,transcriber's ,notes3 ,underscores 80 before and after a word or phrase indicate italics in the original text4 ,equal signs 80 before and after a word or phrase indicate bold in the original text4 ,small capitals have been converted to ,,solid capitals4 ,illustrations and footnotes have been moved so they do not break up paragraphs4 ,deprecated spellings have been preserved4 ,typographical and punctuation errors have been silently corrected4 ,,the ,,universe ,,around ,,us ,cambridge ,university ,press ,fetter ,lane1 ,london ,bombay1 ,calcutta1 ,madras ,toronto ,macmillan ,tokyo ,maruzen ,company1 ,ltd ,copyrighted in the ,united ,states of ,america by the ,macmillan ,company ,all rights reserved ,illustration3 ,lowell ,observatory ,the ,discovery of ,pluto ,the two photographs were taken at the ,lowell ,observatory on the nights of ,march #b and #e1 #aicj4 ,the object indicated by arrows was seen to have moved considerably in the interval1 and this proved that it was of planetary character4 ,the bright object in the bottom left-hand corner is the star ,geminorum 7see p4 #bfj74 ,,the ,,universe ,,around ,,us ,by ,,sir ,,james ,,jeans ,m4,a41 ,d4,sc41 ,sc4,d4 ,,ll4,d41 ,f4,r4,s4 ,illustration ,,cambridge ,,at ,,the ,,university ,,press #aicj ,first ,edition1 ,september #aibi ,reprinted ,november #aibi 0 ,january #aicj ,second ,edition1 ,october #aicj ,,printed ,,in ,,great ,,britain ,,preface ,the present book contains a brief account1 written in simple language1 of the methods and results of modern astronomical research1 both observational and theoretical4 ,special attention has been given to problems of cosmogony and evolution1 and to the general structure of the universe4 ,my ideal1 perhaps never wholly attainable1 has been that of making the entire book intelligible to readers with no special scientific knowledge4 ,parts of the book cover the same ground as various lectures ,i have recently delivered to ,university and other audiences1 including a course of wireless talks ,i gave last autumn4 ,it has been found necessary to re-write these almost in their entirety1 so that very few sentences remain in their original form1 but those who have asked me to publish my lectures and wireless talks will find the substance of them in the present book4 ,j4 ,h4 ,,jeans ,,dorking #a ,may #aibi ,,preface ,,to ,,second ,,edition ,in preparing a second edition1 ,i have taken advantage of a great number of suggestions made by correspondents and reviewers1 to whom ,i offer my sincerest thanks4 ,i have also inserted discussions of the new planet ,pluto1 the rotation of the galaxy1 the apparent expansion of the universe1 and other subjects which have become important since the first edition was published1 and in general have tried to bring the book up to date4 ,j4 ,h4 ,,jeans ,,dorking #b ,august #aicj ,,contents ,,page ,introduction--,the ,study of ,astronomy #a ,chapter ,i ,exploring the ,sky #af ,,ii ,exploring the ,atom #ib ,,iii ,exploring in ,time #aej ,,iv ,carving out the ,universe #aid ,v ,stars #bec ,,vi ,beginnings and ,endings #cbe ,index #cee ,,plates ,the ,discovery of ,pluto ,,frontispiece ,,plate ,,facing ,,page ,i ,the ,milky ,way in the neighbourhood of the ,southern ,cross #bc ,,ii ,planetary ,nebulae3 #a4 ,n4,g4,c4 #bjbb #b4 ,n4,g4,c4 #fgbj 7,the ,ring ,nebula7 #c4 ,n4,g4,c4 #aeja #d4 ,n4,g4,c4 #gffb #bh ,,iii ,the ,nebula in ,cygnus #bi ,,iv ,the ,great ,nebula ,m #ca in ,andromeda #cj ,v ,the ,nebula ,n4,g4,c4 #hia in ,andromeda seen edge-on #ca ,,vi ,the 8,horse's ,head0 in the ,great ,nebula in ,orion #cg ,,vii ,the ,trifid ,nebula ,m #bj in ,sagittarius #dd ,,viii ,stellar ,spectra #ea ,,ix ,the ,globular ,cluster ,m #ac in ,hercules #fc ,x ,the ,region of ,ophiuchi #fe ,,xi ,magnification of part of the outer regions of the ,great ,nebula ,m #ca in ,andromeda #gj ,,xii ,magnification of the central region of the ,great ,nebula ,m #ca in ,andromeda #ga ,,xiii ,the tracks of - and -particles #aac ,,xiv ,collisions of -particles with ,atoms #aag ,,xv ,the ,nebula ,n4,g4,c4 #deid in ,virgo ,the ,nebula ,n4,g4,c4 #gbag #bjd ,,xvi ,a sequence of ,nebular ,configurations3 #a4 ,n4,g4,c4 #ccgi #b4 ,n4,g4,c4 #dfba #c4 ,n4,g4,c4 #caae #d4 ,n4,g4,c4 #deid in ,virgo #e4 ,n4,g4,c4 #defe in ,berenice's hair #bjg ,,xvii ,the 8,whirlpool0 ,nebula ,m #ea in ,canes ,venatici #baj ,,xviii ,the ,nebula ,m #ha in ,ursa ,major #baa ,,xix ,the ,nebula ,m #aja in ,ursa ,major #bab ,,xx ,the ,nebula ,m #cc in ,triangulum #bac ,,xxi ,the ,lesser and ,greater ,magellanic ,clouds #bad ,,xxii ,two ,nebulae 7,n4,g4,c4 #dcie1 #ddja7 suggestive of ,tidal ,action #bcf ,,xxiii ,the twin ,nebulae ,n4,g4,c4 #defg-h ,the ,nebula ,n4,g4,c4 #gdgi #bcg ,,xxiv ,saturn and its ,system of ,rings #bej ,,introduction ,the ,study of ,astronomy ,on the evening of ,january #g1 #afaj1 a fateful day for the human race1 ,galileo ,galilei1 ,professor of ,mathematics in the ,university of ,padua1 sat in front of a telescope he had made with his own hands4 ,more than three centuries previously1 ,roger ,bacon1 the inventor of spectacles1 had explained how a telescope could be constructed so as 8to make the stars appear as near as we please40 ,he had shewn how a lens could be so shaped that it would collect all the rays of light falling on it from a distant object1 bend them until they met in a focus and then pass them on through the pupil of the eye on to the retina4 ,such an instrument would increase the power of the human eye1 just as an ear trumpet increases the power of the human ear by collecting all the waves of sound which fall on a large aperture1 bending them1 and passing them through the orifice of the ear on to the ear drum4 ,yet it was not until #afjh that the first telescope had been constructed by ,lippershey1 a ,flemish spectacle-maker4 ,on hearing of this instrument1 ,galileo had set to work to discover the principles of its construction and had soon made himself a telescope far better than the original4 ,his instrument had created no small sensation in ,italy4 ,such extraordinary stories had been told of its powers that he had been commanded to take it to ,venice and exhibit it to the ,doge and ,senate4 ,the citizens of ,venice had then seen the most aged of their ,senators climbing the highest bell-towers to spy through the telescope at ships which were too far out at sea to be seen at all without its help4 ,the telescope admitted about a hundred times as much light as the unaided human eye1 and1 according to ,galileo1 it shewed an object at fifty miles as clearly as if it were only five miles away4 ,perhaps it need hardly be said that this is quite insignificant in comparison with the power of modern instruments4 ,the telescope of #ajj-;inch aperture at ,mount ,wilson1 ,california1 the largest at present in existence1 admits #bejj times as much light as ,galileo's tiny instrument1 and so #bej1jjj times as much light as the unaided eye4 ,it is hoped that a #bjj-;inch telescope will shortly be built in ,california2 this will admit four times as much light as the #ajj-;inch instrument1 or about a million times as much light as the unaided eye4 ,the absorbing interest of his new instrument had almost driven from ,galileo's mind a problem to which he had at one time given much thought4 ,over two thousand years previously1 ,pythagoras and ,philolaus had taught that the earth is not fixed in space but rotates on its axis every twenty-four hours1 thus causing the alternation of day and night4 ,aristarchus of ,samos1 perhaps the greatest of all the ,greek mathematicians1 had further maintained that the earth not only turned on its axis1 but also described a yearly journey round the sun1 this being the cause of the cycle of the seasons4 ,then these doctrines had fallen into disfavour4 ,aristotle had pronounced against them1 asserting that the earth formed a fixed centre to the universe4 ,later ,ptolemy had explained the tracks of the planets across the sky in terms of a complicated system of cycles and epicycles2 the planets moved in circular paths around moving points1 which themselves moved in circles around an immoveable earth4 ,the ,church had given its sanction and active support to these doctrines4 ,indeed1 it is difficult to see what else it could have done1 for it seemed almost impious to suppose that the great drama of man's fall and redemption1 in which the ,son of ,god had ,himself taken part1 could have been enacted on any lesser stage than the very centre of the ,universe4 ,yet1 even in the ,church1 the doctrine had not gained universal acceptance4 ,oresme1 ,bishop of ,lisieux1 and ,cardinal ,nicholas of ,cusa1 had both declared against it1 the latter writing in #addj3 ,i have long considered that this earth is not fixed1 but moves as do the other stars4 ,to my mind the earth turns upon its axis once every day and night4 ,at a later date those who held these views incurred the active hostility of the ,church1 and in #afjj ,giordano ,bruno was burned at the stake4 ,he had written3 ,it has seemed to me unworthy of the divine goodness and power to create a finite world1 when able to produce beside it another and others infinite2 so that ,i have declared that there are endless particular worlds similar to this of the earth2 with ,pythagoras ,i regard it as a star1 and similar to it are the moon1 the planets and other stars1 which are infinite in number1 and all these bodies are worlds4 ,the most weighty attack on orthodox doctrine had1 however1 been delivered neither by theologians nor philosophers1 but by the ,polish astronomer1 ,nicolaus ,copernicus 7#adgc-aedc74 ,in his great work ,de revolutionibus orbium coelestium ,copernicus had shewn that ,ptolemy's elaborate structure of cycles and epicycles was unnecessary1 because the tracks of the planets across the sky could be explained quite simply by supposing that the earth and the planets all moved round a fixed central sun4 ,the sixty-six years which had elapsed since this book was published had seen these theories hotly debated1 but they were still neither proved nor disproved4 ,galileo had already found that his new telescope provided a means of testing astronomical theories4 ,as soon as he had turned it on to the ,milky ,way1 a whole crowd of legends and fables as to its nature and structure had vanished into thin air2 it proved to be nothing more than a swarm of faint stars scattered like golden dust on the black background of the sky4 ,another glance through the telescope had disclosed the true nature of the moon4 ,it had on it mountains which cast shadows1 and so proved1 as ,giordano ,bruno had maintained1 to be a world like our own4 ,what if the telescope should now in some way prove able to decide between the orthodox doctrine that the earth formed the hub of the universe1 and the new doctrine that the earth was only one of a number of bodies1 all circling round the sun like moths round a candle-flame8 ,and now ,galileo catches ,jupiter in the field of his telescope and sees four small bodies circling around the great mass of the planet--like moths round a candle-flame4 ,what he sees is an exact replica of the solar system as imagined by ,copernicus1 and it provides direct visual proof that such systems are at least not alien to the architectural plan of the universe4 ,on ,january #cjth he writes to ,belisario ,vinta that these small bodies move round the far greater mass of ,jupiter 8just as ,venus and ,mercury1 and perhaps the other planets1 move round the sun40 ,any lingering doubts that ,galileo may have felt as to the significance of his discovery are removed nine months later when he observes the phases of ,venus4 ,venus might have been self-luminous1 in which case she would always appear as a full circle of light4 ,if she were not self-luminous but moved in a ,ptolemaic epicycle1 then1 as ,ptolemy had himself pointed out1 she could never shew more than half her surface illuminated4 ,on the other hand1 the ,copernican view of the solar system required that both ,venus and ,mercury should exhibit 8phases0 like those of the moon1 their shining surfaces ranging in appearance from crescent-shape through half moon to full moon1 and then back through half moon to crescent-shape4 ,that such phases were not shewn by ,venus had indeed been urged as an objection to the ,copernican theory4 ,galileo's telescope now shews that1 as ,copernicus had foretold1 ,venus passes through the full cycle of phases1 so that1 in ,galileo's own words1 we 8are now supplied with a determination most conclusive1 and appealing to the evidence of our senses1 of two very important problems1 which up to this day have been discussed by the greatest intellects with different conclusions4 ,one is that the planets are not self-luminous4 ,the other is that we are absolutely compelled to say that ,venus1 and ,mercury also1 revolve around the sun1 as do also all the rest of the planets1 a truth believed indeed by the ,pythagorean school1 by ,copernicus1 and by ,kepler1 but never proved by the evidence of our senses1 as is now proved in the case of ,venus and ,mercury40 ,these discoveries of ,galileo made it clear that ,aristotle1 ,ptolemy and the majority of those who had thought about these things in the last #bjjj years had been utterly and hopelessly wrong4 ,in estimating his position in the universe1 man had up to now been guided mainly by his own desires1 and his self-esteem2 long fed on boundless hopes1 he had spurned the simpler fare offered by patient scientific thought4 ,inexorable facts now dethroned him from his self-arrogated station at the centre of the universe2 henceforth he must reconcile himself to the humble position of the inhabitant of a speck of dust1 and adjust his views on the meaning of human life accordingly4 ,the adjustment was not made at once4 ,human vanity1 reinforced by the authority of the ,church1 contrived to make a rough road for those who dared draw attention to the earth's insignificant position in the universe4 ,galileo was forced to abjure his beliefs4 ,well on into the eighteenth century the ancient ,university of ,paris taught that the motion of the earth round the sun was a convenient but false hypothesis1 while the newer ,american ,universities of ,harvard and ,yale taught the ,ptolemaic and ,copernican systems of astronomy side by side as though they were equally tenable4 ,yet men could not keep their heads buried in the sand for ever1 and when at last its full implications were accepted1 the revolution of thought initiated by ,galileo's observations of ,january #g1 #afaj1 proved to be the most catastrophic in the history of the race4 ,the cataclysm was not confined to the realms of abstract thought2 henceforth human existence itself was to appear in a new light1 and human aims and aspirations would be judged from a different standpoint4 ,this oft-told story has been told once again1 in the hope that it may serve to explain some of the interest taken in astronomy to-day4 ,the more mundane sciences prove their worth by adding to the amenities and pleasures of life1 or by alleviating pain or distress1 but it may well be asked what reward astronomy has to offer4 ,why does the astronomer devote arduous nights1 and still more arduous days1 to studying the structure1 motions and changes of bodies so remote that they can have no conceivable influence on human life8 ,in part at least the answer would seem to be that many have begun to suspect that the astronomy of to-day1 like that of ,galileo1 may have something to say on the enthralling question of the relation of human life to the universe in which it is placed1 and on the beginnings1 meaning and destiny of the human race4 ,bede records how1 some twelve centuries ago1 human life was compared in poetic simile to the flight of a bird through a warm hall in which men sit feasting1 while the winter storms rage without4 ,the bird is safe from the tempest for a brief moment1 but immediately passes from winter to winter again4 ,so man's life appears for a little while1 but of what is to follow1 or of what went before1 we know nothing4 ,if1 therefore1 a new doctrine tells us something certain1 it seems to deserve to be followed4 ,these words1 originally spoken in advocacy of the ,christian religion1 describe what is perhaps the main interest of astronomy to-day4 ,man only knowing ,life's little lantern between dark and dark wishes to probe further into the past and future than his brief span of life permits4 ,he wishes to see the universe as it existed before man was1 as it will be after the last man has passed again into the darkness from which he came4 ,the wish does not originate solely in mere intellectual curiosity1 in the desire to see over the next range of mountains1 the desire to attain a summit commanding a wide view1 even if it be only of a promised land which he may never hope himself to enter2 it has deeper roots and a more personal interest4 ,before he can understand himself1 man must first understand the universe from which all his sense perceptions are drawn4 ,he wishes to explore the universe1 both in space and time1 because he himself forms part of it1 and it forms part of him4 ,we may well admit that science cannot at present hope to say anything final on the questions of human existence and human destiny1 but this is no justification for not becoming acquainted with the best that it has to offer4 ,it is rare indeed for science to give a final 8,yes0 or 8,no0 answer to any question propounded to her4 ,when we are able to put a question in such a definite form that either of these answers could be given in reply1 we are generally already in a position to supply the answer ourselves4 ,science advances rather by providing a succession of approximations to the truth1 each more accurate than the last1 but each capable of endless degrees of higher accuracy4 ,to the question1 8where does man stand in the universe80 the first attempt at an answer1 at any rate in recent times1 was provided by the astronomy of ,ptolemy3 8at the centre40 ,galileo's telescope provided the next1 and incomparably better1 approximation3 8man's home in space is only one of a number of small bodies revolving round a huge central sun40 ,nineteenth-century astronomy swung the pendulum still further in the same direction1 saying3 8there are millions of stars in the sky1 each similar to our sun1 each doubtless surrounded1 like our sun1 by a family of planets on which life may be kept in being by the light and heat received from its sun40 ,twentieth-century astronomy suggests1 as we shall see1 that the nineteenth century had swung the pendulum too far2 life now seems to be more of a rarity than our fathers thought1 or would have thought if they had given free play to their intellects4 ,we are setting out to explain the approximation to the truth provided by twentieth-century astronomy4 ,no doubt it is not the final truth1 but it is a step on towards it1 and unless we are greatly in error it is very much nearer to the truth than was the teaching of nineteenth-century astronomy4 ,it claims to be nearer the truth1 not because the twentieth-century astronomer claims to be better at guessing than his predecessors of the nineteenth-century1 but because he has incomparably more facts at his disposal4 ,guessing has gone out of fashion in science2 it was at best a poor substitute for knowledge1 and modern science1 eschewing guessing severely1 confines itself1 except on very rare occasions1 to ascertained facts and the inferences which1 so far as can be seen1 follow unequivocally from them4 ,it would of course be futile to pretend that the whole interest of astronomy centres round the questions just mentioned4 ,astronomy offers at least three other groups of interest which may be described as utilitarian1 scientific and aesthetic4 ,at first astronomy1 like other sciences1 was studied for mainly utilitarian reasons4 ,it provided measures of time1 and enabled mankind to keep a tally on the flight of the seasons2 it taught him to find his way across the trackless desert1 and later1 across the trackless ocean4 ,in the guise of astrology1 it held out hopes of telling him his future4 ,there was nothing intrinsically absurd in this1 for even to-day the astronomer is largely occupied with foretelling the future movements of the heavenly bodies1 although not of human affairs--a considerable part of the present book will consist of an attempt to foretell the future1 and predict the final end1 of the material universe4 ,where the astrologers went wrong was in supposing that terrestrial empires1 kings and individuals formed such important items in the scheme of the universe that the motions of the heavenly bodies could be intimately bound up with their fates4 ,as soon as man began to realise1 even faintly1 his own insignificance in the universe1 astrology died a natural and inevitable death4 ,the utilitarian aspect of astronomy has by now shrunk to very modest proportions4 ,the national observatories still broadcast the time of day1 and help to guide ships across the ocean1 but the centre of astronomical interest has shifted so completely that the remotest of nebulae arouse incomparably more enthusiasm than 8clock-stars10 and the average astronomer totally neglects our nearest neighbours in space1 the planets1 for stars so distant that their light takes hundreds1 thousands1 or even millions1 of years to reach us4 ,recently1 astronomy has acquired a new scientific interest through establishing its position as an integral part of the general body of science4 ,the various sciences can no longer be treated as distinct2 scientific discovery advances along a continuous front which extends unbroken from electrons of a fraction of a millionth of a millionth of an inch in diameter1 to nebulae whose diameters are measured in hundreds of thousands of millions of millions of miles4 ,a gain of astronomical knowledge may add to our knowledge of physics and chemistry1 and vice versa4 ,the stars have long ago ceased to be treated as mere points of light4 ,each is now regarded as an experiment on a heroic scale1 a high temperature crucible in which nature herself operates with ranges of temperature and pressure far beyond those available in our laboratories1 and permits us to watch the results4 ,in so doing1 we may happen upon properties of matter which have eluded the terrestrial physicist1 owing to the small range of physical conditions at his command4 ,for instance matter exists in nebulae with a density at least a million times lower than anything we can approach on earth1 and in certain stars at a density nearly a million times greater4 ,how can we expect to understand the whole nature of matter from laboratory experiments in which we can command only one part in a million million of the whole range of density known to nature8 ,yet for each one who feels the purely scientific appeal of astronomy1 there are probably a dozen who are attracted by its aesthetic appeal4 ,many even of those who seek after knowledge for its own sake1 driven by that intellectual curiosity which provides the fundamental distinction between themselves and the beasts1 find their main interest in astronomy1 as the most poetical and the most aesthetically gratifying of the sciences4 ,they want to exercise their faculties and imaginations on something remote from everyday trivialities1 to find an occasional respite from 8the long littleness of life10 and they satisfy their desires in contemplating the serene immensities of the outer universe4 ,to many1 astronomy provides something of the vision without which the people perish4 ,before proceeding to describe the results of the modern astronomer's survey of the sky1 let us try to envisage in its proper perspective the platform from which his observations are made4 ,later on1 we shall see how the earth was born out of the sun1 something like two thousand millions of years ago4 ,it was born in a form in which we should find it hard to recognise the solid earth of to-day with its seas and rivers1 its rich vegetation and overflowing life4 ,our home in space came into being as a globe of intensely hot gas on which no life of any kind could either gain or retain a foothold4 ,gradually this globe of gas cools down1 becoming first liquid1 then plastic4 ,finally its outer crust solidifies1 rocks and mountains forming a permanent record of the irregularities of its earlier plastic form4 ,vapours condense into liquids1 and rivers and oceans come into being1 while the 8permanent0 gases form an atmosphere4 ,gradually the earth assumes a condition suited to the advent of life1 which finally appears1 we know not how1 whence or why4 ,it is not easy to estimate the time since life first appeared on earth1 but it can hardly have been more than a small fraction of the whole #bjjj million years of the earth's existence4 ,still1 there was probably life on earth at least #cjj million years ago4 ,the first life appears to have been wholly aquatic1 but gradually fishes changed into reptiles1 reptiles into mammals1 and finally man emerged from mammals4 ,the evidence favours a period of about #cjj1jjj years ago for this last event4 ,thus life has inhabited the earth for only a fraction of its existence1 and man for only a tiny fraction of this fraction4 ,to put it in another way1 the astronomical time-scale is incomparably longer than the human time-scale--the generations of man1 and even the whole of human existence1 are only ticks of the astronomer's clock4 ,most of the #aj1jjj or so of generations of men who connect us up with our ape-like ancestry must have lived lives which did not differ greatly from those of their animal predecessors4 ,hunting1 fishing and warfare filled their lives1 leaving but little time or opportunity for intellectual contemplation4 ,then1 at last1 man began to awake from his long intellectual slumber1 and1 as civilisation slowly dawned1 to feel the need for occupations other than the mere feeding and clothing of his body4 ,he began to discover revelations of infinite beauty in the grace of the human form or the play of light on the myriad-smiling sea1 which he tried to perpetuate in carefully chiselled marble or exquisitely chosen words4 ,he began to experiment with metals and herbs1 and with the effects of fire and water4 ,he began to notice1 and try to understand1 the motions of the heavenly bodies1 for to those who could read the writing in the sky1 the nightly rising and setting of the stars and planets provided evidence that beyond the confines of the earth lay an unknown universe built on a far grander scale4 ,in this way the arts and sciences came to earth1 bringing astronomy with them4 ,we cannot quite say when1 but compared even with the age of the human race1 they came but yesterday1 while in comparison with the whole age of the earth1 their age is but a twinkling of the eye4 ,scientific astronomy1 as distinguished from mere star-gazing1 can hardly claim an age of more than #cjjj years4 ,it is less than this since ,pythagoras1 ,aristarchus and others explained that the earth moved around a fixed sun4 ,yet the really significant figure for our present purpose is not so much the time since men began to make conjectures about the structure of the universe1 as the time since they began to unravel its true structure by the help of ascertained fact4 ,the important length of time is that which has elapsed since that evening in #afaj when ,galileo first turned his telescope on to ,jupiter--a mere three centuries or so4 ,we begin to grasp the true significance of these round-number estimates when we re-write them in tabular form4 ,we have3 ,age of earth about #b1jjj1jjj1jjj years ,age of life on earth 0 #cjj1jjj1jjj 0 ,age of man on earth 0 #cjj1jjj 0 ,age of astronomical science 0 #c1jjj 0 ,age of telescopic astronomy 0 #cjj 0 ,when the various figures are displayed in this form we see what a very recent phenomenon astronomy is4 ,its total age is only a hundredth part of the age of man1 only a hundred-thousandth part of the time that life has inhabited the earth4 ,during #ii1iii parts out of the #ajj1jjj of its existence1 life on earth was hardly concerned about anything beyond the earth4 ,but whereas the past of astronomy is to be measured on the human time-scale1 a hundred generations or so of men1 there is every reason to expect that its future will be measured on the astronomical time-scale4 ,we shall discuss the probable future stretching before the human race in a later chapter4 ,for the moment it is not unreasonable to suppose that this future will probably be terminated by astronomical causes1 so that its length is to be measured on the astronomical time-scale4 ,as the earth has already existed for #bjjj million years1 it is priori reasonable to suppose that it will exist for at least something of the order of #bjjj million years yet to come1 and humanity and astronomy with it4 ,actually we shall find reasons for expecting it to last far longer than this4 ,but if once it is conceded that its future life is to be estimated on the astronomical time-scale1 no matter in what exact way1 we see that astronomy is still at the very opening of its existence4 ,this is why its message can claim no finality--we are not describing the mature convictions of a man1 so much as the first impressions of a new-born babe which is just opening its eyes4 ,even so they are better than the idle introspective dreamings in which it indulged before it had learned to look around itself and away from itself4 ,and so we set out to learn what astronomy has to tell us about the universe in which we live our lives4 ,our inquiry will not be entirely limited to this one science4 ,we shall call upon other sciences1 physics1 chemistry and geology1 as well as the more closely allied sciences of astrophysics and cosmogony1 to give help1 when they can1 in interpreting the message of observational astronomy4 ,the information we shall obtain will be fragmentary4 ,if it must be compared to anything1 let it be to the pieces of a jig-saw puzzle4 ,could we get hold of all the pieces1 they would1 we are confident1 form a single complete consistent picture1 but many of them are still missing4 ,it is too much to hope that the incomplete series of pieces we have already found will disclose the whole picture1 but we may at least collect them together1 arrange them in some sort of methodical order1 fit together pieces which are obviously contiguous1 and perhaps hazard a guess as to what the finished picture will prove to be when all its pieces have been found and finally fitted together4 ,,chapter ,i ,exploring the ,sky ,we have seen how man1 after inhabiting the earth for #cjj1jjj years1 has within the last #cjj years--the last one-thousandth part of his life on earth--become possessed of an optical means of studying the outer universe4 ,in the present chapter we shall try to describe the impressions he has formed with his newly-awakened eyes4 ,the description will be arranged in a very rough chronological order4 ,this is also an order of increasing telescopic power1 or again of seeing further and further into space1 so that our order of arrangement might equally be described as one of increasing distance from the sun4 ,we shall not attempt any sort of continuous record1 but shall merely mention a few landmarks so as to shew in broad outline the order in which territory was won and consolidated in man's survey of the universe4 ,,the ,,solar ,,system ,we may conveniently start with the solar system1 the structure of which was unravelled by ,galileo and his successors4 ,the sun's family of planets falls naturally into distinct groups4 ,near to the sun are the four small planets1 ,mercury1 ,venus1 the ,earth and ,mars4 ,at much greater distances are the four great planets1 ,jupiter1 ,saturn1 ,uranus and ,neptune4 ,beyond all these is the newly discovered planet ,pluto1 the outermost member of our system so far known4 ,mercury is nearest of all to the sun2 next comes ,venus4 ,the orbits of these two planets lie between the earth's orbit and the sun4 ,as seen from the earth1 these planets appear to describe relatively small circles round the sun1 and so must necessarily appear near to the sun in the sky4 ,as a consequence1 they can only be seen either in the early morning1 if they happen to rise just before the sun1 or in the evening if they set after the sun4 ,the ancients not altogether recognising that the same planets could appear both as morning and evening stars1 gave them different names according as they figured as the one or the other4 ,as a morning star ,venus was called ,phosphoros by the ,greeks and ,lucifer by the ,romans2 as an evening star it was called ,hesperus by both4 ,next beyond the earth1 proceeding outward from the sun into space1 comes ,mars1 completing the group of small planets4 ,mars1 ,venus and ,mercury are all smaller than the earth in size1 although ,venus is only slightly so4 ,there is a wide gap between the orbit of ,mars1 the last of the small planets1 and that of ,jupiter1 the first of the great planets4 ,this is not empty2 it is occupied by the orbits of thousands of tiny planets known as asteroids4 ,none of these approaches the earth in size2 ,ceres1 the largest1 is only #dhj miles in diameter1 and only four are known with diameters of more than #ajj miles4 ,the planets ,mercury1 ,venus and ,mars have all been known from remote antiquity1 but the asteroids only entered astronomy with the nineteenth-century1 ,ceres1 the first and largest1 having been discovered by ,piazzi on ,january #a1 #ahja4 ,beyond the asteroids come the four great planets ,jupiter1 ,saturn1 ,uranus and ,neptune1 all of which are far larger than the earth4 ,jupiter1 the largest1 has1 according to ,sampson1 a diameter of #hh1fdj miles1 or more than eleven times the diameter of the earth2 fourteen hundred bodies of the size of the earth could be packed inside ,jupiter1 and leave room to spare4 ,saturn1 which comes next in order1 is second only to ,jupiter in size1 having a diameter of about #gj1jjj miles4 ,these two are by far the largest of the planets4 ,uranus and ,neptune have each about four times the diameter1 and so about sixty-four times the volume1 of the earth4 ,the size of ,pluto is not yet known with accuracy1 but it can hardly be larger than the earth and is probably considerably smaller4 ,jupiter and ,saturn form such conspicuous objects in the sky that they have necessarily been known from the earliest times1 but ,uranus and ,neptune are comparatively recent discoveries4 ,sir ,william ,herschel discovered ,uranus quite accidentally in #agha1 while looking through his telescope with no motive other than the hope of finding something interesting in the sky4 ,by contrast1 ,neptune was discovered in #ahdf as the result of intricate mathematical calculations1 which many at the time regarded as the greatest triumph of the human mind1 at any rate since the time of ,newton4 ,it was a triumph of youth4 ,the honour must be apportioned in approximately equal shares between an ,englishman1 ,john ,couch ,adams1 then only #bg years old1 who was afterwards ,professor of ,astronomy at ,cambridge1 and a young ,french astronomer1 ,urbain ,j4 ,j4 ,leverrier1 who was only eight years his senior4 ,both attributed certain vagaries in the observed motion of ,uranus to the gravitational pull of an exterior planet1 and both set to work to calculate the orbit in which this supposed outer planet must move to explain these vagaries4 ,adams finished his calculations first1 and informed observers at ,cambridge as to the part of the sky in which the new planet ought to lie4 ,as a result1 ,neptune was observed twice1 although without being immediately identified as the wanted planet4 ,before this identification had been established at ,cambridge1 ,leverrier had finished his computations and communicated his results to ,galle1 an assistant at ,berlin1 who was able to identify the planet at once1 ,berlin possessing better star-charts of the region of the sky in question than were accessible at ,cambridge4 ,gradually it emerged that the gravitational pull of ,neptune was inadequate to account for all the vagaries in the motions of ,uranus1 while similar vagaries began to appear in ,neptune's own motion4 ,this pointed to the existence of yet another planet1 further out even than ,neptune4 ,just as ,adams and ,leverrier had done on the former occasion1 so ,dr ,percival ,lowell1 of ,flagstaff ,observatory1 ,arizona1 computed the orbit in which the conjectured new planet1 8,planet ,x10 ought to move1 but it was only recently 7,march #aicj71 after many years of careful search1 that the ,flagstaff observers discovered the planet ,pluto1 moving in almost precisely the orbit which ,lowell had predicted fifteen years previously4 ,as far back as #aggb1 ,bode had pointed out a simple numerical relation connecting the distances of the various planets from the sun4 ,this is obtained as follows3 ,write first the series of numbers #j #a #b #d #h #af #cb #fd #abh #bef in which each number after the first two is double the preceding4 ,multiply each by three1 thus obtaining #j #c #f #ab #bd #dh #if #aib #chd #gfh and add four to each1 giving #d #g #aj #af #bh #eb #ajj #aif #chh #ggb ,these numbers are very approximately proportional to the actual distances of the planets from the sun1 which are 7taking the earth's distance to be #aj73 ,mercury #ci ,venus #gb ,earth #ajj ,mars #aeb ,asteroids #bfe ,jupiter #ebj ,saturn #ied ,uranus #aiai ,neptune #cjjg ,pluto #djj ,the law was enunciated before ,uranus and the asteroids had been discovered1 so that it is somewhat remarkable that these fit so well into their predicted places4 ,on the other hand1 the law fails completely for ,neptune and the newly discovered ,pluto1 so that it seems more than likely that it is a mere coincidence with no underlying rational explanation4 ,the outermost planets are at enormous distances from the sun4 ,an inhabitant of ,pluto1 if such existed1 would receive only a sixteen-hundredth part as much light and heat from the sun as an inhabitant of the earth receives4 ,it can be calculated that if ,pluto's surface were warmed only by the heat of the sun1 it would be at a very low temperature indeed1 somewhere in the neighbourhood of -#bcj ,centigrade1 or more than #djj degrees of frost on the ,fahrenheit scale4 ,a telescope collects heat as well as light4 ,not only is the heat-gathering power of a large telescope tremendous1 but extremely sensitive instruments have been designed to measure this heat4 ,the #ajj-;inch telescope at ,mount ,wilson is said to be capable of detecting the heat received from a single candle on the banks of the ,mississippi1 #bjjj miles away4 ,this great sensitiveness has made it possible to measure the infinitesimal amounts of heat received from single stars and planets1 and so to estimate the temperatures of their surfaces4 ,recent measurements indicate that the surface of ,jupiter is at a temperature of about -#aej ,centigrade1 which is just about that at which it would be maintained by the sun's heat alone4 ,on the other hand similar measurements assign temperatures of -#aej and -#agj respectively to ,saturn and ,uranus1 both of which are rather higher than would be expected if these planets had no source of heat beyond the sun's radiation4 ,but it seems clear that any sources of internal heat must be quite small1 and that all the major planets are very cold indeed4 ,there can be neither seas nor rivers on their surfaces1 since all water must be frozen into ice1 neither can there be rain or water-vapour in their atmospheres4 ,it has been suggested that the clouds which obscure our view of ,jupiter's surface may be condensed particles of carbon-dioxide1 or some other gas which boils at temperatures far below the freezing point of water4 ,the physical conditions of the smaller planets are much more like those with which we are familiar on earth4 ,owing to its greater distance from the sun1 ,mars is somewhat1 but not enormously1 colder than the earth4 ,its day of #bd hours #cg minutes is only slightly longer than our own1 so that its surface must experience alternations of warmth by day and cold by night similar to those we find on earth4 ,in the equatorial regions the temperature rises well above the freezing point at noon1 occasionally reaching #ej ,fahrenheit or even more4 ,but even here it falls below freezing some time before sunset1 and from then until well on in the next day1 the climate must be very cold4 ,the polar regions are of course colder still1 the temperature of the snowcap which covers the poles being somewhere about -#gj ,centigrade or -#id ,fahrenheit--#abf degrees of frost6 ,venus1 being nearer the sun1 must have a higher average temperature than the earth4 ,but as each of its days and nights is several days of our terrestrial time1 the difference between the temperatures of day and night must be far greater than with us1 so that its surface must experience great extremes of heat by day and of cold by night4 ,the night temperature appears to be fairly uniformly equal to about -#be ,centigrade or -#ac ,fahrenheit4 ,at any point on the planet's surface weeks of this bitterly cold night temperature must alternate with weeks of a roasting day temperature4 ,mercury is so near the sun that its average temperature is necessarily far higher than that of the earth4 ,it reflects only a tiny fraction--about a fourteenth--of the light and heat it receives from the sun4 ,all the rest goes to heating up its surface4 ,a number of considerations make it likely that the planet always turns the same face to the sun1 just as the moon always turns the same face to the earth4 ,if so the unwarmed half of its surface must be intensely cold1 and the warmed half intensely hot4 ,it can be calculated that in this case the warmed hemisphere ought to have a temperature of about #ceg ,centigrade2 if however the planet was in fairly rapid rotation1 its whole surface would have a temperature of only about #agj ,centigrade4 ,quite recently ,pettit and ,nicholson have measured the amount of heat received on earth from the warmed hemisphere1 and find that its temperature must be about #cej ,centigrade or #ffb ,fahrenheit1 thus confirming that the planet always turns the same face to the sun4 ,its warm hemisphere is at a temperature which melts lead2 the other hemisphere1 eternally dark and unwarmed1 is probably colder than anything we can imagine4 ,illustration3 ,,plate ,i ,franklin-,adams ,chart ,the ,milky ,way in the neighbourhood of the ,southern ,cross ,galileo's discovery of the four satellites of ,jupiter was followed in time by the discovery that every planet was attended by satellites1 except the two whose orbits lay inside the earth's4 ,in #afee ,huyghens discovered ,titan1 the largest of ,saturn's satellites1 and by #afhd ,cassini had discovered four more4 ,then1 after the lapse of a full century1 ,sir ,william ,herschel discovered two satellites of ,uranus in #aghg and two more satellites of ,saturn in #aghi4 ,we shall discuss the full system of planetary satellites and also the smaller bodies of the solar system--comets1 meteors and shooting-stars--in a later chapter1 when we come to deal with the way they came into being4 ,,the ,,galactic ,,system ,our next landmark is the survey of the stars by the two ,herschels1 ,sir ,william ,herschel1 the father 7#agch-ahbb7 and ,sir ,john ,herschel1 the son 7#agib-ahga74 ,what ,galileo had done for the solar system1 the two ,herschels set out to do for the huge family of stars--the 8galactic0 system1 bounded by the ,milky ,way--of which our sun is a member4 ,on a clear moonless night the ,milky ,way is seen to stretch1 like a great arch of faint light1 from horizon to horizon4 ,it is found to be only part of a full circle of light--the galactic circle--which stretches completely round the earth and divides the sky into two equal halves1 forming a sort of celestial 8equator10 with reference to which astronomers are accustomed to measure latitude and longitude in the sky4 ,galileo's telescope had shewn that it consists of a crowd of faint stars1 each too dim to be seen individually without telescopic aid 7see ,plate ,i74 ,and1 as might be expected1 the proper interpretation of this great belt of faint stars has proved to be fundamental in understanding the architecture of the universe4 ,if stars were scattered uniformly through infinite space1 we should at last come to a star in whatever direction we looked1 so that the sky would appear as a uniform blaze of intolerable light4 ,it is true that this would not be the case if light were dimmed or blotted out after travelling a certain distance1 but even then1 the sky would appear the same in all directions1 for there would be no reason why one part of the sky should be more lavishly spangled with stars than another4 ,thus the existence of the ,milky ,way shews that the system of the stars does not extend uniformly to infinity4 ,it must have a definite structure1 and it was the architecture of this that ,sir ,william ,herschel set himself to unravel4 ,the work he did for the northern half of the sky was subsequently extended to the southern hemisphere by his son1 ,sir ,john ,herschel4 ,we shall best understand the method employed by the ,herschels if we first imagine all the stars in the sky to be intrinsically similar objects4 ,each would then emit the same amount of light1 so that the nearer stars would appear bright1 and the further stars faint1 merely as an effect of distance4 ,the way in which apparent brightness decreases with distance is of course well known2 the law is that of the 8inverse square of the distance10 which means that the apparent brightness decreases just as rapidly as the square of its distance increases2 a star which is twice as distant as a second similar star appears only a quarter as bright1 and so on4 ,thus if all stars emitted the same amount of light1 we could estimate the relative distances of any two stars in the sky from their relative brightnesses4 ,by cutting wires of lengths proportional to the distances of various stars1 and pointing these in the directions of the stars to which they referred1 we could form a model of the arrangement of the stars in the sky4 ,we should1 in fact1 know the whole structure of the system of stars except for its scale4 ,to represent the faint stars of the ,milky ,way1 a great number of very long wires would be needed4 ,in the model these would all point towards different parts of the ,milky ,way1 forming a flat wheel-like structure4 ,the problem which confronted ,sir ,william ,herschel was more intricate because he knew that the stars were of different intrinsic brightness as well as at different distances1 and both factors combined to produce differences of apparent brightness4 ,one of the main difficulties of astronomy1 both to the ,herschels and to the astronomer of to-day1 is that these two factors have to be disentangled before any definite conclusions are reached4 ,herschel found that the number of stars visible in his telescope-field varied enormously with different directions in space4 ,it was of course greatest when the telescope was pointed at the ,milky ,way1 and fell off1 steadily and rapidly1 as the telescope was moved away from the ,milky ,way4 ,generally speaking1 two telescope-fields which were at equal distances from the ,milky ,way contained about the same number of stars4 ,in the technical language of astronomy1 the richness of the star-field depended mainly on the galactic latitude1 just as the earth's climate depends mainly on the geographic latitude1 and not to any great extent on the longitude4 ,fields at different distances from the ,milky ,way were found to differ in quality as well as in number of stars4 ,the brightest stars of all occurred about equally in all fields1 the difference in the fields resulting mainly from faint stars1 and particularly the faintest stars of all1 becoming enormously more abundant as the ,milky ,way was approached4 ,sir ,william ,herschel rightly interpreted this as shewing that the system of stars surrounding the sun began to thin out within distances reached by his telescope1 and that they began to thin out soonest in directions furthest away from the ,milky ,way4 ,he supposed the general shape of the galactic system of stars to be that of a bun or a biscuit or a watch1 the stars being most thickly scattered near the centre1 and occurring more sparsely in the outer regions4 ,the plane of the ,milky ,way of course formed the central plane of the structure4 ,the fact that the ,milky ,way divides the sky into two almost exactly equal halves suggested to him that the sun must be very nearly in this central plane1 and this is confirmed by the recent very refined investigations of ,seares and van ,rhijn1 and others4 ,from the fact that parts of the sky which were equidistant from the ,milky ,way appeared about equally bright1 ,herschel inferred that the sun not only lay in the central plane of the system1 but was very near to its actual centre4 ,this view has prevailed until quite recently1 but the researches of ,shapley and others now shew it to be untenable 7see p4 #fe below74 ,fig4 #a shews a cross-section of the general kind of structure which ,sir ,william ,herschel assigned to the galactic system1 although the detailed distribution of stars shewn in the diagram is that given at a much later date 7#aibb7 by ,kapteyn4 ,it is easy to see how a structure of this type would account for the general appearance of the sky4 ,those stars which appear brightest of all are1 generally speaking1 the nearest2 they are so near that no appreciable thinning out of stars occurs within this distance4 ,for this reason the very bright stars occur in about equal numbers in all directions4 ,the stars which appear very faint are mostly very distant1 so distant that the great depth of the system in directions in or near to the galactic plane is brought into play4 ,in such directions1 layer after layer of stars1 ranged almost endlessly one behind the other1 give rise to the apparent concentration of faint stars which we call the ,milky ,way4 ,illustration3 ,fig4 #a4 ,the ,structure of the ,galactic ,system according to ,herschel and ,kapteyn4 ,the final acceptance of the ,copernican view of the structure of the solar system was in a large measure due to ,galileo's discovery of the similar system of ,jupiter1 which was so situated in space that a terrestrial observer could obtain a bird's-eye view of it as a whole4 ,we can never obtain a bird's-eye view of the solar system as a whole because we can only see it from inside1 so that optical proof that such systems could exist1 could come only from the discovery of other similar systems1 which we could see from outside4 ,sir ,william ,herschel believed he had confirmed his own view of the structure of the galactic system in the same way1 by discovering similar systems1 of which he could obtain a bird's-eye view because they were entirely extraneous to the galaxy4 ,he spoke of these objects as 8island universes0 and believed them to be clouds of stars4 ,they were of hazy nebular appearance1 and although it was impossible to distinguish the separate stars in them1 he believed that sufficient telescopic power would make this possible1 just as it had enabled ,galileo to see the separate stars in the ,milky ,way4 ,these objects1 which we shall describe almost immediately1 are generally known as 8extra-galactic nebulae8 from their position1 although we shall frequently find it convenient to use the briefer term 8great nebulae10 to which their immense size fully entitles them4 ,,nebulae ,a telescope exhibits a planet as a disc of appreciable size1 and an eye-piece which magnifies #fj times will make ,jupiter look as large as the moon4 ,yet an eye-piece which magnifies #fj times1 or any greater number of times1 can never make a star look as large as the moon4 ,no magnification within our command causes any star to appear as anything other than a mere point of light4 ,the stars are of course enormously larger than ,jupiter1 but they are also enormously more distant1 and it is the distance that wins4 ,illustration3 ,,plate ,,ii ,n4,g4,c4 #bjbb ,n4,g4,c4 #fgbj ,n4,g4,c4 #aeja ,n4,g4,c4 #gffb ,mt ,wilson ,observatory ,planetary ,nebulae ,illustration3 ,,plate ,,iii ,mt ,wilson ,observatory ,the ,nebula in ,cygnus ,the telescope nevertheless shews a number of objects which appear bigger than mere points of light4 ,they are generally of a faint1 hazy appearance1 and so have received the general name of 8nebulae40 ,detailed investigation has shewn that these fall into three distinct classes4 ,,planetary ,,nebulae4 ,the first class are generally described as 8,planetary ,nebulae40 ,there is nothing of a planetary nature about them beyond the fact that1 like the planets1 they shew as finite discs in a telescope4 ,a few hundreds only of these objects are known1 four typical examples being illustrated in ,plate ,,ii4 ,they all lie within the galactic system4 ,we shall discuss their physical structure below 7p4 #cba74 ,for the moment1 it is enough to say that they are probably of the nature of stars which have in some way become surrounded by luminous atmospheres of enormous extent4 ,if so they of course disprove our general statement that no star ever appears as anything but a point of light in a telescope2 we must make an exception in favour of the planetary nebulae4 ,,galactic ,,nebulae4 ,the second class are generally described as 8,galactic ,nebulae10 examples being shewn in ,plates ,,iii1 ,,vi 7p4 #cg7 and ,,vii 7p4 #dd74 ,these are completely irregular in shape4 ,their general appearance is that of huge glowing wisps of gas stretching from star to star1 and in effect this is pretty much what they are4 ,like the planetary nebulae1 they lie entirely within the galactic system4 ,even a cursory glance shews that each irregular nebula contains several stars enmeshed with it2 minute telescopic examination often extends the dimensions of the nebula almost indefinitely1 so that we may have almost the whole of a constellation wrapped up in a single nebula4 ,there is but little doubt as to the physical nature of these nebulae4 ,the space between the stars is not utterly void of matter1 but is occupied by a thin cloud of gas of a tenuity which is generally almost beyond description4 ,here and there this cloud may be denser than usual2 here and there again it may be lighted up and made to incandesce by the radiation of the stars within it4 ,in other places it may be entirely opaque to light1 lying like a black curtain across the sky4 ,the variations of density1 opacity and luminosity in combination produce all the fantastic shapes and varied degrees of light and shade we see in the galactic nebulae4 ,this same opacity is responsible for the dark patches which occur in the general arrangement of the stars4 ,a conspicuous example occurs in the part of the ,milky ,way shewn in ,plate ,i 7p4 #bc74 ,the dark patch1 which looks at first like a hole in the system of stars1 is graphically described as 8,the ,coal ,sack40 ,these black patches in the sky cannot represent actual holes1 because it is inconceivable that there should be so many empty tunnels through the stars all pointing exactly earthward1 so that we are compelled to interpret them as veils of obscuring matter which dim or extinguish the light of the stars behind them4 ,,extra-,,galactic ,,nebulae4 ,the third class of nebula is of an altogether different nature4 ,its members are for the most part of definite and regular shape1 and shew various other characteristics which make them easy of identification4 ,they used to be called 8white nebulae0 from the quality of the light they emitted4 ,later ,lord ,rosse's giant #f-;foot telescope revealed that many of them had a spiral structure2 these were called 8spiral nebulae40 ,the most conspicuous of all the spiral nebulae is the ,great ,nebula ,m #ca in ,andromeda1 shewn in ,plate ,,iv1 which is just1 and only just1 visible to the naked eye4 ,marius1 observing it telescopically in #afab1 described it as looking 8like a candle-light seen through horn40 ,plate ,v shews a second example1 probably of very similar structure1 which is viewed from another angle1 so as to appear almost exactly edge-on4 ,illustration3 ,,plate ,,iv ,yerkes ,observatory ,the ,great ,nebula ,m #ca in ,andromeda ,illustration3 ,,plate ,v ,mt ,wilson ,observatory ,the ,nebula ,n4,g4,c4 #hia in ,andromeda seen edge-on ,it is now abundantly proved that nebulae of this type all lie outside the galactic system1 so that the term 8extra-galactic nebulae0 adequately describes them4 ,their size is colossal4 ,either of the photographs shewn in ,plates ,,iv and ,v would have to be enlarged to the size of the whole of ,europe before a body of the size of the earth became visible in it1 even under a powerful microscope4 ,their general shape is similar to that which ,sir ,william ,herschel assigned to the galactic system1 and it was this that originally led him to regard them as 8island universes0 similar to the galactic system4 ,we shall see later how far his conjecture has been confirmed by recent research4 ,,the ,,distances ,,of ,,the ,,stars ,the year #ahch provides our next landmark2 it is the year in which the distance of a star was first measured4 ,in the second century after ,christ1 ,ptolemy had argued that if the earth moved in space1 its position relative to the surrounding stars must continually change4 ,as the earth swung round the sun1 its inhabitants would be in the position of a child in a swing4 ,and1 just as the swinging child sees the nearer trees1 persons and houses oscillating rhythmically against a remote background of distant hills and clouds1 so the inhabitants of the earth ought to see the nearer stars continually changing their position against their background of more distant stars4 ,yet night after night the constellations remained the same1 or so ,ptolemy argued2 the same stars circled eternally in the same relative positions around the pole1 and conspicuous groups of stars such as the seven stars of the ,great ,bear1 the ,pleiades or the constellation of ,orion shewed no signs of change4 ,for aught the unaided human eye could tell1 the stars might be spots of luminous paint on a canvas background1 with the earth as the unmoving pivot around which the whole structure swung4 ,in opposition to this1 the ,copernican theory of course required that the nearer stars should be seen to move against the background of the more distant stars1 as the earth performed its yearly journey round the sun4 ,yet year after year1 and even century after century1 passed without any such motion being detected4 ,the old ,ptolemaic contention that the earth formed the fixed centre of the universe might almost have regained its former position1 had it not been that various lines of evidence had begun to shew that even the nearest stars were necessarily very distant1 so distant1 indeed1 that their apparent want of motion need cause no surprise4 ,the child in a swing cannot expect to have optical evidence of its motion if the nearest object it can see is twenty miles away4 ,very few stars appear brighter than ,saturn at its brightest2 it looks about as bright as ,altair1 the eleventh brightest star in the sky4 ,yet ,saturn shines only by the light it reflects from the sun1 and its distance from the sun is such that it receives only about one part in #bejj million of the total light emitted by the sun4 ,and1 as the surface of ,saturn only reflects back about two-fifths of the light it receives1 it follows that ,saturn shines with only a #fjjj millionth part of the light of the sun4 ,if1 as ,kepler and others had maintained1 ,altair was essentially similar to the sun1 it would probably be of about the same candle-power as the sun1 and so would give out about #fjjj million times as much light as ,saturn4 ,the fact that ,altair and ,saturn appear about equally bright in the sky can only mean that ,altair is #hj1jjj times as distant as ,saturn#a4 ,this argument is essentially identical with one which ,newton gave in his ,system of the ,world to shew that even the brightest stars1 such as ,altair1 must be very distant indeed4 #a ,for the apparent brightness of an object falls off as the inverse square of its distance1 and the square of #hj1jjj is approximately equal to #fjjj million4 ,and such has proved to be the case4 ,all efforts to discover the apparent swinging motion of the stars--8parallactic motion10 as it is technically called--which results from the earth's orbital motion failed until #ahch1 when three astronomers1 ,bessel1 ,henderson1 and ,struve1 almost simultaneously detected the parallactic motions of the three stars1 #fa ,cygni1 ,centauri and ,lyrae respectively4 ,the amount of their parallactic motion made it possible to calculate the distances of the stars1 so that the inhabitants of the earth were not only placed in possession of definite ocular proof that they were swinging round the sun1 but from the visible effects of this swing they were able to compute the distances of the nearer stars4 ,the calculated values were not accurate when judged by modern standards1 but they provided the first definite estimates of the scale on which the universe is built4 ,let us pause for a minute to consider how this scale is built up4 ,the first step is to select a convenient base-line a few miles in length on the surface of the earth1 and to measure this in terms of standard yards or metres4 ,starting out from this base-line1 a geodetic survey maps out a long narrow strip of the earth's surface1 preferably running due north and south4 ,the difference of latitude at the two ends is then measured by astronomical methods1 as for instance by noticing the difference in the altitude of the pole-star at the two places4 ,as the length of the strip is already known in miles1 this immediately gives the dimensions of the earth4 ,according to ,hayford 7#aiji71 the earth's equatorial radius is #fcghchh kilometres1 or #cifccd miles1 its polar radius being #fcefiji kilometres or #cidiii miles4 ,the next step is to determine the size of the solar system in terms of that of the earth4 ,when the sun is eclipsed by the moon1 the time at which the moon first begins to cover the sun's disc is different for different stations on the earth's surface1 and the observed differences of time enable us to measure the moon's distance in terms of known distances on the surface of the earth4 ,in this way the mean distance of the moon is found to be #chd1djc kilometres or #bch1heg miles4 ,in the same way the transit of the planet ,venus across the disc of the sun provides an opportunity for determining the scale of the solar system in terms of the dimensions of the earth4 ,the asteroid ,eros provides still better opportunities4 ,the ,paris ,conference 7#aiaa7 adopted #adi1dej1jjj kilometres1 or #ib1hgj1jjj miles1 as the most likely value for the mean distance of the earth from the sun4 ,the next and final step1 which the year #ahch saw accomplished1 is that of using the diameter of the earth's orbit as base-line1 and determining the distances of the stars4 ,the first step1 from the standard yard or metre to the measured base-line on the earth's surface1 involves an increase of several thousand-fold in length4 ,the increase involved in the next step1 from the base-line to the earth's diameter1 is again one of thousands4 ,and again the next step1 from the diameter of the earth to that of the earth's orbit1 involves an increase of thousands4 ,but the last step of all1 from the earth's orbit to stellar distances1 involves a million-fold increase4 ,recent measurements shew that the nearest stars are at almost exactly a million times the distances of the nearest planets4 ,at its nearest approach to the earth1 ,venus is #bf million miles distant1 while the nearest star1 ,proxima ,centauri1 is #be1jjj1jjj million miles away2 this latter star is a faint companion of the well-known bright star ,centauri in the southern hemisphere4 ,the distances of the planets when at their nearest1 and of the nearest stars1 are shewn in the following table3 ---------------------------------------- -------------------------- ,,planets ,,stars ---------------------------------------- ----------------------- ,distance ,name ,distance ,name ,distance 7light- 7miles7 7miles7 years7 ---------------------------------------- ----------------------- ,venus #bf1jjj1jjj ,proxima ,centauri #be1jjj1jjj million #dbg ,centauri #dca ,mars #ce1jjj1jjj ,munich #aejdj #cf1jjj1jjj 0 #fjf ,wolf #cei #dg1jjj1jjj 0 #hjg ,mercury#dg1jjj1jjj ,lalande #baahe #di1jjj1jjj 0 #hcc ,sirius #ea1jjj1jjj 0 #hfe ---------------------------------------- ----------------------- ,as it is almost impossible to visualise a million1 the mere statement that the stars are a million times as remote as the planets gives only a feeble indication of the immensity of the gap that divides the solar system from its nearest neighbours in space4 ,perhaps the apparent fixity of the stars gives a more vivid impression4 ,the earth performs its yearly journey round the sun at a speed of about #ah miles a second1 which is about #abjj times the speed of an express train4 ,the sun moves through the stars at nearly the same rate--to be precise1 at about #hjj times the speed of an express train4 ,and1 broadly speaking1 the nearer planets and the majority of the stars move with similar speeds4 ,we shall not obtain a bad approximation to the truth if we imagine that all astronomical bodies move with exactly equal speeds1 let us say1 to fix our thoughts1 a speed equal to #ajjj times the speed of an express train4 ,the distances of astronomical objects are now betrayed by the speed with which they appear to move across the sky--the slower their apparent motion the greater their distances1 and vice versa4 ,now the planets move across the sky so rapidly that it is quite easy to detect their motion from night to night and even from hour to hour2 the stars move so slowly that1 except with telescopic aid1 no motion can be detected from generation to generation1 or even from age to age4 ,even the conspicuous constellations in the sky1 which on the whole are formed of the nearer stars1 have retained their present appearance throughout the whole of historic times4 ,the contrast between the planets which change their positions every hour1 and the stars which fail to shew any appreciable change in a century1 gives a vivid impression of the extent to which the stars are more distant than the planets4 ,it is far more difficult to visualise the actual distances of the stars4 ,the statement that even the nearest of them is #be1jjj1jjj million miles away hardly conveys a definite picture to the mind1 but we may fare better with the alternative statement that the distance is #dbg light-years--that is to say the distance that light1 travelling at #ahf1jjj miles a second1 takes in #dbg years to traverse4 ,illustration3 ,,plate ,,vi ,mt ,wilson ,observatory ,the 8,horse's ,head0 in the ,great ,nebula in ,orion ,light travels with the same speed as wireless signals because both are waves of electric disturbance4 ,incidentally this speed is just about a million times that of sound4 ,the enormous disparity in the speeds of sound and of electric waves is vividly brought out in the ordinary process of broadcasting4 ,when a speaker broadcasts from ,london his voice takes longer to travel #c feet from his mouth to the microphone as a sound wave1 than it does to travel a further #efj miles to ,berlin or ,milan as an electric wave4 ,wireless listeners in ,australia hear the music of a broadcast concert sooner than an ordinary listener at the back of the concert hall who relies on sound alone2 they hear it a fifteenth of a second after it is played4 ,yet light1 or wireless waves travelling with the same speed as light1 takes #dbg years to reach the nearest star1 so that the inhabitants of ,proxima ,centauri would be over four and a quarter years late in hearing a terrestrial concert4 ,and in time we shall have to consider other and even more distant stars which terrestrial music would not yet have reached had it started on its journey before the ,norman ,conquest1 before the ,pyramids were built1 even before man appeared on earth4 ,,the ,,photographic ,,epoch ,if we were only allowed to select one more landmark in the progress of astronomy1 we might well choose the application of photography to astronomy in the closing years of the nineteenth-century2 this opened the floodgates of progress more thoroughly than anything else had done since the invention of the telescope4 ,hitherto the telescope1 after collecting and bending rays of light from the sky1 had projected the concentrated beam of light through the pupil of the human eye on to the retina2 in future it was to project it on to the incomparably more sensitive photographic plate4 ,the eye can retain an impression only for a fraction of a second2 the photographic plate adds up all the impressions it receives for hours or even days1 and records them practically for ever4 ,the eye can only measure distances between astronomical objects by the help of an intricate machinery of cross-wires1 screws and verniers2 the photographic plate records distances automatically4 ,the eye1 betrayed by preconceived ideas1 impatience or hope1 can and does make every conceivable type of error2 the camera cannot lie4 ,and so it comes about that if we try to pick out landmarks in twentieth-century astronomy we find that1 in a sense1 it consists of nothing but landmarks2 the slow1 arduous methods of conquest of the nineteenth century have given place to a sort of gold-rush in which claims are staked out1 the surface scratched1 the more conspicuous nuggets collected1 and the excavation abandoned for something more promising1 all with such rapidity that any attempt to describe the position is out of date almost before it can be printed4 ,we can only attempt a general impression of the new territory1 and with this will be inextricably mixed a discussion of old territory seen in the light of new knowledge4 ,,groups ,,of ,,stars ,,and ,,binary ,,systems ,a glance at the sky1 or1 better1 at a photograph of a fragment of the sky1 suggests that1 in the main1 the stars are scattered at random over the sky1 except for the concentration of faint stars in and towards the ,milky ,way1 which we have already considered4 ,any small bit of the sky does not look very different from what it would if bright and faint stars had been sprinkled haphazard out of a celestial pepperpot4 ,yet this is not quite the whole story4 ,here and there groups of conspicuous stars are to be seen1 which can hardly have come together purely by accident4 ,orion's belt1 the ,pleiades1 ,berenice's hair1 even the ,great ,bear itself1 do not look like accidents1 and in point of fact are not4 ,it is the existence of these natural groups of stars that lies at the root of1 and justifies1 the division of the stars into constellations4 ,we shall explain later how the physical properties of the stars are studied2 for the present it is enough to remark that physical study confirms the suspicion that groups such as those just mentioned are1 generally speaking1 true families1 and not mere accidental concourses1 of stars4 ,the stars of any one group1 such as the ,pleiades1 not only shew the same physical properties1 but also have identical motions through space1 thus journeying perpetually through the sky in one another's society4 ,as such a group of stars are both physically similar1 and travel in company1 they might appropriately be described as a family of stars4 ,the astronomer1 however1 prefers to call them a 8moving cluster40 ,these families are of almost all sizes1 the smallest and commonest type consisting of only two members4 ,after this the next commonest type consists of three members2 our nearest three neighbours in space1 ,proxima ,centauri and the two stars of ,centauri1 form such a triple system4 ,then come systems of four1 five and six members1 and so on indefinitely4 ,let us first turn our attention to families consisting of only two members--8binary systems10 as they are generally called4 ,even if the stars had been sprinkled on to the sky at random out of a pepperpot1 the laws of chance would require that in a certain number of cases1 pairs of stars should appear very close together4 ,and a study of a photograph of any star-field shews that a large number of such close pairs actually exist4 ,the number is1 however1 greater than can be explained by the laws of chance alone4 ,some pairs of stars may be close together by accident1 but a physical cause is needed to account for the remainder4 ,we can unravel the mystery by photographing the field at intervals of a few years and comparing the various results obtained4 ,some of the stars which originally appeared as close pairs will be found to move steadily apart4 ,these are the pairs of stars which1 although they appeared close together in the sky1 were not so in space2 one star merely happened to be almost exactly in line with the other as seen from the earth4 ,other pairs do not break up with the passage of time2 the two components change their relative positions but never become completely separated4 ,in the simplest case of all one star may be found to describe an approximately circular orbit about the other1 just as the earth does round the sun1 and the moon round the earth1 and for precisely the same reason3 gravitation keeps them together4 ,,the ,,law ,,of ,,gravitation4 ,drop a cricket ball from your hand and it falls to the ground4 ,we say that the cause of its fall is the gravitational pull of the earth4 ,in the same way1 a cricket ball thrown into the air does not move on for ever in the direction in which it is thrown2 if it did it would leave the earth for good1 and voyage off into space4 ,it is saved from this fate by the earth's gravitational pull which drags it gradually down1 so that it falls back to earth4 ,the faster we throw it1 the further it travels before this occurs2 a similar ball projected from a gun would travel for many miles before being pulled back to earth4 ,illustration3 ,fig4 #b4 ,the law governing all these phenomena is quite simple4 ,it is that the earth's gravitational pull causes all bodies to fall #af feet earthward in a second4 ,this is true of all bodies which are free to fall1 no matter how they are moving2 every body which is not in some way held up against gravitation is #af feet lower at the end of any second than it would have been if gravitation had not acted through that second4 ,to illustrate what this means1 let the big circular curve ,b,a,c in fig4 #b represent the earth's surface1 and imagine that a shot is fired horizontally from ,a1 the top of an elevation ,,aa4 ,if the shot were not pulled earthwards by gravitation1 it would travel indefinitely along the line ,,ab out into space4 ,if ,,ab is the distance it would travel in a second under these imaginary conditions1 the end of a second's actual flight does not find it at ,b1 but at a point #af feet nearer the earth1 gravitation having pulled it down this #af feet during its flight4 ,for instance1 if ,,bb in fig4 #b should happen to be #af feet1 the shot would strike the earth at ,b after a flight of precisely one second4 ,as another example1 let us suppose that the #af-;foot fall below ,b does not drag the shot down to earth but only to a point b1 which is at precisely the same height above the earth's surface as the point ,a at which the shot started4 ,if gravitation were not acting1 so that the shot travelled along the line ,,ab1 its height above the earth would continually increase4 ,actually in the case we are now considering1 gravitation pulls the shot down at just such a rate as to neutralise the increase of height which would