,stars and ,atoms ,illustration ,illustration3 ,fig4 #a4 ,,the ,,sun4 ,hydrogen photograph ,,stars ,,and ,,atoms ,,by ,a4 ,s4 ,,eddington ,m4,a41 ,d4,sc41 ,,ll4,d41 ,f4,r4,s41 ,plumian ,professor of ,astronomy in the ,university of ,cambridge ,,new ,,haven3 ,,yale ,,university ,,press ,,london3 ,,humphrey ,,milford1 ,,oxford ,,university ,,press #aibg ,ich hufe ungeheure ,zahlen1 ,gebrge ,millionen auf1 ,ich setze ,zeit auf ,zeit und ,welt auf ,welt zu ,hauf4 ,a4 ,,von ,,haller4 ,,preface #8,,stars and ,atoms' was the title of an ,evening ,discourse given at the meeting of the ,british ,association in ,oxford in ,august #aibf4 ,in adapting it for publication the restrictions of a time limit are removed1 and accordingly it appears in this book as three lectures4 ,earlier in the year ,i had given a course of three lectures in ,king's ,college1 ,london1 on the same topics2 these have been combined with the ,oxford lecture and are the origin of most of the additions4 ,a full account of the subject1 including the mathematical theory1 is given in my larger book1 ,the ,internal ,constitution of the ,stars 7,camb4 ,univ4 ,press1 #aibf74 ,here ,i only aim at exposition of some of the leading ideas and results4 ,the advance in our knowledge of atoms and radiation has led to many interesting developments in astronomy2 and reciprocally the study of matter in the extreme conditions prevailing in stars and nebulae has played no mean part in the progress of atomic physics4 ,this is the general theme of the lectures4 ,selection has been made of the advances and discoveries which admit of comparatively elementary exposition2 but it is often necessary to demand from the reader a concentration of thought which1 it is hoped1 will be repaid by the fascination of the subject4 ,the treatment was meant to be discursive rather than systematic2 but habits of mind refuse to be suppressed entirely and a certain amount of system has crept in4 ,in these problems where our thought fluctuates continually from the excessively great to the excessively small1 from the star to the atom and back to the star1 the story of progress is rich in variety2 if it has not lost too much in the telling1 it should convey in full measure the delights--and the troubles--of scientific investigation in all its phases4 ,temperatures are expressed throughout in degrees ,centigrade4 ,the ,english billion1 trillion1 c4 7#ajab1 #ajah1 c47 are used4 ,a4 ,s4 ,e4 ,,contents ,,lecture ,i4 ,,the ,,interior ,,of ,a ,,star #i ,temperature in the ,interior #aa ,ionization of ,atoms #ag ,radiation ,pressure and ,mass #bd ,the ,interior of a ,star #bf ,opacity of ,stellar ,matter #bh ,the ,relation of ,brightness to ,mass #ca ,dense ,stars #cf ,,lecture ,,ii4 ,,some ,,recent ,,investigations #db ,the ,story of ,algol #db ,the ,story of the ,companion of ,sirius #dh ,unknown ,atoms and ,interpretation of ,spectra #ec ,spectral ,series #ei ,the ,cloud in ,space #fc ,the ,sun's ,chromosphere #gj ,the ,story of ,betelgeuse #gf ,,lecture ,,iii4 ,,the ,,age ,,of ,,the ,,stars #he ,pulsating ,stars #he ,the ,cepheid as a #8,standard ,candle' #ij ,the ,contraction ,hypothesis #id ,subatomic ,energy #ii ,evolution of the ,stars #ajf ,radiation of ,mass #aac ,,appendix ,further ,remarks on the ,companion of ,sirius #abb ,,list ,,of ,,illustrations ,,fig4 #a4 ,the ,sun4 ,hydrogen ,spectroheliogram4 7,j4 ,evershed7 #b4 ,solar ,vortices4 ,hydrogen ,spectroheliogram4 7,mount ,wilson ,observatory7 #c4 ,tracks of ,alpha ,particles 7helium atoms74 7,c4 ,t4 ,r4 ,wilson7 #d4 ,tracks of ,beta ,particles 7electrons74 7,c4 ,t4 ,r4 ,wilson7 #e4 ,ionization by ,x-rays4 7,c4 ,t4 ,r4 ,wilson7 #f4 ,ions produced by ,collision of a ,beta particle4 7,c4 ,t4 ,r4 ,wilson7 #g4 ,the ,mass-luminosity ,curve4 #h4 ,the ,ring ,nebula in ,lyra4 ,slitless ,spectrogram4 7,w4 ,h4 ,wright7 #i4 ,flash ,spectrum of ,chromosphere showing ,head of the ,balmer ,series4 7,british ,eclipse ,expedition1 #ad ,jan4 #aibf7 #aj4 ,solar ,prominence4 7,british ,eclipse ,expedition1 #bi ,may #aiai7 #aa4 ,star ,cluster ,centauri4 7,cape ,observatory7 ,,lecture ,i ,,the ,,interior ,,of ,a ,,star ,,the sun belongs to a system containing some #c1jjj million stars4 ,the stars are globes comparable in size with the sun1 that is to say1 of the order of a million miles in diameter4 ,the space for their accommodation is on the most lavish scale4 ,imagine thirty cricket balls roaming the whole interior of the earth2 the stars roaming the heavens are just as little crowded and run as little risk of collision as the cricket balls4 ,we marvel at the grandeur of the stellar system4 ,but this probably is not the limit4 ,evidence is growing that the spiral nebulae are #8island universes' outside our own stellar system4 ,it may well be that our survey covers only one unit of a vaster organization4 ,a drop of water contains several thousand million million million atoms4 ,each atom is about one hundred-millionth of an inch in diameter4 ,here we marvel at the minute delicacy of the workmanship4 ,but this is not the limit4 ,within the atom are the much smaller electrons pursuing orbits1 like planets round the sun1 in a space which relatively to their size is no less roomy than the solar system4 ,nearly midway in scale between the atom and the star there is another structure no less marvellous--the human body4 ,man is slightly nearer to the atom than to the star4 ,about #ajbg atoms build his body2 about #ajbh human bodies constitute enough material to build a star4 ,from his central position man can survey the grandest works of ,nature with the astronomer1 or the minutest works with the physicist4 ,to-night ,i ask you to look both ways4 ,for the road to a knowledge of the stars leads through the atom2 and important knowledge of the atom has been reached through the stars4 99 99 99 99 99 ,the star most familiar to us is the sun4 ,astronomically speaking1 it is close at hand4 ,we can measure its size1 weigh it1 take its temperature1 and so on1 more easily than the other stars4 ,we can take photographs of its surface1 whereas the other stars are so distant that the largest telescope in the world does not magnify them into anything more than points of light4 ,figs4 #a and #ba show recent pictures of the sun's surface4 ,no doubt the stars in general would show similar features if they were near enough to be examined4 ,i must first explain that these are not the ordinary photographs4 ,simple photographs show very well the dark blotches called sunspots1 but otherwise they are rather flat and uninteresting4 ,the pictures here shown were taken with a spectroheliograph1 an instrument which looks out for light of just one variety 7wave-length7 and ignores all the rest4 ,the ultimate effect of this selection is that the instrument sorts out the different levels in the sun's atmosphere and shows what is going on at one level1 instead of giving a single blurred impression of all levels superposed4 ,fig4 #b1 which refers to a high level1 gives a wonderful picture of whirlwinds and commotion4 ,i think that the solar meteorologists would be likely to describe these vortices in terms not unfamiliar to us--#8,a deep depression with secondaries is approaching1 and a renewal of unsettled conditions is probable4' ,however that may be1 there is always one safe weather forecast on the sun2 cyclone or anticyclone1 the temperature will be very warm--about #f1jjj in fact4 ,illustration3 ,fig4 #b4 ,,the ,,sun4 ,hydrogen photograph ,but just now ,i do not wish to linger over the surface layers or atmosphere of the sun4 ,a great many new and interesting discoveries have recently been made in this region1 and much of the new knowledge is very germane to my subject of #8,stars and ,atoms'4 ,but personally ,i am more at home underneath the surface1 and ,i am in a hurry to dive below4 ,therefore with this brief glance at the scenery that we pass we shall plunge into the deep interior--where the eye cannot penetrate1 but where it is yet possible by scientific reasoning to learn a great deal about the conditions4 ,temperature in the ,interior ,by mathematical methods it is possible to work out how fast the pressure increases as we go down into the sun1 and how fast the temperature must increase to withstand the pressure4 ,the architect can work out the stresses inside the piers of his building2 he does not need to bore holes in them4 ,likewise the astronomer can work out the stress or pressure at points inside the sun without boring a hole4 ,perhaps it is more surprising that the temperature can be found by pure calculation4 ,it is natural that you should feel rather sceptical about our claim that we know how hot it is in the very middle of a star--and you may be still more sceptical when ,i divulge the actual figures6 ,therefore ,i had better describe the method as far as ,i can4 ,i shall not attempt to go into detail1 but ,i hope to show you that there is a clue which might be followed up by appropriate mathematical methods4 ,i must premise that the heat of a gas is chiefly the energy of motion of its particles hastening in all directions and tending to scatter apart4 ,it is this which gives a gas its elasticity or expansive force2 the elasticity of a gas is well known to every one through its practical application in a pneumatic tyre4 ,now imagine yourself at some point deep down in the star where you can look upwards towards the surface or downwards towards the centre4 ,wherever you are1 a certain condition of balance must be reached2 on the one hand there is the weight of all the layers above you pressing downwards and trying to squeeze closer the gas beneath2 on the other hand there is the elasticity of the gas below you trying to expand and force the superincumbent layers outwards4 ,since neither one thing nor the other happens and the star remains practically unchanged for hundreds of years1 we must infer that the two tendencies just balance4 ,at each point the elasticity of the gas must be just enough to balance the weight of the layers above2 and since it is the heat which furnishes the elasticity1 this requirement settles how much heat the gas must have4 ,and so we find the degree of heat or temperature at each point4 ,the same thing can be expressed a little differently4 ,as before1 fix attention on a certain point in a star and consider how the matter above it is supported4 ,if it were not supported it would fall to the centre under the attractive force of gravitation4 ,the support is given by a succession of minute blows delivered by the particles underneath2 we have seen that their heat energy causes them to move in all directions1 and they keep on striking the matter above4 ,each blow gives a slight boost upwards1 and the whole succession of blows supports the upper material in shuttlecock fashion4 7,this process is not confined to the stars2 for instance1 it is in this way that a motor car is supported by its tyres47 ,an increase of temperature would mean an increase of activity of the particles1 and therefore an increase in the rapidity and strength of the blows4 ,evidently we have to assign a temperature such that the sum total of the blows is neither too great nor too small to keep the upper material steadily supported4 ,that in principle is our method of calculating the temperature4 ,one obvious difficulty arises1 ,the whole supporting force will depend not only on the activity of the particles 7temperature7 but also on the number of them 7density74 ,initially we do not know the density of the matter at an arbitrary point deep within the sun4 ,it is in this connexion that the ingenuity of the mathematician is required4 ,he has a definite amount of matter to play with1 viz4 the known mass of the sun2 so the more he uses in one part of the globe the less he will have to spare for other parts4 ,he might say to himself1 #8,i do not want to exaggerate the temperature1 so ,i will see if ,i can manage without going beyond #aj1jjj1jjj4' ,that sets a limit to the activity to be ascribed to each particle2 therefore when the mathematician reaches a great depth in the sun and accordingly has a heavy weight of upper material to sustain1 his only resource is to use large numbers of particles to give the required total impulse4 ,he will then find that he has used up all his particles too fast1 and has nothing left to fill up the centre4 ,of course his structure1 supported on nothing1 would come tumbling down into the hollow4 ,in that way we can prove that it is impossible to build up a permanent star of the dimensions of the sun without introducing an activity or temperature exceeding #aj1jjj1jjj4 ,the mathematician can go a step beyond this2 instead of merely finding a lower limit1 he can ascertain what must be nearly the true temperature distribution by taking into account the fact that the temperature must not be #8patchy'4 ,heat flows from one place to another1 and any patchiness would soon be evened out in an actual star4 ,i will leave the mathematician to deal more thoroughly with these considerations1 which belong to the following up of the clue2 ,i am content if ,i have shown you that there is an opening for an attack on the problem4 ,this kind of investigation was started more than fifty years ago4 ,it has been gradually developed and corrected1 until now we believe that the results must be nearly right--that we really know how hot it is inside a star4 ,i mentioned just now a temperature of #f1jjj2 that was the temperature near the surface--the region which we actually see4 ,there is no serious difficulty in determining this surface temperature by observation2 in fact the same method is often used commercially for finding the temperature of a furnace from the outside4 ,it is for the deep regions out of sight that the highly theoretical method of calculation is required4 ,this #f1jjj is only the marginal heat of the great solar furnace giving no idea of the terrific intensity within4 ,going down into the interior the temperature rises rapidly to above a million degrees1 and goes on increasing until at the sun's centre it is about #dj1jjj1jjj4 ,do not imagine that #dj1jjj1jjj is a degree of heat so extreme that temperature has become meaningless4 ,these stellar temperatures are to be taken quite literally4 ,heat is the energy of motion of the atoms or molecules of a substance1 and temperature which indicates the degree of heat is a way of stating how fast these atoms or molecules are moving4 ,for example1 at the temperature of this room the molecules of air are rushing about with an average speed of #ejj yards a second2 if we heated it up to #dj1jjj1jjj the speed would be just over #ajj miles a second4 ,that is nothing to be alarmed about2 the astronomer is quite accustomed to speeds like that4 ,the velocities of the stars1 or of the meteors entering the earth's atmosphere1 are usually between #aj and #ajj miles a second4 ,the velocity of the earth travelling round the sun is #bj miles a second4 ,so that for an astronomer this is the most ordinary degree of speed that could be suggested1 and he naturally considers #dj1jjj1jjj a very comfortable sort of condition to deal with4 ,and if the astronomer is not frightened by a speed of #ajj miles a second1 the experimental physicist is quite contemptuous of it2 for he is used to handling atoms shot off from radium and similar substances with speeds of #aj1jjj miles a second4 ,accustomed as he is to watching these express atoms and testing what they are capable of doing1 the physicist considers the jog-trot atoms of the stars very commonplace4 ,besides the atoms rushing to and fro in all directions we have in the interior of a star great quantities of ether waves also rushing in all directions4 ,ether waves are called by different names according to their wave-length4 ,the longest are the ,hertzian waves used in broadcasting2 then come the infra-red heat waves2 next come waves of ordinary visible light2 then ultra-violet photographic or chemical rays2 then ,x-rays2 then ,gamma rays emitted by radio-active substances4 ,probably the shortest of all are the rays constituting the very penetrating radiation found in our atmosphere1 which according to the investigations of ,kohlhrster and ,millikan are believed to reach us from interstellar space4 ,these are all fundamentally the same but correspond to different octaves4 ,the eye is attuned to only one octave1 so that most of them are invisible2 but essentially they are of the same nature as visible light4 ,the ether waves inside a star belong to the division called ,x-rays4 ,they are the same as the ,x-rays produced artificially in an ,x-ray tube4 ,on the average they are #8softer' 7i4e4 longer7 than the ,x-rays used in hospitals1 but not softer than some of those used in laboratory experiments4 ,thus we have in the interior of a star something familiar and extensively studied in the laboratory4 ,besides the atoms and ether waves there is a third population to join in the dance4 ,there are multitudes of free electrons4 ,the electron is the lightest thing known1 weighing no more than of the lightest atom4 ,it is simply a charge of negative electricity wandering about alone4 ,an atom consists of a heavy nucleus which is usually surrounded by a girdle of electrons4 ,it is often compared to a miniature solar system1 and the comparison gives a proper idea of the emptiness of an atom4 ,the nucleus is compared to the sun1 and the electrons to the planets4 ,each kind of atom--each chemical element--has a different quorum of planet electrons4 ,our own solar system with eight planets might be compared especially with the atom of oxygen which has eight circulating electrons4 ,in terrestrial physics we usually regard the girdle or crinoline of electrons as an essential part of the atom because we rarely meet with atoms incompletely dressed2 when we do meet with an atom which has lost one or two electrons from its system1 we call it an #8ion'4 ,but in the interior of a star1 owing to the great commotion going on1 it would be absurd to exact such a meticulous standard of attire4 ,all our atoms have lost a considerable proportion of their planet electrons and are therefore ions according to the strict nomenclature4 ,ionization of ,atoms ,at the high temperature inside a star the battering of the particles by one another1 and more especially the collision of the ether waves 7,x-rays7 with atoms1 cause electrons to be broken off and set free4 ,these free electrons form the third population to which ,i have referred4 ,for each individual the freedom is only temporary1 because it will presently be captured by some other mutilated atom2 but meanwhile another electron will have been broken off somewhere else to take its place in the free population4 ,this breaking away of electrons from atoms is called ionization1 and as it is extremely important in the study of the stars ,i will presently show you photographs of the process4 ,my subject is #8,stars and ,atoms'2 ,i have already shown you photographs of a star1 so ,i ought to show you a photograph of an atom4 ,nowadays that is quite easy4 ,since there are some trillions of atoms present in the tiniest piece of material it would be very confusing if the photograph showed them all4 ,happily the photograph exercises discrimination and shows only #8express train' atoms which flash past like meteors1 ignoring all the others4 ,we can arrange a particle of radium to shoot only a few express atoms across the field of the camera1 and so have a clear picture of each of them4 ,fig4 #cb is a photograph of three or four atoms which have flashed across the field of view--giving the broad straight tracks4 ,these are atoms of helium discharged at high speed from a radio-active substance4 ,i wonder if there is an under-current of suspicion in your minds that there must be something of a fake about this photograph4 ,are these really the single atoms that are showing themselves--those infinitesimal units which not many years ago seemed to be theoretical concepts far outside any practical apprehension8 ,i will answer that question by asking you one4 ,you see a dirty mark on the picture4 ,is that somebody's thumb8 ,if you say ,yes1 then ,i assure you unhesitatingly that these streaks are single atoms4 ,but if you are hypercritical and say #8,no4 ,that is not anybody's thumb1 but it is a mark that shows that somebody's thumb has been there'1 then ,i must be equally cautious and say that the streak is a mark that shows where an atom has been4 ,the photograph instead of being the impression of an atom is the impression of the impression of an atom1 just as it is not the impression of a thumb but the impression of the impression of a thumb4 ,i don't see that it really matters that the impression is second-hand instead of first-hand4 ,i do not think we have been guilty of any more faking than the criminologist who scatters powder over a finger-print to make it visible1 or a biologist who stains his preparations with the same object4 ,the atom in its passage leaves what we might call a #8scent' along its trail2 and we owe to ,professor ,c4 ,t4 ,r4 ,wilson a most ingenious device for making the scent visible4 ,professor ,wilson's #8pack of hounds' consists of water vapour which flocks to the trail and there condenses into tiny drops4 ,you will next want to see a photograph of an electron4 ,that also can be managed4 ,the broken wavy trail in ,fig4 #c is an electron4 ,owing to its small mass the electron is more easily turned aside in its course than the heavy atom which rushes bull-headed through all obstacles4 ,fig4 #d shows numerous electrons1 and it includes one of very high speed which on that account was able to make a straight track4 ,incidentally it gives away the device used for making the tracks visible1 because you can see the tiny drops of water separately4 ,illustration3 ,fig4 #c ,illustration3 ,fig4 #d4 ,,fast-,,moving ,,atoms ,,and ,,electrons ,we have seen photographs of atoms and free electrons4 ,now we want a photograph of ,x-rays to complete the stellar population4 ,we cannot quite manage that1 but we can very nearly4 ,photographs by ,x-rays are common enough2 but a photograph of ,x-rays is a different matter4 ,i have already said that electrons can be broken away from atoms by ,x-rays colliding with them4 ,when this happens the free electron is usually shot off with high velocity so that it is one of the express electrons which can be photographed4 ,in ,fig4 #e you see four electrons shot off in this way4 ,you notice that they all start from points in the same line1 and it does not require much imagination to see in your mind a mysterious power travelling along this line and creating the explosions4 ,that power is the ,x-rays which were directed in a narrow beam along the line 7from right to left7 when the photograph was taken4 ,although the ,x-rays are left to your imagination1 the photograph at any rate shows the process of ionization which is so important in the stellar interior--the freeing of electrons from the atoms by the incidence of ,x-rays4 ,you notice that it is just a chance whether the ,x-ray ionizes an atom when it meets it4 ,there are trillions of atoms lying about 7of which the photograph takes no notice72 but1 nevertheless1 the ,x-rays travel a long way before meeting the atom which they choose to operate on4 ,finally ,i can show you the other method of ionizing atoms by battering of a more mechanical kind--in this case by the collision of a fast electron4 ,in ,fig4 #f a fast electron was travelling nearly horizontally1 but the tiny water-drops that should mark its track are so spread out that you do not at first trace the connexion4 ,notice that the drops occur in pairs4 ,this is because the fast electron battered some of the atoms along its track1 wrenching away an electron from each4 ,you see at intervals along the track a broken atom and a free electron lying side by side1 though you cannot tell which is which4 ,occasionally the original fast electron was too vigorous and there is more of a mix up1 but usually you can see clearly the two fragments resulting from the smash4#c ,a cynic might remark that the interior of a star is a very safe subject to talk about because no one can go there and prove that you are wrong4 ,i would plead in reply that at least ,i am not abusing the unlimited opportunity for imagination2 ,i am only asking you to allow in the interior of the star quite homely objects and processes which can be photographed4 ,perhaps now you will turn round on me and say1 #8,what right have you to suppose that ,nature is as barren of imagination as you are8 ,perhaps she has hidden in the star something novel which will upset all your ideas4' ,but ,i think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner4 ,at least we may peer gingerly round the corner1 and perhaps we shall find there is nothing very formidable after all4 ,our object in diving into the interior is not merely to admire a fantastic world with conditions transcending ordinary experience2 it is to get at the inner mechanism which makes stars behave as they do4 ,if we are to understand the surface manifestations1 if we are to understand why #8one star differeth from another star in glory'1 we must go below--to the engine-room--to trace the beginning of the stream of heat and energy which pours out through the surface4 ,finally1 then1 our theory will take us back to the surface and we shall be able to test by comparison with observation whether we have been badly misled4 ,meanwhile1 although we naturally cannot prove a general negative1 there is no reason to anticipate anything which our laboratory