with the powers at his disposal1 but yet from its appearance he often felt that the nebula would be probably resolved if ever the time should come that greater powers were applied to the task4 ,it is easy to illustrate the question at issue by the help of the photograph of the ,cluster in ,hercules in ,fig4 #i4 ,each of the stars is there distinct1 except where they are much crowded in the centre4 ,if1 however1 the photograph be examined through one of those large lenses which are often used for the purpose1 and if the lens be held very much out of focus1 the stars will not be distinguishable separately1 and the whole object will be merely a haze of light4 ,this illustration may help to explain how the different optical conditions under which an object is looked at may exhibit1 at one time as a diffused nebula1 an object which in better circumstances is seen to be a star-cluster4 ,the astronomer who was fortunate enough to have the use of a really great telescope would not fail to notice that1 in addition to the so-called nebul already referred to1 which were presumably resolvable1 there were certain other objects1 generally characterised by a bluish hue1 which in no circumstances whatever presented the appearance of being composed of separate stars4 ,we now know for certain that these bluish objects are not clusters of stars1 but that they are in the strictest sense entitled to the name of nebul1 and that they are gaseous masses or mists of fire-cloud4 ,the full demonstration of this important point was not effected until #ahfd4 ,the fact that so very many of the nebul were resolved led not unreasonably to the presumption that all the nebul would in due time also yield4 ,but there were many who could not accept this view1 and there was a long discussion on the subject4 ,at last1 however1 the improvements in astronomical methods have cleared up the question4 ,sir ,w4 ,huggins has shown that there are two totally distinct classes of nebul1 or rather of so-called nebul4 ,there are certain nebul which can be resolved1 and there are certain nebul which cannot4 ,a nebula which can be resolved would be a veritable cluster of stars1 and is not really entitled to the name of nebula2 a nebula which cannot be resolved would be entitled to the name1 for it is a volume of gas or of gaseous material which is itself incandescent4 ,we have been provided with a beautiful criterion by which we can decide to which of these classes any nebulous-looking object belongs4 ,the spectroscope is the instrument which discriminates the two different classes of objects4 ,this remarkable apparatus1 to which we owe so much in every department of astronomy1 receives the beam of light from the celestial body4 ,the instrument then analyses the light into its component rays1 and conducts each one of those rays separately to a distinct place on the photographic plate4 ,when the photograph is developed we find on the various parts of the plate the evidence as to the class of rays which have entered into the composition of the light that has been submitted to this very searching form of examination4 ,the light which comes from a star or any star-like body1 including the sun itself1 may first be described4 ,that light1 after passing through the spectroscope and having been conducted to the photographic plate1 will produce a picture of dark lines on a bright background2 this is1 at least1 the spectrum which a star generally presents4 ,there are1 indeed1 many types of stellar spectra1 for there are many different kinds of stars1 and each kind of star is conveniently characterised by the particular spectrum that it yields4 ,if the star be one of small magnitude1 then the lines in its spectrum may be detected1 but only with great difficulty4 ,it not infrequently happens that the photograph of the spectrum of such a star will show no more than a continuous band of light without recognisable lines2 and this is what occurs in the case of a resolvable nebula1 where the stars are so closely associated that the spectrum of each separate star cannot be distinguished4 ,the spectrum of a resolvable nebula is merely a streak of light1 which is the joint effect of all the spectra4 ,the spectrum is then too faint to show the rainbow hues which present such beautiful features in the spectrum of a bright star1 as they do in the spectrum of the sun itself4 ,i give1 in the adjoining figure 7,fig4 #aj71 portions of the photographs of two spectra of celestial objects4 ,they have been taken from the ,atlas of representative stellar spectra in which ,sir ,william and ,lady ,huggins have recorded the results of their great labours4 ,two spectra are represented in this picture1 the uppermost being the spectrum of the sun1 while the lower and broader one is the spectrum of the bright star ,capella4 ,it has not been possible within the limits of this picture to include the whole length of these two spectra1 and it must therefore be understood that the photographs given in the ,atlas are each about five times as long as the parts which are here reproduced4 ,illustration3 ,fig4 #aj4--,,sun ,,and ,,capella4 ,sun above4 ,capella below4 7,sir ,william and ,lady ,huggins47 ,but the characteristic portions of the spectra selected are sufficient for our present argument4 ,it will be noted1 first of all1 that there is a singular resemblance between the details of the spectrum of the sun and those of the spectrum of the star4 ,no doubt the breadth of the stellar picture in the lower line is greater than that of the solar picture in the upper line2 but this point is not significant4 ,the breadth of the spectrum of the sun could easily have been made as wide or wider if necessary4 ,the breadth is immaterial1 for the character of a spectrum is determined not by its breadth1 but by those lines which cross it transversely4 ,it will be seen that there are here a multitude of lines1 some being very dark1 and some so faint as to be hardly visible4 ,both spectra exhibit every variety of line1 between the delicate marks which can barely be seen and the two bold columns on the right-hand side of the picture4 ,the characteristic of the spectrum is given by the number1 the arrangement1 the breadth1 the darkness1 and the definiteness of the lines by which it is crossed1 and the first point that we note is the remarkable resemblance in these different respects between the two spectra4 ,the lines are practically identical1 at least so far as those parts of the spectrum represented in this picture are concerned4 ,we have thus a striking illustration of the important fact1 to which we have so often to make allusion1 of the general resemblance of the sun to the stars4 ,not only do we know that if the sun were removed about a million times as far as it is at present its light would be reduced to that of a star1 but that the star ,capella transmits to us light consisting essentially of the same waves as those which enter into a beam of sunlight4 ,no more striking illustration of the analogy between the sun and a star can be found than that which is given in this photograph from the famous ,observatory at ,tulse ,hill4 ,but it must not be inferred that because the spectra of sun and star are like each other1 they are therefore absolutely identical4 ,there are many lines and details to be seen on the actual photographic plate which are too delicate to be reproduced in such copies as it is possible to make4 ,when a close comparison is made on the actual plate itself of the lines in the solar spectrum and the lines in the spectrum of ,capella1 it is observed that1 though they are the same so far as the more important lines are concerned1 yet that there are many lines found in the spectrum of ,capella which are not found in the spectrum of the sun4 ,illustration3 ,fig4 #aa4--,,spectrum ,,of ,,nebula ,,in ,,orion ,,and ,,spectrum ,,of ,a ,,white ,,star4 7,sir ,william ,huggins1 ,k4,c4,b47 ,the contrast between the spectrum of a nebula properly so called and the spectrum of a star is well illustrated by the accompanying picture 7,fig4 #aa71 in which ,sir ,w4 ,huggins exhibits the photograph of the spectrum of the ,nebula in ,orion in comparison with the spectrum of a star4 ,the uppermost of the two is the spectrum of the star4 ,it will be noted that this spectrum is very different from that which we have already seen in ,capella4 ,instead of a vast multitude of lines resembling the lines of the solar spectrum1 the spectrum of a star of the type here represented1 of which we may take ,sirius as the most striking example1 exhibits but a few lines4 ,we regard them as one system of lines1 for we know they are physically connected4 ,they are all alike due to the presence of a single element in the star1 that element being in fact hydrogen4 ,but though the spectra of ,capella and ,sirius are so totally different1 the differences relate only to the distribution of the lines1 and to their number1 darkness1 and width4 ,in both cases we observe the characteristic of the light from an ordinary bright star1 namely1 that the spectrum is composed of a bright band with dark lines across it4 ,it ought1 perhaps1 to be mentioned here that there are certain very special stars which do exhibit some bright lines in addition to a more ordinary spectrum2 this is especially the case in the new stars which occasionally appear4 ,thus in the case of the new star which appeared in ,perseus1 in #aija1 there were several remarkable bright lines4 ,this most interesting object will be referred to again in a later chapter4 ,widely different from the spectrum of any star whatever is the lower of the two spectra which are shown in the figure4 ,this lower spectrum is that of the ,great ,nebula in ,orion4 ,at once we see the fundamental characteristic of a nebula2 its spectrum exhibits five bright lines on a dark field4 ,i do not say that the ,great ,nebula in ,orion has not more than five lines2 there are indeed many others1 for ,sir ,william ,huggins has himself pointed out a considerable number1 and the labours of other observers have added still more2 but the five lines here set down are the principal lines4 ,they are those most easily seen2 the others are generally extremely delicate objects arranged in groups of five or six4 ,but the lines which this picture shows are quite sufficient to exhibit that fundamental characteristic of the nebular spectrum1 namely1 a system of bright lines on a dark field4 ,i may further mention that certain lines in the spectrum indicate the presence of the element hydrogen in the ,great ,nebula in ,orion1 and we owe to ,dr4 ,copeland the interesting discovery that the remarkable element helium is also proved to exist in the nebula4 ,the pictures1 at which we have been looking1 will suffice to make clear the criterion1 which astronomers now possess1 for deciding whether an object which looks nebulous is really a gaseous nebula1 or ought rather to be regarded as a star-cluster4 ,if the object be a star-cluster1 then the spectrum that it gives will be the resultant of the spectra of the stars1 and this will be a continuous band of light4 ,if the stars are bright enough1 it may be that dark lines can be detected crossing the spectra1 but in the case of the clusters it will be more usual to find the continuous band of light so faint that the dark lines1 even if they are there1 are not distinguishable4 ,if1 on the other hand1 the object at which we are looking1 not being a cluster of stars1 is indeed a mass of glowing gas1 or true nebula1 then the spectrum that it sends us is not the continuous spectrum such as we expect from the stars4 ,the spectrum which the nebula proper transmits to the plate is said to be discontinuous4 ,in some cases it is characterised by only a single bright line1 and in others there may be two1 or three1 or four bright lines1 or1 as in the case shown in ,fig4 #aa1 the number of bright lines may be as many as five4 ,it may indeed happen1 in the case of some exquisite photographs1 that the number of lines in the spectrum of the nebula will be increased to a score or possibly more4 ,there may also be faint traces of a continuous spectrum present1 this being due to the stars scattered through the object1 from which perhaps even the most gaseous nebula is not entirely free4 ,but the characteristic type of nebular spectrum is that in which the bright lines1 be they one1 or few1 or many1 are separated by intervals of perfect darkness4 ,when it is found that the spectrum of a nebula can be thus described1 it is correct to say that the nebula is truly a gaseous object4 ,in the lists given by ,scheiner in his interesting book1 8,astronomical ,photography10 the number of gaseous nebul is set down as seventy-three4 ,of course no one pretends that this enumeration is exhaustive4 ,it claims to be no more than a statement of the number of nebul which have been proved1 by observations made up to the present1 to be of a gaseous description4 ,seeing that there are1 as we have already stated1 many scores of thousands of nebulous-looking objects1 it is probable that the number above given is not more than a small fraction of the number of gaseous nebul actually within reach of our instruments4 ,it may1 however1 be assumed that more than half the objects which are called nebul are not of the gaseous type4 ,this is a point of some importance1 which appears to follow from the facts stated by ,professor ,keeler in connection with his memorable researches with the ,crossley ,reflector4 ,in a later chapter we discuss important questions connected with what are called spiral nebul4 ,we may1 however1 here record that no spiral nebul have as yet been pronounced gaseous4 ,professor ,keeler assures us that1 of the one hundred and twenty thousand nebul which he estimates to be within reach of the ,crossley ,reflector1 far more than half are of the spiral character4 ,if1 then1 we assume that the spectra of spiral nebul are always continuous1 it seems to follow that less than half the nebulous contents of the heavens possesses the discontinuous spectrum which is characteristic of a gaseous object4 ,we are not entitled to assume that a nebula1 or reputed nebula1 which shows a continuous spectrum1 must necessarily be a cluster1 not merely of star-like bodies1 but of bodies with masses comparable with those of the ordinary stars4 ,our argument does most certainly suggest that the body which yields a continuous spectrum is not a gaseous body2 but it may be going too far to assert that therefore it is a cluster of stars in the ordinary sense4 ,we do often find true nebul and star-clusters in close association4 ,the ,nebula in the ,pleiades 7,fig4 #ac7 is an example4 ,it may be desirable to add a few words here as to the physical difference between a continuous spectrum and a discontinuous spectrum4 ,the light from a body1 known to be gaseous1 shows through the prism the discontinuous spectrum of bright lines upon a dark background4 ,if1 on the other hand1 a solid be raised to incandescence1 such1 for instance1 as a platinum wire heated white-hot by an electric current1 or a cylinder of lime submitted to an oxyhydrogen blowpipe1 then the spectrum that it yields is continuous4 ,all the colours of the rainbow1 red1 orange1 yellow1 green1 blue1 indigo1 violet1 are shown in such a spectrum as a continuous band of light1 though the band is not crossed by dark lines4 ,it would therefore appear that the continuous spectrum is characteristic of an incandescent solid1 and the discontinuous spectrum of a glowing gas4 ,but here it may be urged that the sun presents a difficulty4 ,we so often refer to the spectrum of the sun as continuous1 that it might at first appear as if the spectrum of the sun resembled that produced by radiation from a solid body4 ,but1 as is well known1 the sun is not a solid body4 ,even if the sun be solid at the centre1 it is certainly far from being solid in those superficial regions called the photosphere1 from which alone its copious radiation is emitted4 ,if the sun is not a solid body1 how comes it to emit a radiation characterised in the same way as the radiation from a white-hot solid8 ,why does the solar spectrum not exhibit features characteristic of radiation from an incandescent gas8 ,the point is well worthy of attention2 it finds an explanation in the nature of the photosphere from which the sun's radiation proceeds4 ,the photosphere1 though not1 of course1 to be described as a solid body1 does not most certainly1 so far as its radiation is concerned1 behave like a gaseous body4 ,in the glowing clouds of the photosphere the carbon1 of which they are composed1 is not in the gaseous form2 it has passed into solid particles1 and it is these particles1 in the highest condition of incandescence1 which emit the solar radiation4 ,although these particles are sustained by the gases of the sun1 and are associated in aggregations which form the dazzling clouds of the photosphere1 yet each one of them1 in so far as its individual radiation is concerned1 ought to be regarded as a solid body4 ,the radiation from the sun is1 therefore1 essentially not the radiation from an incandescent gas2 it is the radiation from a glowing solid4 ,this is the reason why the solar spectrum is of the continuous type4 ,illustration3 ,fig4 #ab4--,,solar ,,spectra ,,with ,,bright ,,lines ,,and ,,dark ,,lines ,,during ,,eclipse4 7,photographed by ,captain ,hills1 ,r4,e47 ,by the kindness of ,captain ,hills1 ,r4,e41 ,i am able to show a photograph 7,fig4 #ab7 containing two spectra taken during a recent eclipse1 which will serve as an excellent illustration of the different points which we have been discussing4 ,it is1 indeed1 true that neither of the spectra1 here referred to1 belongs to nebul1 whether genuine gaseous objects or not4 ,both of the spectra in ,captain ,hills' picture are actually taken from the sun4 ,the conditions under which these spectra were obtained make them1 however1 serve as excellent illustrations of the different types of spectra4 ,we are to notice that the upper band1 which contains what is called the 8flash0 spectrum1 exhibits bright lines on a dark background4 ,see1 for instance1 the two lines so very distinctly marked1 which are indicated by the letters ,h and ,k4 ,these lines are very characteristic of the solar spectrum1 and it may be mentioned that they are indications of the presence of a well-known element4 ,these lines prove that the sun contains calcium1 the metal of which common lime is the oxide4 ,it is1 indeed1 the presence of this substance in the sun which gives rise to these lines4 ,we shall refer again to this subject in a later chapter4 ,as the upper of the two spectra exhibit ,h and ,k as white lines on a dark background1 so the lower represents the same lines as dark objects on a white background4 ,these photographs give illustrations of spectra of the two different classes which provide means of discriminating between a genuine nebula and an object which1 though it looks like a nebula1 is not itself gaseous4 ,illustration3 ,fig4 #ac4--,,the ,,nebula ,,in ,,the ,,pleiades 7,exposure #aj hours74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,but1 it will be asked1 how can the spectra of the two distinct types both be obtained from the sun8 ,the explanation of this point is an interesting one4 ,the lower of the two is the ordinary solar spectrum2 it is a continuous spectrum showing dark lines on a bright field4 ,the upper spectrum1 which shows bright lines on a dark field1 is produced by a small part of the sun just at the moment when the eclipse is total4 ,the circumstances in which that picture was secured will explain its character4 ,the moon had completely covered that dazzling part of the sun which we ordinarily see1 but a region of intensely glowing gaseous material in the sun's atmosphere was too high above the surface to be completely hidden by the moon4 ,the spectrum of this region1 consisting of the characteristic bright gaseous lines1 is here represented4 ,the ordinary light of the sun being cut off1 opportunity was thus afforded for the production of the spectrum of the light from the glowing gas1 and we see this spectrum to be of the nebular type4 ,and now we may bring this chapter to a close by calling attention to the very important bearing which its facts have on the ,nebular ,theory4 ,it is essential for us to see how far modern investigation and discovery have tended either to substantiate or refute that famous doctrine which traces the development of the solar system from a nebula4 ,to do this it is necessary to contrast the knowledge of nebul1 as it exists at present1 with the knowledge of nebul as it existed in the days of ,kant and ,laplace and ,herschel4 ,we assuredly do no injustice to ,kant or to ,laplace if we say that their actual knowledge of the nebulous contents of the heavens was vastly inferior to that possessed by ,herschel4 ,there is not a single astronomical observation of nebul recorded by either ,kant or ,laplace2 it may be doubted whether either of them ever even saw a nebula4 ,their splendid contributions to science were made in directions far removed from those of the practical observer1 who passes long hours of darkness in the scrutiny of the celestial bodies4 ,herschel1 on the other hand1 was pre-eminently an observer4 ,his nights were spent in the most diligent practical observation of the heavens1 and at all times the nebul were the objects which received the largest measure of his attention1 with the result that the knowledge of nebul received the most extraordinary development from his labours4 ,earlier astronomers had no doubt observed nebul occasionally1 but with their imperfect appliances only the brighter of these objects were discernible by them4 ,the astonishing advance made by the observations of ,herschel is only paralleled by the advance made a hundred years later by the photographs of ,keeler4 ,but it must be remembered that though ,herschel observed nebul1 and discovered nebul1 and discoursed on nebul in papers which to this day are classics in this important subject1 yet not to the last day of his life could he have felt sure that he had ever seen a genuine nebula4 ,he might have surmised1 and he did surmise1 that many of the objects he set down as nebul were actually gaseous objects1 but he knew that many apparent nebul were in truth clusters of stars1 and he had no means of knowing whether all so-called nebul might not belong to the same category4 ,it was not till nearly half a century after ,sir ,william ,herschel's unrivalled career had closed that the spectroscope was invoked to decide finally on the nature of these mysterious objects4 ,that decision1 which has been of such transcendent importance in the study of the heavens1 was not pronounced till #ahfd4 ,in that year ,sir ,william ,huggins established the fundamental truth that the so-called nebul are not all star-clusters1 but that the universe does contain objects which are most certainly gigantic volumes of incandescent gases4 ,this great achievement provided a complete answer to those who urged an objection1 which seemed once very weighty1 against the ,nebular ,theory4 ,it must be admitted that before #ahfd no one could have affirmed with confidence that any genuine nebula really existed4 ,it was1 therefore1 impossible for the authors of the ,nebular ,theory to point to any object in the heavens which might have illustrated the great principles involved in the theory4 ,the ,nebular ,theory required that in the beginning there should have been a gaseous nebula from which the solar system has been evolved4 ,but the objector1 who was pleased to contend that the gaseous nebula was a figment of the imagination1 could never have been effectively silenced by ,kant or ,laplace or ,herschel4 ,it would have been useless for them to point to the ,nebula in ,orion1 for the objector might say that it was only a cluster of stars1 and at that time there would have been no way of confuting him4 ,the authors of the ,nebular ,theory had1 in respect to this class of objector1 a much more difficult task than falls to its modern advocate4 ,the latter is able to deny in the most emphatic manner that a gaseous nebula is no more than an imaginary conception4 ,the famous discovery of ,sir ,w4 ,huggins has removed the first great objection to the ,nebular ,theory4 ---------------------------------------- -------------------------------- ,,chapter ,v4 ,,the ,,heat ,,of ,,the ,,sun4 ,the ,sun to be first considered3 its ,evolution is in vigorous ,progress--,considerations on ,solar ,heat--,size of the ,sun--,waste of ,sun-heat--,langley's ,illustration--,sun in ,ancient ,days--,problem ,stated--,the ,solar ,constant explained--,its ,value determined--,estimate of ,radiation from a ,square ,foot of the ,sun--,illustrations of ,solar ,energy--,decline of ,solar ,energy--,the ,warehouse of ,grain--,white-hot ,globe of ,iron would ,cool in ,forty-eight ,years--,sun's ,heat is not sustained by ,combustion--,inadequacy of ,combustion ,demonstrated--,joule's ,unit--,energy of a ,moving ,body--,energy of a ,body moving ,five ,miles a ,second--,energy of the ,earth due to its ,motion4 ,,it will be convenient to consider different bodies in the solar system1 and to study them with the special object of ascertaining what information they afford as to the great celestial evolution4 ,we cannot hesitate as to which of the bodies should first claim our attention4 ,not on account of the predominant importance of our sun to the inhabitants of the earth1 but rather because the sun is nearly a thousand times greater than the greatest of the planets1 do we assign to the great luminary the first position in this discussion4 ,the sun is1 indeed1 especially instructive on the subject with which we are occupied4 ,by reason of its great mass1 the process of evolution takes place more slowly in the sun than in the earth or in any other planet4 ,evolution has1 no doubt1 largely transformed the sun from its primval condition1 but it has not yet produced a transformation so radical as that which the earth and the other planets have undergone4 ,on this account the sun can give us information about the process of evolution which is not to be so easily obtained from any of the other heavenly bodies4 ,the sun can still exhibit to us some vestiges1 if we may so speak1 of that great primval nebula from which the whole system has sprung4 ,the heat of the sun is indeed one of the most astonishing conceptions which the study of ,nature offers to us4 ,let me try to illustrate it4 ,think first of a perfect modern furnace in which even steel itself1 having first attained a dazzling brilliance1 can be further melted into a liquid that will run like water4 ,let us imagine the temperature of that liquid to be multiplied seven-fold1 and then we shall obtain some conception of the fearful intensity of the heat which would be found in that wonderful celestial furnace the great sun in the heavens4 ,ponder also upon the stupendous size of that orb1 which glows at every point of its surface with the astonishing fervour that this illustration suggests4 ,the earth on which we stand is a mighty globe2 yet what are the dimensions of our earth in comparison with those of the sun8 ,if we represent the earth by a grain of mustard seed1 then on the same scale the sun should be represented by a cocoanut4 ,we may perhaps obtain a more impressive conception of the proportions of the orb of day in the following manner4 ,look up at the moon which revolves round the heaven1 describing as it does so majestic a track that it is generally at a distance of two hundred and forty thousand miles from the earth4 ,yet the sun is so large that if there were a hollow globe equally great1 and the earth were placed at its centre1 the entire orbit of the moon would lie completely within it4 ,every portion of that stupendous desert of flame is pouring forth torrents of heat4 ,it has1 indeed1 been estimated that the heat which issues from an area of two square feet on the sun would more than suffice1 if it could be all utilised1 to drive the engines of the largest ,atlantic liner between ,liverpool and ,new ,york4 ,this solar heat is scattered through space with boundless prodigality4 ,no doubt the dwellers on the earth do receive a fair supply of sunbeams2 but what is available for the use of mankind can be hardly more than an infinitesimal fraction of what the sun emits4 ,we shall scarcely be so presumptuous as to suppose that the sun has been designed solely for the benefit of the poor humanity which needs light and warmth4 ,the heat and light daily lavished by the sun would suffice to warm and to illuminate two thousand million globes1 each as great as the earth4 ,if1 indeed1 it were true that the only object of the sun's existence was to cherish this immediate world of ours1 then all we can say is that the sun carries on its business in a most outrageously wasteful manner4 ,what would be thought of the prudence of one who1 having been endowed with a fortune of ten million pounds1 spent one single penny of that vast sum in a profitable manner and dissipated every other penny and every other pound of his fortune in aimless extravagance8 ,but this is apparently the way in which the sun manages its affairs1 so far as our earth is concerned4 ,out of every ten million pounds worth of heat issuing from the glorious orb of day1 we on this earth secure one pennyworth1 and all but that solitary pennyworth seems to be utterly squandered4 ,we may say it certainly is squandered so far as humanity is concerned4 ,what1 indeed1 its actual destination may be science is unable to tell4 ,and now for the great question as to how the sun's heat is sustained4 ,how is it that this career of tremendous prodigality has not ages ago been checked by absolute exhaustion8 ,every child knows that the fire on the hearth will go out unless coal be provided4 ,the workman knows that his devouring furnace in the ironworks requires to be incessantly stoked with fresh supplies of fuel4 ,how1 then1 comes it that the wonderful furnace on high can still continue1 as it has continued for ages1 to pour forth its amazing stores of heat without being exhausted8 ,professor ,langley has supplied us with an admirable illustration showing the amount of fuel which would be necessary1 if indeed it were by successive additions of fuel that the sun's heat was sustained4 ,suppose that all the coal-seams which underlie ,england and ,scotland were made to yield up their stores2 that the vast coalfields in ,america1 ,australia1 ,china1 and elsewhere were compelled to contribute every combustible particle they contained2 suppose1 in fact1 that we extracted from this earth every ton of coal which it possesses in every isle and every continent2 suppose that this mighty store of fuel1 sufficient to supply all the wants of the earth for centuries1 were to be accumulated1 and that by some mighty effort that mass were to be hurled into the sun and were forthwith to be burnt to ashes2 there can be no doubt that a stupendous quantity of heat would be produced4 ,but what is that heat in comparison1 we do not say with the heat of the sun1 but with the daily expenditure of the sun's heat8 ,how long1 think you1 would the combustion of so vast a mass of fuel provide for the sun's expenditure8 ,we are giving deliberate expression to a scientific fact when we say that a conflagration which destroyed every particle of coal contained in this earth would not generate as much heat as the sun lavishes in the tenth part of every single second4 ,during the few minutes that you have been reading these words a quantity of heat has gone for ever from the sun which is five thousand times as great as all the heat that ever has been or ever will be produced by the combustion of the coal that this earth has furnished4 ,but we have still another conception to introduce before we can appreciate the full significance of the sun's extraordinary expenditure of heat and light4 ,we have been thinking of the sun as it shines now2 but as the sun shines to-day1 so it has shone yesterday1 and so it shone a hundred years ago1 a thousand years ago2 so it shone in the earliest dawn of history1 so it shone during those still remoter periods when great animals flourished which have now vanished for ever2 so the sun shone during those remote ages when life began to dawn on an earth which still was young4 ,we do not1 indeed1 say that the intensity of the sunbeams has remained actually uniform throughout a period so vast2 but there is every reason to believe that throughout these illimitable periods the sun has expended its radiance with the most lavish generosity4 ,a most important question is suggested by these considerations4 ,the consequences of frightful extravagance are known to us all2 we know that such conduct tends to bankruptcy and ruin2 and certainly the expenditure of heat by the sun is the most magnificent extravagance of which our knowledge gives us any conception4 ,accordingly1 the important question arises3 ,as to how the consequences of such awful prodigality have been hitherto averted4 ,how is it that the sun is still able to draw on its heat reserve1 from year to year1 from century to century1 from on to on1 ever squandering two thousand million times as much heat as that which genially warms our temperate regions1 as that which draws forth the exuberant vegetation of the tropics or which rages in the desert of ,sahara8 ,that is the great problem to which our attention has to be given4 ,we must first ascertain1 with such precision as the circumstances permit1 the actual amount of heat which the sun pours forth in its daily radiation4 ,the determination of this quantity has engaged the attention of many investigators1 and the interpretation of their results is by no means free from difficulty4 ,it is to be observed that what we are now seeking to ascertain is not exactly a question of temperature1 but of something quite different4 ,what we have to measure is a quantity of heat1 which is to be expressed in the proper units for quantities of heat4 ,the unit of heat which we shall employ is the quantity of heat necessary to raise one pound of water through one degree ,fahrenheit4 ,the solar constant is the number of units of heat which fall1 in one minute1 on one square foot of a surface placed at right angles to the sun's rays1 and situated at the mean distance of the earth from the sun4 ,we shall suppose that losses due to atmospheric absorption have been allowed for1 so that the result will express the number of units of heat that would be received in one minute on a square foot turned directly to the sun1 and at a distance of #ic1jjj1jjj miles4 ,illustration3 ,fig4 #ad4--,,the ,,sun 7,july #hth1 #ahib74 7,royal ,observatory1 ,greenwich47 7,from the ,royal ,astronomical ,society ,series47 ,this is a matter for determination by actual observation and measurement4 ,theory can do little more than suggest the precautions to be observed and discuss the actual figures which are obtained4 ,there have been many different methods of making the observations1 and the results are somewhat various1 but the discrepancies are not greater than might be expected in an investigation of such difficulty4 ,the mean value which has been arrived at is fourteen1 and the fundamental fact with regard to the solar radiation which we are thus enabled to state is that an area of a square foot exposed at right angles to the solar rays1 at a distance of #ic millions of miles1 will in each minute receive from the sun as much heat as would raise one pound of water fourteen degrees ,fahrenheit4 ,it follows that the total radiation from the sun must suffice to convey1 in each minute1 to the surface of a sphere whose radius is #ic1jjj1jjj miles1 fourteen units of heat per square foot of that surface4 ,this radiation comes from the surface of the sun4 ,it is easily shown that the heat from each square foot on the sun will have to supply an area of #df1jjj square feet at the distance of the earth4 ,hence the number of units of heat emerging each minute from a square foot on the sun's surface must be about #fdj1jjj4 ,we can best realise what this statement implies by finding the amount of coal which would produce the same quantity of heat4 ,it can be shown that the heat given out by each square foot of the solar surface in one minute will be equivalent to that produced in the combustion of forty-six pounds of coal4 ,if the sun's heat were sustained by combustion1 every part of the sun's surface as large as the grate of an ordinary furnace would have to be doing at least one hundred times as much heating as the most vigorous stoking could extract from any actual furnace4 ,the radiation of heat from a single square foot of the solar surface in the course of a year must1 therefore1 be equivalent to the heat generated in the combustion of #aa1jjj tons of the best coal4 ,if we estimate the annual coal production of ,great ,britain at #bej1jjj1jjj tons1 we find that the total heat which this coal can produce is not greater than the annual emission from a square of the sun's surface of which each side is fifty yards4 ,all the coal exported from ,england in a year does not give as much heat as the sun radiates in the same time from every patch on its surface which is as big as a croquet ground4 ,there is perhaps no greater question in the study of ,nature than that which enquires how the sun's heat is sustained so that the radiation is still dispensed with unstinted liberality4 ,if we are asked how the sun can be fed so as to sustain this expenditure1 we have to explain that the sun is not really fed4 ,if1 then1 it receives no adequate supplies of energy from without1 we have to admit that the sun must be getting exhausted4 ,i ought1 indeed1 to anticipate objection by at once making the admission that the sun does receive some small supply of energy from the meteors which are perennially drawn into it4 ,the quantity of energy they yield is1 however1 insignificant in comparison with the solar expenditure of heat4 ,we may return to this subject at a later period1 and it need not now receive further attention4 ,we must deliberately face the fact that the energy of the sun is becoming exhausted4 ,but the rate of exhaustion is so slow that it affords no prospect of inconvenience to humanity2 it does not excite alarm4 ,we grant that we are not able to observe by instrumental means any perceptible diminution of solar energy4 ,still1 as we know that energy is being steadily dissipated from the sun1 and that energy cannot be created from nothing1 it is certain the decline is in progress4 ,but the reserve of energy which the sun possesses1 and which can be ultimately rendered available to sustain the radiation1 is so enormous in comparison with the annual expenditure of energy1 that myriads of centuries will have to elapse before there is any appreciable alteration in the effectiveness of the sun4 ,let me illustrate the point by likening the sun to a grain warehouse1 in which #b1ejj tons of wheat can be accommodated4 ,let us suppose that the warehouse was quite full at the beginning1 and that the wheat was to be gradually abstracted1 but only at the rate of one grain each day4 ,let us further suppose that no more wheat is to be added to that already in the warehouse1 and let us assume that the wheat thus stored away experiences no deterioration and no loss whatever except by the removal of one grain per diem4 ,it is easy to see that very many centuries would have to elapse before the grain in that warehouse had decreased to any appreciable extent4 ,with a consumption at the rate of a single grain a day a ton of corn would last about four thousand years1 and #b1ejj tons of corn would accordingly last about ten million years4 ,it follows1 therefore1 that if the grain in that store were consumed at the rate of only one grain per day the warehouse would not be emptied for ten million years4 ,illustration3 ,fig4 #ae4--;,i4 ,,spectrum ,,of ,,the ,,sun4 ,,ii4 ,,spectrum ,,of ,,arcturus4 7,professor ,h4 ,c4 ,lord47 ,the quantity of heat1 or rather the reserve of energy equivalent to heat1 which still remains stored up in the sun bears to the quantity of heat which the sun radiates away in a single day a ratio something like that which a single grain of corn bears to #b1ejj tons of corn4 ,the sun's potential store of heat is no doubt very great1 though not indefinitely great4 ,that heat is beyond all doubt to be ultimately exhausted2 but the reserve is so prodigious that for the myriads of years during which the sun has been subjected to human observation there has been no appreciable alteration in the efficiency of radiation4 ,it might be supposed that the sun was merely a white-hot globe cooling down1 and that the solar radiation was to be explained in this way4 ,but a little calculation will prove it to be utterly impossible that the heat of the great luminary could be so accounted for4 ,a knowledge of the current expenditure of solar heat shows that if the sun had been a globe of iron at its fusing point1 then at the present rate of radiation it would have sunk to the temperature of freezing water in forty-eight years4 ,perhaps ,i ought here to explain a point which might otherwise cause misapprehension4 ,for our ordinary sources of artificial heat we1 of course1 employ some form of combustion4 ,whenever combustion takes place there is chemical union between the carbon or other fuel1 whatever it may be1 and the oxygen of the atmosphere4 ,a certain quantity of carbon enters into chemical union with a definite quantity of oxygen1 and1 as an incident in the process1 a definite quantity of heat is liberated4 ,so much coal1 for instance1 requires for complete combustion so much air1 and1 granted a sufficiency of air1 the union of the carbon and hydrogen in the coal will give out a certain quantity of heat which may be conveniently expressed by the number of pounds of water which that heat would suffice to transform into steam4 ,it is necessary to observe that there are definite numerical relations among these quantities4 ,the quantity of heat that can be produced by the combustion of a pound of any particular substance will depend upon the nature of that substance4 ,as chemical combination is the main source of the artificial heat which we employ for innumerable purposes on the earth1 it seems proper to consider whether it can be any form of chemical combination which constitutes the source of the heat which the sun radiates in such abundance4 ,it is easy to show that the solar radiation cannot be thus sustained4 ,the point to which ,i am now referring was very clearly illustrated by ,helmholtz in a lecture he delivered many years ago on the origin of the planetary system4 ,to investigate whether the solar heat can be attributed to chemical combination1 we shall assume for the moment that the sun is composed of those particular materials which would produce the utmost quantity of heat for a given weight2 in other words1 that the sun is formed of hydrogen and oxygen in quantities having the same ratio as that in which they should be united to form water4 ,the quantity of heat generated by the union of known weights of oxygen and hydrogen has been ascertained1 by experiments in the laboratory1 to exceed that which can be generated by corresponding weights of any other materials4 ,we can calculate how much of the sun's mass1 if thus constituted1 would have to enter into combination every hour in order to generate as much heat as the hourly radiation of the sun4 ,we need not here perform the actual calculation1 but merely state the result1 which is a very remarkable one4 ,it shows that the heat arising from the supposed chemical action would not suffice to sustain the radiation of the sun at its present rate for more than #c1jjj years4 ,thirty centuries is a long time1 no doubt1 yet still we must remember that it is no more than a part even of the period known to human history4 ,if1 indeed1 it had been by combustion that the sun's heat was produced1 then from the beginning of the sun's career as a luminous object to its final extinction and death could not be longer than #c1jjj years1 if we assumed that its radiation was to be uniformly that which it now dispenses4 ,but it may be said that we are dealing only with elements known to us and with which terrestrial chemists are familiar1 and it may be urged that the sun possibly contains materials whose chemical union produces heat in much greater abundance than do the elements with which alone we are acquainted4 ,but this argument cannot be sustained4 ,one of the most important discoveries of the last century1 the discovery which perhaps more than any other has tended to place the nebular theory in an impregnable position1 is that which tells us that the elements of which the sun is composed are the same as the elements of which our earth is made4 ,we shall have to refer to this in detail in a later chapter4 ,we now only make this passing reference to it in order to dismiss the notion that there can be unknown substances in the sun whose heat of combustion would be sufficiently great to offer an explanation of the extraordinary abundance of solar radiation4 ,there is nothing more characteristic of the physical science of the century just closed than the famous discovery of the numerical relation which exists between heat and energy4 ,we are indebted to the life-long labours of ,joule1 followed by those of many other investigators1 for the accurate determination of the fundamental constant which is known as the mechanical equivalent of heat4 ,joule showed that the quantity of heat which would suffice to raise one pound of water through a single degree ,fahrenheit was the precise equivalent of the quantity of energy which would suffice to raise #ggb pounds through a height of one foot4 ,it would be hard to say whether this remarkable principle has had a more profound effect on practical engineering or on the course of physical science4 ,in practical engineering1 the knowledge of the mechanical equivalent of heat will show the engineer the utmost amount of work that could by any conceivable apparatus be extracted from the heat potentially contained in a ton of coal4 ,in the study of astronomy the application of the same principle will suffice to explain how the sun's heat has been sustained for illimitable ages4 ,illustration3 ,fig4 #af4--;,,brooks' ,,comet ,,and ,,meteor ,,trail4 7,november #acth1 #ahic4 ,exposure #b hours47 7,photographed by ,professor ,e4 ,e4 ,barnard47 ,it will be convenient to commence with a little calculation1 which will provide us with a result very instructive when considering celestial phenomena in connection with energy4 ,we have seen that the unit of heat--for so we term the quantity of heat necessary to raise a pound of water one degree--will suffice1 when transformed into mechanical energy1 to raise #ggb pounds through a single foot4 ,this would1 of course1 be precisely the same thing as to raise one pound through #ggb feet4 ,suppose a pound weight were carried up #ggb feet high and were then allowed to drop4 ,the pound weight would gradually gather speed in its descent1 and1 at the moment when it was just reaching the earth1 would be moving with a speed of about #bbd feet a second4 ,we may observe that the work which was done in raising the body to this height has been entirely expended in giving the body this particular velocity4 ,a weight of one pound1 moving with a speed of #bbd feet a second1 will therefore contain1 in virtue of that motion1 a quantity of energy precisely equivalent to the unit of heat4 ,it is a well-known principle in mechanics that if a body be dropped from any height1 the velocity with which it would reach the ground is just the velocity with which the body should be projected upwards from the ground in order to re-ascend to the height from which it fell 7the resistance of the air is here overlooked as not having any bearing upon the present argument74 ,thus we see that a weight1 moving with a velocity of #bbd feet per second1 contains within itself1 in virtue of its motion1 energy adequate to make it ascend against gravity to the height of #ggb feet4 ,that is to say1 this velocity in a body of a pound weight can do for the body precisely what the unit of heat can do for it2 hence we say that in virtue of its movement the body contains a quantity of energy equal to the energy in the unit of heat4 ,let us now carry our calculation a little further4 ,if a pound of good coal be burned with a sufficient supply of oxygen1 and if every precaution be taken so that no portion of the heat be wasted1 it can be shown that the combustion of the coal is sufficient to produce #ad1jjj units of heat4 ,in other words1 the burning of one pound of coal ought to be able to raise #ad1jjj pounds of water one degree1 or #adj pounds of water a hundred degrees1 or #gj pounds of water two hundred degrees4 ,i do not mean to say that efficiency like this will be attained in the actual circumstances of the combustion of coal in the fireplace4 ,a pound of coal does1 no doubt1 contain sufficient heat to boil seven gallons of water2 but it cannot be made to effect this1 because the fireplace wastes in the most extravagant manner the heat which the coal produces1 so that no more than a small fraction of that heat is generally rendered available4 ,but in the cosmical operations with which we shall be concerned we consider the full efficiency of the heat2 and so we take for the pound of coal its full theoretical equivalent1 namely1 #ad1jjj thermal units4 ,let us now find the quantity of energy expressed in foot-pounds#b to which this will correspond4 ,it is obtained by multiplying #ad1jjj units of heat by #ggb1 and we get as the result #aj1hjh1jjj4 ,that is to say1 a pound of good coal1 in virtue of the fact that it is combustible and will give out heat1 contains a quantity of energy which is represented by ten or eleven million foot-pounds4 ,footnote #b3 ,a foot-pound is the amount of energy required to raise a pound weight through a height of one foot4 ,we now approach the question in another way4 ,let us think of a piece of coal in rapid motion2 if the coal weighed a pound1 and if it were moving at #bbd feet a second1 then the energy it contains in consequence of that velocity would1 as we have seen1 correspond to one thermal unit4 ,we have1 however1 to suppose that the piece of coal is moving with a speed much higher than that just stated2 and here we should note that the energy which a moving body possesses1 in virtue of its velocity1 increases very rapidly when the speed of that body increases4 ,if the velocity of a moving body be doubled1 the energy that it possesses increases fourfold4 ,if the velocity of the body be increased tenfold1 then the energy that it possesses will be increased a hundredfold4 ,more generally1 we may say that the energy of a moving body is proportional to the square of the velocity with which the body is animated4 ,let us1 then1 suppose that the piece of coal1 weighing one pound1 is moving with a speed as swift as a shot from the finest piece of artillery1 that is to say1 with a speed of #b1bdj feet a second2 and as this figure is ten times #bbd1 it shows us that the moving body will then possess1 in virtue of its velocity1 the equivalent of one hundred units of heat4 ,but we have to suppose a motion a good deal more rapid than that obtained by any artillery2 we shall consider a speed rather more than ten times as fast4 ,it is easy to calculate that if the piece of coal which weighs a pound is moving at the speed of five miles a second1 the energy that it would possess in consequence of that motion would approximate to #ad1jjj thermal units4 ,in other words1 we come to the conclusion that any body moving with a velocity of five miles a second will possess1 in virtue of that velocity1 a quantity of energy just equal to the energy which an equally heavy piece of good coal could produce if burnt in oxygen1 and if every portion of the heat were utilised4 ,it is quite true that the speed of five miles a second here supposed represents a velocity much in excess of any velocity with which we are acquainted in the course of ordinary experience4 ,it is more than ten times as fast as the speed of a rifle bullet4 ,but a velocity of five miles a second is not at all large when we consider the velocities of celestial bodies4 ,we want this fact relating to the energy in a piece of coal to be remembered4 ,we shall find it very instructive as our subject develops1 and therefore we give some illustrations with reference to it4 ,the speed of the earth as it moves round the sun is more than eighteen miles a second--that is to say1 it is three and a half times the critical speed of five miles4 ,in virtue of this speed the earth has a corresponding quantity of energy4 ,to find the equivalent of that energy it must1 as already explained1 be remembered that the energy of a moving body is proportional to the square of its velocity2 it follows that the energy of the earth1 due to its motion round the sun1 must be almost twelve times as great as the energy of the earth would be if it moved at the rate of only five miles a second4 ,but1 we have already seen that a body with the velocity of five miles a second would1 in virtue of that motion1 be endowed with a quantity of energy equal to that which would be given out by the perfect combustion of an equal weight of coal4 ,it follows1 therefore1 that this earth of ours1 solely in consequence of the fact that it is moving in its orbit round the sun1 is endowed with a quantity of energy twelve times as great as all the energy that would be given out in the combustion of a mass of coal equal to the earth in weight4 ,this may seem an astonishing statement2 but its truth is undoubted4 ,if it should happen that the earth came into collision with another body by which its velocity was stopped1 the principle of the conservation of energy tells us that this energy1 which the earth has in consequence of its motion1 must forthwith be transformed1 and the form which it will assume is that of heat4 ,such a collision would generate as much heat as could be produced by the combustion of twelve globes of solid coal1 each as heavy as the earth4 ,we may indeed remark that the coal-seams in our earth's crust contain1 in virtue of the fact that they partake of the earth's orbital motion1 twelve times as much energy as will ever be produced by their combustion4 ,it can hardly be doubted that such collisions as we have here imagined do occasionally happen in some parts of space4 ,those remarkable new stars which from time to time break out derive1 in all probability1 their temporary lustre from collisions between bodies which were previously non-luminous4 ,but we need not go so far as inter-stellar space for a striking illustration of the transformation of energy into heat4 ,in the pleasing phenomena of shooting stars our own atmosphere provides us with beautiful illustrations of the same principle4 ,the shooting star so happily caught on ,professor ,barnard's plate 7,fig4 #af7 may be cited as an example4 ---------------------------------------- -------------------------------- ,,chapter ,,vi4 ,,how ,,the ,,sun',s ,,heat ,,is ,,maintained4 ,the ,contraction of a ,body--,helmholtz ,explained ,sun-heat--,change of a ,mile every ,eleven ,years in the ,sun's ,diameter--,effect of ,contraction on ,temperature--,the ,solar ,constant--,limits to the ,solar ,shrinkage--,astronomers can ,weigh the ,sun--,density of the ,sun--,heat ,developed by the ,falling ,together of the ,solar ,materials--,contraction of ,nebula to ,form the ,earth--,heat ,produced in the ,earth's ,contraction--,similar ,calculation about the ,sun--,earth and ,sun ,contrasted--,heat ,produced in the ,solar ,contraction from an indefinitely ,great ,nebula--,the ,coal-,unit ,employed--,calculation of the ,heat given out by the ,sun4 ,,the law which declares that a body which gives out heat must in general submit to a corresponding diminution in volume appears1 so far as we can judge1 to be one of those laws which have to be obeyed not alone by bodies on which we can experiment1 but by bodies throughout the extent of the universe4 ,the law which bids the mercury ascend the stem of the thermometer when the temperature rises1 and descend when the temperature falls1 affords the principle which explains some of the grandest phenomena of the heavens4 ,applied to the solar system it declares that as the sun1 in dispensing its benefits to the earth day by day1 has to pour forth heat1 so in like manner must it be diminishing in bulk4 ,assuming that this principle extends sufficiently widely through time and space1 we shall venture to apply its consequences over the mighty spaces and periods required for celestial evolution4 ,we disdain to notice the paltry centuries or mere thousands of years which include that infinitesimal trifle known as human history4 ,our time conceptions must undergo a vast extension4 ,it was ,helmholtz who first explained by what agency the sun is able to continue its wonderful radiation of heat1 notwithstanding that it receives no appreciable aid from chemical combination4 ,helmholtz pointed out that inasmuch as the sun is pouring out heat it must1 like every other cooling body1 contract4 ,we ought not1 indeed1 to say every cooling body2 it would be more correct to say1 every body which is giving out heat1 for the two things are not necessarily the same4 ,indeed1 strange as it may appear1 it would be quite possible that a mass of gas should be gaining in temperature even though it were losing heat all the time4 ,at first this seems a paradox1 but the paradox will be explained if we reflect upon the physical changes which the gas undergoes in consequence of its contraction4 ,let us dwell for a moment on the remarkable statement that the sun is becoming gradually smaller4 ,the reduction required to sustain the radiation corresponds to a diminution of the diameter by about a mile every eleven years4 ,it may serve to impress upon us the fact of the sun's shrinkage if we will remember that on that auspicious day when ,queen ,victoria came to the throne the sun had a diameter more than five miles greater than it had at the time when her long and glorious career was ended4 ,the sun that shone on ,palestine at the beginning of the present era must have had a diameter about one hundred and seventy miles greater than the sun which now shines on the ,sea of ,galilee4 ,this process of reduction has been going on for ages1 which from the human point of view we may practically describe as illimitable4 ,the alteration in the sun's diameter within the period covered by the records of man's sway on this earth may be intrinsically large2 it amounts no doubt to several hundreds of miles4 ,but in comparison with the vast bulk of the sun this change in its magnitude is unimportant4 ,a span of ten thousand years will certainly include all human history4 ,let us take a period which is four times as long4 ,it is easy to calculate what the diameter of the sun must have been forty thousand years ago1 or what the diameter of the sun is to become in the next forty thousand years4 ,calculated at the rate we have given1 the alteration in the sun's diameter in this period amounts to rather less than four thousand miles4 ,this seems no doubt a huge alteration in the dimensions of the orb of day4 ,we must1 however1 remember that at the present moment the diameter of the sun is about #hfc1jjj miles1 and that a loss of four thousand miles1 or thereabouts1 would still leave a sun with a diameter of #hei1jjj miles4 ,there would not be much recognisable difference between two suns of these different dimensions4 ,i think ,i may say that if we could imagine two suns in the sky at the same moment1 which differed only in the circumstance that one had a diameter of #hfc1jjj miles and the other a diameter of #hei1jjj miles1 it would not be possible without careful telescopic measurement to tell which of the two was the larger4 ,after a contraction has taken place by loss of heat1 the heat that still remains in the body is contained within a smaller volume than it had originally4 ,the temperature depends not only on the actual quantity of heat that the mass of gas contains1 but also on the volume through which that quantity of heat is diffused4 ,if there be two equal weights of gas1 and if they each have the same absolute quantity of heat1 but if one of them occupies a larger volume than the other1 then the temperature of the gas in the large volume will not be so high as the temperature of the gas in the smaller volume4 ,this is indeed so much the case1 that the reduction of volume by the loss of heat may sometimes have a greater effect in raising the temperature than the very loss of heat which produced the contraction has in depressing it4 ,on the whole1 therefore1 a gain of temperature may be shown4 ,this is what1 indeed1 happens not unfrequently in celestial bodies4 ,the contraction having taken place1 the lesser quantity of heat still shows to such advantage in the reduced volume of the body1 that no decline of temperature will be perceptible4 ,it may happen that simultaneously with the decrease of heat there is even an increase of temperature4 ,the principle under consideration shows that1 though the sun is now giving out heat copiously1 it does not necessarily follow that it must at the same time be sinking in temperature4 ,as a matter of fact1 physicists do not know what course the temperature of the sun is actually taking at this moment4 ,the sun may now be precisely at the same temperature at which it stood a thousand years ago1 or it may be cooler1 or it may be hotter4 ,in any case it is certain that the change of temperature per century is small1 too small1 in fact1 to be decided in the present state of our knowledge4 ,we cannot observe any change1 and to estimate the change from mechanical principles would only be possible if we knew much more about the interior of the sun than we know at present4 ,we are forced to the conclusion that the energy of the sun1 by which we mean either its actual heat or what is equivalent to heat1 must be continually wasting4 ,a thousand years ago there was more heat1 or its equivalent1 in the sun than there is at present4 ,but the sun of a thousand years ago was larger than the sun that we now have1 and the heat1 or its equivalent1 a thousand years ago may not have been so effective in sustaining the temperature of the bigger sun as the lesser quantity of heat is in sustaining the temperature of the sun at