otherwise occur1 so that the height of the shot neither increases nor decreases2 it neither flies off into space nor drops to earth1 but continues to describe circles round the earth indefinitely4 ,a simple geometrical calculation shews that for the distance ,bb to be #af feet1 the distance ,,ab travelled in one second must be #be1hhj feet or #dij miles#b4 ,thus if we could fire a shot horizontally with a speed of #dij miles a second1 it would describe endless circles round the earth1 the earth's gravitational pull exactly neutralising the natural tendency of the shot to fly away along the straight line ,,ab4 #b ,let ,c be the centre of the earth1 and b,c,d the diameter through b4 ,then ,,ba ,bb ,,bd1 where ,bb #af feet1 and ,,bd1 which is #af feet more than the earth's diameter #da1ijj1jjj feet4 ,from this we readily calculate that ,,ba #be1hhj feet4 ,this calculation of course neglects the height of the hill ,,aa by comparison with the earth's diameter4 ,in #affe ,newton began to suspect that this same gravitational pull might be the cause of the moon describing a circular orbit around the earth instead of running away at a tangent into space4 ,the moon's distance from the earth's centre is #bch1heg miles1 or #fjbg times the radius of the earth4 ,as the moon describes a circle of this size every month 7#bg days1 #d hours1 #dc minutes1 #aae seconds71 we can calculate that its speed in its orbit is #bbhg miles an hour4 ,after one second it will have travelled #ccej feet1 and if it kept to a strictly rectilinear course this would carry it #jjjdd feet further away from the earth4 ,thus1 to keep in an exact circular orbit around the earth1 it must fall #jjjdd feet in a second4 ,this is far less than a body falls in a second at the earth's surface1 but ,newton conjectured that the force of gravity must weaken as we recede from the earth's surface4 ,actually a body at the earth's surface falls #cfcb times as fast as the moon's earthward fall in its orbit4 ,now #cfcb is the square of #fjbg 7or #cfcb #fjbg #fjbg71 whence ,newton saw that the moon's fall would be of exactly the right amount if the force of gravity fell off as the inverse square of the distance--that is to say1 if it decreased just as rapidly as the square of the distance increased4 ,as we shall see later1 astronomical observation confirms the truth of this law in innumerable ways4 ,this led ,newton to put forward his famous law of gravitation according to which the gravitational pull of any body1 such as the earth1 falls off inversely as the square of the distance from the body4 ,illustration3 ,fig4 #c4 ,professor ,c4 ,v4 ,boys and others have measured the gravitational pull which a few tons of lead exert in the laboratory1 and1 with this knowledge1 it is easy to calculate how many tons the earth must contain so as to exert its observed gravitational pull on bodies outside it4 ,it is found that the earth's weight must be just under six thousand million million million tons#c1 or1 as we shall write it1 #f #aj tons#d4 #c ,here1 as throughout the book1 we use the ,french or metric ton of a million grammes or #bbjde lbs4 ,the ,english ton of #bbdj lbs4 is equal to #ajafj ,french tons4 #d ,the notation #f #aj stands for the number formed by a #f followed by #ba zeros1 this shorthand notation being essential1 in the interests of brevity1 in discussing astronomical numbers4 ,a million is #aj1 a million million is #aj and so on4 ,a similar notation is needed to express very small numbers4 ,the expression #aj is written for #a_/aj and so on4 ,thus #f #aj stands for #f_/a1jjj1jjj or #jjjjjjf4 ,illustration3 ,,plate ,,vii ,mt ,wilson ,observatory ,the ,trifid ,nebula ,m #bj in ,sagittarius ,just as the earth's gravitational pull keeps the moon perpetually describing circles around it1 so the sun's gravitational pull keeps the earth and all the other planets describing circles around the sun4 ,knowing the distance of any planet from the sun1 and also its speed in its orbit1 we can calculate the distance this planet falls towards the sun in a second4 ,this tells us the amount of the sun's gravitational pull1 and from this we can calculate that the sun's weight must be about #ccb1jjj times the weight of the earth1 or almost exactly #b #aj tons4 ,whichever of the planets we use1 we obtain exactly the same weight for the sun4 ,this not only gives us confidence in our result1 but incidentally it also provides striking confirmation of the truth of ,newton's law of gravitation1 for if this law were inexact or untrue1 the different planets would not all tell exactly the same story as to the sun's weight4 ,einstein has recently shewn that the law is not absolutely exact1 but the amount of inexactness is inappreciable except for the nearest planet1 ,mercury1 and even here it is so exceedingly small that we need not trouble about it for our present purpose4 ,just as we can weigh the sun and earth by studying the motion of a body gripped by their gravitational pull--or 8in their gravitational fields10 as the mathematician would say--so we can weigh any other body which keeps a second small body moving round it by its gravitational attraction4 ,the motions of ,jupiter's satellites make it possible to weigh ,jupiter2 its weight is found to be about #aib #aj tons1 which is #cag times that of the earth1 although only _/ of that of the sun4 ,similarly the weight of ,saturn is found to be #ega #aj tons or about #idi times that of the earth4 ,,weighing ,,the ,,stars4 ,and now we come to a striking application of the principles just explained--when we observe two stars in the sky describing orbits about one another1 we can weigh the stars from a study of their orbits4 ,generally the problem is not quite so simple as those we have just discussed4 ,for its adequate treatment1 we must once again levy toll on the mathematical work of ,newton4 ,we have seen that a projectile fired horizontally with a speed of #dij miles a second1 would describe endless circles round the earth4 ,what would happen if it were fired in some other direction and with some other speed8 ,the answer was provided by ,newton4 ,he shewed that when a small body is allowed to move freely under the gravitational pull of a big body1 it will run away altogether if its speed exceeds a certain critical amount1 in which case its orbit is the curve called a hyperbola4 ,but if its speed is less than this critical amount1 its orbit will always be an ellipse--a sort of pulled out circle or oval curve#e 7fig4 #d1 p4 #dg74 ,previous to this ,kepler had found that the actual paths of the planets round the sun were not exact circles but ellipses1 although for the most part ellipses which did not differ greatly from circles2 they are what the mathematician calls 8ellipses of small eccentricity40 ,this provides still further confirmation of ,newton's law of gravitation1 for it can be proved that if the force of gravitation falls off in any way other than according to ,newton's law of the inverse square of the distance1 the orbits of the planets will not be elliptical4 #e ,the simplest definition of an ellipse is that it is the curve drawn by a moving point ,p which moves in such a way that the sum of its distances ,,ps1 ,,pt from two fixed points ,s1 ,t remains always the same4 ,in practice we can most easily draw an ellipse by slipping an endless string ,,spts round two drawing pins ,s1 ,t stuck into a drawing board4 ,stretch the string tight with a pencil at ,p1 and on letting the pencil move round1 keeping the string always tight1 we shall draw an ellipse4 ,if the pins ,s1 ,t in the drawing board are placed near to one another the curve described by the pencil ,p is nearly circular4 ,the ratio of the distance ,,st to the length of the remainder of the string ,,sp ,,pt is called the 8eccentricity0 of the ellipse2 it is necessarily less than unity1 because two sides of a triangle are together greater than the third side4 ,in the limiting case in which the eccentricity is made zero1 the ellipse becomes a circle4 ,if the eccentricity is nearly as large as unity1 the ellipse is very elongated4 ,all the different shapes of ellipses are obtained by letting the eccentricity change from #j to #a1 and these represent all the different shapes of orbit that a small body can describe around a heavy gravitating mass4 ,the points ,s1 ,t are called the foci of the ellipse1 and the big attracting body always occupies one or other of the two foci of the ellipse4 ,illustration3 ,fig4 #d4 ,the oval curve is an ellipse2 the points ,s1 ,t are its 8foci40 ,when the astronomer studies the motions of a binary star in the sky1 he generally finds that the two components do not move in circles about one another but in ellipses#f4 ,once again1 ,newton's law is confirmed1 and we are entitled to assume that the forces which keep binary stars together are the same gravitational forces as keep the moon from running away from the earth1 or the planets from the sun4 ,by a study of these ellipses it becomes possible to weigh the stars4 ,if one of the component masses were enormously heavier than the other1 the former would stand still while the lighter component described an ellipse around it1 the motion being essentially similar to that of a planet around the sun4 ,such cases are not observed in actual binary stars because the two components are generally comparable in weight1 and this brings new complications into the question4 ,there is no need to enter into mathematical details here4 ,suffice it to say that neither star stands still2 the two components describe ellipses of different sizes1 and from a study of these two ellipses the weights of both the components can be determined4 #f ,what he actually observes is the 8projection0 of the orbit on the sky1 but it is a well-known theorem of geometry that the projection of an ellipse is always an ellipse4 ,the following table shews the result of weighing the four binary systems nearest the sun in this way1 the sun's weight being taken as unity3 ,stellar ,weights ,binary systems near the sun4 ---------------------------------------- ----------------------- ,distance in ,weights of components ,star light-years in terms of sun's ,luminosity from the sun weight 7see p4 #di7 ---------------------------------------- ----------------------- ,centauri ,a #dca #aad #aab 0 ,b #jig #jcb ---------------------------------------- ----------------------- ,sirius ,a #hfe #bde #bfc 0 ,b #jhe #jjjbf ---------------------------------------- ----------------------- ,procyon ,a #aje #abd #ee 0 ,b #jci #jjjjjc ---------------------------------------- ----------------------- ,kruger #fj ,a #abg #jbe #jjjbf 0 ,b #jbj #jjjjg ---------------------------------------- ----------------------- ,we see that the weights of these stars do not differ greatly from that of the sun1 although naturally the whole of space provides a greater range than the four stars of our table which happen to be near the sun4 ,but even in the whole of space1 no star whose weight is known with any accuracy has a weight less than ,kruger #fj ,b1 although at the other end of the scale there are many stars with far greater weights than any in our table4 ,of stars whose weights are known with fair accuracy1 the star ,h4,d4 #accg 7,pearce's star7 is the weightiest1 its two components being respectively #cfc and #cch times as heavy as the sun4 ,plaskett's star ,b4,d4 #f #acji is certainly heavier still1 its components weighing at least #ge and #fc times as much as the sun1 and probably more2 the exact weights are not known 7see p4 #ee below74 ,the system #bg ,canis ,majoris consists of four stars1 whose combined weight1 according to the evidence at present available1 appears to be at least #idj times that of the sun1 but we may properly exercise a certain amount of caution before accepting a figure so far outside the usual run of stellar weights4 ,the average constituent star in the above very short table has #jid times the weight of the sun1 so that our sun appears to be of rather more than average weight1 and this is confirmed by a more extensive study of stellar weights4 ,we might have expected a priori that the stars would prove to have all sorts of weights1 for there is no obvious reason why stars should not exist with weights millions of times that of the sun1 or again with weights only equal to that of the earth or less4 ,actually we find that the weights of the stars are mostly fairly equal1 very few stars having weights greatly dissimilar from that of the sun4 ,this seems to indicate that a star is a definite species of astronomical product1 not a mere random chunk of luminous matter4 ,,luminosity4 ,the last column of the table on p4 #dh gives the 8luminosities0 of the stars1 which means their candle-power as lights1 that of the sun being taken as unity4 ,for instance the entry of #bfc for ,sirius means that ,sirius1 regarded as a lighthouse in space1 has #bfc times the candle-power of the sun4 ,the luminosities of the stars shew an enormously greater range than their weights4 ,in a general way the heaviest stars are found to be the most luminous1 as we should naturally expect1 but their luminosity is out of all proportion to their weight4 ,the heavier component of ,sirius has only #bi times the weight of the lighter component1 but #aj1jjj times its luminosity4 ,again1 in the system of ,procyon the heavier component has #cb times the weight1 but #ahj1jjj times the luminosity1 of the lighter component4 ,it appears to be an almost universal law that the candle-power per ton is far greater in heavy stars than in light4 ,this is one of the central and1 at first sight1 one of the most perplexing facts of physical astronomy3 it is so fundamental and so pervading that no view of stellar mechanism can be accepted which fails to explain it4 ,,spectroscopic ,,velocities4 ,when a star's distance is known1 its motion across the sky tells us its speed in a direction at right angles to the line along which we look at it--i4e4 across the line of sight--but provides no means of discovering its speed along this line4 ,we cannot see the motion of a body which is coming straight towards us1 and a star moving at a million miles a second in a direction exactly along the line of sight would yet appear to be standing still in the sky4 ,to evaluate velocities along the line of sight1 the astronomer calls in the aid of the spectroscope4 ,all light is a blend of lights of different colours1 and just as ,newton1 with his famous prism1 analysed sunlight into all the colours of the rainbow1 so the spectroscope analyses the light from a star1 or indeed from any source whatever1 into its various constituent colours4 ,the instrument spreads out the analysed light into a strip of light of continuously graduated colour1 which is described as a 8spectrum40 ,in this the colours are the same1 and are found to be arranged in the same order1 as in the rainbow1 running from violet through green and orange to red4 ,there is a physical reason for this4 ,we shall see later 7p4 #aad7 that light consists of trains of waves--like the ripples which the wind blows up on a pond--and that the different colours of light result from waves of different lengths1 red light being produced by the longest waves1 and violet light by the shortest4 ,the colours in the spectrum occur in the order of their wave-lengths1 from the longest 7red7 to the shortest 7violet74 ,in the typical stellar spectrum certain short ranges of colour or wave-length are generally missing1 for reasons we shall discuss later 7p4 #abf71 so that the spectrum appears to be crossed by a number of dark lines or bands1 thus forming a pattern rather than a continuous gradation of colours4 ,examples of stellar spectra are shewn in ,plate ,,viii4 ,illustration3 ,,plate ,,viii ,b #j ,orionis ,a #j ,sirius ,f #j ,geminorum ,g #j ,capella ,k #j ,arcturus ,m #j ,betelgeux ,stellar ,spectra 7,the spectral types are indicated on the left7 ,it is frequently convenient to classify stars by the type of spectra they emit4 ,it is now known that a star's spectrum depends primarily upon the temperature of its surface4 ,as a consequence1 stellar spectra can1 in the main1 be arranged in a single continuous sequence1 and their usual classification is by a sequence of letters1 ,o1 ,b1 ,a1 ,f1 ,g1 ,k1 ,m with decimal subdivisions1 the temperature falling as we pass along the sequence1 so that ,o-type stars have the highest surface-temperatures and ,m-type stars the lowest4 ,spectral types are indicated on the left in ,plate ,,viii4 ,when the light received from a star is analysed in a spectroscope1 the pattern of lines or bands may be found to be shifted bodily in one direction or the other4 ,if the shift is towards the red end of the spectrum1 the light emitted by the star is reaching us in a redder state than that in which it ought normally to be1 and as red light has the longest wave-length1 this means that every wave of light is longer--more drawn out--than normal4 ,we conclude that the star is receding from us4 ,in the same way1 if the spectral pattern is shifted toward the violet end of the spectrum1 we know that the star must be approaching us4 ,the shift of a spectrum resulting from the motion of the body which emits it is generally described as the 8,doppler ,effect40 ,from its amount we can calculate a star's actual speed along the line of sight1 and the calculation is surprisingly simple4 ,if each line or band in a spectrum is found to represent a wave-length a hundredth of one per cent4 longer than that usually associated with it1 then the star's speed of recession is a hundredth of one per cent4 of the velocity of light1 or #ahf miles a second--and similarly for all other displacements4 ,,spectroscopic ,,binaries4 ,as the two components of a binary system are generally moving with different speeds1 the normal spectrum of a binary system consists of two distinct superposed spectra1 the two spectra shewing different shifts which correspond to the speeds of the two components4 ,from the observed orbits of the two components of a binary system1 an astronomer might proceed to calculate with what speeds these components would move in the direction of the line of sight1 and could then predict to what extent the two spectra ought to be displaced if the light from the system were analysed in a spectroscope2 the spectroscope would of course confirm his prediction4 ,it is more instructive to imagine the reverse process4 ,suppose that on analysing the light from a star1 the astronomer obtains a composite spectrum in which two distinct spectra shift rhythmically backwards and forwards about their normal position4 ,the fact that there are two spectra tells him that he is dealing with a binary system2 if the rhythmic shift repeats itself every two years1 he knows that its orbit takes two years to complete4 ,he studies the star by direct vision and finds it is a binary system in which the constituents revolve about one another every two years4 ,he examines another spectrum1 and finds that it shifts rhythmically every two days4 ,on looking directly at this star he can only see a single point of light4 ,there must1 of course1 be two stars1 but the mere fact that they get around one another in so short a time as two days proves that they must be very close to one another1 and he need feel no surprise that his telescope has failed to separate the image into two distinct points of light4 ,systems of this kind1 which the spectroscope shews to be binary1 but the telescope usually shews as a single point of light1 are called 8spectroscopic binaries40 ,over a thousand such systems are known4 ,if the astronomer tries to construct the orbit of such a system from the spectroscopic observations alone1 he finds himself in difficulties4 ,his observations only tell him the velocities along the line of sight1 and these depend both on the actual speed and on the degree of foreshortening2 the same velocity may arise either from a big orbit in a plane nearly at right angles to the line of sight1 or from a much foreshortened little orbit4 ,it is impossible to calculate the actual orbit or the weights of the stars from spectroscopic observation alone4 ,illustration3 ,fig4 #e4 ,the little orbit ,,aa and the big orbit ,,bb give the same velocities along the line of sight ,,ce4 ,,eclipsing ,,binaries4 ,there is one exception4 ,suppose that a star's light is seen to diminish in amount at regular intervals and subsequently to return to its original strength4 ,the obvious interpretation of the diminution of light is that one component of the system is eclipsing the other1 and this can only happen if the orbit is so completely foreshortened that its plane passes through1 or at least very close to1 the earth4 ,in such a case it is possible to reconstruct the whole orbit1 and thence to calculate the weights of the two components4 ,not only so1 but the length of time during which the eclipses last tells us the actual sizes of the two components1 so that it is possible to draw a complete picture of the system4 ,diagrams of the dimensions and orbits of two typical eclipsing binaries are shewn in fig4 #f2 these are drawn to the same scale1 this being indicated by the small circle representing the sun4 ,illustration3 ,fig4 #f4 ,components and orbits of ,eclipsing ,binaries4 ,when no eclipse occurs in a spectroscopic binary1 we do not know how much foreshortening to allow for1 but we can obtain a general idea of the weights of the components by assuming an average degree of foreshortening4 ,if we assume different degrees of foreshortening in turn1 we shall find that the computed weights come out least when the plane of the orbit is assumed to pass through the earth--i4e4 when the orbits are computed as though the system were an eclipsing one4 ,thus although we cannot discover the actual weights of the components of a non-eclipsing binary1 we can always state limits above which they must lie1 namely the weights computed as though the system were an eclipsing one4 ,in this way1 we know that the two components of ,plaskett's star must have more than #ge and #fc times the weight of the sun4 ,,variable ,,stars ,the majority of stars shine with a perfectly steady light1 so that we can say that a star is of so many candle-power4 ,the sun1 for instance1 emits a light of #cbc #aj candle-power4 ,yet there are classes of exceptional stars in which the light flickers up and down4 ,in some1 as in the eclipsing binaries just described1 the light-fluctuations are quite regular1 repeating themselves with such precision that the stars might well be used as time-keepers4 ,in others the fluctuations1 though not perfectly regular1 are nearly so1 while still others exist in which the fluctuations appear at present to be completely irregular1 although no doubt the changes in these will be reduced to law and order in due course4 ,for our present discussion1 the various types of irregular variables are not of great importance4 ,,cepheid ,,variables4 ,the really interesting stars are those of a certain class of regular variable1 generally called 8,cepheid variables10 after their prototype ,cephei4 ,the physical nature of these stars and the mechanism of their light-fluctuation is still far from being understood2 competing theories are in the field which we need not discuss at this stage 7see p4 #bbc below74 ,whatever their mechanism may be1 observation shews that these stars possess a certain definite property1 which proves to be of the utmost value4 ,this being so1 we may accept it gratefully without troubling as to its why and wherefore4 ,the perfectly regular light-fluctuations of the eclipsing binaries would make them suitable for time-keepers even though we did not understand the mechanism behind these fluctuations4 ,in the same way the fluctuations of ,cepheid variables have a quality which makes them valuable as measuring-rods with which to survey the distant parts of the universe4 ,in brief1 this property is that we can deduce the intrinsic brightness of these stars1 and so their distances1 from their observed light-fluctuations4 ,the light-fluctuations are so distinctive as to make the stars easy of detection4 ,there is a rapid increase of light1 followed by a slow gradual decline2 then again the same rapid increase and slow decline as before4 ,it is as though someone were throwing armfuls of fuel on to a bonfire at perfectly regular intervals4 ,one other class of variable stars1 generally known as 8long-period variables10 shews somewhat similar light-fluctuations1 but the two classes are easily distinguished by their very different periods of light-fluctuation4 ,the ,cepheid variable completes its cycle in a time which may be a few hours1 or may be days or weeks1 but is never more than about a month1 whereas the long-period variable generally requires about a year4 ,fig4 #g shews the light curves of typical variable stars of the different classes4 ,in each diagram the progress of time is represented by motion across the page from left to right2 the higher the fluctuating curve is above the horizontal line at any instant1 the brighter the star at that instant4 ,out near the boundary of the galactic system is a cluster of stars known as the ,lesser ,magellanic ,cloud 7,plate ,,xxi1 p4 #bad71 in which ,cepheid variables occur in great profusion4 ,in #aiab1 ,miss ,leavitt of ,harvard found that the light of the brighter ,cepheids in this cloud fluctuated more slowly than the light of the fainter ones4 ,whatever was responsible for turning the stellar lights up and down1 acted more rapidly for feeble than for brilliant lights4 ,the apparent brightnesses of a number of ,cepheids at varying distances would of course depend only in part on their intrinsic brightness or candle-power1 but the stars in the ,magellanic ,cloud are all1 nearly enough1 at the same distance from the earth4 ,thus differences in the apparent brightnesses of stars in this cloud must represent real differences of intrinsic brightness1 and ,miss ,leavitt's discovery could be stated in the form that the period of light-fluctuation of a ,cepheid depended on its candle-power4 ,although this was only proved for the ,cepheids in the ,magellanic ,cloud1 it must be true for all ,cepheids wherever they are1 for it is inconceivable that we could make a star's light fluctuate more slowly or more rapidly merely by altering its distance from us--by ourselves receding from it1 in fact4 ,illustration3 ,light ,curve of ,eclipsing ,binary 7 ,aurigae7 ,illustration3 ,light ,curve of ,irregular ,variable 7,,rs ,ophiuchi7 ,illustration3 ,light ,curve of ,cepheid ,variable7 ,lacerbae7 ,illustration3 ,light ,curve of ,long-,period ,variable 7 ,ceti7 ,fig4 #g4 ,light ,curves of typical ,variable ,stars of different classes4 ,professor ,hertzsprung of ,leiden and ,dr ,shapley1 then of ,mount ,wilson ,observatory1 were quick to seize upon the implications of this discovery4 ,if two ,cepheids ,a1 ,b in different parts of the sky are found to fluctuate with equal rapidities1 then their intrinsic candle-powers must be equal4 ,thus any difference in their apparent brightness must be traceable to a difference in their distances from us4 ,if ,a looks a hundred times as bright as ,b1 then ,b must be at ten times the distance of ,a4 ,in the same way1 a third ,cepheid ,c may prove to be at ten times the distance of ,b4 ,we now know that ,c is a hundred times as remote as ,a4 ,and if ,d can be found ten times as distant as ,c1 we know that ,d is a thousand times as remote as ,a4 ,so we can go on constructing and ever extending our measuring-rod2 there is no limit until we reach distances so great that even ,cepheid variables1 which are exceptionally bright stars1 fade into invisibility4 ,so far we have only considered the comparative distances of ,cepheids4 ,the absolute distances of many of the nearer ,cepheids have1 however1 been determined by the parallactic method already explained--i4e4 by measuring their apparent motion in the sky1 resulting from the earth's motion round the sun4 ,taking any one of these stars as our original ,cepheid ,a1 we can step continually from one ,cepheid to another1 and so calculate the absolute distances of all the ,cepheid variables in the sky4 ,in this way the observed relation between the period of fluctuation and the brightness of ,cepheid variables--commonly known as the 8period-luminosity law0--can be made to provide a scale on which the absolute luminosity1 or candle-power1 of a ,cepheid can be read off directly from the observed period of its light-fluctuations4 ,the ,cepheid variables may be regarded as lighthouses set up in distant parts of the universe4 ,we can recognise them1 just as a sailor recognises lighthouses1 by the quality of their light4 ,we can read off their candle-power from the period of their observed light-fluctuations as easily as the sailor could read off the candle-power of a lighthouse from an ,admiralty chart4 ,the apparent brightness of the ,cepheid informs us as to its distance from us#g4 #g ,for instance1 ,cepheids whose light fluctuates in a period of #dj hours have approximately a luminosity #bej times that of the sun1 and so are of #h #aj candle-power2 a period of ten days indicates a luminosity #afjj times that of the sun1 or a candle-power of #eag #aj1 and so on4 ,if a star in a distant astronomical object is observed to fluctuate with a period of ten days1 and the quality of its fluctuations shew it to be a ,cepheid variable1 we know that its actual candle-power must be #eag #aj4 ,its apparent brightness is observed to be that of a star of1 say1 magnitude #af1 which1 stripped of technicalities1 means that we receive as much light from it as from a single candle at a distance of #egj miles4 ,the difference between one candle and #eag #aj candles accordingly corresponds to the difference between #egj miles and the distance of the object in question1 whence1 since light falls off as the inverse square of the distance1 we calculate that the distance of the object must be #eag #aj #egj miles or about #bbj1jjj light-years4 ,it would be difficult to over-estimate the importance of all this to modern astronomical science4 ,it means that a method has been found for surveying1 if not the whole of the universe1 at least those parts of it in which ,cepheid variables are visible4 ,actually this last reservation is unimportant1 for ,cepheid variables are very freely scattered in space4 ,naturally the method is of most value for the exploration of the most distant parts of the universe2 here it achieves triumphant success where other methods fail completely4 ,the parallactic method begins to fail when we try to sound distances of more than about a hundred light-years4 ,the apparent path in the sky1 which a star at this distance describes1 in consequence of the earth's motion round the sun1 is of the size of a pin-head two miles away4 ,with all their refinements1 modern instruments find it difficult enough to detect so small a motion as this1 and it is practically impossible to measure it with accuracy4 ,the 8period-luminosity0 law measures the distances of objects up to a million light-years away1 with a smaller percentage of error than is to be expected in the parallactic measures of stars only a hundred light-years away4 ,,sounding ,,space ,this by no means exhausts the list of modern methods of surveying space4 ,any standard type of astronomical object1 which is easily recognisable and emits the same amount of light no matter where it occurs1 provides an obvious means of measuring astronomical distances1 for when once the intrinsic luminosity of such an object has been determined1 the distance of every example of it can be estimated from its apparent brightness4 ,cepheid variables of assigned periods provide the most striking instance of such standard objects1 but three others are available1 although they are not so generally useful as ,cepheids4 ,first comes another type of variable star1 the 8long-period variables0 already mentioned1 which are generally similar to ,cepheids except that their light fluctuates much more slowly4 ,these stars are intrinsically far more luminous even than ,cepheids1 many of them being #aj1jjj times as luminous as the sun4 ,they are accordingly visible at enormous distances1 and may ultimately be found to provide a means of sounding depths of space at which even ,cepheids are lost to sight4 ,next come 8novae0 or new stars4 ,every now and then an ordinary star in the sky suddenly bursts out in a phenomenal blaze of light1 shining with perhaps a thousand times its original brilliance4 ,the cause of these violent outbursts is still a matter for debate1 and no thoroughly convincing explanation has as yet been given4 ,a study of comparatively near novae has1 however1 provided information as to the luminosity of the average nova when at its brightest1 and as novae appear in various parts of the sky1 and particularly in the extra-galactic nebulae1 they provide a rough means of measuring stellar and nebular distances4 ,blue stars provide yet another method4 ,these are exceedingly luminous1 and they vary but little in intrinsic luminosity4 ,moreover1 the luminosity of any particular star can generally be estimated fairly closely from the quality of the light it emits1 by methods which will be explained later4 ,this makes it possible to determine the distances of blue stars1 and so of course of the astronomical objects in which they occur4 ,still two other methods of a different kind may be briefly mentioned4 ,dr ,w4 ,s4 ,adams1 ,director of ,mount ,wilson ,observatory1 and others have found that certain definite peculiarities in the spectra of certain classes of stars convey information as to the intrinsic brightness of the star emitting them2 with this information it is easy to estimate the star's distance from its apparent brightness4 ,this is commonly described as the method of ,spectroscopic ,parallaxes4 ,finally the diffuse cloud of nebular matter which is spread through interstellar space 7p4 #cj7 is found to affect the quality of light travelling through it1 so that a star's spectrum gives an indication of the amount of cloud through which the light of the star has travelled1 and this again provides a rough means of estimating distances inside the galactic system4 ,illustration3 ,,plate ,,ix ,dominion ,astrophysical ,observatory1 ,b4 ,c4 ,the ,globular ,cluster ,m #ac in ,hercules ,,globular ,,clusters4 ,the law of ,cepheid luminosity was first used by ,hertzsprung to estimate the distance of the ,lesser ,magellanic ,cloud1 the study of which had been responsible for the original discovery of the law4 ,shapley subsequently used it to determine the distances of the rather mysterious groups of stars known as 8,globular ,clusters40 ,a typical example of these is shewn in ,plate ,,ix4 ,about #ajj of these clusters are known and they all look pretty much alike1 except for differences in apparent size4 ,even these latter can be traced mainly to differences of distance1 so that the globular clusters are probably almost identical objects1 and ,plate ,,ix might almost be regarded as a picture of any one of them4 ,cepheid variables abound in them all4 ,shapley found the nearest globular cluster1 ,centauri1 to lie at a distance of about #bb1jjj light-years1 the furthest1 ,n4,g4,c4 #gjjf1 being about ten times as remote1 at a distance of #bbj1jjj light-years4 ,at such distances the parallactic method of measuring distances would of course fail hopelessly4 ,the parallactic orbit of a star at #bbj1jjj light-years' distance is about the size of a pin-head held at a distance of #djjj miles2 no telescope on earth could detect1 still less measure1 such an orbit4 ,the mere figure of #bbj1jjj light-years can convey but little conception of the distance of this remotest of star-clusters from us4 ,we may apprehend it better if we reflect that the light by which we see the cluster started on its long journey from it to us somewhere about the time when primaeval man first appeared on earth4 ,through the childhood1 youth and age of countless generations of men1 through the long prehistoric ages1 through the slow dawn of civilisation and through the whole span of time which history records1 through the rise and fall of dynasties and empires1 this light has travelled steadily on its course1 covering #ahf1jjj miles every second1 and is only just reaching us now4 ,and yet this enormous stretch of space does not carry us to the confines of the universe2 we shall now see that in all probability it has barely carried us to the confines of the galactic system4 ,illustration3 ,fig4 #h4 ,the arrangement of the ,globular ,clusters4 ,shapley has mapped out the complete system of the globular clusters1 and finds that they occupy an oblong region1 lying on both sides of the plane of the ,milky ,way1 its greatest diameter of about #bej1jjj light-years lying in this plane1 and its two transverse diameters being considerably shorter4 ,the sun is nearer to the edge of this oblong region than to its centre1 which explains why all the globular clusters appear in one half of the sky1 as ,hinks first noted in #aiaa4 ,the general arrangement is shewn in fig4 #h4 ,the page of the book represents the plane of the ,milky ,way1 the various dots representing the points in this plane which are nearest to the different clusters1 so that the diagram exhibits the system of globular clusters as they would appear to an observer out in space who viewed the galactic plane 8full-on40 ,all the globular clusters except ,n4,g4,c4 #gjjf lie within a circle of about #abe1jjj light-years' radius1 having its centre at about #ej1jjj light-years from the sun4 ,illustration3 ,,plate ,x ,e4 ,e4 ,barnard ,the ,region of ,ophiuchi ,,the ,,arrangement ,,of ,,the ,,galactic ,,system4 ,although the matter has long been one of vigorous controversy1 it is now becoming clear that the region of space mapped out by these globular clusters approximately coincides with that occupied by the galactic system itself4 ,herschel and ,kapteyn appear to have been in error in supposing the centre of the galactic system to be in the neighbourhood of the sun2 a considerable accumulation of evidence indicates that it lies in a massive star-cloud in the constellations of ,ophiuchus and ,scorpio4 ,dr ,shapley and ,miss ,swope1 at ,harvard ,observatory1 have recently determined the distance of this star-cloud from the sun as #dg1jjj light-years1 which places it almost exactly at the centre of the system of globular clusters1 as shewn in fig4 #h4 ,there is what ,shapley describes as a 8local system0 of fairly bright stars surrounding the sun1 and the error of identifying this with the main galactic system has apparently been responsible for a large part of the confusion which has hitherto beset the problem of the architecture of the galaxy4 ,this local system has the same flattened shape as the main system1 but it does not lie exactly in the plane of the ,milky ,way1 being inclined at an angle of about #ab degrees to it4 ,the sun appears to lie very near to the plane of the central plane of the system2 recent determinations place it about #ajj light-years to the north of this plane4 ,fig4 #i shews a cross-section of the system1 as it is now imagined to lie4 ,illustration3 ,fig4 #i4 ,diagrammatic scheme of cross-section of the ,galactic ,system4 ,the sun is at the head of the arrow4 ,we have already compared the shape of the galactic system to that of a wheel4 ,it obviously could not retain this shape if the stars which formed it were standing still in space4 ,for the gravitational pull of the inner stars would cause the outermost stars--the rim of the wheel--to fall inwards1 and the system would end as a confused jumble of stars somewhere in the vicinity of the hub of the wheel4 ,in #aiac1 ,henri ,poincar1 ,professor of ,mathematics at the ,sorbonne1 suggested that the galactic 8wheel0 might escape this fate if it were in a state of rotation4 ,just as the earth's motion saves it from falling into the sun1 and the moon's motion saves it from falling on to the earth1 so1 ,poincar suggested1 the stars which form the rim of the wheel might be saved from falling into the hub1 by a motion of rotation of the whole wheel4 ,a rough calculation suggested that it would be necessary for the wheel to rotate at the rate of a complete revolution about every #ejj million years4 ,naturally it is no simple matter to detect so slow a rotation4 ,it was first suspected to occur in the following way4 ,we know that when a spinning-top or gyroscope is set in rapid rotation1 a considerable force is needed to twist the top or gyroscope about in space4 ,this is the principle of the gyroscopic compass such as is used to steer ships4 ,a gyroscope1 a sort of big steel spinning-top1 is started spinning with its two ends pivoted in a swinging frame4 ,no matter how the ship turns1 the motion of the gyroscope keeps the frame pointing away in the same direction1 and by the help of this fixed direction the ship is kept on its course4 ,now the solar system has many of the properties of a huge spinning-top1 the revolutions of the planets corresponding to the spin of the top4 ,as there is no twist impressed on this 8spinning-top0 from outside1 its axis of rotation must always point in the same direction1 thus providing a sort of 8gyroscopic compass0 to give us our bearings in space4 ,in #aiac ,charlier believed he had found that this 8gyroscopic compass0 was turning round against the distant background of the ,milky ,way1 at the rate of a complete rotation every #cgj million years1 a period which subsequent measurements increased to #ecj million years4 ,eddington then suggested that it might be the background rather than the gyroscopic compass that was turning1 the ,milky ,way actually rotating in the way imagined by ,poincar1 and at just about the rate which ,poincar had calculated4 ,recent investigations by ,oort1 ,plaskett1 ,lindblad and others prove beyond doubt that such a rotation really occurs1 although it is not of the simple 8cart-wheel type0 we have so far discussed4 ,in the solar system the innermost planets move more rapidly than the outermost3 they must necessarily do so if the motion of each planet is to counteract the sun's attraction4 ,in the same way1 if the rotational motion of the galaxy is to counteract the gravitational attraction of its innermost stars1 its inner parts must rotate more rapidly than its outermost4 ,thus the sun ought to be overtaking those stars which lie outside it on the galactic wheel1 while being itself overtaken by those which lie inside it4 ,such an overtaking motion is fairly easy to detect4 ,a careful analysis of observed stellar motions has disclosed such a motion1 shewing that the galaxy as a whole is in rotation in precisely the way just described1 the inner parts rotating most rapidly4 ,the hub of this gigantic wheel lies almost exactly in the direction which ,shapley assigned to the centre of the galaxy from his study of the globular clusters4 ,its distance from the sun1 which cannot yet be determined with any great accuracy1 is probably somewhere about #cg1jjj light-years4 ,to within the limits of accuracy which are at present attainable1 this places the centre of the galactic wheel at the centre of the system of globular clusters 7see fig4 #h1 p4 #fd74 ,in the vicinity of the sun1 the galactic wheel performs a complete revolution in a period of about #bcj million years1 and this endows the stars near the sun with a motion through space at a speed of nearly #bjj miles a second1 arising from the rotation of the galaxy alone4 ,with these data1 it is possible to weigh the stars of the galactic system en masse4 ,individual stars far away from the centre of the galactic system must be describing orbits under the gravitational pull of the system as a whole1 the pull which prevents the stars from scattering away into space1 and so keeps the galactic system in being4 ,the aggregate of these orbital motions produces the general rotation of the galaxy which we have just discussed4 ,and from the figures just mentioned1 it can be calculated that the total weight of matter inside the sun's orbit must be about that of #bdj1jjj million suns4 ,part of this may of course arise from interstellar dust or gas4 ,nevertheless1 as the average star weighs considerably less than the sun1 the total number of stars in the galactic system may well be of the order of #djj1jjj million4 ,this estimate of course includes all stars1 dark as well as luminous1 but there are reasons for believing that the number of dark stars is comparatively small 7see p4 #bfi below74 ,other estimates of the number of stars in the galaxy have been made1 generally lower than the foregoing4 ,two estimates by ,lindblad1 for instance1 give the total weight of the galaxy as #aaj1jjj and #ahj1jjj million suns respectively4 ,again we are confronted with the difficulty of visualising such large numbers4 ,with perfect eyesight on a clear moonless night we can see about #cjjj stars4 ,imagine each of these #cjjj stars to spread out into a complete sky-full of #cjjj new stars1 and we are contemplating #i million stars1 which is still only the number visible in a telescope of #e inches aperture4 ,we probably cannot ask our imagination to play the same trick for us a second time1 but if it can be persuaded to do so1 and if we can think of each of these #i million stars as again generating a whole sky-full of stars1 we still have only #bg1jjj million stars within our purview--a number which is still far below any permissible estimate of the total number of stars in the galactic system4 ,or again1 let us notice that the number of stars photographically visible in the #ajj-;inch telescope1 namely #aejj million1 is about equal to the number of men1 women and children in the world4 ,each inhabitant of the earth--each man1 woman and child living in the five continents or travelling on the seven seas--can be allowed to choose his own particular star1 and can then repeat the process tens1 and more probably hundreds1 of times without going outside the galactic system4 ,after this we can still go exploring outside the galactic system and find more and ever more stars4 ,the galactic system1 with its hundreds of millions of stars1 no more contains all the stars in space than one house contains all the inhabitants of ,great ,britain4 ,there are millions of other houses and millions of other families of stars4 ,,the ,,extra-,,galactic ,,nebulae4 ,we have already spoken of the faint nebulous objects which ,herschel described1 somewhat conjecturally1 as 8island universes40 ,these are the other houses in which other families of stars are to be found4 ,the most powerful of modern telescopes shew that they consist1 in part at least1 of huge clouds of stars4 ,just as a powerful microscope shews that a puff of cigarette smoke1 in spite of its appearance of continuity1 consists of a cloud of minute but quite distinct particles1 so a powerful modern telescope breaks up the light from the outer regions of these nebulae into distinct spots of light2 the nebula is resolved into a cloud of shining particles1 just as the ,milky ,way was in ,galileo's tiny telescope of three centuries ago4 ,plate ,,xi shews an example2 it represents a magnification of a small area in the top left-hand corner of the ,great ,nebula ,m #ca in ,andromeda already shewn in ,plate ,,iv 7p4 #cj71 and the resolution into distinct spots of light is unmistakable4 ,we know that some at least of these spots of light are stars1 because we recognise them as ,cepheid variables1 their light shewing the unmistakable characteristic fluctuations of the familiar ,cepheid variables nearer home4 ,the other shining particles are of comparable brightness and shew about the range of brightness above and below that of the ,cepheids which is needed to justify us in supposing that they are ordinary stars4 ,illustration3 ,,plate ,,xi ,mt ,wilson ,observatory ,magnification of a part 7left-hand top corner7 of the ,great ,nebula ,m #ca in ,andromeda1 which is shewn complete in ,plate ,,iv 7p4 #cj7 ,illustration3 ,,plate ,,xii ,mt ,wilson ,observatory ,magnification of the central region of the ,great ,nebula ,m #ca in ,andromeda ,from the observed periods of fluctuation of their ,cepheid variables1 in combination with the other methods just explained1 ,dr ,hubble of ,mount ,wilson ,observatory has recently found that even the nearest of these nebulae1 namely the nebula ,m #cc shewn in ,plate ,,xx 7p4 #bac71 is so remote that light takes some #hej1jjj years to travel from it to us4 ,the ,great ,nebula ,m #ca in ,andromeda 7p4 #cj7 is at the slightly greater distance of about #ijj1jjj light-years4 ,this abundantly proves that these nebulae lie right outside the galactic system1 justifying the term 8extra-galactic0 nebulae4 ,one might attempt to estimate the total number of stars in these nebulae by counting those visible in a selected average small area1 but more precise methods are available4 ,just as we have supposed that the outermost stars in the galactic system are describing orbits under the gravitational attraction of the galaxy as a whole1 so we must suppose that the outermost stars in a nebula are describing orbits under the gravitational attraction of the main mass of the nebula2 the forces which keep them from running away from the nebula are similar to those which keep the earth moving in its orbit round the sun4 ,if so1 we can weigh the nebulae1 precisely in the same way as we weigh the sun 7p4 #dd7 or the galactic system 7p4 #fi74 ,dr ,hubble in this way estimates that the weight of the ,great ,nebula ,m #ca in ,andromeda1 shewn in ,plate ,,iv1 must be about #cejj million times that of the sun1 while the nebula ,n4,g4,c4 #deid in ,virgo1 shewn in ,plate ,,xv 7p4 #bjd71 must have about #bjjj million times the weight of the sun4 ,in general it seems likely that each of the extra-galactic nebulae contains about enough matter to make some #bjjj million stars4 ,this is not the same thing as saying that each nebula already contains #bjjj million stars4 ,while many of these nebulae appear to consist largely of clouds of stars1 yet most of them contain also a large central region which no telescopic power has so far succeeded in resolving into distinct points4 ,for instance1 ,plate ,,xii shews the central region of the ,great ,nebula in ,andromeda magnified to the same degree as the left-hand top corner shewn in ,plate ,,xi1 and this is clearly not resolved into stars in the same way as the outer regions shewn in ,plate ,,xi4 ,the whole of the nebula ,n4,g4,c4 #deid in ,virgo1 shewn in ,plate ,,xv1 also refuses to be resolved into separate stars4 ,we shall find reasons later 7,chapter ,,iv7 for interpreting these central regions as masses of gas which are destined in time to form stars1 but have not yet done so4 ,we shall in fact find that the nebulae are the birthplaces of the stars1 so that each nebula consists of stars born and stars not yet born4 ,it is the total weight of stars already born and of matter which is destined to form stars that aggregates #bjjj million suns4 ,about #b1jjj1jjj of these extra-galactic nebulae are visible in the great #ajj-;inch telescope4 ,in general1 they appear to be scattered with a tolerable approach to uniformity through space1 their average distance apart being something of the order of #b1jjj1jjj light-years1 although here and there this uniformity is broken by clouds and clusters of nebulae4 ,for instance1 the sky is remarkably rich in nebulae in the constellations of ,virgo and ,coma ,berenices4 ,here a cloud of about #cjj nebulae is collected1 according to ,shapley1 within a space having only from #e to #aj times the dimensions of the galactic system1 at a distance of some ten million light-years from the sun4 ,the same region of the sky appears also to contain three other and more remote clouds4 ,shapley has suggested that our galactic system1 the ,andromeda nebula and other near nebulae may constitute a similar cloud4 ,,the ,,remotest ,,depths ,,of ,,space4 ,hubble estimates that the most distant of the #b1jjj1jjj nebulae revealed by the #ajj-;inch telescope must be about #adj million light-years away from us4 ,this is the greatest distance which the human eye has so far seen into space4 ,the #bbj1jjj light-years which formed the diameter of the galactic system seemed staggeringly large at first1 but we are now speaking of distances some #fjj times greater4 ,for all but a #ejjth part of its long journey1 the light by which we see this remotest of visible nebulae travelled towards an earth uninhabited by man4 ,just as it was about to arrive1 man came into being on earth1 and built telescopes to receive it4 ,so at least it appears when viewed on the astronomical scale4 ,yet even this last #ejjth part of the journey covers the lives of #aj1jjj generations of men1 through all of which1 as well as through #ejj times as great a span of time1 the light has been travelling steadily onward at #ahf1jjj miles a second4 ,there are so many faint nebulae at the very limit of vision of the #ajj-;inch telescope1 that it seems certain that a still larger telescope would reveal a great many more4 ,the #bjj-;inch telescope1 which it is hoped will shortly be built1 having twice the aperture of the present #ajj-;inch1 ought to probe twice as far into space1 and so may perhaps be expected to shew about eight times as many1 or #af million1 nebulae4 ,,the ,,structure ,,of ,,the ,,universe ,so far every increase of telescopic power has carried us deeper and deeper into space1 and space has seemed to expand at an ever-increasing rate4 ,we may well ask whether this expansion is destined to go on for ever3 are there any limits at all to the extent of space8 ,even a generation ago1 ,i think most scientists would have answered this last question in the negative4 ,they would have argued that space could be limited only by the presence of something which is not space4 ,we1 or rather our imaginations1 could only be prevented from journeying for ever through space by running up against a wall of something different from space4 ,and1 hard though it may be to imagine space extending for ever1 it is far harder to imagine a barrier of something different from space which could prevent our imaginations from passing into further space beyond4 ,the argument is not a sound one4 ,for instance1 the earth's surface is of limited extent1 but there is no barrier which prevents us from travelling on and on as far as we please4 ,a traveller who did not understand that the earth's surface is spherical1 would naturally expect that longer and longer journeys from home would for ever open up new tracts of country awaiting exploration4 ,yet1 as we know1 he would necessarily be reduced in time to repeating his own tracks4 ,as a result of its curvature1 the earth's surface1 although unlimited1 is finite in extent4 ,,the ,,theory ,,of ,,relativity ,through his theory of relativity1 ,einstein claims to have established that space also1 although unlimited1 is finite in extent4 ,the total volume of space in the universe is of finite amount just as the surface of the earth is of finite amount1 and for the same reason2 both bend back on themselves and close up4 ,the analogy is valid and useful only so long as we are careful to compare the whole of space to the surface of the earth1 and not to its volume4 ,the volume of the earth is also finite in amount1 but for quite different reasons4 ,a mole which burrowed on and on through the earth in a straight line would come in time to something which is not earth--it would emerge into the open air2 but we can go on and on over the surface of the earth without ever coming to anything which is not the surface of the earth4 ,the properties of space are those of the surface1 not of the volume1 of the earth4 ,as a consequence of space bending back into itself1 a projectile or a ray of light can travel on for ever without going outside space into something which is not space1 and yet it cannot go on for ever without repeating its own tracks4 ,for this reason it is probable that light can travel round the whole of space and return to its starting point1 so that if we pointed a sufficiently powerful telescope in the right direction in the midnight sky1 we should see the sun and its neighbours in space by light which had made the circuit of the universe4 ,we should not see them as they now are1 but as they were many millions of years ago4 ,light which had left the sun so long ago would have travelled round almost the whole of space and then1 just as it was about to complete the circle1 it would be caught in our telescope instead of being allowed to start on its second journey round space4 ,this curvature of space has other functions than that which it performs on the grand scale1 of limiting the total volume of space4 ,before ,einstein's day the curvatures of the paths of planets1 cricket balls and projectiles in general were all attributed to the pull of a 8force0 of gravitation4 ,the theory of relativity dismisses this supposed force as a pure illusion1 and attributes the curved paths of projectiles of all kinds to their efforts to keep a straight track through a curved space4 ,this curved space is not1 it is true1 the ordinary space of the astronomer4 ,it is a purely mathematical and probably wholly fictitious space1 in which the astronomers' space and the astronomers' time are inextricably bound together and enter as equal partners4 ,to be absolutely exact1 there are four equal partners4 ,the first three are the three dimensions of ordinary space--breadth1 width1 and height1 or1 if we prefer1 north-south1 east-west and up-down4 ,the fourth is ordinary time measured in a way appropriate to the way in which we have measured our space 7a year of time corresponding to a light-year of space1 and so on71 and then multiplied by the square-root of -#a4 ,this last multiplication by the square-root of -#a is of course the remarkable feature of the whole affair4 ,for the square-root of -#a has no real existence2 it is what the mathematician describes as an 8imaginary0 number4 ,no real number can be multiplied by itself and give -#a as the product4 ,yet it is only when time is measured in terms of an imaginary unit of 7-#a7 years that there is true equal partnership between space and time4 ,this shews that the equal partnership is purely formal--it is nothing but a convenient fiction of the mathematician4 ,indeed had it been anything more1 our intuitive conviction that time is something essentially different from space could have had no basis in experience and so would have vanished ere now4 ,these complications with respect to time need not concern us here2 the essential point is that ,einstein's theory of relativity teaches that space ultimately bends back on itself like the earth's surface1 so that the total amount of space is finite4 ,,the ,,cosmology ,,of ,,einstein4 ,according to ,einstein's original theory1 the dimensions of space are determined by the amount of matter it contains4 ,the more matter there is1 the smaller space must be1 and conversely2 space could only be of literally infinite extent if it contained no matter at all4 ,the problem of determining the extent of space accordingly reduces to that of determining how much matter it contains4 ,we have no means of estimating how much matter may exist outside those regions of space which are within the reach of our telescopes1 but within these regions matter seems to be fairly uniformly distributed in the form of extra-galactic nebulae4 ,from the known weights of these1 ,hubble estimates that the mean density of matter in space must be about #ae #aj times that of water4 ,on the assumption that matter is distributed with this density through the whole of space1 including those parts which our telescopes have not yet penetrated1 we can calculate quite definitely that the radius of space is #hd1jjj million light-years1 or #fjj times the distance of the furthest visible nebula4 ,the journey round space would take #ejj1jjj million light-years1 and if ever our telescopes shew us the solar system from behind1 we shall see it as it was #ejj1jjj million years ago4 ,thus1 according to ,einstein's original theory1 even the #adj million light-years through which we can range with our telescopes form only a small fraction of the whole of space--something like one part in a thousand million4 ,there is plenty of space still awaiting exploration4 ,it is perhaps not surprising4 ,mankind1 who has been possessed of telescopes for only #cjj years out of the #cjj1jjj of his residence on earth1 could hardly hope to discover the whole of space in so short a time4 ,our astronomer-explorers are moving from island to island in the small archipelago which surrounds their home in space1 but they are still far from circumnavigating the globe4 ,and1 just as the earliest geographers tried to estimate the size of the earth1 long before they thought of circumnavigating it1 from the curvature of a small part of its surface1 so astronomers are now trying to form estimates1 although necessarily vague1 of the size of the whole universe from the curvature of that part of it with which they are already acquainted4 ,the general theory of relativity has long passed the stage of being regarded as an interesting speculation4 ,it not only accounts for phenomena of planetary motion before which ,newton's law of gravitation failed1 but it has predicted other phenomena--the apparent displacements of stars near the sun at an eclipse1 resulting from the light by which we see them being bent as it passes through the sun's gravitational field1 and a certain displacement of stellar spectra towards the red end--which were entirely unsuspected when the predictions were first made1 but have subsequently been fully confirmed by observation4 ,indeed the theory has by now qualified as one of the ordinary working tools of astronomy4 ,it has been used to measure the diameter of the small faint star ,sirius ,b1 the companion to ,sirius 7p4 #bfb71 as well as to discuss the nature of the stars at the centres of the 8planetary nebulae0 7p4 #cbc74 ,nevertheless1 the general theory of relativity does not lead up to ,einstein's cosmology in a unique way4 ,it is perfectly possible for the former to be true and the latter false4 ,the general theory of relativity fixes the attributes of any small fraction of the universe quite definitely1 but leaves open several alternative ways in which these small fractions can be pieced together to form a whole4 ,einstein's particular view of the cosmos cannot therefore claim the prestige which attaches to the general theory of relativity as a whole4 ,and indeed for some years it fell somewhat into disfavour1 and appeared likely to be superseded by an alternative cosmology which de ,sitter of ,leiden propounded and developed in some detail in #aiag4 ,,the ,,cosmology ,,of ,,de ,,sitter4 ,let us first try to understand the essential differences between these two cosmologies4 ,einstein's cosmology supposes that the size of the cosmos is determined by the amount of matter it contains4 ,if it was decided1 at the creation1 to create a universe containing a certain amount of matter which was to obey certain natural laws1 then space must at once have adjusted itself to the size suited for containing just this amount of matter and no more4 ,or1 if the size of the universe and the natural laws were decided upon1 the creation of a certain definite amount of matter became an inevitable necessity4 ,de ,sitter's universe is less simple1 or1 if we prefer so to put it1 allowed more freedom of choice in its creation4 ,after the laws of nature had been fixed1 it was still possible to make a universe of any size1 and to put any amount of matter1 within limits1 into it4 ,looked at from the strictly scientific point of view1 ,einstein's universe has one element of arbitrariness fewer than de ,sitter's universe1 and to this extent it has the advantage of simplicity4 ,on the other hand this simplicity is acquired at a price4 ,the fundamental corner-stone of the whole theory of relativity is the equal partnership of space and time in the sense already explained4 ,einstein's cosmology gains its simplicity only at the expense of supposing that this equality of partnership disappears when we view the cosmos as a whole4 ,it supposes that space and time are indistinguishable 7in the purely formal sense already indicated7 only to a being whose experience is limited to a small fraction of the universe2 they become utterly distinct for a being who can range through the whole of space and time4 ,it is not altogether clear how much weight ought to be attached to this objection1 if objection it is4 ,real space and real time undoubtedly are distinct4 ,even if we deny the reality of both1 they still remain distinguishable as modes of perception4 ,what reproach1 then1 can it be to a cosmology that it admits that1 in the last resort1 when the universe is contemplated on the grand scale1 space and time resolve themselves into distinct types of entity8 ,somehow we knew it already1 before ever we began to contemplate the universe on the grand scale4 ,whatever the answer to this last question may be1 de ,sitter's cosmology avoids all possible reproach by maintaining the equal partnership of space and time1 not only in individual fractions of the cosmos1 but throughout the cosmos as a whole4 ,it will of course be understood that we are still speaking of equal partnership in the purely formal sense already explained1 a light-year entering the cosmology on the same footing as the square-root of -#a years4 ,even de ,sitter's cosmology does not pretend that a light-year 7#idf million million kilometres7 is the same thing as twelve months4 ,although ,einstein's main theory of relativity has been amply confirmed by observation1 the cosmological part of it did not predict any special features such as permitted of a direct observational test4 ,de ,sitter's cosmology1 on the other hand1 predicted that the spectra of all distant objects must shew a displacement towards the red1 of amount depending on the distance of the object4 ,the equal partnership of space and time results in the vibrations of the light-waves emitted by any specified source being slower in distant than in near parts of the universe2 the stream of time rolls more rapidly just where we happen to be than anywhere else4 ,this sounds paradoxical at first1 but examination shews that it is not2 de ,sitter is not asking us to return to a geocentric universe1 because he shews that the inhabitant of a distant star would also find that terrestrial atoms were keeping slower time than his own4 ,the paradox is completely resolved by the concept of the relativity of all measures of space and time4 ,this displacement to the red as a result of mere distance is peculiar to de ,sitter's cosmology4 ,it is additional to the displacement which1 as all cosmologies agree1 the spectrum of a moving body must shew as the result of its motion1 this latter being towards the red only if the body is receding from the earth 7p4 #ea74 ,on de ,sitter's cosmology1 the two displacements are not entirely independent1 for it is an essential feature of this cosmology that near bodies should tend to move further apart from one another4 ,just as bits of straw thrown together into a stream tend to get separated as they float down the stream1 so objects in de ,sitter's universe move further apart as they float down the stream of time4 ,thus on de ,sitter's theory a displacement of spectral lines to the red cannot be interpreted as evidence either of motion or of distance2 it is a mixture of both4 ,this does not mean that we have been altogether wrong in deducing the velocities of stars in the galactic system from the observed displacements of their spectral lines4 ,no appreciable displacement is produced by distance alone1 unless this distance forms an appreciable fraction of the radius of the universe4 ,systematic displacements to the red are1 it is true1 observed in the spectra of the most distant stars1 but they are of very small amount4 ,it is only when we look to the remote extra-galactic nebulae that we can expect to observe the effect in appreciable strength4 ,now it has long been one of the outstanding puzzles of astronomy that the spectra of the distant nebulae are uniformly displaced towards the red4 ,the observed displacements are not small4 ,interpreted as velocities1 many of them would represent speeds of over #ajjj miles a second4 ,humason has found that two faint nebulae ,n4,g4,c4 #dhfj and #dhec shew apparent speeds of recession of #dijj and #dfjj miles a second respectively4 ,they are both members of a cloud of nebulae in ,coma ,berenices 7p4 #gb71 which is probably at a distance of about #ej million light-years4 ,quite recently the spectrum of another very faint nebula in ,ursa ,major has been found to indicate an apparent motion of recession with a speed of #gbjj miles a second4 ,if de ,sitter's theory is rejected1 almost all the extra-galactic nebulae must be running away from us with terrific1 almost unimaginable1 speeds4 ,and the further away they are the more precipitately they are increasing their distance4 ,yet we can hardly reintroduce simplicity by adopting de ,sitter's theory1 and treating the whole apparent stampede of nebulae as spurious1 since this theory involves that the nebulae may well1 in actual fact1 be running away from us1 scattering being an inherent property of objects in a de ,sitter universe4 ,the fact that the spectra of the most distant nebulae shew these large displacements provides a certain presumption in favour of the truth of de ,sitter's cosmology2 this at least explains them twice over1 while no other cosmology explains them at all4 ,if we tentatively accept this cosmology1 then each observed spectral shift must be regarded as the sum of two parts1 one arising in the ordinary way from a recession of the nebula1 and the other arising merely from its distance4 ,a preliminary study by ,dr ,hubble has shewn that on the whole the spectral displacements are largest for the most distant nebulae1 and that their amounts are roughly proportional to the distances of the nebulae from us4 ,if we interpret the whole of the observed displacements purely as evidence of recession1 we can calculate that the radius of the universe is about #bjjj million light-years1 or some fourteen times the distance of the furthest visible nebula4 ,with so large a radius of the universe1 the further displacement resulting from the mere distance of even remote nebulae is negligible1 so that our assumption that the displacements arise almost entirely from velocities of recession receives posteriori vindication4 ,if the observed displacements of the nebular spectra had been strictly proportional to their distances from us1 we should have obtained a consistent explanation of the observed facts by assuming that we lived in a de ,sitter universe having a radius of about #bjjj million light-years4 ,,the ,,expanding ,,universe4 ,it used to be thought that the cosmologies of ,einstein and de ,sitter were antagonistic to one another1 since obviously no one universe could be an ,einstein universe and a de ,sitter universe at the same time4 ,a recent investigation by a ,belgian mathematician1 the ,abb ,g4 ,lematre1 has put a different complexion on the problem4 ,in brief ,lematre has shewn that no universe could stay permanently in the state considered by ,einstein4 ,a universe in this state is an unstable structure2 immediately it came into being it would start to expand1 and would not cease from expanding until it had become a de ,sitter universe4 ,even after this the expansion would continue1 but it would now become merged in the normal expansion of the de ,sitter universe1 such as we have already considered4 ,in the light of these results1 the question at issue is not whether our universe is an ,einstein universe or a de ,sitter universe1 but rather how far it has travelled along the road which begins with an ,einstein universe and ends with a de ,sitter universe4 ,whatever the answer may be1 we are led to suppose that at the beginning of time the nebulae were much nearer to one another than they now are1 that ever since then they have obeyed their inherent tendency to scatter1 or rather the tendency of the flowing stream of time to scatter them1 and that they are now moving away from us1 and from one another1 with speeds which are proportional to their distances4 ,this is in accordance with ,hubble's conclusion1 that the apparent speeds of recession of the nebulae are roughly proportional to their distances4 ,from ,hubble's data ,eddington has calculated that the original ,einstein universe must have had a radius of about #abjj million light-years4 ,if the apparent speeds of recession of the nebulae had been found to be strictly proportional to their distances1 we could have explained everything by supposing that we lived in an expanding universe1 which had started as an ,einstein universe of #abjj million light-years' radius1 had now expanded to something of the order of #bjjj million light-years' radius1 and was destined to go on expanding to all eternity4 ,this provides a simple and rather fascinating picture of the universe1 but there are many reasons against supposing that it is a true one4 ,in the first place1 if we interpret the spectral displacements as evidence of velocity alone1 the speeds of the nebulae are probably very far from being 7as the foregoing picture would require7 accurately proportional to their distances from us4 ,a group of three nebulae1 all believed to be at the same distance of about #ej million light-years1 differ by nearly #bjjj miles a second in their speeds1 which average about #ejjj miles a second4 ,oort has found a general tendency for the speeds of very distant nebulae not to be strictly proportional to their distances4 ,at from #bj to #dj million light-years the apparent divergences average #gej miles a second1 but it is not clear how far these result merely from inaccurate estimates of the distances of these remote nebulae4 ,in the second place1 if the observed spectral shifts represent mere scattering1 we can calculate the time since this scattering began2 it proves to be many thousands of millions of years4 ,enormous though such a length of time is1 it does not appear to be enough4 ,we shall see later 7,chapter ,,iii7 how time leaves its mark1 its wrinkles and its grey hairs1 on the stars1 so that we can guess their ages tolerably well1 and the evidence is all in favour of stellar lives1 not of thousands of millions1 but of millions of millions1 of years4 ,if the nebulae owe their present motions to mere scattering1 then the stars must have lived the greater parts of their lives before this scattering began4 ,such a hypothesis seems too artificial for acceptance1 at any rate so long as any alternative is open4 ,of course we must frankly admit that our estimates of stellar ages may be found to need revision4 ,indeed they have been calculated on the supposition that no appreciable scattering of the type required by de ,sitter's cosmology has ever taken place4 ,if not only the nebulae1 but also the stars composing the galactic system1 were huddled together at the beginning of time1 our estimates of the lives of the stars would have to be substantially shortened1 and it is conceivable1 although ,i think very unlikely1 that they could be reduced to lengths of the kind we have just considered2 they certainly could not be so reduced if the original universe had a radius anywhere near to ,eddington's estimate of #abjj million light-years4 ,nevertheless the cosmologies of de ,sitter and ,lematre undoubtedly require that the present-day universe must be expanding1 that the nebulae must be retreating