experience does not warn us of4 ,the ,x-rays in a star are the same as the ,x-rays experimented on in a laboratory1 but they are enormously more abundant in the star4 ,we can produce ,x-rays like the stellar ,x-rays1 but we cannot produce them in anything like stellar abundance4 ,the photograph 7,fig4 #e7 showed a laboratory beam of ,x-rays which had wrenched away four electrons from different atoms2 these would be speedily recaptured4 ,in the star you must imagine the intensity multiplied many million-fold1 so that electrons are being wrenched away as fast as they settle and the atoms are kept stripped almost bare4 ,the nearly complete mutilation of the atoms is important in the study of the stars for two main reasons4 ,the first is this4 ,an architect before pronouncing an opinion on the plans of a building will want to know whether the material shown in the plans is to be wood or steel or tin or paper4 ,similarly it would seem essential before working out details about the interior of a star to know whether it is made of heavy stuff like lead or light stuff like carbon4 ,by means of the spectroscope we can find out a great deal about the chemical composition of the sun's atmosphere2 but it would not be fair to take this as a sample of the composition of the sun as a whole4 ,it would be very risky to make a guess at the elements preponderating in the deep interior4 ,thus we seem to have reached a deadlock4 ,but now it turns out that when the atoms are thoroughly smashed up1 they all behave nearly alike--at any rate in those properties with which we are concerned in astronomy4 ,the high temperature--which we were inclined to be afraid of at first--has simplified things for us1 because it has to a large extent eliminated differences between different kinds of material4 ,the structure of a star is an unusually simple physical problem2 it is at low temperatures such as we experience on the earth that matter begins to have troublesome and complicated properties4 ,stellar atoms are nude savages innocent of the class distinctions of our fully arrayed terrestrial atoms4 ,we are thus able to make progress without guessing at the chemical composition of the interior4 ,it is necessary to make one reservation1 viz4 that there is not an excessive proportion of hydrogen4 ,hydrogen has its own way of behaving2 but it makes very little difference which of the other #ia elements predominate4 ,the other point is one about which ,i shall have more to say later4 ,it is that we must realize that the atoms in the stars are mutilated fragments of the bulky atoms with extended electron systems familiar to us on the earth2 and therefore the behaviour of stellar and terrestrial gases is by no means the same in regard to properties which concern the size of the atoms4 ,to illustrate the effect of the chemical composition of a star1 we revert to the problem of the support of the upper layers by the gas underneath4 ,at a given temperature every independent particle contributes the same amount of support no matter what its mass or chemical nature2 the lighter atoms make up for their lack of mass by moving more actively4 ,this is a well-known law originally found in experimental chemistry1 but now explained by the kinetic theory of ,maxwell and ,boltzmann4 ,suppose we had originally assumed the sun to be composed entirely of silver atoms and had made our calculations of temperature accordingly2 afterwards we change our minds and substitute a lighter element1 aluminium4 ,a silver atom weighs just four times as much as an aluminium atom2 hence we must substitute four aluminium atoms for every silver atom in order to keep the mass of the sun unchanged4 ,but now the supporting force will everywhere be quadrupled1 and all the mass will be heaved outwards by it if we make no further change4 ,in order to keep the balance1 the activity of each particle must be reduced in the ratio 2 that means that we must assign throughout the aluminium sun temperatures of those assigned to the silver sun4 ,thus for unsmashed atoms a change in the assigned chemical composition makes a big change in our inference as to the internal temperature4 ,but if electrons are broken away from the atom these also become independent particles rendering support to the upper layers4 ,a free electron gives just as much support as an atom does2 it is of much smaller mass1 but it moves about a hundred times as fast4 ,the smashing of one silver atom provides #dg free electrons1 making with the residual nucleus of the atom #dh particles in all4 ,the aluminium atom gives #ac electrons or #ad particles in all2 thus #d aluminium atoms give #ef independent particles4 ,the change from smashed silver to an equal mass of smashed aluminium only means a change from #dh to #ef particles1 requiring a reduction of temperature by #ad per cent4 ,we can tolerate that degree of uncertainty in our estimates of internal temperature2#d it is a great improvement on the corresponding calculation for unsmashed atoms which was uncertain by a factor #d4 ,besides bringing closer together the results for different varieties of chemical constitution1 ionization by increasing the number of supporting particles lowers the calculated temperatures considerably4 ,it is sometimes thought that the exceedingly high temperature assigned to the interior of a star is a modern sensationalism4 ,that is not so4 ,the early investigators1 who neglected both ionization and radiation pressure1 assigned much higher temperatures than those now accepted4 ,radiation ,pressure and ,mass ,the stars differ from one another in mass1 that is to say1 in the quantity of material gathered together to form them2 but the differences are not so large as we might have expected from the great variety in brightness4 ,we cannot always find out the mass of a star1 but there are a fair number of stars for which the mass has been determined by astronomical measurements4 ,the mass of the sun is--,i will write it on the blackboard-- #bjjjjjjjjjjjjjjjjjjjjjjjjjjj tons ,i hope ,i have counted the #j's rightly1 though ,i dare say you would not mind much if there were one or two too many or too few4 ,but ,nature does mind4 ,when she made the stars she evidently attached great importance to getting the number of #j's right4 ,she has an idea that a star should contain a particular amount of material4 ,of course she allows what the officials at the mint would call a #8remedy'4 ,she may even pass a star with one #j too many and give us an exceptionally large star1 or with one #j too few1 giving a very small star4 ,but these deviations are rare1 and a mistake of two #j's is almost unheard of4 ,usually she adheres much more closely to her pattern4 ,illustration3 ,fig4 #e4 ,,ionization ,,by ,x-,,rays ,illustration3 ,fig4 #f4 ,,ionization ,,by ,,collision ,how does ,nature keep count of the #j's8 ,it seems clear that there must be something inside the star itself which keeps check and1 so to speak1 makes a warning protest as soon as the right amount of material has been gathered together4 ,we think we know how it is done4 ,you remember the ether waves inside the star4 ,these are trying to escape outwards and they exert a pressure on the matter which is caging them in4 ,this outward force1 if it is sufficiently powerful to be worth considering in comparison with other forces1 must be taken into account in any study of the equilibrium or stability of the star4 ,now in all small globes this force is quite trivial2 but its importance increases with the mass of the globe1 and it is calculated that at just about the above mass it reaches equal status with the other forces governing the equilibrium of the star4 ,if we had never seen the stars and were simply considering as a curious problem how big a globe of matter could possibly hold together1 we could calculate that there would be no difficulty up to about two thousand quadrillion tons2 but beyond that the conditions are entirely altered and this new force begins to take control of the situation4 ,here1 ,i am afraid1 strict calculation stops1 and no one has yet been able to calculate what the new force will do with the star when it does take control4 ,but it can scarcely be an accident that the stars are all so near to this critical mass2 and so ,i venture to conjecture the rest of the story4 ,the new force does not prohibit larger mass1 but it makes it risky4 ,it may help a moderate rotation about the axis to break up the star4 ,consequently larger masses will survive only rarely2 for the most part stars will be kept down to the mass at which the new force first becomes a serious menace4 ,the force of gravitation collects together nebulous and chaotic material2 the force of radiation pressure chops it off into suitably sized lumps4 ,this force of radiation pressure is better known to many people under the name #8pressure of light'4 ,the term #8radiation' comprises all kinds of ether-waves including light1 so that the meaning is the same4 ,it was first shown theoretically and afterwards verified experimentally that light exerts a minute pressure on any object on which it falls4 ,theoretically it would be possible to knock a man over by turning a searchlight on him--only the searchlight would have to be excessively intense1 and the man would probably be vaporized first4 ,pressure of light probably plays a great part in many celestial phenomena4 ,one of the earliest suggestions was that the minute particles forming the tail of a comet are driven outwards by the pressure of sunlight1 thus accounting for the fact that a comet's tail points away from the sun4 ,but that particular application must be considered doubtful4 ,inside the star the intense stream of light 7or rather ,x-rays7 is like a wind rushing outwards and distending the star4 ,the ,interior of a ,star ,we can now form some kind of a picture of the inside of a star--a hurly-burly of atoms1 electrons1 and ether-waves4 ,dishevelled atoms tear along at #ajj miles a second1 their normal array of electrons being torn from them in the scrimmage4 ,the lost electrons are speeding #ajj times faster to find new resting places4 ,let us follow the progress of one of them4 ,there is almost a collision as an electron approaches an atomic nucleus1 but putting on speed it sweeps round in a sharp curve4 ,sometimes there is a side-slip at the curve1 but the electron goes on with increased or reduced energy4 ,after a thousand narrow shaves1 all happening within a thousand millionth of a second1 the hectic career is ended by a worse side-slip than usual4 ,the electron is fairly caught1 and attached to an atom4 ,but scarcely has it taken up its place when an ,x-ray bursts into the atom4 ,sucking up the energy of the ray the electron darts off again on its next adventure4 ,i am afraid the knockabout comedy of modern atomic physics is not very tender towards our aesthetic ideals4 ,the stately drama of stellar evolution turns out to be more like the hair-breadth escapades on the films4 ,the music of the spheres has almost a suggestion of--jazz4 ,and what is the result of all this bustle8 ,very little4 ,the atoms and electrons for all their hurry never get anywhere2 they only change places4 ,the ether-waves are the only part of the population which accomplish anything permanent4 ,although apparently darting in all directions indiscriminately1 they do on the average make a slow progress outwards4 ,there is no outward progress of the atoms and electrons2 gravitation sees to that4 ,but slowly the encaged ether-waves leak outwards as through a sieve4 ,an ether-wave hurries from one atom to another1 forwards1 backwards1 now absorbed1 now flung out again in a new direction1 losing its identity1 but living again in its successor4 ,with any luck it will in no unduly long time 7ten thousand to ten million years according to the mass of the star7 find itself near the boundary4 ,it changes at the lower temperature from ,x-rays to light-rays1 being altered a little at each re-birth4 ,at last it is so near the boundary that it can dart outside and travel forward in peace for a few hundred years4 ,perhaps it may in the end reach some distant world where an astronomer lies in wait to trap it in his telescope and extort from it the secrets of its birth-place4 ,it is the leakage that we particularly want to determine2 and that is why we have to study patiently what is going on in the turbulent crowd4 ,to put the problem in another form2 the waves are urged to flow out by the temperature gradient in the star1 but are hindered and turned back by their adventures with the atoms and electrons4 ,it is the task of mathematics1 aided by the laws and theories developed from a study of these same processes in the laboratory1 to calculate the two factors--the factor urging and the factor hindering the outward flow--and hence to find the leakage4 ,this calculated leakage should1 of course1 agree with astronomical measurements of the energy of heat and light pouring out of the star4 ,and so finally we arrive at an observational test of the theories4 ,opacity of ,stellar ,matter ,let us consider the factor which hinders the leakage--the turning back of the ether-waves by their encounters with atoms and electrons4 ,if we were dealing with light waves we should call this obstruction to their passage #8opacity'1 and we may conveniently use the same term for obstruction to ,x-rays4 ,we soon realize that the material of the star must be decidedly opaque4 ,the quantity of radiation in the interior is so great that unless it were very severely confined the leakage would be much greater than the amount which we observe coming out of the stars4 ,the following is an illustration of the typical degree of opacity required to agree with the observed leakage4 ,let us enter the star ,capella and find a region where the density is the same as that of the atmosphere around us2#e a slab of the material only two inches thick would form a screen so opaque that only one-third of the ether-waves falling on one side would get through to the other side1 the rest being absorbed in the screen4 ,a foot or two of the material would be practically a perfect screen4 ,if we are thinking of light-waves this seems an astonishing opacity for material as tenuous as air2 but we have to remember that it is an opacity to ,x-rays1 and the practical physicist knows well the difficulty of getting the softer kinds of ,x-rays to pass through even a few millimetres of air4 ,there is a gratifying accordance in general order of magnitude between the opacity inside the star1 determined from astronomical observation of leakage1 and the opacity of terrestrial substances to ,x-rays of more or less the same wave-length4 ,this gives us some assurance that our theory is on the right track4 ,but a careful comparison shows us that there is some important difference between the stellar and terrestrial opacity4 ,in the laboratory we find that the opacity increases very rapidly with the wave-length of the ,x-rays that are used4 ,we do not find anything like the same difference in the stars although the ,x-rays in the cooler stars must be of considerably greater wave-length than those in the hotter stars4 ,also1 taking care to make the comparison at the same wave-length for both1 we find that the stellar opacity is less than the terrestrial opacity4 ,we must follow up this divergence4 ,there is more than one way in which an atom can obstruct ether-waves1 but there seems to be no doubt that for ,x-rays both in the stars and in the laboratory the main part of the opacity depends on the process of ionization4 ,the ether-wave falls on an atom and its energy is sucked up by one of the planet electrons which uses it to escape from the atom and travel away at high speed4 ,the point to notice is that in the very act of absorption the absorbing mechanism is broken1 and it cannot be used again until it has been repaired4 ,to repair it the atom must capture one of the free electrons wandering about1 inducing it to take the place of the lost electron4 ,in the laboratory we can only produce thin streams of ,x-rays so that each wave-trap is only called upon to act occasionally4 ,there is plenty of time to repair it before the next time it has a chance of catching anything2 and there is practically no loss of efficiency through the traps being out of order4 ,but in the stars the stream of ,x-rays is exceedingly intense4 ,it is like an army of mice marching through your larder springing the mouse-traps as fast as you can set them4 ,here it is the time wasted in resetting the traps--by capturing electrons--which counts1 and the amount of the catch depends almost entirely on this4 ,we have seen that the stellar atoms have lost most of their electrons2 that means that at any moment a large proportion of the absorption traps are awaiting repair4 ,for this reason we find a smaller opacity in the stars than in terrestrial material4 ,the lowered opacity is simply the result of overworking the absorbing mechanisms--they have too much radiation to deal with4 ,we can also see why the laws of stellar and terrestrial opacity are somewhat different4 ,the rate of repair1 which is the main consideration in stellar opacity1 is increased by compressing the material1 because then the atom will not have to wait so long to meet and capture a free electron4 ,consequently the stellar opacity will increase with the density4 ,in terrestrial conditions there is no advantage in accelerating the repair which will in any case be completed in sufficient time2 thus terrestrial opacity is independent of the density4 ,the theory of stellar opacity thus reduces mainly to the theory of the capture of electrons by ionized atoms2 not that this process is attended by absorption of ,x-rays--it is actually attended by emission--but it is the necessary preliminary to absorption4 ,the physical theory of electron-capture is not yet fully definitive2 but it is sufficiently advanced for us to make use of it provisionally in our calculations of the hindering factor in the leakage of radiation from the stars4 ,the ,relation of ,brightness to ,mass ,we do not want to tackle too difficult a problem at first1 and so we shall deal with stars composed of perfect gas4 ,if you do not like the technical phrase #8perfect gas' you can call it simply #8gas'1 because all the terrestrial gases that you are likely to think of are without sensible imperfection4 ,it is only under high compression that terrestrial gases become imperfect4 ,i should mention that there are plenty of examples of gaseous#f stars4 ,in many stars the material is so inflated that it is more tenuous than the air around us2 for example1 if you were inside ,capella you would not notice the material of ,capella any more than you notice the air in this room4 ,for gaseous stars1 then1 the investigation will give formulae by which1 given the mass of the star1 we can calculate how much energy of heat and light will leak out of it--in short1 how bright it will be4 ,in ,fig4 #g a curve is drawn giving this theoretical relation between the brightness and mass of a star4 ,strictly speaking1 there is another factor besides the mass which affects the calculated brightness2 you can have two stars of the same mass1 the one dense and the other puffed out1 and they will not have quite the same brightness4 ,but it turns out 7rather unexpectedly7 that this other factor1 density1 makes very little difference to the brightness1 always provided that the material is not too dense to be a perfect gas4 ,i shall therefore say no more about density in this brief summary4 99 99 99 99 99 ,here are a few details about the scale of the diagram4 ,the brightness is measured in magnitudes1 a rather technical unit4 ,you have to remember that stellar magnitude is like a golfer's handicap--the bigger the number1 the worse the performance4 ,the diagram includes practically the whole range of stellar brightness2 at the top -#d represents almost the brightest stars known1 and at the bottom #ab is nearly the faintest limit4 ,the difference from top to bottom is about the same as the difference between an arc light and a glow worm4 ,the sun is near magnitude #e4 ,these magnitudes refer1 of course1 to the true brightness1 not to the apparent brightness affected by distance2 also1 what is represented here is the #8heat brightness' or heat intensity1 which is sometimes a little different from the light intensity4 ,astronomical instruments have been made which measure directly the heat instead of the light received from a star4 ,these are quite successful2 but there are troublesome corrections on account of the large absorption of heat in the earth's atmosphere1 and it is in most cases easier and more accurate to infer the heat brightness from the light brightness1 making allowance for the colour of the star4 ,illustration3 ,fig4 #g4 ,the ,mass-luminosity ,curve4 ,the horizontal scale refers to mass1 but it is graduated according to the logarithm of the mass4 ,at the extreme left the mass is about x sun1 and on the extreme right about #cj x sun2 there are very few stars with masses outside these limits4 ,the sun's mass corresponds to the division labelled #jj4 ,having obtained our theoretical curve1 the first thing to do is to test it by observation4 ,that is to say1 we gather together as many stars as we can lay hands on for which both the mass and absolute brightness have been measured4 ,we plot the corresponding points 7opposite to the appropriate horizontal and vertical graduations7 and see whether they fall on the curve1 as they ought to do if the theory is right4 ,there are not many stellar masses determined with much precision4 ,everything that is reasonably trustworthy has been included in ,fig4 #g4 ,the circles1 crosses1 squares1 and triangles refer to different kinds of data--some good1 some bad1 some very bad4 ,the circles are the most trustworthy4 ,let us run through them from right to left4 ,first comes the bright component of ,capella1 lying beautifully on the curve--because ,i drew the curve through it4 ,you see1 there was one numerical constant which in the present state of our knowledge of atoms and ether-waves1 c41 it was not possible to determine with any confidence from pure theory4 ,so the curve when it was obtained was loose in one direction and could be raised or lowered4 ,it was anchored by making it pass through the bright component of ,capella which seemed the best star to trust to for this purpose4 ,after that there could be no further tampering with the curve4 ,continuing to the left we have the fainter component of ,capella2 next ,sirius2 then1 in a bunch1 two components of ,centauri 7the nearest fixed star7 with the ,sun between them1 and--lying on the curve--a circle representing the mean of six double stars in the ,hyades4 ,finally1 far on the left there are two components of a well-known double star called ,krueger #fj4 ,the observational data for testing the curve are not so extensive and not so trustworthy as we could wish2 but still ,i think it is plain from ,fig4 #g that the theory is substantially confirmed1 and it really does enable us to predict the brightness of a star from its mass1 or vice versa4 ,that is a useful result1 because there are thousands of stars of which we can measure the absolute brightness but not the mass1 and we can now infer their masses with some confidence4 ,since ,i have not been able to give here the details of the calculation1 ,i should make it plain that the curve in ,fig4 #g is traced by pure theory or terrestrial experiment except for the one constant determined by making it pass through ,capella4 ,we can imagine physicists working on a cloud-bound planet such as ,jupiter who have never seen the stars4 ,they should be able to deduce by the method explained on p4 #be that if there is a universe existing beyond the clouds it is likely to aggregate primarily into masses of the order a thousand quadrillion tons4 ,they could then predict that these aggregations will be globes pouring out light and heat and that their brightness will depend on the mass in the way given by the curve in ,fig4 #g4 ,all the information that we have used for the calculations would be accessible to them beneath the clouds1 except that we have stolen one advantage over them in utilizing the bright component of ,capella4 ,even without this forbidden peep1 present-day physical theory would enable them to assign a brightness to the invisible stellar host which would not be absurdly wrong4 ,unless they were wiser than us they would probably ascribe to all the stars a brilliance about ten times too great#g--not a bad error for a first attempt at so transcendent a problem4 ,we hope to clear up the discrepant factor #aj with further knowledge of atomic processes2 meanwhile we shelve it by fixing the doubtful constant by astronomical observation4 ,dense ,stars ,the agreement of the observational points with the curve is remarkably close1 considering the rough nature of the observational measurements2 and it seems to afford a rather strong confirmation of the theory4 ,but there is one awful confession to make--we have compared the theory with the wrong stars4 ,at least when the comparison was first made at the beginning of #aibd no one entertained any doubt that they were the wrong stars4 ,we must recall that the theory was developed for stars in the condition of a perfect gas4 ,in the right half of ,fig4 #g the stars represented are all diffuse stars2 ,capella with a mean density about equal to that of the air in this room may be taken as typical4 ,material of this tenuity is evidently a true gas1 and in so far as