the present day4 ,it will be noticed that the argument depends essentially on the alteration of the size of the sun4 ,of course if the orb of day had been no greater a thousand years ago than it is now1 then the sun of those early days would not only have contained more heat than our present sun1 but it must have shown that it did contain more heat4 ,in other words1 its temperature would then certainly have been greater than it is at present4 ,thus we see the importance--so far as radiation is concerned--of the gradual shrinking of the sun4 ,the great orb of day decreases1 and its decrease has been estimated numerically4 ,we cannot1 indeed1 determine the rate of decrease by actual telescopic measurement of the sun's disc with the micrometer2 observations extending over a period of thousands of years would be required for this purpose4 ,but from knowing the daily expenditure of heat from the sun it is possible to calculate the amount by which it shrinks4 ,we cannot conveniently explain the matter fully in these pages4 ,those who desire to see the calculation will find it in the ,appendix4 ,suffice it to say here that the sun's diameter diminishes about sixteen inches in every twenty-four hours4 ,this is an important conclusion1 for the rate of contraction of the solar diameter is one of the most significant magnitudes relating to the solar system4 ,it was ,helmholtz who showed that the contraction of the sun's diameter by sixteen inches a day is sufficient to account for the sustentation of the solar radiation4 ,for immense periods of time the heat may be dispensed with practically unaltered liberality4 ,the question then arises as to what time-limit may be assigned to the efficiency of our orb4 ,obviously the sun cannot go on contracting sixteen inches a day indefinitely4 ,if that were the case1 a certain number of millions of years would see it vanish altogether4 ,the limit to the capacity of the sun to act as a dispenser of light and heat can be easily indicated4 ,at present the sun1 in its outer parts at all events1 is strictly a vaporous body4 ,the telescope shows us nothing resembling a solid or a liquid globe4 ,the sun seems composed of gas in which clouds and vapours are suspended4 ,in the sun's centre the temperature is probably very much greater than any temperature which can be produced by artificial means2 it would doubtless be sufficient not only to melt1 but even to drive into vapour the most refractory materials4 ,on the other hand1 the enormous condensing pressure to which those materials are submitted by the stupendous mass of the sun will have the effect of keeping them together and of compressing them to such an extent that the density of the gas1 if indeed we may call it gas1 is probably as great as the density of any known matter4 ,the fact is that the terms liquids1 gases1 and solids cease to retain intelligible distinctions when applied to materials under such pressure as would be found in the interior of the sun4 ,astronomers can weigh the sun4 ,it may well be imagined that this is a delicate and difficult operation4 ,it can1 however1 be effected with but little margin of uncertainty1 and the result is a striking one4 ,it serves no useful purpose to express the sun's weight as so many myriads of tons4 ,it is more useful for our present purpose to set down the density of the sun1 that is to say1 the ratio of the weight of the orb1 to that of a globe of water of the same size4 ,this is the useful form in which to consider the weight of the sun4 ,astronomers are accustomed to think of the weight of our own earth in this same fashion1 and the result shows that the earth is rather more than five times as heavy as a globe of water of the same size4 ,we can best appreciate this by stating that if the earth were made of granite1 and had throughout the density which we find granite to possess at the surface1 our globe would be about three times as heavy as a globe of water of the same size4 ,if1 however1 the earth had been entirely made of iron1 it would be more than seven times as heavy as a globe of water of the same size4 ,as the earth actually has a density of #e1 it follows that our globe taken as a whole is heavier than a globe of granite of the same size1 though not so heavy as a globe of iron4 ,in the matter of density there is a remarkable contrast between the sun and the earth4 ,the sun's density is much less than that of the earth4 ,of course it will be understood that the sun is actually very much heavier than our globe2 it is indeed more than three hundred thousand times greater in weight4 ,but the sun is about a million three hundred thousand times as big as the earth1 and it follows from these figures that its density cannot be more than about a fourth of that of the earth4 ,the result is that1 at present1 the sun is nearly half as heavy again as a globe of water the same size4 ,we have used round numbers3 the density of the sun is actually #a4d4 ,illustration3 ,fig4 #ag4--;,,argo ,,and ,,the ,,surrounding ,,stars ,,and ,,nebulosity4 7,photographed by ,sir ,david ,gill1 ,k4,c4,b47 ,in the following manner we explain how heat is evolved in the contraction of the sun4 ,in its early days the sun1 or rather the materials which in their aggregate form now constitute the sun1 were spread over an immense tract of space1 millions of times greater than the present bulk of the sun4 ,we see nebulosities even now in the heavens which may suggest what the primval nebula may have been before the evolution had made much progress4 ,look for instance at ,sir ,david ,gill's photograph of the ,nebula in ,argo in ,fig4 #ag1 or at the ,trifid ,nebula in ,fig4 #ah4 ,we may1 indeed1 consider the primval nebula to have been so vast that particles from the outside falling into the position of the present solar surface would acquire that velocity of three hundred and ninety miles a second which we know the attraction of the sun is capable of producing on an object which has fallen in from an indefinitely great distance4 ,as these parts are gradually falling together at the centre1 there will be an enormous quantity of heat developed from their concurrence4 ,supposing1 for instance1 that the materials of the sun were arranged in concentric spherical shells around the centre1 and imagining these shells to be separated by long intervals1 so that the whole material of the sun would be thus diffused over a vast extent1 then every pound weight in the outermost shell1 by the very fact of its sinking downwards to the present solar system1 would acquire a speed of #cij miles a second1 and this corresponds to as much energy as could be produced by the burning of three tons of coal4 ,but be the fall ever so gentle1 the great law of the conservation of energy tells us that for the same descent1 however performed1 the same quantity of heat must be given out4 ,each pound in the outer shell would therefore give out as much heat as three tons of coal4 ,every pound in the other shells1 by gradual descent into the interior1 would also render its corresponding contribution4 ,it then becomes easily intelligible how1 in consequence of the original diffusion of the materials of the sun over millions of times its present volume1 a vast quantity of energy was available4 ,as the sun contracted this energy was turned into radiant heat4 ,we may anticipate a future chapter so far as to assume that there was a time when even this solid earth of ours was a nebulous mass diffused through space4 ,we are not concerned as to what the temperature of that nebulous mass may have been4 ,we may suppose it to be any temperature we please4 ,the point that we have now to consider is the quantity of heat which is generated by the contraction of the nebula4 ,that heat is produced in the contraction will be plain from what has gone before4 ,but we may also demonstrate it in a slightly different way4 ,let us take any two points in the nebula1 ,p and ,q4 ,after the nebula has contracted the points which were originally at ,p and ,q will be found at two other points1 ,a and ,b4 ,as the whole nebula in its original form was larger than the nebula after it has undergone its contraction1 the distance ,p ,q is generally greater than the distance ,a ,b4 ,we may suppose the contraction to proceed uniformly1 so that the same will be true of the distance between any other two particles4 ,the distance between every pair of particles in the contracted nebula will be less than the distance between the same particles in the original nebula4 ,illustration3 ,fig4 #ah4--,,trifid ,,nebula ,,in ,,sagittarius 7,lick ,observatory1 ,california74 7,from the ,royal ,astronomical ,society ,series47 ,if two attracting bodies1 ,a and ,b1 are to be moved further apart than they were originally1 force must be applied and work must be done4 ,we may measure the amount of that work in foot-pounds1 and then1 remembering that #ggb foot-pounds of work are equivalent to the unit of heat1 we may express the energy necessary to force the two particles to a greater distance asunder in the equivalent quantity of heat4 ,if1 therefore1 we had to restore the nebula from the contracted state to the original state1 this would involve a forcible enlargement of the distance ,a ,b between every two particles to its original value1 ,p ,q4 ,work would be required to do this in every case1 and that work might1 as we have explained1 be expressed in terms of its equivalent heat value4 ,even though the temperature of the nebula is the same in its contracted state as in its original state1 we see that a quantity of heat might be absorbed or rendered latent in forcing the nebula from one condition to the other4 ,in other words1 keeping the temperature of the nebula always constant1 we should have to apply a large quantity of heat to change the nebula from its contracted form to its expanded form4 ,it is equally true that when the nebula is contracting1 and when the distance between every two particles is lessening1 the nebula must be giving out energy1 because the total energy in the contracted state is less than it was in the expanded state4 ,this energy is equivalent to heat4 ,we need not here pause to consider by what actual process the heat is manifested2 it suffices to say that the heat must1 by one of the general laws of ,nature1 be produced in some form4 ,we are now able to make a numerical estimate4 ,we shall suppose that the earth1 or rather the materials which make the earth1 existed originally as a large nebula distributed through illimitable space4 ,the calculations show that the quantity of heat1 generated by the condensation of those materials from their nebulous form into the condition which the earth now has1 was enormously great4 ,we need not express this quantity of heat in ordinary units4 ,the unit we shall take is one more suited to the other dimensions involved4 ,let us suppose a globe of water as heavy as the earth4 ,this globe would have to be five or six times as large as the earth4 ,next let us realise the quantity of heat that would be required to raise that globe of water from freezing point to boiling point4 ,it can be proved that the heat1 or its equivalent1 which would be generated merely by the contraction of the nebula to form the earth1 would be ninety times as great as the amount of heat which would suffice to raise a mass of water equal in weight to the earth from freezing point to boiling point4 ,we apply similar calculations to the case of the sun4 ,let us suppose that the great luminary was once diffused as a nebula over an exceedingly great area of space4 ,it might at first be thought that the figures we have just given would answer the question4 ,we might perhaps conjecture that the quantity of heat would be such as would raise a mass of water equal to the sun's mass from freezing to boiling point ninety times over4 ,but we should be very wrong in such a determination4 ,the heat that is given out by the sun's contraction is enormously greater than this estimate would represent1 and we shall be prepared to admit this if we reflect on the following circumstances4 ,a stone falling from an indefinitely great distance to the sun would acquire a speed of #cij miles a second by the time it reached the sun's surface4 ,a stone falling from an indefinitely great distance in space to the earth's surface would1 however1 acquire a speed of not more than seven miles a second4 ,the speed acquired by a body falling into the sun by the gravitation of the sun is1 therefore1 fifty-six times as great as the speed acquired by a body falling from infinity to the earth by the gravitation of the earth4 ,as the energy of a moving body is proportional to the square of its velocity1 we see that the energy with which the falling body would strike the sun1 and the heat that it might consequently give forth1 would be about three thousand times as great as the heat which would be the result of the fall of that body to the earth4 ,we need not therefore be surprised that the drawing together of the elements to form the sun should be accompanied by the evolution of a quantity of heat which is enormously greater than the mere ratio of the masses of the earth and sun would have suggested4 ,there is another line of reasoning by which we may also illustrate the same important principle4 ,owing to the immense attraction possessed by the large mass of the sun1 the weights of objects on that luminary would be very much greater than the weights of corresponding objects here4 ,indeed1 a pound on the sun would be found by a spring-balance to weigh as much as twenty-seven pounds here4 ,if the materials of the sun had to be distributed through space1 each pound lifted a foot would require twenty-seven times the amount of work which would be necessary to lift a pound through a foot on the earth's surface4 ,it will thus be seen that not only the quantity of material that would have to be displaced is enormously greater in the sun than in the earth1 but that the actual energy that would have to be applied per unit of mass from the sun would be many times as great as the quantity of energy that would have to be applied per unit of mass from the earth to effect a displacement through the same distance4 ,to distribute the sun's materials into a nebula we should therefore require the expenditure of a quantity of work far more than proportional to the mere mass of the sun4 ,it follows that when the sun is contracting the quantity of work that it will give out1 or1 what comes to the same thing1 the amount of heat that would be poured forth in consequence of the contraction per unit of mass of the sun will largely exceed the quantity of heat given out in the similar contraction of the earth per unit of mass of the earth4 ,these considerations will prepare us to accept the result given by accurate calculation4 ,it has been shown that the heat which would be generated by the condensation of the sun from a nebula filling all space down to its present bulk is two hundred and seventy thousand times the amount of heat which would be required to raise the temperature of a mass of water equal to the sun from freezing point to boiling point4 ,this is a result of a most instructive character4 ,the amount of heat that would be required to raise a pound of water from freezing point to boiling point would1 speaking generally1 be quite enough if applied to a pound of stone or iron to raise either of these masses to a red heat4 ,if1 therefore1 we think of the sun as a mighty globe of stone or iron1 the amount of heat that would be produced by the contraction of the sun from the primval nebula would suffice to raise that globe of stone or iron from freezing point up to a red heat #bgj1jjj times4 ,this will give us some idea of the stupendous amount of heat which has been placed at the disposal of the solar system by the process of contraction of the sun4 ,this contraction is still going on1 and consequently the yield of heat which is the consequence of this contraction is still in progress1 and the heat given out provides the annual supply necessary for the sustenance of our solar system4 ,there is one point which should be specially mentioned in connection with this argument4 ,we have here supposed that the current supply of radiant heat from the sun is entirely in virtue of the sun's contraction4 ,that is to say1 we suppose the sun's temperature to be remaining unaltered4 ,this is perhaps not strictly the case4 ,there may be reason for believing that the temperature of the sun is increasing1 though not to an appreciable extent4 ,it will be convenient to introduce a unit that will be on a scale adapted to our measurements4 ,let us think of a globe of coal as heavy as the sun4 ,now suppose adequate oxygen were supplied to burn that coal1 a definite quantity of heat would be produced4 ,there is no present necessity to evaluate this in the lesser units adapted for other purposes4 ,in discussing the heat of the sun1 we may use what we call the coal-unit1 by which is to be understood the total quantity of heat that would be produced if a mass of coal equal to the sun in weight were burned in oxygen4 ,it can be shown by calculations1 which will be found in the ,appendix1 that in the shrinkage of the sun from an infinitely great extension through space down to its present bulk the contraction would develop the stupendous quantity of heat represented by #c1djj coal-units4 ,it is also shown that one coal unit would be adequate to supply the sun's radiation at its present rate for #b1hjj years4 ---------------------------------------- -------------------------------- ,,chapter ,,vii4 ,,the ,,history ,,of ,,the ,,sun4 ,the ,inconstant ,sun--,representation of the ,solar ,system at different ,epochs--,primval ,density of the ,sun--,illustration of ,gas in ,extreme ,tenuity--,physical ,state of the ,sun at that ,period--,the ,sun was then a ,nebula4 ,,we pointed out in the last chapter how1 in consequence of its perennial loss of heat1 the orb of day must be undergoing a gradual diminution in size4 ,in the present chapter we are to set down the remarkable conclusions with respect to the early history of the sun to which we have been conducted by pursuing to its legitimate consequences the shrinkage which the sun had undergone in times past4 ,the outer circle in ,fig4 #ai represents the track in which our earth now revolves around the sun1 and we are to understand that the radius of this circle is about ninety-three million miles4 ,we must imagine that the innermost of the four circles represents the position of the sun4 ,along its track the earth revolves year after year2 so it has revolved for centuries1 so it has revolved since the days of the first monarch that ever held sway in ,britain1 so it has revolved during all the time over which history extends1 so it has doubtless revolved for illimitable periods anterior to history4 ,for an interval of time that no one presumes to define with any accuracy the earth has revolved in the same track round that sun in heaven which1 during all those ages1 has dispensed its benefits of light and heat for the sustenance of life on our globe4 ,illustration3 ,fig4 #ai4--,,to ,,illustrate ,,the ,,history ,,of ,,the ,,sun4 ,present orbit of ,earth4 ,sun in times very much earlier still4 ,sun in very early times4 ,present ,sun4 ,the sun appears constant during those few years in which man is allowed to strut his little hour4 ,the size of the sun and the lustre of the sun has not appreciably altered4 ,but the sun does not always remain the same4 ,it has not always shone with the brightness and vigour with which it shines now2 it will not continue for ever to dispense its benefits with the same liberality that it does at present4 ,the sun is always in a state of change4 ,it would not indeed be correct to refer to these changes as growths1 in the same sense in which we speak of the growth in a tree4 ,decade after decade the tree waxes greater2 but the sun1 as we have already explained1 does not increase with the time1 for the change indeed lies the other way4 ,it may well be that in this present era the sun is near its prime1 in so far as its capacity to radiate warmth and brightness is concerned4 ,it is1 however1 certain that the sun is not now so large as it was in ancient days4 ,the diminution of the orb is still in progress4 ,in these present days of its glorious splendour the orb of day is much larger than it will be in that gloomy old age which destiny assigns to it4 ,we have already shown how to give numerical precision to our facts4 ,we have stated that the sun's diameter is diminishing at the rate of one mile every eleven years4 ,we have dwelt upon the remarkable significance of that shrinkage in accounting for the sustentation of the sun's heat4 ,we have now to call on this perennial diminution of the sun's diameter to provide some information as to the early history of our luminary4 ,the innermost circle in our sketch is to suggest the sun as it is at present4 ,millions of years ago the orb of day was as large as ,i have indicated it by the circle with the words 8sun in very early times40 ,it will1 of course1 be understood that we do not make any claim to precise representation of the magnitude of the orb4 ,at a period much earlier still1 the sun must have been larger still1 and we venture so to depict it4 ,we know the rate at which the sun is now contracting1 and doubtless this rate has continued sensibly unaltered during thousands of years1 and indeed we might say scores of thousands of years4 ,but it would not be at all safe to assume that the annual rate of change in the sun's radius has remained the same throughout excessively remote periods in its evolutionary history4 ,what we do affirm is1 that in the course of its evolution the sun must have been contracting continually1 and we have been able to learn the particular rate of contraction characteristic of the present time4 ,but though we are ignorant of the rate of contraction at very early epochs1 yet the sun ever looms larger and larger in days earlier and still earlier4 ,but in those early days the sun was not heavier1 was not1 indeed1 quite so heavy as it is at present4 ,for we remember that the sun is perennially adding thousands of tons to its bulk by the influx of meteors4 ,perhaps we ought to add that the gain of mass from the meteors may be to some extent compensated by the loss of substance which the sun not infrequently experiences if1 as is sometimes supposed1 it expels in some violent convulsion a mass of material which takes the form of a comet 7,fig4 #ba74 ,let us now consider what the density of the sun must have been in those primval days1 say1 for example1 when the luminary had ten times the volume that it has at present4 ,even now1 as already stated1 it does not weigh half as much again as a globe of water of the same size1 so that when it was ten times as big its density must have been only a small fraction of that of water4 ,but we may take a stage still earlier4 ,let us think of a time--it was1 perhaps1 many scores of millions of years ago--when the sun was a thousand times as big as it is at present4 ,the same quantity of matter which now constitutes the sun was then expanded over a volume a thousand times greater4 ,a remarkable conclusion follows from this consideration4 ,the air that we breathe has a density which is about the seven-hundredth part of that of water4 ,hence we see that at the time when the materials of the sun were expanded into a volume a thousand times as great as it is at present the density of the luminary must have been about equal to that of ordinary air4 ,we refer1 of course1 in such statements to the average density of the sun4 ,it will be remembered that the density of the sun cannot be uniform4 ,the mutual attractions and pressures of the particles in the interior must make the density greater the nearer we approach to the centre4 ,we must push our argument further still4 ,we have ascertained that the primval sun could not have been a dense solid body like a ball of metal4 ,it must have been more nearly represented by a ball of gas4 ,there was a time when that collection of matter which now constitutes the sun was so big that a balloon of equal size1 filled at ordinary pressure with the lightest of known gases1 would contain within it a heavier weight than the sun4 ,at this early period the sun must have been as light as an equal volume of hydrogen4 ,the reasoning which has conducted us to this point remains still unimpaired4 ,from that early period we may therefore look back to periods earlier still4 ,we see that the sun must have been ever larger and larger1 for the same quantity of material must have been ever more and more diffused4 ,there was a time when the mean density of the sun must have been far less than that of the gas in any balloon4 ,we must not pause to consider intermediate stages4 ,we shall look back at once to an excessively early period when the sun--or perhaps we ought rather to say the matter which in a more condensed form now constitutes the sun--was expanded throughout the volume of a globe whose radius was as great as the present distance from the sun to the earth4 ,have we not here truly an astonishing result1 deduced as a necessary consequence from the fundamental laws of heat8 ,illustration3 ,fig4 #bj4--,,the ,,solar ,,corona 7,january #ast1 #ahii74 7,photographed during ,eclipse by ,professor ,w4 ,h4 ,pickering47 ,i need hardly say that the sun at that early date did not at all resemble the glorious orb to which we owe our very existence4 ,the primval sun must have been a totally different object1 as we can easily imagine if we try to think that the sun's materials then filled a volume twelve million times as great as they occupy at present4 ,instead of comparing such an object with the gases in our ordinary atmosphere1 it should rather be likened to the residue left in an exhausted receiver after the resources of chemistry have been taxed to make as near an approach as possible to a perfect vacuum4 ,we can give a familiar illustration of gas in a state of extreme tenuity4 ,look at the beautiful incandescent light with which in these days our buildings are illuminated4 ,how brilliantly those little globes shine6 ,the globe has to be most carefully sealed against the outside air4 ,if there were the smallest opportunity for access1 the air from outside would rush in and the lamp would be destroyed4 ,in the preparation of such a lamp elaborate precautions have to be taken to secure that the exhaustion of the air from the little globe shall be as nearly perfect as possible4 ,of course it is impossible to remove all the air4 ,no known processes can produce a perfect vacuum4 ,some traces of gas would remain after the air-pump had been applied even for hours4 ,we must now imagine a globe1 not merely two inches in diameter like one of these little lamps1 but a globe #ahf1jjj1jjj miles in diameter1 a globe so large that the earth's orbit would just form a girdle round it4 ,even if this globe had been exhausted1 so that its density was only the twelve-thousandth part of the ordinary atmospheric density1 it would still contain more material than is found in the sun in heaven4 ,thus our reasoning has conducted us to the notion of an epoch when the sun--or rather ,i should say the matter composing the sun--formed something totally different from the orb which we know so well4 ,the matter in that very diffuse state would not dispense light and heat as a sun in the sense in which we understand the word4 ,however vast might be the store of energy which it contained--a store indeed thousands of times greater than our present sun possesses--yet it would hardly be possessed of the power of effective radiation4 ,it would assuredly not be able to warm and light a world associated with it1 in the same way as the sun now provides so gloriously for our wants and comfort4 ,illustration3 ,fig4 #ba4--,,the ,,great ,,comet ,,of #ahhb4 7,photographed on ,november #gth1 #ahhb1 by ,sir ,david ,gill1 ,k4,c4,b47 ,but it is certain that in those early days there was no earth to be warmed and lighted4 ,our globe1 even if it can be said to have existed at all1 was truly 8without form and void40 ,at the time when the sun was swollen into a great globe of gas or rarefied matter1 the elementary substances which were to form the future earth were in a condition utterly different from that of our present globe4 ,the history of this earth itself involves another chapter of the argument4 ,let it suffice to notice1 for the present1 that our reasoning has led us to a time when the sun consisted only of a rarefied gaseous material1 and let us give to the matter in this condition the name which astronomers apply to any object of a similar character wherever they may meet with it in the universe4 ,suppose that we could observe through our telescopes at the present moment an object in remote space which was like what the sun must have been at that early stage of its existence which we have been considering1 ,i do not think that the object would be unfamiliar to astronomers4 ,there is1 indeed1 no doubt that there are many objects visible at this moment1 and nightly studied in our observatories1 which are formed of matter just in the same state as the sun was in those early times4 ,examined with a good telescope1 the object would seem like a small stain of light on the black background of the sky4 ,the observer would at once call it a nebula4 ,in these modern days he would probably apply the spectroscope to it1 and this instrument would assure him that the object he was looking at was a mass of incandescent gas4 ,such an object would in all probability not greatly differ from many nebul now known to us4 ,this being so1 why should we withhold from the sun of primitive days the designation to which it seems to be so fully entitled8 ,why should we not speak of it as a nebula8 ,the application of the laws of heat has shown that the great orb of day was once one of those numerous objects which astronomers know as nebul1 and perhaps it may not be too fanciful to suppose that a trace of the primval nebula still survives in what we call the ,solar ,corona 7,fig4 #bj74 ---------------------------------------- -------------------------------- ,,chapter ,,viii4 ,,the ,,earth',s ,,beginning4 ,the ,earth to be ,studied--,a great ,experiment--,the ,diamond ,drill--,a ,boring upwards of a ,mile ,deep--,a ,mechanical ,feat--,the ,scientific ,importance of the ,work--,increase of ,temperature with the ,depth--,a special ,form of ,thermometer--,taking the ,temperature in the ,boring--,the ,level of ,constant ,temperature--,the ,rate of ,increase of ,temperature with the ,depth--,one degree ,fahrenheit for every ,sixty-six ,feet in ,depth--,temperatures at ,depths above a ,mile--,conclusions as to the ,heat at very great ,depths--,the ,heat developed by ,tidal ,action--,this will not account for the ,earth's ,internal ,heat--,the ,earth must be continually ,cooling--,inferences from the incessant loss of ,heat from the ,earth--,the ,earth's ,surface once ,red-,hot1 or ,molten--,the ,earth must have originated from a ,nebula--,the ,earth's ,beginning4 ,,in the last chapter we endeavoured to ascertain what can be learned from the radiation of the sun with regard to the history of the solar system4 ,in this chapter we shall not consider any body in the heavens1 but the condition of the earth itself4 ,we have learned something of the history of the solar system from the celestial bodies2 we shall now learn something about it in another way--from the condition of our globe at depths far beneath our feet4 ,it will be convenient to commence by mentioning a remarkable experiment which was made a few years ago4 ,though that experiment is of great scientific interest1 yet it was not designed with any scientific object in view4 ,not less than #aj1jjj was expended on the enterprise1 and probably so large a sum has never been expended on a single experiment of which the sole object was to add to scientific knowledge4 ,in the present case the immediate object in view was1 of course1 a commercial one4 ,there was1 it may be presumed1 reasonable expectation that the great initial cost1 and a handsome profit as well1 would be returned as the fruits of the enterprise4 ,whether the great experiment was successful from the money-making point of view does not now concern us1 but it does concern us to know that the experiment was very successful in the sense that it incidentally afforded scientific information of the very highest value4 ,the experiment in question was made in ,germany1 at ,schladebach1 about fifteen miles from ,leipzig4 ,it was undertaken in making a search for coal4 ,some enterprising capitalists consulted the geologists as to whether coal-seams were likely to be found in this locality4 ,they were assured that coal was there1 though it must certainly be a very long way down1 and consequently the pit by which alone the seams could be worked would have to be unusually deep4 ,the capitalists were not daunted by this consideration4 ,but1 before incurring the great expense of sinking the shaft1 they determined to make a preliminary search and verily the actual presence of workable seams of useful fuel4 ,they determined to bore a hole down through the rocks deep enough to reach the coal1 if it could be reached4 ,a boring for coal was1 of course1 by no means a novelty2 but there was an unprecedented degree of mechanical skill and scientific acumen shown in this memorable boring near ,leipzig4 ,the result of this enterprise was to make the deepest hole which1 with perhaps a single more recent exception not of so much scientific interest1 has ever been pierced through the crust of the earth4 ,this boring was merely a preliminary to the operations which would follow if the experiment were successful in discovering coal4 ,it was accordingly only necessary to make a hole large enough to allow specimens of the strata to be brought to the surface4 ,the instrument employed in sinking a hole of such a phenomenal depth through solid rock is characteristic of modern enterprise4 ,the boring tool had a cutting edge of diamonds3 for no other cutting implement is at once hard enough and durable enough to advance steadily1 yard by yard1 through the various rocks and minerals that are met with in the descent through the earth's crust4 ,we might1 perhaps1 illustrate the actual form of the tool as follows3 imagine a piece of iron pipe1 about six inches in diameter1 cut squarely across1 with diamonds inserted round its circular end1 and we have a notion of the diamond drill4 ,if the drill be made to revolve when held vertically1 with the diamonds in contact with the rocks1 the cutting will commence4 ,as the rotation is continued1 the drill advances through the rocks1 and a solid core of the material will occupy the hollow of the pipe4 ,we do not now enter into any description of the many mechanical details2 there are ingenious contrivances for removing the dbris produced by the attrition of the rocks as the diamonds cut their way1 and provision is also made for carefully raising the valuable core which1 as it provides specimens of the different strata pierced1 will show the coal1 if coal is ever reached4 ,there is1 of course1 an arrangement by which1 as the first length of drill becomes buried1 successive lengths can be added1 so as to transmit the motion to the cutting edge and enable the tool to be raised when necessary2 in this manner one length of solid rock after another is brought up for examination4 ,these cores1 when ranged in series1 give to the miner the information he requires as to the different beds of rock through which the instrument has pierced in its descent and as to the depths of the beds4 ,a series of cores will sometimes show astonishing variety in the material through which the drill has passed4 ,here the tool will be seen passing through a bed of hard limestone1 and then entering a bed of soft shale2 now the tool bores through dense and hard masses of greenstone1 anon it pierces1 it may be1 a stratum of white marble2 and finally the explorer may hope to find his expectations realised by the arrival at the surface of a cylinder of solid coal4 ,the famous boring to which we are now referring1 though very deep1 was not large in diameter4 ,as it descended the comparatively large tool first employed was replaced by a succession of smaller tools1 so that the hole gradually tapered from the surface to the lowest point4 ,at its greatest depth the hole was indeed hardly larger than a man's little finger4 ,it increased gradually all the way to the surface1 where it was large enough for a man's arm to enter it easily4 ,how often do we find that the success which rewards mechanical enterprise greatly transcends even the most sanguine estimate previously formed6 ,without the actual experience which has been acquired1 ,i do not think anyone could have anticipated the extraordinary facilities which the diamond drill has given in the operations of a deep boring4 ,this hole at ,schladebach was1 indeed1 a wonderful success4 ,it pierced deeper than any previous excavation1 deeper than any well1 deeper than any coal pit4 ,from the surface of the ground1 where the hole was some six inches in diameter1 down to the lowest point1 where it was only as large as a little finger1 the vertical depth was not less than one mile and a hundred and seventeen yards4 ,it is worth pondering for a moment on the extraordinary mechanical feat which this represents4 ,when the greatest depth was reached1 the total length of the series of boring rods from the surface where the machinery was engaged in rotating the tool down to the cutting diamonds at the lower end where the penetration was being effected1 was as long as from ,piccadilly ,circus to the top of ,portland ,place4 ,if a hole of equal length had been bored downwards from the top of ,ben ,nevis1 it would have reached the sea level and gone down #a1bjj feet lower still4 ,when the foreman in charge wished to look at the tool to see whether it was working satisfactorily1 or whether any of the diamonds had got injured or displaced1 it was necessary to raise that tremendous series of rods4 ,each one of them had to be lifted1 had to be uncoupled1 and had to be laid aside4 ,i need hardly say that such an operation was a very tedious one4 ,the collective weight of the working system of rods was about twenty tons1 and not less than ten hours' hard work was required before the tool was raised from the bottom to the surface4 ,we may1 ,i believe1 conclude that so much ingenuity and so much trouble was never before expended on the act of boring a hole2 but the results are full of information on important problems of science4 ,i am not going to speak of the geological results of this exploration4 ,there is not the least doubt that the remarkable section of the earth's crust thus obtained is of much interest to geologists4 ,our object in now alluding to this wonderful boring is1 however1 very different4 ,its significance will be realised when we say that it gives us more full and definite information about the internal heat of the earth than had ever been obtained by any other experiment on the earth's crust4 ,no doubt many previous observations of the internal heat of the globe were well known to the investigators who feel an interest in these important questions2 but the exceptional depth of this boring1 as well as the exceptionally favourable conditions under which it was made1 have rendered the information derived from it of the utmost value to science4 ,we ought first to record our special obligation to the ,german engineer1 ,captain ,huyssen1 who bored this wonderful hole4 ,he was not only a highly skilful mining engineer1 diligent in the pursuit of his profession1 but1 by the valuable scientific work he has done1 he has shown himself to be one of those cultivated and thoughtful students who love to avail themselves of every opportunity of searching into ,nature's secrets4 ,our thanks are due to him for the remarkable zeal with which he utilised the exceptional opportunities for valuable scientific work that arose1 incidentally as it were1 in connection with the work committed to him4 ,of course1 everybody knows that the temperature of the earth is found to increase gradually as greater depths are reached4 ,the rate at which the increase takes place has been determined on many occasions4 ,but when opportunities have arisen for taking the temperature at considerable depths below the earth's surface1 it has happened sometimes that the observations have been complicated by circumstances which deprived them of a good deal of their accuracy4 ,if our object be to learn the law connecting the earth's temperature with the depth below the surface1 it is not sufficient to study the thermometric readings in different coal pits4 ,throughout the workings in every pit there must be arrangements for ventilation4 ,the cool air has to be drawn down1 and thus the temperature indicated in the pit is forced below the temperature which would really be found at that depth if external sources of change of temperature were absent4 ,captain ,huyssen rightly deemed that the hole which he had pierced presented exceptional opportunities for the study of the important question of the earth's internal temperature4 ,precautions had1 of course1 to be observed4 ,the hole1 as might be expected1 was filled with water1 and the water would tend1 if its circulation were permitted1 to equalise the temperature at different depths4 ,but the ingenious ,captain quickly found an efficient remedy for this source of inaccuracy4 ,he devised an arrangement1 which ,i must not delay to describe1 by which he could place temporary plugs in the hole at any depths he might desire2 he then determined the temperature of the water in a short length1 so plugged above and below that the circulation was stopped1 and accordingly the water thus confined might be relied on to indicate the temperatures of the strata which hold it4 ,illustration3 ,fig4 #bb4--,,special ,,thermometer ,,for ,,use ,,in ,,deep ,,borings4 ,the thermometer employed in an investigation of this sort is ingenious though extremely simple4 ,the ordinary maximum thermometer is not found to be adapted for the purpose4 ,the instrument 7,fig4 #bb7 employed in the determination of underground temperatures is very much less complicated and at the same time much more accurate4 ,the contrivance is indeed so worthy of notice that ,i do not like to pass it by without a few words4 ,the thermometer with which the temperature of the earth is ascertained in such investigations is not like any ordinary thermometer4 ,there is no scale of degrees attached to it or engraved upon it1 as we generally find in such instruments4 ,the instrument with which the temperature of the deep hole was measured was merely a bulb of glass with a slender capillary stem1 the end of which was not closed4 ,when it was about to be lowered to test the temperature of the rocks at the lowest point to which the drill had penetrated1 the bulb and the tube were first filled with mercury to the top1 and brimming over4 ,this simple apparatus was attached to a long wire1 by the aid of which it could be lowered down this deep hole4 ,down it went till at last the thermometer reached the bottom1 which1 as we have explained1 it could not do until more than a mile of wire had been paid out4 ,the instrument was then left quietly until it presently assumed the same temperature as the rocks about it4 ,there could be no interference by heat from other strata1 as the circulation of water was prevented by the plugging already referred to4 ,the temperature to which the thermometer had been exposed must1 therefore1 have been precisely the temperature corresponding in that particular locality to that particular depth below the earth's surface4 ,as the thermometer descended1 it passed through a succession of strata of ever-increasing temperature4 ,consequently the mercury1 which1 it will be remembered1 had completely filled the instrument when it was at the surface1 began to expand according as it was exposed to greater temperatures4 ,as the mercury expanded1 it must1 of course1 flow out of the tube and be lost1 because the tube had been already full4 ,so long as the mercury was gaining in temperature1 more and more of it escaped from the top of the tube1 and the flow only ceased when the instrument was resting at the bottom of the hole1 and the mercury became as hot as the surrounding rocks4 ,no more mercury was then expelled1 the tube1 however1 remaining full to the brim4 ,after allowing a sufficient time for the temperature to settle definitely1 the thermometer was raised to the surface4 ,as it ascended through the long bore the temperature surrounding it steadily declined4 ,with the fall in the temperature of the mercury the volume of that liquid began to shrink2 but the mercury already expelled could not be recalled4 ,when at last the instrument had safely reached the surface1 after its long journey down and up1 and when the mercury had regained the temperature of the air1 the lessened quantity that remained told the tale of the changes of temperature4 ,it is now easy to see how1 even in the absence of an engraved scale on the instrument1 it is possible to determine1 from the amount of mercury remaining1 the temperature to which the thermometer has been subjected at the bottom of the boring4 ,it is only necessary to place this thermometer in a basin of cold water1 and then gradually increase the temperature by adding hot water4 ,as the temperature increases the mercury will1 of course1 rise1 and the hotter the water the more nearly will the mercury approach the top of the tube4 ,at last1 when the mercury has just reached the top of the tube1 and when it is just on the point of overflowing1 we may feel certain that the temperature of the water in the basin has been raised to the same temperature as that to which the instrument was subjected at the bottom of the boring4 ,in each case the temperature is just sufficient to expand the quantity of mercury remaining in the instrument so as to make it fill precisely both bulb and stem4 ,when this critical condition is reached1 it only remains to dip a standard thermometer1 furnished with the ordinary graduation1 into the hot water of the basin4 ,thus we learn the temperature of the basin1 thus we learn the temperature of the mercury in the thermometer1 and thus we determine the temperature at the bottom of the boring over a mile deep4 ,i need not specify the details of the arrangements which enabled the skilful engineer also to determine the temperature at various points of the hole intermediate between the top and the bottom4 ,in fact1 taking every precaution to secure accuracy1 he made measurements of the temperature at a succession of points about a hundred feet distant throughout the whole depth4 ,in each case he was careful1 as ,i have already indicated1 to plug the hole above and below the thermometer1 so as to prevent the circulation of water in the vicinity of the instrument4 ,the thermometer1 therefore1 recorded the temperature of the surrounding rocks without any disturbing element4 ,fifty-eight measurements at equal distances from the surface to the greatest depths were thus obtained4 ,we have now to discuss the instructive results to which we have been conducted by this remarkable series of measurements4 ,first let us notice that there is much less variation in the subterranean temperatures than in the temperatures on the earth's surface4 ,on the surface of the earth we are accustomed to large fluctuations of temperature4 ,we have1 of course1 the diurnal fluctuations in temperature from day to night2 we have also the great seasonal fluctuations between summer and winter4 ,but below a certain depth in the ground the temperature becomes much more equable4 ,whether the temperature on the surface be high or whether it be low1 the temperature of any particular point far beneath the surface does not change to any appreciable extent4 ,in ,arctic regions the surface of the earth may undergo violent seasonal changes of temperature1 while at a few feet below the surface the temperature1 from one end of the year to the other1 may remain sensibly unaltered4 ,in deep and extensive caverns the temperature is sometimes found to remain practically unaffected by the changes in the seasons4 ,the ,mammoth ,cave of ,kentucky is a notable instance4 ,the uniformity of the temperature1 as well as the mildness and dryness of the air1 in those wonderful subterranean vaults is such that many years ago a project was formed to utilise the cavern as an abode for consumptive patients1 for whose cure1 according to the belief then prevailing1 an equable temperature was above all things to be desired4 ,houses were indeed actually built on the sandy floors of the cavern1 and ,i believe they were for some time tenanted by consumptive patients willing to try this desperate remedy4 ,the temperature may have been uniform and the air may have been dry1 but the intolerable gloom of such a residence entirely neutralised any beneficial effects that might otherwise have accrued4 ,the ruins of the houses still remain to testify to the failure of the experiment4 ,the heat received from the sun does not penetrate far into the earth's crust1 and consequently the diurnal and even the seasonal changes of the temperature at the surface produce less and less effect with every increase of the depth4 ,all such variations of temperature are confined to within #ajj feet of the surface4 ,at the depth of about #ajj feet a fixed temperature of #eb ,fahrenheit is reached1 and this is true all over the earth4 ,it matters not whether the surface be hot or cold1 whether the latitude is tropical and the season is midsummer1 whether the latitude lie in the ,arctic regions and the season be the awful winter of iron-bound frost and total absence of sun--in all cases we find that about #ajj feet below the surface the temperature is #eb4 ,with sufficient accuracy we may say that this depth expresses the limit of the penetration of the earth's crust by sunbeams4 ,the remarkable law according to which the temperature changes below the depth of #ajj feet is wholly irrespective of the solar radiation4 ,the study of the internal heat of the earth may be said to begin below the level of #ajj feet1 and the results that were obtained in the great boring are extremely accordant4 ,the deeper the hole1 the hotter the rocks2 and ,captain ,huyssen found that for each sixty-six feet in descent the temperature increased one degree ,fahrenheit4 ,to illustrate the actual observations1 let us take two particular cases4 ,we have said that the hole was one mile and #aag yards deep4 ,let us first suppose the thermometer to be lowered #aag yards and then raised1 after a due observance of the precautions required to obtain an accurate result4 ,the temperature of the rocks at the depth of #aag yards is thus ascertained4 ,in the next observation let the thermometer be lowered from the surface to the bottom of the hole1 that is to say1 exactly one mile below the position which it occupied in the former experiment4 ,the observations indicate a temperature #hj ,fahrenheit higher in the latter case than in the former4 ,we have thus ascertained a most important fact4 ,we have shown that the temperature of the crust of the earth at the depth of one mile increases about #hj4 ,this is at the rate of one degree every sixty-six feet4 ,i should just add1 as a caution1 that if we choose to say the temperature increases one degree per sixty-six feet of descent1 we ought to suppose that we start from a point which is not higher than that level of #ajj feet above which as already explained1 the temperature of the rocks is more or less affected by solar heat4 ,we have described these particular observations in some detail because they have been conducted under conditions far more favourable to accuracy than have ever been available in any previous investigations of the same kind4 ,but now we shall omit further reference to this particular undertaking near ,leipzig4 ,it is not alone in that particular locality1 not alone in ,germany1 not alone in ,europe1 not alone on the surface of any continent1 that this statement may be made4 ,the statement is one universally true so far as our whole earth is concerned4 ,wherever we bore a hole through the earth's crust1 whether that hole be made in the desert of ,sahara or through the icebound coasts of ,greenland1 we should find the general rule to obtain1 that there is an increase of temperature of about #hj for a mile of descent4 ,this is true in every continent1 it is true in every island2 and1 though we cannot here go into the evidence fully1 there is not the least doubt that it is true also under the floor of ocean4 ,if beneath the bed of the ,atlantic a hole a mile deep were pierced1 the temperature of the rocks at the bottom of that hole would1 it is believed1 exceed by about #hj the temperature of the rocks at the surface where the hole had its origin4 ,we learn that at the depth of a mile the temperature of the earth must generally be #hj hotter than it is at the level of constant temperature near the surface4 ,it may perhaps help us to realise the significance of this statement if we think of the following illustration4 ,let us imagine that the waters of the ocean were removed from the earth4 ,the ocean may in places be five or six miles deep1 but that is quite an inconsiderable quantity when compared with the diameter of the earth4 ,the change in the size of the earth by the removal of all the water would not be greater1 proportionally1 than the change produced in a wet football by simply wiping it dry4 ,let us suppose that an outer layer of the earth's surface1 a mile in thickness1 was then to be peeled off4 ,if we remember that the diameter of the earth is #h1jjj miles1 we shall see that this outer layer1 whose removal we have supposed1 does not bear to the whole extent of the earth a ratio even as great as that which the skin of a peach does to the fruit inside4 ,but this much is certain1 that if the earth were so peeled there would be a wonderful difference in its nature4 ,for though practically of the same size as it is at present1 it would be so hot that it would be impossible to live upon it4 ,next comes the very interesting question as to the temperature that would be found at the bottom of a hole deeper still than that we have been considering4 ,our curiosity as to the depths of the earth extends much below the point to which ,captain ,huyssen drove down his diamond drill4 ,the trouble and the cost of still deeper exploration of the same kind seem1 however1 to be actually prohibitive4 ,to bore a hole two miles deep would certainly cost a great deal more than twice the sum which sufficed to bore a hole one mile deep4 ,at a great depth each further foot could only be won with not less difficulty and expense than a dozen1 or many dozen feet1 at the surface4 ,mining enterprise does not at present seem to contemplate actual workings at depths much over a mile1 so there does not seem much chance of any very much deeper boring being attempted4 ,we do not say that a hole two miles deep would be actually impossible2 it may well be wished that some millionaire could be induced to try the experiment4 ,we should greatly like to be able to lower a thermometer down to a depth of two miles through the earth's crust4 ,seeing there is but little chance of our wish for such future experiments being gratified1 it is consolatory to find that actual observations of this kind are not indispensable to the argument on which we are to enter4 ,our argument can indeed be conducted a stage further1 even with our present information4 ,the indications already obtained in the hole one mile deep go a long way towards proving what the temperature of a hole still deeper would be4 ,we have already remarked that it was part of ,captain ,huyssen's scheme to obtain careful readings of his thermometer at intervals of #ajj feet from the surface to the bottom of the hole4 ,a study of these readings shows that the increase of #hj in a mile takes place uniformly at the rate of one degree for each sixty-six feet of depth4 ,as the temperature increases uniformly from the surface down to the lowest point which our thermometers have reached1 it would be unreasonable to suppose that the rate of increase would be found to suffer some abrupt change if it were possible to go a little deeper4 ,as the temperature rises #hj in the first mile1 and as the rate of increase is shown by the observations to be quite as large at the bottom of the hole as it is at the top1 we certainly shall not make any very great mistake if we venture to assume that in the second mile the temperature would also increase to an extent which will not be far from #hj4 ,this inference from the observations leads to the remarkable conclusion that at a depth of two miles the temperature of the earth must be1 we will not say exactly1 but at all events not very far from1 #afj higher than at the level of constant temperature about #ajj feet down4 ,as in the former case1 we need not confine ourselves to any particular locality in drawing this conclusion4 ,the arguments apply not only to the rocks underneath ,leipzig1 but to the rocks over every part of the globe1 whether on continents or islands1 or even if forming the base of an ocean4 ,no one denies that the law of increase in temperature with the depth must submit to some variation in accordance with local circumstances4 ,in essential features it may1 however1 be conceded that the law is the same over all the earth4 ,if we take #eb to be the temperature of the level #ajj feet down1 which limits the seasonal variations1 and if we add that at two miles further down the temperature is somewhere about #afj more1 we come to the conclusion that at a depth of a little over two miles the temperature of the rocks forming the earth's crust is about #bab ,fahrenheit4 ,thus we draw the important inference that if1 the oceans having been removed1 we were then to remove from the earth's surface a rind two miles thick--a thickness which1 it is to be observed1 is only the two-thousandth part of the earth's radius--we should transform the earth into a globe which1 while it still retained appreciably the same size1 would have such a temperature that even the coolest spot would be as hot as boiling water4 ,this is indeed a remarkable result4 ,and now that we have gone so far1 it is impossible for us to resist making a further attempt to determine what the temperature of the earth's crust must be if we could send a thermometer still lower4 ,a hole one mile deep we have seen2 ,i do not think we can hope to see a hole two miles deep1 but still it may not be absolutely impracticable2 but a hole of three or more miles deep we may safely regard as transcending present possibilities in engineering enterprise4 ,are we therefore to be deprived of all information as to the condition of our earth at depths exceeding those already considered8 ,fortunately we can learn something4 ,we are assisted by certain laws of heat1 and1 though the evidence on which we believe those laws is necessarily limited to the experience of ,nature as it comes within our observation1 yet it is impossible to refuse assent to the belief that the same laws will regulate the transmission of heat in the crust of the earth two miles1 three miles1 or many miles beneath our feet4 ,i represent1 in the diagram shown in ,fig4 #bc1 three consecutive beds of rock--,a1 ,b1 and ,c--as they lie in the earth's crust1 a little more than a mile beneath our feet4 ,i shall suppose that the bed ,b is the very lowest rock whose temperature was determined in the great boring4 ,the drill has passed completely through ,a1 it has pierced to the middle of ,b1 but it has not entered ,c4 ,the observations have shown that the temperature of the stratum ,b exceeds that of the stratum ,a1 and we further note that this is a permanent condition--that is to say1 ,b constantly remains hotter than ,a4 ,from this fact alone we can learn something as regards the temperature of the stratum ,c which lies in contact with ,b4 ,of course we are unable to observe the temperature of ,c directly1 because by hypothesis the boring tool has not entered that rock4 ,we can1 however1 prove1 from the laws of the conduction of heat1 that the temperature of ,c must be greater than that of ,b2 and this appears from the following consideration4 ,illustration3 ,fig4 #bc4--;,,at ,,the ,,bottom ,,of ,,the ,,great ,,bore4 ,it is plain that ,c must be either just the same temperature as ,b1 or it must be hotter than ,b1 or it must be colder than ,b4 ,if ,c were the same temperature as ,b1 then the law of conduction of heat tells us that no heat would flow from one of these strata to the other4 ,the laws of heat1 however1 assure us that when two bodies at different temperatures are in contact the heat will flow from the hotter of these bodies into the colder1 so long as the inequality of temperature is maintained4 ,as ,b is hotter than ,a1 then heat must necessarily flow from ,b into ,a1 and this flow must tend to equalise the temperature in these strata1 for ,b is losing heat while none is flowing into it from ,c4 ,therefore ,b and ,a could not continue to preserve indefinitely the different temperatures which observation shows them to do4 ,we are therefore forced to the conclusion that ,b and ,c cannot be at the same temperature4 ,next let us suppose that the temperature of the stratum ,b exceeded that of ,c4 ,then1 as ,a is colder than ,b1 it appears that ,b would be lying between two strata each having a temperature lower than itself4 ,but that1 of course1 cannot be a permanent arrangement1 for the heat would then escape from ,b on both sides4 ,the laws of heat1 therefore1 tell us that ,b could not possibly retain permanently a temperature above both ,a and ,c4 ,observation1 however1 shows that the temperatures of ,a and ,b are persistently unequal4 ,we are therefore obliged to reject the supposition that the temperature of ,c can be less than that of ,b4 ,we have thus demonstrated that the temperature of the stratum ,c cannot be the same as that of ,b4 ,we have also demonstrated that it cannot be colder than ,b4 ,we must therefore believe that ,c is hotter than ,b4 ,this proves that the stratum immediately beneath that stratum to which the observations have extended must be hotter than it4 ,thus1 though the stratum below the bottom of the hole lies beyond the reach of our actual observation1 