both from one another1 and from us1 and that their spectra must1 as a consequence1 shew displacements to the red4 ,but there is nothing to compel us to identify these displacements with those actually observed4 ,many causes1 other than motions of recession1 are capable of reddening spectral lines1 and only after we have deducted all the reddening due to these various other causes shall we be in a position to say that the residue represents a true motion of recession4 ,quite recently ,dr ,zwicky of ,pasadena has suggested that gravitating matter diffused through space may redden all light which passes through the space4 ,he gives dynamical reasons for his suggestion1 calculates the amount of spectral shift to be anticipated in the light reaching us from the nebulae1 and finds that it would account for practically the whole of the observed shift4 ,it is possible that the greater part of the observed reddening of nebular light may be due to this or some similar cause1 only a small fraction representing true motions of recession4 ,if so1 we can extend the age of the universe indefinitely1 and are free to assign to the stars the very great ages which the evidence of general astronomy seems to demand4 ,this we shall discuss fully in ,chapter ,,iii4 ,in de ,sitter's original form of this cosmology1 light would take an infinite time to travel round the universe1 and this would prevent any object being seen by light which had travelled the long way round4 ,this results from de ,sitter having considered only the ideal case of a universe entirely empty of all matter4 ,with even a little matter in the universe1 the path of a ray of light would presumably bend back on itself and return to its starting point after a finite time4 ,it has been quite seriously suggested that two faint nebulae 7h #cdcc and ,m #hc7 may actually be our two nearest neighbours in the sky1 ,m #cc and ,m #ca1 seen the long way round space4 ,if so1 we see the fronts of two objects when we look at ,m #cc and ,m #ca1 and the backs of the same two objects when we point our telescopes in exactly the opposite directions and look at h #cdcc and ,m #hc4 ,no doubt this is only a conjecture1 and perhaps rather a wild one1 but many more startling conjectures have been made in astronomy1 and subsequently proved to be true4 ,all these discussions of the structure of space are of course highly speculative1 but they agree in suggesting the general conclusion that1 if we cannot yet see the whole of space1 we can at least survey an appreciable fraction of it4 ,our astronomer-explorers may not as yet have circumnavigated the globe1 but they are perhaps discovering ,america1 and we can well imagine that even the next generation will have completed the circumnavigation of space1 and will think of a finite but unbounded space in the same way1 and with the same ease1 as we think of the finite but unbounded surface of the earth4 ,a ,,model ,,of ,,the ,,universe ,we found it difficult enough to visualise the #d light-years which constitute the distance to the nearest star1 so we may be well advised not even to attempt to visualise this last distance of thousands of millions of light-years1 the conjectured circumference of the universe4 ,yet we may try to see all these distances in proper proportion relative to one another by the help of a model drawn to scale4 ,we can escape the effort of trying to imagine unimaginably great distances by keeping the scale very small4 ,the earth1 travelling #abjj times faster than an express train1 makes a journey of #fjj million miles around the sun every year4 ,let us represent this journey by a pin-head _/ of an inch in diameter4 ,this fixes the scale of our model2 the sun has shrunk to a minute speck of dust _/ of an inch in diameter1 while the earth is a still more minute speck which is too small to be seen at all even in the most powerful of microscopes4 ,on this scale the nearest star in the sky1 ,proxima ,centauri1 must be placed about #bbe yards away1 and to contain even the hundred stars nearest to our sun in space1 the model must be a mile high1 a mile long and a mile wide4 ,let us go on building the model4 ,we may think of stars indiscriminately as specks of dust1 because their sizes vary about as much as the sizes of specks of dust4 ,in the vicinity of the sun we must place specks of dust at average distances of about a quarter of a mile apart4 ,in other regions of space they are generally even farther apart1 for1 owing to the presence of the 8local cluster10 the immediate neighbourhood of the sun happens to be a rather crowded part of the sky4 ,we go on building the model for hundreds of miles in every direction1 and then1 if we are building in a direction well away from the galactic plane1 the specks of dust begin to thin out2 we are approaching the confines of the galaxy4 ,in the galactic plane itself we build out for about #gjjj miles before we come to the farthest globular cluster1 and still we are inside the galactic system4 ,with our earth's long yearly journey round the sun as a pin-head the whole galactic system is about the size of the ,american continent4 ,it may be well to pause and try to visualise the relative sizes of a pin-head and of the ,american continent1 before we go on with our mental model-building4 ,after we have finished the galactic system1 we must travel about #cj1jjj miles before we begin to set up the next bit of our model1 at any rate if we are keeping it to scale4 ,at this distance we place the next family of stars1 a family which is probably substantially smaller and more compact than our own galactic family1 but is comparable with it both in size and in numbers4 ,so we go on building our model--a family of thousands of millions of stars every #cj1jjj miles or so--until we have two million such families4 ,the model now stretches for about four million miles in every direction4 ,this represents as far as we can see into space with a telescope2 we can imagine the model going on1 although we know not how nor where--all we know is that the part so far built represents only a fraction of the universe4 ,every galactic system or island universe or extra-galactic nebula contains thousands of millions of stars1 or gaseous matter destined ultimately to form thousands of millions of stars1 and we know of two million such systems4 ,there are1 then1 thousands of millions of millions of stars within the range covered by the #ajj-;inch telescope1 and this number must be further multiplied to allow for the parts of the universe which are still unexplored4 ,at a moderate computation1 the total number of stars in the universe must be something like the total number of specks of dust in ,london4 ,think of the sun as something less than a single speck of dust in a vast city1 of the earth as less than a millionth part of such a speck of dust1 and we have perhaps as vivid a picture as the mind can really grasp of the relation of our home in space to the rest of the universe4 ,an alternative procedure would have been to construct our scale-model by taking all the specks of dust in ,london and spreading them out to the right distances to represent the various stars in space4 ,the average actual distances between specks of dust in ,london is a quite small fraction of an inch2 to get our model to correct scale1 this distance must be increased to about a quarter of a mile1 even when we are building the part which represents the crowded part of space round the sun4 ,if we build our model in this way1 we obtain a vivid picture of the emptiness of space4 ,empty ,waterloo ,station of everything except six specks of dust1 and it is still far more crowded with dust than space is with stars4 ,this is true even of the comparatively crowded region inside the galactic system2 it takes no account of the immense empty stretches between one system of stars and the next4 ,on averaging throughout the whole of the model1 the mean distance of a speck of dust from its nearest neighbour proves to be something like #hj miles4 ,the universe consists in the main not of stars but of desolate emptiness--inconceivably vast stretches of desert space in which the presence of a star is a rare and exceptional event4 ,let us in imagination take up a position in space somewhere near the sun1 and watch the stars moving past with speeds about #ajjj times that of an express train4 ,if space were really crowded with stars our position would be as unenviable as if we sat down in the middle of ,regent ,street to watch the traffic go by--our life1 though thrilling1 would be brief4 ,yet1 as exact calculation shews1 the stellar traffic is so little crowded that we would have to wait about a million million million years before a star ran into us4 ,put in another form1 the calculation shews that any one star may expect to move for something of the order of a million million million years before colliding with a second star4 ,the stars move blindly through space1 and the players in the stellar blind-man's-buff are so few and far between that the chance of encountering another star is almost negligible4 ,we shall see later that this concept is of the profoundest significance in our interpretation of the universe4 ,,chapter ,,ii ,exploring the ,atom ,so far our exploration of the universe has been in the direction from man to bigger things than man2 we have been exploring ranges of space which dwarf man and his home in space into utter insignificance4 ,yet we have explored only about half the total range of the universe2 an almost equal range awaits exploration in the direction of the infinitely small4 ,we appreciate only half of the infinite richness of the world around us until we extend our survey down to the smallest units of matter4 ,this survey has been first the task1 and now the brilliant achievement1 of modern physics4 ,it may perhaps be asked why an account of modern astronomy should concern itself with this other end of the universe4 ,the answer is that the stars are something more than huge inert masses2 they are machines in action1 generating and emitting the radiation by which we see them4 ,we shall best understand their mechanism by studying the ways in which radiation is generated and emitted on earth1 and this takes us right into the heart of modern atomic physics4 ,in the present book we naturally cannot attempt to cover the whole of this new field of knowledge2 we shall concern ourselves only with those parts which are important for the interpretation of astronomical results4 ,,atomic ,,theory ,as far back as the fifth century before ,christ1 ,greek philosophy was greatly exercised by the question of whether in the last resort the ultimate substance of the universe was continuous or discontinuous4 ,we stand on the sea-shore1 and all around us see stretches of sand which appear at first to be continuous in structure1 but which a closer examination shews to consist of separate hard particles or grains4 ,in front rolls the ocean1 which also appears at first to be continuous in structure1 and this we find we cannot divide into grains or particles no matter how we try4 ,we can divide it into drops1 but then each drop can be subdivided into smaller drops1 and there seems to be no reason1 on the face of things1 why this process of subdivision should not be continued for ever4 ,the question which agitated the ,greek philosophers was1 in effect1 whether the water of the ocean or the sand of the sea-shore gave the truest picture of the ultimate structure of the substance of the universe4 ,the school of ,democritus1 ,leucippus and ,lucretius believed in the ultimate discontinuity of matter2 they taught that any substance1 after it had been subdivided a sufficient number of times1 would be found to consist of hard discrete particles which did not admit of further subdivision4 ,for them the sand gave a better picture of ultimate structure than the water1 because1 or so they thought1 sufficient subdivision would cause the water to display the granular properties of sand4 ,and this intuitional conjecture is amply confirmed by modern science4 ,the question is1 in effect1 settled as soon as a thin layer of a substance is found to shew qualities essentially different from those of a slightly thicker layer4 ,a layer of yellow sand swept uniformly over a red floor will make the whole floor appear yellow if there is enough sand to make a layer at least one grain thick4 ,if1 however1 there is only half this much sand1 the redness of the floor inevitably shews through2 it is impossible to spread sand in a uniform layer only half a grain thick4 ,this sudden change in the properties of a layer of sand is of course a consequence of the granular structure of sand4 ,similar changes are found to occur in the properties of thin layers of liquid4 ,a teaspoonful of soup will cover the bottom of a soup plate1 but a single drop of soup will only make an untidy splash4 ,in some cases it is possible to measure the exact thickness of layer at which the properties of liquids begin to change4 ,in #ahij ,lord ,rayleigh found that thin films of olive oil floating on water changed their properties entirely as soon as the thickness of the film was reduced to below a millionth of a millimetre 7or a #be1jjj1jjjth part of an inch74 ,the obvious interpretation1 which is confirmed in innumerable ways1 is that olive oil consists of discrete particles--analogous to the 8grains0 in a pile of sand--each having a diameter somewhere in the neighbourhood of a #be1jjj1jjjth part of an inch4 ,every substance consists of such 8grains40 ,they are called molecules1 and the familiar properties of matter are those of layers many molecules thick2 the properties of layers less than a single molecule thick are known only to the physicist in his laboratory4 ,,molecules ,how are we to break up a piece of substance into its ultimate grains1 or molecules8 ,it is easy for the scientist to say that1 by subdividing water for long enough1 we shall come to grains which cannot be subdivided any further2 the plain man would like to see it done4 ,fortunately the process is one of extreme simplicity4 ,take a glass of water1 apply gentle heat underneath1 and the water begins to evaporate4 ,what does this mean8 ,it means that the water is being broken up into its separate ultimate grains or molecules4 ,if the glass of water could be placed on a sufficiently sensitive spring balance1 we should see that the process of evaporation does not proceed continuously1 layer after layer1 but jerkily1 molecule by molecule4 ,we should find the weight of the water changing by jumps1 each jump representing the weight of a single molecule4 ,the glass may contain any integral number of molecules but never fractional numbers--if the fractions of a molecule exist1 at any rate they do not come into play in the evaporation of a glass of water4 ,,the ,,gaseous ,,state4 ,the molecules which break loose from the surface of the water as it evaporates form a gas--water-vapour or steam4 ,a gas consists of a vast number of molecules which fly about entirely independently of one another1 except at the rare instants at which two collide1 and so interfere with each other's motion4 ,the extent to which the molecules interfere with one another must obviously depend on their sizes2 the larger they are1 the more frequent their collisions will be1 and the more they will interfere with one another's motion4 ,actually the extent of this interference provides the best means of estimating the sizes of molecules4 ,they prove to be exceedingly small1 being for the most part about a hundred-millionth of an inch in diameter1 and1 as a general rule1 the simpler molecules have the smaller diameters1 as we should expect4 ,the molecule of water has a diameter of #ah hundred-millionths of an inch 7#df #aj cms471 while that of the simpler hydrogen molecule is only just over a hundred-millionth of an inch 7#bg #aj cms474 ,the fact that a number of different lines of investigation all attribute the same diameters to these molecules provides an excellent proof of the reality of their existence4 ,as molecules are so exceedingly small1 they must also be exceedingly numerous4 ,a pint of water contains #ahi #aj molecules1 each weighing #ajf #aj ounces4 ,if these molecules were placed end to end1 they would form a chain capable of encircling the earth over #bjj million times4 ,if they were scattered over the whole land surface of the earth1 there would be nearly #ajj million molecules to every square inch of land4 ,if we think of the molecules as tiny seeds1 the total amount of seed needed to sow the whole earth at the rate of #ajj million molecules to the square inch could be put into a pint pot4 ,these molecules move with very high speeds2 in the ordinary air of an ordinary room1 the average molecular speed is about #ejj yards a second4 ,this is roughly the speed of a rifle-bullet1 and is rather more than the ordinary speed of sound4 ,as we are familiar with this latter speed from everyday experience1 it is easy to form some conception of molecular speeds in a gas4 ,it is not a mere accident that molecular speeds are comparable with the speed of sound4 ,sound is a disturbance which one molecule passes on to another when it collides with it1 rather like relays of messengers passing a message on to one another1 or ,greek torch-bearers handing on their lights4 ,between collisions the message is carried forward at exactly the speed at which the molecules travel4 ,if these all travelled with precisely the same speed and in precisely the same direction1 the sound would of course travel with just the speed of the molecules4 ,but many of them travel on oblique courses1 so that although the average speed of individual molecules in ordinary air is about #ejj yards a second1 the net forward velocity of the sound is only about #cgj yards a second4 ,at high temperatures the molecules may have even greater speeds2 the molecules of steam in a boiler may move at #ajjj yards a second4 ,it is the high speed of molecular motion that is responsible for the great pressure exerted by a gas2 any surface in contact with the gas is exposed to a hail of molecules each moving with the speed of a rifle-bullet4 ,for instance1 the piston in a locomotive cylinder is bombarded by about #ad #aj molecules every second4 ,this incessant fusillade of innumerable tiny bullets urges the piston forward in the cylinder1 and so propels the train4 ,with each breath we take1 swarms of millions of millions of millions of molecules enter our bodies1 each moving at about #ejj yards a second1 and nothing but their incessant hammering on the walls of our lungs keeps our chests from collapsing4 ,perhaps the best general mental picture we can form of a gas is that of an incessant hail of shot or rifle-bullets flying indiscriminately in all directions1 and running into one another at frequent intervals4 ,in ordinary air each molecule collides with some other molecule about #cjjj million times every second1 and travels an average distance of about #a_/afj1jjj inch between successive collisions4 ,if we compress a gas to a greater density1 more molecules are crowded into a given space1 so that collisions become more frequent and the molecules travel shorter distances between collisions4 ,if1 on the contrary1 we reduce the pressure of the gas1 and so lessen its density1 collisions become less frequent and the distance of travel of a molecule between successive collisions--the 8free-path0 as it is called--is increased4 ,in the lowest vacua which are at present obtainable in the laboratory1 a molecule can travel over #ajj yards without colliding with any other molecule1 although there are still #fjj1jjj million molecules to the cubic inch4 ,under astronomical conditions still lower vacua may occur4 ,in some nebulae molecules of gas may travel millions of miles without a collision1 so few are the molecules to a given volume of space4 ,it might be thought that the flying molecules would soon be brought to rest by their collisions2 rifle-bullets undoubtedly would1 but not the molecule bullets of a gas1 for reasons now to be explained4 ,,energy4 ,the amount of the charge of powder used to fire a rifle-bullet gives a measure of the 8energy of motion0 which is imparted to the bullet4 ,to fire a bullet of double weight requires twice as much powder1 because the energy of motion of a bullet1 or indeed of any other moving body1 is proportional to its weight4 ,but to fire the same bullet with double speed does not merely require double the charge of powder4 ,four times as much powder is needed1 because the energy of motion of a moving body is proportional to the square of its speed4 ,the experienced motorist is familiar with this2 if our brakes stop our car in #bj feet when we are travelling #bj miles an hour1 they will not stop it in #dj feet when travelling at #dj miles an hour2 we need #hj feet4 ,double speed requires four times the distance to pull up in1 because double speed represents fourfold energy of motion4 ,in general1 the energy of motion of any moving body whatever is proportional both to the weight of the body and to the square of its speed#h4 #h ,this is expressed in the mathematical formula mv for the energy of motion of a body of weight m moving with a speed v4 ,if m is measured in grammes1 and v in centimetres per second1 the energy of motion of the body is said to be mv 8ergs40 ,thus an 8erg0 is the energy of motion of a body of #b grammes weight 7so that m #a7 moving with a speed of one centimetre a second4 ,as an example1 the energy of an express train of #cjj tons' weight 7#c #aj gms47 moving at #fj miles an hour 7#bfhb cms4 a second7 is #ajgi #aj ergs2 a cannon-ball or shell weighing a ton and moving at #aebj feet a second has precisely the same energy4 ,one of the great achievements of nineteenth-century physics was to establish the general principle known as the 8conservation of energy40 ,energy can exist in a number of forms1 and can change about almost endlessly from one form to another1 but it can never be utterly destroyed4 ,the energy of a moving body is not lost when the body is brought to rest1 it merely takes some other form4 ,when a bullet is brought to rest by hitting a target1 part of its energy of motion goes into heating up the target1 and part into heating up1 or perhaps even melting1 the bullet4 ,in its new guise of heat1 there is just as much energy as there was in the original motion of the bullet4 ,in accordance with the same principle1 energy cannot be created2 all existing energy must have existed from all time1 although possibly in some form entirely different from its present form4 ,for instance1 gunpowder contains a large amount of energy stored up in the form of chemical energy2 we have to take precautions to prevent this bottled-up energy suddenly breaking free and doing damage1 as1 for instance1 by exploding the vessel in which it is contained1 kicking things up into the air1 and so forth4 ,a rifle is in effect a device for setting free the energy contained in a measured charge of gunpowder1 and directing as much as possible of it into the form of energy of motion of a bullet4 ,when we fire a bullet at a target1 a specified amount of energy 7determined by the charge of powder we have used7 is transformed from chemical energy1 residing in the powder1 first into energy of motion1 residing in the bullet 7and to a minor degree in the recoil of the rifle71 and then finally into heat-energy1 residing partly in the spent bullet and partly in the target4 ,here we have energy taking three different forms in rapid succession4 ,all the life of the universe may be regarded as manifestations of energy masquerading in various forms1 and all the changes in the universe as energy running about from one of these forms to the other1 but always without altering its total amount4 ,such is the great law of conservation of energy4 ,among the commoner forms of energy may be mentioned electric energy1 as exemplified by the energy of a charged accumulator or of a thundercloud3 mechanical energy1 as exemplified in the coiled spring of a watch or the raised weight of a clock3 chemical energy1 as exemplified by the energy stored up in gunpowder or in coal1 wood and oil3 energy of motion1 as exemplified by the motion of a bullet1 and finally heat-energy1 which1 as we have seen1 is exemplified by the heat which appears when the motion of a rifle-bullet is checked4 ,,heat4 ,let us examine further into heat as a possible form of energy4 ,when we want to warm a room1 we light a fire and set free some of the chemical energy which is stored up in coal or wood1 or we turn on an electric heater and let the electric current transport to us some of the energy which is being set free by the burning of coal in a distant power-station4 ,but what1 in the last resort1 is heat1 and how does it come to be a mode of energy8 ,heat1 whether of a gas1 a liquid or a solid1 is merely the energy of motion of individual molecules4 ,when we heat up the air of a room we simply make its molecules move faster1 and the total heat of the substance is the total energy of all the molecules of which it is composed4 ,in pumping up a bicycle tyre1 we drive the piston of the pump forward in opposition to the impact of innumerable millions of molecules of air inside the pump4 ,in kicking the opposing molecules out of its way1 the piston increases their speed of motion4 ,the resulting increase in the energy of motion of the molecules is simply an increase of heat4 ,we could verify this by inserting a thermometer1 or1 still more simply1 by putting our hand on the pump2 it feels hot4 ,the molecules of a solid are not possessed of much energy1 and so do not move very fast--so slowly indeed that they seldom change their relative positions1 the neighbouring molecules gripping them so firmly that their feeble energy of motion cannot extricate them4 ,if we warm the solid up1 the molecules acquire more energy1 and so begin to move faster4 ,after a time they are moving with such speeds that they can laugh at the restraining pulls from their neighbours2 each molecule has enough energy of motion to go where it pleases1 and we have a crowd of molecules moving freely as independent units1 jostling one another and pushing their way past one another2 the substance has assumed the liquid state4 ,to make the picture definite1 ice has melted and become water2 the frozen grip is relaxed1 and the molecules flow freely past one another4 ,each still exerts forces on its neighbours1 but these are no longer strong enough to preclude all motion4 ,heat the liquid further1 thus further increasing the energy of motion of the molecules1 and these begin to break loose entirely from their bonds and fly about freely in space forming a gas or vapour4 ,if we go on supplying heat1 the whole substance will in time assume the gaseous state4 ,heating the gas still further merely causes the molecule-bullets to fly faster2 it increases their energy of motion4 ,the average energy of motion of the molecules in a gas is proportional to the temperature of the gas--indeed1 this is the way in which temperature is defined4 ,the temperature must not1 however1 be measured on the ,fahrenheit or ,centigrade scale in ordinary use1 but on what is called the 8absolute0 scale1 which has its zero at -#bgc ,centigrade1 or -#dfi ,fahrenheit4 ,this 8absolute0 zero1 being the temperature of a body which has no further heat to lose1 is the lowest temperature possible4 ,we can approach to within about one degree of it in the laboratory1 and find that it freezes air1 hydrogen and even helium1 the most refractory gas of all1 solid4 ,a thermometer placed out in interstellar space1 far from any star1 would probably shew a temperature of only about four degrees above absolute zero1 while still lower temperatures must be reached out beyond the limits of the galactic system4 ,,molecular ,,collisions4 ,we may now try to picture a collision between two molecule-bullets in a gas4 ,lead bullets colliding on a battlefield would probably change most of their energy of motion into heat-energy2 they would become hotter1 or perchance even melt4 ,but how can the molecule-bullets transform their energy of motion into heat-energy8 ,for them heat and energy of motion are not two different forms of energy1 they are one and the same thing2 their heat is their energy of motion4 ,the total energy must be conserved1 and there is no new disguise that it can assume4 ,so it comes about that when two molecule-bullets collide1 the most that can happen is that they may exchange a certain amount of energy of motion4 ,if their energies of motion before collision were1 say1 #g and #e respectively1 their energies after collision may be #f and #f1 or #h and #d1 or #i and #c1 or any other combination which adds up to #ab4 ,it is the same at every collision2 energy can neither be lost nor transformed1 and so the bullets on the molecular battlefield go on flying for ever1 happily hitting only one another1 and doing no harm to one another when they hit4 ,their energies of motion go up and down1 down and up1 according as they make lucky hits or the reverse1 but the most they have to fear are fluctuations and never total loss of energy2 their motion is perpetual4 ,,atoms ,in the gaseous state1 each separate molecule retains all the chemical properties of the solid or liquid substance from which it originated2 molecules of steam1 for instance1 moisten salt or sugar1 or combine with thirsty substances such as unslaked lime or potassium chloride1 just as water does4 ,is it possible to break up the molecules still further8 ,lucretius and his predecessors would1 of course1 have said3 8,no40 ,a simple experiment1 which1 however1 was quite beyond their range1 will speedily shew that they were wrong4 ,on sliding the two wires of an ordinary electric bell circuit into a tumbler of water1 down opposite sides1 bubbles of gas will be found to collect on the wires1 and chemical examination shews that the two lots of gas have entirely different properties4 ,they cannot1 then1 both be water-vapour1 and in point of fact neither of them is2 one proves to be hydrogen and the other oxygen4 ,there is found to be twice as much hydrogen as oxygen1 whence we conclude that the electric current has broken up each molecule of water into two parts of hydrogen and one of oxygen4 ,these smaller units into which a molecule is broken are called 8atoms40 ,each molecule of water consists of two atoms of hydrogen 7,h7 and one atom of oxygen 7,o72 this is expressed in its chemical formula ,h,o4 ,all the innumerable substances which occur on earth--shoes1 ships1 sealing-wax1 cabbages1 kings1 carpenters1 walruses1 oysters1 everything we can think of--can be analysed into their constituent atoms1 either in this or in other ways4 ,it might be thought that a quite incredible number of different kinds of atoms would emerge from the rich variety of substances we find on earth4 ,actually the number is quite small4 ,the same atoms turn up again and again1 and the great variety of substances we find on earth result1 not from any great variety of atoms entering into their composition1 but from the great variety of ways in which a few types of atoms can be combined--just as in a colour-print three colours can be combined so as to form almost all the colours we meet in nature1 not to mention other weird hues such as never were on land or sea4 ,analysis of all known terrestrial substances has1 so far1 revealed only #ij different kinds of atoms4 ,probably #ib exist1 there being reasons for thinking that two1 or possibly even more1 still remain to be discovered4 ,even of the #ij already known1 the majority are exceedingly rare1 most common substances being formed out of the combinations of about #ad different atoms1 say hydrogen 7,h71 carbon 7,c71 nitrogen 7,n71 oxygen 7,o71 sodium 7,na71 magnesium 7,mg71 aluminium 7,al71 silicon 7,si71 phosphorus 7,p71 sulphur 7,s71 chlorine 7,cl71 potassium 7,k71 calcium 7,ca71 and iron 7,fe74 ,in this way1 the whole earth1 with its endless diversity of substances1 is found to be a building built of standard bricks--the atoms4 ,and of these only a few types1 about #ad1 occur at all abundantly in the structure1 the others appearing but rarely4 ,,spectroscopy4 ,just as a bell struck with a hammer emits a characteristic note1 so every atom put in a flame or in an electric arc or discharge-tube1 emits a characteristic light4 ,when ,newton passed sunlight through a prism1 he found it to be a blend of all the colours of the rainbow4 ,in the same way the modern spectroscopist1 with infinitely more refined instruments1 can analyse any light into all the constituent colours which enter into its composition4 ,the rainbow of colours so produced--the 8spectrum0--is crossed by the pattern of light or dark lines or bands which the astronomer utilises to determine the speeds of recession or approach of the stars4 ,from an examination of this pattern the skilled spectroscopist can at once announce the type of atom from which the light emanates1 so much so that one of the most delicate tests for the presence of certain substances is the spectroscopic test4 ,this spectroscopic method of analysis is by no means confined to terrestrial substances4 ,in #ahad ,fraunhofer repeated ,newton's analysis of sunlight1 and found its spectrum to be crossed by certain dark lines1 still known as ,fraunhofer lines4 ,the spectroscopist has no difficulty in interpreting these dark lines2 they indicate the presence in the sun of the common terrestrial elements1 hydrogen1 sodium1 calcium1 and iron4 ,for reasons which we shall see later 7p4 #abe below71 the atoms of these substances drink up the light of precisely those colours which the ,fraunhofer lines shew to be absent from the solar spectrum4 ,this spectrum is now known to be incomparably more intricate than ,fraunhofer thought1 but practically all the lines which occur in it can be assigned to atoms known on earth1 and the same is true of the spectra of all the stars in the sky4 ,it is tempting to jump to the generalisation that the whole universe is built solely of the #ij or #ib types of atoms found on earth1 but at present there is no justification for this4 ,the light we receive from the sun and stars comes only from the outermost layers of their surfaces1 and so conveys no information at all as to the types of atoms to be found in the stars' interiors4 ,indeed we have no knowledge of the types of atoms which occur in the interior of our own earth4 ,,the ,,structure ,,of ,,the ,,atom4 ,until quite recently1 atoms were regarded as the permanent bricks of which the whole universe was built4 ,all the changes of the universe were supposed to amount to nothing more drastic than a re-arrangement of permanent indestructible atoms2 like a child's box of bricks1 these built many buildings in turn4 ,the story of twentieth-century physics is primarily the story of the shattering of this concept4 ,it was towards the end of the last century that ,crookes1 ,lenard1 and1 above all1 ,sir ,j4 ,j4 ,thomson first began to break up the atom4 ,the structures which had been deemed the unbreakable bricks of the universe for more than #bjjj years1 were suddenly shown to be very susceptible to having fragments chipped off4 ,a mile-stone was reached in #ahie1 when ,thomson shewed that these fragments were identical1 no matter what type of atom they came from2 they were of equal weight and they carried equal charges of negative electricity4 ,on account of this last property they were called 8electrons40 ,the atom cannot1 however1 be built up of electrons and nothing else1 for as each electron carries a negative charge of electricity1 a structure which consisted of nothing but electrons would also carry a negative charge4 ,two negative charges of electricity repel one another1 as also do two positive charges1 while two charges1 one of positive and one of negative electricity1 attract one another4 ,this makes it easy to determine whether any body or structure carries a positive or a negative charge of electricity1 or no charge at all4 ,observation shews that a complete atom carries no charge at all1 so that somewhere in the atom there must be a positive charge of electricity1 of amount just sufficient to neutralise the combined negative charges of all the electrons4 ,in #aiaa experiments by ,sir ,ernest ,rutherford and others revealed the architecture of the atom4 ,as we shall soon see 7p4 #aab below71 nature herself provides an endless supply of small particles charged with positive electricity1 and moving with very high speeds1 in the -particles shot off from radio-active substances4 ,rutherford's method was in brief to fire these into atoms and observe the result4 ,and the surprising result he obtained was that the vast majority of these bullets passed straight through the atom as though it simply did not exist4 ,it was like shooting at a ghost4 ,yet the atom was not all ghostly4 ,a tiny fraction--perhaps one in #aj1jjj--of the bullets were deflected from their courses as if they had met something very substantial indeed4 ,a mathematical calculation shewed that these obstacles could only be the missing positive charges of the atoms4 ,a detailed study of the paths of these projectiles proved that the whole positive charge of an atom must be concentrated in a single very small space1 having dimensions of the order of only a millionth of a millionth of an inch4 ,in this way1 ,rutherford was led to propound the view of atomic structure which is generally associated with his name4 ,he supposed the chemical properties and nature of the atom to reside in a weighty1 but excessively minute1 central 8nucleus0 carrying a positive charge of electricity1 around which a number of negatively charged electrons described orbits4 ,it was of course necessary to suppose the electrons to be in motion in the atom1 otherwise the attraction of positive for negative electricity would immediately draw them into the central nucleus--just as gravitational attraction would cause the earth to fall into the sun1 were it not for the orbital motion of the former4 ,in brief ,rutherford supposed the atom to be constructed like the solar system1 the heavy central nucleus playing the part of the sun and the electrons acting the parts of the planets4 ,the speeds with which these electrons fly round their tiny orbits are terrific4 ,the average electron revolves around its nucleus several thousand million million times every second1 with a speed of hundreds of miles a second4 ,thus the smallness of their orbits does not prevent the electrons moving with higher orbital speeds than the planets1 or even the stars themselves4 ,by clearing a space around the central nucleus1 and so preventing other atoms from coming too near to it1 these electronic orbits give size to the atom4 ,the volume of space kept clear by the electrons is enormously greater than the total volume of the electrons2 roughly1 the ratio of volumes is that of the battlefield to the bullets4 ,the atom1 with a radius of about #b #aj cms41 has about #ajj1jjj times the diameter1 and so about a thousand million million times the volume1 of a single electron1 which has a radius of only about #b #aj;cms4 ,the nucleus1 although it generally weighs #cjjj or #djjj times as much as all the electrons in the atom together1 is at most comparable in size with1 and may be even smaller than1 a single electron4 ,we have already commented on the extreme emptiness of astronomical space4 ,choose a point in space at random1 and the odds against its being occupied by a star are enormous4 ,even the solar system consists overwhelmingly of empty space2 choose a spot inside the solar system at random1 and there are still immense odds against its being occupied by a planet or even by a comet1 meteorite or smaller body4 ,and now we see that this emptiness extends also to the space of physics4 ,even inside the atom we choose a point at random1 and the odds against there being anything there are immense2 they are of the order of at least millions of millions to one4 ,we saw how six specks of dust inside ,waterloo ,station represented--or rather over-represented--the extent to which space was crowded with stars4 ,in the same way a few wasps--six for the atom of carbon--flying around in ,waterloo ,station will represent the extent to which the atom is crowded with electrons--all the rest is emptiness4 ,as we pass the whole structure of the universe under review1 from the giant nebulae and the vast interstellar and internebular spaces down to the tiny structure of the atom1 little but vacant space passes before our mental gaze4 ,we live in a gossamer universe2 pattern1 plan and design are there in abundance1 but solid substance is rare4 ,,atomic ,,numbers4 ,the number of electrons which fly round in orbits in an atom is called the 8atomic number0 of the atom4 ,atoms of all atomic numbers from #a to #ib have been found1 except for two missing numbers #he and #hg4 ,as already mentioned1 it is highly probable that these also exist1 and that there are #ib 8elements0 whose atomic numbers occupy the whole range of atomic numbers from #a to #ib continuously4 ,the atom of atomic number unity is of course the simplest of all4 ,it is the hydrogen atom1 in which a solitary electron revolves around a nucleus whose charge of positive electricity is exactly equal in amount1 although opposite in sign1 to the charge on the negative electron4 ,next comes the helium atom of atomic number #b1 in which two electrons revolve about a nucleus which has four times the weight of the hydrogen nucleus1 although carrying only twice its electric charge4 ,after this comes the lithium atom of atomic number #c1 in which three electrons revolve around a nucleus having six times the weight of the hydrogen atom and three times its charge4 ,and so it goes on1 until we reach uranium1 the heaviest of all atoms known on earth1 which has #ib electrons describing orbits about a nucleus of #bch times the weight of the hydrogen nucleus4 ,,radio-,,activity ,while it was still engaged in breaking up the atom into its component factors1 physical science was beginning to discover that the nuclei themselves were neither permanent nor indestructible4 ,in #ahif1 ,becquerel had found that various substances containing uranium possessed the remarkable property1 as it then appeared1 of spontaneously affecting photographic plates in their vicinity4 ,this observation led to the discovery of a new property of matter1 namely radio-activity4 ,all the results obtained from the study of radio-activity in the few following years were co-ordinated in the hypothesis of 8spontaneous disintegration0 which ,rutherford and ,soddy advanced in #aijc4 ,according to this hypothesis in its present form1 radio-activity indicates a spontaneous break-up of the nuclei of the atoms of radio-active substances4 ,these atoms are so far from being permanent and indestructible that their very nuclei crumble away with the mere lapse of time1 so that what was once the nucleus of a uranium atom is transformed1 after sufficient time1 into the nucleus of a lead atom4 ,the process of transformation is not instantaneous2 it proceeds gradually and by distinct stages4 ,during its progress1 three types of product are emitted1 which are designated -rays1 -rays1 and -rays4 ,these were originally described as rays because they have the power of penetrating through a certain thickness of air1 metal1 or other substance4 ,their true nature was discovered later4 ,it is well known that magnetic forces such as1 for instance1 occur in the space between the poles of a magnet1 cause a moving particle charged with electricity to deviate from a straight course2 it deviates in one direction or the other according as it is charged with positive or negative electricity4 ,on passing the various rays emitted by radio-active substances through the space between the poles of a powerful magnet1 the -rays were found to consist of particles charged with positive electricity1 and the -rays to consist of particles charged with negative electricity4 ,but the most powerful magnetic forces which could be employed failed to cause the slightest deviation in the paths of the -rays1 from which it was concluded that either the -rays were not material particles at all1 or that1 if they were1 they carried no electric charges4 ,the former of these alternatives was subsequently proved to be the true one4 -,,particles4 ,the positively charged particles which constitute -rays are generally described as -particles4 ,in #aiji ,rutherford and ,royds allowed -particles to penetrate through a thin glass wall of less than a hundredth of a millimetre thickness into a chamber from which they could not escape--a sort of mouse-trap for -particles4 ,they found that so long as the number of -particles in the vessel went on increasing1 an accumulation of helium was forming4 ,in this way it was established that the positively charged -particles are simply nuclei of helium atoms4 ,these particles move with enormous speeds1 which depend upon the nature of the radio-active substance from which they have been shot out4 ,the fastest of all1 those emitted by ,thorium ,c1 move with a speed of #ab1hjj miles a second2 even the slowest1 those from ,uranium #a1 have a speed of #hhjj miles a second1 which is about #cj1jjj times the ordinary molecular velocity in air4 ,particles moving with these speeds knock all ordinary molecules out of their way2 this explains the great penetrating power of the -rays4 -,,particles4 ,by examining their motion under magnetic forces1 the -rays were found to consist of negatively charged electrons1 exactly similar to those which revolve orbitally in all atoms4 ,as an -particle carries a positive charge equal in amount to that of two electrons1 an atom which has ejected an -particle is left with a deficiency of positive charge1 or what comes to the same thing1 with a negative charge1 equal to that of two electrons4 ,consequently it is natural1 and indeed almost inevitable1 that the ejections of -particles should alternate with an ejection of negatively charged electrons1 so that the balance of positive and negative electricity in the atom may be maintained4 ,the -particles move with even greater speeds than the -particles1 many approaching to within a few per cent4 of the velocity of light 7#ahf1jjj miles a second74 ,illustration3 ,,plate ,,xiii ,c4 ,t4 ,r4 ,wilson ,the tracks of - and -particles ,one of the most beautiful devices known to physical science1 the invention of ,professor ,c4 ,t4 ,r4 ,wilson1 makes it possible to study the motions of the - and -particles as they thread their way through a gas1 colliding with its molecules on their way4 ,a chamber through which the particles are made to travel is filled with water-vapour in such a condition that the passage of an electrically charged particle leaves behind it a trail of condensations which can be photographed4 ,as an example1 ,plate ,,xiii shews a photograph taken by ,professor ,wilson himself1 in which the trails of both - and -particles appear on the same plate4 ,as the -particles weigh about #gdjj times as much as the -particles1 they naturally create more disturbance in the gas1 and so leave broader and more pronounced tracks2 also they pursue a comparatively straight course while the lighter -particles are deflected from their courses by many of the molecules they meet4 ,the plate shews four -particle tracks and one 7much fainter7 -ray track4 ,the knobby-looking projections which may be seen on one of the -ray tracks are of interest2 they represent the short paths of electrons knocked out of atoms by the passage of the -particle#i4 #i ,these were called -rays by ,bumstead4 -,,rays4 ,the -rays are not material particles at all2 they prove to be merely radiation of a very special kind1 which we shall now discuss4 ,,radiation ,disturb the surface of a pond with a stick and a series of ripples starts from the stick and travels1 in a series of ever-expanding circles1 over the surface of the pond4 ,as the water resists the motion of the stick1 we have to work to keep the pond in a state of agitation4 ,the energy of this work is transformed1 in part at least1 into the energy of the ripples4 ,we can see that the ripples carry energy about with them1 because they cause a floating cork or a toy boat to rise up against the earth's gravitational pull4 ,thus the ripples provide a mechanism for distributing over the surface of the pond the energy that we put into the pond through the medium of the moving stick4 ,light and all other forms of radiation are analogous to water-ripples or waves1 in that they distribute energy from a central source4 ,the sun's radiation distributes through space the vast amount of energy which is generated inside the sun4 ,we hardly know whether there is any actual wave-motion in light or not1 but we know that both light and all other types of radiation are propagated in such a form that they have some of the properties of a succession of waves4 ,we have seen how the different colours of light which in combination constitute sunlight can be separated out by passing the light through a prism4 ,an alternative instrument1 the diffraction grating1 analyses light into its constituent wave-lengths#aj1 and these are found to correspond to the different colours of the rainbow4 ,this shews that different colours of light represent different wave-lengths1 and at the same time provides a means of measuring the actual wave-lengths of light of different colours4 ,these prove to be very minute4 ,the reddest light we can see1 which is that of longest wave-length1 has a wave-length of only #c_/ajj1jjj inch 7#ge #aj cms472 the most violet light we can see has a wave-length only half of this1 or #jjjjjae inch4 ,light of all colours travels with the same uniform speed of #ahf1jjj miles1 or #c #aj centimetres1 a second4 ,the number of waves of red light which pass any fixed point in a second is accordingly no fewer than four hundred million million4 ,this is called the 8frequency0 of the light4 ,violet light has the still higher frequency of eight hundred million million2 when we see violet light1 eight hundred million million waves of light enter our eyes each second4 #aj ,the wave-length in a system of ripples is the distance from the crest of one ripple to that of the next1 and the term may be applied to all phenomena of an undulatory nature4 ,the spectrum of analysed sunlight appears to the eye to stretch from red light at one end to violet light at the other1 but these are not its true limits4 ,if certain chemical salts are placed beyond the violet end of the visible spectrum1 they are found to shine vividly1 shewing that even out here energy is being transported1 although in invisible form4 ,regions of invisible radiation stretch indefinitely from both ends of the visible spectrum4 ,from one end--the red--we can pass continuously to waves of the type used for wireless transmission1 which have wave-lengths of the order of hundreds1 or even thousands1 of yards4 ,from the violet end1 we pass through waves of shorter and ever shorter wave-length--all the various forms of ultra-violet radiation4 ,at wave-lengths of from about a hundredth to a thousandth of the wave-length of visible light1 we come to the familiar ,x-rays1 which penetrate through inches of our flesh1 so that we can photograph the bones inside4 ,far out even beyond these1 we come to the type of radiation which constitutes the -rays1 its wave-length being of the order of #a_/aj1jjj1jjj1jjj inch1 or only about a hundred-thousandth part of the wave-length of visible light4 ,thus the -rays may be regarded as invisible radiation of extremely short wave-length4 ,we shall discuss the exact function they serve later4 ,for the moment let us merely remark that in the first instance they served the extremely useful function of fogging ,becquerel's photographic plates1 thus leading to the detection of the radio-active property of matter4 ,thus we see that the break-up of a radio-active atom may be compared to the discharge of a gun2 the -particle is the shot fired1 the -particles are the smoke1 and the -rays are the flash4 ,the atom of lead which finally remains is the unloaded gun1 and the original radio-active atom1 of uranium or what not1 was the loaded gun4 ,and the special peculiarity of radio-active guns is that they go off spontaneously and of their own accord4 ,all attempts to pull the trigger have so far failed1 or at least have led to inconclusive results2 we can only wait1 and the gun will be found to fire itself in time4 ,illustration3 ,,plate ,,xiv ,fig4 #a ,illustration3 ,p4 ,m4 ,s4 ,blackett ,fig4 #b ,collisions of -particles with ,nitrogen ,atoms ,in fig4 #a the -particle merely rebounds from a nitrogen atom4 ,in fig4 #b it drives out a proton and then joins itself to the atom ,,atomic ,,nuclei ,with the unimportant exceptions of potassium and rubidium 7of atomic numbers #ai and #cg71 the property of radio-activity occurs only in the most complex and massive of atoms1 being indeed confined to those of atomic numbers above #hc4 ,yet1 although the lighter atoms are not liable to spontaneous disintegration in the same way as the heavy radio-active atoms1 their nuclei are of composite structure1 and can be broken up by artificial means4 ,in #aibj1 ,rutherford1 using radio-active atoms as guns1 fired -particles at light atoms and found that direct hits broke up their nuclei4 ,there is1 however1 found to be a significant difference between the spontaneous disintegration of the heavy radio-active atoms1 and the artificial disintegration of the light atoms2 in the former case1 apart from the ever-present -rays and -rays1 only -particles are ejected1 while in the latter case -particles were not ejected at all1 but particles of only about a quarter their weight1 which proved to be identical with the nuclei of hydrogen atoms4 ,these sensational events in the atomic under-world can be photographed by ,professor ,c4 ,t4 ,r4 ,wilson's condensation method already explained4 ,plate ,,xiv shews two collisions of an -particle with a nitrogen atom photographed by ,mr ,p4 ,m4 ,s4 ,blackett4 ,the straight lines are merely the quite uneventful tracks of ordinary -particles similar to those already shewn in ,plate ,,xiii4 ,but one -particle track in each photograph suddenly branches1 so that the complete figure is of a ,y-shape4 ,there is little room for doubt that in fig4 #a the branch occurs because the -particle has collided with a nitrogen atom2 the stem of the ,y is the track of the -particle before the collision2 the two upper branches are the tracks of the -particle and the nitrogen atom after the collision1 the latter now moving with enormous speed and hitting everything out of its way4 ,by taking simultaneous photographs in two directions at right angles1 as shewn in the ,plate1 ,mr ,blackett was able to reconstruct the whole collision1 and the angles were found to agree exactly with those which dynamical theory would require on this interpretation of the photograph4 ,the occurrence photographed in fig4 #b is of a different type from that seen in fig4 #a1 for the angles do not agree with those which dynamical theory would require if the upper branches of the ,y were the tracks of the -particles and the nitrogen atom as in fig4 #a4 ,the stem of the ,y is still an ordinary -particle track1 but the long faint upper branch is the track of a particle smaller than an -particle1 namely a particle of quarter-weight shot out of the nucleus1 whilst the shorter and clearer branch is that of the nitrogen atom moving along in company with the -particle1 which it has captured4 ,it would take too much space to describe in full the beautiful method by which ,blackett has established this interpretation of his photographs1 but there is little room for doubt that in fig4 #b he has actually succeeded in photographing the break-up of the nucleus of an atom of nitrogen4 ,,isotopes4 ,two atoms have the same chemical properties if the charges of positive electricity carried by their nuclei are the same4 ,the amount of this charge fixes the number of electrons which can revolve around the nucleus1 this number being of course exactly that needed to neutralise the electric field of the nucleus1 and this in turn fixes the atomic number of the element4 ,but ,dr ,aston has shewn that atoms of the same chemical element1 say neon or chlorine1 may have nuclei of different weights4 ,the various forms which the atoms of the same chemical element can assume are known as isotopes1 being of course distinguished by their different weights4 ,aston further made the highly significant discovery that the weights of all atoms are1 to a very close approximation1 multiples of a single definite weight4 ,this unit weight is approximately equal to the weight of the hydrogen atom1 but is more nearly equal to a sixteenth of the weight of the oxygen atom4 ,the weight of any type of atom1 measured in terms of this unit1 is called the 8atomic weight0 of the atom4 ,,protons ,,and ,,electrons4 ,in conjunction with the results of ,rutherford's artificial disintegration of atomic nuclei1 ,aston's results have led to the general acceptance of the hypothesis that the whole universe is built up of only two kinds of ultimate bricks1 namely1 electrons and protons4 ,each proton carries a positive charge of electricity exactly equal in amount to the negative charge carried by an electron1 but has about #ahdj times the weight of the electron4 ,protons are supposed to be identical with the nucleus of the hydrogen atom1 all other nuclei being composite structures in which both protons and electrons are closely packed together4 ,for instance1 the nucleus of the helium atom1 or -particle1 consists of four protons and two electrons1 these giving it approximately four times the weight of the hydrogen atom1 and a resultant charge equal to twice that of the nucleus of the hydrogen atom4 ,yet this is not quite the whole story4 ,if it were1 every complete atom would consist of a certain number ,n of protons1 together with just enough electrons1 namely ,n1 to neutralise the electric charges on the ,n protons1 so that its ingredients would be precisely the same as those of ,n hydrogen atoms4 ,thus the weight of every atom would be an exact multiple of the weight of a hydrogen atom4 ,experiment shews this not to be the case4 ,,electromagnetic ,,energy4 ,to get at the whole truth1 we have to recognise that1 in addition to containing material electrons and protons1 the atom contains yet a third ingredient which we may describe as electromagnetic energy4 ,we may think of this1 although with something short of absolute scientific accuracy1 as bottled radiation4 ,it is a commonplace of modern electromagnetic theory that radiation of every kind carries weight about with it1 weight which is in every sense as real as the weight of a ton of coal4 ,a ray of light causes an impact on any surface on which it falls1 just as a jet of water does1 or a blast of wind1 or the fall of a ton of coal2 with a sufficiently strong light one could knock a man down just as surely as with the jet of water from a fire-hose4 ,this is not a mere theoretical prediction4 ,the pressure of light on a surface has been both detected and measured by direct experiment4 ,the experiments are extraordinarily difficult because1 judged by all ordinary standards1 the weight carried by radiation is exceedingly small2 all the radiation emitted from a #ej horse-power searchlight working continuously for a century weighs only about a twentieth of an ounce4 ,it follows that any substance which is emitting radiation must at the same time be losing weight4 ,in particular1 the disintegration of any radio-active substance must involve a decrease of weight1 since it is accompanied by the emission of radiation in the form of -rays4 ,the ultimate fate of an ounce of uranium may be expressed by the equation3 #jhfec ounce lead1 #a ounce uranium #jacde 0 helium1 #jjjjb 0 radiation4 ,the lead and helium together contain just as many electrons and just as many protons as did the original ounce of uranium1 but their combined weight is short of the weight of the original uranium by about one part in #djjj4 ,where #djjj ounces of matter originally existed1 only #ciii now remain2 the missing ounce has gone off in the form of radiation4 ,this makes it clear that we must not expect the weights of the various atoms to be exact multiples of the weight of the hydrogen atom2 any such expectation would ignore the weight of the bottled-up electromagnetic energy which is capable of being set free and going off into space in the form of radiation as the atom changes its make up4 ,the weight of this energy is relatively small1 so that the weights of the atoms may be expected to be approximately integral multiples of that of the hydrogen atom1 and this expectation is confirmed1 but they will not be so exactly4 ,the exact weight of our atomic building is not simply the total weight of all its bricks2 something must be added for the weight of the mortar--the electromagnetic energy--which keeps the bricks bound together4 ,thus the normal atom consists of protons1 electrons1 and energy1 each of which contributes something to its weight4 ,when the atom re-arranges itself1 either spontaneously or under bombardment1 protons and electrons may be shot off in the form of material particles 7- and -rays7 and energy may also be set free in the form of radiation4 ,this radiation may either take the form of -rays1 or1 as we shall shortly see1 of other forms of visible and invisible radiation4 ,the final weight of the atom will be obtained by deducting from its original weight not only the weight of all the ejected electrons and protons1 but also the weight of all the energy which has been set free as radiation4 ,,quantum ,,theory ,the series of concepts which we now approach are difficult to grasp and still more difficult to explain1 largely1 no doubt1 because our minds receive no assistance from our everyday experience of nature#aa4 ,it becomes necessary to speak mainly in terms of analogies1 parables and models which can make no claim to represent ultimate reality2 indeed it is rash to hazard a guess even as to the direction in which ultimate reality lies4 #aa ,the reader whose interest is limited to astronomy may prefer to proceed at once to ,chapter ,,iii4 ,the laws of electricity which were in vogue up to about the end of the nineteenth century--the famous laws of ,maxwell and ,faraday--required that the energy of an atom should continually decrease1 through the atom scattering energy abroad in the form of radiation1 and so having less and less left for itself4 ,these same laws predicted that all energy set free in space should rapidly transform itself into radiation of almost infinitesimal wave-length4 ,yet these things simply did not happen1 making it obvious that the then prevailing electrodynamical laws had to be given up4 ,,cavity-,,radiation4 ,a crucial case of failure was provided by what is known as 8cavity-radiation40 ,a body with a cavity in its interior is heated up to incandescence2 no notice is taken of the light and heat emitted by its outer surface1 but the light imprisoned in the internal cavity is let out through a small window and analysed into its constituent colours by a spectroscope or diffraction grating4 ,it is this radiation that is known as 8cavity-radiation40 ,it represents the most complete form of radiation possible1 radiation from which no colour is missing1 and in which every colour figures at its full strength4 ,no known substance ever emits quite such complete radiation from its surface1 although many approximate to doing so4 ,we speak of such bodies as 8full radiators40 ,the nineteenth-century laws of electromagnetism predicted that the whole of the radiation emitted by a full radiator or from a cavity ought to be found at or beyond the extreme violet end of the spectrum1 independently of the precise temperature to which the body had been heated4 ,in actual fact the radiation is usually found piled up at exactly the opposite end of the spectrum1 and in no case does it ever conform to the predictions of the nineteenth-century laws1 or even begin to think of doing so4 ,in the year #aijj1 ,professor ,planck of ,berlin discovered experimentally the law by which 8cavity-radiation0 is distributed among the different colours of the spectrum4 ,he further shewed how his newly discovered law could be deduced theoretically from a system of electromagnetic laws which differed very sensationally from those then in vogue4 ,planck imagined all kinds of radiation to be emitted by systems of vibrators which emitted light when excited1 much as tuning forks emit sound when they are struck4 ,the old electrodynamical laws predicted that each vibration should gradually come to rest and then stop1 as the vibrations of a tuning fork do1 until the vibrator was in some way excited again4 ,rejecting all this1 ,planck supposed that a vibrator could change its energy by sudden jerks1 and in no other way2 it might have one1 two1 three1 four or any other integral number of units of energy1 but no intermediate fractional numbers1 so that gradual changes of energy were rendered impossible4 ,the vibrator1 so to speak1 kept no small change1 and could only pay out its energy a shilling at a time until it had none left4 ,not only so1 but it refused to receive small change1 although it was prepared to accept complete shillings4 ,this concept1 sensational1 revolutionary and even ridiculous1 as many thought it at the time1 was found to lead exactly to the distribution of colours actually observed in cavity-radiation4 ,in #aiag1 ,einstein put the concept into the more precise form which now prevails4 ,according to a theory previously advanced by ,professor ,niels ,bohr of ,copenhagen1 an atomic or molecular structure does not change its configuration1 or dissipate away its energy1 by gradual stages4 ,gradualness is driven out of physics1 and discontinuity takes its place4 ,an atomic structure has a number of possible states or configurations which are entirely distinct and detached one from another1 just as a weight placed on a staircase has only a possible number of positions2 it may be #c stairs up1 or #d or #e1 but cannot be #c or #c stairs up4 ,the change from one position to another is generally effected through the medium of radiation4 ,the system can be pushed upstairs by absorbing energy from radiation which falls on it1 or may move downstairs to a state of lower energy and emit energy in the form of radiation in so doing4 ,only radiation of a certain definite colour1 and so of a certain precise wave-length1 is of any account for effecting a particular change of state4 ,the problem of shifting an atomic system is like that of extracting a box of matches from a penny-in-the-slot machine2 it can only be done by a special implement1 to wit a penny1 which must be of precisely the right size and weight--a coin which is either too small or too large1 too light or too heavy1 is doomed to fail4 ,if we pour radiation of the wrong wave-length on to an atom1 we may reproduce the comedy of the millionaire whose total wealth will not procure him a box of matches because he has not a loose penny1 or we may reproduce the tragedy of the child who cannot obtain a slab of chocolate because its hoarded wealth consists of farthings and half-pence1 but we shall not disturb the atom4 ,when mixed radiation is poured on to a collection of atoms1 these absorb the radiation of just those wave-lengths which are needed to change their internal states1 and none other2 radiation of all other wave-lengths passes by unaffected4 ,this selective action of the atom on radiation is put in evidence in a variety of ways2 it is perhaps most simply shewn in the spectra of the sun and stars4 ,dark lines similar to those which ,fraunhofer observed in the solar spectrum are observed in the spectra of practically all stars 7see ,plate ,,viii1 p4 #ea71 and we can now understand why this must be4 ,light of every possible wave-length streams out from the hot interior of a star1 and bombards the atoms which form its atmosphere4 ,each atom drinks up that radiation which is of precisely the right wave-length for it1 but has no interaction of any kind with the rest1 so that the radiation which is finally emitted from the star is deficient in just the particular wave-lengths which suit the atoms4 ,thus the star shews an absorption spectrum of fine lines4 ,the positions of these lines in the spectrum shew what types of radiation the stellar atoms have swallowed1 and so enable us to identify the atoms from our laboratory knowledge of the tastes of different kinds of atoms for radiation4 ,but what ultimately decides which types of radiation an atom will swallow1 and which it will reject8 ,planck had already supposed that radiation of each wave-length has associated with it a certain amount of energy1 called the 8quantum10 which depends on the wave-length and on nothing else4 ,the quantum is supposed to be proportional to the 8frequency0 7p4 #aae71 or number of vibrations of the radiation per second#ab1 and so is inversely proportional to the wave-length of the radiation--the shorter the wave-length1 the greater the energy of the quantum1 and conversely4 ,red light has feeble quanta1 violet light has energetic quanta1 and so on4 #ab ,to be precise1 if v is the frequency of the radiation1 its quantum of energy is hv1 where h is a universal constant of nature1 known as ,planck's constant4 ,this constant is of the physical nature of energy multiplied by time2 its numerical value is3 #fee #aj ergs seconds4 ,einstein now supposes that radiation of a given type can effect an atomic or molecular change1 only if the energy needed for the change is precisely equal to that of a single quantum of the radiation4 ,this is commonly known as ,einstein's law2 it determines the precise type of radiation needed to work any atomic or molecular penny-in-the-slot mechanism#ac4 #ac ,in the form of an equation3 ,e - ,e h1 where ,e1 ,e are the energies of the material system before and after the change1 is the frequency of the radiation1 and h is ,planck's constant already specified4 ,we notice that work which demands one powerful quantum cannot be performed by two1 or indeed by any number whatever1 of feeble quanta4 ,a small amount of violet 7high-frequency7 light can accomplish what no amount of red 7low-frequency7 light can effect--a circumstance with which every photographer is painfully familiar2 we can admit as much red light as we please without any damage being done1 but even the tiniest gleam of violet light spoils our plates4 ,the law prohibits the killing of two birds with one stone1 as well as the killing of one bird with two stones2 the whole quantum is used up in effecting the change1 so that no energy from this particular quantum is left over to contribute to any further change4 ,this aspect of the matter is illustrated by ,einstein's photochemical law3 8in any chemical reaction which is produced by the incidence of light1 the number of molecules which are affected is equal to the number of quanta of light which are absorbed40 ,those who manage penny-in-the-slot machines are familiar with a similar law3 8the number of articles sold is exactly equal to the number of coins in the machine40 ,if we think of energy in terms of its capacity for doing damage1 we see that radiation of short wave-length can work more destruction in atomic structures than radiation of long wave-length4 ,radiation of sufficiently short wave-length may not only re-arrange molecules or atoms2 it may break up any atom on which it happens to fall1 by shooting out one of its electrons1 giving rise to what is known as photoelectric action4 ,again there is a definite limit of frequency1 such that light whose frequency is below this limit does not produce any effect at all1 no matter how intense it may be2 whereas as soon as we pass to frequencies above this limit1 light of even the feeblest intensity starts photoelectric action at once4 ,again the absorption of one quantum breaks up only one atom1 and further ejects only one electron from the atom4 ,if the radiation has a frequency above this limit1 so that its quantum has more energy than the minimum necessary to remove a single electron from the atom1 the whole quantum is still absorbed1 the excess energy now being used in endowing the ejected electron with motion4 ,,electron ,,orbits4 ,these concepts are based upon ,bohr's supposition that only a limited number of orbits are open to the electrons in an atom1 all others being prohibited for reasons which we still do not fully understand1 and that an electron is free to move from one permitted orbit to another under the stimulus of radiation4 ,bohr himself investigated the way in which the various permitted orbits are arranged4 ,modern investigations indicate the need for a good deal of revision of his simple concepts1 but we shall discuss these in some detail1 partly because ,bohr's picture of the atom still provides the best working mechanical model we have1 and partly because an understanding of his simple theory is absolutely essential to the understanding of the far more intricate theories which are beginning to replace it4 ,the hydrogen atom1 as we have already seen1 consists of a single proton as central nucleus1 with a single electron revolving around it4 ,the nucleus1 with about #ahdj times the weight of the electron1 stands practically at rest unagitated by the motion of the latter1 just as the sun remains practically undisturbed by the motion of the earth round it4 ,the nucleus and electron carry charges of positive and negative electricity1 and therefore attract one another2 this is why the electron describes an orbit instead of flying off in a straight line1 again like the earth and sun4 ,furthermore1 the attraction between electric charges of opposite sign1 positive and negative1 follows1 as it happens1 precisely the same law as gravitation1 the attraction falling off as the inverse square of the distance between the two charges4 ,thus the nucleus-electron system is similar in all respects to a sun-planet system1 and the orbits which an electron can describe around a central nucleus are precisely identical with those which a planet can describe about a central sun2 they consist of a system of ellipses each having the nucleus in one focus 7p4 #df74 ,yet the general concepts of quantum-dynamics prohibit the electron from moving in all these orbits indiscriminately4 ,according to ,bohr1 the electron of the hydrogen atom can move in a certain number of circular orbits whose diameters are proportional to the squares of the natural numbers #a1 #d1 #i1 #af1 #be1 4442 it can also move in a series of elliptic orbits whose greatest diameters are respectively equal to the diameters of the possible circular orbits1 although these elliptic orbits are still further limited by the condition that their eccentricities must have certain definite values4 ,all other orbits are in some way prohibited4 ,the smallest orbits which the electron can describe in the hydrogen atom are shewn in fig4 #aj4 ,the smallest orbit of all1 of diameter #a1 is marked #a2 beyond this come two orbits of diameter #d marked #b #b2 then three orbits of diameter #i marked #c1 #c1 #c2 and four orbits of diameter #af marked #d1 #d1 #d1 #d4 ,the diagram stops here for want of space1 but the available orbits go on indefinitely4 ,even under laboratory conditions1 electrons may move in orbits of a hundred times the diameter of that marked #a4 ,under the more rarefied conditions of stellar atmospheres the hydrogen atom may swell out to even greater dimensions1 and stellar spectra provide evidence of orbits having over a