these stars agree with the curve the theory is confirmed4 ,but in the left half of the diagram we have the ,sun whose material is denser than water1 ,krueger #fj denser than iron1 and many other stars of the density usually associated with solid or liquid matter4 ,what business have they on the curve reserved for a perfect gas8 ,when these stars were put into the diagram it was not with any expectation that they would agree with the curve2 in fact1 the agreement was most annoying4 ,something very different was being sought for4 ,the idea was that the theory might perhaps be trusted on its own merits with such confirmation as the diffuse stars had already afforded2 then by measuring how far these dense stars fell below the curve we should have definite information as to how great a deviation from a perfect gas occurred at any given density4 ,according to current ideas it was expected that the sun would fall three or four magnitudes below the curve1 and the still denser ,krueger #fj should be nearly ten magnitudes below4#h ,you see that the expectation was entirely unfulfilled4 ,the shock was even greater than ,i can well indicate to you1 because the great drop in brightness when the star is too dense to behave as a true gas was a fundamental tenet in our conception of stellar evolution4 ,on the strength of it the stars had been divided into two groups known as giants and dwarfs1 the former being the gaseous stars and the latter the dense stars4 ,two alternatives now lie before us4 ,the first is to assume that something must have gone wrong with our theory2 that the true curve for gaseous stars is not as we have drawn it1 but runs high up on the left of the diagram so that the ,sun1 ,krueger #fj1 c41 are at the appropriate distances below it4 ,in short1 our imaginary critic was right2 ,nature had hidden something unexpected inside the star and so frustrated our calculations4 ,well1 if this were so1 it would be something to have found it out by our investigations4 ,the other alternative is to consider this question--,is it impossible that a perfect gas should have the density of iron8 ,the answer is rather surprising4 ,there is no earthly reason why a perfect gas should not have a density far exceeding iron4 ,or it would be more accurate to say1 the reason why it should not is earthly and does not apply to the stars4 ,the sun's material1 in spite of being denser than water1 really is a perfect gas4 ,it sounds incredible1 but it must be so4 ,the feature of a true gas is that there is plenty of room between the separate particles--a gas contains very little substance and lots of emptiness4 ,consequently when you squeeze it you do not have to squeeze the substance2 you just squeeze out some of the waste space4 ,but if you go on squeezing1 there comes a time when you have squeezed out all the empty space2 the atoms are then jammed in contact and any further compression means squeezing the substance itself1 which is quite a different proposition4 ,so as you approach that density the compressibility characteristic of a gas is lost and the matter is no longer a proper gas4 ,in a liquid the atoms are nearly in contact2 that will give you an idea of the density at which the gas loses its characteristic compressibility4 ,the big terrestrial atoms which begin to jam at a density near that of the liquid state do not exist in the stars4 ,the stellar atoms have been trimmed down by the breaking off of all their outer electrons4 ,the lighter atoms are stripped to the bare nucleus--of quite insignificant size4 ,the heavier atoms retain a few of the closer electrons1 but have not much more than a hundredth of the diameter of a fully arrayed atom4 ,consequently we can go on squeezing ever so much more before these tiny atoms or ions jam in contact4 ,at the density of water or even of platinum there is still any amount of room between the trimmed atoms2 and waste space remains to be squeezed out as in a perfect gas4 ,our mistake was that in estimating the congestion in the stellar ball-room we had forgotten that crinolines are no longer in fashion4 ,it was1 ,i suppose1 very blind of us not to have foreseen this result1 considering how much attention we had been paying to the mutilation of the atoms in other branches of the investigation4 ,by a roundabout route we have reached a conclusion which is really very obvious4 ,and so we conclude that the stars on the left of the diagram are after all not the #8wrong' stars4 ,the sun and other dense stars are on the perfect gas curve because their material is perfect gas4 ,careful investigation has shown that in the small stars on the extreme left of ,fig4 #g the electric charges of the atoms and electrons bring about a slight deviation from the ordinary laws of a gas2 it has been shown by ,r4 ,h4 ,fowler that the effect is to make the gas not imperfect but superperfect--it is more easily compressed than an ordinary gas4 ,you will notice that on the average the stars run a little above the curve on the left of ,fig4 #g4 ,it is probable that the deviation is genuine and is partly due to superperfection of the gas2 we have already seen that imperfection would have brought them below the curve4 ,even at the density of platinum there is plenty of waste space1 so that in the stars we might go on squeezing stellar matter to a density transcending anything known on the earth4 ,but that's another story--,i will tell it later on4 99 99 99 99 99 ,the general agreement between the observed and predicted brightness of the stars of various masses is the main test of the correctness of our theories of their internal constitution4 ,the incidence of their masses in a range which is especially critical for radiation pressure is also valuable confirmation4 ,it would be an exaggeration to claim that this limited success is a proof that we have reached the truth about the stellar interior4 ,it is not a proof1 but it is an encouragement to work farther along the line of thought which we have been pursuing4 ,the tangle is beginning to loosen4 ,the more optimistic may assume that it is now straightened out2 the more cautious will make ready for the next knot4 ,the one reason for thinking that the real truth cannot be so very far away is that in the interior of a star1 if anywhere1 the problem of matter is reduced to its utmost simplicity2 and the astronomer is engaged on what is essentially a less ambitious problem than that of the terrestrial physicist to whom matter always appears in the guise of electron systems of the most complex organization4 ,we have taken the present-day theories of physics and pressed them to their remotest conclusions4 ,there is no dogmatic intention in this2 it is the best means we have of testing them and revealing their weaknesses if any4 ,in ancient days two aviators procured to themselves wings4 ,daedalus flew safely through the middle air and was duly honoured on his landing4 ,icarus soared upwards to the sun till the wax melted which bound his wings and his flight ended in fiasco4 ,in weighing their achievements1 there is something to be said for ,icarus4 ,the classical authorities tell us that he was only #8doing a stunt'1 but ,i prefer to think of him as the man who brought to light a serious constructional defect in the flying-machines of his day4 ,so1 too1 in ,science4 ,cautious ,daedalus will apply his theories where he feels confident they will safely go2 but by his excess of caution their hidden weaknesses remain undiscovered4 ,icarus will strain his theories to the breaking-point till the weak joints gape4 ,for the mere adventure8 ,perhaps partly2 that is human nature4 ,but if he is destined not yet to reach the sun and solve finally the riddle of its constitution1 we may at least hope to learn from his journey some hints to build a better machine4 ,,lecture ,,ii ,,some ,,recent ,,investigations ,,it will help us to appreciate the astronomical significance of what we have learnt in the previous lecture if we turn from the general to the particular and see how it applies to individual stars4 ,i will take two stars round which centre stories of special interest1 and relate the history of our knowledge of them4 ,the ,story of ,algol ,this is a detective story1 which we might call #8,the ,missing ,word and the ,false ,clue'4 ,in astronomy1 unlike many sciences1 we cannot handle and probe the objects of our study2 we have to wait passively and receive and decode the messages that they send to us4 ,the whole of our information about the stars comes to us along rays of light2 we watch and try to understand their signals4 ,there are some stars which seem to be sending us a regular series of dots and dashes--like the intermittent light from a lighthouse4 ,we cannot translate this as a morse code2 nevertheless1 by careful measurement we disentangle a great deal of information from the messages4 ,the star ,algol is the most famous of these #8variable stars'4 ,we learn from the signals that it is really two stars revolving round each other4 ,sometimes the brighter of the two stars is hidden1 giving a deep eclipse or #8dash'2 sometimes the faint star is hidden1 giving a #8dot'4 ,this recurs in a period of #b days #ba hours--the period of revolution of the two stars4 ,there was a great deal more information in the message1 but it was rather tantalizing4 ,there was1 so to speak1 just one word missing4 ,if we could supply that word the message would give full and accurate particulars as to the size of the system--the diameters and masses of the two components1 their absolute brightness1 the distance between them1 their distance from the sun4 ,lacking the word the message told us nothing really definite about any of these things4 ,in these circumstances astronomers would scarcely have been human if they had not tried to guess the missing word4 ,the word should have told us how much bigger the bright star was than the fainter1 that is to say1 the ratio of the masses of the two stars4 ,some of the less famous variable stars give us complete messages4 7,these could accordingly be used for testing the relation of mass and absolute brightness1 and are represented by triangles in ,fig4 #g47 ,the difficulty about ,algol arose from the excessive brightness of the bright component which swamped and made illegible the more delicate signals from the faint component4 ,from the other systems we could find the most usual value of the mass ratio1 and base on that a guess as to its probable value for ,algol4 ,different authorities preferred slightly different estimates1 but the general judgement was that in systems like ,algol the bright component is twice as massive as the faint component4 ,and so the missing word was assumed to be #8two'2 on this assumption the various dimensions of the system were worked out and came to be generally accepted as near the truth4 ,that was sixteen years ago4#i ,in this way the sense of the message was made out to be that the brighter star had a radius of #a1ajj1jjj kilometres 7one and a half times the sun's radius71 that it had half the mass of the sun1 and thirty times the sun's light-power1 c4 ,it will be seen at once that this will not fit our curve in ,fig4 #g2 a star of half the sun's mass ought to be very much fainter than the sun4 ,it was rather disconcerting to find so famous a star protesting against the theory2 but after all the theory is to be tested by comparison with facts and not with guesses1 and the theory might well have a sounder basis than the conjecture as to the missing word4 ,moreover1 the spectral type of ,algol is one that is not usually associated with low mass1 and this cast some suspicion on the accepted results4 ,if we are willing to trust the theory given in the last lecture we can do without the missing word4 ,or1 to put it another way1 we can try in succession various guesses instead of #8two' until we reach one that gives the bright component a mass and luminosity agreeing with the curve in ,fig4 #g4 ,the guess #8two' gives1 as we have seen1 a point which falls a long way from the curve4 ,alter the guess to #8three' and recalculate the mass and brightness on this assumption2 the corresponding point is now somewhat nearer to the curve4 ,continue with #8four'1 #8five'1 c42 if the point crosses the curve we know that we have gone too far and must take an intermediate value in order to reach the desired agreement4 ,this was done in ,november #aibe1 and it appeared that the missing word must be #8five'1 not #8two'--a rather startling change4 ,and now the message ran-- ,radius of bright component #b1adj1jjj kilometres4 ,mass of bright component #dc x sun's mass4 ,if you compare these with the original figures you will see that there is a great alteration4 ,the star is now assigned a large mass much more appropriate to a ,b-type star4 ,it also turns out that ,algol is more than a hundred times as bright as the sun2 and its parallax is #jjbh--twice the distance previously supposed4 ,at the time there seemed little likelihood that these conclusions could be tested4 ,possibly the prediction as to the parallax might be proved or disproved by a trigonometrical determination2 but it is so small as to be almost out of range of reasonably accurate measurement4 ,we could only adopt a #8take it or leave it' attitude--#8,if you accept the theory1 this is what ,algol is like2 if you distrust the theory1 these results are of no interest to you4' ,but meanwhile two astronomers at ,ann ,arbor ,observatory had been making a search for the missing word by a remarkable new method4 ,they had in fact found the word and published it a year before1 but it had not become widely known4 ,if a star is rotating1 one edge or #8limb' is coming towards us and the other going away from us4 ,we can measure speeds towards us or away from us by means of the ,doppler effect on the spectrum1 obtaining a definite result in miles per second4 ,thus we can and do measure the equatorial speed of rotation of the sun by observing first the east limb then the west limb and taking the difference of velocity shown4 ,that is all very well on the sun1 where you can cover up the disk except the special part that you want to observe2 but how can you cover up part of a star when a star is a mere point of light8 ,you cannot2 but in ,algol the covering up is done for you4 ,the faint component is your screen4 ,as it passes in front of the bright star there is a moment when it leaves a thin crescent showing on the east and another moment when a thin crescent on the west is uncovered4 ,of course1 the star is too far away for you actually to see the crescent shape1 but at these moments you receive light from the crescents only1 the rest of the disk being hidden4 ,by seizing these moments you can make the measurements just as though you had manipulated the screen yourself4 ,fortunately the speed of rotation of ,algol is large and so can be measured with relatively small error4 ,now multiply the equatorial velocity by the period of rotation2#aj that will give you the circumference of ,algol4 ,divide by #fbh1 and you have the radius4 ,that was the method developed by ,rossiter and ,mc,laughlin4 ,the latter who applied it to ,algol found the radius of the bright component to be #b1ahj1jjj kilometres4 ,so far as can be judged his result has considerable accuracy2 indeed it is probable that the radius is now better known than that of any other star except the sun4 ,if you will now turn back to p4 #dd and compare it with the value found from the theory you will see that there is cause for satisfaction4 ,mc,laughlin evaluated the other constants and dimensions of the system2 these agree equally well1 but that follows automatically because there was only one missing word to be supplied4 ,in both determinations the missing word or mass ratio turned out to be #ej4 ,this is not quite the end of the story4 ,why had the first guess at the mass ratio gone so badly wrong8 ,we understand by now that a disparity in mass is closely associated with a disparity in brightness of the two stars4 ,the disparity in brightness was given in ,algol's original message2 it informed us that the faint component gives about one-thirteenth of the light of the bright one4 7,at least that was how we interpreted it47 ,according to our curve this corresponds to a mass ratio #b1 which is not much improvement on the original guess #b4 ,for a mass ratio #e the companion ought to have been much fainter--in fact its light should have been undetectable4 ,although considerations like these could not have had much influence on the original guess1 they seemed at first to reassure us that there was not very much wrong with it4 ,let us call the bright component ,algol ,a and the faint component ,algol ,b4 ,some years ago a new discovery was made1 namely ,algol ,c4 ,it was found that ,algol ,a and ,b together travel in an orbit round a third star in a period of just under two years--at least they are travelling round in this period1 and we must suppose that there is something present for them to revolve around4 ,hitherto we had believed that when ,algol ,a was nearly hidden at the time of deepest eclipse all the remaining light must come from ,algol ,b2 but now it is clear that it belongs to ,algol ,c1 which is always shining without interference4 ,consequently the mass ratio #b is that of ,algol ,a to ,algol ,c4 ,the light from ,algol ,b is inappreciable as it should be for a mass ratio #e4aa ,the message from ,algol ,a and ,b was confused1 not only on account of the missing word1 but because a word or two of another message from ,algol ,c had got mixed up with it2 so that even when the missing word was found to be #8five' and confirmed in two ways1 the message was not quite coherent4 ,in another place the message seemed to waver and read #8two-and-a-half'4 ,the finishing step is the discovery that #8two-and-a-half' belongs to a different message from a previously unsuspected star1 ,algol ,c4 ,and so it all ends happily4 ,the best detective is not infallible4 ,in this story our astronomical detective made a reasonable but unsuccessful guess near the beginning of the case4 ,he might have seen his error earlier1 only there was a false clue dropped by a third party who happened to be present at the crime1 which seemed to confirm the guess4 ,this was very unlucky4 ,but it makes all the better detective story of it4 ,the ,story of the ,companion of ,sirius ,the title of this detective story is #8,the ,nonsensical ,message'4 ,sirius is the most conspicuous star in the sky4 ,naturally it was observed very often in early days1 and it was used by astronomers along with other bright stars to determine time and set the clocks by4 ,it was a clock star1 as we say4 ,but it turned out that it was not at all a good clock2 it would gain steadily for some years1 and then lose4 ,in #ahdd ,bessel found out the cause of this irregularity2 ,sirius was describing an elliptic orbit4 ,obviously there must be something for it to move around1 and so it came to be recognized that there was a dark star there which no one had ever seen4 ,i doubt whether any one expected it would ever be seen4 ,the ,companion of ,sirius was1 ,i believe1 the first invisible star to be regularly recognized4 ,we ought not to call such a star hypothetical4 ,the mechanical properties of matter are much more crucial than the accidental property of being visible2 we do not consider a transparent pane of glass #8hypothetical'4 ,there was near ,sirius something which exhibited the most universal mechanical property of matter1 namely1 exerting force on neighbouring matter according to the law of gravitation4 ,that is better evidence of the existence of a material mass than ocular evidence would be4 ,however1 eighteen years later the ,companion of ,sirius was actually seen by ,alvan ,clark4 ,this discovery was unique in its way2 ,clark was not looking at ,sirius because he was interested in it1 but because ,sirius was a nice bright point of light with which to test the optical perfection of a large new object-glass that his firm had made4 ,i dare say that when he saw the little point of light close to ,sirius he was disappointed and tried to polish it away4 ,however1 it stayed1 and proved to be the already known but hitherto unseen ,companion4 ,the big modern telescopes easily show the star and rather spoil the romance2 but as romance faded1 knowledge grew1 and we now know that the ,companion is a star not much less massive than the sun4 ,it has ths of the mass of the sun1 but gives out only th of the sun's light4 ,the faintness did not particularly surprise us2#aa presumably there should be white-hot stars glowing very brightly and red-hot stars glowing feebly1 with all sorts of intermediate degrees of brightness4 ,it was assumed that the ,companion was one of the feeble stars only just red hot4 ,in #aiad ,professor ,adams at the ,mount ,wilson ,observatory found that it was not a red star4 ,it was white--white hot4 ,why1 then1 was it not shining brilliantly8 ,apparently the only answer was that it must be a very small star4 ,you see1 the nature and colour of the light show that its surface must be glowing more intensely than the sun's2 but the total light is only th of the sun's2 therefore the surface must be less than th of the sun's4 ,that makes the radius less than th of the sun's radius1 and brings the globe down to a size which we ordinarily associate with a planet rather than with a star4 ,working out the sum more accurately we find that the ,companion of ,sirius is a globe intermediate in size between the earth and the next larger planet ,uranus4 ,but if you are going to put a mass not much less than that of the sun into a globe not very much larger than the earth1 it will be a tight squeeze4 ,the actual density works out at #fj1jjj times that of water--just about a ton to the cubic inch4 ,we learn about the stars by receiving and interpreting the messages which their light brings to us4 ,the message of the ,companion of ,sirius when it was decoded ran3 #8,i am composed of material #c1jjj times denser than anything you have ever come across2 a ton of my material would be a little nugget that you could put in a match-box4' ,what reply can one make to such a message8 ,the reply which most of us made in #aiad was--#8,shut up4 ,don't talk nonsense4' ,but in #aibd the theory described in the last lecture had been developed2 and you will remember that at the end it pointed to the possibility that matter in the stars might be compressed to a density much transcending our terrestrial experience4 ,this called back to mind the strange message of the ,companion of ,sirius4 ,it could no longer be dismissed as obvious nonsense4 ,that does not mean that we could immediately assume it to be true2 but it must be weighed and tested with a caution which we should not care to waste over a mere nonsense jingle4 ,it should be understood that it was very difficult to explain away the original message as a mistake4 ,as to the mass being ths of the sun's mass there can be no serious doubt at all4 ,it is one of the very best determinations of stellar mass4 ,moreover1 it is obvious that the mass must be large if it is to sway ,sirius out of its course and upset its punctuality as a clock4 ,the determination of the radius is less direct1 but it is made by a method which has had conspicuous success when applied to other stars4 ,for example1 the radius of the huge star ,betelgeuse was first calculated in this way2 afterwards it was found possible to measure directly the radius of ,betelgeuse by means of an interferometer devised by ,michelson1 and the direct measurement confirmed the calculated value4 ,again the ,companion of ,sirius does not stand alone in its peculiarity4 ,at least two other stars have sent us messages proclaiming incredibly high density2 and considering our very limited opportunities for detecting this condition1 there can be little doubt that these #8white dwarfs'1 as they are called1 are comparatively abundant in the stellar universe4 ,but we do not want to trust entirely to one clue lest it prove false in some unsuspected way4 ,therefore in #aibd ,professor ,adams set to work again to apply to the message a test which ought to be crucial4 ,einstein's theory of gravitation indicates that all the lines of the spectrum of a star will be slightly displaced towards the red end of the spectrum as compared with the corresponding terrestrial lines4 ,on the sun the effect is almost too small to be detected having regard to the many causes of slight shift which have to be disentangled4 ,to me personally ,einstein's theory gives much stronger assurance of the real existence of the effect than does the observational evidence available4 ,still it is a striking fact that those who have made the investigation are now unanimous in their judgement that the effect really occurs on the sun1 although some of them at first thought that they had evidence against it4 ,hitherto ,einstein's theory has been chiefly regarded by the practical astronomer as something he is asked to test2 but now the theory has a chance to show its mettle by helping us to test something much more doubtful than itself4 ,the ,einstein effect is proportional to the mass divided by the radius of the star2 and since the radius of the ,companion of ,sirius is very small 7if the message is right7 the effect will be very large4 ,it should in fact be thirty times as large as on the sun4 ,that lifts it much above all the secondary causes of shift of the lines which made the test on the sun so uncertain4 ,the observation is very difficult because the ,companion of ,sirius is faint for work