we have1 nevertheless1 been able to learn something with regard to its temperature4 ,having established this much1 we can continue the same argument further2 indeed1 it would seem that we can continue it indefinitely1 so long as there is a succession of such strata4 ,underneath the stratum ,c must lie another stratum ,d4 ,but we have shown that ,c must be hotter than ,b1 and precisely the same argument that has proved this will prove that ,d is hotter than ,c4 ,underneath ,d comes the stratum ,e1 and again the same argument will apply4 ,inasmuch as ,d is hotter than ,c1 it follows that ,e must be hotter than ,d4 ,these three strata1 ,c1 ,d1 and ,e1 are all beyond the reach of the thermometer1 we know nothing of their temperatures by direct observation2 but none the less is the argument1 which we are following strictly1 applicable4 ,thus we obtain the important result that in the crust of the earth the temperature must be always greater1 the greater the depth beneath the surface4 ,we have seen that the rate of increase of temperature with the depth is about #hj for the first mile1 and we deem it probable that the rate of increase may be maintained at about the same for the second mile4 ,but we do not suppose that the rate of increase mile after mile will remain the same at extremely great depths4 ,it may perhaps be presumed that there must be some increase of temperature all the way to the earth's centre2 but the rate of increase per mile may change as the centre is approached4 ,the point of importance for our present argument is1 that the temperature of the earth must increase with the depth1 though the rate of increase is quite unknown to us at depths greatly beyond those which the thermometer has reached4 ,it is easy to see that the conditions prevailing in the earth's interior might greatly modify any conclusion we should draw from observations near the surface4 ,our argument has been based on the laws of heat1 as we find them existing in matter on the surface of the earth submitted to such ranges of different physical conditions as can be dealt with in our laboratories2 but at such excessively high temperatures as may exist in the earth's interior the properties of matter may be widely different from the properties of matter as known to us within the temperatures that we are able to produce and control4 ,the enormous pressure to which matter in the interior of the earth must be subjected should also be mentioned in this connection4 ,it is wholly impossible to produce pressures by any mechanical artifice which even distantly approach in intensity to that awful force to which matter is subjected in the earth's interior4 ,it may be instructive to consider a few facts with respect to this question of pressure in the earth's interior4 ,a column of water #cd feet high gives1 as everybody knows1 a pressure of fifteen pounds on the square inch4 ,it will be quite accurate enough for our present purpose to assume that the average density of rock is three times that of water3 the pressure of ten feet of rock would therefore produce the same pressure as thirty feet of water1 that is to say1 fifteen pounds on the square inch4 ,the pressure due to the superincumbent weight of a mile of rock would be more than three tons on the square inch4 ,at the depth of ten miles beneath the earth's surface the pressure1 amounting as it does to over thirty tons on the square inch1 would very nearly equal the pressure produced on the inside of a #ajj-ton gun when the charge of cordite has been exploded to drive the missile forth4 ,this is indeed about as large a pressure as can well be dealt with artificially1 for we know that the #ajj-ton gun has to be enormously strong if it is to resist this pressure4 ,but ten miles of rock is as nothing compared with the thickness of rock that produces the pressures in the earth's interior4 ,even if a shell of rocks ten miles thick were removed from the surface it would alter the diameter of our globe by no more than one four-hundredth part4 ,at the depth of about thirty miles from the surface the pressure in the earth's interior would amount to some #ajj tons on each square inch4 ,with each increase in depth the pressure increases enormously1 though it may not be correct to say that the pressure is proportional to the depth4 ,a pressure of #a1jjj tons on the square inch must exist at a depth which is still quite small in comparison with the radius of the earth4 ,we have not1 and apparently cannot have1 the least experimental knowledge of the properties of matter at the moment when it is subjected to pressure amounting to thousands of tons per square inch2 still less can we determine the behaviour of matter at that pressure of scores of thousands of tons1 to which much of the interior of the earth is at this moment subjected4 ,professor ,dewar1 in his memorable researches1 has revealed to us the remarkable changes exhibited in the properties of matter when that matter has been cooled to a temperature which lies in the vicinity of absolute zero4 ,we can1 however1 hardly hope that any experiments will give us information as to the properties of matter when heated to a temperature vastly transcending that which could ever be produced in our most powerful electric furnaces1 and at the same time exposed to a pressure hundreds of times1 or indeed we may say thousands of times1 greater than any pressure that has ever been produced artificially by the action of the most violent explosive with which the discoveries of chemistry have made us acquainted4 ,illustration3 ,fig4 #bd4--,,three ,,consecutive ,,shells ,,of ,,the ,,earth',s ,,crust4 ,we really do not know how far the laws of heat1 which have been employed in showing that the temperature must increase as the depth increases1 can be considered as valid under the extreme condition to which matter is subjected in the deep interior of our globe4 ,the laws may be profoundly modified4 ,it suffices1 fortunately for our present argument1 to say that1 so far as observations have been possible1 the temperature does gradually increase with the depth1 and that this increase must still continue from stratum to stratum as greater depths are reached1 unless it should be found that by the excessive exaltation of temperature and the vast intensity of pressure certain properties of matter become so transformed as to render the laws of heat1 as we know them1 inapplicable4 ,in subsequent chapters we shall have some further points to consider with respect to the interior of the earth and its physical characteristics1 which are1 however1 not necessary for our present argument4 ,what we now desire to prove can be deduced from the demonstrated fact that the earth's temperature does steadily increase from the level of constant temperature1 #ajj feet below the surface1 down to the greatest depth to which thermometers have ever been lowered4 ,we may presume that the same law holds at very much greater depths1 even if it does not hold all the way to the centre4 ,to make our argument clear1 let us think of three different strata of rock4 ,this time1 however1 we shall suppose them to cover the whole earth1 and we shall consider them to lie within the first mile from the surface2 they will thus be well within the region explored by observation 7,fig4 #bd74 ,we shall also regard them as shells of uniform thickness1 and it will be convenient to think of them as being so very thin that we may consider any one of the shells called ,a to have practically a uniform temperature4 ,the next shell ,b immediately inside ,a will have a slightly greater temperature1 and be also regarded as uniform1 and the shell immediately inside that again will have a temperature greater still4 ,we shall call the innermost of the three shells ,c1 and ,c is hotter than the next outer shell ,b1 while ,b is hotter than ,a4 ,the laws of heat tell us that as ,b and ,a are in contact1 and that as ,b is continually hotter than ,a1 then ,b must be continuously transmitting heat to ,a4 ,in fact1 ,b appears to be constantly endeavouring to reduce itself to the temperature of ,a by sharing with ,a the excess of temperature which it possesses4 ,but if we consider the relation between the shell ,b and the hotter shell ,c1 immediately beneath it1 we see that precisely the same argument will show that ,b is constantly receiving heat from ,c4 ,we thus see that while ,b is continuously discharging heat from its outside surface1 it is as constantly receiving heat which enters through its inside surface4 ,heat enters ,b from ,c1 and heat passes from ,b into ,a1 so that ,b is in fact a channel through which heat passes from ,c into ,a4 ,that which we have shown to take place in those three consecutive layers in the earth's crust must also take place in every three consecutive layers4 ,each layer is continually receiving heat from the layer below1 and is as constantly communicating heat to the layer above4 ,no doubt the rocks are very bad conductors of heat1 so that the transmission of heat from layer to layer is a very slow process4 ,but even if this flow of heat be slow1 it is incessant1 so that in the course of ages large quantities of heat are gradually transmitted from the earth's interior1 and ultimately reach the level of constant temperature4 ,there is nothing1 however1 to impede their outward progress1 so at last the heat reaches the earth's surface4 ,when the surface has been reached1 then another law of heat declares what must happen next4 ,it is1 of course1 by conduction that the heat passes from layer to layer in its outward progress1 until it ultimately gains the surface4 ,at the surface the heat is then absolutely removed from the solid earth either by the convection through the air or by direct radiation into space4 ,i may here interrupt the argument for a moment to make quite clear a point which might perhaps otherwise offer some difficulty to the reader4 ,when this outward flow of heat reaches the superficial layers it becomes1 of course1 mixed up with the heat which has been absorbed by the soil from the direct radiation of the sun1 and this varies1 of course1 with the hour of the day and with the season of the year4 ,the heat which steadily leaks from the interior has an effect on the rocks near the surface1 which is only infinitesimal in comparison with the heat which they receive from periodic causes4 ,we may1 however1 say that whatever would be the temperature of the rock1 so far as the periodic causes are concerned1 the actual temperature is always to some minute extent increased by reason of the heat from the earth's interior4 ,the argument is1 perhaps1 still clearer if1 instead of attending to the earth's surface1 we think only of that shell1 some #ajj feet down1 which marks the limit of the depth to which the seasonal and diurnal variations of heat extend4 ,the argument shows how the internal heat of the earth1 passing from shell to shell in the interior1 reaches this layer of constant temperature1 and passing through it1 enters into those superficial strata of the earth which are exposed to the seasonal variations4 ,with what befalls that heat ultimately we need not now concern ourselves2 it suffices for our argument to show that there is a current of heat outward across this level4 ,it is a current which is never reversed1 and consequently must produce a never-ceasing drainage from the heat with which it would seem that the interior of the earth is so copiously provided4 ,calculations have been made to ascertain how much heat passes annually from the earth's interior1 across this surface of constant temperature1 out into the superficial regions from which in due course it becomes lost by radiation4 ,a convenient way of measuring a quantity of heat is by the amount of ice it will melt1 for of course a definite quantity of heat is required to melt a definite quantity of ice4 ,it has been estimated by ,professor ,j4 ,d4 ,everett1 ,f4,r4,s41 that the amount of internal heat escaping from our earth each year would be sufficient to melt a shell of ice one-fifth of an inch thick over the whole surface of the globe4 ,we cannot indeed pretend that any determination of the actual loss of heat which our earth experiences could be very precise4 ,sufficient observations have not yet been obtained1 for the operation is so slow that an immense period would have to elapse before the total quantity of heat lost would be sufficient to produce effects large enough to be measured accurately4 ,but now let us hasten to add that1 for the argument as to the nebular theory with which we are at present concerned1 it is not really material to know the precise rate at which heat is lost4 ,it is absolutely certain that a perennial leakage of heat from the interior of the earth does take place4 ,this fact1 and not the amount of that leakage1 is the essential point4 ,and this loss1 which is at present going on1 has been going on continually4 ,heat from the earth has been lost this year and last year2 it has been lost for hundreds of years and for thousands of years4 ,not alone during the periods of human history has the earth's heat been declining4 ,even throughout those periods1 those overwhelming periods which geology has revealed to us1 has this earth of ours been slowly parting with its heat4 ,let us pursue this reflection to its legitimate consequence4 ,whatever may ultimately become of that heat1 it is certain that once radiated into space it is lost for ever so far as this globe is concerned4 ,you must not imagine that the warm beams of the sun possess any power of replenishment by which they can restore to the earth the heat which it has been squandering for unlimited ages2 we have already explained that the effect of the heat radiated to us from the sun is purely superficial4 ,even amid the glories of the tropics1 even in the burning heat of the desert1 the vertical sun produces no appreciable effects at depths greater than this critical limit1 which is about #ajj feet below the surface4 ,the rigours of an ,arctic winter have as little effect in reducing the temperature of the rocks at that depth as the torrid heat at the ,equator has in raising it4 ,the effect in each case is nothing4 ,the argument which we are here employing to deduce the nebulous origin of our earth from the increase of temperature with increase in depth in the earth's crust must be cleared from an objection4 ,it is necessary to explain the matter fully1 because it touches on a doctrine of very great interest and importance4 ,that a rotating body should possess a quantity of energy in virtue of its rotation will be familiar to anyone who has ever turned a grindstone or watched the fly-wheel of an engine4 ,a certain amount of work has to be expended to set the heavy wheel into rotation1 and when the machine is called upon to do work it will yield up energy and its motion will undergo a corresponding abatement4 ,the heavy fly-wheel of the machine in a rolling mill contains1 in virtue of its motion1 enough energy to overcome the tremendous resistance of the materials submitted to it4 ,once upon a time the earth revolved upon its axis in six hours1 instead of in the twenty-four hours which it now requires4 ,at that time the energy of the rotation must have been sixteenfold what it is at present4 ,this consideration shows that fifteen-sixteenths of the energy that the earth originally possessed in its rotation has disappeared1 and we want to know what has become of it4 ,we are here entering upon a matter of some difficulty4 ,it is connected with that remarkable chapter in astronomy which describes the evolution of the earth-moon system4 ,the moon was originally a part of the earth1 for in very early times1 when the earth was still in a plastic state1 a separation would seem to have taken place1 by which a small piece broke off to form the moon1 which has been gradually revolving in an enlarging orbit until it has attained the position it now occupies4 ,a considerable portion of the energy of the earth's rotation has been applied to the purpose of driving the moon out to its present path1 but there is a large remainder which cannot be so accounted for4 ,it is well known that the evolution of the moon has been a remarkable consequence of tidal action4 ,there are tides which sway to and fro in the waters on the earth's surface2 there are tides in any molten or viscous matter that the earth may contain1 and there are even certain small tidal displacements in the solid material of our globe4 ,tides of any kind will generate friction1 and friction produces heat1 and the energy of the earth's rotation1 which we have not been able to account for otherwise1 has been thus transformed into heat4 ,throughout the whole interior of the earth heat has been produced by the tidal displacement of its parts4 ,the question therefore arises as to whether the internal heat of the earth may not receive an adequate explanation from this tidal action1 which is certainly sufficient as to quantity4 ,it is easy to calculate what the total quantity of this tidal heat may have been4 ,we know the energy which the earth had when it rotated in six hours1 and we know that it now retains no more than a sixteenth of that amount4 ,we know also precisely how much was absorbed in the removal of the moon1 and the balance can be evaluated in heat4 ,it can be shown1 and the fact is a very striking one1 that the quantity of heat thus arising would be sufficient to account many times over for the internal heat of the earth4 ,it might therefore be urged plausibly that the internal heat which we actually find has had its origin in this way4 ,and if this were the case the argument which we are using in favour of the nebular origin of the earth1 would be1 of course1 invalidated4 ,we may state the issue in a slightly different manner1 as follows4 ,heat there is undoubtedly in the earth2 that heat might have come from the primval nebula as we have supposed1 and as in actual fact it did come4 ,but apparently it might have come from the tidal friction4 ,why then are we entitled to reject the latter view1 and say that the tidal friction will not explain the internal heat1 and why are we compelled to fall back on the only other explanation8 ,lord ,kelvin suggested a test for deciding to which of these two sources the earth's internal heat was to be attributed4 ,professor ,g4 ,h4 ,darwin applied the test and decided the issue4 ,we have dwelt upon the rate at which the heat increases with the descent1 this rate being about one degree every sixty-six feet4 ,now the distribution of the heat1 if it had come from the tidal action1 would be quite different from the distribution which would result from the gradual efflux of heat from the centre in the process of cooling4 ,and1 speaking quite generally1 we may surmise that the heat produced by tidal friction would be distributed rather more towards the exterior of the earth than at its centre4 ,we might therefore reasonably expect that if the internal heat of the earth arose from tidal friction it would be more uniformly distributed throughout the globe1 and there would not be so great a contrast between the high temperature of the interior and the lesser temperatures near the surface as there is when the heat distribution is merely the result of cooling4 ,it has been proved that if the internal heat had its origin from the tidal friction1 the rate of increase with the depth would be totally different from what it is actually found to be4 ,it would be necessary to go down #b1jjj feet to obtain an increase of one degree1 instead of only sixty-six feet1 as is actually the case4 ,hence we conclude that the increasing heat met with in descending through the earth's crust is not accounted for by tidal friction2 it has its origin in the other alternative1 namely1 from the cooling of the primval nebula4 ,the heat which was undoubtedly produced by the tidal friction has gradually become blended with the heat from the other1 and1 as we must now say1 the principal source4 ,the facts with regard to the rate of increase with depth thus show that1 whatever the tides may have done in producing internal heat1 there has been another and a still more potent cause in operation4 ,the important conclusion for our present purpose is that our argument may justly proceed without taking account of the effect of tidal friction4 ,we are led by these considerations to a knowledge of a great transformation in the nature of our globe which must have occurred in the course of ages4 ,we have seen that this earth is gradually losing heat from its interior1 and we have seen that this loss of heat is incessant4 ,from the fountains of heat1 still so copious1 in the interior the supply is gradually dissipating4 ,now heat is only a form of energy1 and energy1 like matter1 cannot itself be created out of nothing4 ,there can be no creation of heat in our earth without a corresponding expenditure of energy4 ,if1 therefore1 the earth is radiating heat1 then1 as there is no known or1 indeed1 conceivable source of energy by which an equivalent can be restored1 it follows that the earth must have less internal heat now than it had at any earlier period4 ,no doubt the process of cooling is excessively slow4 ,the earth has less internal heat at present than it had a hundred years ago1 but ,i do not suppose that even in a thousand years1 or perhaps in ten thousand years1 there would be any appreciable decline in the quantity of heat1 so far as any obvious manifestations of that heat are concerned4 ,it is1 however1 certain that the earth must have been hotter1 even though there are not any observations to which we can appeal to verify the statement2 and as our retrospect extends further and still further through the ages we see that the globe must have been ever hotter and ever still hotter4 ,whatever be the heat contained in our earth now1 it must have contained vastly more heat ten million years ago2 how otherwise could the daily leakage of heat for all those ten million years have been supplied8 ,it follows that there must have been much more heat somewhere in our earth ten million years ago than there is at present1 and the further our retrospect extends the hotter do we find the earth to have been4 ,there was a time when the temperature of the earth's surface must have been warmed not alone by such sunbeams as fell upon it1 but by the passage of the heat from the interior4 ,no matter how early be the period which we consider1 we find the same causes to be in operation4 ,there was a time when1 owing to the internal heat1 the surface of the earth must have been as hot as boiling water4 ,the loss of heat by radiation must then have taken place much more copiously than it does at present4 ,the argument we are pursuing must therefore have applied with even greater force in those early days4 ,there was a time when the materials at the surface of the earth must have been intensely heated1 when they must have even been red-hot4 ,there was a time when the earth's surface must have had a temperature like that of the lava as it issues from a volcano4 ,there must have been a time when the surface of the earth was not even solid1 when indeed it was a viscid liquid1 and earlier still the liquid must have been more and more incandescent4 ,from that brilliant surface heat was vehemently radiated4 ,each day the globe was hotter than on the succeeding day4 ,there is no break in the argument4 ,we have to think of this glowing globe passing through those phases through which we know that all matter will pass if only we apply to it sufficient heat4 ,the globe assumed the liquid state from that state which is demanded by a temperature still higher1 the state in which the matter is actually in the form of vapour4 ,even the most refractory substances will take the form of vapour at a very high temperature4 ,thus we are conducted to a remarkable conception of the condition in which the materials now forming our solid earth must have been in the exceedingly remote past4 ,what is now our earth must once have been a great quantity of heated vapour4 ,it need hardly be said that in that form the volume of the earth was much larger than the volume which the earth has at present1 while no doubt the mass of the earth then was even less than the mass of the earth now1 by reason of the meteoric matter which has been drawn in by our globe4 ,but even when our earth was in this inflated state of vapour our argument can be still maintained4 ,thus we see that the earth1 or rather the cloud of vapour which was ultimately to form the earth1 is ever growing larger and larger in our retrospect1 ever becoming more and more rarefied2 and it may well have been that there was a time when the materials of this earth occupied a volume thousands of times greater than they do at present4 ,in a previous chapter we have seen how the sun was at one time in the nebulous state1 and now we have been led to a similar conclusion with regard to the earth4 ,at that time1 of course1 the sun was greatly in excess of its present dimensions1 and the earth was also greatly swollen4 ,the nebula which formed our sun1 and the nebula which formed our earth1 were both so vast as to be confluent2 they were indeed both part of the same vast nebula4 ,such has been the ,earth's ,beginning so far as modern science can make it clear to us4 ,we have at least indicated the course which events must have taken according to the laws of nature as we understand them4 ,many of the details of the great evolution are no doubt unknown at present1 and perhaps must ever remain so4 ,that the events which we have endeavoured to describe do substantially represent the actual evolution of our system is the famous ,nebular ,theory4 ---------------------------------------- -------------------------------- ,,chapter ,,ix4 ,,earthquakes ,,and ,,volcanoes4 ,interior of the ,earth--,illustration from ,norway--,solids and ,liquids--,rigidity of the ,interior of the ,earth--,earthquakes1 how caused--,their ,testimony as to the ,rigidity of the ,earth--,delicate ,instrument for ,measuring ,earthquake ,tremors--,the ,seismometer--,professor ,milne's ,work in the ,isle of ,wight--,different ,earthquake ,groups--,precursors and ,echoes--,vibrations transmitted through the ,earth's ,centre--,earthquakes in ,england--,other ,evidence of the ,earth's ,rigidity--,krakatoa1 ,august #bgth1 #ahhc--,the ,sounds from ,krakatoa--,the ,diverging ,waves--,the ,krakatoa ,dust--,the ,hurricane ,overhead--,strange ,signs in the ,heavens--,the ,blood-red ,skies4 ,,in this chapter we shall learn what we can as to the physical condition of the interior of our earth so far as it may be reasonably inferred from the facts of observation4 ,we have already explained in the last chapter that a very high temperature must be found at the depth of even a small fraction of the earth's radius1 and we have pointed out that the excessively high pressure characteristic of the earth's interior must be borne in mind in any consideration as to the condition of the matter there found4 ,let us take1 for instance1 that primary question in terrestrial physics1 as to whether the interior of the earth is liquid or solid4 ,if we were to judge merely from the temperatures reasonably believed to exist at a depth of some twenty miles1 and if we might overlook the question of pressure1 we should certainly say that the earth's interior must be in a fluid state4 ,it seems at least certain that the temperatures to be found at depths of two score miles1 and still more at greater depths1 must be so high that the most refractory solids1 whether metals or minerals1 would at once yield if we could subject them to such temperatures in our laboratories4 ,at such temperatures every metal would become fluid1 even if it were not transformed into a cloud of vapour4 ,but none of our laboratory experiments can tell us whether1 under the pressure of thousands of tons on the square inch1 the application of any heat whatever would be adequate to transform solids into liquids4 ,it may indeed be reasonably doubted whether the terms solids and liquids are applicable1 in the sense in which we understand them1 to the materials forming the interior of the earth4 ,it was my good fortune some years ago to enjoy a most interesting trip to ,norway1 in company with a distinguished geologist4 ,under his guidance ,i there saw evidence which demonstrates conclusively that1 when subjected to great pressure1 solids1 as we should call them1 behave in a manner which1 if not that of actual liquids1 resembles at all events in some of its characteristics the behaviour of liquids4 ,these rocks in some places are conglomerates1 of which the leading constituents are water-worn pebbles of granite4 ,these pebbles are of various sizes1 from marbles to paving-stones4 ,in some parts of the country these granite pebbles remain in the form which they acquired on the beach on which they were rolled by the primval ocean2 in other parts of the same interesting region the form of the pebbles has been greatly changed from what it was originally4 ,for in the course of geological periods1 and after the pebbles had become consolidated into the conglomerate1 the rock so formed had been in some cases submitted to enormous pressure4 ,this may have been lateral pressure1 such as is found to have occurred in many other places1 where it has produced the well-known geological phenomenon of strata crumpled into folds4 ,in the present case1 however1 it seemed more probable that it was the actual weight of the superincumbent rocks1 which once lay over these beds of conglomerate1 which produced the surprising transformation4 ,it seems to be not at all improbable that at one time these beds of conglomerate must have been covered with strata of which the thickness is so great that it may actually be estimated by miles4 ,there has1 however1 been immense denudation of the superficial rocks in this part1 at all events1 of ,norway1 so that in the course of ages these strata1 overlying the conglomerate for ages1 have been so far worn away1 and indeed removed1 by the action of ice and the action of water that the conglomerate is now exposed to view4 ,it offers for our examination striking indications of the enormous pressure to which it was subjected during the incalculable ages of geological time4 ,the effect of this long continuance of great pressure upon the pebbles of the conglomerate in certain parts of the country has been most astonishing4 ,the granite in the pebbles still retains its characteristic crystalline structure2 it has obviously not undergone anything that could be described as fusion2 yet under the influence of the two factors of that pressure1 namely1 its intensity and its long continuance1 the granite pebbles have yielded4 ,in some cases they are slightly elongated1 in others they are much elongated1 while in yet others they are even rolled out flat4 ,at different places along the valley the various phases of the transformation can be studied4 ,we can find places where the pebbles seem little altered1 and then we can trace each stage until the solid granite pebbles have1 by the application of excessive pressure1 been compressed into thin sheets whose character it would not have been easy to divine if it had not been possible to trace out their history4 ,these sheets lie close and parallel1 so that the material thus produced acquires some of the characteristics of slate4 ,it splits easily along the flattened sheets1 and this rolled-out conglomerate is indeed actually used as a substitute for slate1 and in some places there are houses roofed with the conglomerate which has been treated in this extraordinary fashion4 ,this fact will illustrate a principle1 already well known in the arts1 that many1 if not all1 solids may be made to flow like liquids if only adequate pressure be applied4 ,the making of lead tubes is a well-known practical illustration of the same principle1 for these tubes are simply formed by forcing solid lead by the hydraulic press through a mould which imparts the desired form4 ,if then a solid can be made to behave like a liquid1 even with such pressures as are within our control1 how are we to suppose that the solids would behave with such pressures as those to which they are subjected in the interior of the earth8 ,the fact is that the terms solid and liquid1 at least as we understand them1 appear to have no physical meaning with regard to bodies subjected to these stupendous pressures1 and this must be carefully borne in mind when we are discussing the nature of the interior of the earth4 ,it must1 however1 be admitted that the interior of the earth in its actual physical state seems to possess at least one of the most important characteristics of a solid1 for it seems to be intensely rigid4 ,we mean by this1 that the material of the earth1 or rather each particle of that material1 is very little inclined to move from its position with reference to the adjacent particles by the application of force4 ,possibly a liquid1 such as water1 might not behave very differently in this respect from a solid such as cast iron1 if each of them were exposed to a pressure of scores of thousands of tons per square inch1 as are the materials which form the great bulk of the earth4 ,but1 without speculating on these points1 we are able to demonstrate that the earth1 as a whole1 does exhibit extreme rigidity4 ,this is one of the most remarkable discoveries which has ever been made with regard to the physics of our earth4 ,the discovery that the earth is so rigid is mainly due to ,lord ,kelvin4 ,we shall now mention the line of evidence which appears to prove1 in the simplest and most direct manner1 the excessive rigidity of our earth4 ,it is derived from the study of earthquake phenomena1 and we must endeavour to set it forth with the completeness its importance deserves4 ,as to the immediate cause of earthquakes1 there is no doubt considerable difference of opinion4 ,but ,i think it will not be doubted that an earthquake is one of the consequences1 though perhaps a remote one1 of the gradual loss of internal heat from the earth4 ,as this terrestrial heat is gradually declining1 it follows from the law that we have already so often had occasion to use that the bulk of the earth must be shrinking4 ,no doubt the diminution in the earth's diameter1 due to the loss of heat must be excessively small1 even in a long period of time4 ,the cause1 however1 is continually in operation1 and accordingly the crust of the earth has1 from time to time1 to be accommodated to the fact that the whole globe is lessening4 ,the circumference of our earth at the ,equator must be gradually declining2 a certain length in that circumference is lost each year4 ,we may admit that loss to be a quantity far too small to be measured by any observations as yet obtainable1 but1 nevertheless1 it is productive of phenomena so important that it cannot be overlooked4 ,it follows from these considerations that the rocks which form the earth's crust over the surface of the continents and the islands1 or beneath the beds of ocean1 must have a lessening acreage year by year4 ,these rocks must therefore submit to compression1 either continuously or from time to time1 and the necessary yielding of the rocks will in general take place in those regions where the materials of the earth's crust happen to have comparatively small powers of resistance4 ,the acts of compression will often1 and perhaps generally1 not proceed with uniformity1 but rather with small successive shifts1 and even though the displacements of the rocks in these shifts be actually very small1 yet the pressures to which the rocks are subjected are so vast that a very small shift may correspond to a very great terrestrial disturbance4 ,suppose1 for instance1 that there is a slight shift in the rocks on each side of a crack1 or fault1 at a depth of ten miles4 ,it must be remembered that the pressure ten miles down would be about thirty-five tons on the square inch4 ,even a slight displacement of one extensive surface over another1 the sides being pressed together with a force of thirty-five tons on the square inch1 would be an operation necessarily accompanied by violence greatly exceeding that which we might expect from so small a displacement if the forces concerned had been only of more ordinary magnitude4 ,on account of this great multiplication of the intensity of the phenomenon1 merely a small rearrangement of the rocks in the crust of the earth1 in pursuance of the necessary work of accommodating its volume to the perpetual shrinkage1 might produce an excessively violent shock extending far and wide4 ,the effect of such a shock would be propagated in the form of waves through the globe1 just as a violent blow given at one end of a bar of iron by a hammer is propagated through the bar in the form of waves4 ,when the effect of this internal adjustment reaches the earth's surface1 it will sometimes be great enough to be perceptible in the shaking it gives that surface4 ,the shaking may be so violent that buildings may not be able to withstand it4 ,such is the phenomenon of an earthquake4 ,earthquakes have been made to yield testimony of the most striking character with regard to the rigidity of the earth4 ,the researches we are now to describe are mainly due to ,professor ,milne1 who1 having enjoyed the advantage of studying earthquakes in their natural home in ,japan1 where are to be found some of the most earthquake-shaken regions of this earth1 has now transferred his observations of these phenomena to the more peaceful regions of the ,isle of ,wight4 ,but though the ,isle of ,wight is perhaps one of the last places in the world to which anyone who desired to experience violent earthquake shocks would be likely to go1 yet by the help of a beautiful apparatus ,professor ,milne is actually able to witness important earthquakes that are happening all over the world4 ,he has a demonstration of these earthquakes in the indications of an extremely sensitive instrument which he has erected in his home at ,shide4 ,when our earth is shaken by one of those occasional adjustments of the crust which ,i have described1 the wave that spreads like a pulsation from the centre of agitation extends all over our globe and1 indeed ,i may say1 is transmitted right through it4 ,at the surface lying immediately over the centre of disturbance there will be a violent shock4 ,in the surrounding country1 and often over great distances1 the earthquake may also be powerful enough to produce destructive effects4 ,the convulsion may also be manifested over a far larger area of country in a way which makes the shock to be felt1 though the damage wrought may not be appreciable4 ,but beyond a limited distance from the centre of the agitation the earthquake will produce no destructive effects upon buildings1 and will not even cause vibrations that would be appreciable to ordinary observation4 ,this earth of ours may transmit from an earthquake pulses of a very distinct and definite character1 which are too weak to be perceived by our unaided senses2 but1 just as the microscope will render objects visible which are too minute to be perceived without this aid to the ordinary vision1 so these faint earth-pulses may be rendered perceptible by the delicate indications of an instrument which perceives and records tremors that would pass unnoticed by our ordinary observations4 ,the ingenious instrument for studying earthquakes is called a seismometer4 ,it marks on a revolving drum of paper the particulars of those infinitesimal tremors by which the earth is almost daily agitated in one place or another4 ,let us suppose1 for example1 that an earthquake occurs in ,japan1 in which much agitated country it is1 ,i believe1 estimated that no fewer than one thousand earthquakes of varying degrees of intensity occur annually in one district or another4 ,let us suppose that this earthquake behaves as serious earthquakes usually do2 that it knocks down buildings and monuments1 causes landslips1 raises great waves in the sea and hurls them as inundations on the land4 ,we may also suppose that it issues tragically in the loss of many lives and that there is a destruction of much property1 and that its energies in the acutely violent form extend over1 let us say1 an area of a hundred square miles4 ,beyond that area of greatest destruction such an earthquake would be felt over a great extent of country as a shaking more or less vehement1 and characteristic rumbling sounds would be heard4 ,but the intensity declines with the distance1 and we may feel confident that not even the faintest indications of the earthquake would be perceptible by the unaided senses at a thousand miles from its origin4 ,a thousand miles is1 however1 less than a fifth of the distance between ,tokio and ,shide1 in the ,isle of ,wight1 measured in a great circle round the earth's surface4 ,the acutest sense could not perceive the slightest indication of the convulsion in ,japan at even half the distance between these two places4 ,but the earth transmits so faithfully the undulations committed to its care that though the intensity may have declined so as to be no longer perceptible to the unaided sense1 it is still possible that they may be shown distinctly on the seismometer in ,professor ,milne's laboratory1 even after a journey of five thousand miles4 ,this instrument not only announces that an earthquake has been in progress some little time previously1 but the recording pencil reproduces with marvellous fidelity some actual details of the vibration4 ,the movements of the line up and down on the revolving drum of paper show how the convulsions succeed each other1 and their varying intensity4 ,thus ,professor ,milne is enabled to set down some features of the earthquake long before the post brings an account of the convulsion from the unhappy locality4 ,professor ,milne's account of work in studying earthquakes has the charm of a romance1 even while it faithfully sets out the facts of ,nature4 ,i have supposed the earthquake to take place in ,japan2 but we must observe that the seismometer at ,shide will also take account of considerable earthquakes in whatever part of the world the disturbance may arise4 ,there are1 for example1 localities in the ,west ,indies in which earthquakes are by no means infrequent1 though they may not be phenomena of almost daily occurrence1 as they are in ,japan4 ,every considerable earthquake1 no matter where its centre may lie1 produces in our whole globe a vibration or a tingle which is sufficient to be manifested by the delicate indications of the seismometer at ,shide4 ,thus this instrument1 which in the morning may record an earthquake from ,japan1 will in the afternoon of the same day delineate with equal fidelity an earthquake from the opposite hemisphere in the neighbourhood of the ,caribbean ,sea4 ,in each locality in which earthquakes are chronic it would seem as if there must be some particularly weak spot in the earth some miles below the surface4 ,a shrinkage of the earth1 in the course of the incessant adjustment between the interior and the exterior1 will take place by occasional little jumps at this particular centre4 ,the fact that there is this weak spot at which small adjustments are possible may provide1 as it were1 a safety-valve for other places in the same part of the world4 ,instead of a general shrinking1 the materials would be sufficiently elastic and flexible to allow the shrinking for a very large area to be done at this particular locality4 ,in this way we may explain the fact that immense tracts on the earth are practically free from earthquakes of a serious character1 while in the less fortunate regions the earthquakes are more or less perennial4 ,the characteristics of an earthquake record1 a seismogram1 if we give it the correct designation1 depend on the distance of the origin from the locality where the record is made4 ,the length of the journey1 as might be expected1 tells on the character of the inscription which the earthquake waves make on the drum4 ,if1 for instance1 the first intimation of a large earthquake received at ,shide precedes the second by about thirty-five minutes1 it may be concluded that the earthquake has come from ,japan4 ,in like manner the shocks1 with their origin in the ,west ,indies1 will proceed from their particular earthquake centre1 and consequently all the earthquakes from this source will possess a characteristic resemblance4 ,the ,japan group of earthquakes will have1 so to speak1 a family resemblance2 and the ,trinidad group of earthquakes1 though quite different from the ,japan group1 will also possess a family resemblance4 ,these features are faithfully transmitted by undulations through the earth and round the earth2 thus in due course they reach the ,isle of ,wight1 and they are reproduced by the pencil of the seismometer4 ,the different earthquakes of a family may differ in size1 in intensity1 and undulation1 but they will have the features appropriate to the particular group from which they come4 ,from long experience ,professor ,milne has become so familiar with the lineaments of these earthquake families1 that in his study at ,shide1 as he looks at the indications of his instrument1 he is able to say1 for example1 8,here is an earthquake1 and it is a little earthquake from ,japan20 then a little later1 when a new earthquake begins1 he will say1 8,and here is a big earthquake from ,trinidad40 ,professor ,milne's apparatus has brought us remarkable information with regard to the interior of the earth4 ,the story which we have to tell is really one of the most astonishing in physical science4 ,let us suppose that an earthquake originates in ,japan4 ,we shall assume that the earthquake is a vigorous one1 capable of producing bold and definite indications on the seismometer even in the ,isle of ,wight4 ,it is to be noted that this instrument is not content merely with a single version of the story of that earthquake2 it will indeed repeat that story twice more4 ,first of all1 about a quarter of an hour after a shock has taken place in ,japan1 the pencil of the seismometer commences to record4 ,but this record1 though quite distinct1 is not so boldly indicated as the subsequent records of the same event which will presently be received4 ,it is to be regarded as a precursor4 ,after the first record is completed there is a pause of perhaps three-quarters of an hour1 and then the pencil of the seismometer commences again4 ,it commences to give an earthquake record1 but it is obviously only a second version of the same earthquake4 ,for the ups and downs traced by the pencil are just the same relatively as before4 ,the picture given of the earthquake is1 however1 on a much larger scale than the one that is first sent4 ,the extent of the shaking of the instrument in this second record is greater than in the first1 and all the details are more boldly drawn4 ,after the second diagram has been received1 there is yet another pause1 which may be perhaps for half an hour4 ,then1 by the same pencil1 a third and last version is conveyed to the seismometer4 ,this diagram is not quite so strong as the last1 though stronger than the first2 in it again1 however1 the faithful pencil tells1 with many a detail1 what happened in this earthquake at ,japan4 ,we have first to explain how it occurs that there are three versions of the event1 for it need hardly be said that the same earthquake did not take place three different times over4 ,the point is indeed a beautiful one4 ,the explanation is so astonishing that we should hardly credit it were it not established upon evidence that does not admit of a moment's question4 ,illustration3 ,fig4 #be4--;,,earthquake ,,routes ,,from ,,japan ,,to ,,the ,,isle ,,of ,,wight4 ,in the adjoining diagram we represent the position of ,japan at one side of the earth1 and the ,isle of ,wight at the other4 ,when the earthquake takes place at ,japan it originates1 as we have said1 a series of vibrations through our globe4 ,we must here distinguish between the rocks--,i might almost say the comparatively pliant rocks--which form the earth's crust1 and those which form the intensely rigid core of the interior of our globe4 ,the vibrations which carry the tidings of the earthquake spread through the rocks on the surface1 from the centre of the disturbance1 in gradually enlarging circles4 ,we may liken the spread of these vibrations to the ripples in a pool of water which diverge from the spot where a raindrop has fallen1 or to the remarkable air-waves from ,krakatoa1 to which we shall presently refer4 ,the vibrations transmitted by the rocks on the surface1 or on the floor of the ocean1 will carry the message all over the earth4 ,as these rocks are flexible1 at all events by comparison with the earth's interior1 the vibrations will be correspondingly large1 and will travel with vigour over land and under sea4 ,in due time they reach the ,isle of ,wight1 where they set the pencil of the seismometer at work4 ,but there are different ways round the earth from ,japan to the ,isle of ,wight4 ,there is the most direct route across ,asia and ,europe2 there is also the route across the ,pacific1 ,america1 and the ,atlantic4 ,the vibrations will travel by both routes1 and the former is the shorter of the two4 ,the vibrations which take the first route through the crust of the earth's surface are travelling by the shorter distance2 they consequently reach ,shide first1 and render their version of what has happened4 ,but the vibrations which1 starting from the centre of the disturbance1 move through the earth's crust in an opposite direction will also in their due course of expansion reach the ,isle of ,wight4 ,they will have had a longer journey1 and will consequently be somewhat enfeebled1 though they will still retain the characteristics marking the particular earthquake centre from which they arose4 ,we thus account for both the second and the third of the different versions of the earthquake which are received at ,shide4 ,and now for the first of the three versions4 ,this is the one which is of special interest to us at present4 ,the original subterranean impulse was1 as we have seen1 propagated through the rocks forming the earth's crust4 ,part of it1 however1 entered into the core forming the earth's interior4 ,the earthquake had the power not only of shaking the earth's crust all over1 but it produced the astonishing effect of setting the whole interior of our globe into a tremble4 ,there was not a single particle of our earth1 from centre to surface1 which was not made to vibrate1 in some degree1 in consequence of the earthquake4 ,certain of these vibrations1 spreading from the centre of disturbance1 took a direct course to the ,isle of ,wight1 right through the globe4 ,they consequently had a shorter journey in travelling from ,tokio to ,shide than those which went round the earth's crust4 ,the former travelled near the chord1 while the latter travelled on the arc4 ,even for this reason alone the internal vibrations might be expected to accomplish their journey more rapidly than the superficial movements4 ,with the same velocity they would take a shorter time for the journey4 ,there is1 however1 another reason for the lesser time taken by the internal vibrations4 ,not only is the journey shorter1 but the speed with which these vibrations travel through the solid earth is much greater than the speed with which superficial vibrations travel through the crust4 ,it has been shown that the average velocity of these vibrations when travelling through the centre of the earth is rather more than ten miles a second4 ,the velocity varies with the square root of the depth1 and near the surface it is scarcely two miles a second4 ,there are two points to be specially noticed4 ,the vibrations1 which1 passing through the earth's interior with a high velocity1 arrive as precursors1 make a faithful diagram1 but only on a very small scale4 ,we say that these vibrations have but small amplitude4 ,this shows that the particles in the earth's interior are not much displaced by the earthquake1 as compared with those on the earth's crust1 and this is one indication of the effective rigidity of the earth4 ,it is also to be noted that the great speed with which the vibrations traverse the solid earth is a consequence of the extreme rigidity of our globe4 ,these vibrations travel more rapidly through the earth than they would do through a bar of solid steel4 ,in other words1 we have here a proof that1 under the influence of the tremendous pressures characteristic of the earth's interior1 the material of which that earth is composed1 notwithstanding the high temperature to which it is raised1 possesses a rigidity which is practically greater than that of steel itself4 ,illustration3 ,,showing ,,localities ,,of ,,earthquakes ,this is perhaps the most striking testimony that can be borne to the rigidity of our globe2 but we must not imagine that we are dependent solely upon the phenomena of earthquakes for the demonstration of this important point2 there are other proofs4 ,it can be shown that the ebb and flow of the tides on our coasts would be very different from that which they actually are were it not that the earth behaves as a rigid globe4 ,it has also been demonstrated that certain astronomical phenomena connected with the way in which the earth turns round on its axis would not be the same as we actually find them to be if the earth were not solid in its interior4 ,the result of these investigations is to show that1 though this globe of ours must be excessively hot inside1 so hot indeed that at ordinary pressures even the most refractory solids would be liquefied or vaporised1 yet under the influence of the pressure to which its materials are subjected the behaviour of that globe is as that of the most rigidly solid body4 ,happily in this country we do not often experience earthquakes other than delicate movements shown by the record of the seismometer4 ,but though most of us live our lives without ever having felt an earthquake shock1 yet earthquakes do sometimes make themselves felt in ,great ,britain4 ,the map we here give1 which was drawn by ,professor ,j4 ,p4 ,o',reilly1 indicates the localities in ,england in which from time to time earthquake shocks have been experienced4 ,the internal heat of the earth1 derived from the primval nebula1 is in no way more strikingly illustrated than by the phenomena of volcanoes4 ,we have shown in this chapter that there is no longer any reason to believe that the earth is fluid in its interior4 ,the evidence has proved that1 under the extraordinary pressure which prevails in the earth1 the materials in the central portions of our globe behave with the characteristics of solids rather than of liquids4 ,but though this applies to the deep-seated regions of our globe1 it need not universally apply at the surface or within a moderate depth from the surface4 ,when the circumstances are such that the pressure is relaxed1 then the heat is permitted to exercise its property of transforming the solids into liquids4 ,masses of matter near the earth's crust are thus1 in certain circumstances1 and in certain localities1 transformed into the fluid or viscid form4 ,in that state they may issue from a volcano and flow in sluggish currents as lava4 ,there has been much difference of opinion as to the immediate cause of volcanic action1 but there can be little doubt that the energy which is manifested in a volcanic eruption has been originally derived in some way from the contraction of the primval nebula4 ,the extraordinary vehemence that a volcanic eruption sometimes attains may be specially illustrated by the case of the great eruption of ,krakatoa4 ,it is1 indeed1 believed that in the annals of our earth there has been no record of a volcanic eruption so vast as that which bears the name of this little island in far ,eastern seas1 ten thousand miles from our shores4 ,until the year #ahhc few had ever heard of ,krakatoa4 ,it was unknown to fame1 as are hundreds of other gems of glorious vegetation set in tropical waters4 ,it was not inhabited1 but the natives from the surrounding shores of ,sumatra and ,java used occasionally to draw their canoes up on its beach1 while they roamed through the jungle in search of the wild fruits that there abounded4 ,geographers in early days hardly condescended to notice ,krakatoa2 the name of the island on their maps would have been far longer than the island itself4 ,it was known to the mariner who navigated the ,straits of ,sunda1 for it was marked on his charts as one of the perils of the intricate navigation in those waters4 ,it was no doubt recorded that the locality had been once1 or more than once1 the seat of an active volcano4 ,in fact1 the island seemed to owe its existence to some frightful eruption of bygone days2 but for a couple of centuries there had been no fresh outbreak4 ,it almost seemed as if ,krakatoa might be regarded as a volcano that had become extinct4 ,in this respect it would only be like many other similar objects all over the globe1 or the countless extinct volcanoes all over the moon4 ,in #ahhc ,krakatoa suddenly sprang into notoriety4 ,insignificant though it had hitherto seemed1 the little island was soon to compel by its tones of thunder the whole world to pay it instant attention4 ,it was to become the scene of a volcanic outbreak so appalling that it is destined to be remembered throughout the ages4 ,in the spring of that year there were symptoms that the volcanic powers in ,krakatoa were once more about to awake from the slumber that had endured for many generations4 ,notable warnings were given4 ,earthquakes were felt1 and deep rumblings proceeded from the earth1 showing that some disturbance was in preparation1 and that the old volcano was again to burst forth after its long period of rest4 ,at first the eruption did not threaten to be of any serious type2 in fact1 the good people of ,batavia1 so far from being terrified at what was in progress in ,krakatoa1 thought the display was such an attraction that they chartered a steamer and went forth for a pleasant picnic to the island4 ,many of us1 ,i am sure1 would have been delighted to have been able to join the party who were to witness so interesting a spectacle4 ,with cautious steps the more venturesome of the excursion party clambered up the sides of the volcano1 guided by the sounds which were issuing from its summit4 ,there they beheld a vast column of steam pouring forth with terrific noise from a profound opening about thirty yards in width4 ,as the summer of this dread year advanced the vigour of ,krakatoa steadily increased1 the noises became more and more vehement2 these were presently audible on shores ten miles distant1 and then twenty miles distant2 and still those noises waxed louder and louder1 until the great thunders of the volcano1 now so rapidly developing1 astonished the inhabitants that dwelt over an area at least as large as ,great ,britain4 ,and there were other symptoms of the approaching catastrophe4 ,with each successive convulsion a quantity of fine dust was projected aloft into the clouds4 ,the wind could not carry this dust away as rapidly as it was hurled upwards by ,krakatoa1 and accordingly the atmosphere became heavily charged with suspended particles4 ,a pall of darkness thus hung over the adjoining seas and islands4 ,such was the thickness and the density of these atmospheric volumes of ,krakatoa dust that1 for a hundred miles around1 the darkness of midnight prevailed at midday4 ,then the awful tragedy of ,krakatoa took place4 ,many thousands of the unfortunate inhabitants of the adjacent shores of ,sumatra and ,java were destined never to behold the sun again4 ,they were presently swept away to destruction in an invasion of the shore by the tremendous waves with which the seas surrounding ,krakatoa were agitated4 ,gradually the development of the volcanic energy proceeded1 and gradually the terror of the inhabitants of the surrounding coasts rose to a climax4 ,july had ended before the manifestations of ,krakatoa had attained their full violence4 ,as the days of ,august passed by the spasms of ,krakatoa waxed more and more vehement4 ,by the middle of that month the panic was widespread1 for the supreme catastrophe was at hand4 ,illustration3 ,fig4 #bf4--,,showing ,,coasts ,,invaded ,,by ,,the ,,great ,,sea-,,waves ,,from ,,krakatoa4 7,from the ,royal ,society's ,reports47 ,on the night of ,sunday1 ,august #bfth1 #ahhc1 the blackness of the dust-clouds1 now much thicker than ever in the ,straits of ,sunda and adjacent parts of ,sumatra and ,java1 was only occasionally illumined by lurid flashes from the volcano4 ,the ,krakatoan thunders were on the point of attaining their complete development4 ,at the town of ,batavia1 a hundred miles distant1 there was no quiet that night4 ,the houses trembled with the subterranean violence1 and the windows rattled as if heavy artillery were being discharged in the streets4 ,and still these efforts seemed to be only rehearsing for the supreme display4 ,by ten o'clock on the morning of ,monday1 ,august #bgth1 #ahhc1 the rehearsals were over and the performance began4 ,an overture1 consisting of two or three introductory explosions1 was succeeded by a frightful convulsion which tore away a large part of the island of ,krakatoa and scattered it to the winds of heaven4 ,in that final effort all records of previous explosions on this earth were completely broken4 ,this supreme effort it was which produced the mightiest noise that1 so far as we can ascertain1 has ever been heard on this globe4 ,it must have been indeed a loud noise which could travel from ,krakatoa to ,batavia and preserve its vehemence over so great a distance2 but we should form a very inadequate conception of the energy of the eruption of ,krakatoa if we thought that its sounds were heard by those merely a hundred miles off4 ,this would be little indeed compared with what is recorded1 on testimony which it is impossible to doubt4 ,illustration3 ,,the ,,early ,,stage ,,of ,,the ,,eruption ,,of ,,krakatoa4 7,from a ,photograph taken on ,may #bgth1 #ahhc47 ,westward from ,krakatoa stretches the wide expanse of the ,indian ,ocean4 ,on the opposite side from the ,straits of ,sunda lies the island of ,rodriguez1 the distance from ,krakatoa being almost three thousand miles4 ,it has been proved by evidence which cannot be doubted that the booming of the great volcano attracted the attention of an intelligent coastguard on ,rodriguez1 who carefully noted the