thousand times the dimensions of the #a orbit4 ,such an orbit would be represented in fig4 #aj by a circle four yards in diameter4 ,illustration3 ,fig4 #aj4 ,the arrangement of electron orbits in the hydrogen atom 7,bohr's model74 ,all orbits1 whether elliptic or circular1 which have the same diameter1 have also the same energy1 but the energy changes when an electron crosses over from any orbit to another of a different diameter4 ,thus1 to a certain limited extent1 the atom constitutes a reservoir of energy4 ,its changes of energy are easily calculated2 for example1 the two orbits of smallest diameters in the hydrogen atom differ in energy by #af #aj ergs4 ,if we pour radiation of the appropriate wave-length on to an atom in which the electron is describing the smallest orbit of all1 it crosses over to the next orbit1 absorbing #af #aj ergs of energy in the process1 and so becoming temporarily a reservoir of energy holding #af #aj ergs4 ,if the atom is in any way disturbed from outside1 it may of course discharge the energy at any time1 or it may absorb still more energy and so increase its store4 ,if we know all the orbits which are possible for an atom of any type1 it is easy to calculate the changes of energy involved in the various transitions between them4 ,as each transition absorbs or releases exactly one quantum of energy1 we can immediately deduce the frequencies of the light emitted or absorbed in these transitions4 ,in brief1 given the arrangement of atomic orbits1 we can calculate the spectrum of the atom4 ,in practice the problem of course takes the converse form3 given the spectrum1 to find the structure of the atom which emits it4 ,bohr's model of the hydrogen atom is a good model at least to this extent--that the spectrum it would emit reproduces the hydrogen spectrum almost exactly4 ,yet the agreement is not quite perfect1 and it is now generally accepted that ,bohr's scheme of orbits is inadequate to account for actual spectra4 ,we continue to discuss ,bohr's scheme1 not because the atom is actually built that way1 but because it provides a good enough working model for our present purpose4 ,an essential1 although at first sight somewhat unexpected1 feature of the whole theory is that even if the hydrogen atom charged with its #af #aj ergs of energy is left entirely undisturbed1 the electron must1 after a certain time1 lapse back spontaneously to its original smaller orbit1 ejecting its #af #aj ergs of energy in the form of radiation in so doing4 ,einstein shewed that1 if this were not so1 then ,planck's well-established 8cavity-radiation0 law could not be true4 ,thus a collection of hydrogen atoms in which the electrons describe orbits larger than the smallest possible orbit is similar to a collection of uranium or other radio-active atoms1 in that the atoms spontaneously fall back to their states of lower energy as the result merely of the passage of time4 ,the electron orbits in more complicated atoms have much the same general arrangement as in the hydrogen atom1 but are different in size4 ,in the hydrogen atom the electron normally falls1 after sufficient time1 to the orbit of lowest energy and stays there4 ,it might be thought by analogy that in more complicated atoms in which several electrons are describing orbits1 all the electrons would in time fall into the orbit of lowest energy and stay there4 ,such does not prove to be the case4 ,there is never room for more than one electron in the same orbit4 ,this is a special aspect of a general principle which appears to dominate the whole of physics4 ,it has a name--8the exclusion-principle0--but this is about all as yet2 we have hardly begun to understand it4 ,in another of its special aspects it becomes identical with the old familiar corner-stone of science which asserts that two different pieces of matter cannot occupy the same space at the same time4 ,without understanding the underlying principle1 we can accept the fact that two electrons not only cannot occupy the same space1 but cannot even occupy the same orbit4 ,it is as though in some way the electron spread itself out so as to occupy the whole of its orbit1 thus leaving room for no other4 ,no doubt this must not be accepted as a literal picture of things1 and yet it seems not improbable that the orbits of lowest energy in the hydrogen atom are possible orbits just because the electron can completely fill them1 and that adjacent orbits are impossible because the electron would fill them or #a times over1 and similarly for more complicated atoms4 ,in this connection it is perhaps significant that no single known phenomenon of physics makes it possible to say that at a given instant an electron is at such or such a point in an orbit of lowest energy2 such a statement appears to be quite meaningless1 and the condition of an atom is apparently specified with all possible precision by saying that at a given instant an electron is in such an orbit1 as it would be1 for instance1 if the electron had spread itself out into a ring4 ,we cannot say the same of other orbits4 ,as we pass to orbits of higher energy1 and so of greater diameter1 the indeterminateness gradually assumes a different form1 and finally becomes of but little importance4 ,whatever form the electron may assume while it is describing a little orbit near the nucleus1 by the time it is describing a very big orbit far out it has become a plain material particle charged with electricity4 ,thus1 whatever the reason may be1 electrons which are describing orbits in the same atom must all be in different orbits4 ,the electrons in their orbits are like men on a ladder2 just as no two men can stand on the same rung1 so no two electrons can ever follow one another round in the same orbit4 ,the neon atom1 for instance1 with #aj electrons1 is in its normal state of lowest energy when its #aj electrons each occupy one of the #aj orbits whose energy is lowest4 ,for reasons which the quantum theory has at last succeeded in elucidating1 there are1 in every atom1 two orbits in which the energy is equal and lower than in any other orbit4 ,after this come eight orbits of equal but substantially higher energy1 then #ah orbits of equal but still higher energy1 and so on4 ,as the electrons in each of these various groups of orbits all have equal energy1 they are commonly spoken of1 in a graphic but misleading phraseology1 as rings of electrons4 ,they are designated the ,k-ring1 the ,l-ring1 the ,m-ring and so on4 ,the ,k-ring1 which is nearest to the nucleus1 has room for two electrons only4 ,any further electrons are pushed out into the ,l-ring1 which has room for eight electrons1 all describing orbits which are different but of equal energy4 ,if still more electrons remain to be accommodated they must go into the ,m-ring and so on4 ,in their normal states1 the hydrogen atom has one electron in its ,k-ring1 while the helium atom has two1 the ,l1 ,m1 and higher rings being unoccupied4 ,the atom of next higher complexity1 the lithium atom1 has three electrons1 and as only two can be accommodated in its ,k-ring1 one has to wander round in the outer spaces of the ,l-ring4 ,in beryllium with four electrons1 two are driven out into the ,l-ring4 ,and so it goes on1 until we reach neon with #aj electrons1 by which time the ,l-ring as well as the inner ,k-ring is full up4 ,in the next atom1 sodium1 one of the #aa electrons is driven out into the still more remote ,m-ring1 and so on4 ,provided the electrons are not being excited by radiation or other stimulus1 each atom sinks in time to a state in which its electrons are occupying its orbits of lowest energy1 one in each4 ,so far as our experience goes1 an atom1 as soon as it reaches this state1 becomes a true perpetual motion machine1 the electrons continuing to move in their orbits 7at any rate on ,bohr's theory7 without any of the energy of their motion being dissipated away1 either in the form of radiation or otherwise4 ,it seems astonishing and quite incomprehensible that an atom in such a state should not be able to yield up its energy still further1 but1 so far as our experience goes1 it cannot4 ,and this property1 little though we understand it1 is1 in the last resort1 responsible for keeping the universe in being4 ,if no restriction of this kind intervened1 the whole material energy of the universe would disappear in the form of radiation in a few thousand-millionth parts of a second4 ,if the normal hydrogen atom were capable of emitting radiation in the way demanded by the nineteenth-century laws of physics1 it would1 as a direct consequence of this emission of radiation1 begin to shrink at the rate of over a metre a second1 the electron continually falling to orbits of lower and lower energy4 ,after about a thousand-millionth part of a second the nucleus and the electron would run into one another1 and the whole atom would probably disappear in a flash of radiation4 ,by prohibiting any emission of radiation except by complete quanta1 and by prohibiting any emission at all when there are no quanta available for dissipation1 the quantum theory succeeds in keeping the universe in existence as a going concern4 ,it is difficult to form even the remotest conception of the realities underlying all these phenomena4 ,the recent branch of physics known as 8wave-mechanics0 is at present groping after an understanding1 but so far progress has been in the direction of co-ordinating observed phenomena rather than in getting down to realities4 ,indeed it may be doubted whether we shall ever properly understand the realities ultimately involved2 they may well be so fundamental as to be beyond the grasp of the human mind4 ,it is just for this reason that modern theoretical physics is so difficult to explain1 and so difficult to understand4 ,it is easy to explain the motion of the earth round the sun in the solar system4 ,we see the sun in the sky2 we feel the earth under our feet1 and the concept of motion is familiar to us from everyday experience4 ,how different when we try to explain the analogous motion of the electron round the proton in the hydrogen atom6 ,neither you nor ,i have any direct experience of either electrons or protons1 and no one has so far any inkling of what they are really like4 ,so we agree to make a sort of model in which the electron and proton are represented by the simplest things known to us1 tiny hard spheres4 ,the model works well for a time and then suddenly breaks in our hands4 ,in the new light of the wave-mechanics1 the hard sphere is seen to be hopelessly inadequate to represent the electron4 ,a hard sphere has always a definite position in space2 the electron apparently has not4 ,a hard sphere takes up a very definite amount of room1 an electron--well1 it is probably as meaningless to discuss how much room an electron takes up as it is to discuss how much room a fear1 an anxiety or an uncertainty takes up1 but if we are pressed to say how much room an electron takes up1 perhaps the best answer is that it takes up the whole of space4 ,a hard sphere moves from one point to the next2 our model electron1 jumping from orbit to orbit in the model hydrogen atom certainly does not behave like any hard sphere of our waking experience1 and the real electron--if there is any such thing as a real electron in an atom--probably even less4 ,yet as our minds have so far failed to conceive any better picture of the atom than this very imperfect model1 we can only proceed by describing phenomena in terms of it4 ,,the ,,mechanical ,,effects ,,of ,,radiation ,the more compact an electrical structure is1 the greater the amount of energy necessary to disturb it2 and1 as this energy must be supplied in the form of a single quantum1 the greater the energy of the quantum must be1 and so the shorter the wave-length of the radiation4 ,a very compact structure can only be disturbed by radiation of very short wave-length4 ,a ship heading into a rough sea runs most risk of damage1 and its passengers most risk of discomfort1 when its length is about equal to the length of the waves4 ,short waves disturb a short ship and long waves a long ship1 but a long swell does little harm to either4 ,but this provides no real analogy with the effects of radiation1 since the wave-length of radiation which breaks up an electrical structure is hundreds of times the size of the structure4 ,the nautical analogy to such radiation is a very long swell indeed4 ,as a rough working guide we may say that an electrical structure will only be disturbed by radiation whose wave-length is about equal to #hfj times the dimensions of the structure1 and will only be broken up by radiation whose wave-length is below this limit#ad4 ,in brief1 the reason why blue light affects photographic plates1 while red light does not1 is that the wave-length of blue light is less1 and that of red light is greater1 than #hfj times the diameter of the molecule of silver bromide2 we must get below the 8#hfj-limit0 before anything begins to happen4 #ad ,the mathematician will readily see the reason for this rule1 which is1 in brief1 as follows3 the energy needed to separate two electric charges e and - e1 at a distance r apart1 is e_/r1 and the energy needed to re-arrange or break up a structure of electrons and protons of linear dimensions r will generally be comparable with this4 ,if is the wave-length of the requisite radiation1 the energy made available by the absorption of this radiation is the quantum h,c_/4 ,combining this with the circumstance that the value of h is very approximately e #hfj ----------1 ,c we find that the requisite wave-length of radiation is about #hfj times the dimensions of the structure to be broken up4 ,when an atom discharges its reservoir of stored energy1 the light it emits has necessarily the same wave-length as the light which it absorbed in originally storing up this energy2 the two quanta of energy being equal1 their wave-lengths are the same4 ,it follows that the light emitted by any electrical structure will also have a wave-length of about #hfj times the dimensions of the structure4 ,ordinary visible light is emitted mainly by atoms1 and so has a wave-length equal to about #hfj atomic diameters4 ,indeed it is just because it has this wave-length that the light acts on the atoms of our retina1 and so is visible4 ,radiation of this wave-length disturbs only the outermost electrons in an atom1 but radiation of much shorter wave-length may have much more devastating effects2 ,x-radiation1 for instance1 may break up the far more compact inner rings of electrons1 the ,k-ring1 ,l-ring1 etc41 of the atomic structure4 ,radiation of still shorter wave-length may even disturb the protons and electrons of the nucleus4 ,for the nuclei1 like the atoms themselves1 are structures of positive and negative electrical charges1 and so must behave similarly with respect to the radiation falling upon them1 except for the wide difference in the wave-length of the radiation4 ,ellis and others have found that the -radiation emitted during the disintegration of the atoms of the radio-active element radium-,b has wave-lengths of #ceb1 #dbj1 #dhj1 #eac1 and #bc #aj cms4 ,these wave-lengths are only about a hundred-thousandth part of those of visible light1 the reason being that the atomic nucleus has only about a hundred-thousandth part the dimensions of the complete atom4 ,radiation of such wave-lengths ought to be just as effective in re-arranging the nucleus of radium-,b as that of #ajj1jjj times longer wave-length is effective in re-arranging the hydrogen atom4 ,since the wave-length of the radiation absorbed or emitted by an atom is inversely proportional to the quantum of energy1 the quantum needed to 8work0 the atomic nucleus must have something like #ajj1jjj times the energy of that needed to 8work0 the atom4 ,if the hydrogen atom is a penny-in-the-slot machine1 nothing less than five-hundred-pound notes will work the nuclei of the radio-active atoms4 ,the radio-active nuclei1 like those of nitrogen and oxygen1 could probably be broken up by a sufficiently intense bombardment1 although the experimental evidence on this point is not very definite4 ,if so1 each bombarding particle would have to bring to the attack an energy of motion equal at least to that of one quantum of the radiation in question1 this requiring it to move with an enormously high speed4 ,matter at sufficiently high temperatures contains an abundant supply both of quanta of high energy1 and of particles moving with high speeds4 ,,temperature-,,radiation4 ,we speak in ordinary life of a red-heat or a white-heat1 meaning the heat to which a substance must be raised to emit red or white light respectively4 ,the filament in a carbon-filament lamp is said to be raised to a red-heat1 that in a gas-filled lamp to a yellow-heat4 ,it is not necessary to specify the substance we are dealing with2 if carbon emits a red light at a temperature of #cjjj1 then tungsten or any other substance1 raised to this same temperature1 will emit exactly the same red light as the carbon1 and the same is true for other colours of radiation4 ,thus each colour1 and so also each wave-length of radiation1 has a definite temperature associated with it1 this being the temperature at which this particular colour is most abundant in the spectroscopic analysis of the light emitted by a hot body4 ,as soon as this particular temperature begins to be approached1 but not before1 radiation of the wave-length in question becomes plentiful2 at temperatures well below this it is quite inappreciable#ae4 #ae ,the wave-length of the radiation and the associated temperature ,t 7measured in ,centigrade degrees absolute7 are connected through the well-known relation3 ,t #jbhee cm4 degree4 ,just as we speak of a red-heat or a white-heat1 we might1 although we do not do so1 quite legitimately speak of an ,x-ray heat or a -ray heat4 ,the shorter the wave-length of the radiation1 the higher the temperature specially associated with it4 ,thus as we make a substance hotter and hotter1 it emits light of ever shorter wave-length1 and runs in succession through the whole rainbow of colours--red1 orange1 yellow1 green1 blue1 indigo1 violet4 ,we cannot command a sufficient range of temperature to perform the complete experiment in the laboratory1 but nature performs it for us in the stars4 ,,the ,,effects ,,of ,,heat4 ,we have already seen that radiation of short wave-length is needed to break up an electric structure of small dimensions4 ,as short wave-lengths are associated with high temperatures1 it now appears that the smaller an electrical structure is1 the greater the heat needed to break it up4 ,and we can calculate the temperature at which an electric structure of given dimensions will first begin to break up under the influence of heat#af4 #af ,on combining the relation just given between ,t and with that implied in the rough law of the 8#hfj-limit10 we find that a structure whose dimensions are r cms4 will begin to be broken up by temperature-radiation when the temperature first approaches _/r degrees4 ,for instance1 an ordinary atom with a diameter of about #d #aj cms4 will first be broken up at temperatures of the order of thousands of degrees4 ,to take a definite example1 yellow light of wave-length #jjjjjf cm4 is specially associated with the temperature #dhjj degrees2 this temperature represents an average 8yellow-heat40 ,at temperatures well below this1 yellow light only occurs when it is artificially created4 ,but stars1 and all other bodies1 at a temperature of #dhjj degrees emit yellow light naturally1 and show lines in the yellow region of their spectrum1 because yellow light removes the outermost electron from the atoms of calcium and similar elements4 ,the electrons in the calcium atom begin to be disturbed when a temperature of #dhjj degrees begins to be approached1 but not before4 ,this temperature is not approached on earth 7except in the electric arc and other artificial conditions71 so that terrestrial calcium atoms are generally at rest in their states of lowest energy4 ,to take another instance1 the shortest wave-length of radiation emitted in the transformation of uranium is about #je #aj cms41 and this corresponds to the enormously high temperature of #e1hjj1jjj1jjj degrees4 ,when some such temperature begins to be approached1 but not before1 the constituents of the radio-active nuclei ought to begin to re-arrange themselves1 just as the constituents of the calcium atom do when a temperature of #dhjj degrees is approached#ag4 ,this of course explains why no temperature we can command on earth has any appreciable effect in expediting or inhibiting radio-active disintegration4 #ag ,if we suppose that re-arrangements of an electric structure can also be effected by bombarding it with material particles1 the temperature at which bombardment by electrons1 nuclei1 or molecules first becomes effective is about the same as that at which radiation of the effective wave-length would first begin to be appreciable2 the two processes begin at approximately the same temperature4 ,the table on p4 #add shews the wave-lengths of the radiation necessary to effect various atomic transformations4 ,the last two columns shew the corresponding temperatures1 and the kind of place1 so far as we know1 where this temperature is to be found1 these latter entries anticipating certain results which will be given in detail in ,chapter ,v below 7p4 #bhh74 ,in places where the temperature is far below that mentioned in the last column but one1 the transformation in question cannot be affected by heat1 and so can only occur spontaneously4 ,thus it is entirely a one-way process4 ,the available radiation not being of sufficiently short wave-length to work the atomic slot machine1 the atoms absorb no energy from the surrounding radiation and so are continually slipping back into states of lower energy1 if such exist4 ,,highly ,,penetrating ,,radiation ,the shortest wave-lengths we have so far had under discussion are those of the -rays1 but the last line of the table refers to radiation with a wave-length of only about a four-hundredth part of that of the shortest of -rays4 ,since #aijb1 various investigators1 ,rutherford1 ,cooke1 ,mc,lennan1 ,burton1 ,kolhrster and ,millikan in particular1 have found that the earth's atmosphere is continually being traversed by radiation which has enormously higher penetrating power than any known -rays4 ,by sending up balloons to great heights1 ,hess1 ,kolhrster1 and later ,millikan and ,bowen1 have shewn that the radiation is noticeably more intense at great heights1 thus proving that it comes into the earth's atmosphere from outside4 ,if the radiation had its origin in the sun and stars1 the main part of the radiation received on earth would come from the sun1 and the radiation would be more intense by day than by night4 ,this is found not to be the case1 so that the radiation cannot come from the stars1 and so must originate in nebulae or cosmic masses other than stars4 ,millikan is confident that its sources lie outside the galactic system4 ,the ,mechanical ,effects of ,radiation ---------------------------------------- ----------------------- ,wave-lengths ,nature of ,effect on ,atom ,temperature ,where 7cms47 ,radiation 7deg4 abs47 found ---------------------------------------- ----------------------- #gejj #aj ,visible ,disturbs #c1hej ,stellar to light outermost to atmospheres #cgej #aj electrons #g1gjj #bej #aj ,x-rays ,disturbs inner #aae1jjj ,stellar to electrons to interiors #aj #bi1jjj1jjj #e #aj ,soft ,strip off all #eh1jjj1jjj ,central to -rays or nearly all to regions of #aj electrons #bij1jjj1jjj;dense stars #d #aj -rays of ,disturbs nuclear #gbj1jjj1jjj 8 radium-,b arrangement #e #aj ,shortest ---- #e4h #aj -rays #ac #aj ,highly ,annihilation or #b4b #aj penetrating creation of radiation proton and 787 accompanying electron ---------------------------------------- ----------------------- ,the amount of the radiation is very great4 ,even at sea-level1 where it is least1 ,millikan and ,cameron find that it breaks up about #ad atoms in every cubic centimetre of air each second4 ,it must break up millions of atoms in each of our bodies every second--and we do not know what its physiological effects may be4 ,the total energy of the radiation received on earth is just about a tenth of that of the total radiation1 light and heat together1 received from all the stars4 ,this does not mean that light and heat are ten times as abundant as this radiation in the universe as a whole4 ,for if the radiation originates in extra-galactic regions1 then the stars which send us light and heat are comparatively near1 while the sources of the highly penetrating radiation are far more remote4 ,on taking an average through the whole of space1 including the vast stretches of internebular space1 it seems likely that the highly penetrating radiation is far more plentiful than stellar light and heat1 and so is the most abundant form of radiation in the whole universe4 ,it is the most penetrating form of radiation known4 ,ordinary light will hardly pass through metals or solid substances at all2 only a tiny fraction emerges through the thinnest of gold-leaf4 ,on account of their shorter wave-length1 and so of their more energetic quanta1 ,x-rays will pass through foils of a few millimetres thickness of gold or of lead4 ,the most highly penetrating -rays from radium-,b will pass through inches of lead4 ,the radiation we have just been discussing varies in penetrating power2 the most penetrating part of it will pass through #af feet of lead4 ,it is not altogether clear whether the radiation is of the nature of very short -radiation or is of a corpuscular nature1 like -radiation2 it may even be a mixture of both4 ,its penetrating power far exceeds that of any known -radiation1 so that if it is corpuscular1 the corpuscles must be moving with very nearly the velocity of light4 ,if1 as seems far more likely1 the radiation is1 in part at least1 of the nature of -radiation1 then it ought to be possible to determine its wave-length from its penetrating power4 ,until quite recently different theories on the relation between the two have been in the field4 ,the latest theory of all1 that of ,klein and ,nishina1 which is more perfect and more complete than any of the earlier theories1 assigns to the most penetrating part of the radiation the amazingly short wave-length of #ac #aj cms41 as indicated in the table on p4 #add4 ,we perhaps get the clearest conception of what this means if we apply the #hfj-rule2 this shews that the radiation would break up an electric structure whose dimensions are only about #aj cms4 ,no structure formed of electrons and protons can possibly be as small as this1 for the radius of a single electron is about #b #aj cms4 ,the radiation is of about the wave-length needed to break up the proton itself1 the smallest and most compact structure known to science4 ,approaching the problem from another angle1 the numerical relations already given shew that a quantum of radiation of this wave-length must have energy equal to #jjjae erg1 and so must have a weight of about #aff #aj grammes4 ,every physicist recognises this weight at once1 for the best determinations give the weight of the hydrogen atom as #affb #aj grammes4 ,the quantum of highly penetrating radiation has1 then1 just about the weight1 and just about the energy1 that would result from a complete hydrogen atom suddenly being annihilated and having all its energy set free as radiation4 ,it can hardly be supposed that all the highly penetrating radiation received on earth has its origin in the annihilation of hydrogen atoms4 ,if for no other reason1 there are probably not enough hydrogen atoms in the universe for such a hypothesis to be tenable4 ,the hydrogen atom consists of a proton and an electron1 and its weight is roughly the same as the combined weight of a proton and an electron selected from any atom in the universe1 so that1 to a near enough approximation1 the quantum of highly penetrating radiation has the wave-length and energy which would result from a proton and electron in any atom whatever coalescing and annihilating one another4 ,we have seen how the weights of the different known types of atoms approximate to integral multiples of the weight of the hydrogen atom1 or to be more precise1 differ by almost exactly equal steps1 each of which is about equal to the weight of the hydrogen atom4 ,the weight of the quantum of highly penetrating radiation is equal to the change of weight represented by a single step1 so that the quantum could be produced by any transformation which degraded the weight of an atom by a single step4 ,in the most general case possible1 this degradation of weight must1 so far as we can see1 arise from the coalescence of a proton and electron1 with the resulting annihilation of both4 ,while this seems far and away the most probable source of this radiation1 it is not the only conceivable source4 ,for instance1 the most abundant isotope of xenon1 of atomic number #ed and atomic weight #abi1 is built up of #abi protons1 #ge nuclear electrons and #ed orbital electrons4 ,the sudden building up of such an atom out of #abi protons and #abi electrons would involve a loss of weight just about equal to the weight of the hydrogen atom4 ,if the building took place absolutely simultaneously1 so that the whole of the liberated energy was emitted catastrophically as a single quantum1 this quantum would have about the same wave-length and penetrating power as the observed highly penetrating radiation4 ,some time ago ,millikan suggested the formation of other complex atoms out of simpler constituents as a possible source of the radiation1 but it now appears that the schemes he propounded would not result in radiation of sufficiently short wave-length1 at any rate if the modern ,klein-,nishina theory is correct4 ,on the physical evidence alone1 such schemes cannot be dismissed as impossible1 but they must be treated as suspect on account of their high improbability4 ,the xenon atom with its #beh constituent parts is a highly complicated structure1 and it is exceedingly hard to believe that all these #beh parts could be hammered into a fully-formed atom by a single instantaneous act1 accompanied by the catastrophic emission of only one quantum of radiation4 ,if atoms ever are built up out of simpler constituents--and there is no evidence whatever that this process ever occurs in nature--it seems so much more likely that the aggregation would take place by distinct stages1 and that the radiation would be emitted in a number of small quanta rather than in one large quantum4 ,moreover1 any such hypothesis has to explain the numerical agreement of the calculated weight of the observed quanta of radiation with the known weight of the hydrogen atom as a pure coincidence4 ,not only so1 but also we have to suppose that atoms of xenon1 and possibly others of approximately the same atomic weight1 are formed far more frequently than atoms of other atomic weights4 ,indeed the amount of the highly penetrating radiation received on earth is so great that if it were evidence of the creation of xenon1 a large part of the universe ought already to consist of xenon1 mixed perhaps with elements of nearly equal atomic weight4 ,so far is this from being the case1 that xenon and its neighbours in the atomic weight table are among the rarest of elements4 ,for these reasons1 and on the general principle that the simpler and more natural hypothesis is always to be given preference in science1 we may say that the annihilation of electrons and protons forms a more probable and more acceptable origin for the observed highly penetrating radiation4 ,we may leave the problem in this state of uncertainty for the present1 because it will appear later that astronomy has some evidence to give on the question4 ,,chapter ,,iii ,exploring in ,time ,we have explored space to the furthest depths to which our telescopes can probe2 we have explored into the intricacies of the minute structures we call atoms1 of which the whole material universe is built2 we now wish to go exploring in time4 ,man's individual span of life1 and indeed the whole span of time covered by our historical records--some few thousands of years at most--are both far too short to be of any service for our purpose4 ,we must find far longer measuring rods with which to sound the depths of past time and to probe forward into the future4 ,our general method will be one which the study of geology has already made familiar4 ,undeterred by the absence of direct historical evidence1 the geologist insists that life has existed on earth for millions of years1 because fossil remains of life are found to occur under deposits which1 he estimates1 must have taken millions of years to accumulate4 ,as he digs down through different strata in succession1 he is exploring in time just as truly as the geographer who travels over the surface of the earth is exploring in space4 ,a similar method can be used by the astronomer4 ,we find some astronomical effect1 quality1 or property1 which exhibits a continual accumulation or decrease1 like the sand in the bottom or top half of the hour-glass2 we estimate the rate at which this increase or decrease is occurring at the present moment1 and also1 if we can1 the rate at which it must have occurred under the different conditions prevailing in the past4 ,it then becomes a question1 perhaps of mere arithmetic1 although possibly of more complicated mathematics1 to estimate the time which has elapsed since the process first started4 ,,the ,,age ,,of ,,the ,,earth ,the method is well exemplified in the comparatively simple problem of the age of the earth4 ,the first scientific attempt to fix the age of the earth was made by ,halley1 the astronomer1 in the year #agae4 ,each day the rivers carry a certain amount of water down to the sea1 and this contains small amounts of salt in solution4 ,the water evaporates and in due course returns to the rivers2 the salt does not4 ,as a consequence the amount of salt in the oceans goes on increasing2 each day they contain a little more salt than they did on the preceding day1 and the present salinity of the oceans gives an indication of the length of time during which the salt has been accumulating4 8,we are thus furnished with an argument10 said ,halley1 somewhat optimistically1 8for estimating the duration of all things40 ,this line of argument does not lead to very precise estimates of the earth's age1 but calculations based on modern data suggest that it must be many hundreds of millions of years4 ,more valuable information can be obtained from the accumulation of sediment washed down by the rain4 ,every year that passes witnesses a levelling of the earth's surface4 ,soil which was high up on the slopes of hills and mountains last year has by now been washed down to the bottoms of muddy rivers by the rain and is continually being carried out to sea4 ,the ,thames alone carries between one and two million tons of soil out to sea every year4 ,for how long will ,england last at this rate1 and for how long can it have already lasted8 ,in our own lifetimes we have seen large masses of land round our coasts form landslides1 and either fall wholly into the sea or slip down nearer to sea-level4 ,such conspicuous landmarks as the ,needles1 and indeed a large part of the southern coast of the ,isle of ,wight1 are disappearing before our eyes4 ,the geologist can form an estimate of the rapidity with which these and similar processes are happening1 and so can estimate how long sedimentation has been in progress to produce the observed thickness of geological layers4 ,these thicknesses are very great2 ,professor ,arthur ,holmes#ah gives the observed maximum thicknesses as follows3 ,pre-,cambrian at least #ahj1jjj feet ,palaeozoic ,era 7,ancient life7 #ahe1jjj 0 ,mesozoic ,era 7,mediaeval life7 #ia1jjj 0 ,cainozoic ,era 7,modern life7 #gc1jjj 0 #ah ,in discussing the earth's age1 ,i have borrowed extensively from ,professor ,holmes' book1 ,the ,age of the ,earth4 ,we can form a general idea of the rate at which these sediments have been deposited4 ,since ,rameses ,,ii reigned in ,egypt over #cjjj years ago1 sediment has been deposited at ,memphis at the rate of a foot every #djj or #ejj years2 the excavator must dig down #f or #g feet to reach the surface of ,egypt as it stood when ,rameses ,,ii was king4 ,the present rate of denudation in ,north ,america is estimated to be one foot in #hfjj years2 similar estimates for ,great ,britain indicate a rate of one foot in #cjjj years4 ,with geological strata deposited at an average rate of one foot per #ajjj years1 the total #ebi1jjj feet of strata listed above would require over #ejj million years for their deposition4 ,at a rate of one foot per #djjj years1 the time would be about #bajj million years4 ,this method of estimating geological time has been described as the 8,geological hour-glass40 ,we see how much sand has already run1 we notice how fast it is running now1 and a calculation tells us how long it is since it first started to run4 ,the method suffers from the usual defect of hour-glasses1 that there is no guarantee that the sand has always run at a uniform rate4 ,geological methods suffice to shew that the earth must be hundreds of millions of years old1 but to obtain more definite estimates of its age1 the more precise methods of physics and astronomy must be called in4 ,fortunately the radio-active atoms discussed in the previous chapter provide a perfect system of clocks1 whose rate so far as we know does not vary by a hair's breadth from one age to another4 ,we have seen how1 with the lapse of sufficient time1 an ounce of uranium disintegrates into #jhfe ounce of lead and #jace ounce of helium4 ,the process of disintegration is absolutely spontaneous2 no physical agency known in the whole universe can either inhibit or expedite it in the tiniest degree4 ,the following table shews the rate at which it progresses3 ,history of ,one ounce of ,uranium ,initially3 #a oz4 uranium ,no lead ,after #ajj million years #jihe oz4 uranium #jjac oz4 lead 0 #ajjj 0 #jhfe 0 0 #jaaf 0 0 0 #bjjj 0 #jgdg 0 0 #jbai 0 0 0 #cjjj 0 #jfdf 0 0 #jcjf 0 0 and so on4 ,thus a small amount of uranium provides a perfect clock1 provided we are able to measure the amount of lead it has formed1 and also the amount of uranium still surviving1 at any time we please4 ,when the earth first solidified1 many fragments of uranium were imprisoned in its rocks1 and may now be used to disclose the age of the earth4 ,we are not entitled to assume that all the lead which is found associated with uranium has been formed by radio-active integration4 ,but1 by a fortunate chance1 lead which has been formed by the disintegration of uranium is just a bit different from ordinary lead2 the latter has an atomic weight of #bjgb1 while the former is of atomic weight only #bjfj4 ,thus a chemical analysis of any sample of radio-active rock shews exactly how much of the lead present is ordinary lead1 and how much has been formed by radio-active disintegration4 ,the proportion of the amount of lead of this latter kind to the amount of uranium still surviving tells us exactly for how long the process of disintegration has been going on4 ,in general all the samples of rock which are examined tell much the same story1 and the radio-active clock is found to fix the time since the earth solidified at #adjj million years or more4 ,the clock cannot tell us for how long before this the earth had existed in a plastic or fluid state1 since in this earlier state the products of disintegration were liable to become separated from one another4 ,aston has recently discovered a new isotope 7see p4 #aah7 of uranium1 called actino-uranium4 ,as uranium and its isotope have different periods of decay1 the relative abundance of the two is continually changing4 ,from the ratio of the amounts of these substances now surviving on earth1 ,rutherford has calculated that the age of the earth cannot exceed #cdjj million years1 and is probably substantially less4 ,these two physical estimates of the time which has elapsed since the earth solidified stand as follows3 ,age of the ,earth by the ,radio-active ,clock #a4 ,from the lead-uranium ratio in radio-active ,more than #adjj million years4 rocks #b4 ,from the relative abundance of uranium and ,less than #cdjj million years4 actino-uranium ,various astronomical methods are also available for determining the time since the solar system came into being4 ,here the 8clocks0 are provided by the shapes of the orbits of various planets and satellites4 ,the orbits do not change at uniform rates1 but their changes are determined by known laws1 so that the mathematician can calculate the rates at which change occurred under past conditions1 and hence1 by totalling up1 can deduce the time needed to establish present conditions4 ,the following two estimates are both due to ,dr ,h4 ,jeffreys3 ,age of the ,solar ,system by the ,astronomical ,clock #a4 ,from the orbit of ,mercury 444 ,from #ajjj to #aj1jjj million years4 #b4 0 0 the ,moon 444 ,roughly about #djjj million years4 ,while these various figures do not admit of any very exact estimate of the earth's age1 they all indicate that this must be measured in thousands of millions of years4 ,if we wish to fix our thoughts on a round number1 probably #bjjj million years is the best to select4 ,,the ,,ages ,,of ,,the ,,stars ,we now turn to the far more difficult problem of determining the ages of the stars4 ,we shall not approach it by a direct frontal attack1 but start far away from our real objective4 ,let us in fact start at the extreme other end of the universe1 and delve a bit further into the properties of a gas4 ,,equipartition ,,of ,,energy ,,in ,a ,,gas4 ,we have pictured a gas as an indiscriminate flight of molecule-bullets4 ,these fly equally in all directions1 occasionally crashing into one another1 and in so doing1 changing both their speeds and directions of flight4 ,we have seen that the total energy of motion undergoes no decrease when such collisions occur4 ,if one of the molecules taking part in a collision has its speed checked1 the other has its speed increased by such an amount that the energy lost by one molecule is gained by the other4 ,total energy of motion is 8conserved40 ,into this random hail of bullets1 let us imagine that we project a far heavier projectile1 which we may call a cannon-ball1 with a speed equal to about the average speed of the bullets4 ,the energies of the various projectiles are proportional jointly to their weights and to the squares of their speeds1 so that in the present case1 in which the speeds are all much the same1 the big projectile has more energy than the bullets simply on account of its greater weight4 ,if it weighs as much as a thousand bullets1 it has a thousand times as much energy as each single bullet4 ,yet the heavy projectile cannot for long continue swaggering through its lesser companions with a thousand times its fair share of energy4 ,its first experience is to encounter a hail of bullets on its chest4 ,very few bullets hit it in the back1 for they are only moving at about its own speed1 and so can hardly overtake it from behind4 ,moreover1 even if they do1 their blows on its back are very feeble because they are hardly moving faster than it4 ,but the shower of blows on its chest is serious2 every one of these tends to check its speed1 and so to lessen its energy4 ,and as the total energy of motion is conserved at every collision1 it follows that1 while the big projectile is losing energy all the time1 the little ones must be gaining energy at its expense4 ,for how long will this interchange of energy go on8 ,will it1 for instance1 continue until the big projectile has lost all its energy1 and been brought completely to rest8 ,the problem is one for the mathematician1 and it admits of a perfectly exact mathematical solution1 which ,maxwell gave as far back as #ahei4 ,the big projectile is not deprived of all its energy4 ,as its speed gradually decreases1 conditions change in all sorts of ways4 ,when we allow for this change of conditions1 we find that the energy of the big projectile goes on decreasing1 not until it has lost all its energy1 but until it has no more energy than the average bullet4 ,when this stage is reached1 the hits of the bullets are as likely on the average to increase the energy of the big projectile as to decrease it1 so that this ends up by fluctuating around an amount equal to the average energy of the little projectiles4 ,maxwell1 and others after him1 further shewed that no matter how many kinds of molecules there may be mixed together in a gas1 and no matter how widely their weights may differ from one another1 their repeated collisions must ultimately establish a state of things in which big molecules and little1 light and heavy1 all have the same average energy4 ,this is known as the theorem of equipartition of energy4 ,it does not mean that at any single instant all the molecules have precisely the same energy2 obviously such a state of things could not continue for a moment1 since the first collision between any pair of molecules would upset it immediately4 ,but on averaging the energy of each molecule over a sufficiently long period of time--say a second1 which is a very long time indeed in the life of a molecule1 being the time in which at least a hundred million collisions occur--we shall find that the average energy of all the molecules is the same1 regardless of their weights4 ,the same theorem can be stated in a slightly different form4 ,air consists of a mixture of molecules of different kinds and of different weights--molecules of helium which are very light1 molecules of nitrogen which are far heavier1 each weighing as much as seven molecules of helium1 and the still heavier molecules of oxygen1 each with the weight of eight molecules of helium4 ,in its alternative form1 the theorem tells us that at any instant the average energy of all the molecules of helium1 in spite of their light weights1 is exactly equal to the average energy of the molecules of nitrogen1 and again each of these is exactly equal to the average energy of the molecules of oxygen4 ,the lighter types of molecule make up for their small weights by their high speeds of motion4 ,similar statements are of course true for any other mixture of gases4 ,the truth of the theorem is confirmed observationally in a great variety of ways4 ,in #ahdf1 ,graham measured the relative speeds with which the molecules of different kinds of gas moved1 by observing the rates at which they streamed through an orifice into a vacuum2 these proved to be such that the average energies of the various types of molecules were precisely equal to one another4 ,even earlier than this1 ,leslie and others had used this method to determine the relative weights of different molecules1 although without fully understanding the underlying theory4 ,thus it may be accepted as a well-established law of nature that no molecule is allowed permanently to retain more energy than his fellows2 in respect of their energies of motion1 a gas forms a perfectly organised communistic state in which a law1 which they cannot evade1 compels the molecules to share their energies equally and fairly4 ,subject to certain slight modifications1 the same law applies also to liquids and solids4 ,in liquids and gases1 we can actually perform an experiment analogous to that of projecting our imaginary cannon-ball into the hail of molecule-bullets1 and watch events4 ,we may take a few grains of very fine powder1 powdered gamboge or lycopodium seed1 for instance1 and let these play the part of super-molecules amongst the ordinary molecules of a gas or liquid4 ,a powerful microscope shews that these super-molecules are not brought completely to rest1 but retain a certain liveliness of movement1 as they are continually hit about by the smaller and quite invisible true molecules4 ,it looks for all the world as though they were affected by a chronic ,st ,vitus' dance1 which shews no signs of diminishing as time goes on4 ,these movements are called 8,brownian movements10 after ,robert ,brown1 the botanist1 who first observed them in the sap of plants4 ,brown at first interpreted them as evidence of real life in the small particles affected by them1 an interpretation which he had to abandon when he found that particles of wax shewed the same movements4 ,in a series of experiments of amazing delicacy1 ,perrin not only observed1 but also measured1 the ,brownian movements of small solid particles as they were hit about by the molecules of air and other gases1 and deduced the weights of the molecules of these gases with great accuracy4 ,,stellar ,,equipartition ,,of ,,energy4 ,we can now get back to the stars4 ,the theorem of equipartition of energy is true not only of the molecules of a gas1 and of a solid1 and of a liquid2 it is true also of the stars of the sky4 ,the processes of mathematics are applicable to the very great as well as to the very small1 and a theorem which is proved true for the minutest of atoms is equally true for the most stupendous of stars1 provided of course that the premisses on which it is based remain true1 and do not suffer by transference from the small to the great end of the universe4 ,now the conditions which are necessary for the theorem of equipartition of energy to be true happen to be amazingly simple2 indeed it is difficult to believe that such wide consequences can follow from such simple conditions4 ,they amount to practically nothing beyond a law of continuity and a law of causation2 in other words1 that the state of the system at any instant shall follow inevitably from its state at the preceding instant1 or if you like1 that there shall be no free-will among the molecules or stars or other bodies whose motions are under discussion4 ,in the present turmoil as to the fundamental laws of physics1 we cannot be entirely certain as to how far these very simple conditions are fulfilled in the molecular problem1 although abundant observational evidence makes it clear that the law of equipartition holds1 at any rate to an exceedingly good approximation1 in an ordinary gas4 ,on the other hand1 there is not the slightest doubt as to what determines the motions of the stars2 it is the law of gravitation1 every star attracting every other star with a force which varies inversely as the square of their distance apart4 ,this is ,newton's form of the law1 but it is a matter of complete indifference for our present purpose whether we use the law in ,newton's or in ,einstein's form2 for stellar problems the two are practically indistinguishable1 and there is abundant evidence1 particularly from the observed orbits of binary stars1 in favour of either4 ,the essential point is that1 from the single supposition that the motions of the stars are governed by either of these laws of gravitation--or1 for the matter of that1 by any other not entirely dissimilar law--we can prove the theorem of equipartition of energy to be true for these motions4 ,no subtle statement of exact conditions is required2 the mere law of gravitation1 together with the supposition that the stars cannot exercise free-will as to whether they obey it or not1 is enough4 ,it is important to understand quite clearly what precisely the theorem asserts when applied to the stars4 ,it does not of course assert that all the stars in the sky have equal energies4 ,it does not even assert that on the average the heavy-weight stars in the sky have the same energy as the light-weight stars4 ,what it asserts is that if we put any miscellaneous assortment of stars into space1 then1 after they have interacted with one another for a sufficient length of time 7this is the essential point71 those which started with more than their fair share of energy will have been compelled to hand over their excess to stars with lesser energy1 so that the average energy of all the different types of stars must necessarily become reduced to equality in the long run4 ,in the molecular problem1 the interaction between the molecules takes place through the medium of collisions1 and equipartition of energy is established1 to a very good approximation1 after some eight or ten collisions have happened to each molecule4 ,in ordinary air1 this requires a period of only about a hundred-millionth part of a second4 ,in the stellar problem1 we are dealing with very different lengths of time2 collisions only occur at intervals of thousands of millions of millions of years4 ,if the stars only redistributed their energy when actual collisions occurred1 we might surmise that a close approximation to equipartition of energy would not be attained until after each star had experienced eight or ten collisions1 and this would require a really stupendous length of time4 ,actually no such length of time is needed because the numerous gravitational pulls1 even between stars which are at a considerable distance apart1 equalise energy far more efficiently and expeditiously than the very rare direct hits4 ,every time that two stars happen to pass even fairly near to one another in their wanderings1 each pulls the other a bit out of its course1 and the directions and speeds of motion of both stars are changed--by much or little according as the stars pass quite close to one another or keep at a substantial distance apart4 ,in brief1 each approach of stars causes an interchange of energy1 and after sufficient time1 these repeated interchanges of energy result in the total energy being shared equally1 on the average1 between the stars1 regardless of differences in their weights4 ,now the crux of the situation1 to which all this has been leading up1 is that observation shews that stars of different weights are moving with different average speeds1 these average speeds being such that equipartition of energy already prevails among the stars--not absolutely exactly1 but to a tolerably good approximation4 ,the question of how long the stars must have interacted to reach such a condition now becomes one of absolutely fundamental importance1 for the answer tells us the ages of the stars4 ,,stellar ,,velocities4 ,we have already seen 7p4 #dh7 how stars which form binary systems can be weighed1 such weighings disclosing weights ranging from about a hundred times the weight of the sun to only a fifth of its weight4 ,the speeds of motion of binary systems can be measured in precisely the same way as the speeds of single stars4 ,as far back as #aiaa1 ,halm1 with an accumulation of such measurements before him1 pointed out that the heaviest stars moved the most slowly4 ,he found that1 on the average1 the heaviest of known stars had approximately the same energy of motion as the lightest1 the high speeds of the latter just about making up for the smallness of their weights1 and so suggested that the velocities of the stars1 like those of the molecules of a gas1 might be found to conform to the law of equipartition of energy4 ,it appeared to be a case of ,brownian movements on a stupendous scale4 ,since then a great deal more observational evidence has accumulated1 and an exhaustive investigation made by ,dr ,seares of ,mount ,wilson in #aibb leaves very little room for doubt that the motions of the stars shew a real1 and fairly close1 approximation to equipartition of energy4 ,the table overleaf shews the final result of ,seares' discussion4 ,the stars are first classified according to the different types of spectrum their light shews when analysed in a spectroscope4 ,equipartition of ,energy in ,stellar ,motions ---------------------------------------- ---------------------- ,average ,average ,average ,corresponding weight speed energy temperature ,type of star ,m ,c ,,mc 7degrees7 7grammes7 7cms4_/sec47 7ergs7 ---------------------------------------- ---------------------- ,spectral type ,b #c #aih #ajadh #aj #aie #ajaj #aj 0 ,b #heabi #aeh #afb #jh 0 ,a #j #aba #bde #cfc #ah 0 ,a #b #ajj #bgb #cgb #ah 0 ,a #e #hj #bii #cee #ag 0 ,f #j #ej #cei #cbd #af 0 ,f #e #ca #dgi #cee #ag 0 ,g #j #bj #fdf #djg #bj 0 ,g #e #ae #ggf #deg #bb 0 ,k #j #ad #gid #dbg #ba 0 ,k #e #ab #gda #cci #ag 0 ,m #j #ab #ggf #cee #ag ---------------------------------------- ---------------------- ,these different types of stars have very different average weights2 the second column of the table shews that they exhibit a range of over #af to #a4 ,the third column1 which gives the average speeds of these different types of stars1 shews that the heaviest stars move the most slowly1 and the lightest on the whole the most rapidly4 ,the next column gives the average energy of motion of the different types of stars4 ,this shews that the variation in speeds is just about that needed to make the average energies of all types of stars equal4 ,an exception certainly occurs in the first two lines1 which refer to the heaviest stars of all4 ,apart from these1 the remaining ten lines shew a ratio of #aj to #a in weight1 whereas the average deviation of energy from the mean is only one of #i per cent4 ,from this we see that the motions of the stars shew a real approach1 and even a fairly close approach1 to equipartition of energy4 ,the question which naturally presents itself is whether this approximate equality of energy can be attributed to any other cause than long-continued gravitational interaction between the stars4 ,this latter agency could undoubtedly produce it1 but could anything else produce a similar result8 ,the last column of the table provides the answer4 ,it shews the temperatures to which a gas would have to be raised1 in order that each of its molecules should have the same energy as the different types of stars4 ,this may well seem an absurd calculation4 ,a star weighing millions of millions of millions of tons goes hurtling through space at a speed of about #a1jjj1jjj miles an hour2 are we seriously setting out to inquire how hot a gas must be for every single one of its tiny molecules to have the same energy of motion1 the same power of doing damage--for that is what energy of motion really amounts to--as the star8 ,the calculation is undoubtedly absurd1 and it is meant to be1 because it is leading up to a reductio ad absurdum4 ,if the observed equipartition of energy were brought about by any physical agency1 such as pressure of radiation1 bombardment by molecules1 by atoms or by high speed electrons1 this agency would have to be at a temperature1 or in equilibrium with matter at a temperature1 of the order of those given in the last column4 ,these are temperatures of the order of #aj degrees4 ,we can be pretty sure no such temperature exists in nature1 whence the argument runs that the observed equipartition of energy cannot have been brought about by physical means1 and so must be the result of gravitational interaction between the stars4 ,the age of the stars is1 then1 simply the length of time needed for gravitational forces to bring about as good an approximation to equipartition of energy as is observed4 ,the calculation of this length of time presents a complicated but by no means intractable problem4 ,all the necessary data are available1 and as the method of calculation is well understood from previous experience in the theory of gases1 the mathematician may be trusted to supply a reliable and reasonably exact answer when we ask him1 but even without his help we can see that the time must be very long indeed4 ,leaving actual figures aside for the moment1 we may find it easier to think in terms of the scale-model we constructed in the first chapter 7p4 #hh74 ,we took our scale so small that the stars were reduced to tiny specks of dust2 we noticed that space is so little crowded with stars that in our model the specks of dust had to be placed over #bjj yards apart2 to put it all in a concrete form1 we found that ,waterloo ,station with only six specks of dust left in it is more crowded with dust than space is with stars4 ,now let the model come to life1 so as to represent the motions of the stars4 ,to keep the proportions right1 the speed of the stars must of course be reduced in the same proportion as the linear dimensions of the model4 ,in this the earth's yearly journey round the sun of #fjj million miles had become reduced to a pin-head a sixteenth of an inch in diameter1 or1 say1 a fifth of an inch in circumference4 ,as the stars move through space with roughly the same speed as the earth in its orbit1 we may suppose the yearly journey of each speck of dust in our model also to be about a fifth of an inch4 ,thus each speck of dust will move about an inch in five years1 roughly #af feet in a thousand years--or say a ten-millionth part of a snail's pace4 ,even if two specks started moving directly towards one another it would take them about #bj1jjj years to meet4 ,for how long must six particles of dust1 floating blindly about in ,waterloo ,station1 move at this pace before each has had enough close meetings with other specks of dust for their energy of motion to become thoroughly redistributed8 ,the mathematician1 carrying out exact calculations with respect to the actual weights1 speeds and distances of the stars1 finds that the observed degree of approximation to equipartition of energy shews that gravitational interaction must have continued through millions of millions of years1 most probably from #e to #aj millions of millions of years4 ,this1 then1 must be the length of life of the stars4 ,it is a stupendous length of time1 and before finally accepting it we may well look for confirmation from other sources4 ,in estimating the age of the earth we were able to invoke assistance from all kinds of clocks1 astronomical1 geological and physical2 happily they all told much the same story4 ,in the present problem only astronomical clocks are available1 but fortunately there are no fewer than three of these1 and again they agree in saying much the same thing4 ,,the ,,orbits ,,of ,,binary ,,systems4 ,we have already seen 7p4 #dg7 how the two constituents of a binary system permanently describe closed elliptical orbits about one another1 because neither can escape from the gravitational hold of its companion4 ,energy can reside in the orbital motion of these systems1 as well as in their motion through space4 ,and strict mathematical analysis shews that a long succession of gravitational pulls from passing stars must finally result in equipartition of energy1 not only between the energies of motion of one system and another through space1 but also between the various orbital motions of which each binary system is capable4 ,when this final state of equipartition is ultimately reached1 the orbits of the systems will not all be similar1 but it can be shewn that their shapes will be distributed according to a quite simple statistical law#ai4 ,as the orbits of actual systems are not found to conform to this law1 it is clear that the stars have not yet lived long enough to attain equipartition of energy in respect of their orbital motions4 ,it is impossible to discuss how far they have travelled along the road to equipartition without knowing the point1 or points1 from which they started4 #ai ,the eccentricity of orbit e is distributed in such a way that all values of e from e #j to e #a are equally probable4 ,the question of the origin of binary systems will be discussed more fully in the next chapter4 ,for the moment it may be said that they appear to come into being in two distinct ways4 ,practically all astronomical bodies are in a state of rotation about an axis4 ,the earth rotates about its axis once every #bd hours1 and ,jupiter once every #aj hours1 as is shewn by the motion of the red spot and other markings on its surface4 ,the surface of the sun rotates every #bf days or so2 we can follow its rotation by watching sun-spots1 faculae and other features moving round and round its equator4 ,there are theoretical grounds for supposing that the sun's central core rotates considerably faster than this1 most probably performing a complete rotation in comparatively few days4 ,and it is likely that all the other stars in the sky are also in rotation1 some fast and some slow4 ,we shall see later how1 with advancing age1 a star is likely to shrink in size1 and this shrinkage generally causes its speed of rotation to increase4 ,now mathematical theory shews that there is a critical speed of rotation which cannot be exceeded with safety4 ,if the star rotates too fast for safety1 it simply bursts into two1 much as a rotating fly-wheel may burst if it is driven at too high a speed4 ,it is in this way that one class of binary stars come into being4 ,with a few exceptions this class is identical with the class of spectroscopic binaries described in ,chapter ,i 7p4 #eb72 the two component stars are generally too close together to appear as distinct spots of light in the telescope1 only spectroscopic evidence telling us that we are dealing with two distinct bodies4 ,another class of binaries1 the visual binaries1 which appear quite definitely as pairs of spots of light in the telescope1 probably have a different origin4 ,we shall see later how the stars first come into being as condensations of nebulous gas1 a whole shoal being born when a single great nebula breaks up4 ,it must often happen that adjacent condensations are so near as to be unable to elude each other's gravitational grip4 ,in time these shrink down into normal stars1 while the gravitational forces remain just as powerful as before1 and we are left with a pair of stars which must permanently journey through space in double harness1 because they have not energy of motion enough ever to get clear of one another's gravitational hold4 ,this mechanism produces a class of binaries which is precisely similar to that formed by the break-up of single stars1 except for an enormous difference in scale4 ,the distance between the two components of such a system must be comparable with the original distance between separate condensations in the primaeval nebula out of which the stars were born1 and so is enormously greater than the corresponding distance in spectroscopic binaries1 which is comparable only with the diameter of an ordinary star which has broken into pieces4 ,this explains why visual binaries appear as distinct pairs of spots of light1 while spectroscopic binaries do not4 ,in the final state of equipartition of energy1 the shapes of the orbits will1 as we have seen1 be distributed according to a definite statistical law4 ,this law of distribution is the same for all sizes of orbit4 ,on the other hand1 the time needed for equipartition of energy to bring this law about is not the same for all sizes of orbit2 it is far greater for the compact orbits of the spectroscopic binaries than for the more open orbits of the visual binaries4 ,the reason for this is that changes in the shape of an orbit are caused merely by the difference of the gravitational pulls of a passing star on the two components of the binary4 ,if the two components are very close together1 the passing star exerts practically the same forces on both4 ,these forces affect the motions of the two components in precisely the same way1 with the result that the motion of the binary system as a whole through space is changed1 but the shape of orbit remains unaltered4 ,the passing star gets a grip on the motion of the binary as a whole1 but none on the orbits of the components4 ,on the other hand1 when the components are far apart1 the gravitational forces acting on the two may be widely different1 so that a substantial change in the shape of the orbit may result1 even if the encounter is not a very close one4 ,in visual binaries1 in which the components are usually hundreds of millions of miles apart1 the time necessary to establish the final distribution of the 8eccentricities10 by which the shapes of elliptical orbits are measured1 is once again found to be of the order of millions of millions of years1 but it is something like a hundred times as great as this for the far more compact spectroscopic binaries4 ,the following table1 compiled from material given by ,dr ,aitken of ,lick ,observatory1 shews the observed distribution of eccentricities in the orbits of those binaries for which accurate information is available3 ,the ,approach to ,equipartition of ,energy in ,binary ,orbits ---------------------------------------- ------------------ ,observed ,observed ,number to be expected ,eccentricity number of number of theoretically of ,orbits spectroscopic visual when the binaries binaries final state is attained ---------------------------------------- ------------------ #j to #jb #gh #g #f #jb 0 #jd #ah #ah #ah #jd 0 #jf #af #bh #cj #jf 0 #jh #f #aa #db #jh 0 #aj #a #d #ed ---------------------------------------- ------------------ ,let us look first at the spectroscopic binaries4 ,in the observed orbits1 we see that low eccentricities predominate1 no fewer than #gh out of #aai having an eccentricity of less than one-fifth4 ,in other words1 most spectroscopic binaries have nearly circular orbits4 ,both theory and observation shew that when a star first divides up into a spectroscopic binary1 the orbits of the two components must be nearly circular1 so that the table of observed orbits provides very little evidence of any progressive change of shape in the orbits as a whole4 ,in contrast to this1 the last column of the table shews the proportion of orbits of different eccentricities which is to be expected when1 if ever1 equipartition of energy is finally attained4 ,here high eccentricities1 representing very elongated orbits1 predominate2 only one orbit in twenty-five is so nearly circular as to have an eccentricity less than a fifth4 ,in general the observed numbers tabulated in the second column shew no resemblance at all to the theoretical numbers tabulated in the fourth column4 ,in other words1 the spectroscopic binaries shew no suggestion of any near approach to the final state1 most of them retaining the low eccentricity of orbit with which they started life4 ,we should naturally expect this1 since we have seen that hundreds or even thousands of millions of millions of years would be needed for these orbits to attain a final state of equipartition1 and the stars cannot be as old as this1 for if they were1 their motions through space ought to shew absolutely perfect equipartition1 which they certainly do not4 ,turning now to the third column1 we see that the visual binaries shew a good approach to the theoretical final state up to an eccentricity of about #jf1 but not beyond4 ,the deficiency of orbits of high eccentricity may mean that gravitational forces have not had sufficient time to produce the highest eccentricities of all1 but part1 and perhaps all1 of it must be ascribed to the simple fact that orbits of high eccentricity are exceedingly difficult to detect observationally and to measure accurately4 ,clearly1 then1 the study of orbital motions1 like that of motions through space1 points to gravitational action extending over millions of millions of years4 ,in each case there is an exception to 8prove the rule40 ,in the case we have just considered it is provided by the spectroscopic binaries1 which are so compact that their constituents can defy the pulling-apart action of gravitation2 in the former case it was provided by the ,b-type stars1 which are so massive1 possibly also so young1 that the gravitational forces from less weighty stars have not yet greatly affected their motion4 ,when these two lines of evidence are discussed in detail1 they agree in suggesting that the general age of the stars is about that already stated1 namely1 from five to ten millions of millions of years4 ,,moving ,,clusters4 ,a third line of evidence1 which also tells much the same story1 may be briefly mentioned4 ,the conspicuous groups of bright stars in the sky1 such as the ,great ,bear1 the ,pleiades and ,orion's ,belt1 consist for the most part of exceptionally massive stars which move in regular orderly formation through a jumble of slighter stars1 like a flight of swans through a confused crowd of rooks and starlings4 ,swans continually adjust their flight so as to preserve their formation4 ,the stars cannot1 so that their orderly formation must in time be broken by the gravitational pull of other stars4 ,the lighter stars are naturally knocked out of formation first1 while the most massive stars retain their formation longest4 ,observation suggests that this is what actually happens to a moving star-cluster2 at any rate the stars which remain in formation generally have weights far above the average4 ,and1 as we can calculate the time necessary to knock out the lighter stars1 we can at once deduce the ages of those which are left in4 ,the result of the calculation confirms those already mentioned1 so that we find that the three available astronomical clocks all tell much the same time4 ,they agree in indicating an age of the order of five to ten millions of millions of years for the stars as a whole4 ,another line of investigation1 to be mentioned later 7p4 #ahh7 again points to a similar age4 ,it is perhaps a little surprising that this age should prove to be so much longer than the age of the earth1 although there is of course no positive reason why the earth should not have been born during the last few moments of the lives of the stars4 ,it is perhaps also a little surprising that it should prove to be much longer than the age suggested1 very vaguely it is true1 by the cosmologies of de ,sitter and ,lematre4 ,if we accept the apparent velocities of recession of the most distant nebulae as real1 we find that some thousands of millions of years of motion at their present speeds would just about account for their present distances from us1 so that a few thousands of millions of years ago1 the nebulae must have been far more huddled together than they now are4 ,this is of course very different from saying that the time which has elapsed since the creation of the nebulae can only be a few thousands of millions of years1 yet we might reasonably have expected priori that the two periods would be at least comparable4 ,to state the difficulty in a slightly different form1 a period of two thousand million years seems to have made a great deal of difference to the earth1 and if the apparent speeds of nebular motion are real1 it has made a great deal of difference to the general arrangement in space of the great nebulae1 so that it is odd that it should make so little difference to the stars that we need to postulate an age a thousand times as great before we can explain their present condition4 ,these considerations may seem to suggest that the estimate just made of stellar ages should be accepted with caution and perhaps even with suspicion4 ,yet if we reject it1 so many facts of astronomy are left up in the air without any explanation1 and so much of the fabric of astronomy is thrown into disorder 7see p4 #ahg1 below71 that we have little option but to accept it1 and suppose that the stars have actually lived through times of the order of millions of millions of years4 ,,the ,,sun',s ,,radiation ,during the whole of some such vast period of time1 the sun has in all probability been pouring out light and heat at least as profusely as at present4 ,indeed a mass of evidence1 to which we shall return later1 shews that young stars emit more radiation than older stars1 so that during most of its long life the sun must have been pouring out energy even more lavishly than now4 ,if our ancestors thought about the matter at all1 they probably saw nothing remarkable in this profuse outpouring of light and heat1 