of this kind1 and scattered light from its overpoweringly brilliant neighbour causes much trouble4 ,however1 after a year's effort ,professor ,adams made satisfactory measurements1 and he found a large shift as predicted4 ,expressing the results in the usual unit of kilometres per second1 the mean of his measurements came to #ai1 whilst the predicted shift was #bj4 ,professor ,adams has thus killed two birds with one stone4 ,he has carried out a new test of ,einstein's general theory of relativity1 and he has shown that matter at least #b1jjj times denser than platinum is not only possible but actually exists in the stellar universe4#ac ,this is the best confirmation we could have for our view that the sun with a density #a times that of water is still very far indeed from the maximum density of stellar matter2 and it is therefore entirely reasonable that we should find it behaving like a perfect gas4 ,i have said that the observation was exceedingly difficult4 ,however experienced the observer1 ,i do not think we ought to put implicit trust in a result which strains his skill to the utmost until it has been verified by others working independently4 ,therefore you should for the present make the usual reservations in accepting these conclusions4 ,but science is not just a catalogue of ascertained facts about the universe2 it is a mode of progress1 sometimes tortuous1 sometimes uncertain4 ,and our interest in science is not merely a desire to hear the latest facts added to the collection2 we like to discuss our hopes and fears1 probabilities and expectations4 ,i have told the detective story so far as it has yet unrolled itself4 ,i do not know whether we have reached the last chapter4 ,unknown ,atoms and ,interpretation of ,spectra ,it should be understood that this matter of enormous density is not supposed to be any strange substance--a new chemical element or elements4 ,it is just ordinary matter smashed about by the high temperature and so capable of being packed more tightly--just as more people could be squeezed into a room if a few bones were broken4 ,it is one of the features of astronomical physics that it shows us the ordinary elements of the earth in an extraordinary state--smashed or ionized to a degree that has either not been reproduced or has been reproduced with great difficulty in the laboratory4 ,it is not only in the inaccessible interior of the star that we find matter in a state outside terrestrial experience4 ,here is a picture of the ,ring ,nebula in ,lyra 7,fig4 #h74ad ,it is taken through a prism so that we see not one ring but a number of rings corresponding to different lines of the spectrum and representing the different kinds of atoms which are at work producing the light of the nebula4 ,the smallest ring1 which is rather faint 7marked by an arrow71 consists of light produced by the helium atoms in the nebula--not ordinary helium but smashed helium atoms4 ,it was one of the great laboratory achievements of recent times when ,professor ,a4 ,fowler in #aiab succeeded in battering helium atoms in a vacuum tube sufficiently to give this kind of light1 already well known in the stars4 ,two other rings are due to hydrogen4 ,with these three exceptions none of the rings have yet been imitated in the laboratory4 ,for instance1 we do not know what elements are producing the two brightest rings on the extreme right and left respectively4 ,we are sometimes asked whether any new elements show themselves in the stars which are not present or are not yet discovered on the earth4 ,we can give fairly confidently the answer ,no4 ,that1 however1 is not because everything seen in the stars has been identified with known terrestrial elements4 ,the answer is in fact given not by the astronomer but by the physicist4 ,the latter has been able to make out the orderly scheme of the elements2 and it transpires that there are no gaps left for fresh elements until we come to elements of very high atomic weight1 which would not be likely to rise into the atmosphere of a star and show themselves in astronomical observation4 ,every element carries a number1 starting with hydrogen which is ,no4 #a1 and going up to uranium which is ,no4 #ib4 ,illustration3 ,fig4 #h4 ,,the ,,ring ,,nebula ,,in ,,lyra ,illustration3 ,fig4 #i4 ,,hydrogen--,,the ,,balmer ,,series ,and what is more1 the element carries its number-plate so conspicuously that a physicist is able to read it4 ,he can1 for instance1 see that iron is ,no4 #bf without having to count up how many known elements precede it4 ,the elements have been called over by their numbers1 and up to ,no4 #hd they have all answered #8,present'4#ae ,the element helium 7,no4 #b7 was first discovered by ,lockyer in the sun1 and not until many years later was it found on the earth4 ,astrophysicists are not likely to repeat this achievement2 they cannot discover new elements if there aren't any4 ,the unknown source of the two rings close together on the right of the photograph 7a bright ring and a fainter ring7 has been called nebulium4 ,but nebulium is not a new element4 ,it is some quite familiar element which we cannot identify because it has lost several of its electrons4 ,an atom which has lost an electron is like a friend who has shaved off his moustache2 his old acquaintances do not recognize him4 ,we shall recognize nebulium some day4 ,the theoretical physicists are at work trying to find laws which will determine exactly the kind of light given off by atoms in various stages of mutilation--so that it will be purely a matter of calculation to infer the atom from the light it emits4 ,the experimental physicists are at work trying more and more powerful means of battering atoms1 so that one day a terrestrial atom will be stimulated to give nebulium light4 ,it is a great race2 and ,i do not know which side to back4 ,the astronomer cannot do much to help the solution of the problem he has set4 ,i believe that if he would measure with the greatest care the ratio of intensity of the two nebulium lines he would give the physicists a useful hint4 ,he also provides another clue--though it is difficult to make anything of it--namely1 the different sizes of the rings in the photograph1 showing a difference in the distribution of the emitting atoms4 ,evidently nebulium has a fondness for the outer parts of the nebula and helium for the centre2 but it is not clear what inference should be drawn from this difference in their habits4 ,the atoms of different elements1 and atoms of the same element in different states of ionization1 all have distinctive sets of lines which are shown when the light is examined through a spectroscope4 ,under certain conditions 7as in the nebulae7 these appear as bright lines2 but more often they are imprinted as dark lines on a continuous background4 ,in either case the lines enable us to identify the element1 unless they happen to belong to an atom in a state of which we have had no terrestrial experience4 ,the rash prophecy that knowledge of the composition of the heavenly bodies must be for ever beyond our reach has long been disproved2 and the familiar elements1 hydrogen1 carbon1 calcium1 titanium1 iron1 and many others1 can be recognized in the most distant parts of the universe4 ,the thrill of this early discovery has now passed4 ,but meanwhile stellar spectroscopy has greatly extended its scope2 it is no longer chemical analysis1 but physical analysis4 ,when we meet an old acquaintance there is first the stage of recognition2 the next question is #8,how are you8' ,after recognizing the stellar atom we put this question1 and the atom answers1 #8,quite sound' or #8,badly smashed'1 as the case may be4 ,its answer conveys information as to its environment--the severity of the treatment to which it is being subjected--and hence leads to a knowledge of the conditions of temperature and pressure in the object observed4 ,surveying the series of stars from the coolest to the hottest1 we can trace how the calcium atoms are at first whole1 then singly ionized1 then doubly ionized--a sign that the battering becomes more severe as the heat becomes more intense4 7,the last stage is indicated by the disappearance of all visible signs of calcium1 because the ion with two electrons missing has no lines in the observable part of the spectrum47 ,the progressive change of other elements is shown in a similar way4 ,a great advance in this study was made in #aibj by ,professor ,m4 ,n4 ,saha1 who first applied the quantitative physical laws which determine the degree of ionization at any given temperature and pressure4 ,he thereby struck out a new line in astrophysical research which has been widely developed4 ,thus1 if we note the place in the stellar sequence where complete calcium atoms give place to atoms with one electron missing1 the physical theory is able to state the corresponding temperature or pressure4#af ,saha's methods have been improved by ,r4 ,h4 ,fowler and ,e4 ,a4 ,milne4 ,one important application was to determine the surface temperatures of the hottest types of stars 7#ab1jjj--be1jjj71 since alternative methods available for cooler stars are not satisfactory at these high temperatures4 ,another rather striking result was the discovery that the pressure in the star 7at the level surveyed by the spectroscope7 is only th of an atmosphere2 previously it had been assumed on no very definite evidence to be about the same as that of our own atmosphere4 ,we commonly use the method of spectrum analysis when we wish to determine which elements are present in a given mineral on the earth4 ,it is equally trustworthy in examining the stars since it can make no difference whether the light we are studying comes from a body close at hand or has travelled to us for hundreds of years across space4 ,but one limitation in stellar work must always be remembered4 ,when the chemist is looking1 say1 for nitrogen in his mineral1 he takes care to provide the conditions which according to his experience are necessary for the nitrogen spectrum to show itself4 ,but in the stars we have to take the conditions as we find them4 ,if nitrogen does not appear1 that is no proof that nitrogen is absent2 it is much more likely that the stellar atmosphere does not hit off the right conditions for the test4 ,in the spectrum of ,sirius the lines of hydrogen are exceedingly prominent and overwhelm everything else4 ,we do not infer that ,sirius is composed mainly of hydrogen2 we infer instead that its surface is at a temperature near #aj1jjj1 because it can be calculated that that is a temperature most favourable for a great development of these hydrogen lines4 ,in the sun the most prominent spectrum is iron4 ,we do not infer that the sun is unusually rich in iron2 we infer that it is at a comparatively low temperature near #f1jjj favourable for the production of the iron spectrum4 ,at one time it was thought that the prominence of hydrogen in ,sirius and of metallic elements in the sun indicated an evolution of the elements1 hydrogen turning into heavier elements as the star cools from the ,sirian to the solar stage4 ,there is no ground for interpreting the observations in that way2 the fading of the hydrogen spectrum and the increase of the iron spectrum would occur in any case as the result of the fall of temperature2 and similar spurious appearances of evolution of elements can be arranged in the laboratory4 ,it is rather probable that the chemical elements have much the same relative abundance in the stars that they have on the earth4 ,all the evidence is consistent with this view2 and for a few of the commoner elements there is some positive confirmation4 ,but we are limited to the outside of the star as we are limited to the outside of the earth in computing the abundance of the elements1 so that this very provisional conclusion should not be pressed unduly4 ,spectral ,series ,to illustrate further this kind of deduction1 let us consider the spectrum shown in ,fig4 #i and see what may be learnt from it4 ,with a little trouble we can disentangle a beautifully regular series of bright lines4 ,the marks above will assist you to pick out the first few lines of the series from the numerous other spectra mixed up with it4 ,noticing the diminishing spacing from right to left1 you will be able to see that the series continues to the left for at least fifteen lines beyond the last one marked1 the lines ultimately drawing close together and forming a #8head' to the series4 ,this is the famous ,balmer ,series of hydrogen1 and having recognized it we identify hydrogen as one of the elements present in the source of the light4 ,but that is only the first step1 and we can proceed to further inferences4 ,professor ,bohr's theory of the hydrogen atom teaches us that each line of the series is emitted by an atom in a different state4 ,these #8states of excitation' can be numbered consecutively1 starting from the normal state of the hydrogen atom as ,no4 #a4 ,the light emitted in the first few states comes into the part of the spectrum not reproduced here1 and the first line in our picture corresponds to state ,no4 #h4 ,counting to the left from this you will recognize the successive lines without much difficulty up to state ,no4 #cj4 ,now the successive states correspond to more and more swollen atoms1 that is to say1 the planet electron#ag makes a wider and wider circuit4 ,the radius 7or more strictly the semi-axis7 of its orbit is proportional to the square of the number of the state1 so that the orbit for state ,no4 #cj is #ijj times larger than the orbit for the normal atom ,no4 #a4 ,the diameter of the orbit in ,no4 #cj is approximately a ten-thousandth of a millimetre4 ,one inference can be drawn immediately--the spectrum shown in ,fig4 #i was not produced in any terrestrial laboratory4 ,in the highest vacuum that can be used in terrestrial spectroscopy the atoms are still too crowded to leave room for an orbit so large as this4 ,the source must be matter so tenuous that there is vacant space for the electron to make this wide circuit without colliding with or suffering interference from other atoms4 ,without entering into further detail we can conclude that ,fig4 #i is a spectrum of matter more rarefied than the highest vacuum known on the earth4#ah ,it is interesting to notice that1 whereas throughout most of the picture the lines are shown on a dark background1 at the extreme left the background is bright2 the change occurs just at the point where the ,balmer ,series comes to an end4 ,this background of light is also due to hydrogen and it is caused in the following way4 ,the swollen atoms in state ,no4 #cj or thereabouts are perilously near the bursting-point1 so it is natural that along with them there should be atoms which have overstepped the limit and burst4 ,they have lost their planet electrons and are occupied in catching new ones4 ,just as energy is required in order to wrench away an electron from an atom1 so there will be superfluous energy to be got rid of when the atom tames a wild electron4 ,this superfluous energy is radiated and forms the bright background referred to4 ,without entering into technicalities of the theory1 we can see that it is appropriate that this light from the burst atoms should appear in the spectrum immediately beyond the lines from the most swollen atoms1 since bursting is a sequel to overswelling4 ,whilst you have this photograph of the ,balmer ,series before you ,i may take the opportunity of recounting the history of another famous series4 ,in some of the hottest stars a related series of lines known as the ,pickering ,series was discovered in #ahif4 ,this is spaced on precisely the same regular plan1 but the lines fall half way between the lines of the ,balmer ,series--not exactly half way because of the gradually diminishing intervals from right to left1 but just where one would naturally interpolate lines in order to double their number whilst keeping the spacing regular4 ,unlike the ,balmer ,series1 the ,pickering ,series had never been produced in any laboratory4 ,what element was causing it8 ,the answer seemed obvious2 surely these two related series1 one fitting half way between the other1 must belong to different modes of vibration of the same atom1 hydrogen4 ,that seemed to be the only possible answer at the time2 but we have learned more about atoms since then4 ,we may fairly argue that the ideal simplicity of these two series indicates that they are produced by an atomic system of the simplest possible type1 viz4 an atom with one planet electron2 but it must be remembered that this condition only tells us how the atom is clothed1 not what the atom is4 ,the helium atom 7or1 for that matter1 the uranium atom7 can on occasion masquerade in the scanty attire of the hydrogen atom4 ,normal helium has two planet electrons2 but if one of these is lost1 it becomes hydrogen-like and copies the simple hydrogen system on a different scale4 ,it is significant that the ,pickering ,series appears only in the very hottest stars--in conditions likely to cause loss of an electron4 ,the difference between hydrogen and hydrogen-like helium is firstly the difference of atomic weight2 the helium nucleus is four times as massive4 ,but this scarcely affects the spectrum because both nuclei are so massive that they remain almost unshaken by the dancing electron4 ,secondly1 the helium nucleus has a double electric charge2 this is equivalent to substituting in the vibrating system a controlling spring of twice the strength4 ,what can be more natural than that the doubled force of the spring should double the number of lines in the series without otherwise altering its plan8 ,in this way ,professor ,bohr discovered the real origin of the ,pickering ,series2 it is due to ionized helium1 not to hydrogen4#ai ,the heavy nucleus1 whether of hydrogen or helium1 remains almost unshaken by the atomic vibration--almost1 but not quite4 ,at a later date ,professor ,a4 ,fowler succeeded in reproducing the ,pickering ,series in the laboratory and was able to measure the lines with much greater accuracy than could be achieved in stellar spectroscopy2 he was then able to show from his measures that the nucleus is not quite irresponsive4 ,it was a delicate double-star problem transferred to the interior of the atom2 or perhaps a closer analogy would be the mutual influence of the sun and ,jupiter1 because ,jupiter1 having a thousandth of the mass of the sun1 disturbs it to about the same extent that the light electron disturbs the hydrogen nucleus4 ,ionized helium is a faithful copy of the hydrogen atom 7on the altered scale7 in everything except the #8shake'2 the shake is less than in hydrogen because the helium nucleus is still more massive and rock-like4 ,the difference of shake throws the ,pickering ,series of helium and the ,balmer ,series of hydrogen slightly out of step with respect to one another2 and by measuring this misfit ,professor ,fowler was able to make a very accurate determination of the shake and therefore of the mass of the electron4 ,in this way the mass of the electron is found to be th of the mass of the hydrogen nucleus2 this agrees well with the mass found by other methods1 and the determination is probably not inferior in accuracy to any of them4 ,and so the clue first picked up in stars #cjj light years away1 followed in turn by the theoretical and the experimental physicist1 leads in the end to the smallest of all things known4 ,the ,cloud in ,space ,having already considered the densest matter in the universe1 we now turn to consider the rarest4 ,in spite of great improvements in the art of exhausting vessels we are still a long way from producing a real vacuum4 ,the atoms in a vacuum tube before it is exhausted muster a formidable number containing about twenty digits4 ,high exhaustion means knocking off five or six noughts at the end of that number2 and the most strenuous efforts to knock off one more nought seem ludicrously ineffective--a mere nibbling at the huge number that must remain4 ,some of the stars are extremely rarefied4 ,betelgeuse1 for example1 has a density about a thousandth that of air4 ,we should call it a vacuum were it not contrasted with the much greater vacuosity of surrounding space4 ,nowadays physicists have no difficulty in producing a better vacuum than ,betelgeuse2 but in earlier times this star would have been regarded as a very creditable attempt at a vacuum4 ,the outer parts of a star1 and especially the light appendages such as the solar chromosphere and corona1 reach much lower densities4 ,also the gaseous nebulae are1 as their appearance suggests1 extremely tenuous4 ,when there is space enough to put a pin's head between adjacent atoms we can begin to talk about a #8real vacuum4' ,at the centre of the ,orion nebula that degree of rarefaction is probably reached and surpassed4 ,a nebula has no definite boundary and the density gradually fades off4 ,there is reason to think that the fading off becomes slow at great distances4 ,before we pass entirely out of the sphere of one nebula we enter the sphere of another1 so that there is always some residual density in interstellar space4 ,i believe that1 reasoning from the tailing off of the nebulae1 we are in a position to make an estimate of the amount of matter remaining unaggregated in space4 ,an ordinary region where there is no observable nebulosity is the highest vacuum existing--within the limits of the stellar system at least--but there still remains about one atom in every cubic inch4 ,it depends on our point of view whether we regard this as an amazing fullness or an amazing emptiness of space4 ,perhaps it is the fullness that impresses us most4 ,the atom can find no place of real solitude within the system of the stars2 wherever it goes it can nod to a colleague not more than an inch away4 ,let us approach the same subject from a different angle4 ,in the #8,story of ,algol' ,i referred to the way in which we measure the velocity of rotation of the sun4 ,we point the spectroscope first on one limb of the sun and then on the other4 ,taking any one of the dark lines of the spectrum1 we find that it has shifted a little between the two observations4 ,this tells us that the material which imprinted the line was moving towards or away from us with different velocities in the two observations4 ,that is what we expected to find2 the rotation of the sun makes solar material move towards us on one side of the disk and away from us on the other side4 ,but there are a few dark lines which do not show this change4 ,they are in just the same position whether we observe them on the east or on the west of the sun4 ,clearly these cannot originate on the sun4 ,they have been imprinted on the light after it left the sun and before it reached our telescope4 ,we have thus discovered a medium occurring somewhere between the sun and our telescope2 and as some of the lines are recognized as belonging to oxygen1 we can infer that it is a medium containing oxygen4 ,this seems to be the beginning of a great discovery1 but it ends in a bathos4 ,it happens that we were already aware of a medium containing oxygen lying somewhere between our telescope and the sun4 ,it is a medium essential to our existence4 ,the terrestrial atmosphere is responsible for the #8fixed' lines seen in the sun's spectrum4 ,just as the spectroscope can tell us that the sun is turning round 7a fact already familiar to us from watching the surface markings71 so it can tell us that certain stars are wandering round an orbit1 and therefore are under the influence of a second star which may or may not be visible itself4 ,but here again we sometimes find #8fixed' lines which do not change with the others4 ,therefore somewhere between the star and the telescope there exists a stationary medium which imprints these lines on the light4 ,this time it is not the earth's atmosphere4 ,the lines belong to two elements1 calcium and sodium1 neither of which occur in the atmosphere4 ,moreover1 the calcium is in a smashed state1 having lost one of its electrons1 and the conditions in our atmosphere are not such as would cause this loss4 ,there seems to be no doubt that the medium containing the sodium and ionized calcium--and no doubt many other elements which do not show themselves--is separate from the earth and the star4 ,it is the #8fullness' of interstellar space already mentioned4 ,light has to pass one atom per cubic inch all the way from the star to the earth1 and it will pass quite enough atoms during its journey of many hundred billion miles to imprint these dark lines on its spectrum4 ,at first there was a rival interpretation4 ,it was thought that the lines were produced in a cloud attached to the star--forming a kind of aureole round it4 ,the two components travel in orbits round each other1 but their orbital motion need not disturb a diffuse medium filling and surrounding the combined system4 ,this was a very reasonable suggestion1 but it could be put to the test4 ,the test was again velocity4 ,although either component can move periodically to and fro within the surrounding cloud of calcium and sodium1 it is clear that its average approach to us or recession from us taken over a long time must agree with that of the calcium and sodium if the star is not to leave its halo behind4 ,professor ,plaskett with the #gb-;inch reflector at the ,dominion ,observatory in ,british ,columbia carried out this test4 ,he found that the secular or average rate of approach of the star#bj was in general quite different from the rate shown by the fixed calcium or sodium lines4 ,clearly the material responsible for the fixed lines could not be an appendage of the star since it was not keeping pace with it4 ,plaskett went farther and showed that whereas the stars themselves had all sorts of individual velocities1 the material of the fixed lines had the same or nearly the same velocity in all parts of the sky1 as though it were one continuous medium throughout interstellar space4 ,i think there can be no doubt that this research demonstrates the existence of a cosmic cloud pervading the stellar system4 ,the fullness of interstellar space becomes a fact of observation and no longer a theoretical conjecture4 ,the system of the stars is floating in an ocean--not merely an ocean of space1 not merely an ocean of ether1 but an ocean that is so far material that one atom or thereabouts occurs in each cubic inch4 ,it is a placid ocean without much relative motion2 currents probably exist1 but they are of a minor character and do not attain the high speeds commonly possessed by the stars4 ,many points of interest arise1 but ,i will only touch on one or two4 ,why are the calcium atoms ionized8 ,in the calm of interstellar space we seem to have passed away from the turmoil which smashed the calcium atoms in the interior of a star2 so at first it seems difficult to understand why the atoms in the cloud should not be complete4 ,however1 even in the depths of space the breaking-up of the atom continues2 because there is always starlight passing across space1 and some of the light-waves are quite powerful enough to wrench a first or second electron away from the calcium atom4 ,it is one of the most curious discoveries of modern physics that when a light-wave is attenuated by spreading1 what it really suffers from is laziness rather than actual loss of power4 ,what is weakened is not the power but the probability that it will display the power4 ,a light-wave capable of bursting an atom still retains the power when it is attenuated a million-fold by spreading2 only it is a million times more sparing in the exercise of the power4 ,to put it another way1 an atom exposed to the attenuated waves will on the average have to wait a million times longer before a wave chooses to explode it2 but the explosion when it does occur will be of precisely the same strength however great the attenuation4 ,this is entirely unlike the behaviour of water-waves2 a wave which is at first strong enough to capsize a boat will1 after spreading1 become too weak4 ,it is more like machine-gun fire which is more likely to miss a given object at greater distance but is equally destructive if it hits4 ,the property here referred to 7the quantum property7 is the deepest mystery of light4 ,thus in interstellar space electrons are still being torn from calcium atoms1 only very infrequently4 ,the other side of the question is the rate of repair1 and in this connexion the low density of the cosmic cloud is the deciding factor4 ,the atom has so few opportunities for repair4 ,roving through space the atom meets an electron only about once a month1 and it by no means follows that it will capture the first one it meets4 ,consequently very infrequent smashing will suffice to keep the majority of the atoms ionized4 ,the smashed state of the atoms inside a star can be compared to the dilapidation of a house visited by a tornado2 the smashed state in interstellar space is a dilapidation due to ordinary wear and tear coupled with excessive slackness in making repairs4 ,a calculation indicates that most of the calcium atoms in interstellar space have lost two electrons2 these atoms do not interfere with the light and give no visible spectrum4 ,the #8fixed lines' are produced by atoms temporarily in a better state of repair with only one electron missing2 they cannot amount at any moment to more than one-thousandth of the whole number1 but even so they will be sufficiently numerous to produce the observed absorption4 ,we generally think of interstellar space as excessively cold4 ,it is quite true that any thermometer placed there would show a temperature only about #c above the absolute zero--if it were capable of registering so low a reading4 ,compact matter such as a thermometer1 or even matter which from the ordinary standpoint is regarded as highly diffuse1 falls to this low temperature4 ,but the rule does not apply to matter as rarefied as the interstellar cloud4 ,its temperature is governed by other considerations1 and it will probably be not much below the surface-temperature of the hottest stars1 say #ae1jjj4 ,interstellar space is at the same time excessively cold and decidedly hot4#ba ,the ,sun's ,chromosphere ,once again we shift the scene1 and now we are back in the outer parts of the sun4 ,fig4 #ajbb shows one of the huge prominence flames which from time to time shoot out of the sun4 ,the flame in this picture was about #abj1jjj miles high4 ,it went through great changes of form and disappeared in not much more than twenty-four hours4 ,this was rather an exceptional specimen4 ,smaller flames occur commonly enough2 it seems that the curious black marks in ,fig4 #a1 often looking like rifts1 are really prominences seen in projection against the still brighter background of the sun4 ,the flames consist of calcium1 hydrogen1 and several other elements4 ,we are concerned not so much with the prominences as with the layer from which they spring4 ,the ordinary atmosphere of the sun terminates rather abruptly1 but above it there is a deep though very rarefied layer called the chromosphere consisting of a few selected elements which are able to float--float1 not on the top of the sun's atmosphere1 but on the sunbeams4 ,the art of riding a sunbeam is evidently rather difficult1 because only a few of the elements have the necessary skill4 ,the most expert is calcium4 ,the light and nimble hydrogen atom is fairly good at it1 but the ponderous calcium atom does it best4 ,the layer of calcium suspended on the sunlight is at least #e1jjj miles thick4 ,we can observe it best when the main part of the sun is hidden by the moon in an eclipse2 but the spectroheliograph enables us to study it to some extent without an eclipse4 ,illustration3 ,fig4 #aj4 ,,solar ,,prominence ,illustration3 ,fig4 #aa4 ,,star ,,cluster ,,centauri ,on the whole it is steady and quiescent1 although1 as the prominence flames show1 it is liable to be blown sky-high by violent outbursts4 ,the conclusions about the calcium chromosphere that ,i am going to describe rest on a series of remarkable researches by ,professor ,milne4 ,how does an atom float on a sunbeam8 ,the possibility depends on the pressure of light to which we have already referred 7p4 #bf74 ,the sunlight travelling outwards carries a certain outward momentum2 if the atom absorbs the light it absorbs also the momentum and so receives a tiny impulse outwards4 ,this impulse enables it to recover the ground it was losing in falling towards the sun4 ,the atoms in the chromosphere are kept floating above the sun like tiny shuttlecocks1 dropping a little and then ascending again from the impulse of the light4 ,only those atoms which can absorb large quantities of sunlight in proportion to their weight will be able to float successfully4 ,we must look rather closely into the mechanism of absorption of the calcium atom if we are to see why it excels the other elements4 ,the ordinary calcium atom has two rather loose electrons in its attendant system2 the chemists express this by saying that it is a divalent element1 the two loose electrons being especially important in determining the chemical behaviour4 ,each of these electrons possesses a mechanism for absorbing light4 ,but under the conditions prevailing in the chromosphere one of the electrons is broken away1 and the calcium atoms are in the same smashed state that gives rise to the #8fixed lines' in the interstellar cloud4 ,the chromospheric calcium thus supports itself on what sunlight it can gather in with the one loose electron remaining4 ,to part with this would be fatal2 the atom would no longer be able to absorb sunlight1 and would drop like a stone4 ,it is true that after two electrons are lost there are still eighteen remaining2 but these are held so tightly that sunlight has no effect on them and they can only absorb shorter waves which the sun does not radiate in any quantity4 ,the atom therefore could only save itself if it restored its main absorbing mechanism by picking up a passing electron2 it has little chance of catching one in the rarefied chromosphere1 so it would probably fall all the way to the sun's surface4 ,there are two ways in which light can be absorbed4 ,in one the atom absorbs so greedily that it bursts1 and the electron scurries off with the surplus energy4 ,that is the process of ionization which was shown in ,fig4 #e4 ,clearly this cannot be the process of absorption in the chromosphere because1 as we have seen1 the atom cannot afford to lose the electron4 ,in the other method of absorption the atom is not quite so greedy4 ,it does not burst1 but it swells visibly4 ,to accommodate the extra energy the electron is tossed up into a higher orbit4 ,this method is called excitation 7cf4 p4 #ei74 ,after remaining in the excited orbit for a little while the electron comes down again spontaneously4 ,the process has to be repeated #bj1jjj times a second in order to keep the atom balanced in the chromosphere4 ,the point we are leading up to is1 ,why should calcium be able to float better than other elements8 ,it has always seemed odd that a rather heavy element 7,no4 #bj in order of atomic weight7 should be found in these uppermost regions where one would expect only the lightest atoms4 ,we see now that the special skill demanded is to be able to toss up an electron #bj1jjj times a second without ever making the fatal blunder of dropping it4 ,that is not easy even for an atom4 ,calcium#bc scores because it possesses a possible orbit of excitation only a little way above the normal orbit so that it can juggle the electron between these two orbits without serious risk4 ,with most other elements the first available orbit is relatively much higher2 the energy required to reach this orbit is not so very much less than the energy required to detach the electron altogether2 so that we cannot very well have a continuous source of light capable of causing the orbit-jumps without sometimes overdoing it and causing loss of the electron4 ,it is the wide difference between the energy of excitation and the energy of ionization of calcium which is so favourable2 the sun is very rich in ether-waves capable of causing the first1 and is almost lacking in ether-waves capable of causing the second4 ,the average time occupied by each performance is th of a second4 ,this is divided into two periods4 ,there is a period during which the atom is patiently waiting for a light-wave to run into it and throw up the electron4 ,there is another period during which the electron revolves steadily in the higher orbit before deciding to come down again4 ,professor ,milne has shown how to calculate from observations of the chromosphere the durations of both these periods4 ,the first period of waiting depends on the strength of the sun's radiation4 ,but we focus attention especially on the second period1 which is more interesting because it is a definite property of the calcium atom1 having nothing to do with local circumstances4 ,although we measure it for ions in the sun's chromosphere1 the same result must apply to calcium ions anywhere4 ,milne's result is that an electron tossed into the higher orbit remains there for an average time of a hundred-millionth of a second before it spontaneously drops back again4 ,i may add that during this brief time it makes something like a million revolutions in the upper orbit4 ,perhaps this is a piece of information that you were not particularly burning to know4 ,i do not think it can be called interesting except to those who make a hobby of atoms4 ,but it does seem to me interesting that we should have to turn a telescope and spectroscope on the sun to find out this homely property of a substance which we handle daily4 ,it is a kind of measurement of immense importance in physics4 ,the theory of these atomic jumps comes under the quantum theory which is still the greatest puzzle of physical science2 and it is greatly in need of guidance from observation on just such a matter as this4 ,we can imagine what a sensation would be caused if1 after a million revolutions round the sun1 a planet made a jump of this kind4 ,how eagerly we should try to determine the average interval at which such jumps occurred6 ,the atom is rather like a solar system1 and it is not the less interesting because it is on a smaller scale4 ,there is no prospect at present of measuring the time of relaxation of the excited calcium atom in a different way4 ,it has1 however1 been found possible to determine the corresponding time for one or two other kinds of atoms by laboratory experiments4 ,it is not necessary that the time should be at all closely the same for different elements2 but laboratory measurements for hydrogen also give the period as a hundred-millionth of a second1 so there is no fault to find with the astronomical determination for calcium4 ,the excitation of the calcium atom is performed by light of two particular wave-lengths1 and the atoms in the chromosphere support themselves by robbing sunlight of these two constituents4 ,it is true that after a hundred-millionth of a second a relapse comes and the atom has to disgorge what it has appropriated2 but in re-emitting the light it is as likely to send it inwards as outwards1 so that the outflowing sunlight suffers more loss than it recovers4 ,consequently1 when we view the sun through this mantle of calcium the spectrum shows gaps or dark lines at the two wave-lengths concerned4 ,these lines are denoted by the letters ,h and ,k4 ,they are not entirely black1 and it is important to measure the residual light at the centre of the lines1 because we know that it must have an intensity just strong enough to keep calcium atoms floating under solar gravity2 as soon as the outflowing light is so weakened that it can support no more atoms it can suffer no further depredations1 and so it emerges into outer space with this limiting intensity4 ,the measurement gives numerical data for working out the constants of the calcium atom including the time of relaxation mentioned above4 ,the atoms at the top of the chromosphere rest on the weakened light which has passed through the screen below2 the full sunlight would blow them away4 ,milne has deduced a consequence which may perhaps have a practical application in the phenomena of explosion of #8new stars' or novae1 and in any case is curiously interesting4 ,owing to the ,doppler effect a moving atom absorbs a rather different wave-length from a stationary atom2 so that if for any cause an atom moves away from the sun it will support itself on light which is a little to one side of the deepest absorption4 ,this light1 being more intense than that which provided a balance1 will make the atom recede faster4 ,the atom's own absorption will thus gradually draw clear of the absorption of the screen below4 ,speaking rather metaphorically1 the atom is balanced precariously on the summit of the absorption line and it is liable to topple off into the full sunlight on one side4 ,apparently the speed of the atom should go on increasing until it has to climb an adjacent absorption line 7due perhaps to some other element72 if the line is too intense to be surmounted the atom will stick part-way up1 the velocity remaining fixed at a particular value4 ,these later inferences may be rather far-fetched1 but at any rate the argument indicates that there is likely to be an escape of calcium into outer space4 ,by ,milne's theory we can calculate the whole weight of the sun's calcium chromosphere4 ,its mass is about #cjj million tons4 ,one scarcely expects to meet with such a trifling figure in astronomy4 ,it is less than the tonnage handled by our ,english railways each year4 ,i think that solar observers must feel rather hoaxed when they consider the labour that they have been induced to spend on this airy nothing4 ,but science does not despise trifles4 ,and astronomy can still be instructive even when1 for once in a way1 it descends to commonplace numbers4 ,the ,story of ,betelgeuse ,this story has not much to do with atoms1 and scarcely comes under the title of these lectures2 but we have had occasion to allude to ,betelgeuse as the famous example of a star of great size and low density1 and its history is closely associated with some of the developments that we are studying4 ,no star has a disk large enough to be seen with our present telescopes4 ,we can calculate that a lens or mirror of about #bj feet aperture would be needed to show traces even of the largest star disk4 ,imagine for a moment that we have constructed an instrument of this order of size4 ,which would be the most hopeful star to try it on8 ,perhaps ,sirius suggests itself first1 since it is the brightest star in the sky4 ,but ,sirius has a white-hot surface radiating very intensely1 so that it is not necessary that it should have a wide expanse4 ,evidently we should prefer a star which1 although bright1 has its surface in a feebly glowing condition2 then the apparent brightness must be due to large area4 ,we need1 then1 a star which is both red and bright4 ,betelgeuse seems best to satisfy this condition4 ,it is the brighter of the two shoulder-stars of ,orion--the only conspicuous red star in the constellation4 ,there are one or two rivals1 including ,antares1 which might possibly be preferred2 but we cannot go far wrong in turning our new instrument on ,betelgeuse in the hope of finding the largest or nearly the largest star disk4 ,you may notice that ,i have paid no attention to the distances of these stars4 ,it happens that distance is not relevant4 ,it would be relevant if we were trying to find the star of greatest actual dimensions2 but here we are considering the star which presents the largest apparent disk1#bd i4e4 covers the largest area of the sky4 ,if we were at twice our present distance from the sun1 we should receive only one-quarter as much light2 but the sun would look half its present size linearly1 and its apparent area would be one-quarter4 ,thus the light per unit area of disk is unaltered by distance4 ,removing the sun to greater and greater distance its disk will appear smaller but glowing not less intensely1 until it is so far away that the disk cannot be discriminated4 ,by spectroscopic examination we know that ,betelgeuse has a surface temperature about #c1jjj4 ,a temperature of #c1jjj is not unattainable in the laboratory1 and we know partly by experiment and partly by theory what is the radiating power of a surface in this state4 ,thus it is not difficult to compute how large an area of the sky ,betelgeuse must cover in order that the area multiplied by the radiating power may give the observed brightness of ,betelgeuse4 ,the area turns out to be very small4 ,the apparent size of ,betelgeuse is that of a half-penny fifty miles away4 ,using a more scientific measure1 the diameter of ,betelgeuse predicted by this calculation is #jjea of a second of arc4 ,no existing telescope can show so small a disk4 ,let us consider briefly how a telescope forms an image--in particular how it reproduces that detail and contrast of light and darkness which betrays that we are looking at a disk or a double star and not a blur emanating from a single point4 ,this optical performance is called resolving power2 it is not primarily a matter of magnification but of aperture1 and the limit of resolution is determined by the size of aperture of the telescope4 ,to create a sharply defined image the telescope must not only bring light where there ought to be light1 but it must also bring darkness where there ought to be darkness4 ,the latter task is the more difficult4 ,light-waves tend to spread in all directions1 and the telescope cannot prevent individual wavelets from straying on to parts of the picture where they have no business4 ,but it has this one remedy--for every trespassing wavelet it must send a second wavelet by a slightly longer or shorter route so as to arrive in a phase opposite to the first wavelet and cancel its effect4 ,this is where the utility of a wide aperture arises--by affording a wider difference of route of the individual wavelets1 so that those from one part of the aperture may be retarded relatively to and interfere with those from another part4 ,a small object-glass can furnish light2 it takes a big object-glass to furnish darkness in the picture4 ,now we may ask ourselves whether the ordinary circular aperture is necessarily the most efficient for giving the wavelets the required path-differences4 ,any deviation from a symmetrical shape is likely to spoil the definition of the image--to produce wings and fringes4 ,the image will not so closely resemble the object viewed4 ,but on the other hand we may be able to sharpen up the tell-tale features4 ,it does not matter how widely the image-pattern may differ from the object1 provided that we can read the significance of the pattern4 ,if we cannot reproduce a star-disk1 let us try whether we can reproduce something distinctive of a star-disk4 ,a little reflection shows that we ought to improve matters by blocking out the middle of the object-glass1 and using only the extreme regions on one side or the other4 ,for these regions the difference of light-path of the waves is greatest1 and they are the most efficient in furnishing the dark contrast needed to outline the image properly4 ,but if the middle of the object-glass is not going to be used1 why go to the expense of manufacturing it8 ,we are led to the idea of using two widely separated apertures1 each involving a comparatively small lens or mirror4 ,we thus arrive at an instrument after the pattern of a rangefinder4 ,this instrument will not show us the disk of a star4 ,if we look through it the main impression of the star image is very like what we should have seen with either aperture singly--a #8spurious disk' surrounded by diffraction rings4 ,but looking attentively we see that this image is crossed by dark and bright bands which are produced by interference between the light-waves coming from the two apertures4 ,at the centre of the image the waves from the two apertures arrive crest on crest since they have travelled symmetrically along equal paths2 accordingly there is a bright band4 ,a very little to one side the asymmetry causes the waves to arrive crest on trough1 so that they cancel one another2 here there is a dark band4 ,the width of the bands decreases as the separation of the two apertures increases1 and for any given separation the actual width is easily calculated4 ,each point of the star's disk is giving rise to a diffraction image with a system of bands of this kind1 but so long as the disk is small compared with the finest detail of the diffraction image there is no appreciable blurring4 ,if we continually increase the separation of the two apertures and so make the bands narrower1 there comes a time when the bright bands for one part of the disk are falling on the dark bands for another part of the disk4 ,the band system then becomes indistinct4 ,it is a matter of mathematical calculation to determine the resultant effect of summing the band systems for each point of the disk4 ,it can be shown that for a certain separation of the apertures the bands will disappear altogether2 and beyond this separation the system should reappear though not attaining its original sharpness4 ,the complete disappearance occurs when the diameter of the star-disk is equal to #a times the width of the bands 7from the centre of one bright band to the next74 ,as already stated1 the bandwidth can be calculated from the known separation of the apertures4 ,the observation consists in sliding apart the two apertures until the bands disappear4 ,the diameter of the disk is inferred at once from their separation when the disappearance occurred4 ,although we measure the size of the disk in this way we never see the disk4 ,we can summarize the principle of the method in the following way4 ,the image of a point of light seen through a telescope is not a point but a small diffraction pattern4 ,hence1 if we look at an extended object1 say ,mars1 the diffraction pattern will blur the fine detail of the marking on the planet4 ,if1 however1 we are looking at a star which is almost a point1 it is simpler to invert the idea2 the object1 not being an ideal point1 will slightly blur the detail of the diffraction pattern4 ,we shall only perceive the blurring if the diffraction pattern contains detail fine enough to suffer from it4 ,betelgeuse on account of its finite size must theoretically blur a diffraction pattern2 but the ordinary diffraction disk and rings produced with the largest telescope are too coarse to show this4 ,we create a diffraction image with finer detail by using two apertures4 ,theoretically we can make the detail as fine as we please by increasing the separation of the two apertures4 ,the method accordingly consists in widening the separation until the pattern becomes fine enough to be perceptibly blurred by ,betelgeuse4 ,for a smaller star-disk the same effect of blurring would not be apparent until the detail had been made still finer by further separation of the apertures4 ,this method was devised long ago by ,professor ,michelson1 but it was only in #aibj that he tried it on a large scale with a great #bj-;foot beam across the #ajj-;inch reflector at ,mount ,wilson ,observatory4 ,after many attempts ,pease and ,anderson were able to show that the bright and dark bands for ,betelgeuse disappeared when the apertures were separated #aj feet4 ,the deduced diameter is #jjde a second of arc in good enough agreement with the predicted value 7p4 #gh74 ,only five or six stars have disks large enough to be measured with this instrument4 ,it is understood that the construction of a #ej-;foot interferometer is contemplated2 but even this will be insufficient for the great majority of the stars4 ,we are fairly confident that the method of calculation first described gives the correct diameters of the stars1 but confirmation by ,michelson's more direct method of measurement is always desirable4 ,to infer the actual size of the star from its apparent diameter1 we must know the distance4 ,betelgeuse is rather a remote star and its distance cannot be measured very accurately1 but the uncertainty will not change the general order of magnitude of the results4 ,the diameter is about #cjj million miles4 ,betelgeuse is large enough to contain the whole orbit of the earth inside it1 perhaps even the orbit of ,mars4 ,its volume is about fifty million times the volume of the sun4 ,there is no direct way of learning the mass of ,betelgeuse because it has no companion near it whose motion it might influence4 ,we can1 however1 deduce a mass from the mass-brightness relation in ,fig4 #g4 ,this gives the mass equal to #ce x sun4 ,if the result is right1 ,betelgeuse is one of the most massive stars--but1 of course1 not massive in proportion to its bulk4 ,the mean density is about one-millionth of the density of water1 or not much more than one-thousandth of the density of air4#be ,there is one way in which we might have inferred that ,betelgeuse is less dense than the sun1 even if we had had no grounds of theory or analogy for estimating its mass4 ,according to the modern theory of gravitation1 a globe of the size of ,betelgeuse and of the same mean density as the sun would have some remarkable properties3 ,firstly1 owing to the great intensity of its gravitation1 light would be unable to escape2 and any rays shot out would fall back again to the star by their own weight4 ,secondly1 the ,einstein shift 7used to test the density of the ,companion of ,sirius7 would be so great that the spectrum would be shifted out of existence4 ,thirdly1 mass produces a curvature of space1 and in this case the curvature would be so great that space would close up round the star1 leaving us outside--that is to say1 nowhere4 ,except for the last consideration1 it seems rather a pity that the density of ,betelgeuse is so low4 99 99 99 99 99 ,it is now well realized that the stars are a very important adjunct to the physical laboratory--a sort of high-temperature annex where the behaviour of matter can be studied under greatly extended conditions4 ,being an astronomer1 ,i naturally put the connexion somewhat differently and regard the physical laboratory as a low-temperature station attached to the stars4 ,it is the laboratory conditions which should be counted abnormal4 ,apart from the interstellar cloud which is at the moderate temperature of about #ae1jjj1 ,i suppose that nine-tenths of the matter of the universe is above #a1jjj1jjj4 ,under ordinary conditions--you will understand my use of the word--matter has rather simple properties4 ,but there are in the universe exceptional regions with temperature not far removed from the absolute zero1 where the physical properties of matter acquire great complexity2 the ions surround themselves with complete electron systems and become the atoms of terrestrial experience4 ,our earth is one of these chilly places and here the strangest complications can arise4 ,perhaps strangest of all1 some of these complications can meet together and speculate on the significance of the whole scheme4 ,,lecture ,,iii ,,the ,,age ,,of ,,the ,,stars ,,we have seen that spatially the scale of man is about midway between the atom and the star4 ,i am tempted to make a similar comparison as regards time4 ,the span of the life of a man comes perhaps midway in scale between the life of an excited atom 7p4 #gd7 and the life of a star4 ,for those who insist on greater accuracy--though ,i would not like to claim accuracy for present estimates of the life of a star--,i will modify this a little4 ,as regards mass1 man is rather too near to the atom and a stronger claimant for the midway position would be the hippopotamus4 ,as regards time1 man's three score years and ten is a little too near to the stars and it would be better to substitute a butterfly4 ,there is one serious moral in this fantasy4 ,we shall have to consider periods of time which appall our imagination4 ,we fear to make such drafts on eternity4 ,and yet the vastness of the time-scale of stellar evolution is less remote from the scale of human experience than is the minuteness of the time-scale of the processes studied in the atom4 ,our approach to the #8age of the stars' will be devious1 and certain incidental problems will detain us on the way4 ,pulsating ,stars ,the star ,cephei is one of the variable stars4 ,like ,algol1 its fluctuating light sends us a message4 ,but the message when it is decoded is not in the least like the message from ,algol4 ,let me say at once that experts differ as to the interpretation of the message of ,cephei4 ,this is not the place to argue the matter1 or to explain why ,i think that rival interpretations cannot be accepted4 ,i can only tell you what is to the best of my belief the correct story4 ,the interpretation which ,i follow was suggested by ,plummer and ,shapley4 ,the latter in particular made it very convincing1 and subsequent developments have1 ,i think1 tended to strengthen it4 ,i would not1 however1 claim that all doubt is banished4 ,algol turned out to be a pair of stars very close together which from time to time eclipse one another2 ,cephei is a single star which pulsates4 ,it is a globe which swells and contracts symmetrically with a regular period of #e days4 ,and as the globe swells and contracts causing great changes of pressure and temperature in the interior1 so the issuing stream of light rises and falls in intensity and varies also in quality or colour4 ,there is no question of eclipses2 the light signals are not in the form of #8dots' and #8dashes'2 and in any case the change of colour shows that there is a real change in the physical condition of the source of the light4 ,but at first explanations always assumed that two stars were concerned1 and aimed at connecting the physical changes with an orbital motion4 ,for instance1 it was suggested that the principal star in going round its orbit brushed through a resisting medium which heated its front surface2 thus the light of the star varied according as the heated front surface or cooler rear surface was presented towards us4 ,the orbital explanation has now collapsed because it is found that there is literally no room for two stars4 ,the supposed orbit had been worked out in the usual way from spectroscopic measurements of velocity of approach and recession2 later we began to learn more about the true size of stars1 first by calculation1 and afterwards 7for a few stars7 by direct measurement4 ,it turned out that the star was big and the orbit small2 and the second star if it existed would have to be placed inside the principal star4 ,this overlapping of the stars is a reductio ad absurdum of the binary hypothesis1 and some other explanation must be found4 ,what had been taken to be the approach and recession of the star as a whole was really the approach and recession of the surface as it heaved up and down with the pulsation4 ,the stars which vary like ,cephei are diffuse stars enormously larger than the sun1 and the total displacement measured amounts to only a fraction of the star's radius4 ,there is therefore no need to assume a bodily displacement of the star 7orbital motion72 the measures follow the oscillation of that part of the star's surface presented towards us4 ,the decision that ,cephei is a single star and not double has one immediate consequence4 ,it means that the period of #e days is intrinsic in the star and is therefore one of the clues to its physical condition4 ,it is a free period1 not a forced period4 ,it is important to appreciate the significance of this4 ,the number of sunspots fluctuates from a maximum to minimum and back to maximum in a period of about #aa years2 although we do not yet understand the reason for this fluctuation1 we realize that this period is something characteristic of the sun in its present state and would change if any notable change happened to the sun4 ,at one time1 however1 there was some speculation as to whether the fluctuation of the sunspots might not be caused by the revolution of the planet ,jupiter1 which has a period not so very different2 if that explanation had been tenable the #aa-year period would have been something forced on the sun from without and would teach us nothing as to the properties of the sun itself4 ,having convinced ourselves that the light-period of ,cephei is a free period of a single star1 belonging to it in the same way that a particular note belongs to a tuning-fork1 we can accept it as a valuable indicator of the constancy 7or otherwise7 of the star's physical condition4 ,in stellar astronomy we usually feel very happy if we can determine our data--parallax1 radius1 mass1 absolute brightness1 c4--to within #e per cent42 but the measurement of a period offers chances of far superior accuracy4 ,i believe that the most accurately known quantity in the whole of science 7excluding pure mathematics7 is the moon's mean period1 which is commonly given to twelve significant figures4 ,the period of ,cephei can be found to six significant figures at least4 ,by fastening an observable period to the intrinsic conditions of a star we have secured an indicator sensitive enough to show extremely small changes4 ,you will now guess why ,i am approaching #8the age of the stars' through the ,cepheid variables4 ,up to the present they are the only stars known to carry a sensitive indicator1 by which we might hope to test the rate of evolutionary change4 ,we believe that ,cephei like other stars has condensed out of a nebula1 and that the condensation and contraction are still continuing4 ,no one would expect to detect the contraction by our rough determinations of the radius even if continued for a hundred years2 but the evolution must indeed be slow if an intrinsic period measurable to #a part in #aj1jjj1jjj shows no change in a century4 ,it does not greatly matter whether or not we understand the nature of this intrinsic period4 ,if a star contracts1 the period of pulsation1 the period of rotation1 or any other free period associated with it1 will alter4 ,if you prefer to follow any of the rival interpretations of the message of ,cephei1 you can make the necessary alterations in the wording of my argument1 but the general verdict as to the rate of progress of evolution will be unchanged4 ,only if you detach the period from the star itself by going back to the old double star interpretation will the argument collapse2 but ,i do not think any of the rival interpreters propose to do that4 ,it is not surprising that these pulsating stars should be regarded with special interest4 ,ordinary stars must be viewed respectfully like the objects in glass cases in museums2 our fingers are itching to pinch them and test their resilience4 ,pulsating stars are like those fascinating models in the ,science ,museum provided with a button which can be pressed to set the machinery in motion4 ,to be able to see the machinery of a star throbbing with activity is most instructive for the development of our knowledge4 ,the theory of a steady star1 which was described in the first lecture1 can be extended to pulsating stars2 and we can calculate the free period of pulsation for a star of assigned mass and density4 ,you will remember that we have already calculated the heat emission or brightness and compared it with observation1 obtaining one satisfactory test of the truth of the theory2 now we can calculate the period of pulsation and by comparing it with observation obtain another test4 ,owing to lack of information as to a certain constant of stellar material there is an uncertainty in the calculation represented by a factor of about #b2 that is to say1 we calculate two periods1 one double the other1 between which with any reasonable luck the true period ought to lie4 ,the observational confirmation is very good4 ,there are sixteen ,cepheid variables on which the test can be made2 their periods range from #ac hours to #ce days1 and they all agree with the calculated values to within the limits of accuracy expected4 ,in a more indirect way the same confirmation is shown in ,fig4 #g by the close agreement of the squares1 representing ,cepheid variables1 with the theoretical curve4 ,the ,cepheid as a #8,standard ,candle' ,cepheid variables of the same period are closely similar to one another4 ,a ,cepheid of period #e days found in any part of the universe will be practically a replica of ,cephei2 in particular it will be a star of the same absolute brightness4 ,this is a fact discovered by observation1 and is not predicted by any part of the theory yet explored4 ,the brightness1 as we have seen1 depends mainly on the mass2 the period1 on the other hand1 depends mainly on the density2 so that the observed relation between brightness and period involves a relation between mass and density4 ,presumably this relation signifies that for a given mass there is just one special density--one stage in the course of condensation of the star--at which pulsations are liable to occur2 at other densities the star can only burn steadily4 ,this property renders the ,cepheid extremely useful to astronomers4 ,it serves as a standard candle--a source of known light-power4 ,in an ordinary way you cannot tell the real brightness of a light merely by looking at it4 ,if it appears dim1 that may mean either real faintness or great distance4 ,at night time on the sea you observe many lights whose distance and real brightness you cannot estimate2 your judgement of the real brightness may be wrong by a factor of a quintillion if you happen to mistake ,arcturus for a ship's light4 ,but among them you may notice a light which goes through a regular series of changes in a certain number of seconds2 that tells you that it is such-and-such a lighthouse1 known to project a light of so many thousand candlepower4 ,you may now estimate with certainty how far off it is--provided1 of course1 that there is no fog intervening4 ,so1 too1 when we look up at the sky1 most of the lights that we see might be at any distance and have any real brightness4 ,even the most refined measurements of parallax only succeed in locating a few of the nearer lights4 ,but if we see a light winking in the ,cepheid manner with a period of #e days1 we know that it is a replica of ,cephei and is a light of #gjj sun-power4 ,or if the period is any other number of days we can assign the proper sun-power for that period4 ,from this we can judge the distance4 ,the apparent brightness1 which is a combination of distance and true brightness1 is measured2 then it is a simple calculation to answer the question1 ,at what distance must a light of #gjj sun-power be placed in order to give the apparent brightness observed8 ,how about interference by fog8 ,careful discussions have been made1 and it appears that notwithstanding the cosmical cloud in interstellar space there is ordinarily no appreciable absorption or scattering of the starlight on its way to us4 ,with the ,cepheids serving as standard candles distances in the stellar universe have been surveyed far exceeding those reached by previous methods4 ,if the distances were merely those of the ,cepheid variables themselves that would not be so important1 but much more information is yielded4 ,fig4 #aabf shows a famous star-cluster called ,centauri4 ,amongst the thousands of stars in the cluster no less than #gf ,cepheid variables have been discovered4 ,each is a standard candle serving to measure the distance primarily of itself but also incidentally of the great cluster in which it lies4 ,the #gf gauges agree wonderfully among themselves1 the average deviation being less than #e per cent4 ,by this means ,shapley found the distance of the cluster to be #bj1jjj light years4 ,the light messages which we receive to-day were sent from the cluster #bj1jjj years ago4#bg ,the astronomer1 more than other devotees of science1 learns to appreciate the advantage of not being too near the objects he is studying4 ,the nearer stars are all right in their way1 but it is a great nuisance being in the very midst of them4 ,for each star has to be treated singly and located at its proper distance by elaborate measurements2 progress is very laborious4 ,but when we determine the distance of this remote cluster1 we secure at one scoop the distances of many thousands of stars4 ,the distance being known1 the apparent magnitudes can be turned into true magnitudes1 and statistics and correlations of absolute brightness and colour can be ascertained4 ,even before the distance is discovered we can learn a great deal from the stars in clusters which it is impracticable to find out from less remote stars4 ,we can see that the ,cepheids are much above the average brightness and are surpassed by relatively few stars4 ,we can ascertain that the brighter the ,cepheid the longer is its period4 ,we discover that the brightest stars of all are red4#bh ,and so on4 ,there is a reverse side to the picture2 the tiny points of light in the distant cluster are not the most satisfactory objects to measure and analyse1 and we could ill spare the nearer stars2 but the fact remains that there are certain lines of stellar investigation in which remoteness proves to be an actual advantage1 and we turn from the nearer stars to objects fifty thousand light years away4 ,about #hj globular clusters are known with distances ranging from #bj1jjj to #bjj1jjj light years4 ,is there anything yet more remote8 ,it has long been suspected that the spiral nebulae1#bi which seem to be exceedingly numerous1 are outside our stellar system and form #8island universes'4 ,the evidence for this has become gradually stronger1 and now is believed to be decisively confirmed4 ,in #aibd ,hubble discovered a number of ,cepheid variables in the great ,andromeda nebula which is the largest and presumably one of the nearest of the spirals4 ,as soon as their periods had been determined they were available as standard candles to gauge the distance of the nebula4 ,their apparent magnitude was much fainter than that of the corresponding ,cepheids in globular clusters1 showing that they must be even more remote4 ,hubble has since found the distance of one or two other spirals in the same way4 ,with the naked eye you can see the ,andromeda nebula as a faint patch of light4 ,when you look at it you are looking back #ijj1jjj years into the past4 ,the ,contraction ,hypothesis ,the problem of providing sufficient supplies of energy to maintain the sun's output of light and heat has often been debated by astronomers and others4 ,in the last century it was shown by ,helmholtz and ,kelvin that the sun could maintain its heat for a very long time by continually shrinking4 ,contraction involves an approach or fall of the matter towards the centre2 gravitational potential energy is thus converted and made available as heat4 ,it was assumed that this was the sole resource since no other supply capable of yielding anything like so large an amount was known4 ,but the supply is not unlimited1 and on this hypothesis the birth of the sun must be dated not more than #bj1jjj1jjj years ago4 ,even at the time of which ,i am speaking the time-limit was found to be cramping2 but ,kelvin assured the geologists and biologists that they must confine their outlines of terrestrial history within this period4 ,about the beginning of the present century the contraction theory was in the curious position of being generally accepted and generally ignored4 ,whilst few ventured to dispute the hypothesis1 no one seems to have had any hesitation1 if it suited him1 in carrying back the history of the earth or moon to a time long before the supposed era of the formation of the solar system4 ,lord ,kelvin's date of the creation was treated with no more respect than ,archbishop ,ussher's4 ,the serious consequences of the hypothesis become particularly prominent when we consider the diffuse stars of high luminosity2 these are prodigal of their energy and squander it a hundred or a thousand times faster than the sun4 ,the economical sun could have subsisted on its contraction energy for #bj1jjj1jjj years1 but for the high luminosity stars the limit is cut down to #ajj1jjj years4 ,this includes most of the naked-eye stars4 ,dare we believe that they were formed within the last #ajj1jjj years8 ,is the antiquity of man greater than that of the stars now shining8 ,do stars in the ,andromeda nebula run their course in less time than their light takes to reach us8 ,it is one thing to feel a limitation of time-scale irksome1 ruling out ideas and explanations which are otherwise plausible and attractive2 it is another thing to produce definite evidence against the time-scale4 ,i do not think that astronomers had in their own territory any weapon for a direct attack on the ,helmholtz-,kelvin hypothesis until the ,cepheid variables supplied one4 ,to come to figures3 ,cephei emits more than #gjj times as much heat as the sun4 ,we know its mass and radius1 and we can calculate without difficulty how fast the radius must contract in order to provide this heat4 ,the required rate is one part in #dj1jjj per annum4 ,now ,cephei was first observed carefully in #aghe1 so that in the time it has been under observation the radius must have changed by one part in #cjj if the contraction hypothesis is right4 ,you remember that we have in ,cephei a very sensitive indicator of any changes occurring in it1 viz4 the period of pulsation2 clearly changes of the above magnitude could not occur without disturbing this indicator4 ,does the period show any change8 ,it is doubtful2 there is perhaps sufficient evidence for a slight change1 but it is not more than th of the change demanded by the contraction hypothesis4 ,accepting the pulsation theory1 the period should diminish #ag seconds every year--a quantity easily detectable4 ,the actual change is not more than one-tenth of a second per year4 ,at least during the ,cepheid stage the stars are drawing on some source of energy other than that provided by contraction4 ,on such an important question we should not like to put implicit trust in one argument alone1 and we turn to the sister sciences for other and perhaps more conclusive evidence4 ,physical and geological investigations seem to decide definitely that the age of the earth--reckoned from an epoch which by no means goes back to its beginnings as a planet--is far greater than the ,helmholtz-,kelvin estimate of the age of the solar system4 ,it is usual to lay most stress on a determination of the age of the rocks from the uranium-lead ratio of their contents4 ,uranium disintegrates into lead and helium at a known rate4 ,since lead is unlike uranium in chemical properties the two elements would not naturally be deposited together2 so that the lead found with uranium has presumably been formed by its decomposition4#cj ,by measuring how much lead occurs with the uranium we can determine how long ago the uranium was deposited4 ,the age of the older rocks is found to be about #a1bjj million years2 lower estimates have been urged by some authorities1 but none low enough to save the contraction hypothesis4 ,the sun1 of course1 must be very much older than the earth and its rocks4 ,we seem to require a time-scale which will allow at least #aj1jjj1jjj1jjj years for the age of the sun2 certainly we cannot abate our demands below #a1jjj1jjj1jjj years4 ,it is necessary to look for a more prolific source of energy to maintain the heat of the sun and stars through this extended period4 ,we can at once narrow down the field of search4 ,no source of energy is of any avail unless it liberates heat in the deep interior of the star4 ,the crux of the problem is not merely the provision for radiation but the maintenance of the internal heat which keeps the gravitating mass from collapsing4 ,you will remember how in the first lecture we had to assign a certain amount of heat at each point in the stellar interior in order to keep the star in balance4 ,but the internal heat is continually running away towards the cooler outside and then escaping into space as the star's radiation4 ,this1 or its equivalent1 must be put back if the star is to be kept steady--if it is not to contract and evolve at the rate of the ,kelvin time-scale4 ,and it is no use to put it back at the surface of the star--by bombarding the star with meteors1 for example4 ,it could not flow up the temperature-gradient1 and so it would simply take the first opportunity of escaping as additional radiation4 ,you cannot maintain a temperature-gradient by supplying heat at the bottom end4 ,heat must be poured in at the top end1 i4 e4 in the deep interior of the star4 ,since we cannot well imagine an extraneous