character of the sounds and the time of their occurrence4 ,he had heard them just four hours after the actual explosion1 for this is the time the sound occupied on its journey4 ,we shall better realise the extraordinary vehemence of this tremendous noise if we imagine a similar event to take place in localities more known to most of us than are the far ,eastern seas4 ,if ,vesuvius were vigorous enough to thunder forth like ,krakatoa1 how great would be the consternation of the world6 ,such a report might be heard by ,king ,edward at ,windsor1 and by the ,czar of all the ,russias at ,moscow4 ,it would astonish the ,german ,emperor and all his subjects4 ,it would penetrate to the seclusion of the ,sultan at ,constantinople4 ,nansen would still have been within its reach when he was furthest north1 near the ,pole4 ,it would have extended to the sources of the ,nile1 near the ,equator4 ,it would have been heard by ,mohammedan pilgrims at ,mecca4 ,it would have reached the ears of exiles in ,siberia4 ,no inhabitant of ,persia would have been beyond its range1 while passengers on half the liners crossing the ,atlantic would also catch the mighty reverberation4 ,the subject is of such exceptional interest that ,i may venture on another illustration4 ,let us suppose that a similar earth-shaking event took place in a central position in the ,united ,states4 ,let us say1 for example1 that an explosion occurred at ,pike's ,peak as resonant as that from ,krakatoa4 ,it would certainly startle not a little the inhabitants of ,colorado far and wide4 ,the ears of dwellers in the neighbouring ,states would receive a considerable shock4 ,with lessening intensity the sound would spread much further around--indeed1 it might be heard all over the ,united ,states4 ,the sonorous waves would roll over to the ,atlantic coast1 they would be heard on the shores of the ,pacific4 ,florida would not be too far to the south1 nor ,alaska too remote to the north4 ,if1 indeed1 we could believe that the sound would travel as freely over the great continent as it did across the ,indian ,ocean1 then we may boldly assert that every ear in ,north ,america might listen to the thunder from ,pike's ,peak1 if it rivalled ,krakatoa4 ,the reverberation might even be audible by skin-clad ,eskimos amid the snows of ,greenland1 and by naked ,indians sweltering on the ,orinoco4 ,can we doubt that ,krakatoa made the greatest noise that has ever been recorded8 ,illustration3 ,fig4 #bg4--,,spread ,,of ,,the ,,air-,,wave ,,from ,,krakatoa ,,to ,,the ,,antipodes4 7,from the ,royal ,society's ,reports47 ,among the many other incidents connected with this explosion1 ,i may specially mention the wonderful system of divergent ripples that started in our atmosphere from the point at which the eruption took place4 ,i have called them ripples1 from the obvious resemblance which they bear to the circular expanding ripples produced by raindrops which fall upon the still surface of water4 ,but it would be more correct to say that these objects were a series of great undulations which started from ,krakatoa and spread forth in ever-enlarging circles through our atmosphere4 ,the initial impetus was so tremendous that these waves spread for hundreds and thousands of miles4 ,they diverged1 in fact1 until they put a mighty girdle round the earth1 on a great circle of which ,krakatoa was the pole4 ,the atmospheric waves1 with the whole earth now well in their grasp1 advanced into the opposite hemisphere4 ,in their further progress they had necessarily to form gradually contracting circles1 until at last they converged to a point in ,central ,america1 at the very opposite point of the diameter of our earth1 eight thousand miles from ,krakatoa4 ,thus the waves completely embraced the earth4 ,every part of our atmosphere had been set into a tingle by the great eruption4 ,in ,great ,britain the waves passed over our heads1 the air in our streets1 the air in our houses1 trembled from the volcanic impulse4 ,the very oxygen supplying our lungs was responding also to the supreme convulsion which took place ten thousand miles away4 ,it is needless to object that this could not have taken place because we did not feel it4 ,self-registering barometers have enabled these waves to be followed unmistakably all over the globe4 ,such was the energy with which these vibrations were initiated at ,krakatoa1 that even when the waves thus arising had converged to the point diametrically opposite in ,south ,america their vigour was not yet exhausted4 ,the waves were then1 strange to say1 reflected back from their point of convergence to retrace their steps to ,krakatoa4 ,starting from ,central ,america1 they again described a series of enlarging circles1 until they embraced the whole earth4 ,then1 advancing into the opposite hemisphere1 they gradually contracted until they had regained the ,straits of ,sunda1 from which they had set forth about thirty-six hours previously4 ,here was1 indeed1 a unique experience4 ,the air-waves had twice gone from end to end of this globe of ours4 ,even then the atmosphere did not subside until1 after some more oscillations of gradually fading intensity1 at last they became evanescent4 ,but1 besides these phenomenal undulations1 this mighty incident at ,krakatoa has taught us other lessons on the constitution of our atmosphere4 ,we previously knew little1 or ,i might almost say nothing1 as to the conditions prevailing above the height of ten miles overhead4 ,we were almost altogether ignorant of what the wind might be at an altitude of1 let us say1 twenty miles4 ,it was ,krakatoa which first gave us a little information which was greatly wanted4 ,how could we learn what winds were blowing at a height four times as great as the loftiest mountain on the earth1 and twice as great as the loftiest altitude to which a balloon has ever soared8 ,we could neither see these winds nor feel them4 ,how1 then1 could we learn whether they really existed8 ,no doubt a straw will show the way the wind blows1 but there are no straws up there4 ,there was nothing to render the winds perceptible until ,krakatoa came to our aid4 ,krakatoa drove into those winds prodigious quantities of dust4 ,hundreds of cubic miles of air were thus deprived of that invisibility which they had hitherto maintained4 ,they were thus compelled to disclose those movements about which1 neither before nor since1 have we had any opportunity of learning4 ,with eyes full of astonishment men watched those vast volumes of ,krakatoa dust start on a tremendous journey4 ,westward the dust of ,krakatoa took its way4 ,of course1 everyone knows the so-called tradewinds on our earth's surface1 which blow steadily in fixed directions1 and which are of such service to the mariner4 ,but there is yet another constant wind4 ,we cannot call it a trade-wind1 for it never has rendered1 and never will render1 any service to navigation4 ,it was first disclosed by ,krakatoa4 ,before the occurrence of that eruption no one had the slightest suspicion that far up aloft1 twenty miles over our heads1 a mighty tempest is incessantly hurrying with a speed much greater than that of the awful hurricane which once laid so large a part of ,calcutta on the ground1 and slew so many of its inhabitants4 ,fortunately for humanity1 this new trade-wind does not come within less than twenty miles of the earth's surface4 ,we are thus preserved from the fearful destruction that its unintermittent blasts would produce1 blasts against which no tree could stand1 and which would1 in ten minutes1 do as much damage to a city as would the most violent earthquake4 ,when this great wind had become charged with the dust of ,krakatoa1 then1 for the first and1 ,i may add1 for the only time1 it stood revealed to human vision4 ,then it was seen that this wind circled round the earth in the vicinity of the ,equator1 and completed its circuit in about thirteen days4 ,please observe the contrast between this wind of which we are now speaking and the waves to which we have just referred4 ,the waves were merely undulations or vibrations produced by the blow which our atmosphere received from the explosion of ,krakatoa1 and these waves were propagated through the atmosphere much in the same way as sound waves are propagated4 ,indeed1 these waves moved with the same velocity as sound4 ,but the current of air of which we are now speaking was not produced by ,krakatoa2 it existed from all time1 before ,krakatoa was ever heard of1 and it exists at the present moment1 and will doubtless exist as long as the earth's meteorological arrangements remain as they are at present4 ,all that ,krakatoa did was simply to provide the charges of dust by which for one brief period this wind was made visible4 ,in the autumn of #ahhc the newspapers were full of accounts of strange appearances in the heavens4 ,the letters containing these accounts poured in upon us from residents in ,ceylon2 they came from residents in the ,west ,indies1 and from other tropical places4 ,all had the same tale to tell4 ,sometimes experienced observers assured us that the sun looked blue2 sometimes we were told of the amazement with which people beheld the moon draped in vivid green4 ,other accounts told of curious halos1 and1 in short1 of the signs in the sun1 the moon1 and the stars1 which were exceedingly unusual1 even if we do not say that they were absolutely unprecedented4 ,those who wrote to tell of the strange hues that the sun manifested to travellers in ,ceylon1 or to planters in ,jamaica1 never dreamt of attributing the phenomena to ,krakatoa1 many thousands of miles away4 ,in fact1 these observers knew nothing at the time of the ,krakatoa eruption1 and probably few of them1 if any1 had ever heard that such a place existed4 ,it was only gradually that the belief grew that these1 phenomena were due to ,krakatoa4 ,but when the accounts were carefully compared1 and when the dates were studied at which the phenomena were witnessed in the various localities1 it was demonstrated that these phenomena1 notwithstanding their worldwide distribution1 had certainly arisen from the eruption in this little island in the ,straits of ,sunda4 ,it was most assuredly ,krakatoa that painted the sun and the moon1 and produced the other strange and weird phenomena in the tropics4 ,after a little time we learned what had actually happened4 ,the dust manufactured by the supreme convulsion was whirled round the earth in the mighty atmospheric current into which the volcano discharged it4 ,as the dust-cloud was swept along by this incomparable hurricane1 it showed its presence in the most glorious manner by decking the sun and the moon in hues of unaccustomed splendour and beauty4 ,the blue colour in the sky under ordinary circumstances is due to particles in the air1 and when the ordinary motes of the sunbeam were reinforced by the introduction of the myriads of motes produced by ,krakatoa1 even the sun itself sometimes showed a blue tint4 ,thus the progress of the great dust-cloud was traced out by the extraordinary sky effects it produced1 and from the progress of the dust-cloud we inferred the movements of the invisible air current which carried it along4 ,nor need it be thought that the quantity of material projected from ,krakatoa should have been inadequate to produce effects of this worldwide description4 ,imagine that the material which was blown to the winds of heaven by the supreme convulsion of ,krakatoa could be all recovered and swept into one vast heap4 ,imagine that the heap were to have its bulk measured by a vessel consisting of a cube one mile long1 one mile broad1 and one mile deep2 it has been estimated that even this prodigious vessel would have to be filled to the brim at least ten times before all the products of ,krakatoa had been measured4 ,it was in the late autumn of #ahhc that the marvellous series of celestial phenomena connected with the great eruption began to be displayed in ,great ,britain4 ,then it was that the glory of the ordinary sunsets was enhanced by a splendour which has dwelt in the memory of all those who were permitted to see them4 ,the frontispiece of this volume contains a view of the sunset as seen at ,chelsea at #d4dj p4m4 on ,november #bfth1 #ahhc4 ,the picture was painted from nature by ,mr4 ,w4 ,ascroft1 and is given in the great work on ,krakatoa which was published by the ,royal ,society4 ,there is not the least doubt that it was the dust from ,krakatoa which produced the beauty of those sunsets1 and so long as that dust remained suspended in our atmosphere1 so long were strange signs to be witnessed in the heavenly bodies4 ,but the dust which had been borne with unparalleled violence from the interior of the volcano1 the dust which had been shot aloft by the vehemence of the eruption to an altitude of twenty miles1 the dust which had thus been whirled round and round our earth for perhaps a dozen times or more in this air current1 which carried it round in less than a fortnight1 was endowed with no power to resist for ever the law of gravitation which bids it fall to the earth4 ,it therefore gradually sank downwards4 ,owing1 however1 to the great height to which it had been driven1 owing to the impetuous nature of the current by which it was hurried along1 and owing to the exceedingly minute particles of which it was composed1 the act of sinking was greatly protracted4 ,not until two years after the original explosion had all the particles with which the air was charged by the great eruption finally subsided on the earth4 ,at first there were some who refused to believe that the glory of the sunsets in ,london could possibly be due to a volcano in the ,straits of ,sunda1 at a distance from ,england which was but little short of that of ,australia4 ,but the gorgeous phenomena in ,england were found to be simultaneous with like phenomena in other places all round the earth4 ,once again the comparison of dates and other circumstances proved that ,krakatoa was the cause of these exceptional and most interesting appearances4 ,nor was the incident without a historical parallel1 for has not ,tennyson told us of the call to ,st4 ,telemachus-- 8,had the fierce ashes of some fiery peak ,been hurl'd so high they ranged about the globe8 ,for day by day1 thro' many a blood-red eve1 ,in that four-hundredth summer after ,christ1 ,the wrathful sunset glared44440 ---------------------------------------- -------------------------------- ,,chapter ,x4 ,,spiral ,,and ,,planetary ,,nebul4 ,a ,substitute for ,history--,photograph of the ,great ,spiral taken at the ,lick ,observatory--,solar ,system ,relations ,unimportant--,chaotic ,nebul--,lord ,rosse's ,great ,discovery--,dr4 ,roberts' ,photographs--,the ,astonishing ,discovery of ,professor ,keeler--,the ,perspective of the ,spirals--,the ,spiral ,nebul are not ,gaseous--,the ,spiral is a ,nebula in an advanced ,stage of ,development--,character of the ,great ,nebula in ,andromeda4 ,,in a great college in ,america a new educational experiment has been tried with some success4 ,instead of the instruction in history which students receive in most other institutions1 an attempt has been made in this college to give instruction in a very different manner1 which it is believed will not be of less educational value than the more ordinary processes of teaching4 ,in the course of study to which ,i am now referring the student is invited to consider1 not so much the history of the development of the ,constitution of one particular country1 as to make a broad survey of the different ,constitutions under which the several countries of the world are at this moment governed4 ,the promoters of this scheme believe that many of the intellectual advantages which are ordinarily expected to be gained by the study of the history of one country may be secured equally well by studying only existing conditions1 provided that attention is given to several countries which have arrived at different stages of civilisation4 ,without attempting to say how far the study of the existing ,constitutions of ,france and ,germany1 ,america and ,australia1 ,turkey and ,india1 ,morocco and ,fiji1 might be justly used to supersede the study of ,english history1 it may at least be urged that if we had no annals from which history could be compiled it might be instructive to employ such a substitute for historical studies as is here suggested4 ,this is1 indeed1 the course which we are compelled to take in our study of that great chapter in earth-history which we are discussing in these pages4 ,it is obvious from the nature of the case that it can never be possible for us to obtain direct testimony as to what occurred in the bringing together of the materials of this globe4 ,we must1 therefore1 look abroad through the universe1 and see whether we can find1 from the study of other systems at present in various stages of their evolution1 illustrations of the incidents which we may presume to have occurred in the early stages of our own history4 ,if ,kant had never lived1 if ,laplace had never announced his ,nebular ,theory1 if the discoveries of ,sir ,william ,herschel had not been made1 ,i still venture to think that a due consideration of the remarkable photograph of the famous ,great ,spiral1 which was obtained at the famous ,lick ,observatory in ,california1 would have suggested the high probability of that doctrine which we describe as the ,nebular ,theory4 ,illustration3 ,fig4 #bh4--,,the ,,great ,,spiral ,,nebula 7,lick ,observatory74 7,from the ,royal ,astronomical ,series47 ,if an artist thoroughly versed in the great facts of astronomy had been commissioned to represent the nebular origin of our system as perfectly as a highly cultivated yet disciplined imagination would permit1 ,i do not think he could have designed anything which could answer the purpose more perfectly than does that picture which is now before us4 ,we might wish indeed that ,kant and ,laplace and ,herschel could have lived to see this marvellous natural illustration of their views1 for photographs were of course unthought of in those days1 and1 ,i need hardly say1 that for any one celestial nebula that could have been known in the times of ,laplace1 hundreds are now within the reach of astronomers4 ,we entreat special attention to this picture which ,nature has herself given us1 and which represents what we may not unreasonably conclude to be a system in a state of formation4 ,let me say at once that our solar system1 however imposing it may be from our point of view1 is but of infinitesimal importance as compared with the system which is here in the course of development4 ,it is sometimes urged that it is difficult to imagine how a system so large as ours could have been produced by condensation from a primval nebula4 ,the best answer is found in the fact that the ,great ,spiral now before us may be considered to exhibit at this very moment a system in actual evolution1 the central body of which is certainly thousands of times1 and not improbably millions of times1 greater than the sun1 and of which the attending planets or other revolving bodies1 are framed on a scale immensely transcending that of even ,jupiter himself4 ,the details of this remarkable nebula seem to illustrate those particular features which had been previously assigned to the primval nebula of our system1 long before any photograph was available for the purpose of their study4 ,in the ,great ,nebula in ,orion1 to which we have already referred1 as well as in many other similar objects which we might also have adduced1 the nebulous material from which after long ages new systems may be the result1 was shown in an extremely chaotic state4 ,it was little more than an irregular stain of light on the sky4 ,but in the picture of the ,great ,spiral which is before us 7,fig4 #bh7 it is manifest that the evolution of the system has reached an advanced stage2 such considerable progress has been made in the actual formation that the final form seems to be shadowed forth4 ,the luminosity is no longer diffused in a chaotic condition2 it has formed into spirals1 and become much condensed at the centre and somewhat condensed in other regions4 ,as we now see it1 the object seems to represent a system much more advanced in its formation than any of the other great nebul with which we have compared it4 ,in comparison with it the evolution of such an object as the ,great ,nebula in ,orion can hardly be said to have begun4 ,but in the ,great ,spiral many portions of the nebula have already become outlined into masses which1 though still far from resembling the planets in the solar system1 have at least made some approach thereto while the central portions are being drawn together1 just as we may conceive the great primval fire-mist to have drawn together in the actual formation of the sun4 ,the famous nebula which we are discussing1 and which is generally known as the ,great ,spiral1 is found in the constellation of ,canes ,venatici1 very near the end star in the tail of the ,great ,bear1 and one-fourth of the way from it to ,cor ,caroli4 ,it will be easy to find it from the indication given in the adjoining ,fig4 #bi4 ,as a nebulous spot it is an object which can be seen with any moderately good telescope1 but to detect those details which indicate the spiral structure demands an instrument of first-class power4 ,this object had indeed been studied by many astronomers before ,lord ,rosse turned his colossal reflector upon it4 ,then it was that the wonderful whirlpool structure was first discovered1 and thus the earliest spiral nebula became known4 ,illustration3 ,fig4 #bi4--;,,how ,,to ,,find ,,the ,,great ,,spiral ,,nebula4 ,in those days there were few telescopes of great power1 and none of those instruments appeared able to deal with this nebula sufficiently to reveal its spiral character4 ,the announcement of the discovery of the spiral constitution of this object was therefore received with incredulity by some astronomers1 who believed1 or professed to believe1 that the spiral lines of nebulous matter which ,lord ,rosse described so faithfully1 existed only in the imagination of the astronomer4 ,indeed1 in one notable instance1 it was alleged that these features were to be attributed to actual imperfections in the unrivalled telescope4 ,the incredulity widely prevalent in the middle of the last century about the existence of the spiral nebul may be paralleled by the incredulity about other discoveries in more recent years4 ,when a highly skilled observer1 using an instrument of adequate power1 and1 it may be1 enjoying unequalled opportunities for good work1 testifies to certain discoveries2 when he has employed in the verification of his observations the skill and experience that years of practice have procured for him1 it is futile for those who have not the like opportunities1 either from the want of instruments of adequate power or from climatic difficulties1 to deny the truth of discoveries because they are not able to verify them4 ,it was absurd for astronomers to refuse assent to the great discoveries of ,lord ,rosse simply because instruments inferior to his would not show the spiral structure4 ,in due time1 one astronomer after another began to admit that possibly the remarkable form which ,lord ,rosse announced as characteristic of some nebul might not be a mere figment of the imagination4 ,the complete vindication of ,lord ,rosse's great discovery was not1 however1 attained until that wonderful advance in the arts of astronomy when the photographic plate was called in to supplement1 or rather vastly to extend1 the powers of the eye4 ,dr4 ,isaac ,roberts not only showed by a magnificent photograph that the ,great ,spiral discovered by ,lord ,rosse was just as ,lord ,rosse had described it1 he not only showed that the other spirals announced by ,lord ,rosse were equally entitled to the name1 but1 with the newly acquired powers that the photographic plate placed at his disposal1 he was able to show that many other nebul1 which had been frequently observed and had even been sketched1 possessed further features too faint and delicate to be seen by any human eye1 even with the help of the most powerful telescope4 ,these further features were discovered because they came within the ken of the intensely acute perception of the photographic plate4 ,on the plate these features which the camera showed1 were added to those which the eye had already perceived1 and when these additions were made it was not infrequently found that the nebula assumed the form of a spiral4 ,but the most remarkable circumstance has still to be added4 ,some of the plates exposed by ,dr4 ,roberts show clear and unmistakable photographs of spiral nebul as exquisite in detail as the ,great ,spiral itself1 but yet so faint that they have never been seen by the eye in any telescope whatever1 though they could not elude the photographic plate4 ,thus1 ,dr4 ,roberts not only confirmed in the most splendid manner that really great discovery of the spiral nebul of which the honour belongs to ,lord ,rosse1 but the eminent photographic astronomer added many other spirals of the greatest interest to the list of those objects which ,lord ,rosse had himself given4 ,though these discoveries placed the fact of the existence of spiral nebul in an impregnable position1 and though they greatly increased the interest with which astronomers study such objects1 yet another stop had to be taken before the spiral nebula attained the position of extraordinary importance as a celestial object which must now be acknowledged to be its due4 ,illustration3 ,fig4 #cj4--;,a ,,group ,,of ,,nebul 7,lord ,rosse74 7#cddj1 #cdde in n4g4c47 7,from the ,scientific ,transactions of the ,royal ,dublin ,society47 ,we have already had occasion 7page #fg7 to mention the marvellous discoveries of nebul which the lamented ,professor ,keeler made with the ,crossley ,reflector at the ,lick ,observatory4 ,we have explained that his discoveries have shown the number of nebul in the heavens to be probably at least twenty times that which previous observations would have authorised us in asserting4 ,the mere announcement that #abj1jjj new nebul were within the reach of a photographic plate attached to the ,crossley ,reflector1 would1 by itself1 have been a statement so remarkable as to command the immediate attention of the scientific world4 ,but the interest of even this statement shrinks to unimportance relatively to the further fact which ,professor ,keeler has added4 ,i do not know1 in the annals of astronomy1 a pronouncement of greater interest1 certainly none of more importance for our present purpose1 than the statement that of the #abj1jjj new nebul1 at least half are spirals4 ,here is indeed a stupendous revolution in our knowledge of the celestial objects4 ,fifty years ago ,lord ,rosse announced the discovery of a spiral nebula1 and the existence of this spiral was doubted at first1 though it was gradually conceded at last4 ,now we have the announcement1 on the unchallenged evidence of the photographic plate itself1 that to all appearances there are at least #fj1jjj spiral nebul in the heavens4 ,it is1 alas6 too true that ,professor ,keeler did not live long enough to enumerate all those nebul himself1 and1 indeed1 they have not so far been actually counted1 but to those who will study ,professor ,keeler's papers1 the evidence of the substantial accuracy of the statement is incontestable4 ,illustration3 ,fig4 #ca4--;,a ,,ray ,,nebula 7,lord ,rosse74 7#cfbh in n4g4c47 7,from the ,scientific ,transactions of the ,royal ,dublin ,society47 ,and astonishing as this statement may be1 we have still to add that1 in face of the actual facts1 it may be regarded as even a moderate estimate of the abundance of spirals in the universe4 ,we must remember that a spiral nebula is a flat object with long arms extending from it which lie nearly in the same plane4 ,if we are actually to see that such an object is spiral1 it is necessary for it to be turned squarely towards the earth4 ,if the object be too much foreshortened1 it is quite plain that we can hardly expect to detect its spiral character4 ,it is also obvious if the spiral happens to be turned edgeways towards us1 that then its spiral form cannot be seen2 it would merely appear as what astronomers often call a ray4 ,in the enumeration of the spirals it is therefore only possible for us to include those which happen to be so far squarely turned towards the earth as to make their spiral character unmistakable4 ,we might1 therefore1 reasonably expect that the numbers of spiral nebul actually counted would fall short of the reality4 ,we know that there are many nebul of a somewhat elliptical shape 7,fig4 #ca74 ,there are also many nebul that look like long rays 7,fig4 #cj74 ,those who are familiar with the appearance of nebul in great telescopes will recall at once the numerous spindle-shaped objects of this class4 ,it can hardly be doubted that many of the nebul1 more or less oval in form1 and also these rays or the spindle-shaped objects so frequently seen in good telescopes 7,fig4 #cc7 are in reality spiral nebul1 which are turned not squarely towards us1 but which we are merely looking at more or less edgewise1 so that they have been foreshortened enough to hide their peculiar structure 7,figs4 #cd1 #ce74 ,taking these considerations into account1 it becomes obvious that the estimate of ,professor ,keeler as to the number of spiral nebul in the heavens1 vast as that estimate seems1 may still fall short of the truth4 ,thus we are led to one of the most remarkable conclusions of modern astronomy1 viz4 that the spiral nebula1 next to a star itself1 is the most characteristic object in the sidereal heavens4 ,in treating of the nebul in ,chapter ,,iv4 we explained those fundamental features of the different spectra which make it possible to discriminate with confidence between a nebula which is purely gaseous and a nebula which cannot be so described4 ,as the spiral nebul form a class characterised among all the other nebul by the possession of a very particular structure1 it is interesting to enquire what evidence the spectrum gives with regard to the nature of the material which enters into the constitution of the nebul which belong to this strongly-marked group4 ,i do not mean to say that all the #fj1jjj spirals have been examined with the spectroscope1 but1 as already explained on page #fg1 a sufficient number have been examined to decide the question4 ,we learn from ,professor ,scheiner1 a well-known authority on astronomical spectroscopy1 that the spectra of spirals are generally found to be continuous2 in other words1 we learn that a spiral nebula is not gaseous4 ,it does not consist1 like1 for example1 the nebula in ,orion1 of vaporous matter in a state of incandescence4 ,a nebula or a nebulous-looking object which does not give a spectrum of bright lines1 but which does give a continuous spectrum1 is not infrequently set down as being merely a cluster of stars4 ,this is undoubtedly a true statement with regard to some of these nebulous objects1 but it is not true with regard to all4 ,it is much more reasonable to suppose that the greater part of the materials of the spiral nebul1 though certainly not in the form of gas1 are still not condensed into objects large enough to entitle them to be called stars4 ,it must be remembered that when an object of a gaseous nature has lost heat by radiation1 and has begun to draw itself together1 the gas condenses into particles which constitute small portions of liquid or solid1 just as the vapour of water in the atmosphere condenses into the beads of water that form the clouds in our own sky4 ,these small objects1 even if incandescent1 would no longer radiate light with the characteristics of a gaseous nebula4 ,the light they would emit would be of the same character as that dispensed from the particles of carbon in the solar photosphere to which the sun owes its light4 ,radiation from such a source would give light with a continuous spectrum1 like that from the sun or a star4 ,from the fact that the spectra of the spiral nebul are continuous1 we may infer that1 though these nebul have reached an advanced stage in their development1 they have not always1 and1 perhaps1 not generally1 attained to the stage in which condensation transformed them into a cluster of actual stars4 ,they have1 however1 reached a stage in their progress towards those systems of large bodies that they are ultimately to become4 ,the character of its spectrum may show us that the spiral nebula is not very young1 that it has attained a considerable age in its evolution as compared with other nebul which do not show the spiral character and which have a gaseous spectrum4 ,the importance of this consideration will be made apparent in the next chapter1 when we discuss the dynamical conditions to which a spiral nebula must submit4 ,but there is no reason to doubt that some of the spiral nebul may be in reality star-clusters1 in which there are aggregations of myriads of points1 each justly entitled by its dimensions and its lustre to be regarded as a real star4 ,the great nebula in ,andromeda seems to be a greatly foreshortened spiral4 ,this1 at least1 is the interpretation which may perhaps be most reasonably given to ,dr4 ,roberts' famous photograph of this splendid object4 ,the spectrum of the ,andromeda nebula has been photographed by ,scheiner after a protracted exposure of seven and a half hours4 ,that spectrum showed no trace of bright lines1 thus proving that there is no discernible incandescent gas in the nebula of ,andromeda4 ,it gives practically a continuous spectrum1 across which some broad bands can be recognised4 ,it was interesting to compare this spectrum of the great nebula in ,andromeda with the solar spectrum seen by the same apparatus and under the same conditions4 ,professor ,scheiner announces that there was a remarkable coincidence between the two1 and he draws the inference that the stars which enter into the nebula in ,andromeda are stars of that particular type to which the sun belongs4 ,illustration3 ,fig4 #cb4--,,portion ,,of ,,the ,,milky ,,way 7,,near ,,messier ,,ii474 7,photographed by ,professor ,e4 ,e4 ,barnard47 7,from the ,royal ,astronomical ,society ,series47 ,but we have now to point out how the recent study of nebul has afforded a yet more striking confirmation of the nebular theory4 ,laplace showed how a gradually condensing nebula might have formed a sun and a system of planets4 ,had ,laplace known of the spiral nebul he would1 ,i doubt not1 have found in them the most striking illustration of the operation of evolution on a gigantic scale4 ,they would have provided him with admirable arguments in support of the nebular theory4 ,it is possible that they might also have provided suggestions as to the details of the evolution1 which he had not anticipated4 ,but ,laplace did not know of such objects1 and we can only deplore the loss of the instructive lessons which his incomparable genius would have derived from them4 ,we must1 however1 admit that the lessons as to the origin of the solar system1 derived from the spiral nebul1 must be received with due limitation4 ,we may say at once that the great spiral nebul do not appear to be evolving into systems like the sun and planets2 their work is of a higher order of magnitude altogether4 ,the great spiral nebul seem to be more analogous to galaxies1 like the ,milky ,way 7,fig4 #cb71 than to solar systems4 ,the spiral nebula instead of being described as a system1 should perhaps be described as a system of systems4 ,if the solar system were drawn to scale on the photograph of the ,great ,spiral 7,fig4 #bh7 the orbit of ,neptune would not be larger than the smallest recognisable dot4 ---------------------------------------- -------------------------------- ,,chapter ,,xi4 ,,the ,,unerring ,,guide4 ,the ,solar ,system--,orbits nearly ,plane--,satellites1 ,saturn's ,ring1 ,spiral ,nebul--,an ,explanation of this ,tendency of a ,system towards ,flatness--,the ,energy of a ,system--,loss of ,energy by ,collision and ,tidal ,action--,a ,system within a ,system--,movements of ,translation and ,movements of ,rotation--,the ,general ,law of ,conservation of ,moment of ,momentum--,illustrations of the ,principle--,the ,conception of the ,principal ,plane--,the ,utility of this principle arises from its independence of ,collisions or ,friction--,nature does not do ,things infinitely ,improbable--,the ,decline of ,energy and the ,preservation of ,moment of ,momentum--,explanation of the ,motions in one ,plane and in the same ,direction--,the ,satellites of ,uranus--,the ,rotation of ,uranus--,why the ,orbits are not exactly in the same ,plane--,the ,evolution of a ,nebula--,the ,inevitable ,tendency towards the ,spiral--,the ,explanation of the ,spiral4 ,,we have to consider in this chapter the light which the laws of mathematics throw upon certain features which are possessed by a very large number of celestial objects4 ,let us first describe1 as clearly as the circumstances will permit1 the nature of these common features to which we now refer1 and of which mathematics will suggest the explanation4 ,we shall begin with our solar system1 in which the earth describes an orbit around the sun4 ,that orbit is contained within a plane1 which plane passes through the centre of the sun4 ,we may neglect for the present the earth's occasional slight deviations from this plane which are caused by the attractions of the other planets4 ,if we consider the other bodies of our system1 such1 for instance1 as ,venus or ,jupiter1 we find that the orbit of ,venus also lies in a plane1 and that plane also passes through the centre of the sun4 ,the orbit of ,jupiter is found to be contained within a plane1 and it1 too1 passes through the sun's centre4 ,each of the remaining planets in like manner is found to revolve in an orbit which is contained in a plane1 and all these planes have one common point1 that point being the centre of the sun4 ,it is a remarkable fact that the mutual inclinations are very small1 so that the several planes are nearly coincident4 ,if we take the plane of our earth's orbit1 which we call the ecliptic1 as the standard1 then the greatest inclination of the orbit of any other important planet is seven degrees1 which is found in the case of ,mercury4 ,the inclinations to the ecliptic of the planes of the orbits of a few of the asteroids are much more considerable2 to take an extreme case1 the orbit of ,pallas is inclined at an angle of no less than thirty-four degrees4 ,it must1 however1 be remembered that the asteroids are very small objects1 as the collective masses of the five hundred which are at present known would amount to no more than an unimportant fraction of the mass of one of the great planets of our system4 ,three-fourths of the asteroids have inclinations under ten degrees4 ,we may1 therefore1 leave these bodies out of consideration for the present1 though we may find occasion to refer to them again later on4 ,still less need we pay attention at present to the comets1 for though these bodies belong to our system1 and though they move in plane orbits1 which like the orbits of the planets pass through the centre of the sun1 yet their orbits are inclined at angles of very varying magnitudes4 ,indeed1 we cannot detect any tendency in the orbits of comets to approximate to the plane of the ecliptic4 ,the masses of comets are1 however1 inconsiderable in comparison with the robust globes which form the planets1 while the origin of comets has been apparently so different from that of the planets1 that we may leave them out of consideration in our present argument4 ,there is nothing in the motion of either asteroids or comets to invalidate the general proposition which affirms1 that the planes of the orbits of the heaviest and most important bodies in the solar system are very nearly coincident4 ,many of the planets are accompanied by satellites1 and these satellites revolve round the planets1 just as the planet accompanied by its satellites revolves round the sun4 ,the orbit of each satellite is contained within a plane1 and that plane passes through the centre of the planet to which it is appended4 ,we thus have a system of planes appropriate to the satellites1 just as there is a system of planes appropriate to the planets4 ,the orbits of the satellites of each planet are very nearly in the same plane1 with notable exceptions in the cases of ,uranus and ,neptune1 which it will be necessary to consider at full length later on4 ,this plane is very nearly coincident with the planes in which the planets themselves move4 ,omitting the exceptions1 which are unimportant as to magnitude1 though otherwise extremely interesting and instructive1 the fundamental characteristic of the movements of the principal bodies in our system is that their orbits are nearly parallel to the same plane4 ,we draw an average plane through these closely adjacent planes and we term it the principal plane of our system4 ,it is not1 indeed1 coincident with the plane of the orbit of any one planet1 yet the actual plane of the orbit of every important planet1 and of the important satellites1 lies exceedingly close to this principal plane4 ,this is a noteworthy circumstance in the arrangement of the planetary system1 and we expect that it must admit of some physical explanation4 ,when we look into the details of the planetary groups composing the solar system1 we find striking indications of the tendency of the orbits of the bodies in each subordinate system to become adjusted to a plane4 ,the most striking instance is that exhibited by the ,rings of ,saturn4 ,it has been demonstrated that these wonderful rings are composed of myriads of separate particles4 ,each of these particles follows an independent orbit round ,saturn4 ,each such orbit is contained in a plane1 and all these planes appear1 so far as our observations go1 to be absolutely coincident4 ,it is further to be noted that the plane1 thus remarkably related to the system of rings revolving around ,saturn1 is substantially identical with the plane in which the satellites of ,saturn themselves revolve1 and this plane again is inclined at an angle no greater than twenty-eight degrees to the plane of the ecliptic1 and close to that in which ,saturn itself revolves around the sun4 ,overlooking1 as we may for the present1 the varieties in detail which such natural phenomena present1 we may say that the most noticeable characteristic of the revolutions in the solar system is expressed by the statement that they lie approximately in the same plane4 ,illustration3 ,fig4 #cc4--;,a ,,spiral ,,nebula ,,seen ,,edgewise 7n4g4c4 #cfbh2 in ,leo74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,we shall also find that this tendency of the movements in a system to range themselves in orbits which lie in the same plane1 is exhibited in other parts of the universe4 ,let us consider from this point of view the spiral nebul1 those remarkable objects which1 in the last chapter1 we have seen to be so numerous and so characteristic4 ,it is obvious that a spiral nebula must be a flat object4 ,its thickness is small in comparison with its diameter4 ,when a spiral nebula is looked at edgewise 7,fig4 #de71 then it seems long and thin1 so much so that it presents the appearance of a ray such as we have shown in ,fig4 #cc1 which represents a type of object very familiar to those astronomers who are acquainted with nebul4 ,the characteristics of these objects seem consistent only with the supposition that there is a tendency in the materials which enter into a spiral nebula to adapt their movements to a particular plane1 just as there is a tendency for the objects in ,saturn's ring to remain in a particular plane1 and just as there has been a tendency among the bodies belonging to the solar system themselves to revolve in a particular plane4 ,remembering also that there seems excellent reason to believe that spiral nebul exhibiting this characteristic are to be reckoned in scores of thousands1 it is evident that the fundamental feature in which they all agree must be one of very great importance in the universe4 ,illustration3 ,fig4 #cd4--;,a ,,foreshortened ,,spiral 7n4g4c4 #caih2 in ,ursa ,major74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,illustration3 ,fig4 #ce4--;,,edge ,,view ,,of ,a ,,spiral ,,boldly ,,shown 7n4g4c4 #defe2 in ,coma ,berenices74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,we may mention yet one more illustration of the remarkable tendency1 so frequently exhibited by an organised system in space1 to place its parts ultimately in or near the same plane1 or at all events1 to assume a shape of which one dimension is small in comparison with the two others4 ,we have1 in the last chapter1 referred to the ,milky ,way1 and we have alluded to the significance of the obvious fact that1 however the mass of stars which form the ,milky ,way may be arranged1 they are so disposed that the thickness of the mass is certainly much less than its two other dimensions4 ,herschel's famous illustration of a grindstone to represent the shape of the ,milky ,way will serve to illustrate the form we are now considering4 ,when we meet with a characteristic form so widely diffused through the universe1 exhibited not only in the systems attending on the single planets1 not only in the systems of planets which revolve round a single sun1 but also in that marvellous aggregation of innumerable suns which we find in the ,milky ,way1 and in scores of thousands of nebul in all directions1 at all distances1 and apparently of every grade of importance1 we are tempted to ask whether there may not be some physical explanation of a characteristic so universal and so remarkable4 ,let us see whether mathematics can provide any suggestion as to the cause of this tendency towards flatness which seems to affect those systems in the universe which are sufficiently isolated to escape from any large disturbance of their parts by outside interference4 ,we must begin by putting1 as it were1 the problem into shape1 and by enumerating certain conditions which1 though they may not be absolutely fulfilled in nature1 are often so very nearly fulfilled that we make no appreciable error by supposing them to be so4 ,let us suppose that a myriad bodies of various sizes1 shapes1 materials and masses1 are launched in space in any order whatever1 at any distances from each other1 and that they are started with very different movements4 ,some may be going very fast1 some going slowly1 or not at all2 some may be moving up or down or to the right or to the left--there may be1 in fact1 every variety in their distances and their velocities1 and in the directions in which they are started4 ,we assume that each pair of masses attract each other by the well-known law of gravitation1 which expresses that the force between any two bodies is proportional directly to the product of their masses and inversely to the square of their distance4 ,we have one further supposition to make1 and it is an important one4 ,we shall assume that though each one of the bodies which we are considering is affecting all the others1 and is in turn affected by them1 yet that they are subjected to no appreciable disturbing influence from other bodies not included in the system to which they belong4 ,this may seem at first to make the problem we are about to consider a purely imaginary one1 such as could only be applicable to systems different from those which are actually presented to us in nature4 ,it must be admitted that the condition we have inferred can only be approximately fulfilled4 ,but a little consideration will show that the supposition is not an unreasonable one4 ,take1 for instance1 the solar system1 consisting of the sun1 the planets1 and their satellites4 ,every one of these bodies attracts every other body1 and the movement of each of the bodies is produced by the joint effects of the forces exerted upon it by all the others4 ,assuredly this gives a problem quite difficult enough for all the resources that are at our command4 ,but in such investigations we omit altogether the influence of the stars4 ,sirius1 for example1 does exercise some attraction on the bodies of our system1 but owing to its enormous distance1 in comparison with the distances in our solar system1 the effect of the disturbance of ,sirius on the relative movements of the planets is wholly inappreciable4 ,indeed1 we may add that the disturbances in the solar system produced by all the stars1 even including the myriads of the ,milky ,way1 are absolutely negligible4 ,the movements in our solar system1 so far as our observations reveal them1 are performed precisely as if all bodies of the universe foreign to the solar system were non-existent4 ,this consideration shows that in the problem we are now to consider1 we are introducing no unreasonable element when we premise that the system whose movements we are to investigate is to be regarded as free from appreciable disturbance by any foreign influence4 ,to follow the fortunes of a system of bodies1 large or small1 starting under any arbitrary conditions at the commencement1 and then abandoned to their mutual attractions1 is a problem for the mathematician4 ,it certainly presents to him questions of very great difficulty1 and many of these he has to confess are insoluble2 there are1 however1 certain important laws which must be obeyed in all the vicissitudes of the motion4 ,there are certain theorems known to the mathematician which apply to such a system1 and it is these theorems which afford us most interesting and instructive information4 ,i am well aware that the subject upon which ,i am about to enter is not a very easy one1 but its importance is such that ,i must make the effort to explain it4 ,let me commence by describing what is meant when we speak of the energy of a system4 ,take1 first1 the case of merely two bodies1 and let us suppose that they were initially at rest4 ,the energy of a system of this very simple type is represented by the quantity of work which could be done by allowing these two bodies to come together4 ,if1 instead of being in the beginning simply at rest1 the bodies had each been in motion1 the energy of the system would be correspondingly greater4 ,the energy of a moving body1 or its capacity of doing work in virtue of its movement1 is proportional jointly to its mass and to the square of its velocity4 ,the energy of the two moving bodies will therefore be represented by three parts2 first1 there will be that due to their distance apart2 secondly1 there will be that due to the velocity of one of them2 and1 thirdly1 there is that due to the velocity of the other4 ,in the case of a number of bodies1 the energy will consist in the first place of a part which is due to the separation of the bodies1 and measured by the quantity of work that would be produced if1 in obedience to their mutual attraction1 all the bodies were allowed to come together into one mass4 ,in the second place1 the bodies are to be supposed to have been originally started with certain velocities1 and the energy of each of the bodies1 in virtue of its motion1 is to be measured by the product of one-half its mass into the square of its velocity4 ,the total energy of the system consists1 therefore1 of the sum of the parts due to the velocities of the bodies1 and that which is due to their mutual separation4 ,if the bodies could really be perfectly rigid1 unyielding masses1 so that they have no movements analogous to tides1 and if their movements be such that collisions will not take place among them1 then the laws of mechanics tell us that the quantity of energy in that system will remain for ever unaltered4 ,the velocities of the particles may vary1 and the mutual distances of the particles may vary1 but those variations will be always conducted1 subject to the fundamental condition that if we multiply the square of the velocity of each body by one-half its mass1 and add all those quantities together1 and if we increase the sum thus obtained by the quantity of energy equivalent to the separation of the particles1 the total amount thus obtained is constant4 ,this is the fundamental law of mechanics known as the conservation of energy4 ,for such material systems as the universe presents to us1 the conservation of energy1 in the sense in which ,i have here expressed it1 will not be maintained2 for the necessary conditions cannot be fulfilled4 ,let us suppose that the incessant movements of the bodies in the system1 rushing about under the influence of their mutual attractions1 has at last been productive of a collision between two of the bodies4 ,we have already explained in ,chapter ,,vi4 how in the collision of two masses the energy which they possess in virtue of their movements may be to a large extent transformed into heat2 there is consequently an immediate increase in the temperature of the bodies concerned1 and then follows the operation of that fundamental law of heat1 by which the excess of heat so arising will be radiated away4 ,some of it will1 no doubt1 be intercepted by falling on other bodies in the system1 and the amount that might be thus possibly retained would1 of course1 not be lost to the system4 ,the bodies of the solar system at least are so widely scattered1 that the greater part of the heat would certainly escape into space1 and the corresponding quantity of energy would be totally lost to the system4 ,we may generally assume that a collision among the bodies would be most certainly productive of a loss of energy from the system4 ,no doubt collisions can hardly be expected to occur in a system consisting of large1 isolated bodies like the planets4 ,even in any system of solid bodies collisions may be presumed to be infrequent in comparison with the numbers of the bodies4 ,but if1 instead of a system of few bodies of large mass1 we have a gas or nebula composed of innumerable atoms or molecules1 the collisions would be by no means infrequent1 and every collision1 in so far as it led to the production of heat1 would be productive of loss of energy by radiation from the system4 ,it should also be added that1 even independently of actual collisions1 there is1 and must be1 loss of energy in the system from other causes4 ,there are no absolutely rigid bodies known in nature1 for the hardest mineral or the toughest steel must yield to some extent when large forces are applied to it1 and as the bodies in the system are not mere points or particles of inconsiderable dimensions1 they will experience stresses something like those to which our earth is subjected in that action of the moon and sun which produces the tides4 ,in consequence of the influences of each body on the rest1 there will be certain relative changes in the parts of each body2 there will be1 as it were1 tidal movements in their liquid parts and even in their solid substance4 ,these tides will produce friction1 and this will produce heat4 ,this heat will be radiated from the system1 but the heat radiated corresponds to a certain amount of energy2 the energy is therefore lost to the system1 so that even without actual collisions we still find that energy must be gradually lost to the system4 ,thus we have been conducted to an important conclusion1 which may be stated in the following way4 ,let there be any system of bodies1 subject to their mutual attractions1 and sufficiently isolated from the disturbing influence of all bodies which do not belong to the system1 then the original energy with which that system is started must be undergoing a continual decline4 ,it must at least decline until such a condition of the system has been reached that collisions are no longer possible and that tidal influences have ceased4 ,these conditions might be fulfilled if all the bodies of the system coalesced into a single mass4 ,as illustrations of the systems we are now considering1 we may take the sun and planets as a whole4 ,a spiral nebula is a system in the present sense1 while perhaps the grandest illustration of all is provided by the ,milky ,way4 ,it will be noted that we may have a system which is isolated so far as our present argument is concerned1 even while it forms a part of another system of a higher order of magnitude4 ,for instance1 ,saturn with his rings and satellites is sufficiently isolated from the rest of the solar system and the rest of the universe1 to enable us to trace the consequences of the gradual decline of energy in his attendant system4 ,the solar system in which ,saturn appears merely as a unit1 is itself sufficiently isolated from the stars in the ,milky ,way to permit us to study the decline of energy in the solar system1 without considering the action of those stars4 ,this general law of the decline of energy in an isolated system1 is supplemented by another law often known as the conservation of moment of momentum4 ,it may at first seem difficult to grasp the notion which this law involves4 ,the effort is1 however1 worth making1 for the law in question is of fundamental importance in the study of the mechanics of the universe4 ,in the ,appendix will be found an investigation by elementary geometry of the important mechanical principles which are involved in this subject4 ,whatever may have been the origin of the primval nebula1 and whatever may have been the forces concerned in its production we may feel confident that it was not originally at rest4 ,we do not indeed know any object which is at rest4 ,not one of the heavenly bodies is at rest1 nothing on earth is at rest1 for even the molecules of rigid matter are in rapid motion4 ,rest seems unknown in the universe4 ,it would be1 therefore1 infinitely improbable that a primval nebula1 whatever may have been the agency by which it was started on that career which we are considering1 was initially in a condition of absolute rest4 ,we assume without hesitation that the nebula was to some extent in motion1 and we may feel assured that the motions were of a highly complicated description4 ,it is fortunate for us that our argument does not require us to know the precise character of the movements1 as such knowledge would obviously be quite unattainable4 ,we can1 however1 invoke the laws of mechanics as an unerring guide4 ,they will tell us not indeed everything about those motions1 but they will set forth certain characteristics which the movements must have had1 and these characteristics suffice for our argument4 ,to illustrate the important principle on which we are now entering ,i must mention the famous problem of three bodies which has engaged the attention of the greatest mathematicians4 ,let there be a body ,a1 and another ,b1 and another ,c4 ,we shall suppose that these bodies are so small that they may be regarded merely as points in comparison with the distances by which they are separated4 ,we shall suppose that they are all moving in the same plane1 and we shall suppose that each of them attracts the others1 but that except these attractions there are no other forces in the system4 ,to discover all about the motions of these bodies is so difficult a problem that mathematicians have never been able to solve it4 ,but though we are not able to solve the problem completely1 we can learn something with regard to it4 ,we represent by arrows in ,fig4 #cf the directions in which ,a1 ,b1 and ,c are moving at the moment4 ,we choose any point ,o in the plane1 and for simplicity we have so drawn the figure that ,a1 ,b1 and ,c are forces tending to turn round ,o in the same direction4 ,the velocity of a body multiplied into its mass is termed the momentum of the body4 ,draw the perpendicular from ,o to the direction in which the body ,a is moving1 then the product of this perpendicular and the momentum of ,a is called the moment of momentum of ,a around ,o4 ,in like manner we form the moment of momentum of ,b and ,c1 and if we add them together we obtain the total moment of momentum of the system4 ,we can now give expression to a great discovery which mathematicians have made4 ,no matter how complicated may be the movements of ,a1 ,b1 and ,c2 no matter to what extent these particles approximate or how widely they separate2 no matter what changes may occur in their velocities1 or even what actual collision may take place1 the sum of the moments of momentum must remain for ever unaltered4 ,this most important principle in dynamics is known as the conservation of moment of momentum4 ,though ,i have only mentioned three particles1 yet the same principle will be true for any number4 ,if it should happen that any of them are turning round ,o in the opposite direction1 then their moments of momentum are to be taken as negative4 ,in this case we add the moments tending in one direction together2 and then subtract all the opposite moments4 ,the remainder is the quantity which remains constant4 ,illustration3 ,fig4 #cf4--,,to ,,illustrate ,,moment ,,of ,,momentum4 ,we may state this principle in a somewhat different manner as follows3 ,let us consider a multitude of particles in a plane2 let them be severally started in any directions in the plane1 and then be abandoned to their mutual attractions1 it being understood that there are no forces produced by bodies external to the system2 if we then choose any point in the plane1 and measure the areas described round that point by the several moving bodies in one second1 and if we multiply each of1 those areas by the mass of the corresponding body1 then1 if all the bodies are moving in the same direction round the point1 the sum of the quantities so obtained is constant4 ,it will be the same a hundred or a thousand years hence as it is at the present moment1 or as it was a hundred or a thousand years ago4 ,if any of the particles had been turning round the point in the opposite direction1 then the products belonging to such particles are to be subtracted from the others instead of added4 ,we have now to express in a still more general manner the important principle that is here involved4 ,let us consider any system of attracting particles1 no matter what their masses or whether their movements be restricted to a plane or not4 ,let us start them into motion in any directions and with any initial velocities1 and then abandon them to the influence of their mutual attractions1 withholding at the same time the interference of any forces from bodies exterior to the system4 ,draw any plane whatever1 and let fall perpendiculars upon this plane from the different particles of the system4 ,it will