particularly as they had no conception of the stupendous length of time during which it had lasted4 ,it was only in the middle of last century1 when the principle of conservation of energy first began to be clearly understood1 that the source of the sun's energy was seen to constitute a scientific puzzle of really first-class difficulty4 ,the sun's radiation obviously represented a loss of energy to the sun1 and1 as the principle of conservation shewed that energy could not originate out of nothing1 this energy necessarily came from some source or store adequate to supply vast outpourings of energy over a very long period of time4 ,where was such a store to be found8 ,the sun at present pours out radiation at such a rate that if the necessary energy were generated in a power-station outside the sun1 this station would have to burn coal at the rate of many thousands of millions of millions of tons a second4 ,there is of course no such power-station4 ,the sun is entirely dependent on its own resources2 it is a ship on an empty ocean4 ,and if1 like such a ship1 the sun carried its own store of coal1 or if1 as ,kant imagined1 its whole substance were its store of coal1 so that its light and heat came from its own combustion1 the whole would be burnt into ashes and cinders in a few thousand years at most4 ,the history of science records one solitary attempt to explain the sun's energy as coming in from outside4 ,we have seen how the energy of motion of a bullet is transformed into heat when the speed of the bullet is checked4 ,an astronomical example of the same effect is provided by the familiar phenomenon of shooting-stars4 ,these are bullet-like bodies which fall into the earth's atmosphere from outer space4 ,so long as such a body is travelling through empty space1 its fall towards the earth continually increases its speed1 but1 as it enters the earth's atmosphere1 its speed is checked by air-resistance1 and the energy of its motion is gradually transformed into heat4 ,the shooting-star becomes first hot and then incandescent1 emitting the bright light by which we recognise it4 ,finally1 the heat completely vaporises it1 and it disappears from sight1 leaving only a momentary trail of luminous gas behind4 ,the original energy of motion of the shooting-star has been transformed into light and heat--the light by which we see it1 and the heat by which it is ultimately vaporised4 ,in #ahdi1 ,robert ,mayer suggested that the energy which the sun emitted as radiation might accrue to it from a continuous fall of shooting-stars or similar bodies into the solar atmosphere4 ,the suggestion is untenable1 because a simple calculation shews that a mass of such bodies equal to the weight of the whole earth would hardly maintain the sun's radiation for a century1 and that the infall needed to maintain the sun's radiation for #cj million years would double its weight4 ,as it is quite impossible to admit that the sun's weight can be increasing at any such rate1 ,mayer's hypothesis has to be abandoned4 ,in #ahec ,helmholtz put forward a very similar theory1 the famous 8contraction-hypothesis10 according to which the sun's own shrinkage sets free the energy which ultimately appears as radiation4 ,if the sun's radius shrinks by a mile1 its outer atmosphere falls through a height of a mile and sets free as much energy in so doing as would be yielded up by an equal weight of shooting-stars falling through a mile and having their motion checked4 ,on ,helmholtz's theory1 the different parts of the sun's own body performed the rles which ,mayer had allotted to shooting-stars falling in from outside2 they performed these same parts again and again1 until ultimately the sun had shrunk so far that it could shrink no further4 ,yet ,helmholtz's theory1 like that of ,mayer1 failed to survive the test of numerical computation4 ,in #ahfb ,lord ,kelvin calculated that the shrinkage of the sun to its present size could hardly have provided energy for more than about #ej million years of radiation in the past1 whereas the geological evidence already noticed 7p4 #aea7 shews that the sun must have been shining for a period enormously longer than this4 ,to track down the actual source of the sun's energy with any hope of success1 we must give up guessing1 and approach the problem from a new angle4 ,we have seen 7p4 #abj7 how radiation carries weight about with it1 so that any body which is emitting radiation is necessarily losing weight2 the radiation emitted by a searchlight of #ej horse-power would1 we saw1 carry away weight at the rate of about a twentieth of an ounce a century4 ,now each square inch of the sun's surface is in effect a searchlight of just about #ej horse-power1 whence we conclude that weight is streaming away from every square inch of the sun's surface at the rate of about a twentieth of an ounce a century4 ,such a loss of weight seems small enough1 until we multiply it by the total number of square inches which constitute the whole surface of the sun4 ,it then appears that the sun as a whole is losing weight at the rate of rather over #d million tons a second1 or about #bej million tons a minute--something like #fej times the rate at which water is streaming over ,niagara4 ,,the ,,past ,,histories ,,of ,,the ,,sun ,,and ,,stars4 ,let us carry on the multiplication4 ,two hundred and fifty million tons a minute is #cfj1jjj million tons a day4 ,thus the sun must have weighed #cfj1jjj million tons more than now at this time yesterday1 and will weigh #cfj1jjj million tons less at this time to-morrow4 ,and #cfj1jjj million tons a day is #aca million million tons a year4 ,we can dig as far into the past as we like in this way and can probe as far as we like into the future4 ,but soon we encounter the usual trouble which besets all calculations of this kind--the sand does not always run through the hour-glass at the same rate4 ,the rate at which the sun loses weight will not vary appreciably between to-day and to-morrow1 or even over a century or a million years1 but we must be on our guard against going too far4 ,if the sun continued to radiate at precisely its present rate1 a simple sum in division shews that it would last for just about #ae million million years1 by which time its last ounce of weight would be disappearing4 ,incidentally this gives us a vivid conception of the enormous weight of the sun2 it could go on pouring away its substance into space at #fej times the rate at which water is pouring over ,niagara for #ae million million years before becoming exhausted4 ,obviously1 however1 we cannot carry out our calculations in this simple light-hearted way2 it would be absurd to suppose that the sun's last ton of substance will radiate energy at the same rate as his present stupendous mass of two thousand million million million million tons4 ,a series of investigations which culminated in a paper published by ,eddington in #aibd1 disclosed that1 in a general sort of way1 a star's luminosity depends mainly on its weight4 ,the dependence is not very precise1 and neither is it universal1 but when we are told a star's weight we can say that its luminosity is likely1 with a high degree of probability1 to lie within certain fairly narrow limits4 ,for instance most stars whose weight is nearly equal to the sun are found to have about the same luminosity as the sun4 ,in general1 as might be expected1 stars of light weight radiate less than heavy stars1 but also--and this could not have been foreseen--the differences in their radiations are far greater than the differences in their weights4 ,the law which we have already noticed to hold for a few stars in the neighbourhood of the sun is true1 although in a somewhat different sense1 for the stars as a whole--the candle-power per ton is greatest in the heaviest stars4 ,for example1 the average star of half the weight of the sun does not radiate anything like half as much energy as the sun3 the fraction is more like an eighth4 ,this consideration extends the future life of the sun1 and indeed of all the stars1 almost indefinitely4 ,a sort of parsimony seems to creep over the stars in their old age2 so long as they have plenty of weight to squander1 they squander it lavishly1 but they contract their scale of expenditure when they have little left to spend4 ,the sand runs slowly through the hour-glass when there is little left to run4 ,in the same way1 the average star of double the sun's weight does not merely radiate twice as much energy as the sun2 it radiates about eight times as much4 ,we must keep this in view in estimating the past life of the sun2 it shortens the sun's past life just as surely as the opposite effect lengthens its future life4 ,observation tells us at what rate the average star of any given weight spends its weight in the form of radiation1 and1 on the supposition that the sun has behaved like this typical average star at the corresponding stage of its own past history1 we can draw up a table exhibiting its gradual change of weight as its life progressed4 ,selected entries from this table would read somewhat as follows3 #b #aj years ago1 the sun had #ajjjac times its present weight #a1jjj #aj 0 0 #ajg 0 0 #b1jjj #aj 0 0 #aaf 0 0 #e1gjj #aj 0 0 double 0 #g1ajj #aj 0 0 #d times 0 #g1djj #aj 0 0 #h 0 0 #g1ejj #aj 0 0 #bj 0 0 #g1fjj #aj 0 0 #ajj 0 0 ,the first entry represents roughly the time since the earth was born4 ,it shews that1 during the whole existence of the earth1 the sun's weight has changed by only an inappreciable fraction of the whole4 ,consequently1 it seems likely1 although naturally we cannot be certain1 that when the earth was born the sun was much the same as it now is1 and that it has been the same1 in all essential respects1 throughout the whole life of the earth4 ,to come to appreciably different conditions we have to go back to remote aeons far beyond the time of the earth's birth4 ,we are free to do this1 for we have seen that the earth's whole life is only a moment in the lives of the stars4 ,we have estimated the latter as being something of the order of #e to #aj million million years1 and it is only when we go back an appreciable fraction of these long periods that we find the sun's weight differing appreciably from its present weight4 ,we have1 for instance1 to go back more than #e million million years to find the sun with double its present weight4 ,when we go back much further than this a new phenomenon appears2 the weight of our hypothetical past sun begins to go up by leaps and bounds4 ,in time it begins to double and more than double every #ajj1jjj million years1 and we cannot go back as far as #h million million years without postulating a sun of quite impossibly high weight4 ,the sun must1 then1 have been born some time within the last #h million million years4 ,the exact figures of our table may be open to suspicion1 but as a general fact of observation there is no doubt that very massive stars radiate away their energy1 and therefore also their weight1 with extraordinary rapidity4 ,indeed the process is so rapid that we may disregard all that part of a star's life in which it has more than about #aj times the weight of the sun--this is lived at lightning speed4 ,apart from all detailed calculations1 this general principle fixes a definite limit to the ages1 not only of the sun1 but also of every other star4 ,the upper limit to the age of the sun is certainly somewhere in the neighbourhood of #h million million years4 ,this agrees well enough with the general age of from #e to #aj million million years that other calculations have assigned to the stars in general4 ,the calculations thus reinforce one another1 and it looks as if at least two of the pieces of the puzzle were beginning to fit satisfactorily together4 ,if all the stars in the sky were similar to the sun1 we might feel a good deal of confidence in the conclusions we have reached4 ,unfortunately1 difficulties emerge as soon as we discuss the ages of stars which at present have many times the weight of the sun4 ,the table on p4 #afd shews that a class of stars 7spectral type ,a #j7 of six times the weight of the sun have motions in space which conform well enough to the law of equipartition of energy4 ,unless this is a pure coincidence 7and this is unlikely1 in view of the fact that other groups of only slightly less weight conform equally well71 we must assign an age of from #e to #aj million million years to these very massive stars4 ,yet the average star of this weight is emitting about a hundred times as much radiation as the sun1 which means that it is halving its weight every #aej1jjj million years4 ,clearly this process cannot have gone on for anything like #e or #aj million million years4 ,still more luminous stars present the problem in an even more acute form4 ,the star ,s ,doradus in the ,lesser ,magellanic ,cloud is at present emitting #cjj1jjj times as much radiation as the sun4 ,whereas the sun is pouring its weight out into space at the rate of #fej ,niagaras1 ,s ,doradus is pouring it out at the rate of #bjj1jjj1jjj ,niagaras2 every #ej million years it loses a weight equal to the total weight of the sun4 ,it is obviously absurd to imagine that this star can have been losing weight at this rate for millions of millions of years4 ,for such a star as ,s ,doradus only two alternatives seem open4 ,either it was created quite recently 7on the astronomical time-scale71 and so is still at the very beginning of its prodigal youth1 or else its loss of weight has in some way been inhibited through the greater part of its life4 ,a good many arguments weigh against the hypothesis of recent creation4 ,the star is a member of a star-cloud in which we should naturally expect all the members to be of approximately equal age4 ,it is in a region of space in which there are no indications that stars are still being born4 ,and1 even if we accept the hypothesis of recent creation for this particular star1 we are still at a loss to explain how the other massive stars1 which figure in the table on p4 #afd1 can be old enough for equipartition of energy to have become already established4 ,for many reasons it seems preferable1 and indeed almost inevitable1 to suppose that these highly luminous and very weighty stars have in some way been saved from energetic radiation1 with its consequential rapid wasting of weight1 throughout the greater part of their lives4 ,in brief1 we suppose that they are cases of arrested development1 whose weight and general appearance equally belie their true ages4 ,later 7p4 #cah7 we shall come upon a physical mechanism which explains very simply and naturally how this could happen4 ,if this hypothesis can be accepted1 it clears up the whole situation4 ,as soon as we accept it1 we become free to assign any age we please to the stars1 and naturally select that indicated by the law of equipartition of energy1 at any rate for those classes of stars which are found to conform to this law4 ,the exceptionally luminous stars which we have just had under discussion are comparatively rare objects in the sky4 ,the vast majority of stars have luminosities and weights comparable with1 or distinctly less than1 those of the sun1 and for these the difficulty does not exist4 ,indeed the hypothesis of arrested development would break down under its own weight if we had to invoke its help for many stars2 it is tenable just because we seldom need to use it4 ,we may accept the table on p4 #ahj as giving the past history of the sun with tolerable accuracy1 thus fixing its age at something under #h million million years1 and a generally similar table would apply to most of the stars in the sky4 ,,the ,,source ,,of ,,stellar ,,energy ,the ages of #e million million years or more which we have been led to assign to the stars imply that at birth the sun must have had at least double1 and more probably several times1 its present weight4 ,for every ton which existed in the sun at its birth only a few hundred-weight remain to-day4 ,the rest of the ton has been transformed into radiation and1 streaming away into space1 has left the sun for ever4 ,in the preceding chapter1 we had occasion to discuss the transformation of weight into radiation which accompanies the spontaneous disintegration of radio-active atoms4 ,the most energetic instance of this phenomenon known on earth is the transformation of uranium into lead1 in which about one part in #djjj of the total weight is transformed into radiation4 ,in the sun1 the corresponding fraction may be half1 or nine-tenths1 or even #ii per cent41 but1 whatever it is1 it certainly exceeds one part in #djjj4 ,thus the process by which the sun generates its light and heat must involve a far more energetic transformation of material weight into radiation than any process known on earth4 ,perrin and ,eddington at one time suggested that this process may be the building up of complex atomic nuclei out of protons and electrons4 ,the simplest1 and most favourable example of this1 which was especially considered by ,eddington1 is to be found in the building up of the helium nucleus4 ,the constituents of a helium atom are precisely identical with those of four hydrogen atoms1 namely1 four electrons and four protons4 ,if these constituents could be rearranged without any transformation of material weight into radiation1 the helium atom would have precisely four times the weight of the hydrogen atom4 ,in actual fact ,aston finds that the ratio of weights is only #cigj4 ,the difference between this and #djjj must represent the weight of the radiation which goes off when1 if ever1 the helium atom is built up by the coalescence of four hydrogen atoms4 ,the loss of weight1 one part in #acj1 is very much greater than occurs in radio-active transformations1 but even so it does not provide adequate lives for the stars4 ,the transformation of a sun which originally consisted of pure hydrogen into one consisting wholly of helium would only provide radiation at the sun's present rate of radiation for about #ajj1jjj million years1 and the dynamical evidence of equipartition of energy1 etc41 as well as other evidence which we shall consider later 7p4 #ahh below71 demands far longer lives for the stars than this4 ,,the ,,annihilation ,,of ,,matter4 ,modern physics is only able to suggest one process capable of providing a sufficiently long life for a radiating star2 it is the actual annihilation of matter4 ,various lines of evidence go to shew that the atoms in very massive stars are not1 for the most part1 fundamentally different from those in less massive stars4 ,thus the primary cause of the difference in weight between a heavy star and a light star is not a difference in the quality of the atoms2 it is a difference in their number4 ,a heavy star can only change into a light star through the actual disappearance of atoms2 these must be annihilated1 and their weight transformed into radiation4 ,i first drew attention in #aijd to the large amount of energy capable of being liberated by the annihilation of matter1 positive and negative electric charges rushing together1 annihilating one another and setting their energy loose in space as radiation4 ,the next year ,einstein's theory of relativity provided a means for calculating the amount of energy which would be produced by the annihilation of a given amount of matter2 it shewed that energy is set free at the rate of #i #aj ergs per gramme1 regardless of the nature or condition of the substance which is annihilated4 ,i subsequently calculated the length of lives which this source of energy permitted to the stars1 but the calculated lives of millions of millions of years seemed greater than were needed by the astronomical evidence available at the time4 ,since then a continual accumulation of new evidence1 particularly that discussed in the present chapter1 has been seen to demand stellar lives of precisely these lengths1 with the result that the majority of astronomers now regard annihilation of matter as the most probable source of stellar energy4 ,other considerations in addition to those just mentioned point to the annihilation of matter as the fundamental process going on in the stars4 ,if there were no annihilation of matter1 a star could only change its weight by some small fraction of the whole1 such1 for example1 as the one part in #djjj which accompanies radio-active disintegration1 or as the one part in #acj which would result from the building up of helium atoms out of hydrogen4 ,a star would retain its weight practically unaltered through its life4 ,this would of course necessarily impose far shorter lives on the stars than we believe them to have had1 for nothing can alter the fact that the sun loses #cfj1jjj million tons of weight every day in radiation1 so that if its weight cannot change much1 it cannot have radiated for long4 ,we have seen that in the present universe1 a star's luminosity depends mainly on its weight4 ,if we imagine that the same condition of things has always prevailed1 then stars which retained the same weight throughout their lives would have to retain approximately the same luminosity1 at any rate until their capacity for radiation became exhausted4 ,otherwise1 contrary to observation1 we should find stars with weights equal to the sun having all possible degrees of luminosity4 ,thus if we discard the hypothesis of the annihilation of matter1 it becomes necessary to imagine some controlling mechanism1 of a kind which would compel stars having the weight of the sun always to radiate at about the same rate as the sun1 at least until sheer exhaustion prevents them from radiating any more1 and similarly for stars of all other weights4 ,there does not seem to be any general objection against supposing such a controlling mechanism to exist1 and indeed such mechanisms have been advocated by ,russell and ,eddington4 ,but when we consider such a mechanism in detail1 we encounter various objections which we shall consider in ,chapter ,v 7p4 #bid71 the principal of which is that stars controlled by it would1 so far as we can see1 be in a highly explosive state4 ,and immediately we abandon the hypothesis of such a controlling mechanism1 the observed close dependence of luminosity on weight compels us to suppose that a star's weight decreases as its luminosity diminishes1 which leads us back immediately to the annihilation of matter4 ,a further consideration which points in the same direction may be mentioned here4 ,we have seen how the 8candle-power per ton of weight0 is greatest in the heavier stars4 ,as an immediate consequence the loss of weight per ton is greatest in the heaviest stars4 ,in the time in which a massive star loses a hundred-weight per ton1 a star of light weight may lose only a few pounds per ton4 ,the consequence is that the passage of time tends to equalise the weights of the stars4 ,this principle no doubt explains in large part why the present stars shew no very great range of weight4 ,it also leads to interesting consequences when applied to the two components of a binary system4 ,it shews that as a binary system ages1 its two components ought continually to become more nearly equal in weight4 ,thus the two components ought to differ less in weight in old binaries than in young4 ,this last conclusion can be tested observationally4 ,as regards spectroscopic binaries1 ,aitken finds that the ratio of weights of the two constituents of a binary increases from about #jgj for young systems of large weight to #jij for older systems in which the constituents are about similar to the sun4 ,the direction of change is that predicted by theory2 the amount of change indicates a time-interval of the order of millions of millions of years between the two states concerned4 ,other astronomers have studied the corresponding problems presented by eclipsing and visual binaries1 and have reached almost identical conclusions4 ,the predictions of theory seem to be confirmed by each type of binary system separately4 ,on the whole1 in whatever direction we try to escape from the hypothesis of annihilation of matter1 the alternative hypothesis we set up to explain the facts seems to lead back in time to the annihilation of matter4 ,we must not overlook the revolutionary nature of the change which this hypothesis introduces into physical science4 ,the two fundamental corner-stones of nineteenth-century physics1 the conservation of matter and the conservation of energy1 are both abolished1 or rather are replaced by the conservation of a single entity which may be matter and energy in turn4 ,matter and energy cease to be indestructible and become interchangeable1 according to the fixed rate of exchange of #i #aj ergs per gramme4 ,yet1 looked at from another angle1 the hypothesis only carries physics one stage further along the road it has already trodden in the past4 ,heat1 light1 electricity have all in turn proved to be forms of energy2 the annihilation hypothesis only proposes to add another to the list1 so that matter itself also becomes a form of energy4 ,according to this hypothesis all the energy which makes life possible on earth1 the light and heat which keep the earth warm and grow our food1 and the stored up sunlight in the coal and wood we burn1 if traced far enough back1 are found to originate out of the annihilation of electrons and protons in the sun4 ,the sun is destroying its substance in order that we may live1 or1 perhaps we should rather say1 with the consequence that we are able to live4 ,the atoms in the sun and stars are1 in effect1 bottles of energy1 each capable of being broken and having its energy spilled throughout the universe in the form of light and heat4 ,most of the atoms with which the sun and stars started their lives have already met this fate2 the remainder are doubtless destined to meet it in time4 ,scientific writers of half a century ago delighted in the picturesque description of coal as 8bottled sunshine02 they asked us to think of the sunshine as being bottled-up as it fell on the vegetation of the primaeval jungle1 and stored for use in our fireplaces after millions of years4 ,on the modern view we must think of it as re-bottled sunshine1 or rather re-bottled energy4 ,the first bottling took place millions of millions of years ago1 before either sun or earth was in being1 when the energy was first penned up in protons and electrons4 ,instead of thinking prosaically of our sun as a mere collection of atoms1 let us think of it for a moment as a vast storehouse of bottles of energy which have already lain in storage for millions of millions of years4 ,so enormous is the sun's supply of these bottles1 and so great the amount of energy stored in each that1 even after radiating light and heat for #g or #h million million years1 it still has enough left to provide light and heat for millions of millions of years yet to come4 ,two quantitative considerations may help to shew these processes in a clearer light4 ,we have seen that the sun's present store of atoms would1 at the present rate of breakage1 last for #ae million million years4 ,this means that every year only one atom in #ae million million is broken1 a fraction which may seem absurdly small to produce the sun's vast continuous outpourings of energy4 ,let us1 however1 reflect that the energy which is continually pouring out of the sun's surface at the rate of about #ej horse-power per square inch is generated throughout the vast interior of the sun's body2 the stream of energy which emerges from a square inch of surface is the concentration of all the energy generated in a cone of a square inch cross-section1 but of #dcc1jjj miles depth4 ,such a cone contains about #aj atoms1 and although only one in #ae million million is broken each year1 there are still about two million million atoms destroyed each second4 ,even so1 the amount of energy set free by the annihilation of matter is rather surprising2 it is of an entirely different order of magnitude from that made available by any other treatment4 ,the combustion of a ton of the best coal in pure oxygen liberates about #e #aj ergs of energy2 the annihilation of a ton of coal liberates #i #aj ergs1 which is #ah1jjj million times as much4 ,in the ordinary combustion of coal we are merely skimming off the topmost cream of the energy contained in the coal1 with the consequence that #iiiiiiiiiid per cent4 of the total weight remains behind in the form of smoke1 cinders or ash4 ,annihilation leaves nothing behind2 it is a combustion so complete that neither smoke1 ash1 nor cinders is left4 ,if we on earth could burn our coal as completely as this1 a single pound would keep the whole ,british nation going for a fortnight1 domestic fires1 factories1 trains1 power-stations1 ships and all2 a piece of coal smaller than a pea would take the ,mauretania across the ,atlantic and back4 ,purely astronomical evidence has led to the conclusion that atoms are continually being annihilated in the sun and stars4 ,here we have a piece of the puzzle which fits perfectly on to those we tentatively fitted together in the last chapter4 ,as we there saw1 recent investigations in mathematical physics suggest that the highly penetrating radiation received on earth has its origin in the annihilation of matter out in space4 ,and the amount of this radiation received on earth is so great that we had to suppose the underlying annihilation of matter to be one of the fundamental processes of the universe2 we now discover that it is in all probability the process which keeps the sun and stars shining and the universe alive4 ,,physical ,,interpretation4 ,it is perhaps worth trying to probe still one stage further into the physical nature of this process of annihilation of matter1 although it must be premised that what follows is speculative in the sense that no direct observational confirmation is at present available4 ,we saw 7p4 #ace7 how the electrodynamical theory current in the last century required that the nucleus and electron of the hydrogen atom should approach ever closer and closer to one another with the mere passage of time1 until finally they rushed together and coalesced4 ,when this happened1 the negative charge of the electron and the positive charge of the nucleus would neutralise one another and their energy would go off in a flash of radiation similar to the flash of lightning which indicates that the negative and positive charges in two opposing thunderclouds have met and neutralised one another4 ,the more recent quantum theory calls a halt to this motion as soon as the nucleus and electron have approached to within a distance of #jec #aj centimetres of one another1 and by so doing keeps the universe in being as a going concern 7p4 #ace74 ,other halts are also established at #d1 #i1 #af1 etc4 times this distance1 but here the prohibition on further progress is not absolute4 ,at these longer distances the demand of the quantum theory 8thus far shalt thou go and no further0 seems to be replaced by 8thou shalt go no further until after a long time40 ,and it now seems possible1 on the astronomical evidence1 that the prohibition at the shorter distance may not be absolute either4 ,from the physical end nothing is known for certain1 although here again it seems contrary to the newer conceptions of physics1 as embodied in the wave-mechanics1 that any such absolute prohibition should exist1 either for the hydrogen atom or for other more complex atoms4 ,perhaps after waiting a long time in the orbit nearest to the nucleus1 the electron is permitted1 or even encouraged or compelled1 to proceed2 it merges itself into the nucleus and a flash of radiation is born in a star4 ,this provides the most obvious mechanism for the annihilation of electrons and protons which the evidence of astronomy seems to demand4 ,it will1 however1 be clearly understood that this is a purely conjectural conception of the mechanism2 we shall return to a further consideration of this very intricate problem in ,chapter ,v4 ,if this conjecture should prove to be sound1 not only the atoms which provide stellar light and heat1 but also every atom in the universe1 are doomed to destruction1 and must in time dissolve away in radiation4 ,the solid earth and the eternal hills will melt away as surely1 although not as rapidly1 as the stars3 ,the cloud-capped towers1 the gorgeous palaces1 ,the solemn temples1 the great globe itself1 ,yea1 all which it inherit1 shall dissolve1 ,and 444 leave not a rack behind4 ,and if the universe amounts to nothing more than this1 shall we carry on the quotation3 ,we are such stuff ,as dreams are made on2 and our little life ,is rounded with a sleep1 --or shall we not8 ,,chapter ,,iv ,carving out the ,universe ,we have commented on the surprising emptiness of space3 six specks of dust in ,waterloo ,station about represent the extent to which it is occupied by stars in its most crowded parts4 ,the comment might well have taken another form4 ,six specks of dust contain1 let us say1 a thousand million million molecules4 ,our model of space is empty because this great number of molecules happens all to be aggregated into as few as six lumps4 ,in real space the unit of aggregation is the star1 and an average star contains about #aj molecules--a number so large that it is quite useless to try to imagine it4 ,the emptiness of space does not originate from any paucity of molecules2 it originates from the circumstance that1 apart from those which form the tenuous clouds of gas stretching from star to star1 the molecules are aggregated together in the huge colonies we call stars1 with about #aj members to each4 ,why should the molecules in space herd together in this way1 when the molecules in the rooms in which ,i am writing and you are reading do not8 ,following a well-tried scientific method1 we may attempt to discover why these aggregates have formed1 by first examining what keeps them together now that they have formed4 ,the earth's atmosphere consists of about #aj molecules4 ,why do they stay pressed down into an atmosphere instead of spreading out through space8 ,the answer is of course provided by the earth's gravitation4 ,a bullet fired from the earth's surface with a speed of #fic miles a second or more will fly off into space1 because the earth's gravitational pull is inadequate to hold it back when it moves with so high a speed4 ,but a bullet fired with a speed of less than #fic miles a second does not leave the earth2 its speed is inadequate to take it clear of the earth's pull4 ,thus the molecule-bullets which form the earth's atmosphere1 flying with speeds less than a third of a mile a second1 have no chance at all of getting away4 ,the earth's gravitation continually pulls them back to earth1 so that the earth retains its covering of air4 ,at rare intervals a molecule may experience a succession of exceptionally lucky collisions with other molecules1 and so attain a speed of more than #fic miles a second4 ,a molecule which arrives at the outside of the earth's atmosphere with such a speed will leave the earth altogether1 and join the interstellar crowd of stray molecules4 ,the earth is continually shedding its atmosphere in this way1 but calculation shews that the loss1 even in millions of millions of years1 is quite insignificant1 so that we may regard the earth's atmosphere as permanent4 ,it is the same with the sun4 ,the sun's heat has broken up the molecules of its atmosphere into their constituent atoms1 and these move with an average speed of about #b miles a second4 ,but an atom-bullet would have to move at about #chj miles a second to escape altogether from the sun1 so that the solar atoms remain to form an atmosphere4 ,if all the molecules of air in an ordinary room were collected into a bunch at the centre of the room1 the ball of air so formed would of course exert a gravitational pull on its outermost molecules1 of the same kind as the earth and sun exert on the molecules of their atmospheres4 ,but1 because the weight of this ball of air is so small1 the intensity of its gravitational pull would also be small2 indeed it would be so feeble that a speed of about a yard a century would be enough to take the outermost molecules clear of it4 ,as the molecules of ordinary air move at about #ejj yards a second1 such a ball of air would immediately scatter through the whole room4 ,on the other hand1 if the room were big enough to contain the sun1 all its molecules could stay in a ball at the centre1 just as they do in the sun4 ,the outermost molecules would need a speed of at least #chj miles a second to escape1 so that their actual speeds of #ejj yards a second or so would be of no service to them4 ,,planetary ,,atmospheres4 ,in general the question of escape or no escape depends on the outcome of a battle between the molecular speeds of the outermost molecules1 and the intensity of the gravitational hold which the remainder of the mass exerts on them4 ,the solar system provides many examples of this4 ,the moon has only a sixth as much gravitational hold over the molecules of an atmosphere as the earth has1 with the result that any atmosphere the moon may ever have had1 has escaped by now4 ,mercury has two-fifths of the earth's gravitational hold1 but1 owing to its nearness to the sun1 its sunward surface is very hot1 with the consequence that its atmosphere also has escaped4 ,the gravitational hold of ,mars on its molecules is only a fifth of the earth's1 but its surface is cooler4 ,calculation shews that water-vapour and heavier molecules ought to remain1 while the lighter molecules of helium and hydrogen ought to have escaped4 ,this probably represents what has actually happened4 ,the largest satellite of ,saturn and the two largest satellites of ,jupiter would exercise about the same gravitational hold as the moon1 but as their surfaces must be enormously colder than that of the moon1 they ought to be able to retain atmospheres4 ,some observers claim to have seen indications of atmospheres on all three satellites4 ,all the four major planets exert stronger gravitational holds over their molecules than the earth1 and so retain their atmospheres with ease1 while ,venus1 with approximately the same gravitational hold as the earth1 also retains an atmosphere4 ,these considerations amply explain why the molecules of the stars must necessarily remain aggregated now that the aggregates have once been formed1 but the question of how and why these aggregates formed in the first instance is far more complex4 ,what1 for instance1 determined that there should be about #aj molecules in each star rather than #aj or #aj8 ,,gravitational ,,instability ,it is natural to enquire whether the forces which now keep a star together may not also have been responsible for its falling together in the first instance4 ,this leads us to study the aggregating power of gravitation in some detail4 ,five years after ,newton had published his law of gravitation1 ,bentley1 the ,master of ,trinity ,college1 wrote him1 raising the question of whether the newly discovered force of gravitation would not account for the aggregation of matter into stars1 and we find ,newton replying1 in a letter of date ,december #aj1 #afib3 ,it seems to me1 that if the matter of our sun and planets1 and all the matter of the universe1 were evenly scattered throughout all the heavens1 and every particle had an innate gravity towards oil the rest1 and the whole space throughout which this matter was scattered1 was finite1 the matter on the outside of this space would by its gravity tend towards all the matter on the inside1 and by consequence fall down into the middle of the whole space1 and there compose one great spherical mass4 ,but if the matter were evenly disposed throughout an infinite space1 it could never convene into one mass2 but some of it would convene into one mass and some into another1 so as to make an infinite number of great masses1 scattered great distances from one to another throughout all that infinite space4 ,and thus might the sun and fixed stars be formed1 supposing the matter were of a lucid nature4 ,an exact mathematical investigation on which ,i embarked in #aija1 not only confirms ,newton's conjecture in general terms1 but also provides a method for calculating what size of aggregates would be formed under the action of gravitation4 ,,the ,,formation ,,of ,,condensations4 ,you stand in the middle of a room and clap your hands4 ,in common language you are making a noise2 the physicist1 in his professional capacity1 would say you are creating waves of sound4 ,as they approach one another1 your hands expel the intervening molecules of air4 ,these stampede out1 colliding with the molecules of outer layers of air1 which are in turn driven away to collide with still more remote layers2 the disturbance originally created by the motion of your hands is carried on in the form of a wave4 ,although the individual molecules have an average speed of #ejj yards a second1 the zig-zag quality of their motions reduces the speed of the disturbance1 as we have already seen1 to about #cgj yards a second--the ordinary velocity of sound4 ,as the disturbance reaches any point the number of molecules there becomes abnormally high1 for the stampeding molecules add to the normal quota of molecules at the point4 ,this of course produces an excess of pressure4 ,it is this excess pressure acting on my ear-drum that transmits a sensation to my brain1 so that ,i hear the noise of your clapping your hands4 ,this excess of pressure cannot of course persist for long1 so that the excess of molecules which produces it must rapidly dissipate4 ,it is thus that the wave passes on4 ,yet there is one factor which militates against its dissipation4 ,each molecule exerts a gravitational pull on all its neighbours1 so that where there is an excess of molecules1 there is also an excess of gravitational force4 ,in an ordinary sound wave this is of absolutely inappreciable amount1 yet such as it is1 it provides a tiny force holding the molecules back1 and preventing them scattering as freely as they otherwise would do4 ,when the same phenomenon occurs on the astronomical scale1 the corresponding forces may become of overwhelming importance4 ,let us speak of the gas in any region of space where the number of molecules is above the average of the surrounding space1 as a 8condensation40 ,then it can be proved that1 if a condensation is of sufficient extent1 the excess of gravitational force may be sufficient to inhibit scattering altogether4 ,in such a case1 the condensation may continually grow through attracting molecules into it from outside1 whose molecular speeds are then inadequate to carry them away again4 ,whether this happens or not will depend of course on the speed of molecular motion in the gas1 as well as on the size of the condensation4 ,but it will not depend at all on the extent to which the process of condensation has proceeded4 ,by doubling the excess number of molecules in any condensation1 we double the extent to which condensation has proceeded4 ,in so doing1 we double the gravitational pull tending to increase the condensation1 but we also double the excess pressure which tends to dissipate it2 we double the weights on each side of the balance1 but the balance still swings in the same direction4 ,if once conditions are favourable to its growth1 a condensation goes on growing automatically until there are no further molecules left for it to absorb4 ,the greater the extent in space of a condensation1 the more favourable conditions are to its continued growth4 ,other things being equal1 a condensation two million miles in diameter will exert twice the gravitational force of a condensation one million miles in diameter1 but the excess pressures are the same in the two cases4 ,thus1 the larger a condensation is the more likely it is to go on growing1 and by passing in imagination to larger and larger condensations we must in time come to condensations of such a size that they are bound to keep on growing4 ,nature's law here is one of unrestricted competition4 ,nothing succeeds like success1 and so we find that condensations which are big to start with have the capacity of increasing still further1 while those which are small merely dissipate away4 ,suppose now that an enormous mass of uniform gas extends through space for millions of millions of miles in every direction4 ,any disturbance which destroys its uniformity may be regarded as setting up condensations of every conceivable size4 ,this may not seem obvious at first2 it may be thought that a disturbance which only affected a small area of gas would only produce a condensation of small extent4 ,such an argument overlooks the way in which the gravitational pull of a small body acts throughout the universe4 ,the moon raises tides on the distant earth1 and also tides1 although incomparably less in amount1 on the most distant of stars4 ,each time the child throws its toy out of its baby-carriage1 it disturbs the motion of every star in the universe4 ,so long as gravitation acts1 no disturbance can be confined to any area less than the whole of space4 ,the more violent the disturbance which creates them1 the more intense the condensations will be to begin with1 but even the smallest disturbance must set up condensations1 although these may be of extremely feeble intensity4 ,and we have seen that the fate of a condensation is not determined by its intensity but by its size4 ,no matter how feeble their original intensity may have been1 the big condensations go on growing1 the small ones disappear4 ,in time nothing is left but a collection of big condensations4 ,the mathematical analysis already referred to shews that there is a definite minimum weight such that all condensations below this weight merely dissipate away into space4 ,to a good enough approximation for our present purpose1 this minimum weight is such that if a tenth of this weight of gas were isolated in space1 and all the rest of the gas annihilated1 the molecules would just and only just fail to escape from its surface#bj4 #bj ,this is near enough1 but not absolutely accurate4 ,exact mathematical analysis shews that the weight of the minimum condensation ,m is given by ,c ,m --------------1 where ,c1 1 1 are the molecular velocity1 gravitation constant1 initial density1 and ratio of specific heats1 whereas the weight from which molecules moving with velocity ,c just fail to escape is given by #c ,c ,m ---- ------------------4 #d ,with #a the minimum weight of condensation is #ig times the weight which is just adequate to retain the molecules4 ,we may say that the original uniformly distributed mass of gas was 8unstable0 because any disturbance1 however slight1 causes it to change its configuration entirely2 it had the dynamical attributes of a stick balanced on its point1 or of a soap-bubble which is just ready to burst4 ,,primaeval ,,chaos4 ,these general theoretical results may now be applied to any mass of gas we please4 ,let us begin by applying them to ,newton's hypothetical 8matter evenly disposed throughout an infinite space40 ,we return in imagination to a time when all the substance of the present stars and nebulae was spread uniformly throughout space2 in brief1 we start from the primaeval chaos from which most scientific theories of cosmogony have started4 ,hubble has estimated that if the whole of the matter in those parts of the universe we know were redistributed evenly throughout space1 the gas so formed would have only about #ae #aj times the density of water4 ,this estimate is almost certainly on the low side1 even as representing present conditions1 and in trying to reconstruct the primaeval gas we must add something to allow for the molecules and atoms which have melted away into radiation in the intervening period4 ,on the whole1 perhaps #aj is not an unreasonable density to assign to the hypothetical primaeval nebula4 ,it is almost inconceivably low4 ,in ordinary air1 at a density of one eight-hundredth that of water1 the average distance between adjoining molecules is about an eight-millionth part of an inch2 in the primaeval gas we are now considering1 the corresponding distance is two or three yards4 ,the contrast again leads back to the theme of the extreme emptiness of space4 ,what is the minimum weight of condensation that would persist in this primaeval gas8 ,calculation shews that if ordinary air were attenuated to this extraordinary degree1 no condensation could persist and continue to grow unless it had at least #fb million times the weight of the sun2 any smaller weight of gas would exert so slight a gravitational pull on its outermost molecules1 that their normal molecular speeds of #ejj yards a second would lead to the prompt dissipation of the whole condensation4 ,we can carry out similar calculations with reference to other assumed densities of gas1 and other molecular velocities4 ,the following table shews the weights of condensations which would be formed in primaeval masses of chaotic gas having the densities shewn in the first column1 and the various molecular velocities mentioned at the heads of the remaining columns4 ,in each case the weights of the condensations are given in terms of the weight of the sun3 ---------------------------------------- ----------------------- ,density ,mol4 vel4 ,mol4 vel4 of ,mol4 vel4 of ,mol4 vel4 of in terms #ejj yards #ajjj yards #bjjj yards #cjjj yards of water a sec4 a sec4 a sec4 a sec4 ---------------------------------------- ----------------------- #aj #be1jjj1jjj #bjj1jjj1jjj #a1ejj1jjj1jjj #e1jjj1jjj1jjj #aj #fb1ejj1jjj #ejj1jjj1jjj #d1jjj1jjj1jjjac1jjj1jjj1jjj #ae #ajafj1jjj1jjja1cjj1jjj1jjjaj1jjj1jjj1jj jcj1jjj1jjj1jjj ---------------------------------------- ----------------------- ,all known stars have weights comparable with that of the sun4 ,thus if1 as ,newton conjectured1 the stars first came into being as condensations of this kind1 then the entries in this table ought to be comparable with unity4 ,newton's conjecture1 in the form in which we have just considered it1 is clearly untenable1 since all the calculated weights are many millions of times that of the sun4 ,if there ever existed a primaeval chaos of the kind we are now considering1 it would not condense into stars1 but into enormously more massive condensations1 each having the weight of millions of stars4 ,,the ,,birth ,,of ,,the ,,great ,,nebulae ,now it is significant that bodies are known in space having weights equal to those just calculated1 namely the great extra-galactic nebulae4 ,there are two nebulae whose weights can be determined with fair accuracy1 namely the ,great ,nebula in ,andromeda 7,plate ,,iv1 p4 #cj7 and the nebula ,n4,g4,c4 #deid in ,virgo 7,plate ,,xv74 ,hubble estimates these to be as follows3 ,nebula ,m #ca3 weight #cejj million times that of sun 0 ,n4,g4,c4 #deid3 0 #bjjj 0 0 ,these estimates are again probably both on the low side1 but their general order of magnitude is such as to suggest that the condensations which would first be formed out of the primaeval nebula must have been the great extra-galactic nebulae1 and not mere stars4 ,it is of course at best only a conjecture that the great nebulae were formed in this manner--if for no other reason because we can never know whether the hypothetical primaeval nebula even existed--but it seems the most reasonable hypothesis we can frame to explain the fact that the present nebulae exist4 ,these nebulae are so generally similar to one another that it seems likely that they must all have been produced by the action of the same agency1 and that which we have just considered provides a reasonable explanation which1 apart from the postulated existence of the continuous primaeval nebula1 is based on verae causae4 ,the great nebulae are of course not exactly similar1 and our next inquiry must be as to the origin of their differences4 ,illustration3 ,,plate ,,xv ,the ,nebula ,n4,g4,c4 #deid in ,virgo ,illustration3 ,mt ,wilson ,observatory ,the ,nebula ,n4,g4,c4 #gbag ,if the condensations in the primaeval gaseous nebula had formed and contracted in an absolutely regular fashion1 the final product would be an array of perfectly equal and similar masses of gas spaced with perfect regularity4 ,but nature is seldom as regular as this2 and we need not be surprised that the observed nebular array is not evenly spaced1 or that its members are neither equal in weight1 nor symmetrically arranged4 ,as the original condensations in the primaeval gas contracted1 they must have produced currents1 and these would hardly be likely to occur absolutely symmetrically4 ,if the motion in each mass of condensing gas had been directly towards the centre of the condensation at every point1 the final result would have been a spherical nebula devoid of all motion1 but any less symmetrical system of currents would result in a spin being given to each contracting mass4 ,this spin would no doubt be very slow at first1 but the well-known principle of 8conservation of angular momentum0 requires that1 as a spinning body contracts1 its rate of spin must increase4 ,thus when the process of condensation was complete1 the final product would be a series of nebulae rotating at different rates4 ,,nebular ,,rotation4 ,and this is exactly what is observed2 so far as our evidence goes the nebulae are in rotation1 and at different rates4 ,the various parts of the surface of any rotating mass necessarily have different speeds in space4 ,the sun for instance rotates about its axis in such a direction that the surface we see is moving always from east to west2 as a result the eastern limb is always advancing towards the earth1 while the western limb is receding from us4 ,a spectroscope turned on to different parts of the sun's surface in succession at once reveals these differences of speed2 they not only assure us of the sun's rotation1 but enable us to measure its amount4 ,the nebulae may be examined in the same way1 and the examination shews that a large number of them are rotating with the perfectly regular motion of a solid body--a spinning-top1 for instance4 ,measured by terrestrial standards their rates of rotation seem extraordinarily slow2 for instance the ,great ,nebula ,m #ca in ,andromeda requires about #ai1jjj1jjj years to make a complete rotation1 but this apparent slowness is an inevitable result of the huge size of the nebula4 ,even to get round once in #ai1jjj1jjj years1 the outer parts of the nebula have to move with speeds of hundreds of miles a second4 ,a few of the nebulae are quite irregular in shape1 but the majority have regular shapes1 and it is highly significant that these are precisely the shapes which1 it can be calculated mathematically1 would be exhibited by rotating masses of gas4 ,actually there is a far stronger case than this for supposing the nebulae to be rotating masses of gas4 ,from the purely observational evidence of surface-brightness and other characteristics1 ,hubble found that nearly all of these nebulae could be arranged in a single linear sequence--they could be arranged in order like beads on a string4 ,and this order proved to be practically identical with the sequence which had previously been calculated1 by purely theoretical methods1 for the configurations of masses of gas rotating at gradually increasing rates of speed4 ,let us examine this sequence of theoretical configurations in their natural order4 ,a mass of gas which was not rotating at all would of course assume a spherical shape under its own gravitation4 ,a number of perfectly spherical nebulae are known2 a typical example is shewn in fig4 #a on ,plate ,,xvi4 ,illustration3 ,,plate ,,xvi ,fig4 #a ,n4,g4,c4 #ccgi ,illustration3 ,fig4 #b ,n4,g4,c4 #dfba ,illustration3 ,fig4 #c ,n4,g4,c4 #caae ,illustration3 ,fig4 #d ,n4,g4,c4 #deid in ,virgo ,illustration3 ,fig4 #e ,n4,g4,c4 #defe in ,berenice's hair ,mt ,wilson ,observatory ,a sequence of ,nebular ,configurations ,with slight rotation the mass assumes the shape of a slightly flattened orange1 like the earth or ,jupiter4 ,nebulae of this shape are also known in abundance2 an example is shewn in fig4 #b on the same plate4 ,with a higher degree of rotation the degree of flattening increases1 but theoretical calculation shews that the orange shape is soon departed from4 ,the equator first begins to shew a pronounced bulge1 until finally1 with sufficient rotation1 this develops into a sharp edge1 the rotating mass now being shaped like a double-convex lens4 ,this prediction of theory is abundantly confirmed by observation1 a large number of these lens-shaped nebulae being observed in the sky4 ,an example is shewn in fig4 #c on ,plate ,,xvi4 ,the next step is somewhat sensational4 ,further rotation does not1 as might be expected1 result in still further flattening4 ,up to now1 each increase in rotation has made the bulge on the equator sharper1 but this is now as sharp as it can be4 ,theory shews that the flattening has also proceeded to the utmost possible limit1 and that the next stage must consist in matter being ejected through the sharp edge of the equator and spread throughout the equatorial plane4 ,here again observation confirms theory2 figs4 #d and #e 7,plate ,,xvi7 shew types of nebulae actually observed1 the former being the nebula in ,virgo which we have already had under discussion4 ,the comparatively thin layer of gas which now lies in the equatorial plane is similar in one respect at least to ,newton's matter 8evenly disposed throughout an infinite space40 ,disturbances can be set up in it in a variety of ways1 and any disturbance1 no matter how slight1 must result in the creation of a series of condensations4 ,as before1 those below a certain limit of size disappear of themselves1 while those above this limit continually increase in intensity until they have absorbed all the gas in the equatorial plane4 ,again1 as with the hypothetical primaeval chaos1 we can calculate the minimum size of condensation which can be expected to have a permanent existence1 and once again the result proves to be highly significant4 ,hubble's estimates of the total weights of two conspicuous nebulae have already been given4 ,as the distances1 and therefore also the sizes1 of both these nebulae are known1 it is an easy matter to calculate the average density of the gas throughout the whole nebula4 ,the average density in ,m #ca is found to be about #e #aj of that of water2 the corresponding number for ,n4,g4,c4 #deid is #b #aj4 ,these figures give us some idea of the density of matter in the outer regions of the nebulae4 ,although these densities are about a thousand million times as great as the estimated density of the original primaeval nebula of space1 they are still almost inconceivably low4 ,there is still only about one molecule to the cubic inch1 and a single breath from the lungs of a fly could fill a large cathedral with air of this density4 ,on proceeding to calculate the weights of the smallest condensations which could form and persist in a gas of this low density1 we obtain the results shewn in the following table4 ,the molecular velocities are taken rather low1 so as to allow for the cooling which must occur when the gas is spread out in the equatorial plane of the nebula4 ,again the weights of the condensations are given in terms of the weight of the sun4 ,and the significant fact emerges that most of the entries in the table represent weights comparable with that of the sun4 ,we are dealing with stellar weights at last2 the condensations which must form in the outer regions of the great nebulae will have weights comparable with those of the stars4 ---------------------------------------- ---------------------- ,density in ,mol4 vel4 of ,mol4 vel4 of ,mol4 vel4 of terms of water#ajj yards a sec4#cjj yards a sec4#ejj yards a sec4 ---------------------------------------- ---------------------- #aj #ag #cf #bbj #aj #e #acj #fbe #aj #ag #cfj #bbjj ---------------------------------------- ---------------------- ,,the ,,birth ,,of ,,stars ,and indeed there can be but little doubt that the process we have just been considering is that of the birth of stars4 ,even a casual glance at photographs of nebulae suffices to shew that the matter which has been ejected into the equatorial plane of a nebula does not lie uniformly spread out in that plane2 it is seen to have fallen into bunches1 knots or condensations4 ,these are apparent enough in many of the nebular photographs already shewn1 but they can be seen still more clearly in nebulae which are viewed nearly full-on1 such as for instance the two striking nebulae shewn in ,plates ,,xvii and ,,xviii4 ,these bunches are invariably too large to be interpreted as single stars2 they are more probably groups of stars4 ,in the largest telescopes they break up into great numbers of points of light in the way already exhibited in ,plate ,,xi 7p4 #gj74 ,we have already mentioned the reasons which compel us to regard these points of light as actual stars1 the principal being that some of them shew the characteristic light-fluctuations of the ,cepheid variables4 ,it is not altogether clear whether the stars are formed directly as condensations in the equatorial plane of the nebula1 or whether larger condensations form first1 namely the bunches observable in nebular photographs1 which subsequently form smaller condensations1 the stars4 ,on the whole it seems likely that there are two processes involved--first the break-up of the nebular matter into big condensations1 and then the break-up of these big condensations into stars4 ,such a succession of processes might well accompany a gradual cooling of the matter1 and it is of course possible that there are even more than two processes involved4 ,there is no need to form a final opinion on this at present1 as it is in no way essential to the progress of the main argument4 ,a collection of nebular photographs enables us to follow nebular evolution from the earliest stages shewn in ,plate ,,xvi 7p4 #bjg71 through the first appearance of granular bunches1 such as are shewn in ,plate ,,xvii1 and the first distinct appearance of stars shewn in ,plate ,,xviii1 down to the later stages1 such as are shewn in ,plates ,,xix and ,,xx1 in which the nebula appears to be but little more than a cloud of stars4 ,hubble has found it possible to follow the sequence still further1 and can trace a continuous transition from the nebulae of this last type to pure star-clouds such as the ,greater and ,lesser ,magellanic ,clouds shewn in ,plate ,,xxi4 ,illustration3 ,,plate ,,xvii ,mt ,wilson ,observatory ,the 8,whirlpool0 ,nebula ,m #ea in ,canes ,venatici ,illustration3 ,,plate ,,xviii ,mt ,wilson ,observatory ,the ,nebula ,m #ha in ,ursa ,major ,thus the stars appear to have been born in much the same way as we have conjectured that their parents1 the great nebulae1 had been born before them1 namely1 through the agency of what is generally known as 8,gravitational ,instability40 ,this causes any mass of chaotic gas to break up into detached condensations1 and1 the more tenuous the original gas1 the greater the weights of the condensations formed out of it4 ,the original primaeval nebula was of such low density that the condensations which formed in it weighed thousands of millions of times as much as the sun4 ,these increased their density so much in contracting that when their rotation caused them to eject gaseous matter1 this condensed into masses of stellar weight which we believe actually to be stars4 ,we have less certain knowledge of the former process than of the latter4 ,our only reason for thinking that the former process ever occurred is that the extra-galactic nebulae now exist4 ,there is no evidence that the primaeval chaotic nebula ever existed1 beyond the fact that the hypothesis of its previous existence leads to a very satisfactory explanation of the present nebulae existing as they now do4 ,on the other hand1 we not only know that the stars exist3 we also know that the masses of gas exist out of which theory shews that stars must necessarily be born4 ,they are the tenuous equatorial fringes of the great nebulae4 ,our telescopes shew us both the nebular fringes and the stars1 and we can almost study the actual process of birth4 ,,the ,,galactic ,,system ,,of ,,stars4 ,if this is the true account of the birth of the stars1 then our sun and its companions in space must have been born out of a rotating nebula4 ,observation gives strong support to this conclusion4 ,since the time of the ,herschels1 it has been a matter of frequent comment that the galactic system has the general shape of the extra-galactic nebulae1 the galactic plane of course representing the equatorial plane of the original nebula4 ,on purely observational grounds1 present-day astronomical thought is moving rapidly towards regarding the whole galactic system either as a rotating nebula or the remains of one4 ,it is even possible that this may still retain a central region which is as yet uncondensed into stars4 ,in the direction of the constellations ,scorpio and ,ophiuchus are dark clouds which may either veil the centre of the system or may conceivably be the centre itself4 ,in #aijd1 ,kapteyn found that the directions of motion of the stars in the vicinity of the sun were not distributed at random4 ,the stars appeared to prefer to move to and fro along a certain direction in the galactic plane rather than in other directions--8star-streaming10 he called it4 ,this peculiarity in the motion of the stars may be expected to throw some light on their origin4 ,each star moves in a complicated orbit under the gravitational attraction of all the other stars of the galactic system4 ,it is not possible to calculate this orbit in detail4 ,the orbit of a planet round the sun is easily calculated because only two bodies are involved1 the planet and the sun4 ,but even when there are only three bodies involved1 it is impossible to calculate the orbits that each describes under the attractions of the other two jointly3 this is the famous problem of three bodies1 which has never been solved4 ,when1 as in the galactic system1 thousands of millions of stars are involved1 it is naturally useless to try to calculate the orbit of each star--it would be as futile as trying to calculate the path of each molecule in a gas4 ,yet the same statistical methods which give us useful information as to the properties of a gas may be applied to studying the motions of the stars4 ,there are so many stars that we do not trouble about individuals at all1 we just treat them all together as a crowd4 ,to treat them as individuals would be as though the railway company tried to forecast the ,bank ,holiday traffic from ,london to ,brighton by considering the finances1 habits and psychology of each individual ,londoner4 ,illustration3 ,,plate ,,xix ,mt ,wilson ,observatory ,the ,nebula ,m #aja in ,ursa ,major ,illustration3 ,,plate ,,xx ,mt ,wilson ,observatory ,the ,nebula ,m #cc in ,triangulum ,without going into individual details1 we can see that each star must describe an orbit which1 after touring round a large part of the galaxy1 comes back to somewhere near its starting point4 ,calculation shews that each such circuit must take hundreds of millions of years to complete4 ,even so1 the stars will mostly have performed several complete circuits while the earth has been in existence1 and if we are right in supposing the ages of the stars to be millions of millions of years1 each star must have toured round the galaxy several thousands of times4 ,we should accordingly expect the galaxy to have assumed a definite permanent shape by now2 the distribution of stars in its different parts ought to have become something like steady1 and the stars ought to have settled down to a state approximating to one of steady motion4 ,statistical methods of investigation shew that there is not a great number of possible arrangements for a system of stars which has lived long enough to attain a steady state4 ,if the system as a whole has no rotation at all1 there is only one arrangement2 the stars form a globular mass with perfect symmetry in all directions4 ,the observed globular clusters 7,plate ,,ix1 p4 #fc7 provide good approximations to this type of formation1 although ,shapley has found that the majority are not absolutely spherical in shape4 ,if the system as a whole is endowed with rotation1 the possible configurations are all of a flattened symmetrical shape1 like a coin1 a watch or a round biscuit--in other words a system of stars in rotation must be shaped pretty much as we believe the galaxy to be shaped4 ,furthermore the motions of these stars must shew 8star-streaming0 of precisely the kind discovered by ,kapteyn4 ,thus both the shape of the galaxy and the peculiarities of motion of its stars indicate that the galactic system as a whole must be in a state of rotation4 ,and1 as we have seen 7p4 #fg71 recent observational researches by ,oort1 ,plaskett and others make it fairly certain that the rotation required by theory is an actual fact4 ,the motions of the stars indicate that the whole galactic system is rotating at a rate which varies from one region to another1 being about one revolution every #bcj million years in the vicinity of the sun4 ,and the hub of this gigantic wheel is found to coincide very closely with the spot which ,shapley had previously fixed as the geometrical centre of the galactic system from his researches on the distribution of the globular clusters4 ,thus1 since rotation cannot be generated out of nothing1 all the phenomena agree in shewing that the galactic system must have been born out of a rotating body4 ,we are acquainted with only one type of astronomical body which is of sufficient size to turn into a galactic system1 namely the great nebulae1 and as the majority of these are believed1 and some are known with certainty1 to be in rotation1 it seems reasonable to conclude that the galactic system must have been born out of a nebula1 unless indeed its structure is still such that we should even now describe it as a nebula if we saw it from the great distance from which we view the other great nebulae4 ,the observed period of rotation of the galactic system1 of the order of #bcj million years1 is substantially longer than the period1 either known or suspected1 of any of the nebulae1 but the dimensions of the galactic system are also greater than those of any known nebula1 and the two facts hang together4 ,again1 the number of stars in the galactic system is probably substantially higher than in any nebula1 as also is the total weight of these stars#ba4 ,all this makes it clear that if the galaxy is1 or ever has been1 one of the great nebulae1 it must have been one of unusual size and weight4 #ba ,the following estimates have already been mentioned3 ,weight of ,galaxy in terms of sun #bdj1jjj1jjj1jjj 0 nebula ,m #ca in terms of sun #c1ejj1jjj1jjj 0 0 ,n4,g4,c4 #deid in terms of sun #b1jjj1jjj1jjj ,illustration3 ,,plate ,,xxi ,harvard 7,arequipa7 ,observatory ,the ,lesser ,magellanic ,cloud ,illustration3 ,franklin-,adams ,chart ,the ,greater ,magellanic ,cloud ,we have seen how the sun and all the stars are continually losing weight as the result of their emission of radiation4 ,it follows that the total weight of the galactic system is for ever decreasing1 and as a consequence its gravitational hold on its constituent stars is continually weakening4 ,if this gravitational hold were suddenly to vanish altogether1 each star would replace its present curved path by a perfectly straight line1 along which it would travel at its present speed1 undeflected by any gravitational forces from other stars1 so that the stars which now constitute the galactic system would soon be scattered through the whole of space4 ,in brief1 if the gravitational pull of the stars were suddenly abolished1 the galaxy would begin to expand at a great rate4 ,although this is not likely to happen1 the gradual abolition of the gravitational pull of the stars1 as they turn their weight into radiation1 must cause the galaxy to expand all the time at a slow rate3 calculation suggests that its present rate of expansion would double its size in about #cj million million years4 ,the expansion must have been far more rapid in the past1 when the stars were full of youthful vigour and squandered their substance more lavishly than now1 so that it seems probable that the galactic system was substantially smaller and more compact in the past than now1 and the original nebula probably smaller still4 ,we have seen how the stars in the great nebulae appear to be congregated in bunches or clusters4 ,the globular clusters in the galactic system may possibly be bunches of stars of the same general type1 which have remained undisturbed by other groups of stars and so have assumed the globular form under their own attraction--just as a mass of gas would do4 ,shapley finds that these clusters lie somewhat outside the galactic plane2 it looks as though they were broken up or disorganised in travelling through this plane1 where they would encounter other stars4 ,by contrast groups of stars of the type generally described as moving clusters--the ,pleiades1 the ,hyades1 the stars of the ,great ,bear and a crowd of others voyaging in company with them through space--are generally found to move in the galactic plane4 ,these may quite possibly represent the final vestiges of globular clusters which have been broken up by interaction with other stars1 all except the most massive members having been knocked out of formation4 ,mathematical analysis shews that the interaction between the stars of such moving clusters and other stars in the galactic plane would cause each cluster to assume the shape of a flat biscuit or watch1 of diameter equal to #b times its thickness4 ,it is significant that the majority of the moving clusters shew a flattening of this kind1 its amount agreeing tolerably well with the calculated value4 ,it is even conceivable that the 8local cluster0 surrounding the sun 7p4 #fe7 may be the remains of such a bunch of stars4 ,the motions of these clusters may also induce a further flattening1 in a direction perpendicular to their motion4 ,some clusters shew this further flattening1 the ,ursa ,major cluster being a striking example4 ,,the ,,birth ,,of ,,binary ,,systems ,in discussing the way in which nebulae might be born out of chaos1 we noticed that the existence of currents in the primordial medium would endow the resulting nebulae with varying amounts of rotation4 ,for the same reason the children of the nebulae1 the stars1 must also be endowed with rotation at their birth4 ,there is a further reason for such rotation4 ,the general principle of the 8conservation of angular momentum0 requires that rotation1 like energy1 cannot entirely disappear4 ,its total amount is conserved1 so that when a nebula breaks up into stars1 the original rotation of the nebula must be conserved in the rotations of the stars4 ,thus the stars1 as soon as they come into being1 are endowed with rotations transmitted to them by their parent nebula1 in addition to the rotations resulting from the currents set up in the process of condensation4 ,their continual loss of weight causes the physical conditions of the stars to change1 and we shall find in the next chapter that this change generally involves a shrinkage of the star's diameter4 ,the same principle of 8conservation of angular momentum0 now requires that1 as a star shrinks1 its speed of rotation shall increase4 ,in brief1 as a star ages1 it spins faster and faster4 ,now rotation was the essential factor in the birth of the stars out of the parent nebula4 ,a nebula perfectly devoid of rotation would not1 so far as we can see1 break up into stars at all1 and this prediction of theory appears to be