source of heat able to release itself at the centre of a star1 the idea of a star picking up energy as it goes along seems to be definitely ruled out4 ,it follows that the star contains hidden within it the energy which has to last the rest of its life4 ,energy has mass4 ,many people would prefer to say--energy is mass2 but it is not necessary for us to discuss that4 ,the essential fact is that an erg of energy in any form has a mass of #aa4 #aj-ba grammes4 ,the erg is the usual scientific unit of energy2 but we can measure energy also by the gramme or the ton as we measure anything else which possesses mass4 ,there is no real reason why you should not buy a pound of light from an electric light company--except that it is a larger quantity than you are likely to need and at current rates would cost you something over #ajj1jjj1jjj4 ,if you could keep all this light 7ether-waves7 travelling to and fro between mirrors forming a closed vessel1 and then weigh the vessel1 the observed weight would be the ordinary weight of the vessel plus #a lb4 representing the weight of the light4 ,it is evident that an object weighing a ton cannot contain more than a ton of energy2 and the sun with a mass of #b4jjj quadrillion tons 7p4 #bd7 cannot contain more than #b4jjj quadrillion tons of energy at the most4 ,energy of #ah4 #ajed ergs has a mass #b4 #ajcc grammes which is the mass of the sun2 consequently that is the sum total of the energy which the sun contains--the energy which has to last it all the rest of its life4#ca ,we do not know how much of this is capable of being converted into heat and radiation2 if it is all convertible there is enough to maintain the sun's radiation at the present rate for #ae billion years4 ,to put the argument in another form1 the heat emitted by the sun each year has a mass of #abj billion tons2 and if this loss of mass continued there would be no mass left at the end of #ae billion years4 ,subatomic ,energy ,this store of energy is1 with insignificant exception1 energy of constitution of atoms and electrons2 that is to say1 subatomic energy4 ,most of it is inherent in the constitution of the electrons and protons--the elementary negative and positive electric charges--out of which matter is built2 so that it cannot be set free unless these are destroyed4 ,the main store of energy in a star cannot be used for radiation unless the matter composing the star is being annihilated4 ,it is possible that the star may have a long enough life without raiding the main energy store4 ,a small part of the store can be released by a process less drastic than annihilation of matter1 and this might be sufficient to keep the sun burning for #aj1jjj1jjj1jjj years or so1 which is perhaps as long as we can reasonably require4 ,the less drastic process is transmutation of the elements4 ,thus we have reached a point where a choice lies open before us2 we can either pin our faith to transmutation of the elements1 contenting ourselves with a rather cramped time-scale1 or we can assume the annihilation of matter1 which gives a very ample time-scale4 ,but at present ,i can see no possibility of a third choice4 ,let me run over the argument again4 ,first we found that energy of contraction was hopelessly inadequate2 then we found that the energy must be released in the interior of the star1 so that it comes from an internal1 not an external1 source2 now we take stock of the whole internal store of energy4 ,no supply of any importance is found until we come to consider the electrons and atomic nuclei2 here a reasonable amount can be released by regrouping the protons and electrons in the atomic nuclei 7transmutation of elements71 and a much greater amount by annihilating them4 ,transmutation of the elements--so long the dream of the alchemist--is realized in the transformation of radio-active substances4 ,uranium turns slowly into a mixture of lead and helium4 ,but none of the known radio-active processes liberate anything like enough energy to maintain the sun's heat4 ,the only important release of energy by transmutation occurs at the very beginning of the evolution of the elements4 ,we must start with hydrogen4 ,the hydrogen atom consists simply of a positive and negative charge1 a proton for the nucleus plus a planet electron4 ,let us call its mass #a4 ,four hydrogen atoms will make a helium atom4 ,if the mass of the helium atom were exactly #d1 that would show that all the energy of the hydrogen atoms remained in the helium atom4 ,but actually the mass is #cig2 so that energy of mass a #jjc must have escaped during the formation of helium from hydrogen4 ,by annihilating #d grammes of hydrogen we should have released #d grammes of energy1 but by transmuting it into helium we release #jjc grammes of energy4 ,either process might be used to furnish the sun's heat though1 as we have already stated1 the second gives a much smaller supply4 ,the release of energy occurs because in the helium atom only two of the four electrons remain as planet electrons1 the other two being cemented with the four protons close together in the helium nucleus4 ,in bringing positive and negative charges close together you cause a change of the energy of the electric field1 and release electrical energy which spreads away as ether-waves4 ,that is where the #jjc grammes of energy has gone4 ,the star can absorb these ether-waves and utilize them as heat4 ,we can go on from helium to higher elements1 but we do not obtain much more release of energy4 ,for example1 an oxygen atom can be made from #af hydrogen atoms or #d helium atoms2 but as nearly as we can tell it has just the weight of the #d helium atoms1 so that the release of energy is not appreciably greater when the hydrogen is transmuted into oxygen than when it is transmuted into helium4#cb ,this becomes clearer if we take the mass of a hydrogen atom to be #ajjh1 so that the mass of helium is exactly #d and of oxygen #af2 then it is known from ,dr4 ,aston's researches with the mass-spectrograph that the atoms of other elements have masses which are very closely whole numbers4 ,the loss of #jjjh per hydrogen atom applies approximately whatever the element that is formed4 ,the view that the energy of a star is derived by the building up of other elements from hydrogen has the great advantage that there is no doubt about the possibility of the process2 whereas we have no evidence that the annihilation of matter can occur in ,nature4 ,i am not referring to the alleged transmutation of hydrogen into helium in the laboratory2 those whose authority ,i accept are not convinced by these experiments4 ,to my mind the existence of helium is the best evidence we could desire of the possibility of the formation of helium4 ,the four protons and two electrons constituting its nucleus must have been assembled at some time and place2 and why not in the stars8 ,when they were assembled the surplus energy must have been released1 providing a prolific supply of heat4 ,prima facie this suggests the interior of a star as a likely locality1 since undoubtedly a prolific source of heat is there in operation4 ,i am aware that many critics consider the conditions in the stars not sufficiently extreme to bring about the transmutation--the stars are not hot enough4 ,the critics lay themselves open to an obvious retort2 we tell them to go and find a hotter place4 ,but here the advantage seems to end4 ,there are many astronomical indications that the hypothesis attributing the energy of the stars to the transmutation of hydrogen is unsatisfactory4 ,it may perhaps be responsible for the rapid liberation of energy in the earliest 7giant7 stages when the star is a large diffuse body radiating heat abundantly2 but the energy in later life seems to come from a source subject to different laws of emission4 ,there is considerable evidence that as a star grows older it gets rid of a large fraction of the matter which originally constituted it1 and apparently this can only be contrived by the annihilation of the matter4 ,the evidence1 however1 is not very coherent1 and ,i do not think we are in a position to come to a definite decision4 ,on the whole the hypothesis of annihilation of matter seems the more promising2 and ,i shall prefer it in the brief discussion of stellar evolution which ,i propose to give4 ,the phrase #8annihilation of matter' sounds like something supernatural4 ,we do not yet know whether it can occur naturally or not1 but there is no obvious obstacle4 ,the ultimate constituents of matter are minute positive charges and negative charges which we may picture as centres of opposite kinds of strain in the ether4 ,if these could be persuaded to run together they would cancel out1 leaving nothing except a splash in the ether which spreads out as an electromagnetic wave carrying off the energy released by the undoing of the strain4 ,the amount of this energy is amazingly large2 by annihilating a single drop of water we should be supplied with #bjj horsepower for a year4 ,we turn covetous eyes on this store without1 however1 entertaining much hope of ever discovering the secret of releasing it4 ,if it should prove that the stars have discovered the secret and are using this store to maintain their heat1 our prospect of ultimate success would seem distinctly nearer4 ,i suppose that many physicists will regard the subject of subatomic energy as a field of airy speculation4 ,that is not the way in which it presents itself to an astronomer4 ,if it is granted that the stars evolve much more slowly than on the contraction-hypothesis1 the measurement of the output of subatomic energy is one of the commonest astronomical measurements--the measurement of the heat or light of the stars4#cc ,the collection of observational data as to the activity of liberation of subatomic energy is part of the routine of practical astronomy2 and we have to pursue the usual course of arranging the measurements into some kind of coherence1 so as to find out how the output is related to the temperature1 density1 or age of the material supplying it--in short1 to discover the laws of emission4 ,from this point onwards the discussion may be more or less hypothetical according to the temperament of the investigator2 and indeed it is likely that in this as in other branches of knowledge advances may come by a proper use of the scientific imagination4 ,vain speculation is to be condemned in this as in any other subject1 and there is no need for it2 the problem is one of induction from observation with due regard to our theoretical knowledge of the possibilities inherent in atomic structure4 ,i cannot pass from this subject without mentioning the penetrating radiation long known to exist in our atmosphere1 which according to the researches of ,kohlhrster and ,millikan comes from outer space4 ,penetrating power is a sign of short wave-length and intense concentration of energy4 ,hitherto the greatest penetrating power has been displayed by ,gamma rays originated by subatomic processes occurring in radio-active substances4 ,the cosmic radiation is still more penetrating1 and it seems reasonable to refer it to more energetic processes in the atom such as those suggested for the source of stellar energy4 ,careful measurements have been made by ,millikan1 and he concludes that the properties accord with those which should be possessed by radiation liberated in the transmutation of hydrogen2 it is not penetrating enough to be attributed to a process so energetic as the annihilation of protons and electrons4 ,there seems to be no doubt that this radiation is travelling downwards from the sky4 ,this is shown by measurements of its strength at different heights in the atmosphere and at different depths below the surface of mountain lakes2 it is weakened according to the amount of air or water that it has had to traverse4 ,presumably its source must be extra-terrestrial4 ,its strength does not vary with the sun's altitude1 so it is not coming from the sun4 ,there is some evidence that it varies according to the position of the ,milky ,way1 most radiation being received when the greatest extension of the stellar system is overhead4 ,it cannot come from the interior of the stars1 the penetrating power being too limited2 all the hottest and densest matter in the universe is shut off from us by impenetrable walls4 ,at the most it could come only from the outer rind of the stars where the temperature is moderate and the density is low2 but it is more likely that its main source is in the diffuse nebulae or possibly in the matter forming the general cloud in space4#cd ,we must await further developments before we can regard the supposed subatomic origin of this radiation as other than speculative2 we mention it here only as a possible opening for progress4 ,it will be of great interest if we can reach by this means a more direct acquaintance with the processes which we assume to be the source of stellar energy2 and the messages borne to us by the cosmic rays which purport to relate to these processes deserve the closest attention4 ,our views of stellar energy are likely to be affected on one crucial point4 ,hitherto we have usually supposed that the very high temperature in the interior of a star is one of the essential conditions for liberation of subatomic energy1 and that a reasonably high density is also important4 ,theoretically it would seem almost incredible that the building up of higher elements or the annihilation of protons and electrons could proceed with any degree of vigour in regions where encounters are rare and there is no high temperature or intense radiation to wake the atoms from apathy2 but the more we face the difficulties of all theories of the release of subatomic energy the less inclined we are to condemn any evidence as incredible4 ,the presence of sodium and calcium in the cosmical cloud1 of helium and nebulium in the diffuse nebulae1 of titanium and zirconium in large quantities in the atmospheres of the youngest stars1 bears witness that the evolution of the elements is already far advanced during the diffuse prestellar stage--unless indeed our universe is built from the debris of a former creation4 ,from this point of view it is fitting that we should discern symptoms of subatomic activity in open space4 ,but the physicist may well shake his head over the problem4 ,how are four protons and two electrons to gather together to form a helium nucleus in a medium so rare that the free path lasts for days8 ,the only comfort is that the mode of this occurrence is 7according to present knowledge7 so inconceivable under any conditions of density and temperature that we may postulate it in the nebulae--on the principle that we may as well be hung for a sheep as for a lamb4 ,evolution of the ,stars ,twenty years ago stellar evolution seemed to be very simple4 ,the stars begin by being very hot and gradually cool down until they go out4 ,on this view the temperature of a star indicated the stage of evolution that it had reached4 ,the outline of the sequence was sufficiently indicated by the crude observation of colour--white-hot1 yellow-hot1 red-hot2 a more detailed order of temperature was ascertained by examining the light with a spectroscope4 ,the red stars naturally came last in the sequence2 they were the oldest stars on the verge of extinction4 ,sir ,norman ,lockyer strongly opposed this scheme and to a considerable extent anticipated the more modern view2 but most astronomers pinned their faith to it up to about #aiac4 ,ten years ago more knowledge had been gained of the densities of stars4 ,it seemed likely that density would be a more direct criterion of evolutionary development than temperature4 ,granted that a star condenses out of nebulous material1 it must in the youngest stage be very diffuse2 from that stage it will contract and steadily increase in density4 ,but this necessitates an entire rearrangement of the scheme of evolution1 because the order according to density is by no means the same as the order according to surface temperature4 ,on the former view all the cool red stars were old and dying4 ,but a large number of them are now found to be extremely diffuse--stars like ,betelgeuse1 for instance4 ,these must be set down as the very youngest of the stars2 after all it is not unnatural that a star just beginning to condense out of nebulous material should start at the lowest stage of temperature4 ,not all the red stars are diffuse2 there are many like ,krueger #fj which have high density1 and these we leave undisturbed as representing the last stage of evolution4 ,both the first and last periods of a star's life are characterized by low temperature2 in between whiles the temperature must have risen to a maximum and fallen again4 ,the #8giant and dwarf theory' proposed by ,hertzsprung and ,russell brought these conclusions into excellent order4 ,it recognized a series of giant stars1 comparatively diffuse stars with temperature rising1 and a series of dwarf or dense stars with temperature falling4 ,the two series merged at the highest temperatures4 ,an individual star during its lifetime went up the giant series to its highest temperature and then down the dwarf series4 ,the brightness remained fairly steady throughout the giant stage because the continually increasing temperature counterbalanced the reduction of the surface area of the star2 in the dwarf stage the decreasing temperature and the contraction of the surface caused a rapid decrease of brightness as the star progressed down the series4 ,this was in accordance with observation4 ,the theory has dominated most recent astrophysical research and has been instrumental in bringing to light many important facts4 ,one example must suffice4 ,although we may have a giant and a dwarf star with the same surface temperature1 and therefore showing very similar spectra1 nevertheless a close examination of the spectrum reveals tell-tale differences2 and it is now quite easy to ascertain from the spectrum whether the star is a diffuse giant or a dense dwarf4 ,the attractive feature of the giant and dwarf theory was the simple explanation given for the up-and-down progress of the temperature4 ,the passing over from the giant to the dwarf series was supposed to occur when the density had reached such a value 7about one-quarter the density of water7 that the deviation of the material from a perfect gas began to be serious4 ,it was shown by ,lane fifty years ago that a globe of perfect gas must rise in temperature as it contracts1 his method of finding the internal temperature being that considered on p4 #ab2 thus the rising temperature in the giant stage is predicted4 ,but the rise depends essentially on the easy compressibility of the gas2 and when the compressibility is lost at high density the rising temperature may be expected to give place to falling temperature so that the star cools as a solid or liquid would do4 ,that was believed to account for the dwarf stage4 ,i have been trying to recall ideas of twenty and ten years ago1 and you must not suppose that from the standpoint of present-day knowledge ,i can endorse everything here stated4 ,i have intentionally been vague as to whether by the hotness of a star ,i mean the internal or the surface temperature since ideas were formerly very loose on this point2 ,i have made no reference to white dwarfs1 which are now thought to be the densest and presumably the oldest stars of all4 ,but it is the last paragraph especially which conflicts with our latest conclusions1 for we no longer admit that stellar material will cease to behave as a perfect gas at one-quarter the density of water4 ,our result that the material in the dense dwarf stars is still perfect gas 7p4 #ch7 strikes a fatal blow at this part of the giant and dwarf theory4 ,it would be difficult to say what is the accepted theory of stellar evolution to-day4 ,the theory is in the melting-pot and we are still waiting for something satisfactory to emerge4 ,the whole subject is in doubt and we are prepared to reconsider almost anything4 ,provisionally1 however1 ,i shall assume that the former theory was right in assuming that the sequence of evolution is from the most diffuse to the densest stars4 ,although ,i make this assumption ,i do not feel sure that it is allowable4 ,the former theory had strong reasons for making it which no longer apply4 ,so long as contraction was supposed to be the source of a star's heat1 contraction and increasing density were essential throughout its whole career2 with the acceptance of subatomic energy contraction ceases to play this fundamental role4 ,i propose to confine attention to the dwarf stars#ce because it is among them that the upset has occurred4 ,they form a well-defined series stretching from high surface-temperature to low surface-temperature1 high luminosity to low luminosity1 and the density increases steadily along the series4 ,we now call this the ,main ,series4 ,it comprises the great majority of the stars4 ,to fix ideas let us take three typical stars along the series--,algol near the top1 the ,sun near the middle1 and ,krueger #fj near the bottom4 ,the relevant information about them is summarized below3 ,mean ,central density temperature ,surface ,mass 7,water 7million temperature ,luminosity ,star4 7,sun #a74 #a74 deg474 7deg47 ,colour4 7,sun #a74 ,algol #dc #jae #dj #ab1jjj white #aej ,sun #a #ad #dj #f1jjj yellow #a ,krueger #fj #jbg #ia #ce #c1jjj red #jja ,the idea of evolution is that these represent the stages passed through in the life-history of an individual star4#cf ,the increasing density in the third column should be noticed2 according to our accepted criterion it indicates that the order of development is ,algol,sun,krueger #fj4 ,a confusion between internal temperature and surface temperature is responsible for some of the mistakes of the older theories4 ,to outward view the star cools from #ab1jjj to #c1jjj in passing down the series1 but there is no such change in its internal heat4 ,the central temperature remains surprisingly steady4 7,no special reliance can be placed on the slight falling off apparently shown by ,krueger #fj47 ,it is very remarkable that all stars of the main series have a central temperature of about #dj million degrees as nearly as we can calculate4 ,it is difficult to resist the impression that there is some unusual property associated with this temperature1 although all our physical instincts warn us that the idea is absurd4 ,but the vital point is the decrease of mass shown in the second column4 ,if an individual star is to progress any part of the way down the main series it must lose mass4 ,we can put the same inference in a more general way4 ,now that it has been found that luminosity depends mainly on mass1 there can be no important evolution of faint stars from bright stars unless the stars lose a considerable part of their mass4 ,it is this result which has caused the hypothesis of annihilation of matter to be seriously discussed4 ,all progress in the theory of stellar evolution is held up pending a decision on this hypothesis4 ,if it is accepted it provides an easy key to these changes4 ,the star may 7after passing through the giant stage7 reach the stage of ,algol1 and then by the gradual annihilation of the matter in it pass down the main series until when only one-sixteenth of the original mass remains it will be a faint red star like ,krueger #fj4 ,but if there is no annihilation of matter1 the star when once it has reached the dwarf stage seems to be immovable2 it has to stay at the point of the series corresponding to its constant mass4 ,let it be clearly understood what is the point at issue4 ,the stars lose mass by their radiation2 there is no question about that4 ,the sun is losing #abj billion tons annually whether its radiation comes from annihilation of matter or any other internal source4 ,the question is1 ,how long can this loss continue8 ,unless there is annihilation of matter1 all the mass that can escape as radiation will have escaped in a comparatively short time2 the sun will then be extinct and there is an end to the loss and to the evolution4 ,but if there is annihilation of matter the life of the sun and the loss of mass continue far longer1 and an extended track of evolution lies open before the sun2 when it has got rid of three-quarters of its present mass it will have become a faint star like ,krueger #fj4 ,our choice between the possible theories of subatomic energy only affects stellar evolution in one point--but it is the vital point4 ,unless we choose annihilation of matter1 we cut the life of a star so short that there is no time for any significant evolution at all4 ,i feel the same objection that every one must feel to building extensively on a hypothetical process without any direct evidence that the laws of ,nature permit of its occurrence4 ,but the alternative is to leave the stars in sleepy uniformity with no prospect of development or change until their lives come to an end4 ,something is needed to galvanize the scene into that activity1 whether of progress or decay1 in which we have so long believed4 ,rather desperately we seize on the one visible chance4 ,the petrified system wakes4 ,the ultimate particles one by one yield up their energy and pass out of existence4 ,their sacrifice is the life-force of the stars which now progress on their high adventure3 ,atoms or systems into ruin hurl'd1 ,and now a bubble burst1 and now a world4 ,radiation of ,mass ,our first evidence of the extent of the time-scale of stellar evolution was afforded by the steadiness of condition