be obvious that as the particles move the feet of the perpendiculars must move in correspondence with the particles from which the perpendiculars were let fall4 ,we may regard the foot of every perpendicular as the actual position of a moving point1 and it can be proved that if the mass of each particle be multiplied into the area which the foot of its perpendicular describes in a second round any point in the plane1 and then be added to the similar products from all the other particles1 only observing the proper precautions as to sign1 the sum will remain constant1 i4e41 in any other second the total quantity arrived at will be exactly the same4 ,this is a general law of dynamics4 ,it is not a law of merely approximate truth1 it is a law true with absolute accuracy during unlimited periods of time4 ,the actual value of the constant will depend both on the system and on the plane4 ,for a given system the constant will differ for the different planes which may be drawn1 and there will be some planes in which that sum will be zero4 ,in other words1 in those planes the areas described by the feet of the perpendiculars1 multiplied by the masses of the particles which are moving in one way1 will be precisely equal to the similar sum obtained from the particles moving in the opposite direction4 ,but among all possible planes there is one of special significance in its relation to the system4 ,it is called the 8principal plane10 and it is characterised by the fact that the sum 7with due attention to sign7 of the areas described each second by the feet of the perpendiculars1 multiplied into the masses of the corresponding particle1 is greater than the like magnitude for any other plane1 and is thus a maximum4 ,for all planes parallel to this principal plane1 the result will be1 of course1 the same2 it is the direction of the plane and not its absolute situation that is material4 ,we thus see that while this remarkable quantity is constant in any plane1 for all time1 yet the actual value of that constant depends upon the aspect of the plane2 for some planes it is zero1 for others the constant has intermediate values1 and there is one plane for which the constant is a maximum4 ,this is the principal plane1 and a knowledge of it is of vital importance in endeavouring to understand the nebular theory4 ,nor are the principles under consideration limited only to a system consisting of sun and planets2 they apply1 with suitable modifications1 to many other celestial systems as well4 ,the instructive character of this dynamical principle will be seen when we deduce its consequences4 ,the term 8moment of momentum0 of a particle1 with reference to a certain point in a plane1 expresses double the product of the rate at which the area is described by the foot of the perpendicular to this plane1 multiplied by the mass of the particle4 ,the moment of momentum of the system1 with reference to the principal plane1 is a maximum in comparison with all other planes2 that moment of momentum retains precisely the same value throughout all time1 from the first instant the system was started onwards4 ,and it retains this value1 no matter what changes or disturbances may happen in the system1 provided only that the influence of external forces is withheld4 ,subject to this condition1 the transformations of the system may be any whatever4 ,the several bodies may be forced into wide changes of their orbits1 so that there may even be collisions among them2 yet1 notwithstanding those collisions1 and notwithstanding the violent alterations which may be thus produced in the movements of the bodies1 the moment of momentum will not alter4 ,no matter what tides may be produced1 even if those tides be so great as to produce disruption in the masses and force the orbits to change their character radically1 yet the moment of momentum will be conserved without alteration4 ,it is essential to notice the fundamental difference between the principle which has been called the conservation of energy in the system1 and the conservation of moment of momentum4 ,we have pointed out that when collisions take place1 part of the energy due to motion is transformed into heat1 and energy in that form admits of radiation through space1 and thus becomes lost to the system1 with the result that the total energy declines4 ,even without actual collision1 we have shown how certain effects of tides1 or other consequences of friction1 necessarily involve the squandering of energy with which the system was originally endowed4 ,a system started with a certain endowment of energy may conserve that energy indefinitely1 if all such actions as collisions or frictions are absent4 ,if collisions or frictions are present the system will gradually dissipate energy4 ,our interpretation of the future of such a system must always take account of this fundamental fact4 ,it is1 of course1 conceivable that the moment of momentum with which a system was originally endowed might have happened to be zero4 ,a system of particles could be so constructed and so started on their movements that their moment of momentum with regard to a certain plane should be zero4 ,it might happen that the moment of momentum of the system with regard to a second plane1 perpendicular to the former one1 should be also zero2 and1 finally1 that the moment of momentum of the system with regard to a third plane perpendicular to each of the other two1 should be also zero4 ,if these three conditions were found to prevail at the commencement1 they would prevail throughout the movement1 and1 more generally still1 we may state that in such circumstances the moment of momentum of the system would be zero about any plane whatever4 ,there would be no principal plane in such a system4 ,we thus note that though it is inconceivable that a group of mutually attracting bodies should be started into movement without a suitable endowment of energy1 it is yet quite conceivable that a system could be started without having any moment of momentum4 ,and if at the beginning the system had no moment of momentum1 then no matter what may be the future vicissitudes of its motion1 no moment of momentum can ever be acquired by it to all eternity1 so long as the interference of external forces is excluded4 ,but having said this much as to the conceivability of the initiation of a system with no moment of momentum1 we now hasten to add that1 so far as ,nature is actually concerned1 this bare possibility may be set aside as one which is infinitely improbable4 ,nature does not do things which are infinitely improbable1 and1 therefore1 we may affirm that all material systems1 with which we shall have to deal1 do possess moment of momentum4 ,however the system may have originated1 whatever may have been the actions of forces by which it was brought into being1 we may feel assured that the system received at its initiation some endowment of moment of momentum1 as well as of energy4 ,hence we may conclude that every such system as is presented to us in the infinite variety of ,nature1 must stand in intimate relation to some particular plane1 being that which is known as the principal plane of moment of momentum4 ,in our effort to interpret ,nature1 the physical importance of this fact can hardly be over-estimated4 ,in a future chapter we shall make some attempt to sketch the natural operations by which individual systems have been started on their careers4 ,postponing1 then1 such questions1 we propose to deal now with the phenomena which the principles of dynamics declare must accompany the evolution of a system under the action of the exclusive attraction of the various parts of that system for each other4 ,the system commences its career with a certain endowment of energy1 with a certain endowment of moment of momentum1 and with a certain principal plane to which that moment of momentum is specially related4 ,in the course of the evolution through which1 in myriads of ages1 the system is destined to pass1 the energy that it contains will undergo vast loss by dissipation4 ,on the other hand1 the moment of momentum will never vary1 and the position of the principal plane will remain the same for all time4 ,we have to consider what features1 connected with the evolution1 may be attributed to the operation of these dynamical laws4 ,we have1 in fact1 to deduce the consequences which seem to follow from the fact that1 in consequence of collisions1 and in consequence of friction1 an isolated system in space must gradually part with its initial store of energy1 but that1 notwithstanding any collisions and any friction1 the total moment of momentum of the system suffers no abatement4 ,as the system advances in development1 we have to deal with a gradual decline in the ratio of the original store of energy to the original store of moment of momentum4 ,and hence we must expect that a system will ultimately tend towards a form in which1 while preserving its moment of momentum1 it shall do so with such a distribution of the bodies of which it consists as shall be compatible with a diminishing quantity of energy4 ,it is not hard to see that in the course of ages this tends1 as one consequence1 to make the movements of each of the bodies in the system ultimately approximate to movements in a plane4 ,let us1 for simplicity1 begin with the case of three attracting particles1 ,a1 ,b and ,c4 ,let ,b be started in any direction in the plane ,l1 and let ,a be started in an orbit round it1 and in the same plane ,l4 ,now let ,c be started into motion1 in any direction1 from some point also in ,l4 ,it is certain that the sum of the areas projected parallel to any plane1 which are described in a second by these three bodies1 must be constant1 each of the areas being1 as usual1 multiplied by the mass of the corresponding body4 ,let us specially consider the plane ,l in which the motions of ,a and ,b already lie4 ,it is on this plane that the area described by ,c has to be projected4 ,the essential point now to remember is that the projected area is less than the actual area4 ,it is plain that if ,c has to describe a certain projected area in a certain time1 the velocity with which ,c has to move must be greater when ,c starts off at an inclination to the plane than would have been necessary if ,c had started in the plane1 other things being the same4 ,thus we see that1 if the three bodies were all moving in the same plane1 they could1 speaking generally1 maintain more easily the requisite description of areas1 that is1 the requisite moment of momentum with smaller velocities than if they were moving in directions which were not so regulated2 that is to say1 the moment of momentum can be kept up with less energy when the particles move in the same plane4 ,in a more general manner we see that any system in which the bodies are moving in the same plane will1 for equal moment of momentum1 require less energy than it would have done had the bodies been moving in directions which were not limited to a plane4 ,thus we are led to the conclusion that the ultimate result of the collisions and the friction and the tides1 which are caused by the action of one particle on another1 is to make the movements tend towards the same plane4 ,in this dynamical principle we have in all probability a physical explanation of that remarkable characteristic of celestial movements to which we have referred4 ,the solar system possesses less energy in proportion to its moment of momentum than it would require to have if the orbits of the important planets1 instead of lying practically in the same plane1 were inclined at various angles4 ,whatever may have been the original disposition of the materials forming the solar system1 they must once have contained much more energy than they have at present4 ,the moment of momentum in the principal plane1 at the beginning1 was not1 however1 different from the moment of momentum that the system now possesses4 ,as the energy of the system gradually declined1 the system has gradually been compelled to adjust itself in such a manner that1 with the reduced quantity of energy1 the requisite moment of momentum shall still be preserved4 ,this is the reason why1 in the course of the myriads of ages during which the solar system has been acquiring its present form1 the movements have gradually become nearly conformed to a plane4 ,the operation of the principle1 now before us1 may be seen in a striking manner in ,saturn's ring4 7,fig4 #cg47 ,the particles constituting this exquisite object1 so far as observations have revealed them1 seem to present to us an almost absolutely plane movement4 ,the fact that the movements of the constituents of ,saturn's ring lie in a plane is doubtless to be accounted for by the operation of the fundamental dynamical principle to which we have referred4 ,saturn1 in its great motion round the luminary1 is1 of course1 controlled by the sun1 yet the system attached to ,saturn is so close to that globe as to be attracted by the sun in a manner which need not here be distinguished from the solar attraction on ,saturn itself4 ,it follows that the differential action1 so to speak1 of the sun on ,saturn1 and on the myriad objects which constitute its ring1 may be disregarded4 ,we are therefore entitled1 as already mentioned1 to view ,saturn and its system as an isolated group1 not acted upon by any forces exterior to the system4 ,it is therefore subject to the laws which declare that1 though the energy declines1 the moment of momentum is to remain unaltered4 ,this it is which has apparently caused the extreme flatness of ,saturn's ring4 ,the energy of the rotation of that system has been expended until it might seem that no more energy has been left than just suffices to preserve the unalterable moment of momentum1 under the most economical conditions1 so far as energy is concerned4 ,illustration3 ,fig4 #cg4--,,saturn4 ,drawn by ,e4 ,m4 ,antoniadi4 7,july #cjth1 #ahii47 ,let us suppose that one of the innumerable myriads of particles which constitute the ring of ,saturn were to forsake the plane in which it now revolves1 and move in an orbit inclined to the present plane4 ,we shall suppose that the original track of the orbit was a circle1 and we shall assume that in the new plane to which the motion is transferred the motion is also circular4 ,that particle will have still to do its share of preserving the requisite total moment of momentum1 for we are to suppose that each of the other particles remains unaltered in its pace and in the other circumstances of its motion4 ,the aberrant particle will describe1 in a second1 an area which1 for the purpose of the present calculation1 must be projected upon the plane containing the other particles4 ,the area1 when projected1 must still be as large as the area that the particle would have described if it had remained in the plane4 ,it is therefore necessary that the area swept over by the particle in the inclined plane1 in one second1 shall be greater than the area which sufficed in the original plane4 ,this requires the circle in which the particle revolves to be enlarged1 and this necessitates that its energy should be increased4 ,in other words1 while the moment of momentum was no greater than before1 the energy of the system would have to be greater4 ,we thus see that inasmuch as the particles forming the rings of ,saturn move in circles in the same plane1 they require a smaller amount of energy in the system to preserve the requisite moment of momentum than would be required if they moved in circular orbits which were not in the same plane4 ,in such a system as ,saturn's ring1 in which the particles are excessively numerous and excessively close together1 it may be presumed that there may once have been sufficient collisions and frictions among the particles to cause the exhaustion of energy to the lowest point at which the moment of momentum would be sustained4 ,in the course of ages this has been accomplished by the remarkable adjustment of the movements to that plane in which we now find them4 ,the importance of this subject is so great that we shall present the matter in a somewhat different manner as follows3 ,we shall simplify the matter by regarding the orbits of the planets or other bodies as circles ,the fact that these orbits are ellipses1 which are1 however1 very nearly circles1 will not appreciably affect the argument4 ,let us1 then1 suppose a single planet revolving round a fixed sun1 in the centre4 ,the energy of this system has two parts4 ,there is first the energy due to the velocity of the planet1 and this is found by taking half the product of the mass of the planet and the square of its velocity4 ,the second part of the energy depends1 as we have already explained1 on the distance of the planet from the sun4 ,the planet possesses energy on account of its situation1 for the attraction of the sun on the planet is capable of doing work4 ,the further the planet is from the sun the larger is the quantity of energy that it possesses from this cause4 ,on the other hand1 the further the planet is from the sun the smaller is its velocity1 and the less is the quantity of energy that it possesses of the first kind4 ,we unite the two parts1 and we find that the net result may be expressed in the following manner3 ,if a planet be revolving in a circular path round the sun1 then the total energy of that system 7apart from any rotation of the sun and planet on their axes71 when added to the reciprocal of the distance between the two bodies1 measured with a proper unit of length1 is the same for all distances of the same two bodies4 ,this shows the connection between the energy and the distance of the planet from the sun4 ,thus we see that if the circle is enlarged the energy of the system increases4 ,the moment of momentum of the system is proportional to the square root of the distance of the two bodies4 ,if1 therefore1 the distance of the two bodies is increased1 the moment of momentum increases also4 ,it will illustrate the application of the argument to take a particular case in which a system of particles is revolving round a central sun in circular orbits1 all of which lie in the same plane4 ,let us suppose that1 while the moment of momentum of the system of particles is to remain unaltered1 one of the particles is to be shifted into a plane which is inclined at an angle of #fj to the plane of the other orbits2 it can easily be seen that an area in the new plane1 when projected down into the original plane1 will be reduced to half its amount4 ,hence1 as the moment of momentum of the whole system is to be kept up1 it will be necessary for the particle to have a moment of momentum in the circle which it describes in the new plane which is double that which it had in the original plane4 ,it follows that the radius of the circle in the new plane must be four times the radius of the circle which defined the orbit of the particle in the old plane4 ,the energy of the particle in this orbit is therefore correspondingly greater1 and thus the energy of the whole system is increased4 ,this illustrates how a system1 in which the circular orbits are in different planes1 requires more energy for a given moment of momentum than would suffice if the circular orbits had all been in the same plane4 ,so long as the orbits are in different planes there will still remain a reserve of energy for possible dissipation4 ,but the dissipation is always in progress1 and hence there is an incessant tendency towards a flattening of the system by the mutual actions of its parts4 ,it may help to elucidate this subject to state the matter as follows3 ,the more the system contracts1 the faster it must generally revolve2 this is the universal law when disturbing influences are excluded4 ,take1 for instance1 the sun1 which is at this moment contracting on account of its loss of heat4 ,in consequence of that contraction it is essential that the sun shall gradually turn faster round on its axis4 ,at present the sun requires twenty-five days1 four hours and twenty-nine minutes for each rotation4 ,that period must certainly be diminishing1 although no doubt the rate of diminution is very slow4 ,indeed1 it is too slow for us to observe2 nevertheless1 some diminution must be in progress4 ,applying the same principle to the primitive nebula1 we see1 that as the contraction of the original volume proceeds1 the speed with which the several parts will rotate must increase4 ,the periodic times of the planets are here instructive4 ,the materials now forming ,jupiter were situated towards the exterior of the nebula1 so that1 as the nebula contracted1 it tended to leave ,jupiter behind4 ,the period in which ,jupiter now revolves round the sun may give some notion of the period of the rotation of the nebula at the time that it extended so far as ,jupiter4 ,subsequently to the formation1 and the detachment of ,jupiter1 a body which was henceforth no longer in contact with the nebula1 the latter proceeded further in its contraction4 ,passing over the intermediate stages1 we find the nebula contracting until it extended no further than the line now marked by the earth's orbit2 the speed with which the nebula was rotating must have been increasing all the time1 so that though the nebula required several years to go round when it extended as far as ,jupiter1 only a fraction of that period was necessary when it had reached the position indicated by the earth's track at the present time4 ,leaving the earth behind it1 just as it had previously left ,jupiter1 the nebula started on a still further condensation4 ,it drew in1 until at last it reached a further stage by contraction into the sun1 which rotates in less than a month4 ,thus the period of ,jupiter namely1 twelve years1 the period of the earth1 namely1 one year1 and the period of the sun1 namely1 twenty-five days1 illustrate the successive accelerations of the rotation of the nebula in the process of contraction4 ,no doubt these statements must be received with much qualification1 but they will illustrate the nature of the argument4 ,we may also here mention the satellites of ,uranus1 all the more so because it has been frequently urged as an objection to the nebular theory that the orbits of the satellites of ,uranus lie in a plane which is inclined at a very large angle2 no less than #hb to the general plane of the solar system4 ,i shall refer in a later chapter to this subject1 and consider what explanation can be offered with regard to the great inclination of this plane1 which is one of the anomalies of our system4 ,for the present ,i merely draw attention to the fact that the movements of all four satellites of ,uranus do actually lie in the same plane1 though1 as already indicated1 it stands nearly at right angles to the ecliptic4 ,professor ,newcomb has shown that the four satellites of ,uranus revolve in orbits which are almost exactly circular1 and which1 so far as observation shows1 are absolutely in the same plane4 ,from our present point of view this is a matter of much interest4 ,whatever may have been the influence by which this plane departs so widely from the plane of the ecliptic1 it seems certain that it must be regarded as having acted at a very early period in the evolution of the ,uranian system2 and when this system had once started on its course of evolution1 the operation of that dynamical principle to which we have so often referred was gradually brought to bear on the orbits of the satellites4 ,we have here another isolated case resembling that of ,saturn and its rings4 ,the fundamental law ordained that the moment of momentum of ,uranus and its moons must remain constant1 though the total quantity of energy in that system should decline4 ,in the course of ages this has led to the adjustment of the orbits of the four satellites into the same plane4 ,i ought here to mention that the rotation of ,uranus on its axis presents a problem which has not yet been solved by telescopic observation4 ,it is extremely interesting to note that1 as a rule1 the axes on which the important planets rotate are inclined at no great angles to the principal plane of the solar system4 ,the great distance of ,uranus has1 however1 prevented astronomers from studying the rotation of that planet in the ordinary manner1 by observation of the displacement of marks on its surface4 ,so far as telescopic observations are concerned1 we are therefore in ignorance as to the axis about which ,uranus revolves4 ,if1 following the analogy of ,jupiter1 or ,saturn1 or ,mars1 or the earth1 the rotation of ,uranus was conducted about an axis1 not greatly inclined from the perpendicular to the ecliptic1 then the rotation of ,uranus would be about an axis very far from perpendicular to the plane in which its satellites revolve4 ,the analogy of the other planets seems to suggest that the rotation of a planet should be nearly perpendicular to the plane in which its satellites revolve4 ,as the question is one which does not admit of being decided by observation1 we may venture to remark that the necessity for a declining ratio of energy to moment of momentum in the ,uranian system provides a suggestion4 ,the moment of momentum of a system1 such as that of ,uranus and its satellites1 is derived partly from the movements of the satellites and partly from the rotation of the planet itself4 ,from the illustrations we have already given1 it is plain that the requisite moment of momentum is compatible with a comparatively small energy only when the system is so adjusted that the axis of rotation of the planet is perpendicular to the plane in which the satellites revolve1 or in other words when the satellites revolve in the plane of the equator of the planet4 ,we do not expect that this condition will be complied with to the fullest extent in any members of the solar system4 ,there is indeed an obvious exception2 for the moon1 in its revolution about the earth1 does not revolve exactly in the earth's equator4 ,we might1 however1 expect that the tendency would be for the movements to adjust themselves in this manner4 ,it seems therefore likely that the direction of the axis of ,uranus is perpendicular1 or nearly so1 to the plane of the movements of its satellites4 ,at this point we take occasion to answer an objection which may perhaps be urged against the doctrine of moment of momentum as here applied4 ,i have shown that the tendency of this dynamical principle is to reduce the movements towards one plane4 ,it may be objected that if there is this tendency1 why is it that the movements have not all been brought into the same plane exactly8 ,this has been accomplished in the case of the bodies forming ,saturn's ring1 and perhaps in the satellites of ,uranus4 ,but why is it that all the great planets of our solar system have not been brought to revolve absolutely in the same plane8 ,we answer that the operations of the forces by which this adjustment is effected are necessarily extremely slow4 ,the process is still going on1 and it may ultimately reach completion4 ,but it is to be particularly observed that the nearer the approach is made to the final adjustment1 the slower must be the process of adjustment1 and the less efficient are the forces tending to bring it about4 ,for the purpose of illustrating this1 we may estimate the efficiency of the forces in flattening down the system in the following manner4 ,suppose that there are two circular orbits at right angles to each other1 and that we measure the efficiency of the action tending to bring the planes to coincide by #ajj4 ,when the planes are at an angle of thirty degrees the efficiency is represented by #ej1 and when the inclination is only five degrees the efficiency is no more than #i1 and the efficiency gradually lessens as the angle declines4 ,as the angles of inclination of the planes in the solar system are so small1 we see that the efficiency of the flattening operation in the solar system must have dwindled correspondingly4 ,hence we need not be surprised that the final reduction of the orbits into the same plane has not yet been absolutely completed4 ,certainly the most numerous1 and perhaps the grandest1 illustrations of the operation of the great natural principles we have been considering are to be found in the case of the spiral nebul4 ,the characteristic appearance of these objects demands special explanation1 and it is to dynamics we must look for that explanation4 ,as to the original cause of a nebula we shall have something to say in a future chapter4 ,at present we are only considering how1 when a nebula has come into existence1 the action of known dynamical principles will mould that nebula into form4 ,as an illustration of a nebula1 in what we may describe as its comparatively primitive shape1 we may take the ,great ,nebula in ,orion4 ,this stupendous mass of vaguely diffused vapour may probably be regarded as in an early stage when contrasted with the spirals4 ,we have already shown how the spectroscopic evidence demonstrates that the famous nebula is actually a gaseous object4 ,it stands thus in marked contrast with many other nebul which1 by not yielding a gaseous spectrum1 seem to inform us that they are objects which have advanced to a further stage in their development than such masses of mere glowing gas as are found in the splendid object in ,orion4 ,the development of a nebula must from dynamical principles proceed along the lines that we have already indicated4 ,we shall assume that the nebula is sufficiently isolated from surrounding objects in space as to be practically free from disturbing influences produced by these objects4 ,we shall therefore suppose that the evolution of the nebula proceeds solely in consequence of the mutual attractions of its various parts4 ,in its original formation the nebula receives a certain endowment of energy and a certain endowment of moment of momentum2 the mere fact that we see the nebula1 the fact that it radiates light1 shows that it must be expending energy1 and the decline of the energy will proceed continuously from the formation of the object4 ,the laws of dynamics assure us that no matter what may be the losses of energy which the nebula suffers through radiation or through the collisions of its particles1 or through their tidal actions1 or in any way whatever from their mutual actions1 the moment of momentum must remain unchanged4 ,as the ages roll by1 the nebula must gradually come to dispose itself1 so that the moment of momentum shall be maintained1 notwithstanding that the energy may have wasted away to no more than a fraction of its original amount4 ,originally there was1 of course1 one plane1 in which the moment of momentum was a maximum4 ,it is what we have called the principal plane of the system1 and the evolution tends in the direction of making the nebula gradually settle down towards this plane4 ,we have seen that the moment of momentum can be sustained with the utmost economy of energy by adjusting the movements of the particles so that they all take place in orbits parallel to this plane1 and the mutual attractions of the several parts will gradually tend to bring the planes of the different orbits into coincidence4 ,every collision between two atoms1 every ray of light sent forth1 conduce to the final result4 ,hence it is that the nebula gradually tends to the form of a flat plane4 ,this is the first point to be noticed in the formation of a spiral nebula4 ,but there is a further consideration4 ,as the nebula radiates its light and its heat1 and thus loses its energy1 it must be undergoing continual contraction4 ,concurrently with its gradual assumption of a flat form1 the nebula is also becoming smaller4 ,here again that fundamental conception of the conservation of moment of momentum will give us important information4 ,if the nebula contracts1 that is to say1 if each of its particles draws in closer to the centre1 the orbits of each of its particles will be reduced4 ,but the quantity of areas to be described each second must be kept up4 ,we have pointed out that it is infinitely improbable the system should have been started without any moment of momentum1 and this condition of affairs being infinitely improbable1 we dismiss any thought of its occurrence4 ,as the particles settle towards the plane1 the areas swept out by the movements to the right1 and those areas swept out by the movements to the left1 will not be identical2 there will therefore be a balance on one side1 and that balance must be maintained without the slightest alteration throughout all time4 ,as the particles get closer together1 and as their orbits lessen1 it will necessarily happen that the velocities of the particles must increase1 for not otherwise can the fundamental principle of the constant moment of momentum be maintained4 ,and as the system gets smaller and smaller1 by contraction from an original widely diffused nebulosity1 like1 perhaps1 the nebula in ,orion1 down to a spiral nebula which may occupy not a thousandth or a millionth part of the original volume1 the areas will be kept up by currents of particles moving in the two opposite ways around a central point4 ,as the contraction proceeds1 the opposing particles will occasionally collide1 and consequently the tendency will be for the predominant side to assert itself more and more1 until at last we may expect a condition to be reached in which all the movements will take place in one direction1 and when the sum of the areas described in a second1 by each of the particles1 multiplied by their respective masses1 will represent the original endowment of moment of momentum4 ,thus we find that the whole object becomes ultimately possessed of a movement of rotation4 ,the same argument will show that the inner parts of the nebula will revolve more rapidly than those in the exterior4 ,thus we find the whirlpool structure produced1 and thus we obtain an explanation1 not only of the flatness of the nebula1 but also of the spiral form which it possesses4 ,it is not too much to say that the operation of the causes we have specified1 if external influence be withheld1 tends ultimately to produce the spiral1 whatever may have been the original form of the object4 ,no longer1 therefore1 need we feel any hesitation in believing the assurance of ,professor ,keeler that out of the one hundred and twenty thousand nebul1 at least one-half must be spirals4 ,we have found in dynamics an explanation of that remarkable type of object which we have now reason to think is one of the great fundamental forms of nature4 ---------------------------------------- -------------------------------- ,,chapter ,,xii4 ,,the ,,evolution ,,of ,,the ,,solar ,,system4 ,the ,primval ,nebula--,a ,planetary ,nebula--,the ,progress of its ,evolution--,unsymmetrical ,contraction--,centres of ,condensation--,the ,form ultimately assumed--,difference between ,small ,bodies and ,large--,earth and ,sun--,acceleration of ,velocities--,formation of the ,subordinate ,systems--,special ,circumstances in the case of the ,earth and ,moon--,vast ,scale of the ,spirals--,spectra of the ,spiral ,nebul4 ,,we shall consider in this chapter what we believe to have been the history of that splendid system1 formed by the planets under the presiding control of the sun4 ,the ground over which we have already passed will prepare us for the famous doctrine that the sun1 the planets and their satellites1 together with the other bodies which form the group we call the solar system1 have originated from the contraction of a primval nebula4 ,as the ages rolled by1 this great primval nebula began to undergo modification4 ,in accordance with the universal law which we find obeyed in our laboratories1 and which we have reason to believe must be equally obeyed throughout the whole extent of space1 this nebula1 if warmer than the surrounding space1 must begin to radiate forth its heat4 ,we are to assume that the nebula does not receive heat from other bodies1 adequate to compensate for that which it dissipates by radiation4 ,there is thus a loss of heat and consequently the nebula must begin to contract4 ,its material must gradually draw together1 and must do so under the operation of those fundamental laws which we have explained in the last chapter4 ,the contraction1 or rather the condensation1 of the material would of course generally be greatest at the central portion of the nebula4 ,this is especially noticeable in the photograph of the great spiral already referred to4 ,but in addition to this special condensation at the centre1 the concentration takes place also1 though in a lesser degree1 at many other points throughout the whole extent of the glowing mass4 ,each centre of condensation which in this way becomes established tends continually to increase4 ,in consequence of this law1 as the great nebula contracted and as the great bulk of the material drew in towards the centre1 there were isolated regions in the nebula which became subordinate centres of condensation4 ,perhaps in the primval nebula1 from which the solar system originated1 there were half-a-dozen or more of these centres that were of conspicuous importance1 while a much larger number of small points were also distinguished from the surrounding nebula4 7,figs4 #dj and #da47 ,and still the contraction went on4 ,the heat1 or rather the energy with which the nebula had been originally charged1 was still being dissipated by radiation4 ,we give no estimate of the myriads of years that each stage of the mighty process must have occupied4 ,the tendency of the transformation was1 however1 always in one direction4 ,it did at last result in a great increase of the density of the substance of the nebula1 both in the central regions as well as in the subordinate parts4 ,in due time this increase in density had reached such a point that the materials in the condensing centres could be no longer described as retaining the gaseous form4 ,but though heat was incessantly being radiated from the great nebula1 it did not necessarily follow that the nebula was itself losing temperature4 ,this is a seeming paradox to which we have already had occasion to refer in ,chapter ,,vi4 ,we need not now further refer to it than to remember that1 in speaking of the loss of heat from the nebula1 it would sometimes not be correct to describe the operation as that of cooling4 ,up to a certain stage in the condensation1 the loss of heat leads rather to an augmentation of temperature than to its decline4 ,we are thus led to see how the laws of heat1 after being in action on the primitive nebula for a period of illimitable ages1 have at last effected a marvellous transformation4 ,that nebula has condensed into a vast central mass with a number of associated subordinate portions4 ,we may suppose that the original nebula in the course of time does practically disappear4 ,it is absorbed by the attraction of those ponderous centres which have gradually developed throughout its extent4 ,the large central body1 and perhaps some of the other bodies thus evolved1 are at first of so high a temperature that a copious radiation of heat still goes forth from the system4 ,as they discharge their stores of heat1 the smaller bodies show the effects of loss of heat more rapidly than those which are larger4 ,it is indeed obvious that a small body must cool more rapidly than a big one4 ,it is sufficient to note that the cooling takes place from the surface1 and that the bigger the body the larger the quantity of material that it contains for each unit of superficial area4 ,if the radius of a sphere be doubled1 its volume is increased eightfold1 while its surface is only increased fourfold4 ,illustration3 ,fig4 #ch4--,,the ,,ring ,,nebula ,,in ,,lyra 7,lick ,observatory74 7,from the ,royal ,astronomical ,society ,series47 ,let us now concentrate our attention on two of the bodies which1 after immense ages1 have been formed from the condensation of the primval nebula4 ,let one of the two bodies be that central object1 which preponderates so enormously that its mass is a thousandfold that of all the others taken together4 ,let the other be one of the smaller bodies4 ,as it parts with its heat1 the smaller body1 which has originally condensed from the nebula1 will assume some of the features of a mass of molten liquid4 ,from the liquid condition1 the body will pass with comparative rapidity into a solid state1 at least on its outer parts4 ,the exterior of this body will therefore become solid while the interior is still at an excessively high temperature4 ,the outer material1 which has assumed the solid form1 is constituted of the elements with which we are acquainted1 and is in the form of what the geologist would class as the igneous rocks1 of which granite is the best known example4 ,the shell of hard rocks outside encloses the material which is still heated and molten inside4 ,such a crust would certainly be an extremely bad conductor of heat4 ,the internal heat is therefore greatly obstructed in its passage outwards to the surface4 ,the internal heat may consequently be preserved in the interior of the body for an enormously protracted period1 a period perhaps comparable with those immense ages which the evolution of the body from the primval nebula has demanded4 ,the smaller body may have thus attained a condition in which the temperature reigning on its surface is regulated chiefly by the external conditions of the space around1 while the internal parts are still highly charged with the primitive heat from the original nebula4 ,the great central mass1 which we may regard as thousands of times greater than that of the subordinate body1 cools much more slowly4 ,the cooling of this great mass is so enormously protracted in comparison with that of the smaller body that it is quite conceivable the central mass may continue to glow with intense fervour for immense ages after the smaller body has become covered with hard rock4 ,it will1 ,i hope1 be clear that the two bodies to which ,i am here alluding are not merely imaginary objects4 ,the small body1 which has so far cooled down that its surface has lost all indication of internal heat1 is of course our earth4 ,the great central mass which still glows with intense fervour is the sun4 ,such is in outline the origin of the sun and the earth as suggested by the nebular theory4 ,what we have said of the formation of the earth will equally apply to the evolution of other detached portions of the primitive nebula4 ,there may be several of these1 and they may vary greatly in size4 ,the smaller they are the more rapidly in general will the superabundant heat be radiated away1 and the sooner will the surface of that planet acquire the temperature which is determined by the surrounding conditions4 ,there are1 however1 many modifying circumstances4 ,it is essential to notice that the primval nebula must have had some initial moment of momentum1 unless we are to assume the occurrence of that which is infinitely improbable4 ,it would have been infinitely improbable for the system not to have had some moment of momentum originally4 ,as the evolution proceeds1 and as the energy is expended1 while this original endowment of moment of momentum is preserved1 we find1 as explained in the last chapter1 the system gradually settling down into proximity to a plane1 and gradually acquiring a uniform direction of revolution4 ,hence we see that each of the subordinate masses which ultimately consolidate to form a planet have a motion of revolution around the central body4 ,in like manner the central body itself rotates1 and all these motions are performed in the same direction4 ,in addition to the revolutions of the planets around the sun1 there are other motions which can be accounted for as consequences of the contraction of the nebula4 ,we now refer to that central portion which is to form the sun1 and consider1 in the first instance1 only one of the subordinate portions which is to form a planet4 ,as these two bodies form part of the same nebulous mass they will to a certain extent rotate together as one piece4 ,if any body is rotating as a whole1 every part of that body is also in actual rotation4 ,we shall refer to this again later on2 but for the present it is sufficient to observe that as the planet was originally continuous with the sun1 it had a motion of rotation besides its motion of revolution1 and it revolved round its own axis in a period equal to that of its revolution round the sun4 ,in the beginning the rotation of the planet was therefore an exceedingly slow movement4 ,but it became subsequently accelerated4 ,for we have already explained that each planet is by itself subjected to the law of the conservation of moment of momentum4 ,as each planet assumes a separate existence1 it draws to itself its share of the moment of momentum1 and that must be strictly preserved4 ,but the planet1 or rather the materials which are to form the future planet1 are all the time shrinking2 they are drawing more closely together4 ,if1 therefore1 the area which each particle of the planet describes when multiplied by the mass of that particle and added to the similar products arising from all the other particles1 is to remain constant1 it becomes necessary that just as the orbits of these particles diminish in size1 so must the speed at which they revolve increase4 ,we thus find that there is a tendency in the planet to accelerate its rotation4 ,and thus we see that a time will come when the planet1 having assumed an independent existence1 will be found rotating round its axis with a velocity which must be considered high in comparison with the angular velocity which the planet had while it still formed part of the original nebula4 ,as the planets have been evolved so as to describe their several orbits around the sun1 so in like manner the smaller systems of satellites have been so evolved as to describe their orbits round the several planets that are their respective primaries4 ,when a planet1 or rather the materials which were drawing together to form a planet1 had acquired a predominant attraction for the parts of the primval nebula in their locality1 a portion of the nebulous material became specially associated with the planet4 ,as the planet with this nebulous material became separated from the central contracting sun1 or became1 as it were1 left behind while the sun was drawing into itself the material which surrounded it the planet and its associated nebula underwent on a miniature scale an evolution similar to that which had already taken place in the formation of the sun and the planets as a whole4 ,in this manner secondary systems seem sometimes to have had their origin4 ,we should1 however1 say that though what we have here indicated appears to explain fully the evolution of some of the systems1 such1 for instance1 as that of ,jupiter and his four moons1 or ,saturn and his eight or nine1 the circumstances with regard to the earth and the moon are such as to require a very different explanation of the origin of our satellite4 ,in the first place we may notice that the great mass of the moon1 in comparison with the earth1 is a wholly exceptional feature in the relations between the planets and their satellites in the other parts of the system4 ,in no other instance does the mass of a satellite bear to the mass of the planet a ratio anything like so great as the ratio of our moon to the earth4 ,the moon has a mass which is about one-eightieth of the mass of the earth1 while even the largest of ,jupiter's satellites has not one ten-thousandth part of the mass of the planet itself4 ,the evolution of the earth and moon system has been brought about in a manner very different from that of the evolution of the other systems of satellites4 ,we do not here enter into any discussion of the matter4 ,we merely remind the reader that it is now known1 mainly by the researches of ,professor ,g4 ,h4 ,darwin1 that in all probability the moon was originally part of the earth1 and that a partition having occurred while the materials of the earth and moon were still in a plastic state1 a small portion broke away to form the moon1 leaving behind the greater mass to form the earth4 ,then1 under the influence of tides1 which may agitate a mass of molten rock1 as the moon was once 7,fig4 #ci71 just as they may agitate an ocean1 the moon was forced away1 and was ultimately conducted to its present orbit4 ,illustration3 ,fig4 #ci4--,,lunar ,,craters3 ,,hyginus ,,and ,,albategnius4 7,photographed by ,,mm4 ,loewy and ,puiseux47 ,it was at first tempting to imagine that a theory which accounted so satisfactorily for the evolution of the moon from the earth might also account in a similar manner for the evolution of the earth from the sun4 ,had this been the case1 it is needless to say that the principles we now accept in the nebular theory would have needed large modification1 if not actual abandonment4 ,a close examination into the actual statistics brings forcibly before us the exceptional character of the earth-moon system4 ,it can be demonstrated that the earth could not have been evolved from the sun in the same manner as there is every reason to believe that the moon has been evolved from the earth4 ,the evolution of the satellites of ,jupiter has proceeded along lines quite different from those of the evolution of the moon from the earth1 so that we may1 perhaps1 find in the evolution of the satellites of ,jupiter an illustration in miniature of the way in which the planets themselves have been evolved in relation to the sun4 ,we must not forget that the only spiral nebul which lie within the reach of our powers of observation1 whether telescopic or photographic1 appear to be objects of enormously greater cosmical magnificence than was that primval nebula from which so insignificant an object as the solar system has sprung4 ,the great spirals1 so far as we can tell at present1 appear to be thousands of times1 or even millions of times1 greater in area than the solar system4 ,at this point1 however1 we must speak with special caution1 having due regard to the paucity of our knowledge of a most important element4 ,astronomers must confess that no efforts which have yet been made to determine the dimensions of a nebula have been crowned with success4 ,we have not any precise idea as to what the distance of the great spiral might be4 ,we generally take for granted that these nebul are at distances comparable with the distances of the stars4 ,on this assumption we estimate that the spiral nebul must transcend enormously the dimensions of the primval nebula from which the solar system has sprung4 ,the spiral nebul that have so far come within our observation seem to be objects of an order of magnitude altogether higher than a solar system4 ,they seem to be engaged on the majestic function of evolving systems of stars like the ,milky ,way1 rather than on the inconsiderable task of producing a system which concerns only a single star and not a galaxy4 ,illustration3 ,fig4 #dj4--;,a ,,remarkable ,,spiral 7n4g4c4 #fbh2 in ,pisces74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,the spiral form of structure is one in which ,nature seems to delight4 ,we find it in the organic world allied with objects of the greatest interest and beauty4 ,the ammonite1 a magnificent spiral shell sometimes exceeding three feet in diameter1 belongs to a type which dominated the waters of the globe in secondary times1 and which still survives in the nautilus4 ,the same form is reproduced in minute creations totally different from ammonites in their zoological relations4 ,among the exquisite foraminifera which the microscopist knows so well may be found most delicate and beautiful spirals4 ,just as we see every range of spiral in the animal world1 from an organism invisible to the naked eye1 up to an ammonite a yard or more across1 so it would seem that there are spiral nebul ranging from such vast objects as the great spiral in ,canes ,venatici down to such relatively minute spirals as those whose humble function it is to develop a solar system4 ,it is no more than a reasonable supposition that the great spirals in the heavens are probably only the more majestic objects of an extremely numerous class4 ,the smaller objects of this type--among which we might expect to find nebul like1 in size and importance1 to the primval nebula of our system--are so small that they have not yet been recognised4 ,it should at this stage be mentioned that several curious small planetary nebul have in these modern days been discovered by their peculiar spectra4 ,if the nebulous character of these most interesting objects had not been accidentally disclosed by characteristic lines in their spectra1 these undoubted nebul would each have been classified merely as stars4 ,this fact will lead us to the surmise that there must be myriads of nebul in the heavens1 too small to come within the range of our telescopes or of our most sensitive photographic plates4 ,suppose that a facsimile of the primval nebula of our system1 precisely corresponding with it in size and identical with it in every detail1 were at the present moment located in space1 but at a distance from our standpoint1 as great as the distance of1 let us say1 the great spiral2 it seems certain that this nebula1 even though it contained the materials for a huge sun and a potential system of mighty planets1 if not actually invisible to us here1 would in all probability demand the best powers of our instruments to reveal it1 and then it would be classed not as a nebula at all but as a star of perhaps the #abth or #aeth1 or even smaller magnitude4 ,illustration3 ,fig4 #da4--;,a ,,clearly ,,cut ,,spiral 7n4g4c4 #dcba2 in ,coma ,berenices74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,it is to be remembered that the class of minute planetary nebul make themselves known solely by the fact that they exhibit the bright line indicative of gaseous spectra4 ,if these objects 7though still nebul7 had not displayed gaseous spectra1 it is certain they would have escaped detection1 at least by the process which has actually proved so successful4 ,the continuous band of light which they would then have presented could not be discriminated from the band of light from a star4 ,it is therefore not improbable that among the star-like bodies which have been represented on our photographs1 there may be some which are really minute spiral nebul4 ,in general a star is a minute point of light which no augmentation of telescopic power and no magnification will show otherwise than as a point1 granted only good optical conditions and good opportunity so far as the atmosphere is concerned4 ,it has1 however1 been occasionally noted that certain so-called stars are not mere points of light2 they do possess what is described as a disc4 ,it is not at all impossible that the objects so referred to are spiral nebul4 ,we may describe them as formed on a small scale in comparison with the great spiral or the nebula in ,andromeda4 ,but the smallness here referred to is only relative4 ,they are in all probability quite as vast as the primval spiral nebula from which the solar system has been evolved1 though not so large as those curious ring-shaped nebul of which the most celebrated example lies in the constellation ,lyra 7,fig4 #ch74 ,such is an outline of what we believe to have been the history of our solar system4 ,we have already given the evidence derived from the laws of heat4 ,we have now to consider the evidence which has been derived from the constitution of the system itself4 ,we shall see how strongly it supports the belief that the origin of sun and planets has been such as the nebular theory suggests4 ---------------------------------------- -------------------------------- ,,chapter ,,xiii4 ,,the ,,unity ,,of ,,material ,,in ,,the ,,heavens ,,and ,,the ,,earth4 ,clouds--,fire-,mist--,vapour of ,platinum--,components of ,chalk--,constituents of the ,primval ,fire-,mist--,objections--,origin of the ,mist--,remarkable ,discovery of the ,century--,analysis of the ,sun--,spectroscopic ,analysis--,simplicity of ,solar ,chemistry--,potassium--,a ,drop of ,water--,the ,solar ,elements--,calcium--,the ,most ,important ,lines in the ,solar ,spectrum--,photograph of the ,sun--,carbon in the ,solar ,clouds--,function of ,carbon--,bunsen's ,burner ,illustrates ,carbon in the ,sun--,carbon ,vapours in the ,sun--,the ,supposed ,limit to our ,knowledge of the ,heavens--,characteristics of ,spectroscopic ,work--,bearing on the ,nebular ,theory4 ,,in considering how the formation of our solar system was brought about1 we naturally first enquire as to the material of which this superb scheme is constructed4 ,what were the materials already to hand from which1 in pursuance of the laws of ,nature1 the solar system was evolved8 ,see the robust and solid nature of this earth of ours1 and the robust and solid nature of the moon and the planets4 ,it might at first sight be concluded that the primitive materials of our earth had also been in the solid state4 ,but such is not the case4 ,the primitive material of the solar system was not solid1 it was not even liquid4 ,what we may describe as the mother-substance of the universe must have been of quite a different nature2 we can give an illustration of the physical character of that substance4 ,the lover of ,nature delights to look at the mountains and the trees1 the lakes and the rivers4 ,but he will not confine his regard merely to the objects on the earth's surface4 ,he1 no less than the artist and the poet1 delights to gaze at that enchanting scenery which1 day by day1 is displayed in infinite beauty overhead2 that scenery which is not wholly withheld even from observers whose lives may be passed amid the busy haunts of men1 that scenery which is so often displayed on fine days at all seasons4 ,we are alluding to those clouds which add the charm of infinite variety to the sky above us4 ,it is necessary for us now to think of matter when it possesses neither the density of a solid1 nor the qualities of a liquid1 but rather when it has that delicate texture which the clouds exhibit4 ,the primval material from which the solar system has been evolved is of a texture somewhat similar to that of the clouds4 ,this primval material is neither solid nor liquid2 it is what we may describe as vapour4 ,but having pointed to the clouds in our own sky as illustrating1 in a sense1 the texture of this original mother-substance of the solar system1 we can carry the analogy no further4 ,those dark and threatening masses which forbode the thunderstorm1 or those beautiful fleecy clouds which enhance the loveliness of a summer's day1 are1 of course1 merely the vapours of water4 ,but the vapours in the mother-substance from which systems have been evolved were by no means the vapours of water4 ,they were vapours of a very different character--vapours that suggest the abodes of ,pluto rather than the gentle rain that blesses the earth4 ,in the mother-substance of the solar system vapours of a great variety of substances were blended4 ,for in the potent laboratory of ,nature every substance1 be it a metal or any other element1 or any compound1 no matter how refractory1 will1 under suitable circumstances1 be dissolved into vapour4 ,take1 for instance1 such a material as platinum4 ,could anything be less like a vapour than this silvery metal8 ,we know that platinum is the densest of all the elements4 ,we know that platinum1 more effectually than other metals1 resists liquefaction from the application of heat4 ,no ordinary furnace can fuse platinum2 yet in another way we can overcome the resistance of this metal4 ,the electric arc1 when suitably managed1 yields a temperature higher than that of any furnace4 ,let the electric current spring from one pole of platinum to another1 and a brilliant arc of light is produced by the glowing gas1 which is characteristic of platinum4 ,the light dispensed from that arc is different from the light that would be radiated if the poles were of any material other than platinum4 ,some of the platinum has not alone been melted1 it has actually been turned into vapour by the overpowering heat to which it has been subjected4 ,thus the solidity of this substance1 which resists so stubbornly the action of lower temperatures1 can be overcome1 and the very densest of all metals is dissolved into wisps of vapour4 ,we choose the case of platinum as an illustration because it is a substance exceptionally dense and exceptionally refractory4 ,if platinum can be vaporised1 there is not much difficulty in seeing that other elements must be capable of being vaporised also4 ,in fact1 given such heat as is found abundantly in natural sources1 there is no known element1 or combination of elements1 which will not assume the form of gas or vapour or cloud4 ,at the temperature of the sun a drop of water would be forthwith resolved into its component gases of oxygen and hydrogen4 ,in like manner a piece of chalk1 if exposed to the sun1 would be speedily transformed2 it would first be heated red-hot and then white-hot2 it is1 indeed1 white-hot chalk that gives us that limelight which we know so well4 ,but the heat of the sun is far greater than the temperature of the incandescent lime4 ,the lime would not only be heated white-hot by contact with solar heat1 but still further stages would be reached4 ,it would suffer decomposition4 ,it would break up into three different elements3 there would be the metal which we call calcium1 there would be oxygen1 and there would be carbon4 ,owing to the tremendous temperature of the sun the metal would not remain in the metallic form2 it would not be even in a liquid form2 it would become a gas4 ,the elements which unite to form this chalk would be not only decomposed1 but they would be vaporised4 ,what is thus stated about the drop of water and the chalk may1 so far as we know1 be stated equally with regard to any other compounds4 ,it matters not how close may be the chemical association in which the elements are joined3 no matter how successfully those compounds may resist the decomposition under the conditions ordinarily prevailing on earth1 they have to yield under the overwhelming trial to which the sun would subject them4 ,though there are many elements in the solar chemistry1 there are no compounds4 ,at the exalted temperature to which they are exposed in the sun the elements are indisposed for union with the other elements there met with1 and which are at the same temperature4 ,in these circumstances1 they successfully resist all alliances4 ,until the last few years no elements were known in our