confirmed by observation1 since nebulae of the perfectly spherical type shewn in fig4 #a of ,plate ,,xvi can never be resolved into stars in the telescope4 ,on the other hand we saw how nebulae which were initially endowed with rotation would continually increase their speed of rotation under shrinkage1 until finally their rotation broke them up and produced a family of stars out of each4 ,the question now obviously arises whether1 as the speed of rotation of the stars increases1 these are likely to break up in their turn1 and produce yet a third generation of astronomical bodies4 ,again we might expect that mathematical analysis would apply to large and small bodies equally1 irrespective of scale4 ,and a detailed examination of the problem shews that in actual fact the process we have had under consideration would repeat itself1 and again bring a further generation of smaller bodies into being1 provided the physical conditions were suitable4 ,the physical conditions1 however1 prove not to be suitable2 they certainly fail in one respect at least4 ,although a rotating star may eject gaseous matter in its equatorial plane1 the whole process will be on a much smaller scale than in the nebulae4 ,we might expect the ejected matter to form condensations as before1 but calculation shews that1 unless the molecular velocity is extraordinarily low1 no condensation can survive unless it has a weight greater than the whole weight of the star6 ,this means that with any reasonable molecular velocity1 the ejected gas would not form condensations at all4 ,it would merely scatter into the surrounding space1 forming an atmosphere without any distinct condensations4 ,such is the course of events if the stars1 like the nebulae before them1 are treated as pure masses of gas4 ,another alternative must1 however1 be considered4 ,,the ,,fission ,,of ,,liquid ,,stars4 ,we have seen how a gaseous nebula devoid of rotation would assume a strictly spherical shape under its own gravitational attraction1 while slight rotation would cause it to flatten into an orange shape1 like the earth4 ,the earth also has assumed this shape on account of its rotation1 although its internal structure is very different from that of a gaseous nebula4 ,strict mathematical investigation shews that this flattened-orange shape must be common to all slowly rotating bodies1 regardless of their internal composition2 gases1 liquids1 and plastic bodies assume it equally4 ,but the shape of a rapidly rotating body must depend very greatly on its internal arrangement and constitution1 being especially affected by the extent to which the weight of the body is concentrated near its centre4 ,as a consequence of the high compressibility of gases1 this central concentration of weight reaches its extreme limit in a purely gaseous mass4 ,the opposite extreme is reached in a mass of uniform incompressible liquid such as water1 in which there can be no central concentration at all4 ,as a mass of this latter type increases its speed of rotation1 the slightly flattened-orange shape merely gives place to the shape of a more flattened orange4 ,the tendency of a gaseous mass to form a sharp edge round the equator is entirely absent1 and the cross-section of its figure remains elliptical throughout4 ,at a still higher speed of rotation1 the equator loses its circular shape and it too becomes elliptical4 ,the figure has now three unequal diameters1 but every cross-section is strictly elliptical2 the figure is an 8ellipsoid40 ,after this1 its longest diameter begins to elongate until the mass1 still ellipsoidal in shape1 has formed a cigar-shaped figure with a length nearly three times its shortest diameter4 ,a new series of events now begins4 ,the mass of liquid gradually concentrates about two distinct points on its longest diameter1 a waist or furrow forming across its middle4 ,this furrow gets deeper and deeper until it has cut the body into two distinct detached masses1 which now rotate in orbital motion about one another and form a binary star4 ,the sequence of events is shewn in fig4 #aa2 diagrams of the final stage as represented by actual binary stars have already been given on p4 #ed4 ,for comparison the sequence of shapes assumed by a rotating mass of gas is shewn in fig4 #ab1 this being identical with the sequence of observed nebular shapes which is actually observed1 and is illustrated photographically in ,plate ,,xvi 7p4 #bjg74 ,the two chains of configurations shewn in figs4 #aa and #ab represent1 it will be remembered1 the two extreme cases of a rotating body whose substance is distributed with complete uniformity1 and of a rotating body whose substance is very highly condensed towards its centre4 ,as the constitutions of actual astronomical bodies must lie somewhere between these two extremes1 we might naturally expect such a body to follow a series of configurations intermediate between the two shewn in figs4 #aa and #ab4 ,theory shews that as a matter of fact it does not4 ,all bodies having less than a certain critical degree of central condensation follow the sequence shewn in fig4 #aa1 or a sequence differing only immaterially from this2 all bodies having more than this critical amount of central condensation follow the sequence shewn in fig4 #ab4 ,thus when this critical degree of central condensation is reached there is a sudden swing over from fig4 #aa to fig4 #ab4 ,in brief1 every rotating body conducts itself either as if it were purely liquid1 or as if it were purely gaseous2 there are no intermediate possibilities4 ,illustration3 ,fig4 #aa4 ,the sequence of configurations of a rotating mass of liquid4 ,illustration3 ,fig4 #ab4 ,the sequence of configurations of a rotating mass of gas4 ,observational astronomy leaves no room for doubt that a great number of stars1 possibly even all stars1 follow the sequence shewn in fig4 #aa4 ,no other mechanism1 so far as we know1 is available for the formation of the numerous spectroscopic binary systems1 in which two constituents describe small orbits about one another4 ,in these stars1 then1 the central condensation of mass must be below the critical amount just mentioned2 to this extent they behave like liquids rather than gases4 ,we have relied entirely on mathematical analysis in tracing out the details of the process of fission just described4 ,and we are totally unable to check our theoretical results by observation4 ,there is not a single star in the sky of which we can say3 here is a star which has certainly started to break up by fission1 and will certainly end as a binary system4 ,it is perhaps not altogether surprising4 ,the breaking up process is in all probability of very short duration by comparison with the lives of the stars1 so that in any case we should have to investigate a great many stars before catching one in the act of breaking into two4 ,on the other hand1 a star in the act of breaking up ought to be very easily differentiated from ordinary stars4 ,mathematical analysis shews that its interior would be in a state of considerable turmoil1 so that it would hardly be likely to shine with a steady light3 it would be a 8variable0 star4 ,further1 its condition ought to shew a progressive change1 although it is an open question whether this would be rapid enough to be detected in a few years of observation4 ,finally1 if any group or class of stars were suspected of being stars in process of fission1 it ought to be possible to arrange them in an order corresponding to the extent to which the fissional process had advanced1 and the sequence so formed ought to end with stars in the physical condition of newly formed binaries4 ,i have recently suggested that the ,cepheid variables1 whose unknown mechanism of light-variation renders such valuable service to the astronomer1 are merely stars in the act of fission4 ,want of space prevents our entering here into the intricate question of how far they exhibit the peculiarities which mathematical analysis requires of stars in process of fission1 but it is easily seen that they satisfy the three simple tests outlined above4 ,they are certainly variable stars1 and the light-variations of different stars are so similar as to suggest very strongly that they all arise from the same cause4 ,the periods of a number of ,cepheids are suspected of change1 and ,hertzsprung has estimated that the prototype star1 ,cephei1 which has now been observed for #abf years1 is decreasing its period of light-fluctuation at the rate of about a tenth of a second per annum2 thus a million years would reduce its present period of #e days by over a day4 ,finally ,dr ,otto ,struve has found that the sequence of ,cepheids fits almost perfectly on to that of newly formed binaries4 ,thus the prospects for the 8fission theory0 of ,cepheid variables seem hopeful1 but the theory must be very thoroughly tested before it can be accepted1 and it cannot be claimed that it has been so far either tested thoroughly or accepted extensively4 ,an alternative view1 first propounded by ,plummer and ,shapley1 regards ,cepheid variables as pulsating spheres of gas4 ,the behaviour of such masses of gas has been investigated mathematically by ,eddington and others1 but it does not appear that it can be reconciled with the observed behaviour of ,cepheid variables4 ,,the ,,development ,,of ,,binary ,,systems ,whatever the process of formation of binary systems may be1 we experience fairly plain sailing in attempting to trace out the subsequent development of such systems4 ,three factors are simultaneously in operation4 ,,tidal ,,friction4 ,the first of these three factors1 which is only of brief duration1 was designated 8tidal friction0 by ,sir ,george ,darwin1 who first drew attention to it1 and investigated the manner of its operation4 ,when first a rotating mass breaks up and forms a binary system1 the two components are so near that they necessarily raise tremendous tides on one another2 ,darwin shewed that these drive the two bodies apart1 and equalise their rates of rotation in so doing4 ,after these processes have been in operation for millions of years1 the rates of rotation of the two bodies and their rate of revolution about one another must all become equal1 so that each body perpetually turns the same face to its companion1 and the two rotate about one another like the two masses of a dumb-bell joined by an invisible arm4 ,although a sun and planet do not form a binary system in the strict technical sense1 they are necessarily subject to the same forces as true binary systems4 ,thus we can see the operation of tidal friction in the fact that ,mercury always turns the same face to the sun1 and that ,venus rotates so slowly on its axis that it turns the same face to the sun day after day1 and probably also week after week4 ,as we pass further out into space the effects of tidal friction rapidly diminish1 but it is probably significant that the nearer planets1 ,earth and ,mars1 have days of about #bd hours each1 while the remote planets ,jupiter1 ,saturn and ,uranus each have days of only about #aj hours4 ,the periods of rotation of ,neptune and ,pluto are unknown4 ,apart from these we find1 in a general way1 that the further we recede from the sun the more rapidly the planets rotate1 which is precisely the effect that ought to be produced by tidal friction4 ,in the same way1 tidal friction has in all probability been mainly responsible for the present configuration of the earth-moon system1 driving the moon away to its present distance from the earth and causing it always to turn the same face towards us4 ,tidal friction must of course still be in operation4 ,the moon is responsible for the greater part of the tides raised in the oceans of the earth2 these1 exerting a pull on the solid earth underneath1 slow down its speed of rotation1 with the result that the day is continually lengthening1 and will continue to do so until the earth and moon are rotating and revolving in complete unison4 ,when1 if ever1 that time arrives1 the earth will continually turn the same face to the moon1 so that the inhabitants of one of the hemispheres of the earth will never see the moon at all1 while the other side will be lighted by it every night4 ,by this time the length of the day and the month will be identical1 each being equal to about #dg of our present days4 ,jeffreys has calculated that this state of things is likely to be attained after about #ej1jjj million years4 ,after this1 tidal friction will no longer operate in the sense of driving the moon further away from the earth4 ,the joint effect of solar and lunar tides will be to slow down the earth's rotation still further1 the moon at the same time gradually lessening its distance from the earth4 ,when it has finally1 after unthinkable ages1 been dragged down to within about #ab1jjj miles of the earth1 the tides raised by the earth in the solid body of the moon will shatter the latter into fragments 7p4 #bej below71 which will form a system of tiny satellites revolving around the earth in the same way as the particles of ,saturn's rings revolve around ,saturn1 or as the asteroids revolve around the sun4 ,we have already noticed how the present arrangement of the earth-moon system enables us to calculate the earth's age2 ,jeffreys estimates that the system must have taken something of the order of #djjj million years to reach its present configuration 7p4 #aee74 ,this period1 which seems so long when judged by terrestrial standards1 is only a moment in the life of a star4 ,the components of the true binary star attain a configuration like that of the earth-moon system in a brief fraction of their lives1 and1 passing on1 reach in time the configuration in which each perpetually turns the same face to the other4 ,up to now1 tidal friction has been driving the masses ever further apart1 but as soon as this stage is attained1 the tides become stationary on both components1 so that tidal friction goes out of operation4 ,thus the separation produced by tidal friction has now reached its limit1 and1 so far as tidal friction is concerned1 the two bodies might rotate in the way just described to all eternity4 ,,loss ,,of ,,weight4 ,as tidal friction becomes inoperative1 a new agency takes hold4 ,we have calculated that the sun is losing weight at the rate of #bej million tons a minute1 that it has been losing weight at this rate1 or some comparable rate1 for millions of millions of years1 and will continue so to do for millions of millions of years yet to come4 ,the earth is at its present distance from the sun because this distance is exactly suited to the present weight of the sun4 ,if the sun's weight were suddenly reduced to half1 its gravitational pull on the earth would also be reduced to half1 and the earth would move to a greater distance from the sun#bb4 #bb ,although the details are unimportant1 the actual course of events would be that the earth would begin to describe an elliptic instead of a circular orbit about the sun1 the earth's average distance being greater than now4 ,the sun's weight is not likely to be suddenly reduced to half1 but it has been reduced by a thousand million tons in the last four minutes1 with the result that its gravitational grip on the earth has been weakened and the earth has moved out to a wider orbit2 at this moment the radius of the earth's orbit is greater than it was four minutes ago4 ,the details can be traced out mathematically with complete precision4 ,it appears that the earth's orbit round the sun is not a circle1 or even an ellipse of small eccentricity2 it is a spiral curve1 like an uncoiled watch spring4 ,every year the earth moves a tiny step further out into the outer cold and darkness2 exact calculation shews that its average distance from the sun increases at the rate of about a metre 7#cicg inches7 a century4 ,the effect is of course of precisely the same kind as we have seen must be produced in the galactic system by the loss of weight of the stars4 ,the only difference is that in the galaxy a system of thousands of millions of stars is expanding1 whereas the sun-earth system consists of only two members4 ,precisely similar effects must be produced by the loss of weight in the two components of a binary star4 ,here both components are radiating away energy1 and so are simultaneously losing weight4 ,detailed calculation shews that they must continually recede from one another1 but that the shape of their orbit will undergo no change4 ,neither separately nor in combination do the two effects just described explain either the shapes or the sizes of the observed orbits of binary stars as a whole4 ,to interpret these we must call on yet a third agency1 the gravitational forces from passing stars4 ,we have already seen how these account for the statistical distribution of orbits which is actually observed4 ,the combination of all three agencies1 tidal friction1 extending over millions of years1 loss of weight1 extending over millions of millions of years1 and disturbance from passing stars1 extending over a similar period1 is responsible for the evolution of binary star systems4 ,their aggregate effect is to widen the distance between the two stars1 while at the same time knocking the orbit out of shape4 ,,subdivision4 ,while these changes are going on in the orbital arrangement of a binary system1 the two components are themselves changing their physical condition on account of their continual loss of weight1 and1 as with the parent stars1 this loss of weight will generally result in a shrinkage in the size of the star4 ,the shrinkage of either component of the system causes its shape to run through the sequence of configurations we have already enumerated1 and if the shrinkage continues for long enough1 the component may end by further dividing into two separate masses4 ,either or both of the constituents of a binary system may subdivide into binary sub-systems in this way1 resulting in a system of either three or four stars4 ,h4 ,n4 ,russell has shewn mathematically that when a binary system ,p1 ,q divides into a triple system1 ,p1 q1 q1 through ,q breaking up into two constituents q1 q1 the distance between q and q cannot be more than about a fifth of the original distance ,,pq4 ,this theoretical law is well confirmed by observation4 ,fig4 #ac shews a typical multiple system1 and we notice that the separations in each of the various sub-systems are all quite small in comparison with those of the main systems4 ,illustration3 ,fig4 #ac4 ,a typical multiple star4 ,the development of the hypothetical primitive chaos has now been traced through five generations of astronomical bodies1 chaos--nebulae--stars--binary systems--sub-systems1 to which a sixth generation must be added if the stars of the sub-system happen to fission further1 as1 for instance1 they have done in the star shewn in fig4 #ac4 ,the genealogy of the stars begins with a vast tenuous nebula filling all space2 the last generation consists of small1 shrunken1 dying stars with no capacity for further subdivision4 ,the genealogy has been traced out primarily on theoretical grounds alone1 but we need have no doubts as to its general accuracy1 since observation confirms it repeatedly and at almost every step4 ,indeed it is hardly too much to say that the evolutionary sequence could have been discovered almost equally well from observational evidence alone1 except for the hypothetical primaeval chaos1 about which1 from the nature of the case1 observation cannot have anything to say4 ,,the ,,origin ,,of ,,the ,,solar ,,system ,almost all observed astronomical formations can be placed in the evolutionary sequence we have just discussed1 either with fair certainty or with reasonable plausibility1 except for one outstanding and conspicuous exception--the ,solar ,system4 ,cosmogony came into being as an attempt to discover the origin of the solar system4 ,the reasons why it limited its efforts to this particular problem are chronological2 in the early days of cosmogony1 astronomy was barely conscious of anything outside the solar system4 ,the sketch just given of the findings of modern scientific cosmogony has been remarkable in that it has exhibited cosmogony taking us a tour round the whole universe1 explaining the origin and life-history of practically every object we encounter on this tour1 and then becoming speechless when it is brought back home and confronted with its birthplace1 the solar system4 ,,laplace',s ,,nebular ,,hypothesis4 ,the first serious scientific cosmogony was that embodied in the famous ,nebular ,hypothesis of ,laplace4 ,in #agee ,kant had pictured a primaeval chaos condensing into spinning nebulae1 and1 identifying one of these nebulae with the sun1 had imagined the planets to be formed by the solidification of masses of gas shed from the nebula1 much in the way in which we have supposed the stars to be born4 ,in #agif1 ,laplace advanced similar ideas1 which he developed in detail with a mathematical precision quite beyond the capacities of ,kant4 ,he shewed how1 as its shrinkage made it spin ever faster and faster1 a rotating mass of gas would flatten out1 develop the lenticular form we have already discussed 7fig4 #c of ,plate ,,xvi71 and then proceed to eject matter in its equatorial plane1 or rather to leave it behind as the shrinkage of the main mass continued4 ,at this stage it would look somewhat like the nebulae shewn in figs4 #d and #e of ,plate ,,xvi1 although ,laplace1 being unacquainted with nebulae of this type1 adduced ,saturn surrounded by its rings as an example of the formation to be expected at this stage 7,plate ,,xxiv1 p4 #bej74 ,laplace imagined that the fringe of abandoned gas would then condense and form a single planet4 ,as the main mass shrunk further1 more gas was abandoned in the equatorial plane1 which in due course condensed into another planet1 and so on1 until the sun left off shrinking and no more planets were born4 ,a repetition of the same process1 but on a far smaller scale1 resulted in the satellites being born out of the planets4 ,that the hypothesis is prima facie plausible1 is evident from its having survived1 and indeed been generally accepted1 for nearly a century before it encountered any serious opposition4 ,recently criticisms have accumulated1 of so vital a nature as to make it clear that the hypothesis must be abandoned4 ,the sun1 according to ,laplace1 broke up and gave birth to planets through excess of rotation4 ,yet both theory and observation indicate quite clearly the fate in store for a star which rotates too fast for safety2 it does not found a family1 but merely bursts1 like an overdriven fly-wheel1 into parts of nearly equal size4 ,spectroscopic binary and multiple systems are the relics of stars which have broken up through excess of rotation1 and they do not in the least resemble the solar system4 ,again1 the principle of 8conservation of angular momentum0 requires that the rotation of the primaeval sun shall persist in the rotation of the present sun1 and in the revolutions of the planets around it4 ,on adding together the contributions from all of these1 we obtain a total which ought to represent the angular momentum of the primaeval sun4 ,in strictness a further contribution ought to be added on account of the weight of all the radiation which the sun has emitted since the planets were born4 ,we can calculate the amount of this contribution1 because we know the age of the earth with tolerable accuracy1 but it proves to be entirely negligible4 ,the total angular momentum of the primaeval sun can be calculated with very fair accuracy1 because more than #ie per cent4 of the total angular momentum of the present solar system resides in the orbital motion of ,jupiter4 ,this contribution can be calculated with great exactness1 so that some uncertainty in the minor contributions which make up the remaining #e per cent4 can have but little influence on the total4 ,when this total is calculated the startling fact emerges that the primaeval sun cannot have had enough rotation to cause break-up at all4 ,clearly the sun is very far from being broken up by its present rotation4 ,flattening of figure is the first step towards break-up1 and the sun's figure is so little flattened by its present rotation that the most refined measurements have so far failed to detect any flattening at all4 ,on adding the further angular momentum now represented in the motions of ,jupiter and all the other members of the solar system1 we arrive at a primaeval sun rotating about as fast as ,jupiter now rotates1 and shewing about the same degree of flattening of figure as ,jupiter--enough to measure quite easily in a telescope1 or even to detect with the eye alone1 but nothing like enough to cause break-up4 ,the sun is hardly likely to have altered much since its planets were born1 for the intervening #bjjj million years or so represent but a minute fraction of the sun's total life4 ,if1 however1 we imagine it to have shrunk appreciably in the interval1 then the available amount of angular momentum would have been even more unable to break up the large primaeval sun than it is to break up the present shrunken sun4 ,whichever way we look at it1 we reach the conclusion that the sun cannot have broken up1 as ,laplace imagined1 through excess of rotation2 indeed it can never have possessed more than a quite tiny fraction of the amount of rotation needed to break it up4 ,a third objection is of a somewhat different character4 ,laplace was a very great mathematician1 and there was nothing the matter with his abstract mathematical theory1 so far as it went4 ,more refined modern analysis has confirmed it at every step1 and observation does the same1 as photographs of rotating nebulae 7,plate ,,xvi7 bear witness4 ,these photographs exhibit a process taking place before our eyes1 which is essentially identical with that imagined by ,laplace1 except for a colossal difference of scale4 ,everything happens qualitatively as ,laplace imagined1 but on a scale incomparably grander than he ever dreamed of4 ,in these photographs the primitive nebula is not a single sun in the making1 but contains substance sufficient to form hundreds of millions of suns2 the condensations do not form puny planets of the size of our earth1 but are themselves suns2 they are not eight or so in number1 but must be counted in millions4 ,we may ask why the same thing cannot happen on the smaller scale imagined by ,laplace--for are not the conclusions of mathematics applicable independently of the size of the body with which we are dealing8 ,the answer has in effect been given already 7p4 #bah74 ,everything happens on the smaller scale according to plan until we come to the formation of the condensations2 here the question of scale proves to be vital4 ,we have seen 7p4 #aif7 how the molecules which form the sun have condensed into a star because of their great number2 the molecules in a room do not condense into anything at all because they are too few4 ,in the same way1 the molecules left behind by the slow shrinkage of a sun 7assuming this for the moment to rotate rapidly enough to leave molecules behind7 would not condense1 because at any instant there would be too few of them available for condensation4 ,they would be shed by driblets1 and a driblet of gas does not condense but scatters into space4 ,a mathematical calculation decides the question definitely1 and the decision is entirely adverse to the hypothesis of ,laplace4 ,apart from minor details1 the process imagined by ,laplace explains the birth of suns out of nebulae2 it cannot explain the birth of planets out of suns4 ,,second ,,body ,,theories4 ,laplace imagined his sun to be alone in space1 even its nearest neighbours being too remote to influence it in any way4 ,it was the natural supposition to make2 we have already remarked how exceedingly rare an event it must be for two stars to approach near enough to influence one another4 ,yet no possible mode of evolution of a star which remains alone in space seems able to explain the origin of the solar system4 ,as far back as #agej1 ,buffon had suggested that the solar system might have been produced through the disruption of the sun by another body1 which he described as a 8comet40 ,in propounding his ,nebular ,hypothesis1 ,laplace mentioned ,buffon's idea1 but dismissed it somewhat curtly on the grounds that it seemed unable to account for the nearly circular orbits of the planets--an ill-founded objection1 as we shall soon see4 ,yet when we find that a single star cannot of itself give birth to a solar system1 it becomes natural to investigate what happens on the rare occasions on which the evolution of a star is directed along other paths by the near approach of a second star4 ,in #ahhj1 ,bickerton of ,new ,zealand1 reviving ,buffon's idea1 supposed that the solar system had been formed by the collision of the sun with another star4 ,he imagined the dbris of the collision to form a third nebulous body1 condensations in which formed the planets4 ,he shewed how the resistance which the planets would encounter as they moved through the surrounding nebula would gradually make their orbits more circular1 and so account for their present nearly circular shapes4 ,ten years earlier1 the ,english writer1 ,r4 ,a4 ,proctor1 had advanced similar ideas1 although with less precision4 ,in #aije ,professors ,chamberlin and ,moulton of ,chicago advanced a modification of the same ideas1 under the name of the 8,planetesimal ,hypothesis40 ,discarding the idea of material collision1 they supposed that a passing star exerted a powerful tidal pull on the sun1 with the result that the ordinary solar prominences temporarily attained an extraordinary violence2 the ejected matter was supposed to rise to unusual heights and condense into small solid bodies1 the 8planetesimals10 out of the aggregation of which the planets were ultimately formed4 ,these various theories were all purely speculative4 ,they have shewn very little capacity either for surviving the acid test of mathematical analysis1 or for explaining the more salient features of the solar system2 none of them1 for instance1 explains why the larger planets in the solar system are accompanied by families of satellites4 ,three years before ,chamberlin and ,moulton advanced their planetesimal theory1 ,i had speculated as to the possibility of tidal forces breaking up a star1 and generating a solar system4 ,in #aiaf1 ,i investigated mathematically what would actually happen when one star raised violent tidal forces on another4 ,the results ,i obtained seemed to me to demolish the planetesimal theory of ,chamberlin and ,moulton1 and led me to put forward the present-day 8,tidal ,theory10 which ,i believe a large proportion of astronomers now accept as giving the most probable origin of the solar system2 it can of course make no claim to finality or certainty4 ,,tidal ,,theory4 ,when two stars or other bodies pass close to one another without collision1 the primary effect must be that each raises tides in the other4 ,the closer the approach1 the higher the tides in general1 although something must depend also on the speed with which the bodies pass one another1 because this determines the length of time during which they influence one another4 ,it is likely that the two spiral arms which give their name and characteristic appearance to the spiral nebulae may owe their inception to a somewhat similar tidal action4 ,conditions here are different in that the rotation of the nebulae in any case causes them to emit matter in their equatorial planes1 so that even small tidal forces should then cause this matter to concentrate in two symmetrical arms4 ,under stellar conditions a far closer approach is necessary to draw matter out from the star1 and it is then most likely that there will be two unequal and dissimilar arms1 or possibly only one arm4 ,illustration3 ,,plate ,,xxii ,mt ,wilson ,observatory ,two ,nebulae 7,n4,g4,c4 #dcie1 #ddja7 suggestive of ,tidal ,action ,illustration3 ,,plate ,,xxiii ,the twin ,nebulae ,n4,g4,c4 #defg-h ,illustration3 ,mt ,wilson ,observatory ,the ,nebula ,n4,g4,c4 #gdgi ,if the approach is very close indeed1 the tides may assume an entirely different aspect from the feeble tides which the sun and moon raise in our oceans2 they may take the exaggerated forms of high mountains of matter moving over the surface of the star4 ,an even closer approach may transform these mountains into long arms of gas drawn out from the body of the star4 ,if1 as will generally be the case1 the two stars are of unequal weights1 the lesser will in general suffer more disturbance than the weightier4 ,,the ,,birth ,,of ,,planets4 ,the long arm or filament of matter drawn out of a star by tidal action is at first continuous in its structure1 but analysis shews that it provides a fit subject for the operation of what we have called 8,gravitational ,instability40 ,condensations begin to form in this long arm of gas1 in the way already described4 ,as before1 the smaller condensations are dissipated1 while the larger increase in intensity until finally the filament breaks up into a number of detached masses--planets have been born out of the smaller star4 ,the pairs of nebulae shewn in ,plate ,,xxii and the upper half of ,plate ,,xxiii are very probably under one another's tidal influence1 and may serve to suggest the general nature of the process we are now considering1 although it must be remembered that whatever is happening here is on an enormously greater scale than that of the solar system--if it were not1 the telescope would be utterly unable to shew it to us4 ,when the new-born planets first begin to move as separate and independent bodies1 they are acted on by the gravitational pulls of both stars1 and so describe highly complicated orbits4 ,gradually the bigger star recedes until its gravitational effect becomes negligible1 and the planets are left describing orbits around the smaller star alone4 ,if the planets moved in a clear field of empty space1 these orbits would be exact ellipses4 ,but the great cataclysm which has just occurred must have left all sorts of dbris behind4 ,comets1 meteors and other minor bodies which still survive in the solar system may represent a small part of it1 but probably the main part was left in the form of dust or gas1 so that the new-born planets had at first to plough their way through a medium which offered some resistance to their motions4 ,under these circumstances their orbits would not be strict ellipses4 ,it can be proved that a resistance of the kind just described would change the shape of the orbits1 and that with the progress of time they would become more circular1 finally becoming absolutely circular if the medium should last long enough4 ,the dbris of gas and dust would1 however1 continually be swept up by the planets and would disappear completely in time1 probably leaving the planetary orbits something short of absolute circles4 ,assuming that all this has happened in the solar system1 very little of the original dbris can now remain1 its last vestiges being probably represented by the particles of dust which are responsible for the zodiacal light4 ,nevertheless1 the resisting medium appears to have existed for long enough to make the orbits1 both of the planets and of their satellites1 very nearly circular for the most part4 ,the exceptional cases are fully as significant as the cases of conformity4 ,comparatively elongated orbits still exist in just those regions where we should expect the primaeval resisting medium to have been most sparsely spread in space1 namely on the outermost confines of the solar system and of the various satellite system4 ,pluto1 the outermost planet of all1 has a more elongated orbit than any other planet4 ,again1 in the systems of ,jupiter and ,saturn1 the satellites with the most elongated orbits are those which are furthest away from their primaries4 ,in addition to this1 a general tendency may be discerned for elongated orbits to be associated with small weights1 both in planets and their satellites4 ,mercury1 with a weight of only a twenty-fifth that of the earth1 has a quite elongated orbit1 as also to a less degree has ,mars with a ninth of the weight of the earth4 ,an explanation of this has been suggested by ,jeffreys4 ,massive planets such as ,jupiter and ,saturn must have collected a large mass of the resisting medium round them1 and carried it through space with them as a far-reaching envelope4 ,the massive planets would have their motion checked by the interaction of the whole of this big envelope with the remainder of the medium1 and so would attain circular orbits more rapidly than the lighter planets which had accumulated envelopes of very much smaller dimensions4 ,and the same1 with the appropriate modifications1 is true of the satellite systems4 ,jeffreys has calculated the rate at which planetary orbits would change their shape under the action of this resisting medium4 ,the data of the problem are necessarily uncertain1 and this uncertainty naturally affects his conclusions1 but his study has yielded a valuable confirmation of other estimates of the length of time which has elapsed since the planets were born4 ,we may next turn our attention to the physical changes which must all this time be affecting the various planets4 ,the long filament of matter pulled out of the sun is likely to have been richest in matter in its middle parts1 these parts having been pulled out when the second star was nearest and its gravitational pull was strongest4 ,diagrammatically at least1 we may think of this filament as shaped like a cigar--thick near the middle1 thin at the ends--so that when condensations begin to form1 those near the middle are likely to be richer in matter than those at the ends4 ,this probably explains why the two most massive planets1 ,jupiter and ,saturn1 occupy the middle positions in the sequence of planets4 ,illustration3 ,fig4 #ad4 ,diagrammatic scheme shewing the birth of planets out of a cigar-shaped filament of gas4 ,the number of satellites is indicated under each planet 7see p4 #bdc74 ,fig4 #ad shews the planets arranged in the order of their distances from the sun1 with their sizes drawn roughly to scale4 ,the thousands of asteroids whose orbits now fill the space between the orbits of ,mars and ,jupiter are represented as a single planet1 it being generally supposed that these asteroids were formed by the break-up of what was originally a single planet in a way we shall shortly describe4 ,if we surround the planets by a continuous outline1 as in the diagram1 we can reconstruct in imagination the cigar-shaped filament out of which they were produced1 and we see at once how the biggest planets were produced where matter was most abundant4 ,the tidal theory which predicts all these features had been propounded1 and its consequences worked out1 many years before the new planet ,pluto had been discovered4 ,valuable support for the theory may thus be found in the circumstance that ,pluto behaves in every way according to the requirements of the tidal theory4 ,,the ,,birth ,,of ,,satellites4 ,we have already noticed how the great disparity of weight between the sun and planets distinguishes the sun-planet formation from that of the normal binary star1 and so suggests entirely different origins for the two formations4 ,exactly the same disparity repeats itself in the planet-satellite systems4 ,just as the parent sun is enormously more massive than its children the planets1 so these in turn are far more massive than their satellite children4 ,the sun has #ajdg times the weight of its most massive planet and many millions of times the weight of the smallest4 ,in the system of ,saturn the corresponding figures are #daej and about #af1jjj1jjj4 ,the nearest approach to equality of weights is provided by the earth-moon system1 the earth having only #ha times the weight of the moon4 ,and1 like the planetary system of the sun1 the satellite systems of ,saturn and1 to a lesser degree1 of ,jupiter shew a general tendency for the weights of the various satellites to increase up to a maximum as we pass outwards from the planet1 and then to decrease again4 ,this again suggests formation out of a cigar-shaped filament with matter occurring most richly near the middle4 ,in conjunction with the repetition of the great disparity of weights between primary and secondaries1 this indicates very forcibly that the satellites of the planets must have been born by the same type of process as had previously resulted in the birth of their parents4 ,we can imagine the process in a general way4 ,immediately after their birth1 the planets must begin to cool down4 ,the largest planets1 ,jupiter and ,saturn1 naturally cool most slowly and the smallest most rapidly4 ,the latter may lose heat so speedily that they liquefy1 and perhaps even solidify1 almost immediately after their birth4 ,while these events are in progress1 the planets are still pursuing somewhat erratic orbits1 in describing which they may pass so near to the sun that a second series of tidal disruptions occurs4 ,in these the sun itself plays the rle originally played by the passing star from space1 the planets playing the part originally taken by the sun4 ,the sun may now tear long filaments of matter out of the surfaces of the planets1 and these1 forming condensations1 may give birth to yet another generation of astronomical bodies1 the satellites of the planets4 ,in some such way the tidal theory imagines the planetary satellites to have come into being4 ,mathematical investigation shews that the more liquid a planet was at birth1 the less likely it would be to be broken up by the still gaseous sun4 ,if1 however1 such a break-up occurred1 the weights of primary and satellites would be more nearly equal than if the planet had been more gaseous4 ,thus1 on passing from wholly gaseous planets to planets which liquefied at or immediately after their birth1 we should expect at first to find planets with large numbers of relatively small satellites1 and then1 after passing through the border-line cases of planets with small numbers of relatively large satellites1 we should expect to come to planets having no satellites at all4 ,we have already seen that the big central planets1 ,jupiter and ,saturn1 ought to have remained gaseous for longest and the smaller planets to have liquefied earliest2 we now see that this prediction of theory exactly describes what is actually found in the solar system4 ,starting from ,jupiter and ,saturn1 each with nine relatively small satellites1 we pass ,mars with only two satellites1 and come to the earth with its one relatively large satellite1 followed by ,venus and ,mercury which have no satellites at all4 ,proceeding in the other direction we leave ,jupiter and ,saturn each with their nine tiny satellites1 to discover ,uranus with four small satellites and ,neptune with one comparatively big satellite4 ,the number placed under each planet in fig4 #ad gives the number of its satellites4 ,when the numbers are exhibited in this way1 the law and order in the arrangement of the satellite systems becomes very apparent1 and this arrangement is seen to be exactly in accordance with the prediction of the tidal theory4 ,the cigar-shaped arrangement applies not only to the sizes of the planets1 but also1 as it ought1 to the numbers of their satellites4 ,the earth and ,neptune1 with only one satellite each1 and those comparatively large ones1 form the obvious lines of demarcation between planets which were originally liquid and those which were originally gaseous4 ,this leads us to conjecture that ,mercury1 ,venus and ,pluto must have become liquid or solid immediately after birth1 that the earth and ,neptune were partly liquid and partly gaseous1 and that ,mars1 ,jupiter1 ,saturn and ,uranus were born gaseous and remained gaseous at least until after the birth of their families of satellites4 ,we may perhaps find further evidence confirmatory of the tidal theory in the circumstance that the weights of ,mars and ,uranus are abnormally small for their positions in the sequence of planets4 ,if1 as we have supposed1 the planets were all born out of a continuous filament of matter1 the weight of ,mars at birth would in all probability have been intermediate between those of the earth and ,jupiter1 and the weight of ,uranus intermediate between those of ,neptune and ,saturn4 ,but if1 as we have already been led to suppose1 the two anomalous planets ,mars and ,uranus were the two smallest planets to be born in the gaseous state1 they would be likely to lose more of their substance than the other planets through their outermost layers of molecules dissipating away into space before they had cooled down into the liquid state4 ,if ,mars and ,uranus are supposed to be mere relics of planets which were initially far more massive than they now are1 the anomalies begin to disappear and the pieces of the puzzle to fit together in a very satisfactory manner4 ,,orbital ,,planes4 ,every rotating mass1 whether gaseous1 liquid or solid1 has a definite axis of rotation1 and1 perpendicular to this1 a definite equatorial plane which divides the mass symmetrically into two exactly equal and similar halves4 ,when a mass breaks up under its own rotation1 the equatorial plane and the symmetry still persist4 ,illustrations of this can be found in any set of photographs of rotating nebulae1 as1 for instance1 those shewn in ,plates ,,xv and ,,xvi4 ,in more humble life an illustration is provided by the splashes of mud thrown off by a spinning bicycle-wheel1 which all keep in the plane in which the wheel is spinning4 ,if the sun's equatorial plane had proved to be a plane of symmetry for the solar system1 so that the whole system was similarly arranged as regards the two sides of this plane1 it might have been possible to explain the system as the result of a rotational break-up4 ,but the sun's equatorial plane is not a plane of symmetry4 ,the planets do not move in it1 most of them moving in a plane which makes an angle of #e or #f degrees with it4 ,in terms of our humble analogy1 the splashes of mud are not flying about in the plane in which the bicycle-wheel is spinning4 ,the hypothesis that the planets came into being through a rotational break-up of the sun fails completely before this fact1 but the tidal theory provides a simple explanation of it at once4 ,the sun is still rotating much as it was before the planets were born1 and so retains its original equatorial plane4 ,the quite different plane in1 or very close to1 which the planets are describing orbits must clearly be the plane in which the long tidal filament was originally drawn out by the passing star4 ,thus the plane in which the outer planets now move must record the position of the plane in which the two stars1 the sun and the wandering star1 the second parent of the sun's family of children1 described orbits about one another #bjjj million years ago4 ,it is the only clue the latter has left of his identity1 and is of course far too slight to make identification possible after this long lapse of time4 ,to sum up1 we have seen that the normal mechanism by which the greater part of the universe has been carved out is the birth of successive generations of astronomical bodies through the action of 8gravitational instability40 ,the normal genealogy runs somewhat as follows3 chaos--nebulae--stars--binary systems--sub-systems4 ,not all stars have passed on to the last two generations2 where only a small amount of rotation was present1 a star might well live its whole life without further subdivision4 ,our sun would have provided an instance of this had it not been for the rare accident of the close approach of a second star4 ,from the interaction of these1 two other generations came into being1 still through the mechanism of gravitational instability4 ,for our solar system1 as for any other similar systems there may be in the sky1 the genealogy runs as follows3 chaos--nebula--sun--planets--satellites4 ,both types of genealogy shew five generations1 each born from its parent through the action of gravitational instability1 and between them the two genealogies include practically all the large size astronomical objects with which we are acquainted4 ,it is then fair to say that 8gravitational instability0 appears to be the agency primarily responsible for the main architecture of the universe4 ,,roche',s ,,limit4 ,the reign of gravitational instability must end with the birth of planetary satellites1 since gaseous bodies of less weight than these could not hold together4 ,even under the most favourable circumstances their feeble gravitational pulls would be unable to restrain their outermost molecules from escaping1 so that the whole mass would speedily scatter into space4 ,yet astronomy provides many instances of smaller bodies2 we have already mentioned the asteroids1 meteors or shooting-stars1 and the particles of ,saturn's rings4 ,as all these are too small to have been born in the gaseous state1 we must suppose them to be the broken-up fragments of larger masses4 ,this accords with the circumstance that these small bodies as a rule do not occur individually but in swarms4 ,the asteroids occur as a single swarm4 ,if these were found scattered throughout the solar system1 their origin might present a difficult problem4 ,as things are1 the whole swarm can be explained quite simply as the broken fragments of a primaeval planet4 ,saturn's rings again admit of a natural explanation as the fragments of a former shattered moon of ,saturn4 ,comets1 which we have hardly had occasion to mention so far1 are in all probability swarms of minute bodies which are just held together sufficiently by their mutual gravitational attraction to describe a common orbit in space4 ,at its apparition in #aiji1 ,halley's comet was estimated to reflect as much of the sun's light as a single body #be miles in diameter4 ,yet its apparent surface was #cjj1jjj times that of such a body1 and was quite transparent4 ,it is difficult to resist the conclusion that the comet consisted of a widely-spaced swarm of small bodies1 and such a swarm again admits of a simple explanation as the broken fragments of a single mass4 ,shooting-stars1 or meteors1 also are encountered in swarms4 ,as we shall see later1 the motion of many of these swarms makes it possible to identify them as broken-up comets4 ,thus the broken fragments which compose a comet are identical with the meteors which we see as shooting-stars when they penetrate into the earth's atmosphere4 ,shapley has estimated that the earth's atmosphere must catch thousands of millions of shooting-stars every day1 of which at most only one in a hundred is bright enough to be visible to the naked eye4 ,generally they dissolve into vapour before they reach the earth's surface 7see p4 #agf72 occasionally one is so big that the earth's atmosphere fails to dissipate it entirely1 and what remains of it strikes the earth as a solid body--a meteorite4 ,every shooting-star and meteorite may be regarded as a miniature comet1 consisting of only a single fragment4 ,on occasions a whole group of fragments1 moving in parallel paths at only small distances apart1 may strike the earth's atmosphere and appear as a 8fireball40 ,generally speaking all the small fry of the solar system move in swarms1 and can be naturally interpreted as the broken-up fragments of larger bodies4 ,if the meteorites are broken fragments of bodies which were born out of the sun at the same time as the planets1 they must have solidified at about the same time as the earth1 at an epoch which we have placed at about #bjjj million years ago4 ,but if they had been born out of some other star1 the time of their solidification might have been anywhere up to millions of millions of years ago4 ,professor ,paneth and two colleagues at ,knigsberg have recently estimated the ages of various meteoric stones by methods similar to those employed to fix the age of the earth 7p4 #aed74 ,they obtain ages which range from a few million years up to #bijj million years1 but there is nothing beyond this last figure4 ,not a single stone suggests an age even approaching millions of millions of years4 ,this provides very strong evidence that these stones were products of the same cataclysm as produced the earth1 and incidentally provides valuable confirmation of our previous estimate of the earth's age4 ,we can easily see how larger bodies might be broken up into swarms of meteors4 ,we have supposed the sun to have been broken up1 at least to the extent of ejecting a family of planets1 by the tidal pull of a passing star4 ,what would have happened if the passing star had not passed1 but had come to stay8 ,so long as it remained within a certain distance of the sun1 its tidal forces were pulling the sun to pieces4 ,we can imagine how a longer visit from it would have resulted in a greater upheaval in the sun1 and the birth of a larger family of planets4 ,finally a visit of unlimited duration would have shattered the sun into fragments4 ,in #ahej ,roche gave a mathematical investigation of this process of tidal break-up4 ,his discussion dealt only with solid or liquid bodies1 but the underlying mechanism is the same whether the bodies are solid1 liquid or gaseous4 ,we have seen that the smaller of the two bodies involved in a tidal encounter suffers the most4 ,roche dealt only with the case in which one body was very small in comparison with the other2 in such a case the small body was completely broken up1 while the larger one remained unscathed4 ,roche imagined the small body to describe an orbit of gradually decreasing size around the big body4 ,if the two bodies were of equal density1 he calculated that the small body would be broken up as soon as the radius of its orbit fell to #bde times the radius of the large body4 ,if the bodies are of different density the matter is slightly more complicated4 ,we must imagine the larger body to expand or contract until it has the same average density as the smaller body2 the critical distance is then #bde radii of the larger body in its imaginary expanded or contracted state4 ,this distance is generally known as ,roche's limit4 ,a satellite can with safety describe a circular orbit about its primary so long as this orbit lies beyond ,roche's limit1 but it is broken into fragments as soon as it trespasses within the limit4 ,the following figures confirm ,roche's mathematical analysis3 ,radius of ,saturn's outermost ring #bcj radii of ,saturn ,roche's limit #bde radii of primary ,radius of orbit of ,saturn's innermost satellite #caa radii of ,saturn ,radius of orbit of ,jupiter's innermost satellite #bed radii of ,jupiter ,radius of orbit of ,mars' innermost satellite #bgi radii of ,mars ,at the same time they suggest very forcibly that ,saturn's rings are the broken-up fragments of a former satellite which ventured into the danger-zone marked out by ,roche's limit4 ,we have seen how our own moon is destined in time to contract its orbit1 until it is finally drawn within the ,roche's limit surrounding the earth and broken into fragments4 ,after this the earth will have no moon1 but will be surrounded by rings like ,saturn4 ,we speak of ,saturn's rings in the plural1 because two distinct circular gaps cause an appearance of three detached rings4 ,there is a tendency to jump to the hasty inference that the rings are the shattered remains of three distinct satellites1 but it is not so4 ,goldsbrough has shewn how certain orbits around ,saturn are rendered unstable by the motions of the larger satellites of ,saturn1 so that no particle could permanently remain in such an orbit4 ,he has calculated positions for these unstable orbits1 and these are found to agree exactly with the positions of the observed divisions between the rings4 ,thus ,saturn's rings were in all probability produced by the breakage of a single satellite4 ,the ring of small satellites which our moon will ultimately form round the earth will contain no divisions1 because the earth has no other moons to render certain orbits unstable4 ,illustration3 ,,plate ,,xxiv ,saturn in #aiaf ,illustration3 ,saturn in #aiag ,illustration3 ,lowell ,observatory ,saturn in #aiba ,saturn and its ,system of ,rings ,roche's fundamental idea can be extended in many directions and admits of varied applications4 ,there must1 for instance1 be a danger-zone1 marked off by a ,roche's limit1 surrounding the sun4 ,the distance of this danger-zone from the sun depends on the density of the body for which it is dangerous 7p4 #bdi74 ,for a body having the low density of a comet the distance will be very great indeed4 ,whatever the distances of their danger-zones1 comets must occasionally pass through them and become broken up in so doing4 ,two comets1 ,biela's comet 7#ahdf7 and ,taylor's comet 7#aiaf71 were observed actually to break in two while at about the earth's distance from the sun1 and in #ahhb a comet was seen to divide into four parts4 ,biela's comet returned in due course 7#aheb7 in the form of two distinct comets a million and a half miles apart1 since which time neither part of the original comet has been seen again4 ,the orbit of this comet was identical with that of the ,andromedid meteors1 which make a display of shooting-stars in the earth's atmosphere on favourable #bgths of ,november1 so that it is likely that these shooting-stars are the broken remains of ,biela's comet4 ,other conspicuous swarms of shooting-stars also move in the tracks of comets--the ,leonids which used to make a magnificent show every #cc years move in the track of ,comet #ahff ,i1 the ,perseids in the track of another ,comet 7#ahfb ,,ii71 and the ,aquarids in the track of ,halley's famous comet4 ,in each case1 there can be little doubt that the shooting-stars are scattered fragments of the comets4 ,besides this there are several families of comets whose members follow one another round and round in the same orbit1 as though they had originally formed a single mass4 ,in the same way a ,roche's limit must surround the planet ,jupiter1 so that comets and other bodies may be broken up through getting inside the danger-zone marked off by this limit4 ,jupiter's innermost satellite is already perilously near it4 ,but the greatest interest of this particular danger-zone is that it probably accounts for the existence of the asteroids4 ,in the early days of the solar system1 when the orbits of the planets were less nearly circular than they now are1 a primaeval planet between ,mars and ,jupiter may well have described an orbit so elongated as to take it repeatedly within the danger-zone of ,jupiter4 ,if so1 we need look no further for the origin of the asteroids4 ,it is significant that the average orbit of all the asteroids agrees almost exactly with that of the planet which ,bode's law 7p4 #ai7 would require to exist between ,mars and ,jupiter4 ,,chapter ,v ,stars ,the process of carving out the universe which we considered in the last chapter ends normally with a simple star1 although special accidents may have other consequences4 ,as the result of close approaches with other stars1 a tiny fraction of the total number of the stars1 perhaps about one star in #ajj1jjj 7p4 #cda below71 may be attended by a retinue of planets4 ,another fraction1 still small1 although far greater than the foregoing1 appears to have broken up as the result of excessive rotation1 and formed binary or perchance multiple systems4 ,but the destiny of the majority of stars is to pursue their paths solitary through space1 neither breaking up of themselves nor being broken up by other stars4 ,the only contact such stars have with the outer universe is that they are incessantly pouring away radiation into space4 ,this outpouring of radiation is almost entirely a one-way process1 any radiation a star may receive from other stars being quite inappreciable in comparison with the amount it is itself emitting4 ,the radiation is accompanied by a loss of weight1 and this again is all give and no take1 the weight of any stray matter the star may sweep up out of space1 like that of any radiation it receives1 being quite inappreciable in comparison with the weight it loses by radiation4 ,without unduly straining the facts1 the normal object in the sky may be idealised as a solitary body1 alone in endless space1 which continually pours out radiation and receives nothing in return4 ,in the present chapter we shall consider the sequence of changes which such a star may be expected to experience during the course of its life4 ,having already discussed the mechanical accidents to which stars are liable1 namely1 fission through rotation and break-up through the tidal action of a passing star1 we now turn to consider the life of a normal star which escapes all accidents until it finally becomes extinct through mere old age4 ,it will be necessary in the first place to describe the physical states of the various types of stars observed in the sky1 and as a preliminary to this we must explain how the observations of the astronomer are translated into a form which gives us direct information as to the condition of the star4 ,,surface-,,temperature4 ,in ,chapter ,,ii 7p4 #adj7 we saw how each colour of light or wave-length of radiation has a special temperature associated with it1 light of this colour predominating when a body is heated up to the temperature in question4 ,for instance1 a body raised to what we call a red-heat emits more red light than light of any other colour1 and so looks red to the eye4 ,thus if a star looks red1 it is legitimate to infer that its surface is at the temperature we describe as a red-heat4 ,if another star has the colour of the carbon of an arc-light1 we may conclude that its surface is at about the same temperature as the arc4 ,in this way we can estimate the temperatures of the surfaces of the stars4 ,in practice the procedure is not so crude as the foregoing description might seem to imply4 ,the astronomer passes the light from a star through a spectroscope1 thus analysing it into its different colours4 ,by a process of exact measurement1 he then determines the proportions in which the different colours of light occur4 ,this shews at once which colour of light is most plentiful in the spectrum of the star4 ,either from this or from the general distribution of colours1 he can deduce the temperature of the star's surface4 ,illustration3 ,fig4 #ae4 ,distribution of radiation of different wave-lengths at various temperatures4 ,we have already seen 7p4 #abc7 how ,planck discovered the law according to which the radiation emitted by a full radiator is distributed amongst the different colours or wave-lengths of the spectrum4 ,the four curves shewn in fig4 #ae represent the theoretical distribution for the radiation emitted by surfaces at the four temperatures #cjjj1 #djjj1 #ejjj and #fjjj degrees respectively4 ,the different wave-lengths of light are represented by points on the horizontal axis1 the marked wave-lengths being measured in the unit of a hundred-millionth part of a centimetre1 which is usually called an ,angstrom4 ,the height of the curve above such a point represents the abundance of radiation of the wave-length in question4 ,the two methods of determining stellar temperature will be easily understood by reference to these curves4 ,the #fjjj degrees curve reaches its greatest height at a wave-length of #dhjj ,angstroms1 so that if light of wave-length #dhjj ,angstroms proves to be most abundant in the spectrum of any star1 we know that the star's surface has a temperature of #fjjj degrees4 ,the second method consists merely in examining to which of the theoretical curves shewn in fig4 #ae the observed curve can be fitted most closely4 ,either of these methods indicates that the temperature of the sun's surface is about #fjjj degrees absolute1 which is nearly twice the temperature of the hottest part of the electric arc4 ,the total amount of light and heat received on earth from the sun shews that the sun's radiation must be very nearly1 although not quite1 the 8full temperature radiation0 7p4 #abc7 of a body at this temperature4 ,this is also shewn by the sun's radiation being distributed among the various colours in a way which conforms very closely to the theoretical curve for a full radiator at #fjjj degrees shewn in fig4 #ae4 ,the surface-temperature of a star can also be estimated from its spectral type4 ,many of the lines in stellar spectra are emitted by atoms from which one or more electrons have been torn off by the heat of the star's atmosphere4 ,we know the temperatures at which the electrons in question are first stripped off their atoms1 and so can deduce the star's temperature4 ,the temperatures which correspond to the different types of stellar spectra as shewn in ,plate ,,viii 7p4 #ea71 are approximately as follows3 ------------------------ ,spectral type,temperature ------------------------ ,b #bc1jjj ,a #aa1jjj ,f #g1djj ,g #f1jjj ,k #e1ajj ,m #c1djj ------------------------ ,the last three entries in the table refer only to normal stars having diameters comparable with that of the sun4 ,we shall find 7p4 #bgf7 that a second class of stars 7giants7 exist1 whose diameters are enormously greater than the sun's4 ,these have the substantially lower temperatures shewn below3 ------------------------ ,spectral type,temperature ------------------------ ,g #efjj ,k #dbjj ,m #cbjj ------------------------ ,in studying stellar structure and mechanism1 we are less concerned with the heat of the star's surface as measured by its temperature1 than with the amount of radiation it pours out per square inch4 ,this of course depends on the temperature2 the hotter a surface1 the more radiation it emits4 ,but the temperature does not measure the quantity of radiation emitted4 ,if we double the temperature of a surface it emits #af times1 not twice1 its previous amount of radiation2 the radiation from each square inch of surface varies as the fourth power of the temperature4 ,as a consequence1 a star with a surface-temperature of #cjjj degrees1 or half that of the sun1 emits only a sixteenth part as much radiation per square inch as the sun#bc4 ,the radiation of each star is a compound of light1 heat and ultra-violet radiation1 and the proportions of these are not the same in different stars2 the cooler a star's surface the greater the fraction of its radiation which is emitted as heat4 ,thus the star at #cjjj degrees will emit nothing like as much as a sixteenth of the sun's light per square inch1 but will emit more than a sixteenth of the sun's heat4 #bc ,this is shewn in fig4 #ae1 the area of the #cjjj degree curve being only a sixteenth of the area of the #fjjj degree curve4 ,this shews that the total emission of radiation of a star cannot be estimated from its visual brightness alone2 a substantial allowance must always be made for invisible radiations1 both for the invisible heat at the red end of the spectrum and for the invisible ultra-violet radiation at the other end4 ,the importance of these corrections is shewn in fig4 #af4 ,the four thick curves are identical with those already given in fig4 #ae1 and shew how the radiation from a star of given surface-temperature is distributed over the different wave-lengths4 ,the total radiation emitted at any temperature is of course represented by the whole area enclosed between the corresponding curve and the horizontal axis4 ,the eye is only sensitive to radiation of wave-lengths lying between #cgej and #gejj ,angstroms1 so that of all this radiation only that part in the shaded strip is visible1 all the rest representing invisible radiation4 ,we see at once that a fair proportion of the radiation emitted by a star at #fjjj degrees comes within the range of visibility1 but only a small fraction of that emitted by a star at #cjjj degrees4 ,taking the stars as a whole1 star-light forms only a small part of the total radiation of the stars4 ,illustration3 ,fig4 #af4 ,distribution of radiation into visible and invisible4 ,if our eyes were suddenly to become sensitive to all kinds of radiation1 and not to visual light alone1 the appearance of the sky would undergo a strange metamorphosis4 ,the red stars ,betelgeux and ,antares1 which are at present only #abth and #afth in order of brightness1 would flash out as the two brightest stars in the sky1 while ,sirius1 at present the brightest of all1 would sink to third place4 ,a star in the very undistinguished constellation of ,hercules would be seen as the sixth brightest star in the sky4 ,it is the star ,herculis1 at present outshone by about #bej stars4 ,as a consequence of its extremely low temperature of #bfej degrees1 this star emits its radiation almost entirely in the form of invisible heat4 ,for instance it emits #fj times as much heat as the blue star ,aurigae1 whose temperature is about #bj1jjj degrees1 but only four-fifths as much light4 ,allowances for invisible radiation have been made in all the calculations referred to in the present book1 although it has not been thought necessary continually to restate this4 ,,stellar ,,diameters4 ,it is easy to measure the diameter of a planet1 because this appears in the telescope as a disc of finite size4 ,but the stars are too remote for their diameters to be measured in the same way4 ,no star appears larger in the sky than a pin-head held at a distance of six miles1 and no telescope yet built can shew an object of this size as a disc4 ,all stars1 even the nearest and largest1 appear as mere points of light#bd1 so that their diameters can only be measured by roundabout methods4 #bd ,the large round images of stars shewn in the frontispiece result merely from over-exposure1 and have nothing to do with the sizes of the stars4 ,when a star's distance is known1 we can tell its luminosity from its apparent brightness4 ,from this1 after allowing for invisible radiation1 we can deduce the star's total outpouring of energy--so many million million million million horse-power4 ,we also know its outpouring of energy per square inch of surface1 because this depends only on its surface-temperature which we deduce directly from spectroscopic observation4 ,knowing these two data1 it is a mere matter of simple division to calculate the number of square inches which make up the star's surface1 and this immediately tells us the diameter of the star4 ,the diameters of exceptionally large stars may be measured more directly by an instrument known as the interferometer4 ,when we focus a telescope on a star we do not1 strictly speaking1 see only a point of light1 but a point of light surrounded by a rather elaborate system of rings of alternating light and darkness1 called a diffraction pattern4 ,it might be thought that the size of these rings would tell us the size of the star1 but the two have nothing to do with one another4 ,the rings represent a mere instrumental defect1 their size depending solely on the size and optical arrangement of the telescope4 ,following a method suggested by ,fizeau in #ahfh1 ,professor ,michelson has shewn how even this defect can be turned to useful ends1 and by its aid has produced what is perhaps the most ingenious and sensational instrument in the service of modern astronomy--the interferometer4 ,in effect1 this instrument superposes two separate diffraction patterns of the same star1 and sets one off against the other in such a way as to disclose the size of star producing them4 ,the diameters of a few of the largest stars have been measured in this way1 so that we may say that we know their sizes from direct observation4 ,in every case the directly measured diameter agrees fairly well1 although not perfectly1 with that calculated indirectly in the way already explained4 ,the discrepancies1 which are not serious1 appear to result from red stars not being accurate 8full radiators0 in the sense explained on p4 #abc4 ,the interferometer method is only available for the largest stars1 but at the extreme other end of the scale the theory of relativity has come to the rescue4 ,einstein shewed it to be a necessary consequence of his theory of relativity that the spectrum of a star should be shifted towards the red end by an amount depending on both the weight and the diameter of the star4 ,if1 then1 a star's weight is known1 the observed spectral shift ought immediately to tell us its diameter4 ,this spectral shift has recently been observed in the light received from the companion of ,sirius1 and measurements of its amount lead to a value for the star's diameter which agrees exactly with that calculated from its luminosity4 ,thus at both ends of the scale1 for the very largest as well as for the very smallest of stars1 direct observation confirms the values calculated for the diameters of the stars4 ,we may accordingly feel every confidence in the calculated diameters of all stars1 even when these cannot be checked by direct measurement4 ,indeed a discrepancy between the true and calculated diameters could only arise in one way4 ,the diameters are calculated on the assumption that the stars emit their full temperature-radiation4 ,if the stars had been partially transparent like the nebulae1 or solid bodies like the moon1 this assumption would have been false1 and its falsity would at once have been shewn by discordances between the calculated and measured diameters of the stars4 ,the fact that no large discordances appear suggests that the stars emit nearly full temperature-radiation throughout the whole range of size from the largest to the smallest4 ,,the ,,variety ,,of ,,stars ,observation shews that the physical characteristics of the stars vary enormously1 so that it is easy1 as we shall soon see1 to tell a sensational story by contrasting extremes1 setting the brightest against the dimmest1 the biggest against the smallest1 and so on4 ,this would1 however1 give a very unfair impression of the inhabitants of the sky2 it would be like judging a nation from the giants and dwarfs1 the strong men and the fasting men1 seen inside the showman's tent4 ,we shall obtain a more balanced impression of the actual degree of diversity shewn by the stars as a whole if we consider the physical states of those stars which are nearest the sun4 ,by taking these precisely in the order in which they come1 we avoid any suspicion of going out of our way to introduce stars merely because they are bizarre or exceptional4 ,the small group of stars obtained in this way may be expected to form a fair sample of the stars in the sky1 although of course it will not be a large enough sample to include extremes4 ,we need not discuss the sun itself in detail because it will figure as our standard star1 with reference to which all comparisons are made4 ,the ,system of ,centauri4 ,this system consists of three constituent stars1 which are believed to be our three nearest neighbours in space4 ,the brightest1 ,centauri ,a1 is very similar to the sun4 ,it is of the same colour and spectral type1 but weighs #ad per cent4 more and is about #ab per cent4 more luminous4 ,being of the same colour as the sun1 it emits the same amount of radiation per square inch4 ,thus its #ab per cent4 greater luminosity shews that it must have a surface #ab per cent4 greater1 and therefore a diameter #f per cent4 greater1 than the sun4 ,the second constituent1 ,centauri ,b1 is considerably redder than the sun1 its surface-temperature being only about #ddjj degrees against the sun's #fjjj degrees or so4 ,it has #ig per cent4 of the sun's weight1 but only about a third of its luminosity4 ,yet1 as a consequence of its low temperature1 it needs #ej per cent4 more area than the sun to discharge a third of the sun's radiation2 this makes its diameter #bb per cent4 greater than that of the sun4 ,centauri ,a and ,centauri ,b together form a visual binary1 the two components revolving about one another in a period of #gi years4 ,neither of these two constituents is very dissimilar from the sun1 but the third star of the system1 ,proxima ,centauri1 is of an altogether different type4 ,it is red in colour1 with a surface-temperature of only about #cjjj degrees4 ,it is exceedingly dim1 emitting only a ten-thousandth part as much light as the sun1 and has only a fourteenth part of the sun's diameter4 ,its weight is unknown4 ,illustration3 ,fig4 #ag4 ,the ,system of ,centauri1 with the ,sun for comparison4 ,the sizes of the three stars of this system1 with that of the sun for comparison1 are shewn in fig4 #ag4 ,munich #aejdj4 ,this is a single faint star about which little is known4 ,its surface is red1 with a temperature probably little above #bejj degrees1 and it emits only _/th of the light of the sun4 ,wolf #cei4 ,this is the faintest star yet discovered1 but beyond this very little is known about it4 ,it is red in colour and emits only about #a_/ej1jjjth of the light of the sun4 ,lalande #baahe4 ,another faint red star1 emitting _/th of the light of the sun4 ,the ,system of ,sirius4 ,this consists of two very dissimilar stars1 there being some suspicion that a third also may exist4 ,the principal star1 ,sirius ,a1 which appears as the brightest star in the sky 7the ,dog-star71 is white in colour and has a surface-temperature of about #aa1jjj degrees4 ,as this is nearly twice the sun's temperature1 ,sirius ,a emits nearly #af times as much radiation per square inch as the sun4 ,its luminosity is about #bf times that of the sun1 and this requires the star's diameter to be #eh per cent4 greater than that of the sun4 ,it has nearly four times the sun's volume1 but only #bde times its weight1 so that matter is not as closely packed in ,sirius ,a as in the sun4 ,an average cubic metre contains #adb ton in the sun1 but only #jic ton in ,sirius ,a4 ,illustration3 ,fig4 #ah4 ,the ,system of ,sirius1 with the ,sun for comparison4 ,the faint companion ,sirius ,b is one of the most interesting stars in the sky4 ,it is of nearly the same colour and spectral type as ,sirius ,a1 but emits only a ten-thousandth part as much light4 ,after allowing for the slight difference in surface-temperature1 we find that its surface is only _/th1 and its diameter _/th of that of ,sirius ,a4 ,yet ,sirius ,a weighs only three times as much as ,sirius ,b1 although having #abe1jjj times its volume4 ,it is not ,sirius ,a but ,sirius ,b that is remarkable2 the average density of matter in the latter is about #fj1jjj times that of water1 the average cubic inch containing nearly a ton of matter4 ,fig4 #ah shews the sizes of the two components of ,sirius drawn to the same scale as fig4 #ag4 ,b4,d4 #ab #debc and ,innes #aa h4 #ab m41 #egb4 ,two stars1 as to the physical state of which nothing is known1 except that they are very faint1 emitting _/th and #a_/aj1jjjth of the sun's light respectively4 ,cordoba #e h4 #cdc and ,ceti4 ,two faint stars1 both of reddish colour1 emitting _/th and a third of the sun's light respectively4 ,illustration3 ,fig4 #ai4 ,the ,system of ,procyon1 with the ,sun for comparison4 ,the ,system of ,procyon4 ,this is a binary system1 similar in many respects to ,sirius4 ,the main star1 ,procyon ,a1 is of the same general type as the sun1 but weighs #bd per cent4 more1 and emits #e times as much light4 ,its surface-temperature is about #gjjj degrees1 and its diameter is #ahj times that of the sun4 ,the faint companion1 ,procyon ,b1 is so faint that nothing is known as to its physical condition except that it emits only #a_/cj1jjjth of the light of the sun4 ,its weight is #ci per cent4 of the sun's weight4 ,fig4 #ai shews the sizes of the two components of ,procyon on the same scale as before4 ,next in order1 as we recede from the sun1 come eight very undistinguished stars1 every one of which is redder and fainter than the sun1 none of them having a surface-temperature higher than #ejjj degrees1 and none of them emitting more than a quarter of the sun's light4 ,after these we come to3 ,the ,system of ,kruger #fj4 ,this is a binary system in which both components are small1 red and dim4 ,illustration3 ,fig4 #bj4 ,the ,system of ,kruger #fj1 with the ,sun for comparison4 ,the brighter component1 ,kruger #fj ,a1 has a surface-temperature of #cbjj degrees1 and emits _/th of the light of the sun4 ,its diameter is a third1 and its weight a quarter of the sun's2 so that its substance must be packed about #g times as closely as that of the sun4 ,the fainter component1 ,kruger #fj ,b1 has a similar surface-temperature but emits only #a_/ad1jjjth of the sun's light4 ,its diameter is a sixth1 and its weight a fifth of the sun's2 so that its substance must be packed about #dj times as closely as that of the sun4 ,the system is illustrated in fig4 #bj4 van ,maanen's star4 ,another very faint star1 which has the high surface-temperature of #gjjj degrees4 ,notwithstanding this1 it only emits _/th of the sun's light4 ,consequently its diameter is only about _/th of the sun's1 the star being if anything smaller than the earth4 ,its weight is unknown1 but its substance is in all probability packed even more closely than in ,sirius ,b4 ,the discussion of this sample of stars suggests that the majority of stars in space are smaller1 cooler and fainter than the sun4 ,stars exist which are far brighter than the sun1 but they are exceptional1 the average star in the sky being a small dull dim affair in comparison with our sun4 ,with this sample of the average population of the sky before us1 we may proceed to discuss the various characteristics of stars in a systematic way1 without fearing to mention extremes4 ,let us begin with their weights4 ,,stellar ,,weights4 ,the two stars of smallest known weight in the whole sky are the faint constituent of ,kruger #fj1 just discussed1 and the faintest constituent of the triple system ,eridani1 each of which has a fifth of the sun's weight4 ,but the stars whose weights are known are so few that there can be no justification for supposing these to be the smallest weights which occur in the whole universe of stars4 ,a general survey of the situation1 on lines to be indicated later 7p4 #bha71 suggests that there may be many stars of still smaller weight1 but that very few are likely to have weights which are enormously smaller4 ,probably very few stars weigh as little as a tenth of the sun's weight4 ,the vast majority of stars have weights intermediate between this and ten times the sun's weight4 ,stars which weigh even three times as much as the sun are rare1 those which weigh ten times as much are very rare1 probably only about one star in #ajj1jjj having ten times the weight of the sun4 ,even higher weights undoubtedly occur--we have already mentioned ,plaskett's star1 whose two constituents have more than #ge and #fc times the sun's weight respectively1 and the quadruple system #bg ,canis ,majoris which to all appearances weighs #idj times as much as the sun--but such instances are very1 very unusual4 ,we may say that as a general rule the weights of the stars lie within the range of from a tenth to ten times the sun's weight1 and we shall find that stars differ less in their weights than in most of their other physical characteristics4 ,,luminosity4 ,a far greater range is shewn1 for instance1 in the luminosities of the stars--in their candle-powers measured in terms of the sun's candle-power as unity4 ,the most luminous star known is ,s ,doradus1 already mentioned1 with #cjj1jjj times the luminosity of the sun1 while the least luminous is ,wolf #cei with only a fifty-thousandth part of the luminosity of the sun4 ,the range of stellar luminosities1 as of stellar weights1 extends about equally on the two sides of the sun1 so that the sun is rather a medium star in respect both of weight and luminosity4 ,it is medium in the sense of being about half-way between extremes1 but we have seen that there are many more stars below than above it4 ,in comparison with the very moderate range of stellar weights1 the range of luminosity is enormous2 ,s ,doradus is #ae1jjj1jjj1jjj times as luminous as ,wolf #cei4 ,if ,s ,doradus is a lighthouse1 ,wolf #cei is something less than a firefly1 the sun being an ordinary candle4 ,if the sun suddenly started to emit as much light and heat as ,s ,doradus1 the temperature of the earth and everything on it would run up to about #gjjj degrees1 so that both we and the solid earth would disappear into a cloud of vapour4 ,on the other hand1 if the sun's emission of light and heat were suddenly to sink to that of ,wolf #cei1 people at the earth's equator would find that their new sun only gave as much light and heat at mid-day as a coal fire a mile away2 we should all be frozen solid1 while the earth's atmosphere would surround us in the form of an ocean of liquid air4 ,so far as we know1 there is no possibility of the sun suddenly beginning to behave like ,s ,doradus1 but we shall see later that the possibility of its behaving like ,wolf #cei is not altogether a visionary dream4 ,,surface-,,temperature ,,and ,,radiation4 ,sirius has been found to have the highest surface-temperature of all the stars near the sun2 it is about #aa1jjj degrees1 or nearly double that of the sun4 ,going further afield1 we find many stars with far higher surface-temperatures4 ,for instance1 ,plaskett's star is credited with a temperature of #bh1jjj degrees1 although it must be admitted that a substantial element of uncertainty enters into all estimates of very high stellar temperatures4 ,at the other extreme1 stellar temperatures ranging down to about #bejj degrees are comparatively common4 ,the lowest temperatures of all are confined to variable stars of a very special type 7long period variables7 in which the light-variation is accompanied by1 and indeed mainly arises from1 a variation in the temperature of the star's surface4 ,the temperature of these stars when at the lowest1 ranges down to #afej degrees1 which is but little above the temperature of an ordinary coal fire4 ,in many of them1 the temperature varies through a large range1 but it never sinks so low that the star becomes completely invisible4 ,thus there is a range of temperature below about #bejj degrees which no star is known to occupy1 except for the long-period variables which only enter it at intervals4 ,this would seem to suggest that the number of absolutely dark stars in the sky is relatively small4 ,other lines of evidence lead to the same conclusion4 ,if a star ceased to shine1 its gravitational pull would still betray its existence4 ,although we could not detect a single dark star in this way1 we could detect a multitude4 ,if a great proportion of stars were dark1 we should probably suspect the existence of the dark stars from their effects on the motions of the remainder1 so that general gravitational considerations preclude the possibility of there being a great number of dark stars4 ,so far as our present knowledge goes1 the temperature of stellar surfaces ranges1 in the main1 from about #cj1jjj degrees down to about #bejj1 the lower limit being extended to about #afej for long-period variables at their lowest temperatures4 ,apart from the long-period variables1 this is only a #ab to #a range1 so that the temperatures of the stars are more uniform than either their luminosities or their weights4 ,we must1 however1 remember that a star's radiation per square inch is far more fundamental than its surface-temperature1 and that a #ab to #a range in the latter involves a range of over #bj1jjj to #a in the former4 ,if we include the long-period variables1 there is a range of about #aaj1jjj to #a in the emission of radiation per square inch4 ,in terms of horse-power1 the sun emits energy at the rate of #ej horse-power per square inch1 a star with a surface-temperature of #afej degrees emits only #jce horse-power per square inch1 while ,plaskett's star1 with a surface-temperature of #bh1jjj degrees1 emits about #bh1jjj horse-power per square inch4 ,in plain ,english1 each square inch of this last star pours out enough energy to keep an ,atlantic liner going at full speed1 hour after hour1 and century after century4 ,and the energy emitted per square inch by the surfaces of various stars covers the whole range from the power of a liner to that of a man in a row-boat4 ,,size4 ,the four stars of largest known diameter are the following3 ---------------------------------------- -- ,star ,diameter in ,diameter terms of sun in miles ---------------------------------------- -- ,antares #dej #cij1jjj1jjj ,herculis about #djj #cdf1jjj1jjj ,ceti 7at max47 #cjj #bfj1jjj1jjj ,betelgeux 7average7 #bej #baf1jjj1jjj ---------------------------------------- -- ,all these diameters have been measured directly by the interferometer4 ,on the scale used in figs4 #ag to #bj1 in which the sun is about the size of a sixpence1 the circle necessary to represent ,ceti would be as large as the floor of a good-sized room1 while the second star of the system 7for ,ceti is binary7 would be the size of a grain of sand4 ,we may obtain some idea of the immense size of these stars by noticing that every one of their diameters is larger than the diameter of the earth's orbit1 so that if the sun were to expand to the size of any one of them we should find ourselves inside it4 ,these stars must be exceedingly tenuous4 ,antares1 for instance1 occupies #ij1jjj1jjj times as much space as the sun1 so that if its substance were as closely packed1 it would weigh #ij1jjj1jjj times as much as the sun4 ,yet1 in actual fact1 it probably has only about #dj or #ej times the sun's weight1 the difference between this number and #ij1jjj1jjj arising from the difference between the densities of ,antares and the sun4 ,on the average a ton of matter in the sun occupies considerably less than a cubic yard2 in ,antares it occupies rather more space than the interior of ,saint ,paul's ,cathedral4 ,yet a detailed study of stellar interiors shews that we can attach but little meaning to an average of this sort4 ,it is quite likely that matter at the centre of ,antares is packed nearly 7but not quite7 as closely as matter at the centre of the sun 7p4 #bia below74 ,the huge size of ,antares is probably due mainly to an enormously extended atmosphere of very tenuous gas1 and there is not much point in striking an average between this and the compact matter at the centre of the star4 ,the mysterious objects known as planetary nebulae1 of which examples are shewn in ,plate ,,ii 7p4 #bh71 ought perhaps to be regarded as stars of still larger diameter4 ,at the centre of each of these the telescope discloses a comparatively faint star with an extremely high surface-temperature4 ,surrounding this is the nebulosity from which these objects derive their somewhat unfortunate name4 ,this is in all probability merely an atmosphere of even greater extent than that surrounding the four stars of our table4 ,van ,maanen estimates the diameter of the nebulosity of the ,ring ,nebula in ,lyra 7fig4 #b of ,plate ,,ii7 to be #egj times that of the earth's orbit1 or about #ajf1jjj1jjj1jjj miles4 ,this nebulosity1 however1 differs from the atmosphere of an ordinary star in being very nearly transparent2 we can see through #ajf1jjj1jjj1jjj miles of the ,ring ,nebula but can only see a few tens or hundreds of miles into an ordinary star4 ,at the other extreme of size1 the smallest known star1 van ,maanen's star 7p4 #bfh7 is just about as large as the earth2 over a million such stars could be packed inside the sun and still leave room to spare4 ,and yet its weight is in all probability comparable1 not with that of the earth1 but with that of the sun2 at a guess it may have about a fifth of the sun's weight4 ,to pack a fifth of the sun's substance inside a globe of the size of the earth1 the average ton of matter must be packed into a space of about the size of a small cherry--ten tons or so to the cubic inch4 ,the solidity of the earth suggests that its atoms must be packed pretty closely together1 but the atoms in van ,maanen's star must be packed #ff1jjj times more closely4 ,how is it done8 ,as we shall shortly see1 there is only one possible answer4 ,the atom consists mostly of emptiness--we compared the carbon atom to six wasps buzzing about in ,waterloo ,station4 ,let us break the atom up into its constituent parts1 pack these together as closely as they will go1 and we see the way in which matter is packed in van ,maanen's star4 ,six wasps which can roam throughout the whole of ,waterloo ,station can nevertheless be packed inside a very small box4 ,,giants ,,and ,,dwarfs4 ,there is a continuous series of stars between the limits of weight we have mentioned1 and the same is true of the limits of temperature 7and so also of colour7 and of size4 ,illustration3 ,fig4 #ba4 ,stars of different colours arranged in order of luminosity4 ,within these specified limits1 ,i can find you a star of any weight or of any colour or of any size you like4 ,but this does not mean that you may specify the weight and colour and size of the star you want1 and that ,i will undertake to find it for you2 if the weight is right the colour may be wrong1 and so on4 ,for instance1 if you ask for a red star ,i can find you a very heavy one or a very light one1 but it is no good your asking for one of intermediate weight4 ,so far as we know1 red stars of intermediate weight simply do not exist4 ,the same is true as regards size--there are no red stars of intermediate size4 ,hertzsprung noticed in #aije that the red stars could be divided sharply into two distinct classes characterised by large and small size--he called them ,giants and ,dwarfs4 ,russell1 studying the question further in #aiac1 confirmed ,hertzsprung's earlier conclusions1 and shewed that the giant-dwarf division extended to stars of other colours than red4 ,imagine that we have a series of coloured ladders1 one for each colour of star--red1 orange1 etc4 ,take all the red stars and stand them 7in imagination7 on the different rungs of the red ladder4 ,do not merely place them on at random2 arrange them in order of their luminosities1 placing those of highest luminosity upper-most4 ,further let several stars stand on the same rung if their luminosities are about equal4 ,to make the arrangement definite1 let each rung of the ladder represent #e times higher luminosity than the rung immediately below it1 so that each rung has a definite luminosity associated with it#be4 #be ,for purely practical reasons the height is not taken proportional to the luminosity but to its logarithm2 without some such device as this it would be impossible to represent the range of more than #a1jjj1jjj to #a in the observed luminosities of red stars4 ,with this agreement we are now ready to proceed4 ,we take our red stars and place each on the appropriate rung of the red ladder1 and so on for each other colour4 ,the result is shewn diagrammatically in fig4 #ba1 the different stars being represented by crosses4 ,the red stars will be found to lie as on the right of the diagram1 ,hertzsprung's division into giants and dwarfs being very clearly marked4 ,the orange stars lie as on the next ladder to the left2 as ,russell found1 the division again appears1 but is less marked4 ,,the ,,russell ,,diagram4 ,let us make ladder diagrams of this kind for each colour of star1 and put them side by side in their proper order1 so as to represent stars of all possible colours4 ,we obtain a diagram of the kind shewn in fig4 #bb4 ,this type of diagram was introduced by ,russell in #aiac1 and is now generally known as a ,russell diagram4 ,the letters at the top of the diagram represent spectral types of stars1 because these provide a better and more exact working classification than the names of colours4 ,the colours which approximately correspond to the various spectral types are indicated at the bottom of the diagram4 ,only a very few sample stars are shewn1 but all known stars are found to be concentrated around the positions of these few typical stars4 ,broadly speaking1 there are two distinct and disconnected regions which are occupied by stars4 ,first1 and most important1 is a region shaped rather like a reversed 3 the central line of this region is marked in by a continuous thick line1 following a determination of its position by ,redman4 ,second1 there is a smaller region near the left-hand bottom corner of the diagram4 ,the stars which occupy this region are very faint1 and have far higher surface-temperatures than other stars of similar luminosity4 ,we have already seen how a star's diameter can be calculated from its surface-temperature and luminosity4 ,this amounts to the same thing as saying that two stars which occupy the same position in the ,russell diagram must have the same diameter4 ,thus there is a definite diameter associated with each point in the diagram1 and we can map out stellar diameters in the diagram1 just as we can map out heights above sea-level on a geographical map1 by a system of 8contour lines40 ,in the present case the 8contour lines0 prove to be a system of almost parallel curves4 ,these lie roughly as shewn by the broken lines in fig4 #bb1 all stars lying on any one line having the same diameter4 ,illustration3 ,fig4 #bb4 ,the ,russell diagram4 ,this diagram throws a flood of light on the general question of stellar diameters4 ,we see at once that stars of the biggest diameters--#ajj times the sun's diameter or more--must necessarily be red stars of high luminosity4 ,and in actual fact the stars of large diameter shewn in the table on p4 #bgb are all red and have very high luminosities2 they are red giants4 ,the majority of the stars in the sky lie in the belt which runs across the diagram of fig4 #bb from top left-hand to bottom right-hand4 ,this is known as the 8main-sequence40 ,the position of this band with reference to the 8contour lines0 of diameters shews that main-sequence stars are of moderate diameters4 ,the brightest of all may have twenty times the diameter of the sun1 while the faintest may have only about a twentieth of the sun's diameter1 but they all have diameters which are at least comparable with that of the sun4 ,the sample of stars from near the sun1 which we have already discussed1 provides many instances of main-sequence stars2 we have1 in order of decreasing luminosity3 ------------------------------------- ,star ,luminosity,diameter 7in terms of sun7 ------------------------------------- ,sirius ,a #bfc #aeh ,procyon ,a #ee #ahj ,centauri ,a #aab #ajg ,sun #ajj #ajj ,centauri ,b #jcb #abb ,ceti #jcb #jie ,indi #jae #jhb ,kruger #fj ,a #jjjbf #jcc 0 ,b #jjjjg #jag ,wolf #cei #jjjjjb #jjc ------------------------------------- ,this table shews clearly how stellar luminosity and diameter decrease together as we pass down the main-sequence4 ,the remaining group of stars in fig4 #bb1 those in the bottom left-hand corner1 are generally known as 8white dwarfs40 ,their position in the diagram shews that their diameters must be excessively small4 ,the vicinity of the sun provides three examples of this class of star1 as shewn in the following table3 ---------------------------------------- --------- ,star ,luminosity ,diameter 7in terms of sun7 ---------------------------------------- --------- ,sirius ,b #jjjbf #jjc ,eridani ,b #jjjca #jjah van ,maanen's star #jjjjaf #jjji ---------------------------------------- --------- ,in addition to these1 the faint companion of ,ceti is certainly a white dwarf1 while ,procyon ,b may be4 ,these are the only known examples of white dwarfs1 but the extreme faintness of these stars makes them very difficult of detection1 so that it is quite likely that they are fairly frequent objects in space4 ,in the table on p4 #bgi1 the main-sequence stars were intended to be arranged in the order of luminosity1 but this happens also to be the order of weights4 ,the weights of three of the stars are unknown2 those of the remainder are as follows3 ---------------------------------------- --------- ,star ,luminosity ,weight 7in terms of sun7 ---------------------------------------- --------- ,sirius ,a #bfc #bde ,procyon ,a #ee #abd ,centauri ,a #aab #aad ,sun #ajj #ajj ,centauri ,b #jcb #jig ,kruger #fj ,a #jjjbf #jbe 0 ,b #jjjjg #jbj ---------------------------------------- --------- ,like the luminosities1 the weights fall off steadily as we pass down the main-sequence1 although1 as already remarked1 weight falls far less rapidly than luminosity4 ,the only stars whose weights can be measured directly are the components of binary systems1 and these are relatively few in number4 ,seares found1 however1 that the weights of binary systems conformed to the law of equipartition of energy already explained in ,chapter ,,iii1 so that it is highly probable that other stars which are not binary also conform1 for it is difficult to imagine any reason why binary systems should attain to a state of equipartition sooner than other stars4 ,it will be remembered that this state is defined by a purely statistical law connecting the weights and speeds of motion of stars1 so that the fact that a system of stars has attained this state can give no information as to the weight of an individual star whose speed is known1 but it makes it possible to determine the average weight of any group of stars in terms of their average speeds of motion4 ,in this way ,seares has determined the average weights of stars of different assigned luminosities and spectral types--in other words1 the average weights of the stars represented at the various points in the diagram of fig4 #bb4 ,the results he obtained are shewn by the thick curved lines in fig4 #bc4 ,the arrangement of these curves confirms the inference we have drawn from a few selected stars2 the weight of main-sequence stars falls off steadily as we pass down the sequence from high luminosity to low4 ,these curved lines specify the average weight of the stars represented at each point in the ,russell diagram1 and the diameters are already known from fig4 #bb4 ,from these two data the mean density of the star can of course be calculated4 ,the mean densities as calculated by ,seares are shewn by the broken lines in fig4 #bc4 ,illustration3 ,fig4 #bc4 ,stellar weights and densities in the ,russell diagram1 according to ,seares4 ,this completes our collection of observational material4 ,we now turn to the far more difficult problem of discussing what it all means4 ,here we leave the firm ground of ascertained fact1 to enter the shadowy morasses of conjecture1 hypothesis and speculation4 ,the questions we shall discuss are some of the most interesting in the whole of astronomy1 to which it must be admitted that science has so far obtained only lamentably dusty answers4 ,the reader who is hot for certainties may prefer to read something other than the remainder of the present chapter4 ,,the ,,physical ,,condition ,,of ,,the ,,stars ,the foregoing collection of observational data has provided abundant proof that stars to certain specifications do not exist at all4 ,to put the same thing in another way1 there are certain regions in the ,russell diagram which are wholly unoccupied by stars4 ,to take the most conspicuous instance of all1 there are no stars at all to the left of the main-sequence in the ,russell diagram 7fig4 #bb71 until we come to the quite detached group of white dwarfs4 ,why are there no stars in intermediate conditions8 ,why1 to make the example still more precise1 does no star exist of the same colour as ,sirius but with only a tenth of its luminosity8 ,why do we have to go down to the white dwarf ,eridani ,b1 with a luminosity of only a ten-thousandth of that of ,sirius1 before we can find a star to match ,sirius in colour8 ,a hypothesis which occurs naturally to the mind is that the main-sequence stars and the white dwarfs may form distinct groups because they are of entirely different ages--they may represent distinct creations4 ,as stars age they decrease in weight and in luminosity1 so that it is natural to interpret the small weights and extremely low luminosity of the white dwarfs as evidence of an age far greater than the age of the normal main-sequence stars4 ,yet this hypothesis does not appear to be tenable4 ,with the single exception of van ,maanen's star1 every star which is either known or suspected to be a white dwarf forms one component of a binary system1 and in every case its companion is a main-sequence star or 7in the case of ,ceti7 a red giant4 ,we have already seen how rare it is for two stars to approach near to one another in space4 ,it must be an almost inconceivably rare event for two stars1 originally moving as independent bodies1 so to meet in their random wanderings1 that the big one 8captures0 the little one1 and they henceforth journey together through space4 ,for it can be shewn that1 for such an event to occur1 something more than a close approach is needed2 a close approach must take place in the presence of yet a third star1 so that no fewer than three stars must chance to come near one another simultaneously in their wanderings through the vast emptinesses of space4 ,it is almost inconceivable that this should happen in a single instance1 but it is straining the probabilities too far to suppose that it has happened in the case of every single known white dwarf but one4 ,thus we have to suppose that the white dwarfs and their more normal companions have been together since birth1 and so were born at the same time out of the same nebula4 ,the difference between white dwarfs and main-sequence stars cannot1 then1 be a mere difference of age1 and it would seem as though there must be some physical reason militating against the existence of stars in intermediate conditions4 ,taking a more general view of the question1 we are led to investigate whether the absence of stars built to certain specifications can be attributed to such stars needing physical properties which nature cannot provide4 ,this leads directly into the general question of the structure and mechanism of the stars4 ,,the ,,internal ,,constitution ,,of ,,the ,,stars ,most investigations on the structure of the stars have proceeded on the supposition that their interiors are gaseous throughout4 ,without accepting this supposition as final truth1 we may adopt it for the moment1 for the purely opportunist reason that it provides the most convenient line of approach to an excessively difficult problem4 ,a mathematical theorem1 generally known as ,poincar's theorem1 proves to be of the utmost service in discussing the internal state of a gaseous star4 ,we have seen how ,helmholtz thought that the energy of the sun's radiation might come from the sun's contraction1 each layer falling in upon the next inner layer as the latter shrunk1 and transforming the energy set free by its fall into heat and light4 ,it is easy to estimate how much energy would be set free by a contraction of this kind4 ,for instance1 ,lord ,kelvin calculated that the contraction of the sun1 as it shrunk from infinite size to its present diameter of #hfe1jjj miles1 would liberate about as much energy as the sun now radiates in #ej million years4 ,in terms of ergs1 the sun's shrinkage would liberate #f #aj ergs of energy4 ,poincar's theorem states that the total energy of motion of all the molecules in any gaseous star whatever is equal to precisely half the total energy which the star would have liberated in shrinking down to its present size4 ,the theorem is true quite independently of whether the star ever has so shrunk or not3 nothing is involved but the present state of the star4 ,one interesting consequence is that the further a gaseous star shrinks1 the hotter it becomes2 if a star shrinks to half its present size1 the total energy set free by its shrinkage from infinite size is doubled1 so that the total energy of motion of its molecules is doubled1 and therefore its average temperature is doubled4 ,this is a special case of what is generally known as ,lane's law4 ,let us go on with our calculation for the special case of the sun4 ,poincar's theorem tells us that1 if the sun is gaseous1 the total energy of motion of all its molecules is #c #aj ergs4 ,the next thing we want to know is how many molecules there are in the sun4 ,the sun's weight is #b #aj grammes1 but how many molecules are there to a gramme8 ,the answer of course depends on the type of molecule concerned2 there are #c #aj molecules in a gramme of hydrogen1 #b #aj in a gramme of air and only #be #aj in a gramme of uranium4 ,if we suppose the sun to be made of air1 it must consist of #d #aj molecules1 so that the average energy of motion of each molecule must be #ge #aj ergs1 and this represents an average temperature1 for the sun's interior1 of #cge million degrees4 ,in #aijg ,emden1 by a different calculation1 found that if the sun were made of air1 the temperature at its centre would be #dee million degrees4 ,apart from details1 it is clear that the interior temperature of a sun made of air would be one of hundreds of millions of degrees4 ,so far all study of stellar interiors had proceeded on the supposition that the stars were formed of complete atoms or even molecules4 ,in #aiag1 ,i made a simple calculation1 of the type already explained on p4 #ada1 and found that the quanta of radiation which fly about at such temperatures would be energetic enough not merely to break up the molecules of air into atoms1 but also to strip all1 or nearly all1 of the electrons from the atoms4 ,at such temperatures each molecule of air would break up into its constituent nuclei and electrons just as surely as1 on a hot day1 a lump of ice breaks up into its constituent molecules4 ,the electric forces which1 in quieter surroundings1 would unite the electrons and nuclei1 first into atoms and then into complete molecules1 find themselves powerless against the incessant hail of rapidly moving projectiles and the shattering blows of quanta of high energy2 it would be like trying to build a house of cards in a hurricane4 ,a sun consisting of molecules of air proves to be an inconsistency1 a contradiction2 our hypothesis has defeated itself1 and we must start again from the beginning4 ,we may start wherever we like1 but the conclusion which we must finally reach is that1 no matter what kind of molecules the sun consists of1 the heat at the sun's centre will break them up1 either completely or nearly so1 into their constituent nuclei and electrons4 ,the same is true for all other stars1 and this introduces an extreme simplification into the problem of the interior constitution of the stars4 ,we cannot say how many complete molecules there are to a gramme without knowing the nature of the molecules1 but once let these molecules be broken up into their constituent parts1 and we know at once the total number of constituent parts1 nuclei and electrons1 which go to make up a gramme4 ,for1 the atomic weights of all elements except hydrogen are nearly double their atomic numbers 7p4 #aaj74 ,hence1 as ,eddington first pointed out1 the total number of nuclei and protons in a fully broken-up atom of any substance except hydrogen must be equal to about half the atomic weight of the atom4 ,we may probably disregard the possibility of a star consisting to any great extent of hydrogen4 ,if so1 the number of constituent parts in a gramme of fully broken-up stellar matter must be about #c #aj1 regardless of the type of molecule from which these parts originate4 ,and when we know the total number of such parts in any star1 it becomes easy to calculate the temperature of the star's interior1 either from the theorem of ,poincar just mentioned or otherwise4 ,the temperature will be the same as though the star were made of unbroken molecules of hydrogen4 ,emden calculated in #aijg that the central temperature of a sun of this kind would be about #ca1ejj1jjj degrees4 ,later and more refined calculations by ,eddington led to an almost identical temperature1 but some still later calculations of my own give the substantially higher figure of #ee1jjj1jjj degrees4 ,there is no need for the moment to discuss which of these figures is nearest the truth4 ,their diversity will indicate what kind of degree of uncertainty attaches to all calculations of this type4 ,it is easy to see the physical necessity for this high temperature4 ,the heat which flows away from the sun's surface must first have been brought there from its interior4 ,heat only flows from a hotter to a cooler place1 and a vigorous flow of heat is evidence of a steep temperature gradient4 ,the temperature must rise sharply as we pass from the sun's surface towards its centre1 and this rise1 continued along the whole #dcc1jjj miles to the centre1 must result in a very high temperature indeed being reached there4 ,the calculated central temperature of #cj to #fj million degrees so far transcends our experience that it is difficult to realise what it means4 ,let us1 in imagination1 keep a cubic millimetre of ordinary matter--a piece the size of an ordinary pin-head--at a temperature of #ej1jjj1jjj degrees1 the approximate temperature at the centre of the sun4 ,incredible though it may seem1 merely to maintain this pin-head of matter at such a temperature--i4e4 to replenish the energy it loses by radiation from its six faces--will need all the energy generated by an engine of three thousand million million horse-power2 the pin-head of matter would emit enough heat to kill anyone who ventured within a thousand miles of it4 ,high though this temperature is1 calculations shew that it would not suffice to break up the stellar molecules completely4 ,it would strip the atoms of all their electrons down to the ,k-rings 7p4 #acd71 but these would remain intact4 ,it needs temperatures even higher than those we are now considering to strip the ,k-ring electrons from the nucleus of an atom4 ,this result is true for the whole range1 from about #cj to #fj million degrees1 within which the temperature of the sun's centre is at all likely to lie1 and it is true almost independently of the atomic weight or atomic number of the atoms of which we suppose the sun to be built4 ,thus if the sun is wholly gaseous1 its central parts must consist of a collection of atoms stripped down to their ,k-rings1 but not beyond1 flying about independently like the molecules of a gas1 and with them1 also flying about like the molecules of a gas1 all the stripped-off electrons which originally formed the ,l-ring1 the ,m-ring1 etc41 of the atoms1 the whole being at a temperature of somewhere between #cj and #fj million degrees4 ,as we pass outwards towards the sun's surface we come to lower temperatures1 at which the atoms are less completely broken up4 ,finally1 close to the sun's surface1 we may meet atoms which are completely formed except perhaps for one or two of their outermost electrons4 ,in the surfaces of the coolest stars of all1 we even find complete molecules1 as1 for example1 the molecules of titanium oxide and magnesium hydride1 which shew themselves in the spectra of the red stars4 ,when the internal constitution of other stars is investigated in the same way1 all main-sequence stars are found to have about the same central temperatures as the sun4 ,moreover1 this is not the only property which they have in common4 ,fig4 #bc1 which exhibits ,seares' calculations of mean stellar densities1 shews that the mean densities of main-sequence stars are all approximately the same1 except for comparatively small deviations at the two extremities4 ,the mean density of the sun is #ad1 which means that the average cubic metre in the sun contains #ad ton of matter4 ,at the sun's centre1 the density is about #ajj times this1 so that a cubic metre there contains about #adj tons of matter4 ,for comparison1 a cubic metre of lead contains only about #aa tons4 ,if all stars were built on the same model as the sun1 any two stars which had the same mean density would also have equal densities at their centres4 ,but in stars having several times the weight of the sun1 a new factor comes into play1 namely pressure of radiation--the pressure which radiation exerts in virtue of the weight it carries about with it4 ,in most stars this pressure is insignificant in comparison with the pressure produced by the impact of material atoms and electrons1 but in very massive stars it is large enough to influence the structure of the star4 ,it is to this that the very massive stars whose diameters are tabulated on p4 #bgb owe their abnormally large size4 ,it is a general consequence of the disturbing effects of radiation-pressure1 that the weight of a very massive star is far more concentrated in its central regions than that of a lighter star1 so that if a light and a massive star have the same average density1 the latter will have by far the higher density at its centre4 ,when this disturbing factor is allowed for1 all stars in the upper part of the main-sequence are found to have approximately the same densities in their central regions1 a density about equal to that at the centre of the sun1 which we may estimate at #adj tons to the cubic metre4 ,and we have already seen that the central regions of these stars have also approximately the same temperatures as the centre of the sun1 whence it follows that their physical conditions are all substantially the same4 ,thus the atoms in the central regions of all these stars must be broken down to the same extent as the atoms in the central regions of the sun4 ,the ,k-rings of electrons survive intact1 but the outer rings are transformed into a hail of electrons flying about like independent molecules4 ,with sufficient accuracy for our present purpose1 all the stars on the main-sequence1 except perhaps those at its extreme lower end1 may be supposed to be in the same physical condition4 ,on account of this property1 the main-sequence forms an admirable base-line from which to carry out a survey of the ,russell diagram in respect of the physical conditions of stellar interiors4 ,fig4 #bb shews that a star to the right of the main-sequence has a greater diameter than a main-sequence star of the same weight4 ,consequently the energy it would emit in shrinking to its present diameter is less1 and hence its molecular energy of motion is less 7by ,poincar's theorem74 ,it follows that its internal temperatures are lower1 and its atoms are less completely broken up4 ,red giants such as ,antares are found only to have central temperatures of from one to five million degrees1 and their atoms probably retain intact not only their ,k-rings of electrons1 but also their ,l-rings and part at least of their ,m-rings4 ,to the left of the main-sequence we come to a region in which stars1 if they occurred at all1 would have shrunk further1 and so would have higher temperatures and more thoroughly broken atoms4 ,actually no stars are encountered until we come to the white dwarfs4 ,calculation shews that the central temperatures of these must be many hundreds of millions of degrees at least1 and that their atoms must be stripped of electrons right down to the nuclei4 ,except for a small number of atoms which may have escaped this general fate1 the stellar matter must consist of nuclei stripped absolutely bare1 and of free electrons1 all flying independently through the star4 ,the high densities of these stars provide a convincing proof of the accuracy of this result4 ,the mean density of ,sirius ,b is certainly over #ej1jjj1 while that of van ,maanen's star is probably over #cjj1jjj4 ,there is no way in which matter can be packed as closely as this1 except that of stripping the atoms of electrons right down to their bare nuclei4 ,the clearest general impression we can form of the ,russell diagram in terms of physical condition is probably obtained as follows3 ,we think first of two detached bands of stars1 one1 the white dwarf group1 formed by stars in which all the electrons are torn off the atoms2 and the other1 the main-sequence1 formed of stars in which the atoms are still surrounded by their ,k-rings of electrons1 while the exterior rings have been torn off4 ,starting from about the middle of the main-sequence is the spur branch leading up to the red giants1 as shewn in fig4 #bb4 ,as we pass along this1 the internal temperatures of the stars decrease1 so that the stellar atoms are less broken up than in main-sequence stars4 ,in the red giants at the extreme end1 even ,m-ring electrons may still remain4 ,,russell',s ,,hypothesis ,two entirely different explanations of this distribution of stars have been suggested4 ,in #aibe ,russell put forward a theory which centred primarily around the fact that the temperatures at the centres of the main-sequence stars are all very nearly equal4 ,let us simplify the situation for a moment by imagining it to be an ascertained fact that the temperatures at the centres of all stars are precisely the same1 say #cb1jjj1jjj degrees4 ,if this were a sure fact1 it would be natural to conjecture that the stars had some sort of controlling mechanism by which they continually adjusted their central temperatures to this exact figure1 so that if ever the temperature fell below #cb1jjj1jjj degrees the mechanism would come into play and raise the temperature to precisely this amount1 while if it increased to above this figure1 the mechanism would come into play and depress it4 ,such controlling mechanisms are of course common in engineering practice2 there are for instance the safety-valves which keep the pressure in a boiler always uniform1 the ,watts-governor which keeps an engine going always at the same rate of speed1 and the thermostat which keeps the temperature of a room constant4 ,a mechanism is already known for raising the temperature at a star's centre4 ,if a star is not generating any energy at all in its interior1 either by the annihilation of matter or otherwise1 its emission of radiation causes it to shrink1 and this1 as we have seen 7p4 #bhe71 causes its temperature to rise4 ,thus it is easy to keep a star's central temperature up to #cb1jjj1jjj degrees by arranging that no energy shall be generated so long as the temperature at the centre is below #cb1jjj1jjj degrees1 and this is the main hypothesis on which ,russell's theory is based4 ,he supposes that no energy at all is generated by matter at temperatures below #cb1jjj1jjj degrees1 but that1 as soon as this temperature is reached1 matter begins to annihilate itself in sufficient quantity to provide for the radiation of a star4 ,the trouble with the theory is that it seems impossible to regulate the temperature from the other end4 ,a star whose central temperature is below #cb1jjj1jjj degrees must be contracting without generating heat4 ,the contraction will not stop dead the moment the critical temperature is attained2 its momentum will carry it on until the central temperature substantially exceeds #cb1jjj1jjj degrees4 ,as soon as the temperature seriously exceeds #cb1jjj1jjj degrees at the centre1 that of a substantial piece of the star will be #cb1jjj1jjj degrees or higher4 ,the annihilation of all this matter must produce a profusion of heat which would raise the temperature of the star still further1 resulting in more and more annihilation of matter1 until finally the whole star disappeared in a flash of radiation4 ,indeed ,russell's theory supposes that matter at #cb1jjj1jjj degrees is in a similar condition to gunpowder at its flash point4 ,mathematical analysis then shews that a star whose centre is at a temperature of #cb1jjj1jjj degrees would be in the state of a keg of gunpowder with a spark at its centre1 and--well1 8ohne hast1 ohne rast0 hardly describes the subsequent course of events4 ,eddington has suggested that the stability of the stars might be saved by imagining a time-lag between the instant at which matter attained the critical temperature necessary for annihilation and the instant at which this annihilation occurred4 ,it has not yet been proved that the proposed remedy could be made effective1 but even if it could1 other difficulties remain4 ,as the normal star inhabits the main-sequence1 ,russell supposed it to be a property of normal matter to annihilate itself at a temperature of about #cb1jjj1jjj degrees1 the supposedly uniform central temperature of all main-sequence stars4 ,it then became necessary to introduce further special assumptions to explain the luminosity of white dwarfs and of stars on the red giant spur line1 whose centres are at temperatures very different from #cb1jjj1jjj degrees4 ,he accordingly supposed that such stars contained other types of matter which dissolved into radiation at temperatures which were respectively higher and lower than #cb1jjj1jjj degrees4 ,even if the stability difficulty could be overcome1 this latter series of assumptions seems to me to be so artificial as to compel the abandonment of this interesting theory4 ,a discussion of the difficulties of ,russell's theory led me to undertake a mathematical investigation of the stability of stars in general1 and this was found to provide a simple and somewhat unexpected explanation of the otherwise incomprehensible distribution of stars in the ,russell diagram2 it is in brief that the unoccupied regions of the diagram represent stars in an unstable condition4 ,i do not know what proportion of astronomers accept this explanation2 some1 whose opinion ,i value1 do not4 ,i do not think that much so far written in this book would be seriously challenged by competent critics1 but it is only fair to say that at this point we are entering controversial ground4 ,,the ,,hypothesis ,,of ,,liquid ,,stars ,let us begin by imagining an enormous number of stars built on all possible plans1 out of all kinds of substances4 ,mathematical investigation shews that some of these stars may be unable to shine with a steady light for either or both of two reasons--they may explode1 like a heated keg of gunpowder1 or they may have an inherent tendency to contract or expand without limit4 ,whether a star escapes the first pitfall or not depends mainly upon the properties of the substance of which it is built2 whether it escapes the second depends mainly upon the way it is built4 ,the two pitfalls are not altogether distinct1 and when we consider the stability of wholly gaseous stars of enormously great weight1 we find that the pits on the two sides of the path merge into one1 or at most only a narrow strip of safe ground is left between them4 ,nevertheless stars of enormously great weight are known to exist1 and continue shining steadily4 ,if then1 these stars are wholly gaseous1 they must occupy the one safe spot of ground between the two pits1 and this informs us both as to the way they are built and as to the properties of the substance of which they are built4 ,we find that such stars only escape both pitfalls if their substance possesses properties which appear very improbable1 and contrary to anything of which we have any experience or knowledge in physics2 in brief1 for such a star to remain stable1 the annihilation of its matter must proceed at a rate which depends on the temperature4 ,such a property seems in every way contrary to the physical principles explained in ,chapter ,,ii1 as it is to all our expectations of atomic behaviour4 ,the annihilation of matter is a far more violent change1 and involves quanta of far higher energy1 than mere radio-active disintegration1 and as the latter process is not affected by temperature changes1 it hardly seems possible that the process of annihilation should be1 at any rate until we reach temperatures of the order of the #b1bjj1jjj1jjj1jjj degrees tabulated on p4 #addbf4 #bf ,this provides a further objection to ,russell's hypothesis1 which1 to avoid confusion1 was not mentioned on p4 #bie4 ,we have1 however1 already found indications that the stars are not purely gaseous1 since purely gaseous masses could not form close binary systems of the type observed in the spectroscopic binaries 7p4 #bbb74 ,such systems can only be formed out of a mass which simulates the properties of a liquid rather than those of a gas2 the mass need not be wholly liquid1 but there must be a considerable divergence from the state of a pure gas1 at any rate in its central regions4 ,additional evidence to the same effect will also emerge later 7pp4 #caj1 #caa74 ,as soon as we admit that the interiors of the stars need not be in a completely gaseous state1 the whole situation changes1 even a slight departure from the gaseous state being found to impart a great deal of additional stability to the star4 ,if a star of great weight is purely gaseous in its structure1 the region of stability between the two pitfalls is reduced to a narrow strip1 and only by treading this can the star escape the alternative fates of exploding or collapsing4 ,but if the star has a liquid1 or partially liquid1 centre1 this strip of safe land is so wide that1 consistently with stability1 the stellar material may have exactly the property that we should priori expect to find1 namely1 that its annihilation proceeds1 like radio-active disintegration1 at the same rate at all temperatures4 ,if the substance of the star has this property1 the star can be in no danger of exploding1 for a mass of uranium or radium does not explode whatever we do to it4 ,and mathematical analysis shews that if the centre of the star is either liquid1 or partially so1 there is no danger of collapse2 the liquid centre provides so firm a basis for the star as to render a collapse impossible4 ,these considerations suggest the two complementary hypotheses3 #a4 ,that the annihilation of stellar matter proceeds spontaneously1 not being affected by the temperature of the star4 #b4 ,that the central regions of the stars are not in a purely gaseous state2 their atoms1 nuclei and electrons are so closely packed that they cannot move freely past one another1 as in a gas1 but rather jostle one another about like the molecules of a liquid4 ,if we have been right 7p4 #adi7 in attributing the observed highly penetrating radiation in the earth's atmosphere to the annihilation of matter in distant astronomical bodies1 then the first hypothesis is confirmed4 ,for the radiation could not retain its observed high penetrating power if it had already penetrated any great thickness of matter4 ,the struggle of passing through matter lengthens the wave-length of all kinds of radiation 7the quanta get weaker all the time71 and so diminishes its penetrating power4 ,thus1 wherever the highly penetrating radiation originated1 it must have got out into empty space without much of a struggle1 and this is the same thing as saying that it must have originated in matter at a comparatively low temperature4 ,thus the existence of the highly penetrating radiation proves that matter can be annihilated in great quantities at quite low temperatures2 the high temperatures of stellar interiors are not needed1 as ,russell's theory asserts1 for annihilation to occur4 ,a simple calculation shews that there can be no appreciable annihilation of the earth's substance4 ,in the sun about one atom in every #aj is annihilated every minute2 if even a ten-thousandth part as many atoms as this were annihilated in the earth1 its surface would be too hot for human habitation4 ,we can no longer explain this by saying that the sun is hot and the earth cool1 so that annihilation goes on in the former but not in the latter4 ,we must rather suppose that the atoms in the sun are of a different type from those on earth4 ,solar atoms spontaneously annihilate themselves1 terrestrial atoms do not1 or at least do not to any appreciable extent4 ,the second of our hypotheses1 that the central regions of the stars are more like a liquid than a gas1 is1 as we have seen1 a necessary consequence of the first1 but independent evidence in its favour is found in the formation of binary systems by fission4 ,for in ,chapter ,,iv 7p4 #bbb7 we saw that a star could only break up by fission if it had a liquid1 or a nearly liquid1 centre4 ,,the ,,stability ,,of ,,stellar ,,structures ,for the present1 let us tentatively accept the hypothesis that the generation of stellar energy occurs spontaneously1 like the disintegration of radio-active atoms4 ,the atoms which are responsible for the light and heat of the stars may be regarded as super-radio-active atoms which spontaneously annihilate themselves and so change their substance into radiation4 ,we have already seen that1 on this view of the mechanism of generation of stellar energy1 a star can only continue to shine steadily if its central regions are not in a purely gaseous condition4 ,a star built on foundations of highly compressible gas meets the same fate as a house built on sand3 it collapses4 ,a purely gaseous star is a dynamically unstable structure1 and must continually contract until the atoms in its central regions are so closely packed that their state can no longer be regarded as gaseous4 ,then1 and then only1 can the star exist permanently as a stable structure4 ,thus the central regions of any actual permanent star1 the sun for instance1 must be in a state which for brevity we may describe as liquid4 ,now let us imagine the sun to be expanded to ten times its present diameter4 ,this would diminish its density to a thousandth part of its original value4 ,the actual sun is #dj per cent4 more dense than water1 but the expanded sun would only be as dense as ordinary atmospheric air4 ,the atoms and electrons1 having moved ten times farther apart1 would be so distant from one another that the new sun might be regarded as wholly gaseous4 ,thus it would be dynamically unstable and could not remain in its wholly gaseous state4 ,our imaginary expanded sun is of course no longer a main-sequence star in the ,russell diagram4 ,in expanding the sun to ten times its present size we move it off the main-sequence into a region entirely vacant of stars--in fact1 into the great gulf which lies between the red giants and the red dwarfs 7see fig4 #bb1 p4 #bgh74 ,thus1 it appears that even if we deliberately place a star in this region1 it does not stay there but immediately contracts until it gets on to the main-sequence4 ,may not this explain why the region in question is untenanted by stars8 ,next let us imagine the sun contracted to a tenth of its present diameter1 so that its atoms and electrons move ten times nearer to one another4 ,its mean density is thereby increased from #ad to #adjj times that of water1 and its central density from about #adj to #adj1jjj4 ,you may check me here by pointing out that if the sun is already in a liquid state it cannot be compressed to any such extent--a liquid cannot usually have its density increased a thousand-fold4 ,but we have already noticed that halving a star's diameter doubles its temperature throughout4 ,in the same way reducing a star's diameter to a tenth increases its temperature ten-fold1 so that the sun's central temperature will be increased from1 say1 #ej million degrees to #ejj million degrees4 ,and at this latter temperature atoms hardly exist any longer as such--the stellar matter consists almost entirely of free electrons and nuclei4 ,and these are so minute1 that the increase of the sun's mean density from #ad to #adjj times the density of water is not only possible1 but leaves the sun's substance in a state which may best be described as gaseous4 ,once again1 then1 the new sun is dynamically unstable4 ,it would be represented by a point well to the left of the main-sequence1 near the middle of the unoccupied region between the main-sequence and the white dwarfs1 but as it is unstable it cannot maintain its position here4 ,again we see that even if we place a star in this region it cannot stay there4 ,and1 again--may it not be that the reason why this region is unoccupied is that it represents unstable stars8 ,once more you may check me4 ,if ,i have made my point1 it has been by the help of the rise of temperature which accompanies contraction4 ,when we imagined the sun to expand1 ought we not to have considered the fall of temperature which accompanies expansion8 ,the answer is that we ought1 but it would have made no difference4 ,lowering the temperature will cause a number of ,l-rings1 and possibly also of ,m-rings1 of electrons to re-form1 so that the new atoms will be of larger size1 but they will not lose their freedom of motion sufficiently to make the sun stable4 ,it would have been different if we had been discussing a star of #aj or #ej times the sun's weight2 then it can be shewn that the re-formation of ,k- and ,l-rings would have produced a series of stable configurations4 ,and the spur branch in the ,russell diagram exists to provide a home for just such stars4 ,the whole problem is too complicated to be discussed satisfactorily in this fragmentary way2 its proper discussion involves very complicated mathematical analysis4 ,mathematical discussion shews that the ,russell diagram can be divided into regions representing stable and unstable configurations in the manner shewn in fig4 #bd4 ,illustration3 ,fig4 #bd4 ,stable and unstable configurations in the ,russell diagram4 ,the unstable areas are so marked2 the remaining areas are stable4 ,the dots which form a sort of background to the diagram represent #bajj stars whose absolute magnitudes are known through their parallaxes having been determined spectroscopically at ,mount ,wilson4 ,the observational material is not perfect1 for considerable uncertainty attaches to all spectroscopic parallaxes of ,b-type stars1 and ,a-type stars are almost unrepresented because it is practically impossible to obtain their parallaxes by the spectroscopic method4 ,the theoretical curves are probably still more imperfect1 yet1 such as they are1 they seem to suggest very forcibly that the occupied and unoccupied regions coincide with those representing stable and unstable configurations2 after making all possible allowances for the imperfections both of theory and of observation1 too much agreement remains to be explained away as mere coincidence4 ,thus the conclusion to which mathematical discussion seems to lead is that the regions in the ,russell diagram which are occupied1 represent stars whose central regions are in a liquid1 or nearly liquid1 state4 ,all other stars are unstable1 so that the corresponding regions in the ,russell diagram are necessarily vacant4 ,to put it in less technical language1 all the stars in the sky must have liquid1 or nearly liquid1 centres4 ,here we have a piece of the puzzle which seems to fit on to the piece we unearthed in ,chapter ,,iv1 where we found that a star could only break up by fission if it had a liquid1 or nearly liquid centre4 ,evidence accumulates that the stars have liquid rather than gaseous centres4 ,criticism of the foregoing hypothesis--generally described as the 8liquid-star0 hypothesis--has mainly taken the form that the diameters of the ,k-rings of atoms are so small that the ,k-ring atoms in the sun's central regions cannot possibly be packed closely enough to involve any substantial departure from the gaseous state4 ,it is difficult to discuss1 and still more to meet1 this criticism without knowing the precise diameters of these ,k-ring atoms4 ,we of course know the diameters assigned to the ,k-ring by ,bohr's theory 7p4 #abi71 but no one any longer contends that this theory gives a true picture of the atom4 ,it provides a good working model within limits1 but we do not know where the limits end4 ,the only practical experience we have of ,k-ring atoms is with helium atoms2 ,bohr's theory assigns to these a diameter of #jed #aj cms4 ,yet solid and liquid helium provide a practical illustration of the closeness with which helium atoms can be packed2 in these each atom occupies a sphere of diameter #d #aj cms41 or over #djj times the space allotted to it by ,bohr's theory4 ,it looks as though we are still far from definite knowledge of the dimensions of ,k-rings of electrons4 ,the new wave-mechanics of ,schrdinger draws a very different picture of atomic interiors from the simpler theory of ,bohr which it is rapidly superseding4 ,even the electron is something very different from the electron of ,bohr's old theory4 ,it is the old-fashioned electron only when it is at an infinite distance from the nucleus4 ,as it gradually approaches this nucleus1 it undergoes a metamorphosis of a kind which no one has yet succeeded in describing1 and it is utterly impossible to say what form it may have assumed by the time it is doing what we call 8describing a ,k-ring orbit40 ,all we know about the ,k-ring orbit is its energy1 and it seems impossible to predict the amount of space occupied by such an orbit until we have a better knowledge of the qualities of the article which is describing it4 ,we have of course to admit that the physical evidence1 such as it is1 seems to point to ,k-ring atoms being substantially smaller than is needed for the liquid-star hypothesis4 ,but the astronomical evidence seems to me stronger and more reliable1 and to point in exactly the opposite direction4 ,and here we must leave the puzzle until further pieces come to light4 ,until we know the kind of atoms of which a particular star is composed1 we cannot calculate the extent to which they will be broken up by the temperature of the star's interior4 ,as a consequence1 the theoretical curves of demarcation between stable and unstable configurations cannot be calculated without assuming definite atomic numbers for the stellar atoms4 ,the curves shewn in fig4 #bd have been drawn for an atomic number of about #ie1 this being slightly higher than the atomic number1 #ib1 of uranium4 ,this atomic number was selected because it was found to produce the best agreement between theory and observation1 but we shall see that other considerations justify our choice4 ,,stellar ,,structure ,a star1 like a house or a pile of sand1 is a structure which would collapse under its own weight were it not that each layer is held up against gravity by the pressure which the next inner layer of the star exerts upon it4 ,this pressure is not1 like ordinary gas-pressure1 the result of the impacts of complete molecules4 ,it is produced in part by the impact of a certain number of atoms which have been stripped of electrons almost or quite down to their nuclei1 but to a far greater extent by the impact of a hail of free electrons4 ,in massive stars1 an additional pressure is produced by the impact of radiation which1 as we have seen1 carries weight about with it1 and so exerts pressure on any obstacle it encounters4 ,the combined impacts of free electrons1 of atoms 7or bare nuclei71 and of radiation prevent the star from falling in under its own gravitational attraction4 ,this gives a reasonably good snapshot picture of a star's structure4 ,the corresponding picture of its mechanism is obtained by thinking of the nuclei as -ray particles1 of the free electrons as -ray particles1 and of the radiation as -rays 7although in most stars the main bulk of the radiation has the wave-length of ,x-rays74 ,all these thread their way through the star1 and1 precisely as in laboratory work1 the -rays are more penetrating than the -rays1 and the -rays are more penetrating than either4 ,,the ,,transport ,,of ,,energy ,,in ,a ,,star4 ,we have seen how the heat of a gas is merely the energy of its molecular motion4 ,conduction of heat in a gas is usually studied by regarding each molecule as a carrier of energy2 when it collides with a second molecule the energy of the two colliding molecules is redistributed between them1 and in this way heat is transported from hotter to cooler regions4 ,each molecule has a power of transport which is jointly proportional to its energy of motion1 its speed of motion1 and its 8free-path0--the distance it travels between successive collisions4 ,in the interior of a star1 there are three distinct types of carrier in action--atoms 7or bare nuclei71 free electrons1 and radiation4 ,we can compare their relative capacities as carriers by multiplying up the energy1 speeds and free-paths of each4 ,for this purpose the 8free-path0 of radiation may be taken to be the distance the radiation travels before #cg per cent4 of it has been absorbed1 since it can be shewn that this is the average distance it carries its energy4 ,on carrying out the calculation1 the carrying capacity of both nuclei and electrons is found to be insignificant in comparison with that of the radiation4 ,the nuclei and electrons may have the greater amount of energy to carry1 but owing to their feebler penetrating powers1 the distance over which they carry it1 their free-path1 is far less than that of the radiation4 ,their speed of transport is also less1 since radiation transports its energy with the velocity of light4 ,in this way it comes about that practically the whole transport of energy from the interior of a star to its surface is by the vehicle of radiation4 ,this general principle was first clearly stated by ,sampson in #ahid4 ,he also shewed how the temperature of any small fragment of a star's interior must be determined by the condition that it receives just as much radiation as it emits1 but his detailed applications were vitiated through his using an erroneous law of radiation4 ,twelve years later1 ,schwarzschild independently advanced the same idea1 and expressed it in mathematical equations of 8radiative equilibrium0 which have formed the basis of every subsequent discussion of the problem4 ,just because radiation completely outstrips atoms and electrons in carrying energy from a star's interior to its surface1 it follows that the build of a star must be determined by the opacity of the matter in its interior4 ,if this is altered1 the carrying power of the radiation is altered1 and this affects the whole structure of the star4 ,a star whose interior was entirely transparent could not retain any heat at all2 its whole interior would be at a very low temperature and the star would be of enormous extent4 ,on the other hand1 in a very opaque star1 all energy would remain accumulated at the spot at which it was generated1 so that the interior temperature would become very high and the star's diameter would be correspondingly small4 ,it is1 of course1 the intermediate cases which are of practical interest1 but the extreme instances just mentioned shew how a star's build depends on its opacity4 ,unfortunately it is impossible to obtain any sort of direct measurement of the opacity of stellar matter4 ,we cannot even measure the opacity of terrestrial matter under stellar conditions1 since the interiors of the stars are at incomparably higher temperatures than any available in the laboratory4 ,however1 we know that the opacity of stellar matter is due to the atoms1 nuclei and free electrons of which it is composed checking the onward journey of radiation1 and although we cannot obtain a sample of stellar matter1 we know fairly definitely how many atoms1 nuclei and electrons such a sample would contain4 ,thus it becomes a matter of theoretical calculation to determine its opacity4 ,such a calculation was carried through by ,dr ,kramers of ,copenhagen in #aibc1 and his results gained general acceptance4 ,quite recently ,mr ,gaunt of ,cambridge has made a much more refined calculation1 and obtained results which agree very closely with those originally given by ,kramers4 ,in so far as these results can be tested in the laboratory1 they agree well with observation4 ,and1 although there is a big gap between laboratory conditions and stellar conditions1 it is difficult to see how ,kramers' formula could fail in the stars4 ,from this formula we can determine the build of the stars completely1 or1 if the build of the star is supposed to be known1 ,kramers' formula tells us the rate at which energy flows to its surface 7this depending entirely on the opacity of the star's substance71 and this in turn tells us at what rate energy must be generated inside the star for it to be able to remain in equilibrium in the configuration in question4 ,as might be expected1 configurations of different diameters are found to require different rates of generation of energy4 ,in nature1 a star must adjust its diameter to suit the rate at which it is generating energy2 in so doing it fixes not only its diameter but also its surface-temperature1 colour and spectral type4 ,if a star's rate of generation of energy were suddenly to change1 the star would expand or contract until it had assumed the radius and temperature suited to its new rate of generation of energy4 ,detailed calculation shews that1 for wholly gaseous stars1 large diameters correspond to feeble generation of energy and vice versa4 ,thus1 if the stars were wholly gaseous1 red giants would be less luminous than main-sequence stars of the same weight4 ,seares' diagram1 reproduced on p4 #bhb1 shews that the reverse is actually the case1 a red giant emitting from #aj to #bj times as much total radiation as an equally massive main-sequence star4 ,this provides evidence against the stars being wholly gaseous1 but there is stronger evidence than this4 ,for wholly gaseous stars1 the thick lines shewn in ,seares' diagram would be straight slant lines1 slanting upwards to the left4 ,the wide divergence between such a system of slant lines and the curves shewn in fig4 #bc gives some indication of the extent to which the condition of stellar matter diverges from the purely gaseous state4 ,according to ,kramers' theory1 the opacity of matter depends on the atomic numbers and atomic weights of the atoms of which it is built1 a large clot of matter in the form of a massive atomic nucleus being far more effective in absorbing radiation than a large number of small clots of the same total weight4 ,everyday terrestrial experience shews that this is so4 ,it is for this reason that the physicist and surgeon both select lead as the material with which to screen their ,x-ray apparatus2 they find that a ton of lead is far more effective in stopping unwanted ,x-rays than a ton of wood or of iron4 ,if we knew the strength of an ,x-ray apparatus1 and the total weight of shielding material round it1 we could form a very fair estimate of the atomic weight of the shielding material by measuring the amount of ,x-radiation which escaped through it4 ,a very similar method may be used to determine the atomic weights of the atoms of which the stars are composed4 ,a star is in effect nothing but a huge ,x-ray apparatus4 ,we know the weights of many of the stars1 and the rate at which they are generating ,x-rays is merely the rate at which they are radiating energy away into space4 ,if we could cut each atomic nucleus in a star into two halves1 we should halve the opacity of the star1 so that radiation would travel twice as far through the star before being absorbed4 ,if the star were wholly gaseous1 this would result in its expanding to four times its original diameter1 and in its surface-temperature being halved4 ,it follows that we can calculate the atomic weight of the atoms of which a star is composed from the weight1 luminosity and surface-temperature of the star4 ,the atomic weights of a number of stars1 which ,i calculated on the supposition that the stars were wholly gaseous1 came out in practically every case higher than that of uranium1 which is the weightiest atom known on earth4 ,they not only proved to be higher1 but enormously higher2 so high indeed1 as to seem utterly improbable4 ,again the explanation seems to be that the stars are not wholly gaseous4 ,as soon as stellar interiors are supposed to be partially liquid1 the calculated atomic weights are reduced enormously4 ,they can