terrestrial experience which possessed at ordinary temperatures the same qualities of resolute isolation which all elements seem to display at extreme temperatures4 ,the famous discovery of argon1 and of other strange gases associated with argon in the atmosphere and elsewhere1 has revealed1 to the astonishment of chemists and to the great extension of knowledge1 that we have with us here elements which resist all solicitations to enter into chemical union with other substances4 ,it is doubtless in consequence of this absolute refusal to unite that1 in spite of their abundance and their wide distribution1 these elements have eluded detection for centuries4 ,to the astronomer argon is both interesting and instructive4 ,it shows us an element which possesses1 at the ordinary temperatures of the surface of the earth1 a property which is true of all elements when subjected to such temperatures as are found in the sun4 ,think of the rocks which form the earth's crust and of the minerals which lie far below4 ,think of the soil which lies on its surface1 of the forests which that soil supports1 and the crops which it brings forth4 ,think of the waters of the ocean1 and the ice of the ,poles4 ,think of the objects of every kind on this globe4 ,think of the stone walls of a great building1 of the iron used to give it strength1 of the slates which cover it1 and of the timber which forms its floors2 think of the innumerable other materials which have gone towards its construction2 think even of the elementary substances which go to form the bodies of animals1 of the lime in their bones1 and of the carbon which is so intimately associated with life itself4 ,the nebular theory declares that those materials have not always been in the condition in which we now see them2 that there was a time in which they were so hot that they were not in the solid state2 they were not even in the fluid state1 but were all in rolling volumes of glowing vapour which formed the great primval fire-cloud4 ,we must understand the composite nature of the primitive fire-mist from which our solar system originated4 ,let me illustrate the matter thus3 ,we shall suppose that a heterogeneous collection of substances is brought together1 the items of which may be somewhat as follows3 let there be many tons of iron and barrels of lime1 some pieces of timber1 and cargoes of flint2 let there be lead and tin and zinc1 and many other metals1 from which copper and silver and several of the rarest metals must not be excluded2 let there be innumerable loads of clay1 which shall represent aluminium and silicon1 and hogsheads of sea-water to supply oxygen1 hydrogen1 and sodium4 ,there should be also1 ,i need hardly add1 many other elements2 but there is no occasion to mention more2 indeed1 it would be impossible to give a list which would be complete4 ,suppose that this diverse material is submitted to a heat as intense as the most perfect furnace can make it4 ,let the heat be indeed as great as that which we can get from the electric arc1 or even greater still4 ,let us suppose this heat to be raised to such a point that1 not only have the most refractory metals been transformed into vapour1 but the elements which were closely in combination have also been rent asunder4 ,this we know will happen when compound substances are raised to a very high temperature4 ,we shall suppose that the heat has been sufficient to separate each particle of water into its constituent atoms of oxygen and hydrogen2 we shall suppose that the heat has been sufficient to decompose even lime itself into its constituent parts1 and exhibit them in the form of vapour4 ,the heat is to be so great that even carbon itself1 the most refractory of substances1 has had to yield1 so that after passing through a stage of dazzling incandescence it has melted and ultimately dissolved into vapour4 ,next let us suppose that these several vapours are blended1 though we need not assume that the separate elements are diffused uniformly throughout all parts of the cloud4 ,let us suppose that these bodies1 which contributed to form the nebula1 have been employed in amounts1 not to be measured in tons1 or in hundreds of tons1 but in a thousand millions of millions of millions of millions of tons4 ,let the mass of vapour thus arising be expanded freely through open space4 ,let it extend over a region which is to measure hundreds of thousands of millions of miles in length and breadth and depth4 ,then the doctrine of the earth's beginning1 which we are striving to unfold in these lectures1 declares that in a fire-mist such as is here outlined the solar system had its origin4 ,various objections may occur to the thoughtful reader when asked to accept such statements4 ,we must do our best to meet these objections4 ,the evidence we submit must be of an indirect or circumstantial kind4 ,direct testimony on such a subject is from the nature of the case impossible4 ,the actual fire-mist in which our system had its origin is a mist no longer4 ,the material that forms the solid earth beneath our feet did once1 we verily believe1 float in the great primval fire-mist4 ,of course we cannot show you that mist4 ,darwin could not show the original monkeys from which it would seem the human race has descended2 none the less do most of us believe that our descent has really taken the line that ,darwin's theory indicates4 ,in connection with this subject1 as with most others1 it is easy to ask questions which1 ,i think we may say1 no one can answer with any confidence4 ,it may1 for instance1 be asked how this vast fire-mist came into existence4 ,if it arose from heat1 how did that heat happen to be present8 ,why was all the material in the state of vapour8 ,what1 in short1 was the origin of that great primval nebula8 ,here we must admit that we have proposed questions to which it is impossible for us to do more than suggest answers4 ,as to what brought the mist into existence1 as to whence the materials came1 and as to whence the energy was derived which has been gradually expended ever since1 we do not know anything1 and1 so far as ,i can see1 we have no means of knowing4 ,conjectures on the subject are not wanting1 of course1 and in a later chapter we shall discuss what may be said on this matter4 ,i have shown you to some extent our reasons for believing that our solar system did originate in a fire-mist ,and even if we are not able to explain how the mist itself arose1 yet we do not admit that our argument as to the origin of our system is thereby invalidated4 ,that such a fire-mist as the solar system required did once exist1 must surely be regarded as not at all improbable so long as we can point to the analogous nebul or fire-mists which exist at the present moment1 and which we see with our telescopes4 ,many of these are millions of times as great as the comparatively small fire-mist that would have evolved into our solar system4 ,a question has sometimes been asked as to the most important discovery in astronomy which has been made in the century that has just closed4 ,if1 by the most important discovery1 we mean that which has most widely extended our knowledge of the ,universe1 ,i do not think there need be much hesitation in stating the answer4 ,it seems to me beyond doubt that the most astonishing discovery of the last century in regard to the heavenly bodies is that which has revealed the elementary substances of which the orbs of heaven are composed4 ,this discovery is the more interesting and instructive because it has taught us that the materials of the sun1 of the stars1 and of the nebul are essentially the elements of which our own earth is formed1 and with which chemists had already become well acquainted4 ,we know1 of course1 that this earth1 no matter how various may be the rocks and minerals which form its crust1 and how infinite the variety of objects1 organic and inorganic1 which diversify its surface1 is really formed from different combinations of about eighty different elements4 ,there are gases like oxygen and hydrogen1 there are other substances like carbon and sulphur1 and there are metals like iron and copper4 ,these elements are sometimes met with in their free or uncombined state1 like oxygen in the atmosphere1 or like gold in ,klondike4 ,more frequently they are found in combination1 and in such combinations the characters of the constituent elements are sometimes completely transformed4 ,a deadly gas and a curious metal1 which burns as it floats on water1 most certainly renounce their special characters when they unite to form the salt on our breakfast-table4 ,who would have guessed1 if the chemist had not told him1 that in every wheelbarrowful of ordinary earth there are pounds of silvery aluminium1 and that marble is largely composed of an extremely rare metal1 which but few people have ever seen8 ,until the middle of the century just completed it seemed utterly impossible to form any notion as to the substances actually present in the sun4 ,how could anyone possibly discern them by the resources of the older chemists8 ,it might well have been doubted whether the elements of which the sun was made were the elements of which our earth was formed1 and with which ordinary chemistry had made us familiar4 ,just as the animals and plants which met the gaze of the discoverers when they landed in the ,new ,world were essentially different from those in the ,old ,world1 so it might have been supposed1 with good share of reason1 that this great solar orb1 ninety-three million miles distant1 would be composed of elements totally different from those with which dwellers on the earth had been permitted to become acquainted4 ,this great discovery of the last century revealed to us the character of the elements which constitute the sun4 ,it also added the astonishing information that they are essentially the same elements as those of which our earth itself and all which it contains are formed4 ,if any one had asked in the early years of the century what those elements were which entered into the composition of the sun1 the question would have been deemed a silly one2 it would have been regarded as hopelessly beyond the possibility of solution1 and it would have been as little likely to receive an answer as the questions people sometimes ask now as to the possible inhabitants on ,mars4 ,but about the middle of the century a new era dawned2 the wonderful method of spectroscopic analysis was discovered1 and it became possible to examine the chemistry of the sun4 ,the most important result was to show that the elements which enter into the composition of the sun are the same elements which enter into the composition of the earth4 ,the student of the solar chemistry enjoys1 however1 one advantage over the terrestrial chemist1 if it be an advantage to have his science simplified to the utmost extent4 ,chemistry would1 however1 lose its chief interest if all the elements remained as obstinately neutral as argon1 and disdained alliance with all other elements4 ,it would seem that those elements which most eagerly enter into combination here1 and which resist with such vehemence our efforts to divorce them1 must renounce all chemical union when exposed to the tremendous temperature of the sun4 ,those elements which unite with the utmost eagerness at ordinary temperatures1 seem to become indifferent to each other when subjected to the extremes of heat and cold4 ,potassium unites fiercely with oxygen in the most familiar of all chemical experiments4 ,potassium is indeed a strange metal1 for it is of such small density that a piece cast on a basin of water will float like a chip of wood4 ,it has such avidity for oxygen that it will decompose the water to wrench the molecules of oxygen from those of hydrogen4 ,the union of the metal with the gas generates such heat that the strange substance bursts into flame4 ,this is what takes place at the ordinary temperatures in the well-known experiment of the chemical lecture-table4 ,but at extreme temperatures the greed of potassium for oxygen abates1 if it does not vanish altogether4 ,in those excessively low temperatures at which ,professor ,dewar experiments chemical affinities languish4 ,he has reduced oxygen to a liquid1 and he tells us that 8a berg of silvery potassium might float for ever untarnished on an ocean of liquid oxygen40 ,at the excessively high temperature of the electric arc the oxygen and the potassium1 whose union has been accomplished with such vehemence1 cease to possess affinity1 and they separate again4 ,the solar chemistry seems to know no combination4 ,if a drop of water were transferred to the sun and subjected to the heat of the solar surface1 it must immediately undergo decomposition4 ,that which was a drop of water here would not remain a drop of water there2 it would be at once resolved into its component elements of oxygen and hydrogen4 ,the considerations just given greatly simplify the search for the particular bodies which are at present in the sun4 ,we have only to test for the presence of each of eighty elements4 ,we have not to take account of the thousands of chemical combinations of which these elements are susceptible under terrestrial conditions4 ,we are specially indebted to the late ,professor ,henry ,rowland1 of ,baltimore1 for a profound study of the solar spectrum4 ,in his great work he enumerates thirty-six elements present in the sun1 and the number may be increased now by at least two4 ,eight elements he classes as doubtful1 fifteen are set down as absent from the solar spectrum1 and several had not been tried4 ,iron stands foremost among all the solar elements1 so far as the number of its lines are concerned4 ,no fewer than #b1jjj lines in the spectrum of the sun are attributed to this element4 ,at the other end of the list lead is found4 ,there is only one line apparently due to this metal4 ,carbon is represented by about #bjj lines1 and calcium by about #ge4 ,if1 however1 we test the significance of lines not by their number1 but by their intensity1 then iron no longer heads the list1 its place being taken by calcium 7,fig4 #db74 ,among the elements which ,rowland sets down as not contributing any recognisable lines to the solar spectrum we may mention arsenic and sulphur1 phosphorus1 mercury1 and gold4 ,of the more prominent solar elements there are two or three of such special importance that we pause to give them a little consideration4 ,who does not remember the delight of the first occasion in childhood when he was permitted to peep into a bird's-nest and there see a group of eggs1 often so exquisitely marked or so delicately tinted8 ,how beautiful they seemed as they lay in their cosy receptacle concealed with so much cunning6 ,among other delightful recollections of early youth many will recall a ramble by the sea-shore4 ,we may suppose the tide had retreated1 and with other objects left by the sea on the gleaming sand a little cowrie shell is found4 ,how enchanted we were with our prize6 ,how we looked at the curious marks on its lips1 and the inimitable beauty of its tints6 ,the shell of the hedge-sparrow and the shell cast up by the sea have another quality in common besides their beauty4 ,they have both been fabricated from the same material4 ,lime is of course the substance from which the bird1 by some subtle art of physiology1 forms those exquisite walls by which the vital part of the egg is protected4 ,the soft organism that once dwelt in the cowrie was endowed with some power by which it extracted from the waters of the ocean the lime with which it gradually built an inimitable shell4 ,is it an exaggeration to say that this particular element calcium1 this element so excessively abundant and so rarely seen1 seems to enjoy some peculiar distinction by association with exquisite grace and beauty8 ,the white marble wrought to an unparalleled loveliness by the genius of a ,phidias or a ,canova is but a form of lime4 ,so is the ivory on which the ,japanese artist works with such delicacy and refinement4 ,whether as coral in a ,pacific island1 as a pearl in a necklace or as a stone in the ,parthenon1 lime seems often privileged to form the material basis of beauty in nature and beauty in art4 ,though lime in its different forms1 in the rocks of the earth or the waters of the ocean1 is one of the most ordinary substances met with on our globe1 yet calcium1 the essential element which goes to the composition of lime1 is1 as we have already said1 not by any means a familiar body1 and not many of us1 ,i imagine1 can ever have seen it4 ,chemistry teaches that lime is the result of a union in definite proportions between oxygen gas and the very shy metal1 calcium4 ,this metal is never found in nature unless in such intimate chemical union with some other element like oxygen or chlorine1 that its characteristic features are altogether obscured1 and would indeed never be suspected from the mere appearance of the results of the union4 ,to see the metal calcium you must visit a chemical laboratory where1 by electrical decomposition or other ingenious process1 this elusive element can be induced to part temporarily from its union with the oxygen or other body for which it has so eager an affinity1 and to which it returns with such alacrity4 ,though calcium is certainly a metal1 it is very unlike the more familiar metals such as gold or silver1 copper or iron4 ,a coin might conceivably be formed out of calcium1 but it would have no stability like the coins of the well-known metals4 ,calcium has such an unconquerable desire to unite with oxygen that the unstable metal will speedily grasp from the surrounding air the vital element4 ,unless special precautions are taken to withhold from the calcium the air1 or other source from whence it could obtain oxygen1 the union will most certainly take place1 and the calcium will resume the stable form of lime4 ,thus it happens that though this earth contains incalculable billions of tons of calcium in its various combinations1 yet calcium itself is almost unknown except to the chemist4 ,it is plain that calcium plays a part of tremendous significance on this earth4 ,i do not say that it is the most important of all the elements4 ,it would indeed seem impossible to assign that distinction to any particular element4 ,many are1 of course1 of vital importance1 though there are1 no doubt1 certain of the rarer elements with which this earth could perhaps dispense without being to any appreciable extent different from what it is at present4 ,i do not know that we should be specially inconvenienced or feel any appreciable want unsatisfied1 if1 let us say1 the element lanthanum were to be struck out of existence2 and there are perhaps certain other rare bodies among the known eighty elements1 about which the same remark might be made4 ,illustration3 ,fig4 #db4--,,the ,h4 ,,and ,k4 ,,lines ,,in ,,the ,,photographic ,,solar ,,spectrum 7,higgs74 ,but without calcium there would neither be fertile soil for plants nor bones for animals1 and consequently a world1 inhabited in the same manner as our present globe1 would be clearly impossible4 ,there may be lowly organisms on this earth to which calcium is of no appreciable consequence1 and it is of course conceivable that a world of living types could be constructed without the aid of that particular element which is to us so indispensable4 ,but a world without calcium would be radically different from that world which we know1 so that we are disposed to feel special interest in the important modern discovery that this same element1 calcium1 is abundantly distributed throughout the universe4 ,the boldest and most striking features in the photograph of the solar spectrum are those due to calcium 7,figs4 #db and #dd74 ,in the solar spectrum are two very broad1 very dark1 and very conspicuous lines1 known as ,h and ,k4 ,in every photograph of that portion of the solar spectrum which1 lying beyond the extreme violet1 is invisible to our eyes1 though intensely active on the photographic plate1 these lines stand forth so boldly as to arrest the attention more than any other features of the spectrum4 ,it had been known that these lines were due to calcium1 but there were certain difficulties connected with their interpretation4 ,some recent beautiful researches by ,sir ,william and ,lady ,huggins have cleared away all doubt4 ,it is now certain that the presence of these lines in the spectrum demonstrates that that remarkable element which is the essential feature of lime on this earth is also found in the sun4 ,we have also to note that these same lines have been detected in the photographic spectra of many other bodies in widely different regions of space4 ,thus we establish the interesting result that this particular element which plays a part so remarkable on our earth is not restricted to our globe1 but is diffused far and wide throughout the universe4 ,perhaps the most astonishing discovery made in modern times about the sun is connected with the wonderful element1 helium4 ,so long ago as #ahfh ,sir ,norman ,lockyer discovered1 during an eclipse1 that the light of the sun contained evidence of the presence in that orb of some element which was then totally unknown to chemists4 ,this new body was not unnaturally named the sun-element1 or helium4 ,but more than a quarter of a century had to elapse before any chemist could enjoy the opportunity of experimenting directly upon helium4 ,no labour could prepare the smallest particle of this substance1 no money could purchase it1 for at that time no specimen of the element was known to exist nearer than the sun1 ninety-three million miles distant4 ,but in #ahie an astonishing discovery was made by ,professor ,ramsay4 ,he was examining a rare piece of mineral from ,norway4 ,from this mineral1 clevite1 the ,professor extracted a little gas which was to him and to all other chemists quite unknown4 ,but on applying the spectroscope to examine the character of the light which this gas emitted when submitted to the electric current1 it yielded1 to their amazement1 the characteristic light of helium4 ,thus was the sun-element at last shown to be a terrestrial body1 though no doubt a rare one4 ,the circumstances that ,i have mentioned make helium for ever famous among the constituents of the universe4 ,it will never be forgotten that though from henceforth it may be regarded as a terrestrial body1 yet it was first discovered1 not in the earth beneath our feet1 but in the far-distant sun4 ,in a previous picture 7,fig4 #ad7 we showed a photograph of a part of the sun's surface2 this striking view displays those glowing clouds from which the sun dispenses its light and heat4 ,these clouds form a comparatively thin stratum around the sun1 the interior of which is very much darker4 ,the layer of clouds is so thin that it may perhaps be likened to the delicate skin of a peach in comparison with the luscious interior4 ,it is in these dazzling white clouds that we find the source of the sun's brightness4 ,were those clouds removed1 though the sun's diameter would not be appreciably reduced1 yet its unparalleled lustre would be at once lessened4 ,we use the expression 8clouds0 in speaking of these objects1 for clouds they certainly are1 in the sense of being aggregates of innumerable myriads of minute beads of some substance2 but those solar clouds are very unlike the clouds of our own sky1 in so far as the material of which they are made is concerned4 ,the solar clouds are not little beads of water2 they are little beads of white-hot material so dazzlingly bright as to radiate forth the characteristic brilliance and splendour of the sun4 ,the solar clouds drift to and fro2 they are occasionally the sport of terrific hurricanes2 they are sometimes driven away from limited areas1 and in their absence we see merely the black interior of the solar globe1 which we call a sun-spot4 ,now comes the important question as to the material present in these clouds which confers on the sun its ability to radiate forth such abundant light and heat4 ,the profound truth already stated1 that the solar elements are the same as the terrestrial elements1 greatly simplifies the search for that particular element which forms those solar clouds4 ,as the sun is made of substances already known to us by terrestrial chemistry1 and as there are no chemical compounds to embarrass us1 the choice of the possible constituents of those solar clouds becomes narrowed to the list of elements experimented on in our laboratories4 ,we owe to ,dr4 ,g4 ,johnstone ,stoney1 ,f4,r4,s41 the discovery of the particular element which forms those fire-clouds in the sun1 and confers on the presiding body of the solar system the power of being so useful to the planets which owe it allegiance4 ,carbon is the element in question4 ,i need hardly add that carbon is well known as one of the most commonplace and one of the most remarkable substances in ,nature4 ,a piece of coke differs from a piece of pure carbon only by the ash which the coke leaves behind when burned4 ,timber is principally composed of this same element1 and when the timber is transformed into charcoal but little more than the carbon remains4 ,carbon is indeed everywhere present4 ,it is1 as we have mentioned1 one of the elements which enter into the composition of a piece of chalk4 ,carbon is in the earth beneath our feet2 it is in the air above us4 ,carbon is one of the chief ingredients in our food1 and it is by carbon that the heat of the body is sustained4 ,indeed1 this remarkable element is intimately connected with life in every phase4 ,every organic substance contains carbon1 and it courses with the blood in our veins4 ,it assumes the widest variety of forms1 renders the greatest diversity of services1 and appears in the most widely different places4 ,carbon is indeed of a protean character1 and there is a beautiful symbol of the unique position which it occupies in the scheme of ,nature 7,fig4 #dc74 ,carbon is associated not alone with articles of daily utility and of plenteous abundance1 but it is carbon which forms the most exquisite gems 8of purest ray serene40 ,the diamond is1 of course1 merely a specimen of carbon of absolute purity and in crystalline form4 ,great as is the importance of carbon on this earth1 it is spread far more widely2 it is not confined merely to the earth1 for carbon abounds on other bodies in space4 ,the most important functions of carbon in the universe are not those it renders on this earth4 ,it was shown by ,dr4 ,stoney that this same wonderful substance is indeed a solar element of vast utility4 ,it is carbon which forms the glowing solar clouds to which our very life owes its origin4 ,in the incandescent lamp the brilliant light is produced by a glowing filament of carbon1 and one reason why we employ this element in the electric lamp1 instead of any other1 may be easily stated4 ,if we tried to make one of these lamps with an iron wire1 we should find that when the electric current is turned on and begins to flow through the wire1 the wire will1 in accordance with a well-known law1 become warm1 then hot1 red-hot1 and white-hot2 but even when white-hot the wire will not glow with the brightness that we expect from one of these lamps4 ,ere a sufficient temperature can be reached the iron will have yielded1 it will have melted into drops of liquid1 continuity will be broken1 the circuit will be interrupted1 and the lamp destroyed4 ,we should not have been much more successful if instead of iron we had tried any other metal4 ,even a platinum wire1 though it will admit of being raised to a much higher temperature than a wire of iron or a wire of steel1 cannot remain in the solid condition at the temperature which would be necessary if the requisite incandescence is to be produced4 ,there is no known metal1 and perhaps no substance whatever1 which has so high a temperature of fusion as carbon4 ,a filament of carbon1 alone among the available elements1 will remain continuous and unfused while transmitting a current intense enough to produce that dazzling brilliance which is expected from the incandescent lamp4 ,this is the reason why this particular element carbon is an indispensable material for the electrician4 ,modern research has now demonstrated that just as we employ carbon as the immediate agent for producing our beautiful artificial light1 so the sun uses precisely the same element as the agent of its light and heat-giving power4 ,in the extraordinary fervour which prevails in the interior of the sun all substances of every description must submit to be melted1 nay1 even to be driven into vapour4 ,an iron poker1 for instance1 would vanish into iron vapour if submitted to this appalling solar furnace4 ,even carbon itself is unable to remain solid when subjected to the intense heat prevailing in the inner parts of the sun4 ,at that heat carbon must assume the form of gas or vapour1 just as iron or the other substances which yield more readily to the application of heat4 ,by the help of a simple experiment we may illustrate the significance of the carbon vapours in the solar economy4 ,let us take a ,bunsen burner1 in which the air and gas are freely mingled before they enter into combustion4 ,if the air and the gas be properly proportioned1 the combustion is so perfect that though a great deal of heat is produced there is but little light4 ,the gas burned in this experiment ought to be the ordinary gas of our mains1 which depends for its illuminating power on the circumstance that the hydrogen1 of which the gas is chiefly composed1 is largely charged with carbon4 ,the illuminating power of the gas may indeed be measured by its available richness in carbon4 ,as it enters the burner the carbon is itself in a gaseous form4 ,this is not1 of course1 on account of a high temperature4 ,the carbon of the coal-gas is in chemical union with hydrogen1 and the result is in the form of invisible gases4 ,it is these composite gases1 blended with large volumes of ordinary hydrogen1 which form the illuminating gas of our mains4 ,in the ,bunsen burner the admission of a proper proportion of air1 which becomes thoroughly mixed with the coal gas1 produces perfect combustion4 ,in the act of burning1 the oxygen of the air unites immediately with the gas2 it combines with the hydrogen to form watery vapour1 and it combines with the carbon to form gases which are the well-understood products of combustion4 ,suppose1 now1 we cut off the supply of air from the ,bunsen burner1 which can be done in a moment by placing the hand over the ring of holes at the bottom at which the air is admitted4 ,immediately a change takes place in the combustion4 ,in place of the steady1 hardly visible1 but intensely hot flame which we had before1 we have now a very much larger flame which makes a bright and flickering flare that lights up the room4 ,if we re-admit the air at the bottom of the burner the light goes down instantly2 the small1 pale flame replaces it1 and again the perfect combustion gives out intense heat at the expense of the light4 ,the remarkable change in the character of a gas-flame produced by admitting air to mix with the gas before combustion is1 of course1 easily explained4 ,the chemical action takes place with much greater facility under these circumstances4 ,the union of the carbon in the coal gas with the oxygen then takes place so thoroughly and instantaneously that the carbon never seems to have abandoned the gaseous form even for a moment in the course of the transformation4 ,but in the case where air is not permitted to mingle with the gas1 the supply of oxygen to unite with the incandescent gases can only be obtained from the exterior of the flame4 ,the consequence is that the glowing gas charged with carbon vapour is chilled to some extent by contact with the cold air4 ,it therefore seems as if the union of the hydrogen with the oxygen permitted the particles of carbon in the flame to resume their solid form for a moment4 ,but in that solid form these particles1 being at a high temperature1 have a wonderful efficiency for radiation1 and consequently brilliance is conferred upon the light4 ,most of the particles of carbon speedily unite with the surrounding oxygen1 and re-enter the gaseous state in a different combination4 ,some of them1 however1 may escape this fate1 in which case they assume the undesirable form of smoke4 ,the ,bunsen lamp can thus be made to give an illustration of the fact that when carbon vapours receive a chill1 the immediate effect of the chill is to transform the carbon from the gaseous form to myriads of particles in the liquid1 or more probably in the solid form4 ,in the latter state the carbon possesses a power of radiation greatly in excess of that which it possessed in the gaseous state1 even though the gas may have been at a much higher temperature than the white-hot solid particles4 ,we can now apply these principles to the explanation of the marvellous radiation of light and heat from the great orb of day4 ,the buoyancy of the carbon vapours is one of their most remarkable characteristics2 they tend to soar upwards through the solar atmosphere until they attain an elevation considerably over that of many of the other materials in the heated vapours surrounding the great luminary4 ,we may illustrate what happens to these carbon vapours by considering the analogous case presented in the formation of ordinary clouds in our own skins4 ,it is true1 no doubt1 that terrestrial clouds are composed of material very different from that which enters into the solar clouds4 ,terrestrial clouds of course arise in this way2 the generous warmth of the sun evaporates water from the great oceans1 and transforms it into vapour4 ,this vapour ascends through our atmosphere1 not at first as a visible cloud1 but in the form of an invisible vapour4 ,it is gradually diffused throughout the upper air1 until at last particles of water1 but recently withdrawn from the oceans1 attain an altitude of a mile or more above the surface of the earth4 ,a transformation then awaits this aqueous vapour4 ,in the coldness of those elevated regions the water can no longer remain in the form of vapour4 ,the laws of heat require that it shall revert to the liquid state4 ,in obedience to this law the vapour collects into liquid beads1 and it is these liquid beads1 associated in countless myriads1 which form the clouds we know so well4 ,the same phenomenon of cloud-production is witnessed on a smaller scale in the formation of the visible puffs which issue from the funnel of a locomotive4 ,we generally describe these rolling white volumes as steam2 but this language is hardly correct4 ,steam1 properly so called1 is truly as invisible as the air itself2 it is only after the steam has done its work and is discharged into the atmosphere1 and there receives a chill1 that it becomes suddenly transformed from the purely gaseous state into clustering masses of microscopic spheres of water1 and thus becomes visible4 ,we can now understand the transformation of these buoyant carbon vapours which soar upwards in the sun4 ,they attain an elevation at which the fearful intensity of the solar heat has been so far abated by the cold of outer space that the carbon gas is not permitted to remain any longer in the form of gas2 it must return to the liquid or to the solid state4 ,in the first stage on this return the carbon gas becomes transformed1 just in the same way as watery vapour ascending from the earth becomes transformed into the fleecy cloud4 ,under the influence of its fall in temperature the carbon vapour collects into a clustering host of little beads of carbon4 ,this is the origin of the glorious solar clouds4 ,each particle of carbon in that magnificent radiant surface has a temperature1 and consequently a power of radiation1 probably exceeding that with which the filament of carbon glows in the incandescent electric arc4 ,when we consider that millions of millions of square miles on our luminary are covered with clouds1 of which every particle is so intensely bright1 we shall perhaps be able to form some idea of that inimitable splendour which even across the awful gulf of ninety-three million miles transmits the indescribable glory of daylight4 ,we are perhaps at present living rather too close to the period itself to be able to appreciate to its full extent the greatness of that characteristic discovery made in astronomy during the century just closed1 to which the present chapter relates4 ,in the early part of the last century it might have been said--indeed1 by a certain very distinguished philosopher it actually was said--that a limit could be laid down bounding the possibilities of our knowledge of the heavenly bodies4 ,it was admitted that we might study the movements of the different orbs in vastly greater detail than had been hitherto attempted1 and that we might calculate the forces to which those orbs were submitted4 ,with the help of mathematical analysis we might pursue the consequences of these forces to their remote ramifications2 we might determine where the various orbs were situated at inimitably remote periods in the past4 ,we might calculate the positions which they shall attain at epochs to be reached in the illimitably remote future2 we might discover innumerable new stars and worlds2 and we might map down and survey the distant parts of the universe4 ,we might even sound the depths of space and determine the distances of the more remote celestial bodies1 much more distant than any of those which have already yielded their secrets2 we might measure the dimensions of those bodies and determine their weights2 we might add scores or hundreds to the list of the known planets2 we might multiply many times the number of known nebul and star-clusters2 we might make measurements of many thousands of double stars2 we might essay the sublime task of forming an inventory of the stars of the universe and compiling a catalogue in which the stars and their positions would be recorded in their millions2 but1 said the philosopher to whom ,i have referred1 though you might accomplish all this1 and much more in the same direction1 yet there is a well-marked limit to your possible achievements2 you can1 he said1 never expect to discover the actual chemical elements of which the heavenly bodies are composed4 ,nobody could dispute the reasonableness of this statement at the time he made it2 indeed1 it seemed to be a necessary deduction from our knowledge of the arts of chemistry1 as those arts were understood before the middle of the last century4 ,in the prosecution of his researches by the older method1 the chemist could no doubt discover the different elements of which the body was formed4 ,that is to say1 his art enabled him to accomplish this task1 provided one very essential and fundamental condition could be complied with4 ,however accomplished the chemist of fifty years ago might have been1 he would assuredly have thought that he was being mocked if asked to determine the composition of a body which was #ic1jjj1jjj miles away from him4 ,the very idea of forming an analysis under such conditions would have been scouted as preposterous4 ,he would naturally ask that a specimen of the body should be delivered into his hands1 a specimen which he could take into his laboratory1 pulverise in his mortars1 place in his test-tubes1 treat with his re-agents1 or examine with his blowpipe4 ,only by such methods was it then thought possible to obtain an analysis and discover the elements from which any given substance was formed4 ,for in the early part of this century the splendid method of spectrum analysis1 that method which has revealed to us so many of the secrets of ,nature1 had not yet come into being4 ,when that memorable event took place it was at once perceived that the spectroscope required no actual contact with the object to be tested1 but only asked to receive some of the rays of light which that object dispersed when sufficiently heated4 ,it was obvious that this new method must be capable of an enormously enlarged application4 ,the flame producing the vapour might be at one end of the room1 while the spectroscope testing the elements in that vapour might be at the other end4 ,this new and beautiful optical instrument could analyse an object at a distance of a hundred feet4 ,but if applicable at a distance of a hundred feet1 why not at a hundred yards1 or a hundred miles1 or a hundred million miles8 ,why might the method not be used if the source of light were as far as the sun1 or as far as a star1 or even as far as the remotest nebula1 whose faint gleam on the sky is all that the mightiest telescope can show4 ,presently another great advance was recorded4 ,as the study of this subject progressed1 it was soon found that a spectrum visible to the human eye was not always indispensable for the success of the analysis4 ,the photographic plate1 which so frequently replaces the eye in other classes of observation1 has also been used to replace the eye in the use of the spectroscope4 ,a picture has thus been obtained showing the characteristic lines in the spectrum of a celestial object4 ,that object may have been sunk in space to a distance so tremendous that even though the light travelled at a pace sufficient to complete seven circuits of our earth in each second of time1 yet the rays from the object in question may have been travelling for centuries before they reached our instrument4 ,however the rays of light may have become weakened in the course of that journey1 they still faithfully preserve the credentials of their origin4 ,at last the light is decomposed in the spectroscope1 and the several rays1 which have been so closely commingled in their long voyage of myriads of miles1 are now for the first time forced to pursue different tracks2 they thus reach their different destinations on the photographic plate1 and they there engrave their characteristic inscriptions4 ,nature in this operation imparts for our instruction a message which it is our business to interpret4 ,it is true that these inscriptions are not always easily deciphered2 many of them have not yet been understood4 ,a portion of the solar spectrum showing many of the lines in the visible region is represented in the accompanying plate4 ,illustration3 ,fig4 #dc4--,,spectrum ,,of ,,comet ,,showing ,,carbon ,,lines4 7,sir ,w4 ,huggins1 ,k4,c4,b47 ,considering the insignificance of our earth when viewed in comparison with the millions of other orbs in the universe1 considering also the stupendous distances by which the earth is separated from innumerable globes which are very much greater1 it is certainly not a little astonishing to learn that the elements from which the various bodies in the universe have been composed are practically the same elements as those of which our earth is built4 ,is not this a weighty piece of evidence in favour of the theory that earth1 sun1 and planets are all portions of the same primval nebula in which these elements were blended8 ,illustration3 ,,the ,,solar ,,spectrum4 ,we do not1 of course1 mean to affirm that the great primval nebula was homogeneous throughout its vast extent4 ,the waters of ocean are not strictly the same in all places2 even the atmosphere is not absolutely uniform4 ,nature does not like homogeneity4 ,the original nebula1 we may well believe1 was irregular in form1 and denser in some places than in others4 ,we do not suppose that if we could procure a sample of nebula in one place and another sample from the same nebula1 but in a different place1 say a hundred million miles distant1 the two would show an identity of chemical composition2 two samples of rock from different parts of the same quarry will not always be identical4 ,but we may be assured that1 in general1 whatever elements are present in the nebula will be widely dispersed through its extent4 ,if from different parts of the nebula two globes are formed by condensation1 though we should not affirm1 and though in fact we could not believe1 that those globes would be of identical composition1 yet we should reasonably expect that the elementary bodies which entered into their composition would be in substantial agreement4 ,if one element1 say iron1 was abundant in one globe1 we should expect that iron would not be absent from the other4 ,thus the elements represented in one body should be essentially those which were represented in the other4 ,illustration3 ,fig4 #dd4--,,spectrum ,,of ,,sun ,,during ,,eclipse4 ,,the ,,two ,,chief ,,lines ,,are ,,due ,,to ,,calcium4 7,evershed47 ,it is obvious that if the sun and the earth--to confine our attention solely to those two bodies--had originated from the primval nebula1 they would bear with them1 as a mark of their common origin1 a resemblance in the elementary bodies of which they were composed4 ,when ,laplace framed his theory1 he had not1 he could not have had1 the slightest notion as to the particular elements in the sun4 ,for anything he could tell1 those elements might be absolutely different from the elements in the earth4 ,yet1 even without information on this critical point1 the evidence for the nebular theory appeared to him so cogent that he gave it the sanction of his name4 ,it cannot be denied that if spectroscopic analysis had demonstrated that the elements in the sun were totally different from the elements in the earth a serious blow would have been dealt to the nebular theory4 ,the collateral evidence1 strong as it undoubtedly is1 might hardly have withstood so damaging an admission4 ,if1 on the other hand1 we find1 as we actually have found1 that the elements in the sun and the elements in the earth are practically identical1 we obtain the most striking corroboration of the truth of the nebular theory4 ,had ,kant and ,laplace been aware of this most significant fact1 they would probably have cited it as most important testimony4 ,they would have pointed out that the iron so abundant in the earth beneath our feet is also abundant in the sun overhead4 ,they would1 ,i doubt not1 if they had known it1 have dwelt upon the circumstance that with that element1 carbon1 which enters into every organic body on this earth1 our sun is also richly supplied1 and they would have hardly failed to allude to the wide distribution in space of calcium1 hydrogen1 and many other well-known elements4 ,laplace mainly based his belief in the nebular theory on some remarkable deductions from the theory of probabilities4 ,to the consideration of these we proceed in the next three chapters4 ,we may1 however1 remark at the outset that if the evidence derived from probabilities seemed satisfactory to ,laplace one hundred years ago1 this same line of evidence1 strengthened as it has been by recent discoveries1 is enormously more weighty1 at the present day4 ---------------------------------------- -------------------------------- ,,chapter ,,xiv4 ,,the ,,first ,,concord4 ,certain ,remarkable ,coincidences--,the ,plane of ,movement of a ,planet--,consideration of ,planes of ,several ,planetary ,orbits--,a ,characteristic of the ,actual ,planetary ,motions not to be ,explained by ,chance--,the ,first ,concord--,the ,planes not at ,random--,a ,division of the ,right ,angle--,statement of the ,coincidences--,an ,illustration by ,parable--,the ,cause of the ,coincidences--,the ,argument ,strengthened by the ,asteroids--,an ,explanation by the ,nebular ,theory4 ,,in the present chapter1 and in the two chapters which are to follow1 ,i propose to give an outline of those arguments in favour of the nebular theory which are presented by certain remarkable coincidences observed in the movements of the bodies of our solar system4 ,there are1 indeed1 certain features in the movements of the planets which would seem so inexplicable if the arrangement of the system had taken place by chance1 that it is impossible not to seek for some physical explanation4 ,we have already had occasion to refer in previous chapters to the movements of the bodies of our system4 ,it will be our object at present to show that it is hardly conceivable that the movements could have acquired the peculiar characteristics they possess unless the solar system has itself had an origin such as that which the nebular theory assigns4 ,the argument on which we are to enter is1 it must be confessed1 somewhat subtle1 but its cogency is irresistible4 ,for this argument we are indebted to one of the great founders of the nebular theory4 ,it was given by ,kant himself in his famous essay4 ,we will commence with a preliminary point which relates to elementary mechanics4 ,it may1 however1 help to clear up a difficult point in our argument if ,i now state some well-known principles in a manner specially adapted for our present purpose4 ,let us think of two bodies1 ,a and ,s1 and1 for the sake of clearness1 we may suppose that each of these bodies is a perfect sphere4 ,we might think of them as billiard balls1 or balls of stone1 or balls of iron4 ,we shall1 however1 suppose them to be formed of material which is perfectly rigid4 ,they may be of any size whatever1 large or small1 equal or unequal4 ,one of them may be no greater than a grain of mustard-seed1 and the other may be as large as the moon or the earth or the sun4 ,let us further suppose that there is no other body in the universe by which the mutual attraction of the two bodies we are considering can be interfered with4 ,if these two bodies are abandoned to their mutual attraction1 let us now see what the laws of mechanics assure us must necessarily happen4 ,illustration3 ,fig4 #de4--;,a ,,spiral ,,presented ,,edgewise 7n4g4c4 #dfca2 in ,coma ,berenices74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,let ,a and ,s be simply released from initial positions of absolute rest4 ,in these circumstances1 the two points will start off towards each other4 ,the time that must elapse before the two bodies collide will depend upon circumstances4 ,the greater the initial distance between the two balls1 their sizes being the same1 the longer must be the interval before they come together4 ,the relation between the distance separating the bodies and the time that must elapse before they meet may be illustrated in this way4 ,suppose that two balls1 both starting from rest at a certain distance1 should take a year to come together by their mutual attraction1 then we know that if the distance of the two balls had been four times as great eight years would have to elapse before the two balls collided4 ,if the distances were nine times as great then twenty-seven years would elapse before the balls collided1 and generally the squares of the times would increase as the cubes of the distances4 ,in such statements we are supposing that the radii of the balls are inconsiderable in comparison with the distances apart from which they are started4 ,the time occupied in the journey must also generally depend on the masses of the two bodies1 or1 to speak more precisely1 on the sum of the masses of the two bodies4 ,if the two balls each weighed five hundred tons1 then they would take precisely the same time to rush together as would two balls of one ton and nine hundred and ninety-nine tons respectively1 provided the distances between the centres of the two balls had been the same in each case4 ,if the united masses of the two bodies amounted to four thousand tons1 then they would meet in half the time that would have been required if their united masses were one thousand tons1 it being understood that in each case they started with the same initial distance between the centres4 ,instead of simply releasing the two bodies ,a and ,s so that neither of them shall have any impulse tending to make it swerve from the line directly joining them1 let us now suppose that we give one of the bodies4 ,a1 a slight push sideways4 ,the question will be somewhat simpler if we think of ,s as very massive1 while ,a is relatively small4 ,if1 for instance1 ,s be as heavy as a cannon-ball1 while ,a is no heavier than a grain of shot1 then we may consider that ,s remains practically at rest during the movement4 ,the small pull which ,a is able to give will produce no more than an inappreciable effect on ,s4 ,if the two bodies come together1 ,a will practically do all the moving4 ,illustration3 ,fig4 #df4--,,the ,,plane ,,of ,a ,,planet',s ,,orbit4 ,we represent the movement in the adjoining figure4 ,if ,a is started off with an initial velocity in the direction ,a ,t1 the attraction of ,s will1 however1 make itself felt1 even though ,a cannot move directly towards ,s4 ,the body will not be allowed to travel along ,a ,t2 it will be forced to swerve by the attraction of ,s2 it will move from ,p to ,q1 gradually getting nearer to ,s4 ,to enter into the details of the movement would require rather more calculation than it would be convenient to give here4 ,even though ,s is much more massive than ,a1 we may suppose that the path which ,a follows is so great that the diameter of the globe ,s is quite insignificant in comparison with the diameter of the orbit which the smaller body describes4 ,we shall thus regard both ,a and ,s as particles1 and ,kepler's well-known law1 to which we so often refer1 tells us that ,a will revolve around ,s in that beautiful figure which the mathematician calls an ellipse4 ,for our present purpose we are particularly to observe that the movement is restricted to a plane4 ,the plane in which ,a moves depends entirely on the direction in which it was first started4 ,the body will always continue to move in the same plane as that in which its motion originally commenced4 ,this plane is determined by the point ,s and the straight line in which ,a was originally projected4 ,it is essential for our argument to note that ,a will never swerve from its plane so long as there are not other forces in action beside those arising from the mutual attractions of ,a and ,s4 ,the ordinary perturbations of one body by the action of others need not here concern us4 ,the case we have supposed will1 of course1 include that of the movement of a planet round the sun4 ,the planet is small and represented by the body ,a1 which revolves round the great body ,s1 which stands for the sun4 ,however the motion of the planet may actually have originated1 it moves just as if it had received a certain initial impulse1 in consequence of which it started into motion1 and thus defined a certain plane1 to which for all time its motion would be restricted4 ,so far we have spoken of only a single planet2 let us now suppose that a second planet1 ,b1 is also to move in revolution about the same sun4 ,this planet may be as great as ,a1 or bigger1 or smaller1 but we shall still assume that both planets are inconsiderable in comparison with ,s4 ,we may assume that ,b revolves at the same distance as ,a1 or it may be nearer1 or further4 ,the orbit of ,b might also have been in the same plane as ,a1 or--and here is the important point--it might have been in a plane inclined at any angle whatever to the orbit of ,a4 ,the two planes might1 indeed1 have been perpendicular4 ,no matter how varied may be the circumstances of the two planets1 the sun would accept the control of each of them2 each would be guided in its own orbit1 whether that orbit be a circle1 or whether it be an ellipse of any eccentricity whatever4 ,so far as the attraction of the sun is concerned1 each of these planets would remain for ever in the same plane as that in which it originally started4 ,let us now suppose a third planet to be added4 ,here again we may assume every variety in the conditions of mass and distance4 ,we may also assume that the plane which contains the orbit of this third planet is inclined at any angle whatever to the planes of the preceding planets4 ,in the same way we may add a fourth planet1 and a fifth2 and in order to parallel the actual circumstance of our solar system1 so far as its more important members are concerned1 we may add a sixth1 and a seventh1 and an eighth4 ,the planes of these orbits are subjected to a single condition only4 ,each one of them passes through the centre of the sun4 ,if this requirement is fulfilled1 the planes may be in other respects as different as possible4 ,in the actual solar system the circumstances are1 however1 very different from what we have represented in this imaginary solar system4 ,it is the most obvious characteristic of the tracks of ,jupiter and ,venus1 and the other planets belonging to the sun1 that the planes in which they respectively move coincide very nearly with the plane in which the earth revolves4 ,we must suppose all the orbits of our imaginary system to be flattened down1 nearly into a plane1 before we can transform the imaginary system of planets ,i have described into the semblance of an actual solar system4 ,if the orbits of the planets had been arranged in planes which were placed at random1 we may presume they would have been inclined at very varied angles4 ,as they are not so disposed1 we may conclude that the planes have not been put down at random2 we must conclude that there has been some cause in action which1 if we may so describe it1 has superintended the planes of these orbits and ordained that they should be placed in a very particular manner4 ,two planets' orbits might conceivably coincide or be perpendicular1 or they might contain any intermediate angle4 ,the plane of the second planet might be inclined to the first at an angle containing any number of degrees4 ,to make some numerical estimate of the matter1 we proceed as follows3 ,if we divide the right angle into ten parts of nine degrees each 7,fig4 #dg71 then the inclination of the two planes might1 for example1 lie between ,o and #i1 or between #ah and #bg1 or between #de and #ed1 or between #ha and #ij1 or in any one of the ten divisions4 ,let us think of the orbit of ,jupiter4 ,then the inclination of the plane in which it moves to the plane in which the earth moves must fall into one of the ten divisions4 ,as a matter of fact1 it does fall into the angle between #j and #i4 ,illustration3 ,fig4 #dg4--;,a ,,right ,,angle ,,divided ,,into ,,ten ,,parts4 ,but now let us consider a second planet1 for example ,venus4 ,if the orbit of ,venus were to be placed at random1 its inclination might with equal probability lie in any one of the ten divisions1 each of nine degrees1 into which we have divided the right angle4 ,it would be just as likely to lie between forty-five and fifty-four1 or between seventy-two and eighty-one1 as in any other division4 ,but we find another curious coincidence4 ,it was already remarkable that the plane of ,jupiter's orbit should have been included in the first angle of nine degrees from the orbit of the earth4 ,it is therefore specially noteworthy to find that the planet ,venus follows the same law1 though each one of the ten angular divisions was equally available4 ,the coincidences we have mentioned1 remarkable as they are1 represent only the first of the series4 ,what has been said with respect to the positions of the orbits of ,jupiter and ,venus may be repeated with regard to the orbits of ,mercury and ,mars1 ,saturn1 ,uranus1 and ,neptune4 ,if the tracks of these planets had been placed merely at random1 their inclinations would have been equally likely to fall into any of the ten divisions4 ,as a matter of fact1 they all agree in choosing that one particular division which is adjacent to the track of the earth4 ,if the orbits of the planets had indeed been arranged fortuitously1 it is almost inconceivable that such coincidences could have occurred4 ,let me illustrate the matter by the following little parable4 ,there were seven classes in a school1 and there were ten boys in each class4 ,there was one boy named ,smith in the first class1 but only one4 ,there was also one ,smith1 but only one1 in each of the other classes4 ,the others were named ,brown1 ,jones1 ,robinson1 etc4 ,an old boy1 named ,captain ,smith1 who had gone out to ,australia many years before1 came back to visit his old school4 ,he had succeeded well in the world1 and he wanted to do something generous for the boys at the place of which he had such kindly recollections4 ,he determined to give a plum-cake to one boy in each class2 and the fortunate boy was to be chosen by lot4 ,the ten boys in each class were to draw1 and each successful boy was to be sent in to ,captain ,smith to receive his cake4 ,the ,captain sat at a table1 and the seven winners were shown in to receive their prizes4 8,what is your name80 he said to the boy in the first class1 as he shook hands with him4 8,smith10 replied the boy4 8,dear me10 said the ,captain1 8how odd that our names should be the same4 ,never mind1 it's a good name4 ,here's your cake4 ,good-bye1 ,smith40 ,then up came the boy from the second class4 8,what is your name80 said the ,captain4 8,smith1 sir10 was the reply4 8,dear me10 said the visitor4 8,this is very singular4 ,it is indeed a very curious coincidence that two ,smiths should have succeeded4 ,were you really chosen by drawing lots80 8,yes1 sir10 said the boy4 8,then are all the boys in your class named ,smith80 8,no1 sir2 ,i'm the only one of that name in the ten40 8,well10 said the ,captain1 8it really is most curious4 ,i never heard anything so extraordinary as that two namesakes of my own should happen to be the winners4 ,now then for the boy from class three40 ,a cheerful youth advanced with a smile4 8,well1 at all events10 said the good-natured old boy1 8your name is not ,smith80 8,oh1 but it is10 said the youth4 ,the gallant ,captain jumped up1 and declared that there must have been some tremendous imposition4 ,either the whole school consisted of ,smiths1 or they called themselves ,smiths1 or they had picked out the ,smiths4 ,the four remaining boys1 still expecting their cakes1 here burst out laughing4 8,what are your names80 shouted the donor4 8,smith60 8,smith660 8,smith6660 8,smith66660 were the astounding replies4 ,the good man could stand this no longer4 ,he sent for the schoolmaster1 and said1 8,i particularly requested that you would choose a boy drawn by lot from each of your seven classes1 but you have not done so4 ,you have merely picked out my namesakes and sent them up for the cakes40 ,but the master replied1 8,no1 ,i assure you1 they have been honestly chosen by lot4 ,nine black beans and one white bean were placed in a bag2 each class of ten then drew in succession1 and in each class it happened that the boy named ,smith drew the white bean40 8,but10 said the visitor1 8this is not credible4 ,only once in ten million times would all the seven ,smiths have drawn the