no longer be determined exactly1 but the atomic number of about #ie to which we were led from a consideration of the ,russell diagram seems to be entirely consistent with all the known facts4 ,indeed other considerations seem to suggest that the atomic numbers of stellar atoms must be higher than #ib4 ,a priori stellar radiation might either originate in types of matter known to us on earth or else in other and unknown types4 ,when once it is accepted that high temperature and density can do nothing to accelerate the generation of radiation by ordinary matter1 it becomes clear that stellar radiation cannot originate in types of matter known to us on earth4 ,other types of matter must exist1 and as1 with two exceptions1 all atomic numbers up to #ib 7uranium7 are already occupied by terrestrial elements1 it seems probable that these other types must be elements of higher atomic weight than uranium4 ,these super-heavy atoms must not be expected to disclose their presence in stellar spectra1 for these only inform us as to the constitution of the atmospheres of the stars4 ,and as the lighter atoms float to the top it is these1 in the main1 which figure in stellar spectra4 ,if the sun's atmosphere had contained any considerable number of super-heavy atoms when the planets were born1 some of them ought still to exist in the earth4 ,there cannot be any great number1 or their high generation of energy would betray them4 ,the simplest view seems to be that the heavier atoms sink to the centre in the stars1 and that the earth was formed mainly or solely out of the lighter atoms which had floated to the sun's surface4 ,,stellar ,,evolution ,we have supposed that the stars were born initially as condensations in the outer fringes of spiral nebulae4 ,these condensations would1 from the mode of their formation1 necessarily be of all sorts of sizes1 and subject only to the single restriction that none of them could be below a certain limit of weight4 ,thus we should not expect the stars1 either at birth or subsequently1 to be all of the same size or weight1 or all in the same physical condition4 ,the stars would start their existences at different points in the ,russell diagram1 but we may imagine that their initial positions are limited to those parts of the diagram which can be occupied by stars--either1 as the liquid-star hypothesis would suggest1 because these are the only stable configurations1 or else for some other reason so far undiscovered4 ,each year a star loses a certain amount of weight1 and its rate of generating energy1 and so also its luminosity1 are correspondingly reduced1 with the result that it moves to a new position in the diagram4 ,turning to ,seares' diagram of stellar weights on p4 #bhb1 we may think of the curves of equal weight as a flight of steps--very uneven steps1 it is true--each representing a lower weight than the one above4 ,whatever a star's evolution may be1 it is essential that it should always be down the steps3 any upward step is impossible4 ,we can trace out two possible paths of stellar evolution in the ,russell diagram which involve no entry into regions unoccupied by stars--two roads along which the stellar army may march as they transform their substance into radiation4 ,the first is of course the 8main-sequence10 which a great number of considerations suggest to be the main line of march of the stellar army4 ,the branch which starts from the red giants in the ,russell diagram represents a second possible line of march1 a certain number of stars travelling along this branch until they reach the main-sequence as blue or white stars1 and then travelling down the lower half of the main-sequence to end as faint red stars passing on to ultimate extinction4 ,progress along each of these roads is accompanied by a continuous shrinkage in the size of the star1 its diameter steadily decreasing4 ,this is not the same thing as saying that the star's density continually increases1 for the star is continually diminishing in weight1 so that even if the star's density remained the same1 its diameter would decrease4 ,nevertheless a study of ,seares' determinations of mean densities1 as shewn in the diagram on p4 #bhb1 suggests that there is a continuous increase of density1 although this becomes very slight in the middle reaches of the main-sequence4 ,practically every theory of stellar evolution which has ever been propounded has imagined the march of the stellar army to be of the same general type as that just described1 although perhaps present-day opinion is inclined to treat the main-sequence as the principal line of march1 whereas earlier theories supposed the youngest stars to march solely along the red giant branch1 only joining the main-sequence with middle age4 ,the first serious theory of all1 that of ,lockyer1 was expressed in terms of branches of ascending and descending temperature1 these together forming the last-mentioned line of march in the ,russell diagram4 ,a theory which ,russell propounded in #aiac again assigned to the stars the lines of march just described4 ,it also attempted a physical explanation1 since abandoned1 as to why the stars followed these particular paths rather than others4 ,his more recent theory of #aibe only differed from his earlier theory in giving the new explanation1 which we have already discussed 7p4 #bic71 as to why the stars followed these particular paths4 ,at present1 it is probably fair to say that nearly1 and perhaps quite1 all astronomers are agreed that the evolutionary paths of the stars are of the general type we have described4 ,some stars start as red giants1 some as blue1 some possibly in intermediate conditions4 ,as they age1 all move downwards in the ,russell diagram1 their various paths converging to a point at the fork of the reversed shewn in fig4 #bb1 and after passing this point they move down the main-sequence4 ,on the other hand1 there is the widest difference of opinion as to the physical interpretation which is to be assigned to these paths4 ,most astronomers are probably suspending judgment until some definite observational evidence is obtained to decide between conflicting theories4 ,when the stars first came into being as flecks of fiery spray thrown off by spinning nebulae1 they would consist of mixtures of atoms of all kinds1 some perhaps being so short-lived as to transform themselves almost at once into radiation1 and others having such long lives that they may properly be described as permanent4 ,except for a small number of radio-active atoms1 the earth must consist entirely of atoms of this latter type4 ,calculation shews that terrestrial atoms must have enormously longer lives than the average stellar atom1 otherwise their self-annihilation would make the earth too hot for habitation4 ,the permanent atoms in a star contribute almost nothing to its energy-generating capacity1 and so merely add to its weight4 ,the shortest lived atoms of all contribute greatly to the star's generation of energy while adding but little to its weight4 ,in general the shorter the life of any type of atom1 the greater the proportion of its numbers annihilated per year1 and so the greater the amount of energy it generates per ton of weight4 ,a star begins life with a large proportion of short-lived atoms1 and so at first generates energy furiously4 ,as it ages1 the shortest lived atoms disappear first1 and in so doing reduce the average energy-generation of the star per ton so that1 as a star's weight decreases1 so also must its rate of generation of energy per ton4 ,finally all the atoms with much energy-generating capacity have disappeared1 and the star is left1 a shrunken and diminished mass of atoms which have very little capacity for generating radiation4 ,to put the same thing in another way1 the rate at which a star generates energy per ton is proportional to the death-rate in its population of atoms4 ,to say that ,sirius generates #af times as much energy per ton as the sun is only another way of saying that the average atom in ,sirius has only a sixteenth of the expectation of life of the solar atoms2 their death-rate is #af times as high4 ,as those types of atoms which have the highest death-rate gradually die off in any star1 the average death-rate of the population decreases1 or1 in other words1 as a star ages its capacity for energy-generation per ton decreases4 ,this agrees with the findings of observational astronomy4 ,the most massive stars not only generate more energy than less massive stars1 as is in any case to be expected2 they also generate enormously more energy per ton4 ,this is illustrated by the following list of main-sequence stars3 ---------------------------------------- -------------- ,star ,weight ,generation of energy 7in terms of sun7 7ergs per gramme7 ---------------------------------------- -------------- ,pearce's ,star ,a #cfc #ae1jjj ,v ,puppis ,a #aib #a1jjj ,sirius ,a #bde #bi ,sun #ajj #aij ,eridani 7#jde7 #jbf ,kruger #fj ,b #jbj #jjba ---------------------------------------- -------------- ,seares' diagram of stellar weights 7p4 #bhb7 shews that this is a general property of the stars4 ,to repeat our former metaphor1 the stars squander their substance lavishly in their youth1 while they have plenty left to spend1 but parsimony comes over them with old age4 ,theoretical considerations have now given us an explanation of this phenomenon4 ,the same diagram shews that two stars of the same weight do not usually have the same luminosity4 ,in general1 giant stars on the spur branch leading out to the red giants have substantially higher luminosities than the main-sequence stars of equal weight4 ,we have already noticed how a red giant may emit as much as #aj or #bj times the radiation of an equally massive main-sequence star4 ,the same story is repeated when we pass from the main-sequence stars to the white dwarfs4 ,main-sequence stars emit enormously more radiation--anything up to #ejj times more--than white dwarfs of equal weight4 ,this is illustrated by the three following white dwarfs1 which may be compared with the last three stars of the preceding table3 ---------------------------------------- -------------- ,star ,weight ,generation of energy 7in terms of sun7 7ergs per gramme7 ---------------------------------------- -------------- ,sirius ,b #jhe #jjjbg ,eridani ,b #jdd #jjjb van ,maanen's star 7#jbj7 7#jjjjee7 ---------------------------------------- -------------- ,we have hitherto supposed generation of energy to be spontaneous and so unaffected by changes of physical conditions4 ,yet the facts just mentioned seem to suggest that this can hardly be the whole truth of the matter4 ,to state the objection in terms of a concrete instance1 ,sirius ,a and its white dwarf companion ,sirius ,b must in all probability have been born at the same time out of the same nebula 7p4 #bhd71 yet the former generates #djjj times as much energy per ton as the latter4 ,it seems improbable that so great a difference can be attributed to different types of atoms2 the common origin of the two stars almost precludes this4 ,we know that the atoms are in different physical conditions in the two stars2 in ,sirius ,a they have retained their ,k-rings intact1 while in ,sirius ,b1 the white dwarf1 they are completely broken up into bare nuclei and free electrons4 ,if the two components of ,sirius consist of essentially the same types of atoms1 as their common origin would lead us to expect1 then the enormous difference in the rates at which these atoms generate energy would seem to depend on the different physical conditions of their atoms4 ,the considerations brought forward in ,chapter ,,iii make it highly probable that a star's rate of generation of energy depends on the physical condition of its atoms4 ,we there supposed stellar energy to be generated through electrons coalescing with protons2 protons exist only in atomic nuclei1 and purely physical considerations led to the conjecture that the only electrons which can coalesce with a particular proton are those which are momentarily describing orbits around the nucleus in which the proton resides4 ,a study of stellar structure supports this hypothesis1 for if energy could be generated by free electrons falling into nuclei1 it can be shewn that the whole star would be unstable and would explode in a flash of radiation4 ,on this hypothesis1 a star in which only a few atoms have any electrons left in orbital motion can of course generate but little energy4 ,this at once explains the feeble energy-generating powers of the white dwarfs1 and also gives an inkling as to why the red giants1 in which ,l- and ,m-rings of electrons survive1 generate more energy than main-sequence stars of equal weights4 ,as a star ages and its weight decreases1 it continually has to pick out new configurations such as make its emission of energy equal to its internal rate of generation of energy4 ,the same star may be a red giant1 a main-sequence star and a white dwarf in turn4 ,stripped of technicalities this means that a star continually adjusts its diameter to suit its varying rate of generation of energy4 ,on the hypothesis just considered1 a star alters both its emission and its generation of energy on changing its diameter4 ,at every instant it has to select a diameter for which the two exactly balance4 ,the star has so large a range of rates of generation1 according as it has few or many electrons left in orbital motion1 that it is likely always to be able to find a configuration of equilibrium4 ,at any rate all the stars in the sky appear to have done so1 with the exception of the long period variables which are continually expanding and contracting as though they could not hit upon a diameter at which their income and expenditure of energy would just balance4 ,this same hypothesis immediately makes it possible for all the great variety of stars in the galactic system to be of approximately the same age1 and so to have been all born out of the same nebula4 ,the most luminous galactic stars can hardly have been generating energy at their present rate for more than about #ajj1jjj million years--any longer age would require an impossibly high weight to start with4 ,yet the motions of the stars indicate that even these highly luminous stars must have been in existence for at least #ej times this period4 ,the apparent contradiction disappears if we admit that the extreme luminosity of the very brightest stars may be a recent development1 and that for perhaps #ih per cent4 of its life such a star was losing but little energy because most of its atoms were stripped bare of electrons and so were immune from annihilation4 ,the requisite proportion of #ih per cent4 may seem suspiciously large1 but we have stated an extreme case2 we need only demand so large a proportion in the case of a very rare type of star3 probably not more than one star in ten million is of such a type4 ,in their earlier dormant state1 these stars1 which are now so luminous1 would in effect have been white dwarfs of enormous weight4 ,observational astronomy provides no evidence that any such stars exist1 but there is certainly no evidence that they do not exist4 ,very massive stars are known to be very rare objects1 so that in all probability we should have to travel a long distance from the sun before finding one1 and then it might be so distant as to be invisible from the earth4 ,in any case1 a very distant star of feeble luminosity would be exceedingly likely to escape detection4 ,we could not infer that no such stars existed from the fact of none having yet been found4 ,moreover1 it is far from absolutely certain that such stars have not been found4 ,very massive white dwarfs ought to have higher surface-temperatures than either massive main-sequence stars or than the known white dwarfs1 all of which are of small weight4 ,a whole group of stars is known--the ,o-type stars--whose spectra indicate very high temperatures indeed4 ,these are usually interpreted as stars of enormous luminosity at enormous distances1 but it is possible that some at least of them may be stars of feeble luminosity at moderate distances4 ,in particular the central stars of the planetary nebulae are of types ,o and ,b4 ,but whereas the normal main-sequence star of these spectral types is generally about a thousand times as luminous as the sun1 the central stars of the planetary nebulae are found to be considerably less luminous than the sun4 ,dr ,gerasimovi has recently shewn that #eb of these stars have an average luminosity only about two-thirds of that of the sun4 ,other observers have found even lower luminosities4 ,as the surface-temperatures of these stars must be of the order of #cj1jjj degrees1 they must be minute in size2 indeed a simple calculation shews that they can hardly have more than about a tenth of the sun's radius4 ,not only are they small in size1 but there are indications that they are of great weight4 ,spectroscopic evidence shews that in many cases the surrounding nebulae are in rotation1 and1 just as with the galaxy 7p4 #fi7 and the huge extra-galactic nebulae 7p4 #ga71 their weights can be calculated from their observed speeds of rotation4 ,these seem to indicate average weights of something like #dj or #ej times the weight of the sun4 ,campbell and ,moore1 of ,lick ,observatory1 have calculated that the planetary nebula ,n4,g4,c4 #gjji must have #afb times the weight of the sun1 but many factors combine to make this estimate rather uncertain4 ,all this goes to suggest that the central stars of the planetary nebulae must1 in all probability1 be regarded as 8white dwarfs0 of enormous weight4 ,it seems possible that they are exactly the type of star needed by our theory4 ,the #eb planetary nebulae already mentioned have the same average distance from the sun1 and the same distribution with respect to the galaxy1 as the ,o-type stars1 so that it is possible that ,o-type stars and planetary nebulae are forms assumed either successively or alternatively in the course of evolution of similar bodies4 ,it should be mentioned that the planetary nebulae exhibit spectral displacements which1 if interpreted in the ordinary way1 would indicate that they are moving with very high speeds1 in some cases reaching hundreds of miles a second4 ,such speeds would be entirely inappropriate to stars of large weight4 ,yet this objection rather defeats itself1 for if the spectral shifts really arose from high speeds of motion1 the highest of the observed speeds would suffice to carry the planetary nebulae possessing them clear of the galactic system altogether2 they would be random travellers through our system of stars1 whereas their orderly arrangement and concentration near the galactic plane suggests very forcibly that they are permanent members of it4 ,thus the observed large shifts of the spectral lines can hardly indicate large speeds in space2 some other interpretation must be found4 ,professor ,perrine considers that they arise in the main from internal motions1 contraction1 expansion and rotation of the nebulae4 ,if so1 the motions in space cannot be determined1 but at least they no longer present any difficulty4 ,if these stars are1 as our hypothesis requires1 white dwarfs of very great weight and small radius1 their spectra ought to exhibit a relativity displacement to the red of the same type as that actually observed in ,sirius ,b4 ,it is possible that this may be found to present a more serious difficulty1 although it is also possible that it again may prove to be merged in the large observed displacements4 ,in view of all this1 it seems quite possible that both the planetary nebulae1 and also other ,o- or ,b-type stars of feeble luminosity1 may be very massive stars in the dormant condition contemplated by the hypothesis we have just been discussing4 ,in brief1 we imagine that a massive star may have its weight conserved through existing as a planetary nebula or a dwarf ,o-type star for millions of millions of years1 and then burst out as a highly luminous star with all the appearance of extreme youth4 ,but there is at present insufficient observational evidence either for or against such a hypothesis4 ,some pieces of the puzzle are missing1 and we can only wait until they turn up4 ,,white ,,dwarfs4 ,apart from these hypothetical massive white dwarfs1 astronomers generally regard ordinary white dwarfs as the final stage in stellar evolution4 ,there is general agreement that they are stars with central temperatures so high that their atoms are stripped bare of electrons1 but there is no general consensus of opinion as to why stars shrink to this condition4 ,on the liquid-star hypothesis1 the unoccupied regions in the ,russell diagram represent unstable configurations4 ,usually a slight loss of weight by a star merely moves it to a new position in the diagram contiguous to the old one4 ,sometimes1 however1 this slight move may happen to carry the star into an unstable region of the diagram1 in which case it will hurriedly traverse this region1 until finally it ends up in some entirely different stable configuration4 ,the liquid-star hypothesis explains the white dwarf state quite simply as the final state to which a star shrinks cataclysmically when its generation of energy is no longer sufficient to entitle it to a place in the main-sequence4 ,in this state the star radiates so little energy that annihilation and decay are almost entirely checked4 ,we have seen that if the sun went on radiating at its present rate for #ae million million years1 its whole weight would be transformed into radiation4 ,by contrast1 van ,maanen's star can1 and probably will1 go on radiating at its present rate for #ae million million years without losing more than about a thousandth part of its present weight4 ,we may think of the white dwarf state as a final state from which change and decay have so nearly disappeared that a star which shrinks to this state acquires a new lease of life for a period of thousands of millions of millions of years--we can only wonder to what purpose4 ,,chapter ,,vi ,beginnings and ,endings ,we have seen how the solid substance of the material universe is continually dissolving away into intangible radiation4 ,the sun weighed #cfj1jjj million tons more yesterday than to-day1 the difference being the weight of #bd-;hours' emission of radiation which is now travelling through space1 and1 so far as direct observation goes1 is destined to journey on through space until the end of time4 ,the same transformation of material weight into radiation is in progress in all the stars1 and to a lesser degree on earth1 where complex atoms such as uranium are continually changing into the simpler atoms of lead and helium1 and setting radiation free in the process4 ,but against the sun's daily loss of weight of #cfj1jjj million tons1 the earth is only losing weight from this cause at the rate of about ninety pounds a day4 ,,cyclic ,,processes4 ,it is natural to ask whether a study of the universe as a whole reveals these processes as part only of a closed cycle1 so that the wastage which we see in progress in the sun and stars and on the earth is made good elsewhere4 ,when we stand on the banks of a river and watch its current ever carrying water out to sea1 we know that this water is in due course transformed into clouds and rain which replenish the river4 ,is the physical universe a similar cyclic system1 or ought it rather to be compared to a stream which1 having no source of replenishment1 must cease flowing after it has spent itself8 ,,thermodynamics ,to this question1 the wide scientific principle known as the second law of thermodynamics provides an answer in very general terms4 ,if we ask what is the underlying cause of all the varied animation we see around us in the world1 the answer is in every case1 energy--the chemical energy of the fuel which drives our ships1 trains and cars1 or of the food which keeps our bodies alive and is used in muscular effort1 the mechanical energy of the earth's motion which is responsible for the alternations of day and night1 of summer and winter1 of high tide and low tide1 the heat-energy of the sun which makes our crops grow and provides us with wind and rain4 ,the first law of thermodynamics1 which embodies the principle of 8conservation of energy10 teaches that energy is indestructible2 it may change about from one form to another1 but its total amount remains unaltered through all these changes1 so that the total energy of the universe remains always the same4 ,as the energy which is the cause of all the life of the universe is indestructible1 it might be thought that this life could go on for ever undiminished in amount4 ,,availability ,,of ,,energy4 ,the second law of thermodynamics rules out any such possibility4 ,energy is indestructible as regards its amount1 but it continually changes in form1 and generally speaking there are upward and downward directions of change4 ,it is the usual story--the downward journey is easy1 while the upward is either hard or impossible4 ,as a consequence1 more energy passes in one direction than in the other4 ,for instance1 both light and heat are forms of energy1 and a million ergs of light-energy can be transformed into a million ergs of heat with the utmost ease2 let the light fall on any cool1 black surface1 and the thing is done4 ,but the reverse transformation is impossible2 a million ergs which have once assumed the form of heat1 can never again assume the form of a million ergs of light4 ,this is a special example of the general principle that radiative energy tends always to change into a form of longer1 not shorter1 wave-length4 ,in general1 for instance1 fluorescence increases the wave-length of the light2 it changes blue light into green1 yellow or red1 but not red light into yellow1 green or blue4 ,exceptions to the general principle are known1 but they are of special type1 admitting of special explanations1 and do not affect the general principle4 ,it may be objected that the everyday act of lighting a fire disproves all this4 ,has not the sun's heat been stored up in the coal we burn1 and cannot we produce light by burning coal8 ,the answer is that the sun's radiation is a mixture of both light and heat1 and indeed of radiation of all wave-lengths4 ,what is stored up in the coal is primarily the sun's light and other radiation of still shorter wave-length4 ,when we burn coal we get some light1 but not as much as the sun originally put into the coal2 we also get some heat1 and this is more than the amount of heat which was originally put in4 ,on balance1 the net result of the whole transaction is that a certain amount of light has been transformed into a certain amount of heat4 ,all this shews that we must learn to think of energy1 not only in terms of quantity1 but also in terms of quality4 ,its total quantity remains always the same2 this is the first law of thermodynamics4 ,but its quality changes1 and tends to change always in the same direction4 ,turnstiles are set up between the different qualities of energy2 the passage is easy in one direction1 impossible in the other4 ,a human crowd may contrive to find a way round without jumping over turnstiles1 but in nature there is no way round2 this is the second law of thermodynamics4 ,energy flows always in the same direction1 as surely as water flows downhill4 ,part of the downward path consists1 as we have seen1 of the transition from radiation of short wave-length into radiation of longer wave-length4 ,in terms of quanta 7p4 #abf7 the transition is from a few quanta of high energy to a large number of quanta of low energy1 the total amount of energy of course remaining unaltered4 ,the downfall of the energy accordingly consists in the breaking of its quanta into smaller units4 ,and when once the fall and breakage have taken place1 it is as impossible to reconstitute the original large quanta as it was to put ,humpty-,dumpty back on his wall4 ,although this is the main part of the downward path1 it is not the whole of it4 ,thermodynamics teaches that all the different forms of energy have different degrees of 8availability10 and that the downward path is always from higher to lower availability4 ,and now we may return to the question with which we started the present chapter3 8,what is it that keeps the varied life of the universe going80 ,our original answer 8energy0 is seen to be incomplete4 ,energy is no doubt essential1 but the really complete answer is that it is the transformation of energy from a more available to a less available form2 it is the running downhill of energy4 ,to argue that the total energy of the universe cannot diminish1 and therefore the universe must go on for ever1 is like arguing that as a clock-weight cannot diminish1 the clock-hand must go round and round for ever4 ,,the ,,final ,,end ,,of ,,the ,,universe ,energy cannot run downhill for ever1 and1 like the clock-weight1 it must touch bottom at last4 ,and so the universe cannot go on for ever2 sooner or later the time must come when its last erg of energy has reached the lowest rung on the ladder of descending availability1 and at this moment the active life of the universe must cease4 ,the energy is still there1 but it has lost all capacity for change2 it is as little able to work the universe as the water in a flat pond is able to turn a water-wheel4 ,we are left with a dead1 although possibly a warm1 universe--a 8heat-death40 ,such is the teaching of modern thermodynamics4 ,there is no reason for doubting or challenging it1 and indeed it is so fully confirmed by the whole of our terrestrial experience1 that it is difficult to see at what point it could be open to attack4 ,it disposes at once of any possibility of a cyclic universe in which the events we see are as the pouring of river water into the sea1 while events we do not see restore this water back to the river4 ,the water of the river can go round and round in this way1 just because it is not the whole of the universe2 something extraneous to the river-cycle keeps it continually in motion--namely1 the heat of the sun4 ,but the universe as a whole cannot so go round and round4 ,short of postulating continuous action from outside the universe1 whatever this may mean1 the energy of the universe must continually lose availability2 a universe in which the energy had no further availability to lose would be dead already4 ,change can occur only in the one direction1 which leads to the heat-death4 ,with universes as with mortals1 the only possible life is progress to the grave4 ,even the flow of the river to the sea1 which we selected as an obvious instance of true cyclic motion1 is seen to illustrate this1 as soon as all the relevant factors are taken into account4 ,as the river pours seaward over its falls and cascades1 the tumbling of its waters generates heat1 which ultimately passes off into space in the form of heat radiation4 ,but the energy which keeps the river pouring along comes ultimately from the sun in the form mainly of light2 shut off the sun's radiation and the river will soon stop flowing4 ,the river flows only by continually transforming light-energy into heat-energy1 and as soon as the cooling sun ceases to supply energy of sufficiently high availability the flow must cease4 ,the same general principles may be applied to the astronomical universe4 ,there is no question as to the way in which energy runs down here4 ,it is first liberated in the hot interior of a star in the form of quanta of extremely short wave-length and excessively high energy4 ,as this radiant energy struggles out to the star's surface1 it continually adjusts itself1 through repeated absorption and re-emission1 to the temperature of that part of the star through which it is passing4 ,as longer wave-lengths are associated with lower temperatures 7p4 #adj71 the wave-length of the radiation is continually lengthened2 a few energetic quanta are being transformed into numerous feeble quanta4 ,once these are free in space1 they travel onward unchanged until they meet dust particles1 stray atoms1 free electrons1 or some other form of interstellar matter4 ,except in the highly improbable event of this matter being at a higher temperature than the surfaces of the stars1 these encounters still further increase the wave-length of the radiation1 and the final result of innumerable encounters is radiation of very great wave-length4 ,the quanta have increased enormously in numbers1 but have paid for their increase by a corresponding decrease in individual strength4 ,in all probability1 the original very energetic quanta had their source in the annihilation of protons and electrons1 so that the main process of the universe consists in the energy of exceedingly high availability which is bottled up in electrons and protons being transformed into heat-energy at the lowest level of availability4 ,many1 giving rein to their fancy1 have speculated that this low-level heat-energy may in due course re-form itself into new electrons and protons4 ,as the existing universe dissolves away into radiation1 their imagination sees new heavens and a new earth coming into being out of the ashes of the old4 ,but science can give no support to such fancies4 ,perhaps it is as well2 it is hard to see what advantage could accrue from an eternal reiteration of the same theme1 or even from endless variations of it4 ,the final state of the universe will1 then1 be attained when every atom which is capable of annihilation has been annihilated1 and its energy transformed into heat-energy wandering for ever round space1 and when all the weight of any kind whatever which is capable of being transformed into radiation has been so transformed4 ,we have mentioned ,hubble's estimate that matter is distributed in space at an average rate of #ae #aj grammes per cubic centimetre4 ,the annihilation of a gramme of matter liberates #i #aj ergs of energy1 so that the annihilation of #ae #aj grammes of matter liberates #ace #aj ergs of energy4 ,it follows that the total annihilation of all the substance of the existing universe would only fill space with energy at the rate of #ace #aj ergs per cubic centimetre4 ,this amount of energy is only enough to raise the temperature of space from absolute zero to a temperature far below that of liquid air2 it would only raise the temperature of the earth's surface by a #fjjjth part of a degree ,centigrade4 ,the reason why the effect of annihilating a whole universe is so extraordinarily slight is of course that space is so extraordinarily empty of matter2 trying to warm space by annihilating all the matter in it is like trying to warm a room by burning a speck of dust here and a speck of dust there4 ,as compared with any amount of radiation that is ever likely to be poured into it1 the capacity of space is that of a bottomless pit4 ,indeed1 so far as scientific observation goes1 it is entirely possible that the radiation of thousands of dead universes may even now be wandering round space without our suspecting it4 ,such is the final end of things to which1 so far as present-day science can see1 the material universe must inevitably come in some far-off age1 unless the course of nature is changed in the meantime4 ,let us now try to peer back towards the beginnings of things4 ,,the ,,beginnings ,,of ,,the ,,universe ,as we go forwards in time1 material weight continually changes into radiation4 ,conversely1 as we go backwards in time1 the total material weight of the universe must continually increase4 ,we have seen how the present weights of the stars are incompatible with their having existed for more than some #e or #aj million million years1 and that they would need approximately the whole of this enormous period to acquire certain signs of age which their present arrangement and motions reveal4 ,we have seen that the break-up of the huge extra-galactic nebulae must result in the birth of stars1 and have found that the most consistent account of the origin of the galactic system of stars is provided by the supposition that the whole system originated out of the break-up of a single huge nebula some #e to #aj million million years ago4 ,let us pause for a moment to compare this with an alternative hypothesis1 which some astronomers have favoured1 that stars are being created all the time4 ,on this hypothesis we picture the stars as passing in an endless steady stream from creation to extinction1 just as men pass in an endless steady stream from their cradles to their graves1 a new generation always coming into being to step into the place vacated by the old4 ,on this view ,plaskett's star1 with about a hundred times the weight of the sun1 must be a recent creation1 while ,kruger #fj1 with only a fraction of the sun's weight1 would be very1 very old--perhaps #ajj million million years older than ,plaskett's star4 ,at present direct observation cannot definitely decide between the two conflicting hypotheses1 but it rather frowns upon the 8steady stream0 view of the stars4 ,in a steady population the number of people in any assigned condition is exactly proportional to the time taken to pass through that condition4 ,suppose for instance that human beings possess infant teeth for a quarter as long as they possess adult teeth4 ,if examination of the teeth of a population shewed that four times as many had adult teeth as infant teeth1 this would create a prima facie expectation that we were dealing with a steady population4 ,if1 on the contrary1 #ajj times as many people were found with adult teeth as with infant teeth1 we should know we were not dealing with a steady population4 ,if other evidence pointed to the population all being of approximately the same age1 we should be inclined to accept this and regard the #a per cent4 of cases of infant teeth as cases of arrested development4 ,we do not judge the ages of stars by their teeth but by their weights and luminosities4 ,and the luminosities of the stars are not found to conform to the statistical laws which would prevail in a steady population of stars4 ,there appear to be so many middle-aged stars and so few infants and veterans as to make the hypothesis of a steady continuous creation hardly tenable4 ,indeed there is rather distinct evidence of a special creation of stars at about the time our sun was born4 ,this leads back again quite naturally to the view that the galactic system was born out of a spiral nebula whose main activity as a parent of stars occurred some #e to #aj million million years ago4 ,,pre-,,stellar ,,existence4 ,on the whole it seems likely that we must assign ages of #e to #aj million million years to most or all of the stars in the galactic system4 ,this is as far as we can probe back into time with any reasonable plausibility4 ,the atoms which now form the sun and stars must no doubt have had a previous existence as atoms of a nebula1 but we cannot say for how long4 ,the temperatures at the centres of the spiral nebulae may be1 and in all probability are1 so high that atoms are stripped bare of electrons and so shielded from annihilation4 ,we may in fact regard the gaseous centres of nebulae as a sort of 8white dwarfs0 built on a colossal scale4 ,this fits on to the fact that the nebulae generate very little energy for their weights and so shine very feebly4 ,we have seen that the weights of two extra-galactic nebulae can be estimated to a reasonable degree of accuracy4 ,the great ,andromeda nebula ,m #ca has the weight of #cejj million suns1 its total luminosity being that of #ffj million suns4 ,the nebula ,n4,g4,c4 #deid has the weight of #bjjj million suns1 and the luminosity of #bfj million suns4 ,a simple calculation shews that the atoms in the ,andromeda nebula have an average expectation of life of #hj million million years1 while the corresponding figure in ,n4,g4,c4 #deid is #aae million million years4 ,from these two instances1 we may guess that the average life1 before annihilation1 of the atoms in such nebulae must be of the order of #ajj million million years4 ,it cannot be claimed that this calculation is either very convincing or very exact1 but it supplies the only evidence at present available as to the probable length of life of matter in the nebular state4 ,we can say that the stars have existed as such for from #e to #aj million million years1 and that their atoms may have previously existed in nebulae for at least a comparable1 and possibly for a much longer1 time4 ,apart from detailed figures1 however1 it is clear that we cannot go backward in time for ever4 ,each step back in time involves an increase in the total weight of the matter of the universe1 and1 just as with individual stars1 we cannot go so far back that this total weight becomes infinite4 ,indeed a limit may quite possibly be set by considerations which we have already mentioned4 ,the complete annihilation of all the matter now in the universe would raise the temperature of the earth's surface by the six-thousandth part of a degree2 the annihilation of a million times as much matter would raise it by #afj degrees4 ,we cannot admit that as much radiation as this can be wandering about space4 ,the earth's temperature is determined by the amount of radiation it receives from the sun2 it adjusts its temperature so that it radiates away just as much energy as it receives4 ,a small correction is required on account of the earth's own radio-activity1 but this need not bother us4 ,what would bother us1 and would indeed upset the balance entirely1 would be the radiation of a million dead universes if this were for ever streaming on to us out of space2 in this event the earth's surface would have to rise to a temperature well above that of boiling water before it could restore the balance between the radiation it received and that it emitted4 ,in a word1 the radiation of a million dead universes would boil our seas1 rivers and ourselves4 ,,the ,,creation ,,of ,,matter4 ,all this makes it clear that the present matter of the universe cannot have existed for ever3 indeed we can probably assign an upper limit to its age of1 say1 some such round number as #bjj million million years4 ,and1 wherever we fix it1 our next step back in time leads us to contemplate a definite event1 or series of events1 or continuous process1 of creation of matter at some time not infinitely remote4 ,in some way matter which had not previously existed1 came1 or was brought1 into being4 ,if we want a naturalistic interpretation of this creation of matter1 we may imagine radiant energy of any wave-length less than #ac #aj cms4 being poured into empty space2 this is energy of higher 8availability0 than any known in the present universe1 and the running down of such energy might well create a universe similar to our own4 ,the table on p4 #add shews that radiation of the wave-length just mentioned might conceivably crystallise into electrons and protons1 and finally form atoms4 ,if we want a concrete picture of such a creation1 we may think of the finger of ,god agitating the ether4 ,we may avoid this sort of crude imagery by insisting on space1 time1 and matter being treated together and inseparably as a single system1 so that it becomes meaningless to speak of space and time as existing at all before matter existed4 ,such a view is consonant not only with ancient metaphysical theories1 but also with the modern theory of relativity 7p4 #gd74 ,the universe now becomes a finite picture whose dimensions are a certain amount of space and a certain amount of time2 the protons and electrons are the streaks of paint which define the picture against its space-time background4 ,travelling as far back in time as we can1 brings us not to the creation of the picture1 but to its edge2 the creation of the picture lies as much outside the picture as the artist is outside his canvas4 ,on this view1 discussing the creation of the universe in terms of time and space is like trying to discover the artist and the action of painting1 by going to the edge of the picture4 ,this brings us very near to those philosophical systems which regard the universe as a thought in the mind of its ,creator1 thereby reducing all discussion of material creation to futility4 ,both these points of view are impregnable1 but so also is that of the plain man who1 recognising that it is impossible for the human mind to comprehend the full plan of the universe1 decides that his own efforts shall stop this side of the creation of matter4 ,this last point of view is perhaps the most justifiable of all from the purely philosophic standpoint4 ,it is now a full quarter of a century since physical science1 largely under the leadership of ,poincar1 left off trying to explain phenomena and resigned itself merely to describing them in the simplest way possible4 ,to take the simplest illustration1 the ,victorian scientist thought it necessary to 8explain0 light as a wave-motion in the mechanical ether which he was for ever trying to construct out of jellies and gyroscopes2 the scientist of to-day1 fortunately for his sanity1 has given up the attempt and is well satisfied if he can obtain a mathematical formula which will predict what light will do under specified conditions4 ,it does not matter much whether the formula admits of a mechanical explanation or not1 or whether such an explanation corresponds to any thinkable ultimate reality4 ,the formulae of modern science are judged mainly1 if not entirely1 by their capacity for describing the phenomena of nature with simplicity1 accuracy1 and completeness4 ,for instance1 the ether has dropped out of science1 not because scientists as a whole have formed a reasoned judgment that no such thing exists1 but because they find they can describe all the phenomena of nature quite perfectly without it4 ,it merely cumbers the picture1 so they leave it out4 ,if at some future time they find they need it1 they will put it back again4 ,this does not imply any lowering of the standards or ideals of science2 it implies merely a growing conviction that the ultimate realities of the universe are at present quite beyond the reach of science1 and may be--and probably are--for ever beyond the comprehension of the human mind4 ,it is priori probable that only the artist can understand the full significance of the picture he has painted1 and that this will remain for ever impossible for a few specks of paint on the canvas4 ,it is for this kind of reason that1 when1 as in ,chapter ,,ii1 we try to discuss the ultimate structure of the atom1 we are driven to speak in terms of similes1 metaphors1 and parables4 ,there is no need even to worry overmuch about apparent contradictions4 ,the higher unity of ultimate reality must no doubt reconcile them all1 although it remains to be seen whether this higher unity is within our comprehension or not4 ,in the meantime a contradiction worries us about as much as an unexplained fact1 but hardly more2 it may or may not disappear in the progress of science4 ,if some such train of thought may be applied to our efforts to understand the most minute processes of the universe 7and it is the common everyday train of thought of those who are working in this field71 then it must surely be still more applicable to our efforts to understand the universe as a whole4 ,phenomena come to us disguised in their frameworks of time and space2 they are messages in cypher of which we shall not understand the ultimate significance until we have discovered how to decode them out of their space-time wrappings4 ,whatever may be thought about our final ability to decode the difficult messages we have recently received about the ultimate structure of the minutest parts of matter1 it seems natural that we should feel some apprehension with regard to those about the structure of the universe as a whole1 and particularly those about its beginnings and endings4 ,often enough the message itself may help us to discover the code in which it reaches us--with sufficient skill we can often do this--but we are now speaking of problems as to when1 by whom1 and for what purpose1 the code was devised4 ,there is no reason why a code message should throw any light on this4 ,the astronomer must leave the problem at this stage4 ,the message of astronomy is of obvious concern to philosophy1 to religion and to humanity in general1 but it is not the business of the astronomer to decode it4 ,the observing astronomer watches and records the dots and dashes of the needle which delivers the message1 the theoretical astronomer translates these into words--and according as they are found to form known consistent words or not1 it is known whether he has done his job well or ill--but it is for others to try to understand and explain the ultimate decoded meaning of the words he writes down4 ,,life ,,and ,,the ,,universe ,abandoning our efforts to understand the universe as a whole1 let us glance for a moment at the relation of life to the universe we know4 ,the old view that every point of light in the sky represented a possible home for life is quite foreign to modern astronomy4 ,the stars themselves have surface-temperatures of anything from #afej degrees to #cj1jjj degrees or more1 and are of course at far higher temperatures inside4 ,by far the greater part of the matter of the universe is at a temperature of millions of degrees1 so that its molecules are broken up into atoms1 and the atoms are broken up1 partially at least1 into their constituent parts4 ,now the very concept of life implies duration in time2 there can be no life where atoms change their make up millions of times a second and no pair of atoms can ever stay joined together4 ,it also implies a certain mobility in space1 and these two implications restrict life to the small range of physical conditions in which the liquid state is possible4 ,our survey of the universe has shewn how small this range is in comparison with that exhibited by the universe as a whole4 ,it is not to be found in the stars1 nor in the nebulae out of which the stars are born4 ,we know of no type of astronomical body in which the conditions can be favourable to life except planets like our own revolving round a sun4 ,now1 to the best of our present knowledge1 planets are very rare4 ,we have seen how a single star cannot of itself produce planets4 ,a family of planets must have two parents2 it only comes into being as the result of the close approach of two stars1 and stars are so sparsely scattered in space that it is an inconceivably rare event for one to pass near to a neighbour4 ,on the ,tidal ,theory1 explained on p4 #bcf1 planets cannot be born except when two stars pass within about three diameters of one another4 ,as we know how the stars are scattered in space1 we can estimate fairly closely how often two stars will approach within this distance of one another4 ,the calculation shews that even after a star has lived its life of millions of millions of years1 the chance is still about a hundred thousand to one against its being a sun surrounded by planets4 ,even so1 if life is to obtain a footing1 the planets must not be too hot or too cold4 ,in the solar system1 for instance1 we cannot imagine life existing on ,mercury or on ,neptune2 liquids boil on the former and freeze hard on the latter4 ,these planets are unsuitable for life because they are too near to1 or too far from1 the sun4 ,we can imagine other planets which are unsuitable because their substance itself generates energy at such a rate as to make them unsuitable for habitation4 ,the inert atoms which form our earth seem to be the end products of a long series of atomic changes1 a sort of final ash resulting from the combustion of the universe4 ,we have seen how such atoms probably float to the top in every star1 as being the lightest in weight1 but it is by no means a foregone conclusion that all planets will consist of nothing but inert atoms1 and so will cool down until life can obtain a footing on them4 ,this has happened with our earth1 but we do not know how many planets and planetary systems may be unsuited for life because it has not happened with them4 ,all this suggests that only an infinitesimally small corner of the universe can be in the least suited to form an abode of life4 ,primaeval matter must go on transforming itself into radiation for millions of millions of years to produce a minute quantity of the inert ash on which life can exist4 ,then by an almost incredible accident this ash1 and nothing else1 must be torn out of the sun which has produced it1 and condense into a planet4 ,even then1 this residue of ash must not be too hot or too cold1 or life will be impossible4 ,finally1 after all these conditions are satisfied1 will life come or will it not8 ,we must probably discard the at one time widely accepted view that once life had come into the universe in any way whatsoever1 it would rapidly spread from planet to planet and from one planetary system to another until the whole universe teemed with life2 space now seems too cold1 and planetary systems too far apart4 ,our terrestrial life must in all probability have originated on the earth itself4 ,what we would like to know is whether it originated as the result of still another amazing accident or succession of coincidences1 or whether it is the normal event for inanimate matter to produce life in due course1 when the physical environment is suitable4 ,we look to the biologist for the answer1 which so far he has not been able to produce4 ,the astronomer might be able to give a partial answer if he could find evidence of life on some other planet1 for we should then at least know that life had occurred more than once in the history of the universe1 but so far no convincing evidence has been forthcoming4 ,some astronomers interpret certain markings on ,mars as canals1 which they believe to be the handiwork of intelligent beings1 but this interpretation is not generally accepted4 ,again1 seasonal changes necessarily occur on ,mars as on the earth1 and certain phenomena accompany these which many astronomers are inclined to ascribe to the growth and decline of vegetation1 although they may represent nothing more than rains watering the desert4 ,there is no definite evidence of life1 and certainly no evidence of conscious life1 on ,mars--or indeed anywhere else in the universe4 ,it seems at first somewhat surprising that oxygen figures so largely in the earth's atmosphere1 in view of its readiness to enter into chemical combination with other substances4 ,we know1 however1 that vegetation is continually discharging oxygen into the atmosphere1 and it has often been suggested that the oxygen of the earth's atmosphere may be mainly or entirely of vegetable origin4 ,if so1 the presence or absence of oxygen in the atmospheres of other planets should shew whether vegetation similar to that we have on earth exists on these planets or not4 ,oxygen certainly exists in the ,martian atmosphere1 but its amount is small4 ,adams and ,st ,john estimate that there cannot be more than #ae per cent4 as much1 per square mile1 as on earth4 ,on the other hand it is either completely absent1 or of negligible amount1 in the atmosphere of ,venus4 ,if any is present at all1 ,st ,john estimates that the amount above the clouds which cover the surface of ,venus is less than #ja per cent4 of the terrestrial amount4 ,the evidence1 for what it is worth1 goes to suggest that ,venus1 the only planet in the solar system outside ,mars and the earth on which life could possibly exist1 possesses no vegetation and no oxygen for higher forms of life to breathe4 ,apart from the certain knowledge that life exists on earth1 we have no definite knowledge whatever except that1 at the best1 life must be limited to a tiny fraction of the universe4 ,millions of millions of stars exist which support no life1 which have never done so and never will do so4 ,of the rare planetary systems in the sky1 many must be entirely lifeless1 and in others life1 if it exists at all1 is probably limited to a few planets4 ,the three centuries which have elapsed since ,giordano ,bruno suffered martyrdom for believing in the plurality of worlds have changed our conception of the universe almost beyond description1 but they have not brought us appreciably nearer to understanding the relation of life to the universe4 ,we can still only guess as to the meaning of this life which1 to all appearances1 is so rare4 ,is it the final climax towards which the whole creation moves1 for which the millions of millions of years of transformation of matter in uninhabited stars and nebulae1 and of the waste of radiation in desert space1 have been only an incredibly extravagant preparation8 ,or is it a mere accidental and possibly quite unimportant by-product of natural processes1 which have some other and more stupendous end in view8 ,or1 to glance at a still more modest line of thought1 must we regard it as something of the nature of a disease1 which affects matter in its old age when it has lost the high temperature and capacity for generating high-frequency radiation with which younger and more vigorous matter would at once destroy life8 ,or1 throwing humility aside1 shall we venture to imagine that it is the only reality1 which creates1 instead of being created by1 the colossal masses of the stars and nebulae and the almost inconceivably long vistas of astronomical time8 ,again it is not for the astronomer to select between these alternative guesses2 his task is done when he has delivered the message of astronomy4 ,perhaps it is over-rash for him even to formulate the questions this message suggests4 ,,the ,,earth ,,and ,,its ,,future ,,prospects ,let us leave these rather abstract regions of thought and come down to earth4 ,we feel the solid earth under our feet1 and the rays of the sun overhead4 ,somehow1 but we know not how or why1 life also is here2 we ourselves are part of it4 ,and it is natural to enquire what astronomy has to say as to its future prospects4 ,the central facts which dominate the whole situation are that we are dependent on the light and heat of the sun1 and that these cannot remain for ever as they now are4 ,so far as we can at present see1 solar conditions can hardly have changed much since the earth was born2 the earth's #bjjj million years form so small a fraction of the sun's whole life that we can almost suppose the sun to have stood still throughout it4 ,this of itself suggests that1 in so far as astronomical factors are concerned1 life may look to a tenancy of the earth of far longer duration than the total past age of the earth4 ,the earth1 which started life as a hot mass of gas1 has gradually cooled1 until it has now about touched bottom1 and has almost no heat beyond that which it receives from the sun4 ,this just about balances the amount it radiates away into space1 so that it would stay at its present temperature for ever if external conditions did not change1 and any changes in its condition will be forced on it by changes occurring outside4 ,these external changes may be of many kinds4 ,the sun's loss of weight causes the earth to recede from it at the rate of about a yard a century1 so that after a million million years1 the earth will be #aj per cent4 further away from the source of its light and life than now4 ,consequently even if the sun then radiated as much light and heat as now1 the earth would receive #bj per cent4 less of this radiation1 and its mean temperature would be some #ae degrees ,centigrade or so lower than at present4 ,but after a million million years the sun will not radiate as much light and heat as now2 it will have lost some #f per cent4 of its present weight through radiation1 and1 judging from other stars1 this loss will probably reduce its energy-generating capacity by about #bj per cent4 ,this will reduce the earth's temperature by about another #ae degrees1 so that after a million million years the inevitable course of events will have reduced the earth's temperature by about #cj degrees ,centigrade4 ,it would be rash to attempt to predict how such a fall of temperature may affect terrestrial life1 and human life in particular4 ,given sufficient time1 life has such an enormous capacity for adapting itself to its environment that it seems possible that1 even with a temperature #cj degrees ,centigrade lower than now1 life may still exist on earth a million million years hence4 ,if so1 ,i am glad that my life has not fallen in this far distant future4 ,mountains and seas1 which provide some of the keenest pleasures of our present life1 will exist only as traditions handed down from a remote and almost incredible past4 ,the denudation of a million million years will have reduced the mountains almost to plains1 while seas and rivers will be frozen packs of solid ice4 ,we may well imagine that man will have infinitely more knowledge than now1 but he will no longer know the thrill of pleasure of the pioneer who opens up new realms of knowledge4 ,disease1 and perhaps death1 will have been conquered1 and life will doubtless be safer and incomparably better-ordered than now4 ,it will seem incredible that a time could have existed when men risked1 and lost1 their lives in traversing unexplored country1 in climbing hitherto unclimbed peaks1 in fighting wild beasts for the fun of it4 ,life will be more of a routine and less of an adventure than now2 it will also be more purposeless when the human race knows that within a measurable space of time it must face extinction and the eternal destruction of all its hopes1 endeavours1 and achievements4 ,without laying too much stress on these visionary concepts of life a million million years hence1 we may nevertheless think of this as the period in round numbers after which the inevitable wastage of the sun's weight is likely to drive life off the earth4 ,venus1 with a mean temperature some #fj degrees higher than the earth1 is probably rather too hot for life at present4 ,but after a million million years1 the temperature of ,venus will have fallen by #dj degrees1 and what the earth is now1 ,venus may perhaps be somewhere between one and two million million years hence4 ,whether life will then inhabit ,venus we cannot know1 and it would be futile to guess1 but there is at least a chance that as the earth fails1 ,venus may step into its place4 ,possibly ,venus may be followed by ,mercury in due course1 but the present evidence is that ,mercury is devoid of atmosphere1 in which case it is hard to imagine it as a home for life at all resembling that which now inhabits the earth4 ,so far we have considered only the normal course of events2 a variety of accidents may bring the human race to an end long before a million million years have elapsed4 ,to mention only possible astronomical occurrences1 the sun may run into another star1 any asteroid may hit any other asteroid and1 as a result1 be so deflected from its path as to strike the earth1 any of the stars in space may wander into the solar system and1 in so doing1 upset all the planetary orbits to such an extent that the earth becomes impossible as an abode of life4 ,it is difficult to estimate the likelihood of any of these events happening but they all seem very improbable1 and the first and last highly so4 ,let us disregard them all4 ,a danger remains which cannot be so lightly dismissed4 ,let us first state it in technical language4 ,the sun is a main-sequence star1 and is moreover very near to the left-hand edge of the main-sequence in the ,russell diagram 7p4 #bgh74 ,beyond this edge is a region of the diagram which is completely untenanted by stars4 ,we have supposed this region to be untenanted by stars because the stellar configurations it represents would be unstable4 ,stars pass through it rapidly until they find a stable configuration1 and so end up in a region which can be permanently tenanted by stars4 ,now the next stable configurations beyond this region are those of the white dwarfs1 and as these are less massive as a class than the main-sequence stars1 the general trend of stellar evolution appears to be from main-sequence star to white dwarf4 ,on this view the white dwarfs must have previously been main-sequence stars which wandered across the left-hand edge of the band of stable configurations and then fell through the unstable region until they resumed stability as white dwarfs4 ,the danger lies in the fact that the sun is already perilously near to the left-hand edge of the main-sequence4 ,according to ,redman's determinations1 which are probably by far the most reliable at present available1 the main-sequence belt of stable configurations for stars of the same spectral type as the sun 7,g #j7 extends roughly between stellar absolute magnitudes1 #dhh and #ced1 the former marking the dangerous left-hand edge4 ,the sun's present absolute magnitude is estimated as #dhe4 ,thus if the sun were to become #jjc magnitudes fainter1 this representing a reduction of only #c per cent4 in its luminosity1 it would arrive exactly at the edge of the main-sequence1 and would proceed to contract precipitately to the white dwarf state4 ,in so doing1 its light and heat would diminish to such an extent that life would be banished from the earth4 ,the known white dwarf star which it would most closely resemble is the companion of ,sirius1 and this emits only a four-hundredth part as much light and heat as the sun4 ,to put the same thing in non-technical language1 the sun is in1 or is not far from1 a precarious state in which stars are liable to begin to shrink and in so doing to reduce their radiation to a tiny fraction of that at present emitted by the sun4 ,the shrinkage of the sun to this state would transform our oceans into ice and our atmosphere into liquid air2 it seems impossible that terrestrial life could survive4 ,the vast museum of the sky must almost certainly contain examples of shrunken suns of this type with planets like our earth revolving round them4 ,whether these planets carry on them the frozen remains of a life which was once as active as our present life on earth we can hardly even surmise4 ,this may be thought to open up a startling prospect for the earth1 but we can take courage for several reasons4 ,in the first place a #c per cent4 decrease in the sun's luminosity can hardly occur in less than about #aej1jjj million years4 ,this in itself is not too bad1 but the prospect becomes enormously more hopeful when we reflect that the evolution of the stars1 including the sun1 takes place in a direction almost parallel to the edge of the main-sequence4 ,the sun is not heading for the precipice1 so much as skirting along its edge4 ,whether it is approaching the edge1 and is ultimately destined to fall over1 we do not know1 but it is in any case unlikely to reach the edge within the next million million years4 ,finally1 the sun's distance from the edge of the main-sequence cannot be estimated with anything like the degree of accuracy assumed in the foregoing calculations4 ,the figure of #jjc appeared as the difference of two much larger numbers1 and although both of these can be estimated with fair accuracy1 neither can be estimated with sufficient accuracy to justify us in treating their small difference of #jjc as exact4 ,the most we can say is that the sun is quite fairly near to the dangerous edge1 but that any appreciable motion towards this edge is a matter of millions of millions of years4 ,another danger1 of a more speculative kind1 must also be mentioned4 ,we have seen 7p4 #fa7 how every now and then a new star appears in the sky1 shines with terrific brilliancy for a short time1 and then either fades away entirely or continues to shine as an ordinary star4 ,these apparitions are known as 8novae0--new stars4 ,in many cases the nova has been proved to be an ordinary star which was visible as a very faint star long before it appeared as a nova1 flashed into brilliance for a brief span of life1 and then lapsed back into commonplaceness1 and it seems reasonable to suppose that all novae are of this kind1 although the star may often escape detection until it assumes its brilliant nova state4 ,these apparitions are by no means rare2 something like six appear every year in the galactic system alone4 ,now if we suppose the galactic system to consist of #cjj1jjj million stars1 this means that1 on the average1 each star becomes a nova once in every #ej1jjj million years4 ,what we would like to know is whether our sun is in danger of becoming a nova2 for1 if all kinds of stars run equal chances1 it is likely to become a nova some twenty times in the next million million years4 ,so far there is no agreement among astronomers either as to the physical causes which turn an ordinary star into a nova1 or as to the physical conditions which prevail in novae4 ,various suggestions are in the field1 but none of them wins general acceptance4 ,it seems fairly certain that if our sun were suddenly to become a nova1 its emission of light and heat would so increase as to scorch all life off the earth1 but we are completely in the dark as to whether our sun runs any risk of entering the nova stage4 ,if it does1 this is probably the greatest of all the risks to which life on earth is exposed4 ,apart from accidents1 we have seen that if the solar system is left to the natural course of evolution1 the earth is likely to remain a possible abode of life for something of the order of a million million years to come4 ,this is some five hundred times the past age of the earth1 and over three million times the period through which humanity has so far existed on earth4 ,let us try to see these times in their proper proportion by the help of yet another simple model4 ,take a postage-stamp1 and stick it on to a penny4 ,now climb ,cleopatra's needle and lay the penny flat1 postage-stamp upper-most1 on top of the obelisk4 ,the height of the whole structure may be taken to represent the time that has elapsed since the earth was born4 ,on this scale1 the thickness of the penny and postage-stamp together represents the time that man has lived on earth4 ,the thickness of the postage-stamp represents the time he has been civilised1 the thickness of the penny representing the time he lived in an uncivilised state4 ,now stick another postage-stamp on top of the first to represent the next #ejjj years of civilisation1 and keep sticking on postage-stamps until you have a pile as high as ,mont ,blanc4 ,even now the pile forms an inadequate representation of the length of the future which1 so far as astronomy can see1 probably stretches before civilised humanity1 unless an accident cuts it short4 ,the first postage-stamp was the past of civilisation2 the column higher than ,mont ,blanc is its future4 ,or1 to look at it in another way1 the first postage-stamp represents what man has already achieved2 the pile which outtops ,mont ,blanc represents what he may achieve1 if his future achievement is proportional to his time on earth4 ,yet we have seen that we cannot count on such a length of future with any certainty4 ,accidents may happen to the race as to the individual4 ,celestial collisions may occur2 shrinking into a white dwarf1 the sun may freeze terrestrial life out of existence2 bursting out as a nova it may scorch our race to death4 ,accident may replace our ,mont ,blanc of postage-stamps by a truncated column of only a fraction of the height of ,mont ,blanc4 ,even so1 there is a prospect of tens of thousands of millions of years before our race4 ,and the human mind1 as apart from the mind of the mathematician1 can hardly distinguish clearly between such a period as this and the million million years to which we may look forward if accidents do not overtake us4 ,for all practical purpose the only statement that conveys any real meaning is that our race may look forward to occupying the earth for a time incomparably longer than any we can imagine4 ,looked at in terms of space1 the message of astronomy is at best one of melancholy grandeur and oppressive vastness4 ,looked at in terms of time1 it becomes one of almost endless possibility and hope4 ,as denizens of the universe we may be living near its end rather than its beginning2 for it seems likely that most of the universe had melted into radiation before we appeared on the scene4 ,but as inhabitants of the earth1 we are living at the very beginning of time4 ,we have come into being in the fresh glory of the dawn1 and a day of almost unthinkable length stretches before us with unimaginable opportunities for accomplishment4 ,our descendants of far-off ages1 looking down this long vista of time from the other end1 will see our present age as the misty morning of the world's history2 our contemporaries of to-day will appear as dim heroic figures who fought their way through jungles of ignorance1 error and superstition to discover truth1 to learn how to harness the forces of nature1 and to make a world worthy for mankind to live in4 ,we are still too much engulfed in the greyness of the morning mists to be able to imagine1 however vaguely1 how this world of ours will appear to those who will come after us and see it in the full light of day4 ,but by what light we have1 we seem to discern that the main message of astronomy is one of hope to the race and of responsibility to the individual--of responsibility because we are drawing plans and laying foundations for a longer future than we can well imagine4 ,,index ,aquil1 see ,altair ,canis ,majoris1 see ,sirius ,canis ,minoris1 see ,procyon ,centauri1 distance1 #cc1 #ce luminosity and weight1 #dh system of1 #dj1 #bfc1 #bgi1 #bhj ,herculis1 #bei1 #bgb ,lyrae1 #cc ,orionis1 see ,betelgeux -particles1 #aab1 #aaf1 #aag1 #aah and ,plate ,,xiii 7p4 #aac7 -rays1 #aaa ,scorpii1 see ,antares ,absolute temperature1 #ajb ,absorption lines and spectrum1 #ea1 #abf ,actino-uranium1 #aed1 #aee ,adams1 ,j4 ,c41 #ah1 #ai ,adams1 ,w4 ,s41 #fb1 #cdc ,age of earth1 #ad1 #aea ff41 #bdh of stars1 #aee ff4 of sun1 #ahj1 #ahd of universe1 #ccf ,aitken1 ,r4 ,g41 #aga1 #ahh ,altair 7 ,aquil71 #cc1 #bgh ,andromeda1 ,great ,nebula ,m #ca in1 ,plate ,,iv 7p4 #cj71 #cj1 #gj1 #ga1 #gb1 #bjd1 #bjf1 #bjh1 #bae1 #cce age1 #cce distance1 #ga rotation1 #bjf size1 #cj weight1 #ga1 #bjh1 #bae ,andromedid meteors1 #bea ,angstrom unit1 defined1 #bef ,angular momentum1 conservation of1 #bje1 #bag1 #bcb of solar system1 #bcb ,annihilation of matter1 #ahe1 #aia1 #aic1 #bih1 #cca ,antares 7 ,scorpii71 #bei1 #bgb1 #bgc1 #bgh internal constitution of1 #bgc1 #bia ,aquarid meteors1 #bea ,aristarchus of ,samos1 #b1 #ac ,aristotle1 #b1 #e ,arrangement of solar system1 #af1 #bdj ff4 ,bode's law1 #ai1 #bj ,copernican1 #c1 #e1 #f1 #bg1 #cb ,ptolemaic1 #b1 #d1 #f1 #h1 #ca ,asteroids1 #ag1 #bbf1 #bdj1 #bdg1 #beb1 #cdh ,ceres1 #ag distance of1 #ai1 #bj1 #beb ,eros1 #cd origin of1 #bdg1 #beb ,aston1 ,f4 ,w41 #aai1 #aed1 #ahe ,atmosphere1 of earth1 #aie1 #cdc of moon1 #aif of planets1 #aif1 #cdc1 #cdd1 #cdh of sun1 #aie ,atomic nuclei1 #ajh1 #aag disintegration of1 #aaa1 #aag size and weight of1 #aji structure of1 #aai1 #aci1 #adg ,atomic numbers and weights1 #aaj1 #bhg in stellar matter1 #cjf1 #caa ,atomic theory1 #ib1 #ajc ,atoms1 #ajc1 #cah structure of1 #ajf synthesis of1 #adh1 #adi1 #ahe ,availability of ,energy1 #cbf1 #cbi ,aurigae1 #ed1 #eh -particles1 #aab1 #aac1 #aaf1 #ade and ,plate ,,xiii 7p4 #aac7 -rays1 #aaa1 #ade ,b4,d4 #f #acji1 see ,plaskett's star ,bacon1 ,roger1 #a ,becquerel1 ,h41 #aaj ,bentley1 ,r41 #aig ,berenice's hair1 #ci ,bessel1 ,f4 ,w41 #cc ,betelgeux 7 ,orionis71 #bei1 #bgb1 #bgh ,bickerton1 ,a4 ,w41 #bce ,biela's comet1 #bea ,binary systems1 #ci1 #dj1 #eb1 #ed birth of1 #bag eclipsing1 #ed1 #eh loss of weight in1 #ahh1 #bbh orbits of1 #df1 #dg1 #afg origins of1 #afi1 #bai1 #big relative weights of 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