white beans if left solely to chance4 ,and do you mean to tell me that what can happen only once out of ten million times did actually happen on this occasion--the only occasion in my life on which ,i have attempted such a thing8 ,i don't believe the drawing was made fairly by lot4 ,there must have been some interference with the operation of chance4 ,i insist on having the lots drawn again under my own inspection40 8,yes1 yes10 shouted all the other boys4 ,but all the successful ,smiths roared out1 8,no40 ,they did not feel at all desirous of another trial4 ,they knew enough of the theory of probabilities to be aware that they might wait till another ten million fortunate old boys came back to the school before they would have such luck again4 ,the situation came to a deadlock4 ,the ,captain protested that some fraud had been perpetrated1 and in spite of their assurances he would not believe them4 ,the seven ,smiths declared they had won their cakes honestly1 and that they would not surrender them4 ,the ,captain was getting furious1 the boys were on the point of rebellion1 when the schoolmaster's wife1 alarmed by the tumult1 came on the scene4 ,she asked what was the cause of the disturbance4 ,it was explained to her1 and then ,captain ,smith added that by mathematical probabilities it was almost inconceivable that the only seven ,smiths in the school should have been chosen4 ,the gracious lady replied that she knew nothing1 and cared as little1 about the theory of probabilities1 but she did care greatly that the school should not be thrown into tumult4 8,there is only one solution of this difficulty10 she added4 8,it is that you forthwith provide cakes1 not only for the seven ,smiths1 but for every one of the boys in the school40 ,this resolute pronouncement was received with shouts of approval4 ,the ,captain1 with a somewhat rueful countenance1 acknowledged that it only remained for him to comply4 ,he returned1 shortly afterwards1 to his gold-diggings in ,australia1 there to meditate during his leisure on this remarkable illustration of the theory of probabilities4 ,this parable illustrates the improbability of such arrangements as we find in the planets having originated by chance4 ,the chances against their having thus occurred are #aj1jjj1jjj to #a4 ,hence we find it reasonable to come to the conclusion that the arrangement1 by which the planets move round the sun in planes which are nearly coincident1 cannot have originated by chance4 ,there must have been some cause which produced this special disposition4 ,we have1 therefore1 to search for some common cause which must have operated on all the planets4 ,as the planets are at present absolutely separated from each other1 it is impossible for us to conceive a common cause acting upon them in their present condition4 ,the cause must have operated at some primval time1 before the planets assumed the separate individual existence that they now have4 ,we have spoken so far of the great planets only1 and we have seen how the probability stands4 ,we should also remark that there are also nearly #ejj small planets1 or asteroids1 as they are more generally called4 ,among them are1 no doubt1 a few whose orbits have inclinations to the ecliptic larger than those of the great planets4 ,the great majority of the asteroids revolve1 however1 very close to that remarkable plane with which the orbits of the great planets so nearly coincide4 ,every one of these asteroids increases the improbability that the planes of the orbits could have been arranged as we find them1 without some special disposing cause4 ,it is not possible or necessary to write down the exact figures4 ,the probability is absolutely overwhelming against such an arrangement being found if the orbits of the planets had been decided by chance1 and chance alone4 ,we may feel confident that there must have been some particular circumstances accompanying the formation of the solar system which rendered it absolutely necessary for the orbits of the planets to possess this particular characteristic4 ,we have pointed out in ,chapter ,,xii4 that the nebular theory offers such an explanation1 and we do not know of any other natural explanation which would be worthy of serious attention4 ,indeed1 we may say that no other such explanation has ever been offered4 ---------------------------------------- -------------------------------- ,,chapter ,,xv4 ,,the ,,second ,,concord4 ,another ,remarkable ,coincidence in the ,solar ,system--,the ,second ,concord--,the ,direction of the ,movements of the ,great ,planets--,the ,movement of ,ceres--,yet ,another ,planet--,discovery of ,eros--,the ,nearest ,neighbour of the ,earth--,throwing ,heads and ,tails--,a ,calculation of the ,chances--,the ,numerical ,strength of the ,argument--,an ,illustration of the ,probability of the ,origin of the ,solar ,system from the ,nebula--,the ,explanation of the ,second ,concord offered by the ,nebular ,theory--,the ,relation of ,energy and ,moment of ,momentum--,different ,systems ,illustrated--,that all the ,movements should be in the same ,direction is a ,consequence of ,evolution from the ,primval ,nebula4 ,,we have seen in the last chapter that there is a very remarkable concordance in the positions of the planes of the orbits of the planets1 and we have shown that this concordance finds a natural historical explanation in the nebular origin of our system4 ,we have now to consider another striking concord in the movements of the planets in their several orbits1 and this also furnishes us with important evidence as to the truth of the nebular theory4 ,the argument on which we are now to enter is one which specially appealed to ,laplace1 and was put forward by him as the main foundation of the nebular theory4 ,illustration3 ,fig4 #dh4--;,,illustration ,,of ,,the ,,second ,,concord4 ,in the adjoining ,fig4 #dh we have a diagram of a portion of the solar system4 ,we shall regard the movements as somewhat simplified4 ,the sun is supposed to be at the centre1 turning round once every twenty-five days1 on an axis which is supposed to be perpendicular to the plane of the paper4 ,we may also for our present purpose assume that the orbits of the earth and the other planets lie in this same plane4 ,in the first place we observe that the earth might have gone round its track in either direction so far as the welfare of mankind is concerned4 ,the succession of day and night1 and the due changes of the seasons1 could have been equally well secured whichever be the direction in which the earth revolves4 ,we do1 however1 most certainly find that the direction in which the earth revolves round the sun is the same as the direction in which the sun rotates on its axis4 ,this is the first coincidence4 ,we may now consider other planets4 ,look1 for instance1 at the orbit of ,jupiter4 ,it seems obvious that ,jupiter might have been made to revolve round the sun either one way or the other2 indeed1 it will be remembered that though ,kepler's laws indicate so particularly the shape of the track in which the planet revolves1 and prescribe so beautifully the way in which the planet must moderate or accelerate its velocity at the different parts of its track1 yet they are quite silent as to the direction in which the planets shall revolve in that track4 ,if we could imagine a planet to be stopped to have its velocity reversed1 and then to be started in a precisely opposite direction1 it would still continue to describe precisely the same path2 it would still obey ,kepler's laws with unfailing accuracy1 so far as our present argument is concerned1 and the velocity which it would have at each point of the track would be quite the same whether the planet were going one way or whether it was going the other4 ,it is therefore equally possible for ,jupiter to pursue his actual track by going round the sun in the same direction as the earth1 or by going in the opposite direction4 ,but we actually find that ,jupiter does take the same direction as the earth1 and this1 as we have already seen1 is the direction in which the sun rotates4 ,here we have the second coincidence4 ,we now take another planet2 for example1 ,mars4 ,again we affirm that ,mars could have moved in either direction1 but1 as a matter of fact1 it pursues the same direction as ,jupiter and the earth4 ,in the orbital movement of ,saturn we have the fourth coincidence of the same kind1 and we have a fifth in the case of ,mercury1 and a sixth in ,venus1 a seventh in ,uranus1 and an eighth in ,neptune4 ,the seven great planets and the earth all revolve around the sun1 not only in orbits which are very nearly in the same plane1 but they also revolve in the same direction4 ,the coincidences we have pointed out with regard to the movements of the great planets of our system may be also observed with regard to the numerous bodies of asteroids4 ,on the first night of the century just closed1 the #ast of ,january1 #ahja1 the first of the asteroids1 now known as ,ceres1 was discovered4 ,this was a small planet1 not a thousandth part of the bulk of one of the older planets1 and visible1 of course1 only in the telescope4 ,like the older planets1 it was found to obey ,kepler's laws2 but this we might have foreseen1 because ,kepler's laws depend upon the attraction of gravitation1 and must apply to any planet1 whatever its size4 ,when1 therefore1 the new planet was found1 and its track was known1 it was of much interest to see whether the planet in moving round that track observed the same direction in which all the older planets had agreed to travel1 or whether it moved in the opposite direction4 ,in the orbit of ,ceres we have a repetition of the coincidence which has been noticed in each of the other planets4 ,the new planets1 like all the rest1 move round the sun in the same direction as the sun rotates on its axis4 ,the discovery of this first asteroid was quickly followed by other similar discoveries2 each of the new planets described1 of course1 an ellipse1 and the directions which these planets followed in their movements round the sun were in absolute harmony with those of the older planets4 ,but1 besides the great planets and the asteroids properly so called1 there is yet another planet1 ,eros4 ,its testimony is of special value1 inasmuch as it seems to stand apart from all other bodies in the solar system1 and with1 of course1 the exception of the moon1 it is the earth's nearest neighbour4 ,but whatever may be the exceptional features of ,eros1 however it may differ from the great planets and the asteroids already known1 yet ,eros makes no exception to the law which we have found to be obeyed by all the other planets4 ,it also revolves round the sun in the same direction as all the planets revolve1 in the same direction as the rotation of the sun 7,fig4 #di74 ,we may pause at this moment to make a calculation as to the improbability that the sun1 the earth1 the seven great planets1 and ,ceres1 numbering altogether ten1 should move round in the same direction if their movements had been left to chance4 ,this will show what we can reasonably infer from this concord in their movements4 ,the theory of probabilities will again enlighten a difficult subject4 ,there are only two possible directions for the motion of a planet in its orbit4 ,it must move like the hands of a watch1 or it must move in the opposite direction4 ,the planet must move one way or the other1 just as a penny must always fall head or tail4 ,illustration3 ,fig4 #di4--,,orbits ,,of ,,earth1 ,,eros ,,and ,,mars4 ,we may illustrate this remarkable coincidence in the following manner3 ,suppose we take ten coins in the hand1 and toss them all up together and let them fall on the table2 in the vast majority of cases in which the experiment may be tried1 there would be some heads and some tails2 they would not all be heads4 ,but it is1 of course1 not impossible that the coins should all turn up heads4 ,we should1 however1 deem it a very remarkable circumstance if it happened3 yet it would certainly not be more remarkable than that the ten celestial movements should all take place in the same direction1 unless1 indeed1 it should turn out that there is some sound physical cause which imposes on the planets of the solar system an obligation1 restricting their movements round the sun to the same direction as that in which the sun itself rotates4 ,it will be useful to study the matter numerically2 and the rules of probabilities will enable us to do so1 as we may see by the following illustration3 ,we deem the captain of a cricket team fortunate when he wins the toss for innings4 ,we should deem him lucky indeed if he won it three times in successive matches4 ,if he won it five times running1 his luck would be phenomenal2 while1 if it was stated that he won it ten times consecutively1 we should consider the statement well-nigh incredible4 ,for it is easy to calculate that the chances against such an occurrence are one thousand and twenty-four to one4 ,in like manner we may say1 that for nine planets and the sun all to go round in the same direction would be indeed surprising if the arrangement of the planets had been determined by chance2 there are more than a thousand chances to one against such an occurrence4 ,but ,ceres was only the earliest of many other similar discoveries4 ,and as each asteroid was successively brought to light1 it became most interesting to test whether it followed the rest of the planets in that wonderful unanimity in the direction of their movements of revolution1 or whether it made a new departure by going in the opposite direction4 ,no such exception has ever yet been observed4 ,let us take1 then1 ten more planets1 in addition to those we have already considered1 so that we have now nineteen planets all revolving in the same direction as the sun rotates4 ,it is easy to compute the improbability that these twenty movements should all be in the same direction1 if1 indeed1 it were by chance that their directions had been determined4 ,it is the same problem as the following3 ,what is the chance that twenty coins1 taken together in the hand and tossed into the air at once1 shall all alight with their heads uppermost8 ,we have seen that the chances against this occurrence1 if there were ten coins1 is about a thousand to one4 ,it can easily be shown that if there were twenty coins the chances against the occurrence would be a million to one4 ,we thus see that1 even with no more than nineteen planets and the sun1 there is a million to one against a unanimity in the directions of the movements1 if the determination of the motions was made by chance4 ,we may1 however1 express the result in a different manner1 which is more to the purpose of our argument4 ,there are a million chances to one in favour of the supposition that the disposition of the movements of the planets has not been the result of chance2 or we may say that there are a million chances to one in favour of the supposition that some physical agent has caused the unanimity4 ,we can add almost any desired amount of numerical strength to the argument4 ,the discoveries of minor planets went on with ever-increasing success through the whole of the last century4 ,when ten more had been found1 and when each one was shown to obey the same invisible guide as to the direction in which it should pursue its elliptic orbit1 the chances in favour of some physical cause for the unanimity became multiplied by yet another thousand4 ,the probability then stood at a thousand millions to one4 ,as the years rolled by1 asteroids were found in ever-increasing abundance4 ,sometimes a single astronomer discovered two1 and sometimes even more than two1 on a single night4 ,in the course of a lifetime a diligent astronomer has placed fifty discoveries of asteroids1 or even more than fifty1 on his record4 ,by combined efforts the tale of the asteroids has now approached five hundred1 and out of that huge number of independent planetary bodies there is not one single dissentient in the direction of its motion4 ,without any exception whatever1 they all perform their revolutions in the same direction as the sun rotates at the centre4 ,when this great host is considered1 the numerical strength of the argument would require about #aej figures for expression4 ,each new asteroid simply doubled the strength of the argument as it stood before4 ,professor ,j4 ,j4 ,thomson recently discovered that there are corpuscles of matter very much smaller than atoms4 ,let us think of one of these corpuscles1 of which many millions would be required to make the smallest grain of sand which would just be visible under a microscope4 ,think1 on the other hand1 of a sphere extending through space to so vast a distance that every star in the ,milky ,way will be contained within its compass4 ,then the number of those corpuscles which would be required to fill that sphere is still far too small to represent the hugeness of the improbability that all the five hundred planetary bodies should revolve in the same direction1 if chance1 and chance alone1 had guided the direction which each planet was to pursue in moving round its orbit4 ,the mere statement of these facts is sufficient to show that some physical agent must have caused this marvellous concord in the movements of the solar system4 ,how the argument would have stood if there had been even a single dissentient it is not necessary to consider1 for there is no dissentient ,no reasonable person will deny that these facts impose an obligation to search for the physical explanation of this feature in the planetary movements4 ,as in the last chapter1 where we were dealing with the positions of the planes of the orbits1 there can here be no hesitation as to the true cause of this most striking characteristic of the planetary movements4 ,the nebular theory is at once ready with an explanation1 as has been already indicated in ,chapter ,,xi4 ,the primval nebula1 endowed in the beginning with a certain amount of moment of momentum1 has been gradually contracting4 ,it has been gradually expending its energy1 as we have already had occasion to explain2 but the moment of momentum has remained undiminished4 ,and from this it can be shown that the dynamical principles guiding the evolution of the nebula must ultimately refuse permission for any planet to revolve in opposition to the general movement4 ,this point is a very interesting one1 and as it is of very great importance in connection with our system1 ,i must give it some further illustration and explanation4 ,the two figures that are shown in ,fig4 #ej represent two imaginary systems4 ,we have a sun in each1 and we have two planets in each4 ,the sun is marked with the letter ,s1 and the two planets are designated by ,a and ,b4 ,for simplicity ,i have represented the orbits as circles1 and for the same reason ,i have left out the rest of the planets2 we shall also suppose the orbits of the two planets that are involved to lie exactly in the same plane4 ,in the two systems that ,i have here supposed1 the two suns are to be of the same weight1 the planet ,a in one system is of equal mass to the planet ,a in the other2 and the planets ,b in the two systems are also equal4 ,it is also assumed that the orbit of ,a in one diagram shall be the same as the orbit of ,a in the other1 and that the orbit of ,b in one shall be precisely the same as the orbit of ,b in the other4 ,the sun rotates in precisely the same manner in both1 and takes the same time for each rotation4 ,a1 in one system1 goes round in the same time that ,a does in the other2 and ,b1 in one system1 goes round in the same time that ,b does in the other4 ,there is1 therefore1 a perfect resemblance between the two systems ,i have here supposed in every point but one4 ,i have indicated1 as usual1 the movements of the bodies by arrows1 and1 while in one of the systems the sun and ,a and ,b all go round in the same direction1 in the other system the sun and ,a go round1 no doubt1 in the same direction1 but the direction of ,b is opposite4 ,we are not1 in this illustration1 considering the rotations of the planets on their axes4 ,that will be dealt with in the next chapter4 ,illustration3 ,fig4 #ej4--;,i4 ,a ,,natural ,,system ,,on ,,the ,,left4 ,,ii4 ,,an ,,unnatural ,,system ,,on ,,the ,,right4 ,there can be no doubt that either of these two systems would be possible for thousands of revolutions4 ,there is nothing whatever to prevent ,a and ,b from being started in the same direction round the sun as in the first figure1 or with ,a in one direction and ,b in the opposite direction1 as in the second figure4 ,it is equally conceivable that1 while ,a and ,b revolve in the same direction1 both should be opposite to that of the sun4 ,but one system is permanent1 and the other is not4 ,for1 as a matter of fact1 we do not find in ,nature such an arrangement as that in the second figure1 or as that in which both the planets revolve in opposite directions to the sun's rotation2 what we do find is1 that the planets go round in the same direction as the sun4 ,and the explanation is undoubtedly connected with the important principle already illustrated1 namely1 that natural systems are in a condition in which the total quantity of energy undergoes continuous reduction in comparison with the moment of momentum4 ,in the arrangements made in the two figures1 it will be recollected that the masses of the three bodies were respectively the same1 and also their distances apart1 and their velocities4 ,as the energy depends only on the masses1 the distances1 and the velocities1 the energies of the two systems must be identical4 ,but the moment of momentum of the two systems is very different1 for while in the one case the sum of the moments of momentum of the sun's rotation and that of the planet ,a1 which is going in the same direction1 are to be increased by the moment of momentum of ,b1 the same is not the case in the other system4 ,the moment of momentum of the sun and of ,a conspire1 no doubt1 and must be added together2 but as ,b is revolving in the opposite direction1 the moment of momentum of this planet has to be subtracted before we obtain the nett moment of momentum of the system4 ,hence1 we perceive a remarkable difference between the two systems2 for1 though in each the total energy is the same1 yet in the latter case the moment of momentum is smaller than in the former4 ,it has been pointed out that the effect of the mutual actions of the different bodies of a system is to lessen1 in course of time1 the total quantity of energy that they receive in the beginning1 while it is not in the power of the mutual actions of the particles of the system to affect the sum total of the moment of momentum4 ,hence we see that1 so long as the system is isolated from external interference1 the tendency must ever be towards the reduction of the quantity of energy to as low a point as may be compatible with the preservation of the necessary amount of moment of momentum4 ,the first of the two systems given in ,fig4 #ej is much more in conformity with this principle than the second4 ,the moment of momentum in the former case must be nearly as large as could be obtained by any other disposition of the matter forming it1 with the same amount of energy4 ,but in the second diagram the moment of momentum is much less1 though the energy is the same4 ,it follows that the energy of this system might be largely reduced1 for if accompanied by a suitable rearrangement of the planets the reduced amount of moment of momentum might be easily provided for4 ,we thus see that this system is not one to which the evolution of a material arrangement would ultimately tend4 ,it is1 therefore1 not to be expected in ,nature1 and we do not find it4 ,of course1 the same would be equally true if1 instead of having merely two planets1 as ,i have here supposed for the sake of illustration1 the planets were much more numerous4 ,the operation of the causes we have been considering will show that1 in the evolution of such a system1 there will be a tendency for the planets to revolve in the same direction4 ,it is easy to see how1 in the contraction of the original nebula1 there must have been a strong influence to check and efface any movements antagonistic to the general direction of the rotation of the nebula4 ,if particles revolve in a direction opposite to the current pursued by the majority of particles1 there would be collisions and frictions1 and these collisions and frictions will1 of course1 find expression in the production of equivalent quantities of heat4 ,that heat will1 in due course1 be radiated away at the expense of the energy of the system1 and consequently1 so long as any contrary movements exist1 there will be an exceptional loss of energy from this cause4 ,thus the energy would incessantly tend to decline4 ,as the shrinking of the body proceeded while the moment of momentum would have to be sustained1 this would incessantly tend more and more to require from all the particles a movement in the same direction4 ,the second concord of the planetary system1 which is implied in the fact that all the planets go round in the same direction1 need not therefore surprise us4 ,it is a consequence1 an inevitable consequence1 of the evolution of that system from the great primval nebula4 ,we have seen that it would be excessively improbable that even nine or ten planets should revolve round the sun in the same direction1 if the directions of their movements had been merely decided by chance4 ,we have seen that the movements of the hosts of planets1 which actually form our system1 would be inconceivable1 unless there were some reason for those movements4 ,the chances against such an arrangement having arisen without some predisposing cause is so vast that1 even if the chances were infinite1 the case would be hardly strengthened4 ,but once we grant that the system originated from the contraction of the primval nebula1 dynamics offers ready aid1 and the difficulty vanishes4 ,not only do we see most excellent reasons why all the planets should revolve in the same direction2 we are also provided with illustrations of similar evolutions in progress in other parts of the universe2 we learn that the evolving nebula1 however erratic may have been its primitive motion1 whatever cross currents may have agitated it in the early phases of a possibly violent origin1 will ultimately attain a rotation uniform in direction4 ,as the evolution proceeds1 the various parts of the nebula draw together to form the planets of the future system1 and the planets retain the movement possessed by their component particles4 ,thus we see that the nebular theory not only extricates us from the difficulty of trying to explain something which seemed almost infinitely improbable1 but it also shows why no other disposition of the motions than that which we actually find could be expected4 ,the nebular theory explains to us why there is no exception to that fundamental law in the solar system which declares that the orbits of the planets shall all be followed in the same direction4 ,this wonderful agreement in the movements of the planets1 which we have called the second concord1 thus affords us striking evidence of the general truth of the nebular theory4 ,but there is yet a third concord in the solar system which1 like the other two1 lends wonderful corroboration to the sublime doctrine of ,kant and ,laplace4 ,this we shall consider in the next chapter4 ---------------------------------------- -------------------------------- ,,chapter ,,xvi4 ,,the ,,third ,,concord4 ,rotations of the ,planets on their ,axes4--,the ,older ,planets--,no ,information about ,uranus or ,neptune or the ,asteroids--,the ,speed of ,rotation is ,arbitrary so far as ,kepler's ,laws are concerned--,the ,third ,concord--,a ,remarkable ,unanimity--,kant's ,argument--,illustration of the ,rotation of the ,moon on its ,axis--,how the ,nebular ,theory explains the ,rotation--,the ,moon's ,evolution--,special ,action of ,tides--,the ,evolution of the other ,satellites--,the case of ,mars--,jupiter and ,saturn as ,miniatures of the ,solar ,system--,uranus and ,neptune offer ,difficulties4 ,,we have seen in the last chapter how the rotation of the sun beat time1 as it were1 for the planets1 by giving to them an indication of the direction in which the revolutions round the sun should be performed1 and we have observed with what marvellous unanimity the planets follow the precept thus given4 ,we have now to consider yet another concord1 which has perhaps not the great numerical strength of that last considered1 but is1 nevertheless1 worthy of our most special attention4 ,the earth revolves about an axis which is not very far from being perpendicular to the principal plane to which the movements of the solar system are related4 ,from a dynamical point of view it would1 of course1 have been equally possible for the earth to revolve on its axis in the same direction as the rotation of the sun1 or in the opposite direction4 ,there is nothing so far as the welfare of man is concerned to make one direction of rotation preferable to the other1 but1 as a matter of fact1 the earth does turn round in the same way as the sun turns4 ,jupiter also turns on its axis1 and ,jupiter again1 like the earth1 might turn either with the sun or it might turn in the opposite direction4 ,here1 again1 we find a unanimity between the earth and ,jupiter2 they both turn in the same direction1 and that is the direction in which the sun rotates4 ,the same may be said of ,mars1 and the same may be said of ,saturn4 ,in the case of the planets ,mercury and ,venus we cannot speak with equal definiteness on the subject of their rotations about their axes4 ,the circumstances of these planets are such that there are great difficulties attending the exact telescopic determination of their periods of rotation4 ,the widest variations appear in the periods which have been assigned4 ,it has1 for instance1 been believed that ,venus rotates in a period not greatly differing from the period of twenty-four hours in which our earth revolves4 ,but it has been lately supposed that the period of ,venus is very much longer1 and is in fact no less than seven months1 which is1 indeed1 that of the revolution of ,venus about the sun4 ,according to this view1 ,venus rotates round the sun in a period equal to its revolution4 ,if this be so1 then ,venus constantly turns the same face to the sun1 and the movement of the planet would thus resemble the movement of the moon around the earth4 ,as a matter of observation1 the question must still be considered unsettled1 though there are sound dynamical reasons for believing that the long period is much more probable than the short one4 ,we do not now enter into this question1 or into the still more difficult matter of the rotation of ,mercury2 it suffices to say that whichever period be adopted for either of these planets is really not material to our present argument4 ,in both cases it has never been doubted that the direction of the rotation of the planets is the same as the direction in which ,jupiter and ,mars and the earth rotate1 these being also the same as the direction of the solar rotation4 ,as to the rotations of ,uranus and ,neptune about their respective axes1 the telescope can show us nothing4 ,the remoteness of both these planets is such that we are unable to discern objects on their discs with the definiteness that would be required if we desired to watch their rotations4 ,we have also no information as to the rotation of the several asteroids4 ,no one1 ,i think1 will doubt that each of these small planets1 equally with the large planets1 does rotate about its axis2 but it is impossible for us to say so from actual knowledge4 ,but undoubtedly the five old planets1 ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn1 as well as the earth1 all rotate in the same direction as the sun4 ,each planet might rotate twice as fast1 or half as fast1 as it does at present4 ,they might all rotate in the opposite direction from that in which they do now1 or some of them might go in one direction1 and some in the other1 with every variety in their diurnal periods1 while the primary condition of ,kepler's ,laws would have still been complied with4 ,we may also note that the direction in which the rotation takes place seems quite immaterial so far as the welfare of the inhabitants on these planets is concerned4 ,the fact that the planets and the sun have this third concord demands special attention4 ,the chance that the earth should rotate in the same direction as the sun is1 of course1 expressed by one-half4 ,it is easy to show1 that out of sixty-four possible arrangements of the directions of rotation of the five planets and the earth1 there would be only one in which all the movements coincided with the direction of the rotation of the sun4 ,if1 therefore1 it had been by chance that the direction of these motions was determined1 then ,nature would have taken a course of which the probability was only one sixty-fourth4 ,no doubt this figure is by no means so large as those which expressed the probabilities of the other planetary concords2 it is1 however1 quite sufficient to convince us that the direction of the rotation of the planets on their axes has not been determined merely by the operation of chance4 ,we are to see if there is any physical agent by which the planets have been forced to turn round in the same direction4 ,and here comes in one of those subtle points which the metaphysical genius of ,kant suggested4 ,let us take any two planets--say1 for instance1 the earth and ,jupiter--and let us endeavour to see what the nature of the agent must have been which has operated on these planets so as to make them both rotate in the same direction4 ,kant urged that there must have been some material agent working on the materials in ,jupiter1 and some material agent working on those of the earth1 and that to produce the like effect in each planet there must have been at one time a material connection existing between that body which is now ,jupiter and that body which is now the earth4 ,in like manner ,kant saw this material connection existing between the other planets and the sun1 and thus he was led to see that the whole material of our solar system must once have formed a more or less continuous object4 ,the argument is a delicate one1 but it seems certainly true that in the present arrangement of the orbits it is impossible for us to conceive how1 with intervals of empty space between the tracks of the planets1 a common influence can have been exerted so as to give them all rotations in the same direction4 ,the nebular theory at once supplies the explanation of the unanimity in the rotation of the planets1 just as it supplied the explanation of the unanimity in the directions of their revolutions4 ,to explain the rotation of a planet on its axis1 let us imagine that one portion of the contracting nebula has acquired exceptional density4 ,in virtue of its superior attraction it absorbs more and more material from the adjacent parts of the nebula1 and this will ultimately be consolidated into the planet1 though in its initial stages this contracting matter will remain part of the nebula4 ,we have shown that the law which decrees that the moment of momentum must remain constant will require that1 after a certain advance in the contraction1 all the parts of the nebula shall rotate in the same direction4 ,thus we find that the sun1 or rather the parts of the nebula that are to form the sun1 and the parts that are to form the planets are all turning round together4 ,illustration3 ,fig4 #ea4--;,,an ,,elongated ,,irregular ,,nebula 7n4g4c4 #fiib2 in ,cygnus74 7,dr4 ,w4 ,e4 ,wilson1 ,f4,r4,s47 7,from the ,astronomical and ,physical ,researches at ,daramona ,observatory47 ,at this point we may consider a geometrical principle which1 though really quite simple1 is not always easily understood4 ,it has indeed presented considerable difficulty to many people4 ,suppose that an ordinary card is laid on a flat board1 and that1 with a bradawl1 a hole is made through the card into the board4 ,the hole may be at the centre1 or at one of the corners1 or a little way in from one of the edges1 or in any other position whatever on the card4 ,now suppose that a postage stamp is stuck upon the card anywhere1 and that the card is then moved around the bradawl4 ,how are we to describe the motion of that postage stamp8 ,it would certainly be revolving around the bradawl2 but this motion we may consider as composed of two others4 ,at any instant we may accurately represent the movement of the postage stamp by considering that its centre was moving in a direction perpendicular to the line joining that centre to the hole made by the bradawl1 and that it also had a rotation around its centre1 the period of that rotation being just the same as the time the card would take to go round the bradawl4 ,thus we see that the movement of the postage stamp contains at any moment a movement of translation and a movement of rotation4 ,we may illustrate the case we have supposed by the movement of the moon around the earth4 ,if the centre of the earth be considered to be at the centre of rotation the moon may be considered to be in the position of the postage stamp4 ,as our satellite revolves1 the same side of the moon is continually turned towards the earth1 but this is due to the fact that the moon1 at each moment1 really possesses two movements1 namely1 a movement of translation of its centre1 in a direction perpendicular to the line from the moon's centre to the earth's centre1 coupled with a slow rotation of the moon round its axis4 ,the contracting nebula we may liken to our piece of cardboard1 the stamp will represent the spot in which the nebulous material has contracted to form the planet1 and the position of the bradawl is the centre of the sun4 ,as we have seen by our illustration1 the nebulous planet is endowed with a certain movement of rotation1 the period of its rotation on its axis being equal to that of its revolution around the centre2 and it is important also to notice that both these movements take place in the same direction4 ,thus we see from the nebular theory how the primval nebula1 in the course of its contraction1 originated a planet1 and how that planet was also endowed with a movement of rotation2 its period of rotation being originally equal to the period of rotation of the whole nebula4 ,this explains how the planet1 or rather the materials which are to form the future planet1 derived from the nebula their movement of rotation1 which must have been extremely slow in the beginning4 ,as the contraction continued1 the materials of the gradually growing globe drew themselves together1 and tended to become separate from the surrounding nebula4 ,at length the time arrived when the planet became sufficiently isolated from the rest of the nebula to permit the conservation of moment of momentum to be applied to it individually4 ,thus1 though the rotation was at first excessively slow1 yet1 as the contraction proceeded1 and as the parts of the forming planet drew themselves closer together1 in consequence of their mutual attractions1 it became necessary that the speed with which these parts accomplished their revolutions should be accelerated4 ,at last1 when the planet had become consolidated1 and when consequently the mutual distances of the several particles constituting the planet had been reduced to but a fraction of what those distances were originally1 the speed of the planet's rotation had become enormously increased4 ,in this manner we learn how1 from the very slow rotation which the nebulous material had at first1 a solid planet may be made to rotate on its axis as rapidly as the planets in the solar system do to-day4 ,we thus find that the third concord1 namely1 the agreement in the directions of the planets' rotations1 is a further strong corroboration of the nebular theory4 ,the unanimity of all these various movements is the dominant characteristic of the solar system4 ,but this third concord1 derived from the rotation of the planets1 may be yet further strengthened4 ,the movements of the satellites1 which accompany so many of the planets1 must also find their explanation from the primval nebula4 ,the circumstances of the satellites are1 however1 different in the different cases4 ,as regards the moon1 the theory of its evolution is now well known1 mainly by the researches of ,professor ,george ,darwin4 ,in the moon there appear to have been causes at work of a somewhat special kind4 ,we must just refer to what is well known with regard to the history of the moon4 ,here1 again1 we observe the importance of the principles of the conservation of moment of momentum4 ,as the moon raises tides on the ocean surrounding the earth1 and as those tides flow around the globe1 they cause friction1 and that friction involves1 as we have so often pointed out1 the loss of energy to the system4 ,thus1 the energy of the earth-moon system must be declining1 while the moment of momentum remains constant4 ,now there are only two sources from which the energy can be derived4 ,one of those sources is that due to the rotation of the earth on its axis4 ,the other is due to the moon1 and consists of two parts1 namely1 the energy arising from the velocity of the moon in its orbit1 and the energy due to the distance by which the earth is separated from the moon4 ,as the moon's velocity depends upon its distance1 we cannot view these two portions as independent4 ,they are connected together1 and we associate them into one4 ,so that we say the total energy of the earth-moon system consists partly of that due to the rotation of the earth on its axis1 and partly of that due to the revolution of the moon around the earth4 ,it might also seem that we ought to add to this the energy due to the rotation of the moon around its own axis2 but this is too inconsiderable to need attention4 ,in the first place1 the moon is so small that even if it rotated as rapidly as the earth the energy due to the rotation would not be important4 ,seeing1 however1 that the moon has for the rotation on its axis a period of between twenty-seven and twenty-eight days1 its velocity of rotation is so small that1 for this reason also1 the energy of rotation would be inconsiderable4 ,we are1 therefore1 amply justified in omitting from our present consideration the energy due to the rotation of the moon on its axis4 ,the energy of the earth-moon system is on the decline3 the lost energy might conceivably be drawn from the rotation of the earth1 or it might be drawn from the revolution of the moon1 or it might be drawn from both ,if it were drawn from the revolution of the moon1 that would imply that the moon would lose some of its speed or some of its distance1 or in any case that the moon would get nearer to the earth and revolve more slowly1 the speed of the earth being on this supposition unaltered4 ,in this case1 the moment of momentum of the earth would remain the same as before1 while the moment of momentum of the moon would be lessened2 the total moment of momentum would therefore have decreased1 but this we have seen to be impossible4 ,it therefore follows that the energy withdrawn from the earth-moon system is not to be obtained at the expense of the revolution of the moon4 ,the energy must therefore be obtained at the expense of the rotation of the earth on its axis4 ,but if this be the case1 the speed with which the earth rotates must be diminished2 that is to say1 the length of the day must be increased4 ,and if the speed of the earth's rotation be reduced1 that means that the amount of moment of momentum contributed by the earth is lessened4 ,but the total quantity of moment of momentum must be sustained1 and this can only be done by making the moon go further away and describe a larger orbit4 ,we thus see that in consequence of the tides the length of the day must be increasing1 and the moon must be gradually retreating4 ,thus we find that at earlier periods the moon's distance from the earth must have been less than it is at present1 and the further we look back through remote periods the less do we find the distance between the earth and the moon4 ,thus we see that there must have been a time when the moon or the materials of the moon were in actual contact with the materials of the earth4 ,in fact1 it seems quite possible that the moon may have been a portion of the earth1 broken off at some very early period1 while the earth was still in a liquid state1 if indeed it had condensed to even that extent4 ,thus the revolution of the moon round the earth is hardly to be used as an argument in favour of the nebular hypothesis4 ,the moon is indeed a consequence of the earth's rotation4 ,the satellites of ,mars offer conditions of a very different kind1 though here1 again1 tidal influences have been so important1 that it is perhaps questions relating to tides that are illustrated by these satellites rather than the nebular theory4 ,a remarkable circumstance may be noted with regard to the movements of the satellites of ,mars4 ,the inner satellite has a period of about seven and a half hours1 which is not a third of the period that the planet itself takes to go round on its axis4 ,this leads to a somewhat curious consequence4 ,the tides raised on ,mars by this inner satellite would certainly tend rather to accelerate the rotation of the planet than to retard it2 for these tides must course round the planet in the direction of its rotation1 but with a speed in excess of that rotation4 ,any tidal friction1 so far as this satellite is concerned1 will tend to augment the velocity of the planet's rotation1 just as in the opposite case1 where the moon raises tides on the earth1 it is the lagging of the tides behind the movement due to the rotation that acts as a brake1 and tends to check that speed4 ,if1 therefore4 ,mars is accelerated by this satellite1 it will do more than its original share of the moment of momentum of the ,martian system2 it is therefore imperative that the satellite shall do less4 ,accordingly1 we find that this satellite must go in towards the planet4 ,no doubt this effect is much complicated by the influence of the other satellite of the same planet1 but the illustration may suffice to show that if the satellites of the earth and ,mars do not convey to us much direct evidence with regard to the nebular theory1 this is largely because the effect of the tides has been a preponderating influence4 ,the ,martian system as we now see it has acquired its characteristic features by tidal influence1 so that the more simple influences which would immediately illustrate the nebular theory have become hidden4 ,as to the satellites of ,jupiter and ,saturn1 the circumstances are again quite different from those that we find in the earth and in ,mars4 ,there is little more to be said with regard to them than that everything that they present to us is consistent with the indications of the nebular theory4 ,the evolution in each case has been a reproduction in miniature of the evolution of the solar system4 ,but the satellites of ,uranus and ,neptune present1 it must be admitted1 the greatest stumbling block to the acceptance of the nebular theory4 ,both as to the directions in which they move and as to the planes in which their orbits lie1 it must be admitted that the satellites of ,uranus are distinctly at variance with what the nebular theory would suggest4 ,the consideration of this subject will be found in the next chapter4 ---------------------------------------- -------------------------------- ,,chapter ,,xvii4 ,,objections ,,to ,,the ,,nebular ,,theory4 ,there are ,difficulties in the ,nebular ,theory--,the ,general ,conformity of the ,movements--,details of the ,uranian ,movements--,the ,anomaly in the ,satellite of ,neptune--,where the ,difficulty ,lies--,the ,fundamental ,principle which ,dynamics ,offers for our ,guidance--,the ,immense ,contrast between the ,nebula in its ,original ,form and its ,final ,form--,energy that could be ,obtained by a rearrangement of our ,system--,probable ,nature of the ,present ,change in the ,plane of the ,orbits of the ,satellites of ,uranus--,the ,similar ,explanation in the ,case of ,neptune4 ,,no one will deny that there are points in connection with the nebular theory which present difficulties which to some seem important4 ,we shall endeavour to estimate the significance of these difficulties in this chapter4 ,they are certain anomalous phenomena presented by the planets ,uranus and ,neptune4 ,the satellites which attend upon the planets exhibit a general conformity with those movements of the planets themselves on which we have dwelt in ,chapters ,,xiv41 ,,xv41 ,,xvi4 ,the planes in which the orbits of the satellites are contained are usually not much inclined to the plane of the ecliptic1 and the directions in which the satellites revolve also agree with the general direction of the planetary movement4 ,we find these conditions in the one satellite of the earth1 in the two satellites of ,mars1 in the five satellites of ,jupiter1 in the eight or nine satellites of ,saturn2 but1 when we come to ,uranus and ,neptune1 the two outermost planets1 we observe a striking but most instructive violation of the laws which we have found so consistently prevailing in the other parts of the solar system4 ,let me first mention the special circumstances of ,uranus4 ,it is now known that this planet has four satellites4 ,of these1 ,titania and ,oberon were both discovered by ,sir ,william ,herschel on ,january #aath1 #aghg4 ,the two remaining satellites1 named ,ariel and ,umbriel1 were not discovered for more than half a century later by ,mr4 ,lassell1 on ,october #bdth1 #ahea4 ,it is1 however1 just possible that they were previously seen by ,sir ,william ,herschel4 ,the innermost of the four satellites1 ,ariel1 accomplishes a revolution in a day and a half1 ,umbriel goes round in four days and three hours1 ,titania in eight days and seventeen hours1 and ,oberon in thirteen days and eleven hours4 ,we have already mentioned how the investigations of ,newcomb show that these four satellites of ,uranus revolve in the same direction and in the same plane2 but this plane1 instead of lying in or near the ecliptic1 is very nearly perpendicular thereto1 the actual angle being eighty-three degrees4 ,this is one of the features in which the satellites of ,uranus are in startling disobedience to the laws which have been so rigidly observed in most other parts of the system4 ,but there is also a second anomaly4 ,the direction in which the satellites move1 when projected on the plane of the ecliptic1 is found to be opposite to the universal direction in which all the other movements in the solar system are performed4 ,of course the fact that the plane of the orbits of the satellites lies so nearly at right angles to the plane of the ecliptic detracts somewhat from the significance of this circumstance4 ,if the two planes were absolutely at right angles1 there would be1 of course1 no projection at all1 and1 in the actual circumstances1 the moment of momentum1 when projected1 loses nineteen-twentieths of its amount4 ,it follows that in the actual position of the plane the abnormal direction in which the satellites are moving is not very material4 ,it must be admitted that1 in the position of the plane of their orbits and the direction of their movements1 the satellites of ,uranus are in contrast to what a hasty consideration of the nebular theory might have led us to expect4 ,if the orbits of those satellites had all lain close to the plane of the ecliptic1 and if the direction in which the satellites revolved had also conspired with that of the revolution of ,uranus round the sun1 and with all the other hundreds of movements which are in the same direction1 there can be no doubt that we should in this place have been appealing to the satellites of ,uranus as confirmatory evidence of the truth of the nebular theory4 ,the fact that they move in a manner so totally at variance with what might have been expected cannot therefore be overlooked4 ,neptune1 the outermost planet of our system1 presents us also with difficulties of an analogous character4 ,so far as the orbit of ,neptune itself is concerned1 it agrees entirely with the general planetary convention2 the inclination of that orbit to the plane of the ecliptic is no more than six degrees1 and the direction in which the outermost planet revolves round the frontier of our system is not different from the directions in which all the other planets revolve4 ,we know nothing about the axis of rotation of ,neptune except that it may be reasonably presumed to be in the same plane as the movement of its satellite4 ,on ,october #ajth1 #ahdf1 ,lassell1 with the help of his great telescope1 suspected the existence of a satellite to ,neptune1 and he announced it definitely on ,july #gth1 #ahdg4 ,we are indebted to ,newcomb for a careful investigation of the orbit of this satellite4 ,it moves in a track which is practically circular1 and it requires about five days and twenty-one hours to accomplish each revolution4 ,its inclination to the ecliptic is not so anomalous as in the case of ,uranus1 the inclination being in this case not more than thirty-five degrees4 ,this is not much greater than the inclinations of the orbits of some of the asteroids1 and it might have passed without much comment had it not been for the circumstance that the direction of motion of the satellite in this track is antagonistic to all the other movements in the solar system4 ,this is indeed a more startling fact in some respects than the movements of the satellites of ,uranus1 for1 as we pointed out1 the plane of the orbits of the satellites of ,uranus is so nearly perpendicular to the plane of the ecliptic that the direction of the movement could not be held to be of much significance4 ,the satellite of ,neptune1 having an orbital inclination barely more than a third of a right angle1 exhibits a retrograde movement which is in some respects the most anomalous feature in the solar system4 ,these circumstances connected with the satellites of ,uranus and ,neptune have been sometimes brought forward as arguments against the nebular theory4 ,what ,laplace would have said to them we can only conjecture1 for1 at the time he brought out his theory1 ,neptune was entirely unknown1 and none of the satellites of ,uranus had been observed4 ,but it has sometimes been urged that the movements of these two systems are inconsistent with the principles of the nebular theory1 and that1 therefore1 the nebular theory must be abandoned4 ,i have no desire to minimise the difficulties1 but ,i think the considerations to which ,i now invite attention may help to lessen them even if they do not altogether remove them4 ,i trust1 at least1 we may be able to show that even those anomalous movements are not incompatible with the acceptance of the account of the origin of our solar system given by the nebular theory4 ,the primval nebula may be regarded as chaotic in its earliest stages2 perhaps it was like the nebulous wisps in ,fig4 #ea4 ,it was chaotic in the arrangement of the material of which it is formed1 and in the movements of that material4 ,before a disorganised nebula can become evolved into a nebula with any definite form like that in ,fig4 #eb1 or into anything resembling a solar system1 an immense period of time must elapse1 and during that time the operation of the laws of dynamics gradually impresses certain well-marked features on the nebula1 and disposes it to assume an orderly form4 ,we have explained that no matter how the nebula originated1 or no matter what may have been the irregularities in its extent or distribution1 and no matter how diverse may have been the agitations of its various parts1 the principles of dynamics assure us that each such nebula must1 for all time1 stand in some special relation to a certain particular plane4 ,the moment of momentum which the nebula has with respect to this plane1 exceeds the moment of momentum that it has with respect to any other plane4 ,we have pointed out how1 notwithstanding the vicissitudes and transformations to which1 in the course of illimitable ages1 the nebula must submit1 its moment of momentum relatively to this plane will remain absolutely unaltered4 ,we have shown how the energy of the nebula becomes gradually exhausted4 ,the collisions between various particles1 the frictions that will necessarily arise1 and the actions which we may sufficiently describe by saying that they are of a tidal character1 will all result in the transformation of energy into heat4 ,this heat is radiated away and lost1 and there is a corresponding decline in the energy of the system4 ,to preserve its moment of momentum unaltered in the course of ages1 notwithstanding the continuous reduction of energy1 the materials of the nebula will ever find themselves more and more approximating to the plane1 and will ever find themselves more and more compelled to revolve in the same direction4 ,if the original size of the nebula be compared with the area of the ,atlantic ,ocean1 the condensed form which the nebula may ultimately assume may be no larger than a coral island4 ,if the nett moment of momentum1 diffused over the space as large as the ocean1 has still to be preserved in the space as large as the island1 we need not be surprised that the spin of the system in its condensed form is its dominating characteristic4 ,in the evolution of our solar system from the primval nebula1 this operation of reducing the movements to the same plane and of requiring that all the movements shall take place in the same direction1 having had play for unmeasured ages1 has in the main accomplished its end4 ,all the important bodies of the system do go round in the same direction2 that much1 at least1 has been attained4 ,all of them also go round in planes which are nearly coincident1 but1 as we have already noted1 they are not yet absolutely coincident4 ,the greatest planets have1 however1 very nearly become reconciled1 so far as the planes of their orbits are concerned1 to the condition which dynamics imposes4 ,the same is true of the rotation of the sun on its axis4 ,that axis is inclined at an angle of eighty-three degrees to the plane of the ecliptic1 so that the sun's equator would have to be shifted only through an angle no greater than seven degrees1 if it were to be placed in the plane in which it should be situated1 if the condition of the smallest quantity of energy for a given amount of moment of momentum was to be realised4 ,we find a greater discrepancy in the plane of the earth's equator4 ,this is inclined by about twenty-three degrees to the plane of the ecliptic4 ,here there is some energy which might yet be expended without a diminution of the amount of moment of momentum in the system2 for if the earth's axis were to be made perpendicular to the plane of the ecliptic1 then the velocity of rotation of the earth about its axis might undergo a corresponding abatement1 and yet keep up the requisite moment of momentum4 ,we thus see that even with the older planets the conditions which would be enforced1 if the moment of momentum was to be sustained with the least quantity of energy1 are not absolutely complied with2 which simply means that there has not yet been time enough for our system to arrive at the perfect state1 to which it must be approximating4 ,if we have found that in the rotations of the earth and of the sun1 and in the revolutions of the planets round the sun1 the conditions ultimately aimed at have not yet been reached1 why should we feel surprised that in the outer planets of our system1 ,uranus and ,neptune1 the conditions which evolution tends to produce have not yet been fully attained8 ,that the operation of the conservation of moment of momentum is in progress in the internal economy of the ,uranian system1 we have already had occasion to explain in ,chapter ,,xi4 ,the fact which ,newcomb demonstrated1 that the four satellites revolve in the same plane1 can only be accounted for by the supposition that in that system the conservation of moment of momentum1 with declining energy1 has gradually imposed this condition on the system belonging to ,uranus4 ,with reference to the position of the plane of the satellites1 in the case of ,uranus and ,neptune1 we would say1 that though at present their arrangement appears anomalous1 it will probably not always remain so4 ,the fact that the satellites of ,uranus are in a plane nearly perpendicular to the plane of the ecliptic really implies that there is a certain amount of energy still disposable in our system1 if by readjustment of the plane of the ,uranian satellites the necessary moment of momentum in the system is still preserved4 ,illustration3 ,fig4 #eb4--,,two-,,branched ,,spiral 7n4g4c4 #gdgi2 in ,pegasus74 7,lick ,observatory47 ,the laws of dynamics tell us that the orbits of planets must be gradually1 if with excessive slowness1 tending still further to the same plane4 ,in this process energy can be expended by the system1 while the moment of momentum is unabated4 ,we can at least suggest what seems to be at this moment in progress in the system belonging to ,uranus4 ,it will readily be admitted that there may be a difficulty in seeing how the movement of a planet1 which is going in the wrong direction1 could be stopped and turned into the right direction4 ,but we need not suppose that so violent a change as this would imply is to be expected in our system4 ,we are quite accustomed to find the planes of the orbits of all planets in gradual movement4 ,the plane containing the orbits of the four satellites of ,uranus is at this moment probably moving gradually upwards4 ,it will in due course become actually at right angles to the ecliptic1 and we may then reasonably assume that it will advance further in the same direction4 ,at the moment the right angle is passed1 this continuous movement will have the effect of changing the directions of the satellites' movement from retrograde to direct4 ,the present anomaly will then tend to become evanescent1 for1 as the exhaustion of the energy continues1 the planes of the satellites of ,uranus will gradually come into conformity with the plane of the ecliptic4 ,we make no doubt that there may be a similar explanation of the movements of the satellite of ,neptune4 ,the inclination of the plane of the orbit of the satellite to the ecliptic is probably now increasing4 ,it will ultimately come to be at right angles thereto1 and then the next advance of the plane will convert1 by a continuous action1 the retrograde motion of the satellite1 at present so disconcerting1 into a direct motion4 ,the change of the plane will still continue until it1 too1 may ultimately coalesce with the ecliptic4 ,the fact appears to be1 that though an enormous quantity of energy must have been lost by radiation from our system during the illimitable ages through which the evolution has been running its course1 the disposable energy is not yet quite exhausted4 ,there are certain adjustments in our system which may still be made and which will allow of yet further radiation of energy1 while still preserving sufficient to keep up the necessary moment of momentum4 ,it seems obvious that the system is tending towards a condition in which the planes of all the orbits shall be coincident1 and in which all the directions shall be absolutely unanimous4 ,if we were at once to alter the system by moving all the orbits into the plane of the ecliptic1 but making no change in the dimensions of those orbits1 or the velocities concerned2 if we were also to adjust the rotations of the earth1 as well as of the other planets1 so that all the axes of rotation should be perpendicular to the plane of the ecliptic2 if we were to turn the plane of the satellites of ,uranus through that angle of #ig1 which would suffice at the same time to bring it into coincidence with the ecliptic1 and lay the movements of the satellites in the right direction2 if we were also to turn the orbit of the satellite of ,neptune through #ade1 thus bringing that orbit to coincide with the plane of the ecliptic1 in such a manner that the direction of the movement of the satellite of ,neptune conspired with all the other movements of the system1 then this rearrangement of the system would increase the moment of momentum1 while the quantity of energy was not altered4 ,but this is the same thing as saying that some energy yet remains to be disposed of1 while the system still preserves the requisite moment of momentum4 ,the conclusion we come to may be thus expressed3 the movements of the satellites of ,uranus and ,neptune do not disprove the nebular hypothesis4 ,they rather illustrate the fact that the great evolution which has wrought the solar system into form has not yet finished its work2 it is still in progress4 ,the work is very nearly done1 and when that work shall have been completed1 the satellites of ,uranus and ,neptune will no longer be dissociated from the general concord4 ---------------------------------------- -------------------------------- ,,chapter ,,xviii4 ,,the ,,beginning ,,of ,,the ,,nebula4 ,nebula not of ,infinite ,duration--#h1cjj ,coal-,units was the ,total ,energy of the ,system--#dfj ,miles a ,second--,solar ,nebula from a ,collision--,what we ,know as to the ,colliding ,bodies--,probability of ,celestial ,collisions--,multitudes of ,dark ,objects--,new ,star in ,perseus--,characteristics of ,new ,stars--,incandescent ,hydrogen--,the ,ruby in the ,spectrum--,photographs of the ,spectrum--,rarity of a ,collision on a ,scale ,adequate to a ,solar ,system4 ,,whatever may have been the antiquity of the actual elements that formed the primval nebula from which the solar system has been evolved1 the nebula itself has certainly not been of infinite duration4 ,the question then arises as to what has been the origin of the nebula as such1 or rather by what agency the material from which the nebula was formed underwent so radical a transformation from its previous condition as to be changed into that glowing object which we have considered so frequently in this book4 ,we have to explain how1 by the operation of natural causes1 a dark body can be transformed into a glowing nebula4 ,let us first estimate what the quantity of energy in that system is4 ,the sun has been pouring forth heat for inimitable ages1 and will doubtless continue to pour forth heat for millions of years to come4 ,but the destiny which awaits the sun1 though it may be protracted1 yet cannot be averted4 ,the sun will go on pouring forth its heat and gradually shrinking4 ,the time will come at last when the radius of the sun will have appreciably decreased1 and when once it has assumed a density corresponding to a solid state its history as a radiant globe will be approaching its close4 ,a period of insignificant extent1 a century or less1 will then suffice for that solid globe to cool down so as to be no longer an efficient source of light and heat4 ,we shall assume that when the sun has ultimately become solid and cold1 and when it is no longer the life and light of our system1 it will have attained a mean density of #ba4e1 which we have chosen because that is the density of platinum1 the heaviest substance known4 ,in all probability the solar density will never become so great as this1 but to include the most extreme case in our argument ,i am making the assumption in the form stated4 ,we are now to estimate what will have been the total energy that the sun has radiated from the moment when as an indefinitely great nebula it first began to radiate at all1 down to that moment in the future when1 having shrunk to the density of platinum1 and having parted with all its heat1 the solar radiation is at an end4 ,in the beginning of the evolutionary history the sun was a nebula1 which we have supposed to extend in every direction to an indefinitely great distance4 ,the system has resulted from the contraction of that nebula1 and the energy liberated in that contraction has supplied the sun's radiation4 ,we calculate 7see ,appendix7 the energy that would be given out in the contraction of a nebula whose materials were originally at infinity1 and which ultimately coalesced to form a cold1 solid globe of the density of platinum1 and as heavy as the sun4 ,there is no object in attempting to express this quantity of energy in foot-pounds--the figures would convey no distinct impression--we shall employ the coal-unit explained in ,chapter ,,vi4 ,we imagine a globe of coal the weight of the sun2 then1 if that globe of coal were adequately supplied with oxygen1 it would1 on combustion1 give out a certain amount of heat1 which is a convenient unit for our measurements4 ,it is demonstrated that the quantity of energy given out by the contraction of the nebula from infinity1 to this globe of the density of platinum1 would be about equal to the quantity of energy which would be produced by the combustion of #h1cjj globes of coal as heavy as the sun1 an adequate contribution of oxygen being supposed to be supplied4 ,this expresses the original endowment of energy in the solar system1 or rather a major limit to that endowment2 it shows that the solar system can never have developed more energy by contraction than that which could be produced by the combustion of #h1cjj globes of coal as heavy as the sun4 ,we may mention that of this great endowment of energy an amount which is rather less than half 7#c1djj7 has been already expended1 so that rather more than half of the sun's career as a radiant globe may yet have to be run4 ,we can also express the total energy of the solar system in a different manner4 ,we shall consider what must be the velocity of the sun1 so that the energy that it will possess1 in virtue of that velocity1 shall be equal to the energy which could be produced by the combustion of #h1cjj globes of coal of the same weight4 ,this calculation is very much simplified by making use of a principle which we have already stated and applied in ,chapter ,v4 ,we have shown that if a piece of coal be animated with a velocity of five miles a second1 the energy it possesses in virtue of that motion is equal to the energy produced by the coal in the act of combustion4 ,if a body were moving at the rate of1 let us say1 #ajj miles a second--its speed being then twenty times as great as the particular speed just mentioned--its energy1 which depends on the square of the velocity1 would be #djj times as much as would be produced by the burning of a piece of coal equal to it in weight4 ,we can easily calculate that if the sun were moving at a speed of #dfj miles a second1 it would possess1 in virtue of its motion1 as much energy as would be generated by the contraction of the primval nebula from infinity down to a globe of the density of platinum4 ,it is thus easy to form a supposition as to how the nebula constituting our solar system may have come into being2 most probably it originated in this way4 ,let us suppose that two masses1 either dark or bright1 either hot or of the temperature of space1 or the temperature of frozen air1 were moving with speeds of #dfj miles a second4 ,no doubt the velocities we are here postulating are very high velocities1 but they are not unprecedentedly high4 ,we know of stars which at this present moment move quite as fast1 so that there is nothing unreasonable in our supposition so far as the velocities are concerned4 ,let us suppose that each of these bodies had a mass which is half that of our present solar system4 ,if these two bodies dashed into collision1 when moving from opposite directions1 the effect of the blow would be to transform the energy into heat4 ,that heat would be so great that it would be sufficient not alone to render these globes red-hot and white-hot1 but even to fuse them--nay1 further1 to drive them into vapour1 even to a vapour which might expand to an enormously great distance4 ,in other words1 it is quite conceivable that a collision of two such masses as we have here supposed might be adequate to the formation of a nebula such as that one which in the lapse of indefinite ages has shaped itself into the solar system4 ,before the collision1 which resulted in the formation of the nebula1 each of these bodies1 or rather their centres of gravity1 would be moving in what may be regarded for the moment as straight lines1 and a plane through those two straight lines will be a plane which for ever afterwards will stand in important relation to the system4 ,it will be1 in fact1 that principal plane of which we have so often spoken4 ,as those two bodies met they would possess a certain moment of momentum1 and this moment of momentum would remain for ever unaltered1 no matter what may be the future vicissitudes of the system4 ,for the sake of simplicity in describing what has occurred1 we have spoken as if the two bodies were of equal mass1 and1 moving with equal velocities from opposite points of the heavens1 dashed into collision4 ,but what actually happens cannot have been quite so symmetrical4 ,there is one feature in the solar system which absolutely proves that the collision cannot have taken place precisely in the way we have laid down4 ,if it had happened that two equal masses had been hurled into collision with equal velocities from precisely opposite directions1 then there could have been no resultant moment of momentum4 ,from the principle of the conservation of moment of momentum1 we can see that1 if absent in the beginning1 it could never originate later4 ,as1 however1 we have a large moment of momentum in the movements of the planets and the sun1 it is certain that the collision cannot have taken place in a manner quite so simple4 ,illustration3 ,fig4 #ec4--;,,cluster ,,with ,,stars ,,of #ag,,th ,,magnitude 7n4g4c4 #fgje2 in ,antinous74 7,photographed by ,dr4 ,isaac ,roberts1 ,f4,r4,s47 ,the probabilities of the case show that it is almost infinitely unlikely that two bodies of equal dimensions1 and moving with equal velocities in opposite directions1 should come squarely into collision4 ,it would be much more likely that the bodies should be not of the same size1 not moving with the same velocity1 and should collide partially rather than squarely4 ,the collision may have been1 in fact1 little more than a graze4 ,the probabilities of the case are such as to show that what actually occurred was a collision between two unequal masses1 which were moving in directions inclined to each other and with different velocities4 ,it is easy to show that1 granted sufficiently great velocities1 an impact which fell far short of direct collision might still produce enough heat to transform the whole solar system into vapour4 ,the circumstances which would naturally accompany so transcendent an incident will also go far to account for a difficulty which has been often felt with regard to the evolution of the system from a nebula4 ,were such a collision to take place we should certainly not expect that the resulting nebulous mass1 the product of a shock of such stupendous violence1 would be a homogeneous or symmetrical object4 ,portions of the colliding body would become more highly heated than others2 portions of the bodies would not be so completely transformed into vapour as would other parts4 ,there would thus be differences in the nebula at the different parts of its mass4 ,this non-homogeneity would be connected with the formation and growth of planets in the different parts of the nebula4 ,there is another circumstance connected with the movement of the sun which should here be mentioned4 ,it is well known that the sun has a velocity which carries it on through space at the rate of half a million miles a day4 ,in this movement the whole solar system1 of course1 participates4 ,this movement of translation of our system must also be a result of the movements of the two original colliding masses4 ,these two masses imparted to the system1 which resulted from their union1 both the lineal velocity with which it advances through space1 and also that moment of momentum which is of such vast importance in the theory4 ,a consideration of the probabilities of the case make it quite certain that the celestial bodies we see are as nothing compared with the dark bodies we do not see4 ,the stars we see are moving1 and the natural assumption is that the dark objects with which the heavens teem are also in motion4 ,we shall1 under these conditions1 not feel any insuperable difficulty in the supposition that collisions between different bodies in the heavens may have taken place from time to time4 ,we remember that these bodies are moving in all directions1 and at extremely high velocities4 ,we are quite willing to grant the excessive improbability that any two bodies particularly specified should come into collision4 ,within view of our telescopes we have1 however1 a hundred millions of stars1 and if we multiply that figure even by millions1 it will still1 we may well suppose1 not be too large to express the number of bodies which1 though contained within the region of space ranged over by our telescopes1 are still totally invisible4 ,in these circumstances1 we may admit that occasional collisions are not impossible4 ,please note the strength which the argument derives from the enormous increase in our estimate of the number of bodies1 when we include the dark objects as well as the stars4 ,if we were asked whether it would ever be possible for two bright stars to come into collision1 we might well hesitate about the answer4 ,we know1 of course1 that the stars have proper motions2 we know1 too1 that the stars1 in this respect unlike the planets1 have no definite directions of movement under the control of a supreme co-ordinating attraction4 ,some stars move to the right1 and some to the left1 some one way and some another2 but even still1 notwithstanding their great number1 the extent of space is such that the stars keep widely apart1 and thus collisions can hardly be expected to take place1 unless perhaps in a cluster such as that shown in ,fig4 #ec4 ,we have no reason to think that a collision between two actual bright stars was the origin of the primval nebula of our system4 ,but when we reflect that the stars1 properly so called1 are but the visible members of an enormously greater host of objects1 then the possibilities of occasional collision between a pair of these incomparably more abundant dark bodies seems to merit our close attention4 ,we are not by any means claiming that such collisions occur frequently4 ,but what we do say is1 that if1 as we believe1 these bodies are to be reckoned in many millions of millions1 then it does sometimes happen that two of them1 moving about in space1 will approach together sufficiently to give rise to a collision4 ,it was from some such collision that we believe the nebula took its rise from which the solar system originated4 ,we have the best reason for knowing that celestial collisions do sometimes occur4 ,it will be in the recollection of the readers of this chapter that in ,february1 #aija1 the astronomical world was startled by the announcement of the outbreak of a new star in ,perseus4 ,a photograph of that part of the heavens had been taken a few days before4 ,there were the ordinary stars1 such as existed from time immemorial1 and such as have been represented on the numerous maps in which the stars are faithfully set down4 ,but1 on ,february #bbnd1 ,dr4 ,anderson1 already famous by similar discoveries1 noticed that the constellation of ,perseus contained a star which he had not seen before4 ,instantly the astronomical world was apprised by telegraph that a new star had appeared in ,perseus1 and forthwith most diligent attention was paid to its observation4 ,photographs then obtained show the stars that had been seen there before1 with the addition of the new star that had suddenly come into view4 ,for a few nights after its discovery the object increased in lustre1 until it attained a brightness as great as that of ,capella or ,vega4 ,but in this state it did not long remain4 ,this brilliant object began to wane4 ,presently it could not be classed as a star of the first magnitude1 nor yet of the second1 and then it ran down until a little below the third1 and even below the fourth4 ,in the subsequent decline of the star there were several curious oscillations4 ,on one night the star might be seen1 the next night it would be hardly discerned1 while the night after it had again risen considerably4 ,but1 notwithstanding such temporary rallies1 the brightness1 on the whole1 declined1 until at last the star dwindled to the dimensions of a small point of light1 scarcely distinguishable with the naked eye4 ,the decline was apparently not so rapid as the increase1 but nevertheless from the first moment of its appearance to the last was not longer than a few weeks4 ,this new star in ,perseus established1 in one sense1 a record4 ,for the star was brighter than any new star which had been noticed since the days of accurate astronomical observations4 ,not indeed for three centuries had a star of such lustre sprung into existence4 ,but a temporary star1 such as this was1 has been by no means an infrequent occurrence4 ,many such have been recorded4 ,those who have been acquainted with astronomical matters for thirty years will recollect four or five such stars4 ,in each of them the general character was somewhat the same4 ,there was a sudden outbreak1 and then a gradual decline4 ,the questions have sometimes arisen as to whether the outbreak of such an object is really the temporary exaltation of a star which was previously visible1 or whether it ought not to be regarded as the creation of a totally new star4 ,in some cases it does seem possible that a new star may have been partly1 at all events1 due to a large increase of brightness of some star which had been known before4 ,in the case of ,nova ,persei1 however1 we have the best authority that this is not the case4 ,professor ,pickering1 the distinguished astronomer of ,harvard ,college ,observatory1 happened to photograph the region in which ,nova ,persei appeared a few days before the outbreak took place4 ,he tells us that there is not the least indication on his photograph of the presence of a star in that region4 ,illustration3 ,fig4 #ed4--,,spectrum ,,of ,,nova ,,persei 7#aija74 7,photographed with the #dj in4 ,yerkes ,telescope by ,mr4 ,ferdinand ,ellerman47 ,the spectrum of ,nova ,persei1 in an instrument of sufficient power1 appeared a truly magnificent object4 ,like other stellar spectra1 it displayed the long line of light marked with the hues of the rainbow1 but it was unlike the spectra of ordinary stars in respect of the enormous enhancements of the brightness at various parts of this spectrum4 ,for instance1 at one end of the long coloured band a brilliant ruby line glowed with a lustre that would at once attract attention1 and demonstrated that the object under view must be something totally different from ordinary stars4 ,this superb feature is one of the lines of hydrogen4 ,the presence of that line showed that m the source from which the light came there must have been a remarkable outbreak of incandescent hydrogen gas4 ,at various points along the spectrum there were other beautiful bright lines which1 in each case1 must have been due to glowing gas4 ,here we have the evidence of the spectrum telling us in unmistakable language that there were features in this star wholly unlike the features found in any ordinary star4 ,it is impossible to dissociate these facts from the history of the star4 ,much of what we have said with regard to the spectrum of ,nova ,persei might be repeated with regard to the spectrum of the other temporary stars which1 from time to time1 have burst forth4 ,in each case the spectrum characteristic of an ordinary star is present1 but superadded to it are bright lines which indicate that some great convulsion has taken place1 a convulsion by which vast volumes of gas have been rendered incandescent4 ,in ,fig4 #ed we show the spectrum of ,nova ,persei on five dates1 from ,february #bgth to ,march #bhth1 #aija4 ,these photographs were taken by ,mr4 ,ferdinand ,ellerman with the great telescope of the ,yerkes ,observatory4 ,they show in the clearest manner the bright lines indicating the incandescent gases4 ,we have pointed out the high probability that among the millions and millions of bodies in the universe it may now and then happen that a collision takes place4 ,have we not also explained how the heat generated in virtue of such a collision might be sufficient1 and1 indeed1 much more than sufficient1 to raise the masses of the two colliding bodies to a state of vivid incandescence8 ,a collision affords the simplest explanation of the sudden outbreak of the star1 and also accounts for the remarkable spectrum which the star exhibits4 ---------------------------------------- -------------------------------- ,,chapter ,,xix4 ,,concluding ,,chapter4 ,comprehensiveness of the ,nebular ,theory--,illustration--,huxley and the ,origin of ,species--,rudimentary ,organs--,the ,apteryx--,its ,evanescent ,wings--,the ,skeleton--,an ,historical ,explanation--,application of the ,same ,method to the ,nebular ,theory--,the ,internal ,heat of the ,earth--,the ,lady ,psyche4 ,,it is not difficult to show that the nebular theory occupies a unique position among other speculations of the human intellect4 ,it is so comprehensive that almost every conceivable topic will bear some relation to it4 ,perhaps ,i may venture to give a rather curious illustration of this fact1 which was told me many years ago by one who attended a course of lectures by an eminent ,professor in the medical faculty at1 let us say1 ,vienna4 ,the subject of the course was the no doubt highly important1 but possibly not generally interesting1 subject of 8inflammation40 ,i think ,i am right in saying that the course had to last for six months1 because the subject was to be treated with characteristic breadth and profundity4 ,at all events1 ,i distinctly remember that the learned ,professor commenced his long series of professional discourses with an account of the nebular theory1 and from that starting point he gradually evolved the sequence of events which ultimately culminated in--inflammation6 ,it may be remembered that in the year #ahhj1 ,professor ,huxley delivered at the ,royal ,institution a famous lecture which he termed 8,the ,coming of ,age of the ,origin of ,species40 ,among the many remarkable and forcible illustrations which this lecture contained1 ,i recall one which brought before the audience1 in the most convincing manner1 the truth of the great ,darwinian ,theory of ,evolution4 ,huxley pointed out how the discoveries in ,biology1 during the twenty-one years which immediately succeeded the publication of the 8,origin of ,species10 had been so numerous and so important1 and had a bearing so remarkable on the great evolutionary theory1 that even if the ,darwinian ,theory had not been formed to explain the facts of ,nature1 as they were known at the time when ,darwin published his immortal book1 the same theory would have had to be formed1 were it only to explain the additional facts which had come to light since the great theory itself had been first given to the world4 ,i believe we may use similar language with regard to the nebular theory and its great founders1 ,kant1 ,laplace1 and ,herschel4 ,if the facts which were known to these philosophers led them to adopt in one form or another that view of the ,origin of the ,universe which the nebular theory suggests1 how stands the theory now in the light of the additional facts that have been since disclosed8 ,if we merely took the discoveries which have been made since the last of the three great philosophers passed away1 it might well be maintained that a nebular theory would be demanded to account for the facts brought to light1 in the interval4 ,the argument on which the nebular theory of the solar system is founded has other parallels with that wonderful doctrine of ,natural ,selection by which ,darwin revealed the history of life on our globe4 ,it not unfrequently happens that an animal has in its organisation some rudiments of a structure which is obviously of no use to the animal in his present mode of life1 and would be unintelligible if we supposed the animal to have been created as he is4 ,a curious instance of a rudimentary structure is furnished in the apteryx1 the famous wingless bird which still lives in ,new ,zealand4 ,the arrival of civilisation in ,new ,zealand seems likely to be accompanied with fatal results1 so far as the unfortunate apteryx is concerned4 ,weasels and other fierce enemies have been introduced1 with which this quaint bird of antiquity is unable to cope4 ,the apteryx is defenceless against such foes4 ,nature had not endowed it with weapons wherewith to fight1 for it had1 apparently1 no serious adversaries until these importations appeared in its island home4 ,unlike the ostrich1 the apteryx has neither strength to fight his enemies1 nor speed to run away from them1 though1 like the ostrich1 it has no wings for flight2 indeed1 the apteryx has no wings at all4 ,as its name signifies the apteryx is the wingless bird4 ,living specimens are still to be seen in the ,zoological ,gardens4 ,the special point to notice is that1 though he has no wings whatever1 still there are small rudimentary wing-bones which can be easily seen4 ,you need not be afraid to put your hand on the apteryx1 and feel the puny little remnants of wings 7,fig4 #ee74 ,if1 having seen the bird in the ,zoological ,gardens1 you go to the ,natural ,history ,museum1 you will there find a skeleton of the apteryx 7,fig4 #ef74 ,look near the ribs in the photograph1 and there you will see those poor little wing-bones--wing-bones where there never was a wing4 ,from our present point of view these wings are1 however1 more interesting and instructive than the most perfect wings of an eagle or a carrier-pigeon4 ,those wings in the apteryx may be incapable of flight1 but they are full of instruction to the lover of ,nature4 ,as it is certain that they are absolutely of no use whatever to the bird1 we may well ask1 why are they there8 ,they are not there to give assistance to the bird in his struggle for life2 they cannot help him to escape from his enemies or to procure his food2 they cannot help him to tend and nurture the young one which is hatched from the egg2 they can help him in no way4 ,the explanation of those ineffectual wings is historical4 ,those bones are present in the apteryx simply because that bird has come down by a long line of descent from birds which were endowed with genuine wings1 with wings which enabled them to fly like rooks or partridges4 ,illustration3 ,fig4 #ee4--,,the ,,apteryx3 ,a ,,wingless ,,bird ,,of ,,new ,,zealand4 ,illustration3 ,fig4 #ef4--,,skeleton ,,of ,,the ,,apteryx1 ,,showing ,,rudimentary ,,wings4 ,but if this be the explanation1 how has it come to pass that the wings have dwindled to useless little bones8 ,we cannot of course feel certain of the reason1 but it seems possible to make surmises4 ,in early times winged birds flew over the sea into ,new ,zealand1 and found it a country of abundance1 as many other immigrants have done in later times4 ,it may have been that the food in ,new ,zealand was so plentiful that the wants of the birds could be readily supplied1 without the necessity for ranging over large tracts4 ,it may have been that the newly arrived birds found that they had few or no enemies in ,new ,zealand1 from which flight would be necessary as a means of escape4 ,it may possibly have been both causes together1 and doubtless there must have been other causes as well4 ,the fact is1 however1 certain1 that in the course of long generations this bird gradually lost the power of flight4 ,natural selection decrees that an organ which has ceased to serve a useful purpose shall deteriorate in the course of generations4 ,if the wings had become needless in the search for food1 unnecessary for escape from enemies1 and useless for protection of its young1 they would certainly tend towards disappearance4 ,the organism finds it uneconomical to maintain the nutrition of a structure which discharges no useful end4 ,the wings1 in such circumstances1 would be an encumbrance rather than an aid1 and so we may readily conjecture that1 in accordance with this well-known principle1 the wings gradually declined1 until they ceased to be useful organs1 so that now merely a few rudimentary bones remain to show that the bird's ancestors had once been as other birds4 ,whatever may have been the cause1 it seems certain that in the course of thousands of years1 or it may be in scores of thousands of years1 these birds lost the power of flight2 thus they gradually ceased to have wings1 and these little bones are all that now remain to render it almost certain that1 if we could learn what this bird's ancestry has been1 we should find that it was descended from a bird which had useful wings and vigorous flight4 ,whenever we find an organ which is obviously rudimentary1 or of no use to its possessor in its present form1 ,darwin has taught us to look for an historical explanation4 ,let us see if we cannot apply this principle to the illustration of the nebular theory4 ,illustration3 ,,spirals ,,in ,,other ,,departments ,,of ,,nature4 ,fig4 #eg4--;,,foraminifer4 ,fig4 #eh4--,,nautilus4 ,we liken the internal heat of the earth to the rudimentary wing-bones of the apteryx4 ,in each case we find a survival devoid of much significance1 unless in regard to its historical interpretation4 ,but that historical significance can hardly be over-estimated4 ,unimportant as the wing-bones may be1 they admit of explanation only on the supposition that the apteryx was descended from a winged ancestor4 ,unimportant as the internal heat1 still lingering in our globe1 may seem1 it admits of explanation only on the supposition that the earth has had the origin which the nebular theory suggests4 ,that the earth's beginning has been substantially in accordance with the great ,nebular ,theory is1 ,i believe1 now very generally admitted4 ,but the only authority ,i shall cite in illustration of this final statement is the ,lady ,psyche1 who commences her exquisite address to her 8patient range of pupils0 with the words3-- 8,this world was once a fluid haze of light1 ,till toward the centre set the starry tides1 ,and eddied into suns1 that wheeling1 cast ,the planets20 ---------------------------------------- -------------------------------- ,,appendices4 ------- ,i4--,,on ,,the ,,heat ,,given ,,out ,,in ,,the ,,contraction ,,of ,,the ,,nebula4 #a4 ,,fundamental ,,theorems ,,in ,,the ,,attraction ,,of ,,gravitation4 ,the first theorem to be proved is as follows3-- ,the attraction of a thin homogeneous spherical shell on any point in its interior vanishes4 ,illustration3 ,fig4 #ei4 ,take any point ,p within the sphere4 ,let this be the vertex of a cone produced both ways1 but with a very small vertical angle1 so that the small areas ,s and ,s1 in which the two parts of the cone cut the sphere1 may be regarded as planes4 ,draw the tangent planes at ,s and ,s4 ,let the plane of the paper pass through ,p and be perpendicular to both these tangent planes4 ,let ,o ,p ,o be one of the generators of the cone1 and let fall ,p ,q perpendicular to the tangent plane at ,o1 and ,p ,q perpendicular to the tangent plane at ,o4 ,the volume of the cone with the vertex at ,p and the base ,s is ,p ,q ,s1 and the other part of the cone has the volume ,p ,q ,s4 ,as the vertical angles of the cones are small1 their volumes will1 in the limit1 be in the ratio of ,o ,p#c to ,o ,p#c1 and accordingly ,p ,q ,s ,p ,q ,s ,p ,o#c ,o ,p#c4 ,but from the figure ,p ,q ,p ,q ,p ,o ,p ,o1 and hence ,s ,o ,p#b ,s ,o ,p#b4 ,as the shell is uniform1 the masses of the parts cut out by the cones are respectively proportional to ,s and ,s4 ,hence we see that the attractions of ,s and ,s on ,p will neutralise4 ,the same must be true for every such cone through ,p1 and accordingly the total attraction of the shell on a particle inside is zero4 ,the second fundamental theorem is as follows3-- ,a thin spherical homogeneous shell produces the same attraction at an external point as if its entire mass were concentrated at the centre of the sphere4 ,this is another famous theorem due to ,newton4 ,he gives a beautiful geometrical proof in ,section ,,xii4 of the first book of the 8,principia40 ,we shall here take it for granted1 and we shall consequently assume that-- ,the attraction by the law of gravitation of a homogeneous sphere on an external point is the same as if the entire mass of the sphere were concentrated at its centre4 #b4 ,,on ,,the ,,energy ,,between ,,two ,,attracting ,,masses4 ,let m and m be two attracting bodies supposed to be small in comparison with their distance x4 ,let the force between them be m m x#b when is the force between two unit masses at unit distance4 ,it is required to find the energy necessary to separate them to infinity1 it being supposed that they start from an initial distance a4 ,the energy required is obtained by integrating between the limits infinity and a1 and is consequently m m a4 #c4 ,,on ,,the ,,energy ,,given ,,out ,,in ,,the ,,contraction ,,of ,,the ,,nebula4 ,we assume that the nebula is contracting symmetrically1 so that at any moment it is a homogeneous sphere4 ,we shall consider the shell which lies between the two spheres of radii1 r dr and r respectively4 ,let ,m be the mass of the nebula contained within the sphere of radius r1 and let d,m be the mass of the shell just defined4 ,then it follows from #a that the condensation of the shell will have been effected by the attraction of the mass ,m solely4 ,the exterior parts of the nebula can have had no effect1 for the outer part has always been in symmetrical spherical shells exterior to d,m1 and the attraction of these is zero4 ,we see from #b that the contraction of d,m from infinity1 until it forms a shell with radius r1 represents a quantity of energy1 7 ,md,m7_/r 2 for it is obvious that the energy involved in the contraction of the whole shell is the sum of the energies corresponding to its several parts4 ,if ,m be the total mass and a the radius of the nebula always supposed homogeneous ,m ,m 7r#c_/;a#c71 and therefore d,m #c ,m 7r#b_/;a#c7 dr4 ,hence the work done in the contraction is 7_/r7 ,m 7r#c_/;a#c7 #c ,m 7r#b_/;a#c7 dr 7#c _/a#f7 ,m#b r#d dr4 ,integrating1 therefore1 the total work of contraction is 7 ,m#b_/;a7 ,at the present moment a mass of #a lb4 at the surface of the sun would weigh #bg lbs4 if tested by a spring balance4 ,hence ,m_/a#b #bg4 ,with this substitution we find the expression for the foot-pounds of work corresponding to the contraction of the nebula from infinity to a sphere of radius a to be1 #bg a ,m #af a ,m very nearly4 ,hence we have the following fundamental theorem due to ,helmholtz1 which is the basis of the theory of sun heat4 ,if the sun he regarded as a homogeneous sphere of mass ,m pounds and radius a feet1 then the foot-pounds of energy rendered available for sun heat by the contraction of the solar material from1 an infinite distance is #af a ,m4 #d4 ,,evaluation ,,of ,,the ,,sun ,,heat ,,given ,,out ,,in ,,contraction4 ,the number of foot-pounds of work given out in the contraction from infinity is #af a ,m4 ,as #ggb foot-pounds are equal to one unit of heat1 i4e4 to the quantity of heat necessary to raise #a lb4 of water #a ,fahrenheit1 we see that #ggb ,m is the work required to raise a mass of water equal to the mass of the sun through #a ,fahrenheit4 ,hence the number of globes of water1 each equal to the sun in mass1 which would be raised #a ,fahrenheit by the total heat arising from the contraction1 is 7#af a7_/#ggb1 but a1 the radius of the sun in feet1 is #b1bhj1jjj1jjj1 and hence we have the following theorem3-- ,the energy liberated in the contraction of the sun from infinity to its present dimensions would1 if turned into heat1 suffice to raise #dg1jjj1jjj globes of water1 each having the same mass as the sun1 through #a ,fahr4 ,it is found by experiment that #a lb4 of good coal may develop #ad1jjj units of heat1 and is therefore equivalent to #ad1jjj #ggb foot-pounds of work4 ,a mass of coal equal to the sun would therefore 7granted oxygen enough7 be equivalent to #ad1jjj #ggb ,m foot-pounds of work4 ,but we have 7#af a ,m7 #af #b1bhj1jjj1jjj -------------- --------------- #c1djj4 #ad1jjj #ggb ,m #ad1jjj #ggb ,hence we see that ,the energy liberated in the contraction of the sun from infinity to its present dimensions1 is as great as could be produced by the combustion of #c1djj globes of coal1 each as heavy as the sun4 ,we may speak of #c1djj in this case as the coal equivalent4 #e4 ,,on ,,the ,,further ,,contraction ,,of ,,the ,,sun ,,and ,,the ,,heat ,,that ,,may ,,thus ,,be ,,given ,,out4 ,let us suppose the sun contracts to the radius r1 and then1 as already proved1 #c1 the energy it gives out is 7 ,m#b7_/r1 but we have ,m_/a#b #bg1 whence on contraction to the radius r the total energy given out from the commencement is #af ,m 7a#b_/r7 ,the average density of the sun at present is #a4d4 ,let us suppose it condenses until it has a density 4 r#c a#c #a4d 1 whence the energy becomes #ad a ,m 2 but the coal equivalent of #af a ,m has been found in #d to be #c1djj1 and hence the coal equivalent in this case is #c1jjj 4 ,if we take to be the density of platinum 7#ba4e71 we get a coal equivalent #h1cjj4 ,this1 therefore1 seems to represent a major limit to the quantity of heat which can be obtained from the condensation of the nebula from infinity into a sun of the utmost density4 #f4 ,,on ,,the ,,present ,,emission ,,of ,,sun ,,heat4 ,according to ,scheiner1 8,strahlung und ,temperatur der ,sonne1 ,leipzig1 #ahii10 the value of the solar constant1 i4e4 the number of cubic centimetres of water which would be raised #a ,centigrade by the quantity of sun heat which1 if there were no atmospheric absorption1 would fall perpendicularly on a square centimetre1 at the earth's mean distance from the sun1 is between #c4e and #d4j4 ,if we take the mean value1 we have 7translated into ,british units71 the following statement3-- ,if at a point in space1 distant from the sun by the earth's mean distance1 one square foot was exposed perpendicularly to the solar rays1 then the sun heat that would fall upon it in one minute would raise one pound of water #ad ,fahr4 ,this shows that the solar energy emitted daily amounts to #gjj1jjj1jjj1jjj #d a#b foot-pounds4 #g4 ,,on ,,the ,,daily ,,contraction ,,of ,,the ,,sun ,,necessary ,,to ,,supply ,,the ,,present ,,expenditure ,,of ,,heat4 ,we have seen that at the radius r the energy is #af ,m 7a#b_/r74 ,hence for a change dr it is -#af ,m 7a#b_/r#b7 dr4 ,at its present size1 accordingly1 the energy given out by a shrinkage dr is #af ,m dr4 ,one cubic foot of the sun averages #hg pounds1 so that ,m #d_/c a#c #hg #af ,m dr #dfd #d a#c dr4 ,we have to equate this to the expression in the last article1 and we get dr #gjj1jjj1jjj1jjj_/7dfd a7 4#fe4 ,this is the shrinkage of the sun's radius expressed in feet4 ,hence the daily reduction of the sun's diameter is #af inches4 ,one coal equivalent possesses energy represented by ,m #ad1jjj #ggb4 ,hence we can calculate that one coal equivalent would supply the solar radiation at its present rate for about #b1hjj years4 ,,ii4--,,the ,,conservation ,,of ,,moment ,,of ,,momentum4 ,we give here an elementary investigation of the fundamental dynamical principle which has been of such importance throughout this volume4 #h4 ,,case ,,where ,,there ,,are ,,no ,,forces4 ,newton's first law of motion tells us that a particle in motion if unacted upon by force1 will move continuously in a straight line without change of velocity4 ,let ,a#j1 ,fig4 #fj1 be the position of the particle at any moment4 ,let ,a#a be its position after the time t2 ,a#b be the position at the time #bt2 ,a#c be the position at the time #ct1 and so on4 ,then the first law of motion tells us that the distances ,a#j ,a#a1 ,a#a ,a#b1 ,a#b ,a#c1 ,a#c ,a#d1 must form parts of the same straight line and must be all equal4 ,if lines ,o ,a#j1 ,o ,a#a1 ,o ,a#b1 etc41 be drawn from any fixed point #j1 then the areas of the triangles ,o ,a#j ,a#a1 ,o ,a#a ,a#b1 ,o ,a#b ,a#c1 #j ,a#c ,a#d1 will be all equal4 ,for each area is one-half the product of the base of the triangle into the perpendicular ,o ,t from ,o on ,a#j ,a#a1 and1 as the bases of all the triangles are equal1 it follows that their areas are equal4 ,thus we learn that a particle moving without the action of force will describe around any fixed point ,o equal areas in equal times4 ,illustration3 ,fig4 #fj4--;,,first ,,law ,,of ,,motion ,,exemplifies ,,constant ,,moment ,,of ,,momentum4 ,the product of the mass of the particle and its velocity is termed the momentum4 ,if the momentum be multiplied by ,o ,t the product is termed the moment of momentum around ,o4 ,we have in this case the simplest example of the important principle known as the conservation of moment of momentum4 ,the moment of momentum of a system of particles moving in a plane is defined to be the excess of the sum of the moments of momentum of those particles which tend round ,o in one direction1 over the sum of the moments of momentum of those particles which tend round ,o in the opposite direction4 ,if we deem those moments in one direction round ,o as positive1 and those in the other direction as negative1 then we may say that the moment of momentum of a system of particles moving in a plane is the algebraical sum of the several moments of momentum of each of the particles4 #i4 ,a ,,geometrical ,,proposition4 ,the following theorem in elementary geometry will be required3-- ,illustration3 ,fig4 #fa4--;,a ,,useful ,,geometrical ,,proposition4 ,let ,a ,b and ,a ,c be adjacent sides of a parallelogram1 ,fig4 #fa1 of which ,a ,d is the diagonal1 and let ,o be any point in its plane4 ,then the area ,o ,a ,c is the difference of the areas ,o ,a ,d and ,o ,a ,b4 ,draw ,d ,q and ,c ,p parallel to ,o ,a4 ,then ,o ,a ,d ,o ,a ,q1 whence ,o ,a ,d - ,o ,a ,b ,o ,b ,q ,o ,a ,p ,o ,a ,c4 #aj4 ,,relation ,,between ,,the ,,change ,,of ,,moment ,,of ,,momentum ,,and ,,the ,,force ,,acting ,,on ,,the ,,particle4 ,illustration3 ,fig4 #fb4--;,,acceleration ,,of ,,moment ,,of ,,momentum ,,equals ,,moment ,,of ,,force4 ,let ,a#a and ,a#b1 ,fig4 #fb1 be two adjacent points on the path of the particle1 and let ,a#a ,q and ,a#b ,r be the tangents at those points4 ,let ,s ,q represent the velocity of the particle at ,a#a1 and ,,sr the velocity of the particle at ,a#b4 ,then ,q ,r represents both in magnitude and direction the change in velocity due to the force ,f1 which we suppose constant both in magnitude and direction1 while the particle moves from ,a#a to ,a#b in the small time t2 we have also ,q ,r ,f t m4 ,complete the parallelogram ,s ,q ,r ,u1 and let fall ,o ,p#a1 ,o ,p#b1 ,o ,t perpendiculars from ,o on ,s ,q1 ,s ,r1 ,s ,u respectively4 ,since ,s ,q is the velocity of the particle when at ,a#a the moment of momentum is m ,o ,p#a ,s ,q2 when the particle is at ,a#b the moment of momentum is m ,o ,p#b ,s ,r4 ,whence the difference of the moments of momentum at ,a#a and ,a#b is m 7,o ,p#b ,s ,r - ,o ,p#a ,s ,q7 #b m 7,o ,s ,r - ,o ,s ,q7 #b m ,o ,s ,u m ,o ,t ,s ,u m ,o ,t4 ,q ,r ,f t ,o ,t4 ,but in the limit ,s coincides with ,a#a and ,a#b1 and we see that the gain in moment of momentum is t times the moment of the force around ,o4 ,hence we deduce the following fundamental theorem1 in which1 by the expression acceleration of moment of momentum1 we mean the rate at which the moment of momentum increases3-- ,if a particle under the action of force describes a plane orbit1 then the acceleration of the moment of momentum around any point in the plane is equal to the moment of the force around the point4 ,if the force is constantly directed to a fixed point1 then the moment of the force about this point is always zero4 ,hence the acceleration of the moment of momentum around this point is zero1 and the moment of momentum is constant4 ,thus we have ,kepler's law of the description of equal areas in equal times1 and we learn that the velocity is inversely proportional to the perpendicular on the tangent4 #aa4 ,,if ,,two ,,or ,,more ,,forces ,,act ,,on ,a ,,point1 ,,then ,,the ,,acceleration ,,of ,,the ,,moment ,,of ,,momentum1 ,,due ,,to ,,the ,,resultant ,,of ,,these ,,forces1 ,,is ,,equal ,,to ,,the ,,algebraic ,,sum ,,of ,,the ,,moments ,,of ,,momentum ,,due ,,to ,,the ,,action ,,of ,,the ,,several ,,components4 ,let ,a ,d1 ,fig4 #fa1 be a force1 and ,a ,c and ,a ,b its two components4 ,then1 since ,o ,a ,d ,o ,a ,b ,o ,a ,c1 we see that the moment of ,a ,d around ,o is equal to the sum of the moments of its components4 ,hence we easily infer that if a force be resolved into several components the moment of that force around a point is equal to the algebraical sum of the moments of its several components4 ,the acceleration of the moment of momentum around ,o1 due to the resultant of a number of forces1 is equal to the moment of that resultant around ,o4 ,but1 as we have just shown1 this is equal to the sum of the moments of the separate forces1 and hence the theorem is proved4 #ab4 ,,if ,,any ,,number ,,of ,,particles ,,be ,,moving ,,in ,a ,,plane1 ,,and ,,if ,,they ,,are ,,not ,,subjected ,,to ,,any ,,forces ,,save ,,those ,,which ,,arise ,,from ,,their ,,mutual ,,actions1 ,,then ,,the ,,algebraic ,,sum ,,of ,,their ,,moments ,,of ,,momentum ,,round ,,any ,,point ,,is ,,constant4 ,this important theorem is deduced from the fact stated in the third law of motion1 that action and reaction are equal and opposite4 ,let us take any two particles2 then1 the acceleration of the moment of momentum of one of them1 ,a1 by the action of the other1 ,b1 will be the moment of the force between them4 ,the acceleration of the moment of momentum of ,b by the action of ,a will be the same moment1 but with an opposite sign4 ,hence the total acceleration of the moment of momentum of the system by the mutual action of ,a and ,b is zero4 ,in like manner we dispose of every other pair of actions1 and thus1 as the total acceleration of the moment of momentum is zero1 it follows that the moment of momentum of the system itself must be constant4 ,this fundamental principle is also known as the doctrine of the conservation of areas4 ,it may be stated in the following manner3-- ,if a system of particles are moving in a plane under the influence of their mutual actions only1 the algebraic sum of the areas swept out around a point1 each multiplied by the mass of the particle1 is directly proportional to the time4 #ac4 ,,if ,a ,,particle ,,of ,,mass m1 ,,is ,,moving ,,in ,,space ,,under ,,the ,,action ,,of ,,any ,,force ,f1 ,,then ,,the ,,projection ,,of ,,that ,,particle ,,on ,,any ,,fixed ,,plane ,,will ,,move ,,as ,,if ,,it ,,were ,a ,,particle ,,of ,,mass m ,,acted ,,upon ,,by ,,that ,,component ,,of ,f ,,which ,,is ,,parallel ,,to ,,the ,,plane4 ,this is evident from the consideration that the acceleration of the particle parallel to the plane must be proportional to this component of ,f4 ,let us now suppose a system of particles moving in space under their mutual actions4 ,the projections of these particles on a plane will move as if they were the particles themselves subjected to the action of forces which are the projections of the actual forces on the same plane1 and as the reactions between any two particles are equal and opposite1 the projections of those reactions on the plane are equal and opposite4 ,hence the proof already given of the constancy of the moments of momentum of a plane system1 will apply equally to prove the constancy of the moments of momentum of the projections of the particles on the plane4 ,hence we have the following important theorem3-- ,let a system of particles be moving in space under the action of forces internal to the system only4 ,let any plane be taken1 and any point in that plane1 and let the momentum of each particle be projected into the plane1 then the algebraic sum of the moments of these projections around the point is constant4 #ad4 ,,on ,,the ,,principal ,,plane ,,of ,a ,,system4 ,let us suppose a system of particles moving under the influence of their mutual actions4 ,let ,o be any point1 and draw any plane ,l through ,o4 ,then the moment of momentum of the system around the point ,o and projected into the plane ,l is constant4 ,let us call it ,s4 ,if another plane1 ,l1 had been drawn through ,o1 the similar moment with regard to ,l is ,s4 ,thus for each plane through ,o there will be a corresponding value of ,s4 ,we have now to show that one plane can be drawn through ,o1 such that the value of ,s is greater than it is for any other plane4 ,this is the principal plane of the system4 ,if v be the velocity of a particle1 then in a small time t it moves over the distance v t4 ,if p be the perpendicular from ,o on the tangent to the motion1 then the area of the triangle swept round ,o in the time t is p v t1 and we see that the momentum is proportional to the mass of the particle multiplied into the area swept over in the time t4 ,the quantity ,s will1 therefore1 be proportional to the sum of the projections of the areas in ,l1 swept over in the time t1 each increased in the proportion of the mass of the particle4 ,it is easily seen that the projection of an area in one plane on another is obtained by multiplying the original area by the cosine of the angle between the two planes4 ,for if the area be divided into thin strips by lines parallel to the line of intersection of the planes1 then in the projection of these strips the lengths are unchanged1 while the breadths are altered by being multiplied by the cosine of the angle between the two planes4 ,if1 therefore1 we mark off on the normal to a plane ,l a length h proportional to any area in that plane1 then the projection of this area on any other plane ,l may be measured by the projection of h on the normal to ,l4 ,illustration3 ,fig4 #fc4--,,moment ,,of ,,momentum ,,unaltered ,,by ,,collision4 ,to determine the moment of momentum resolved in any plane we therefore proceed as follows3 ,draw a plane through ,o1 and the tangent to the path of one of the particles1 and mark off on the normal drawn through ,o to this plane a length l proportional to the moment of momentum4 ,repeat the same process for each of the other particles with lengths l1 l1 etc41 on their several normals4 ,suppose that l1 l1 l represent forces acting at ,o1 and determine their resultant ,r4 ,then ,r1 resolved along any other direction1 will give the component of moment of momentum in the plane to which that direction is normal4 ,in any plane which passes through ,r the component of moment of momentum is zero4 ,the plane perpendicular to ,r contains the maximum projection of moment of momentum4 ,this is the principal plane of the system which we have seen to be of such importance in connection with the nebular theory4 #ae4 ,,collisions4 ,the conservation of moment of momentum remains true in a system1 even though there may have been actual collisions between the several parts4 ,this is included in the proof already given1 for collisions are among the mutual actions referred to4 ,it may1 however1 be instructive to give a direct proof of a particular case4 ,let two particles collide when meeting in the directions ,a ,p and ,b ,p 7,fig4 #fc7 respectively4 ,whether the particles be elastic or inelastic is quite immaterial1 for in both cases the action and reaction must be equal and opposite1 and take place along some line ,p ,q4 ,the action on the particle moving along ,a ,p will give to it an acceleration of moment of momentum which is equal to the moment of the action around ,o4 ,the acceleration of the moment of momentum coming along ,b ,p will be equal and opposite4 ,thus the total acceleration of the moment of momentum is zero4 ,hence the collision has no effect on the total moment of momentum4 #af4 ,,friction ,,and ,,tides4 ,we have shown that such actions as collisions cannot affect the moment of momentum of the system1 neither can it be affected by friction of one body on another4 ,here1 as in the former case1 the actions and reactions are equal and opposite1 and consequently the accelerations of moment of momentum are zero4 ,nor is it possible for any tidal action to affect the total moment of momentum of the system4 ,every such action must be composed of the effects of one particle in the system on another1 and as this must invariably produce an equal and opposite reaction the total moment of momentum is unaltered4 ---------------------------------------- -------------------------------- ,,index4 ,acceleration of moment of momentum1 #cgg ,aldebaran1 #bg1 #bh ,anderson1 ,dr41 #cef ,andromeda1 ,great ,nebula in1 #dc1 #bjd ,antinous1 ,cluster of stars in1 #cec ,apteryx1 ,rudimentary wing-bones of1 #cfd1 #cff ----1 ,skeleton of1 #cfd1 #cff ----1 ,the1 #cfc1 #cfe ,arcturus1 ,spectrum of1 #he ,argon1 #bfe ,argus and surrounding stars1 #ajc ,ariel1 #cch ,boring1 ,the great1 #abc ,brooks' comet1 #hi ,bunsen burner1 ,the1 #bhc ,butterfly and the oak-tree1 ,the1 #ae ,calcium1 #bgd ,capella1 ,spectrum of1 #fa-fd ,carbon1 #bhj ,ceres1 #caa ,change of moment of momentum1 #cge ,cluster1 ,nebulous region round a1 #cc ,clusters of stars1 #ec-fj1 #bjc ---- ---- of #agth magnitude1 #cec ,coal-unit1 #aaj ,collisions1 #bai1 #chj ----1 ,cause of formation of nebul1 #cef ,comets1 #cg ,comet1 ,brooks'1 #hi ---- of #ahhb1 #aai ----1 ,spectrum of1 #bij ,common1 ,dr4 ,a4 ,a41 #dd ,concord1 ,the first1 #bid-cjg ----1 ,the second1 #cjh-cbc ----1 ,the third1 #cbd-ccf ,conglomerates1 #aei ,conservation of moment of momentum1 #cgd ,corona of the sun1 #aag ,crab nebula1 ,the1 #ai1 #dd ,crossley ,reflector1 ,the1 #de1 #df1 #dh1 #di1 #ej1 #fg1 #aii ,cygnus1 ,nebula in1 #cbi ,dark bodies in universe1 #cee ,darwin1 ,professor ,g4 ,h41 #aec1 #bed1 #ccb ,darwinian theory1 #aj1 #bfh1 #cfb ,dewar1 ,professor1 #add1 #bgb ,diurnal motion1 ,the1 #ba ,dumb-bell nebula1 #dc1 #dd1 #de1 #df1 #ej1 #gd1 #aie ,dust from ,krakatoa1 #ahe ,earth1 ,heat in interior of1 #acd1 #cfg ----1 ----1 ,cause of1 #aec ----1 ,history of1 #abb-aeg1 #bea ----1 ,rigidity of1 #afb ,earth-moon system1 #bec1 #ccb ,earthquakes1 #aeh-aij ---- in ,england1 #age ----1 ,routes of1 #aga ,emission of sun heat1 #cgc ,energy between two attracting masses1 #cgj ---- given out in contraction of nebula1 #cgj ---- of a system1 #baf1 #bce ,equivalent of heat1 #hh ,eros1 #cab ,evaluation of sun heat given out in contraction1 #cga ,everett1 ,professor1 #adi ,fire-mist1 ,the1 #bfh 8,flash0 spectrum1 #gj ,foot-pound1 #ia ,foraminifera1 #cfg ,friction and tides1 #cha ,gas in rarefaction1 #aah ,h and ,k lines1 #gj1 #bgf ,heat1 ,cause of1 #aec ----1 ,equivalent of1 #hh ---- given out in contraction of nebula1 #cfi ---- in interior of the earth1 #acd1 #cfg ----1 ,unit of1 #hj1 #hi ,helium1 #bgg ,helmholtz1 #hf1 #if1 #ajj ,hercules1 ,star-cluster in1 #eb1 #ec1 #ef1 #eg1 #ei ,herschel1 ,sir ,william1 #d1 #aa1 #gb1 #gc1 #gd ,huggins1 ,sir ,w41 #fj1 #fa1 #fc1 #fe ,huxley1 ,professor1 and ,darwinian theory1 #cfb ,huyssen1 ,captain1 #abg ,hydrogen in spectrum of ,nova ,persei1 #ceh 8,inflammation0 and nebular theory1 #cfa ,joule's equivalent of heat1 #hh ,jupiter1 #bc1 #be1 #bf1 #bi1 #bjh1 #bcg1 #caj1 #cbg ,k and ,h lines1 #gj1 #bgf ,kant1 ,immanuel1 #d1 #e1 #gb1 #gc1 #gd1 #cbg ,keeler1 ,professor1 #de-dh1 #fg1 #gc1 #aii1 #bjj1 #bjb1 #bde ,kelvin1 ,lord1 #aec1 #afb ,krakatoa1 #agf-ahi ,langley1 ,professor1 #gh ,laplace1 #d1 #gb1 #gc1 #gd1 #bjf ,lassell1 ,mr41 #cch1 #cdj ,lick ,observatory1 #da1 #dc1 #dd1 #de ,lockyer1 ,sir ,norman1 #bgg ,lyra1 ,ring nebula in1 #bdi ,mars1 #be1 #bf1 #bg1 #bh1 #bi1 #caa1 #cda1 #cdi ----1 ,satellites of1 #cda ,mcanique ,cleste1 #e1 #h ,mercury1 #bc1 #be1 #bf1 #bi1 #bjh ,meteors1 #cg ,milky ,way1 #bje1 #bjf1 #bad1 #bbj ,milne1 ,professor1 #afe ,moment of momentum1 #bbb1 #bbf1 #bdj1 #ceb ---- ----1 ,acceleration of1 #cgg ---- ----1 ,change of1 #cge ---- ----1 ,conservation of1 #cgd ,momentum1 ,moment of1 #bbb1 #bbj1 #bdj1 #ceb ,monoceros1 ,nebulous region round a cluster in1 #cc ,moon1 ,origin of1 #bed ----1 ,surface of1 #bee ,nautilus1 ,the1 #cfg ,nebula1 ,contraction of1 ,heat given out in1 #cfi ----1 ----1 ,energy given out in1 #cgj ---- in ,orion1 ,the great1 #dj1 #da1 #db1 #dd1 #df1 #ej1 #gd1 #aie1 #bdb ---- ----1 ----1 ,spectrum of1 #fc1 #fd1 #fe ----1 ,the great spiral1 #aib1 #aic ,nebul1 #dj1 #da1 #dc1 #de1 #dg1 #ej1 #eg1 #eh1 #ff1 #fg1 #ga1 #gc1 #aje1 #abj1 #aeg1 #aia-bjf1 #bdb1 #bdg1 #bdi1 #bef1 #beg1 #beh1 #bei1 #bif1 #cbi1 #cde1 #cdh-cfj ----1 ,development of1 #bdb ----1 ,discovery of1 #aa ----1 ,number of1 #fg1 #bjj ,nebular anecdote1 #cfb ---- ,theory1 ,the1 #b1 #c1 #gb1 #gd1 #aeg1 #bje1 #bff1 #bib1 #cjg1 #cbc1 #cbh1 #cca1 #ccg-cdg1 #cfb1 #cfh ,nebulosity1 ,faint diffused1 in ,perseus1 #ag ,neptune1 #cg ----1 ,satellites of1 #ccj1 #cdj ,newcomb1 ,professor1 #bch ,norway1 ,conglomerates in1 #aei ,nova ,persei1 #ceh ---- ----1 ,spectrum of1 #ceh1 #cei1 #cfj ,oak-tree and the butterfly1 ,the1 #ae ,oberon1 #cch ,orbits of the planets1 #bjh ,orion1 #bb ,orion1 ,great nebula in1 #dj1 #da1 #db1 #dd1 #df1 #ej1 #gd1 #aie1 #bdb ----1 ,spectrum of1 #fc1 #fd1 #fe ,pegasus1 ,nebula in1 #dg1 #cde ,perseus1 ,a faint diffused nebulosity in1 #ag ----1 ,new star in1 #cef ,photosphere1 ,the1 #fi ,pickering1 ,professor1 #ceh 8,plane1 ,principal10 ,the1 #bbe1 #ceb1 #cgi ,planetary system1 ,the1 #cg1 #bjh ,planets1 #bb1 #bf1 #bh ----1 ,movement of1 #ce1 #caa ----1 ,orbits of1 #bjh1 #bih ----1 ,rotation of1 on their axes1 #cbe ,platinum1 #bfc ,pleiades1 #bb ----1 ,nebulae in1 #ga ,potassium1 #bgb 8,plane1 ,principal0 ,the1 #bbe1 #ceb1 #cgi ,probabilities1 ,theory of1 #cje ,radiation of sun's heat1 #hb ,ramsay1 ,professor1 #bgh ,ray nebul1 #bja1 #baa ,rigidity of the earth1 #afb ,ring nebula in ,lyra1 ,the1 #bdi ,roberts1 ,dr4 ,isaac1 #aih ,rosse1 ,lord1 #eg1 #aif-bja ,rowland1 ,prof4 ,henry1 #bgc ,sagittarius1 ,nebula in1 #aje ,satellites1 #cg1 #bji ,saturn1 #be1 #bf1 #bi1 #bbj1 #bcc ----1 ,dweller in1 and the ,sirian1 #ad ----1 ,ring of1 #baj1 #bbj1 #bca1 #bcb1 #bcc1 #bcd ,scheiner1 ,professor1 #bjb1 #bjd ,seismometer1 ,the1 #afe ,sirian1 ,the1 and the dweller in ,saturn1 #ad ,sirius1 #bae1 #baf ,smiths1 ,the parable of the1 #cjc ,solar system1 #cf1 #bjg ----1 ,energy of1 #cej ----1 ,evolution of1 #bj1 #bdf-bfj1 #cdi ----1 ,origin of1 #cea ,solar system1 ,scale of1 #bi1 #cj1 #ca ,spectra1 ,continuous1 #fh1 #bjc ----1 ,discontinuous1 #fh ,spectroscope1 ,the1 #fj1 #bga ,spiral form in ,nature1 #bef1 #beg ,spiral nebula1 ,the great1 #aib1 #aic1 #bdg ,spiral nebul1 #aia-bjf1 #baa1 #bab1 #bac1 #bbj1 #bdc1 #bdg1 #bef1 #beg1 #beh1 #bei1 #bif1 #cde ,star-clusters1 #ec-fj ,star1 ,spectrum of1 #fd ,stars distinguished from planets1 #bh1 #bi ,stoney1 ,dr4 ,g4 ,johnstone1 #bgi ,sun compared with the planets1 #bf1 #bi ----1 ,corona of1 #aag ----1 ,contraction of1 #ii1 #cgc ----1 ,density of1 #ajb1 #aae ----1 ,heat of1 #ge-id1 #ie-aaa1 #cga1 #cgb1 #cgc ----1 ,history of1 #aab-aba1 #bea ----1 ,nebulous part of1 #aba ----1 ,spectrum of1 #fa1 #fb1 #fi1 #gj1 #he1 #bgc ----1 ,surface of1 #bgh ----1 ,velocity of1 #ced ----1 ,weight of1 #aja ,sun heat1 given out in contraction1 ,evaluation of1 #cga1 #cgb ----1 ,present emission of1 #cgc ,sunsets1 ,the ,krakatoa1 #ahi ,systme du ,monde1 #h ,thermometer for testing the heat of the earth's interior1 #abi ,thomson1 ,prof4 ,j4 ,j41 #caf ,tides and friction1 #cha ,titania1 #cch ,umbriel1 #cch ,unit of heat1 #hj1 #hi ,uranus1 #cg1 #bch1 #bci ----1 ,satellites of1 #bch1 #cch ,venus1 #bc1 #be1 #bf1 #bi1 #bjh1 #cbe ,volcanoes1 #aeh-aij ,voltaire1 ,fable of1 #ad ,waves caused by ,krakatoa earth quake1 #agi1 #ahb1 #ahc ---------------------------------------- ---------- ,,printed ,,by ,,cassell ,,company1 ,,limited1 ,,la ,,belle ,,sauvage1 ,,london1 ,e4,c4 #bj4eji ---------------------------------------- -------------------------------- ,transcriber's ,notes3 ,the raised dot 771 used to indicate multiplication1 was confused with the decimal point in several numbers4 ,the raised dot has been changed to the decimal point in numbers and the raised dot used only for multiplication4 ,in places where 80 was used for multiplication1 it was left as the author wrote it4 ,missing or obscured punctuation was silently corrected4 ,typographical errors were silently corrected4 ,inconsistent spelling and hyphenation were made consistent only when a predominant form was found in this book4 ,superscripts are used to indicate numbers raised to a power4 ,in this plain text document1 they are represented by characters like this3 8,p#c0 or 8#ajah01 i4e4 ,p cubed or #aj to the #ahth power4 ,variables in formul sometimes use subscripts1 which look like this3 8,a#j04 ,this would be read 8,a sub #j04 ,text that was in italics is enclosed by underscores 7italics74