of ,cephei4 ,this was supplemented by evidence of the great extension of geological time on the earth4 ,we could not do more than set an upper limit to the rate of progress of evolution and a lower limit to the age of the stars4 ,but this limit was sufficient to rule out the contraction hypothesis and drive us to consider the store of subatomic energy4 ,we now make a new attack1 which depends on the belief that the rate of evolution is determined by the rate at which a star can get rid of its mass4 ,we are here considering only the evolution of faint stars from bright stars1 and there will remain scope for a certain amount of development in the giant stage to which our arguments will not directly apply4 ,but to abandon all lines of evolution between bright stars and faint stars would mean admitting that one star differs from another star in brightness because it was different originally4 ,this may be true2 but we ought not to surrender the main field of stellar evolution without making a fight for it4 ,by the new line of attack we reach a definite determination of the time-scale and not merely a lower limit4 ,we know the rate at which stars in each stage are losing mass by radiation2 therefore we can find the time taken to lose a given mass and thereby pass on to a stage of smaller mass4 ,evolution from ,algol to the ,sun requires five billion years2 evolution from the ,sun to ,krueger #fj requires #ejj billion years4 ,it is interesting to note that stars in the stage between the ,sun and ,krueger #fj are much more abundant than those between ,algol and the ,sun--a fact somewhat confirmatory of the calculated duration of the two stages4 ,the abundance of faint stars does not1 however1 increase so rapidly as the calculated duration2 perhaps the stellar universe has not existed long enough for the old stars to be fully represented4 ,a star of greater mass than ,algol squanders its mass very rapidly1 so that we do not increase the age of the ,sun appreciably by supposing it to have started with greater mass than ,algol4 ,the upper limit to the present age of the ,sun is #eb billion years however great its initial mass4 ,but1 it may be asked1 cannot a star accelerate its progress by getting rid of matter in some other way than by radiation8 ,cannot atoms escape from its surface8 ,if so the loss of mass and consequent evolution will be speeded up1 and the time required may perhaps even be brought within range of the alternative theory of transmutation of the elements4 ,but it is fairly certain that the mass escaping in the form of material atoms is negligible compared with that which imperceptibly glides away in the form of radiation4 ,you will perhaps be in doubt as to whether the #abj billion tons per annum lost by the sun in radiation is 7astronomically regarded7 a large quantity or a small quantity4 ,from certain aspects it is a large quantity4 ,it is more than #ajj1jjj times the mass of the calcium chromosphere4 ,the sun would have to blow off its chromosphere and form an entirely fresh one every five minutes in order to get rid of as much mass in this way as it loses by radiation4 ,it is obvious from solar observation that there is no such outrush of material4 ,to put it another way--in order to halve the time-scale of evolution stated above it would be necessary that a billion atoms should escape each second through each square centimetre of the sun's surface4 ,i think we may conclude that there is no short cut to smaller mass and that radiation is responsible for practically the whole loss4 ,we noticed earlier 7p4 #be7 that ,nature builds stars which are much alike in mass1 but allows herself some deviation from her pattern amounting sometimes to a mistake of one #j4 ,i think we may have done her an injustice1 and that she is more careful over her work than we supposed4 ,we ought to have examined coins fresh from her mint2 it was not fair to take coins promiscuously1 including many that had been in circulation for some hundreds of billions of years and had worn rather thin4 ,taking the newly formed stars1 i4 e4 the diffuse stars1 we find that #ij per cent4 of them are between #b and #e times the mass of the sun--showing that initially the stars are made nearly as closely to pattern as human beings are4 ,in this range radiation pressure increases from #ag to #ce per cent1 of the whole pressure2 ,i think this would be expected to be the crucial stage in its rise to importance4 ,our idea is that the stellar masses initially have this rather close uniformity 7which does not exclude a small proportion of exceptional stars outside the above limits72 the smaller masses are evolved from these in course of time by the radiation of mass4 ,for the time being the sun is comfortably settled in its present state1 the amount of energy radiated being just balanced by the subatomic energy liberated inside it4 ,ultimately1 however1 it must move on4 ,the moving on1 or evolution1 is continuous1 but for convenience of explanation we shall speak of it as though it occurred in steps4 ,two possible motives for change can be imagined1 7#a7 the supply of subatomic energy might fall off by exhaustion and no longer balance the radiation1 and 7#b7 the sun is slowly becoming a star of smaller mass4 ,in former theories the first motive has generally been assumed1 and we may still regard it as effective during the giant stage of the stars2 but it is clear that the motive to move down the main series must be loss of mass4#cg ,apparently the distinction between giant and dwarf stars1 replacing the old distinction of perfect and imperfect gas1 is that the prolific and soon exhausted supplies of subatomic energy in the giant stage disappear and leave a much steadier supply in the dwarf stage4 ,when the sun has become a star of smaller mass it will need to resettle its internal conditions4 ,suppose that at first it tries to retain its present density4 ,as explained on p4 #ab1 we can calculate the internal temperature1 and we find that the reduced mass coupled with constant density involves lower temperature4 ,this will slightly turn off the tap of subatomic energy1 because there can be little doubt that the release of subatomic energy is more rapid at higher temperature4 ,the reduced supply will no longer be sufficient to balance the radiation2 accordingly the star will contract just as it was supposed to do on the old contraction hypothesis which corresponds to the tap of subatomic energy being turned off altogether4 ,the motive is loss of mass2 the first consequence is an increase of density which is another characteristic of progress down the main series4 ,tracing the consequences a little farther1 the increasing density causes a rising temperature which in turn reopens the tap of subatomic energy4 ,as soon as the tap is opened enough to balance the rate of radiation of the star1 the contraction stops and the star remains settled in equilibrium at the smaller mass and higher density4 ,you will see that the laws of release of subatomic energy must be invoked if we are to explain quantitatively why a particular density corresponds to a particular mass in the progress down the main series4 ,the contraction has to proceed so far as to bring the internal conditions to a state in which the release of energy is at the exact rate required to balance the radiation4 ,i am afraid this all sounds very complicated1 but my purpose is to show that the adjustment of the star after an alteration of mass is automatic4 ,after a change of mass the star has to re-solve the problem of the internal conditions necessary for its equilibrium4 ,so far as mechanical conditions are concerned 7supporting the weight of the upper layers7 it can choose any one of a series of states of different density provided it has the internal temperature appropriate to that density4 ,but such equilibrium is only temporary1 and the star will not really settle down until the tap of subatomic energy is opened to the right extent to balance the rate of radiation which1 as we have already seen1 is practically fixed by the mass4 ,the star fiddles about with the tap until it secures this balance4 ,one important conclusion has been pointed out by ,professor ,russell4 ,when the star is adjusting the tap it does not do so intelligently2 one trial must automatically lead to the next trial1 and it is all-important that the next trial should automatically be nearer to and not farther from the right rate4 ,the condition that it shall be nearer to the right rate is that the liberation of subatomic energy shall increase with temperature or density4#ch ,if it decreases1 or even if it is unaltered1 the trials will be successively farther and farther from the required rate1 so that although a steady balance is possible the star will never be able to find it4 ,it is therefore essential to admit as one of the laws of liberation of subatomic energy that the rate increases with temperature or with density or with both2 otherwise subatomic energy will not fulfil the purpose for which it was introduced1 viz4 to keep the star steady for a very long time4 ,the strange thing is that the condition of balance is reached when the central temperature is near #dj million degrees--the same whether the star is at the top1 middle1 or bottom of the main series4 ,stars at the top release from each gramme of material #gjj ergs of energy per second2 the sun releases #a ergs per second2 ,krueger #fj releases #jjh ergs per second4 ,it seems extraordinary that stars requiring such different supplies should all have to ascend to the same temperature to procure them4 ,it looks as though at temperatures below this standard not even #jjh ergs per second is available1 but on reaching the standard the supply is practically unlimited4 ,we can scarcely believe that there is a kind of boiling-point 7independent of pressure7 at which matter boils off into energy4 ,the whole phenomenon is most perplexing4 ,i may add that the giant stars have temperatures considerably below #dj million degrees4 ,it would appear that they are tapping special supplies of subatomic energy released at lower temperatures4 ,after using up these supplies the star passes on to the main series1 and proceeds to tap the main supply4 ,it seems necessary to suppose further that the main supply does not last indefinitely1 so that ultimately the star 7or what is left of it7 leaves the main series and passes on to the white dwarf stage4 ,we are now in a position to deal with a question which you may have wished to ask earlier4 ,why does ,cephei pulsate8 ,one possible answer is that the oscillation was started off by some accident4 ,so far as we can calculate an oscillation1 if once started1 would continue for something like #aj1jjj years before becoming damped down4 ,but #aj1jjj years is now deemed to be an insignificant period in the life of a star1 and1 having regard to the abundance of ,cepheids1 the explanation seems inadequate even if we could envisage the kind of accident supposed4 ,it is much more likely that the pulsation arises spontaneously4 ,enormous supplies of heat energy are being released in the star--far more than enough to start and maintain the pulsation--and there are at least two alternative ways in which this heat can be supposed to operate a mechanism of pulsation4 ,here is one alternative4 ,suppose first that there is a very small pulsation4 ,when compressed the star has higher temperature and density than usual and the tap of subatomic energy is opened more fully4 ,the star gains heat1 and the expansive force of the extra heat assists the rebound from compression4 ,at greatest expansion the tap is turned off a little and the loss of heat diminishes the resistance to the ensuing compression4 ,thus the successive expansions and compressions become more and more vigorous and a large pulsation grows out of an infinitesimal beginning4 ,it will be seen that the star works the tap of subatomic energy just as an engine works the valve admitting heat into its cylinder2 so that the pulsations of a star are started up like the pulsations of an engine4 ,the only objection that ,i can find to this explanation is that it is too successful4 ,it shows why a star may be expected to pulsate2 but the trouble is that stars in general do not pulsate--it is only the rare exceptions that behave in this way4 ,it is now so easy to account for the ,cepheids that we have to turn back and face the more difficult problem of accounting for the normal steady stars4 ,whether the pulsation will start up or not depends on whether the engine of pulsation is sufficiently powerful to overcome the forces tending to damp out and dissipate pulsations4 ,we cannot predict the occurrence or non-occurrence from any settled theory2 we have rather to seek to frame the laws of release of subatomic energy so as to conform to our knowledge that the majority of the stars remain steady1 but certain conditions of mass and density give the pulsatory forces the upper hand4 ,cepheid pulsation is a kind of distemper which happens to stars at a certain youthful period2 after passing through it they burn steadily4 ,there may be another attack of disease later in life when the star is subject to those catastrophic outbursts which occasion the appearance of #8new stars' or novae4 ,but very little is known as to the conditions for this1 and it is not certain whether the outbreak is spontaneous or provoked from outside4 ,so long as we stick to generalities the theory of subatomic energy and especially the theory of annihilation of matter makes a fairly promising opening4 ,it is when we come to technical details that doubts and perplexities arise4 ,difficulties appear in the simultaneous presence of giant and dwarf stars in coeval clusters1 notwithstanding their widely different rates of evolution4 ,there are difficulties in devising laws of release of subatomic energy which will safeguard the stability of the stars without setting every star into pulsation4 ,difficulties arise from the fact that as a rule in the giant stage the lower the temperature and density the more rapid the release of energy2 and although we account for this in a general way by considering the exhaustibility of the more prolific sources of energy1 the facts are not all straightened out by such a scheme4 ,finally grave difficulties arise in reconciling the laws of release inferred from astronomical observation with any theoretical picture we can form of the process of annihilation of matter by the interplay of atoms1 electrons1 and radiation4 ,the subject is highly important1 but we cannot very well pursue it further in this lecture4 ,when the guidance of theory is clear interest centres round the broad principles2 when the theory is rudimentary1 interest centres round technical details which are anxiously scrutinized as they appear to favour now one view now another4 ,i have dealt mainly with two salient points--the problem of the source of a star's energy and the change of mass which must occur if there is any evolution of faint stars from bright stars4 ,i have shown how these appear to meet in the hypothesis of annihilation of matter4 ,i do not hold this as a secure conclusion4 ,i hesitate even to advocate it as probable1 because there are many details which seem to me to throw considerable doubt on it1 and ,i have formed a strong impression that there must be some essential point which has not yet been grasped4 ,i simply tell it you as the clue which at the moment we are trying to follow up--not knowing whether it is false scent or true4 ,i should have liked to have closed these lectures by leading up to some great climax4 ,but perhaps it is more in accordance with the true conditions of scientific progress that they should fizzle out with a glimpse of the obscurity which marks the frontiers of present knowledge4 ,i do not apologize for the lameness of the conclusion1 for it is not a conclusion4 ,i wish ,i could feel confident that it is even a beginning4 ,,footnotes3 ,footnote #a3 ,fig4 #a is from a photograph taken by ,mr4 ,evershed at ,kodaikanal ,observatory1 ,madras4 ,fig4 #b is from the ,mount ,wilson ,observatory1 ,california4 ,footnote #b3 ,i am indebted to ,professor ,c4 ,t4 ,r4 ,wilson for ,figs4 #c-f4 ,footnote #c3 ,primarily it is the electric charge and not the high speed of particles which determines their appearance in these photographs4 ,but a high-speed particle leaves behind it a trail of electrically charged particles--the victims of its furious driving--so that it is shown indirectly by its line of victims4 ,footnote #d3 ,other substitutions for silver do not as a rule cause greater change1 and the differences are likely to be toned down by mixture of many elements4 ,excluding hydrogen1 the most extreme change is from #dh particles for silver to #ha particles for an equal mass of helium4 ,but for hydrogen the change is from #dh to #baf1 so that hydrogen gives widely different results from other elements4 ,footnote #e3 ,the mean density of ,capella is nearly the same as the density of the air4 ,footnote #f3 ,unless otherwise indicated #8gaseous' is intended to mean #8composed of perfect gas'4 ,footnote #g3 ,for this prediction it is unnecessary to know the chemical composition of the stars1 provided that extreme cases 7e4 g4 an excessive proportion of hydrogen7 are excluded4 ,for example1 consider the hypotheses that ,capella is made respectively of 7a7 iron1 7b7 gold4 ,according to theory the opacity of a star made of the heavier element would be #b times the opacity of a star made of iron4 ,this by itself would make the golden star a magnitude 7 #b times7 fainter4 ,but the temperature is raised by the substitution2 and although1 as explained on p4 #bc1 the change is not very great1 it increases the outflow of heat approximately #b times4 ,the resultant effect on the brightness is practically no change4 ,whilst this independence of chemical constitution is satisfactory in regard to definiteness of the results1 it makes the discrepant factor #aj particularly difficult to explain4 ,footnote #h3 ,observation shows that the sun is about #d magnitudes fainter than the average diffuse star of the same spectral class1 and ,krueger #fj is #aj magnitudes fainter than diffuse stars of its class4 ,the whole drop was generally assumed to be due to deviation from a perfect gas2 but this made no allowance for a possible difference of mass4 ,the comparison with the curve enables the dense star to be compared with a gaseous star of its own mass1 and we see that the difference then disappears4 ,so that 7if there has been no mistake7 the dense star is a gaseous star1 and the differences above mentioned were due wholly to differences of mass4 ,footnote #i3 ,rougher estimates were made much earlier4 ,footnote #aj3 ,the observed period of ,algol is the period of revolution1 not of rotation4 ,but the two components are very close together1 and there can be no doubt that owing to the large tidal forces they keep the same faces turned towards each other2 that is to say1 the periods of rotation and of revolution are equal4 ,footnote #aa3 ,it may be of interest to add that although the proper light of ,algol ,b is inappreciable1 we can observe a reflection 7or re-radiation7 of the light of ,algol ,a by it4 ,this reflected light changes like moonlight according as ,algol ,b is #8new' or #8full'4 ,footnote #aa3 ,the mass-luminosity relation was not suspected at the time of which ,i am speaking4 ,footnote #ac3 ,my references to #8perfect gas of the density of platinum' and #8material #b1jjj times denser than platinum' have often been run together by reporters into #8perfect gas #b1jjj times denser than platinum'4 ,it is scarcely possible to calculate what is the condition of the material in the ,companion of ,sirius1 but ,i do not expect it to be a perfect gas4 ,footnote #ad3 ,photographed by ,dr4 ,w4 ,h4 ,wright at the ,lick ,observatory1 ,california4 ,footnote #ae3 ,nos4 #dc1 #fa1 #ge are recent discoveries and may require confirmation4 ,there now remain only two gaps 7#he and #hg7 apart from possible elements beyond uranium4 ,footnote #af3 ,it does not give both temperature and pressure1 but it gives one if the other is known4 ,this is valuable information which may be pieced together with other knowledge of the conditions at the surface of the stars4 ,footnote #ag3 ,hydrogen 7being element ,no4 #a7 has only one planet electron4 ,footnote #ah3 ,fig4 #i is a photograph of the #8flash spectrum' of the sun's chromosphere taken by ,mr4 ,davidson in ,sumatra at the eclipse of #ad ,january #aibf4 ,footnote #ai3 ,the helium line in the ,ring ,nebula on which we have already commented is not a member of the ,pickering ,series1 but it has had the same history4 ,it was first supposed to be due to hydrogen1 later 7in #aiab7 reproduced by ,fowler terrestrially in a mixture of helium and hydrogen1 and finally discovered by ,bohr to belong to helium4 ,footnote #bj3 ,this1 of course1 is found from the other lines of the spectrum which genuinely belong to the star and shift to and fro as it describes its orbit4 ,footnote #ba3 ,as the word temperature is sometimes used with new-fangled meanings1 ,i may add that #ae1jjj is the temperature corresponding to the individual speeds of the atoms and electrons--the old-fashioned gas-temperature4 ,footnote #bb3 ,photograph taken by ,e4 ,t4 ,cottingham and the author in ,principe at the total eclipse of #bi ,may #aiai4 ,footnote #bc3 ,we refer to calcium as it occurs in the chromosphere1 i4 e4 with one electron missing4 ,footnote #bd3 ,there is an awkwardness in applying the term #8apparent' to something too small to be seen2 but1 remembering that we have armed ourselves with an imaginary telescope capable of showing the disk1 the meaning will be clear4 ,footnote #be3 ,densities below that of air have been found for some of the ,algol variables by an entirely different kind of investigation1 and also for some of the ,cepheid variables by still another method4 ,there are also many other examples of stars of bulk comparable with that of ,betelgeuse4 ,footnote #bf3 ,from a photograph taken at the ,royal ,observatory1 ,cape of ,good ,hope4 ,footnote #bg3 ,for comparison1 the nearest fixed star is distant #d light years4 ,apart from clusters we rarely deal with distances above #b1jjj light years4 ,footnote #bh3 ,one cannot always be sure that what is true of the cluster stars will be true of stars in general2 and our knowledge of the nearer stars1 though lagging behind that of the stars in clusters1 does not entirely agree with this association of colour and brightness4 ,footnote #bi3 ,the term nebula covers a variety of objects1 and it is only the nebulae classed as spirals that are likely to be outside our stellar system4 ,footnote #cj3 ,this can be checked because uranium lead has a different atomic weight from lead not so derived4 ,ordinary lead is a mixture of several kinds of atoms 7isotopes74 ,footnote #ca3 ,you may wonder why1 having said that the sun contains #b1jjj quadrillion tons of energy at the most1 ,i now assume that it contains just this amount4 ,it is really only a verbal point depending on the scientific definition of energy4 ,all mass is mass of something1 and we now call that something #8energy' whether it is one of the familiar forms of energy or not4 ,you will see in the next sentence that we do not assume that the energy is convertible into known forms1 so that it is a terminology which commits us to nothing4 ,footnote #cb3 ,aston in his latest researches has been able to detect that the oxygen atom is just appreciably lighter than the four helium atoms4 ,footnote #cc3 ,a measurement of the heat observed to flow from a continuous fountain of heat is a measurement of the output of the fountain1 unless there is a storing of energy between the output and the outflow4 ,the breakdown of the ,kelvin time-scale indicates that the storing in the stars 7positive or negative7 and consequent expansion or contraction is negligible compared to the output or outflow4 ,footnote #cd3 ,the stars all put together cover an area of the sky much less than the apparent disk of the sun1 so that unless their surface-layers are generating this radiation very much more abundantly than the sun does1 they cannot be responsible for it4 ,footnote #ce3 ,the term #8dwarf stars' is not meant to include white dwarfs4 ,footnote #cf3 ,we can scarcely suppose that all stars after reaching the main series pass through precisely the same stages4 ,for example1 ,algol1 when it has become reduced to the mass of the ,sun1 may have slightly different density and temperature4 ,but the observational evidence indicates that these individual differences are small4 ,the main series is nearly a linear sequence2 it must have some #8breadth' as well as #8length'1 but at present the scatter of the individual stars away from the central line of the sequence seems to be due chiefly to the probable errors of the observational data and the true breadth has not been determined4 ,footnote #cg3 ,exhaustion of supply without change of mass would cause the star to contract to higher density2 it would thus have a combination of density and mass which 7according to observation7 is not found in any actual stars4 ,footnote #ch3 ,this increase was assumed in our detailed description of the automatic adjustment of the star1 and it will be seen that it was essential to assume it4 ,,appendix ,further ,remarks on the ,companion of ,sirius ,i ,,have preferred not to complicate the ,story of the ,companion of ,sirius with details of a technical kind2 some further information may1 therefore1 be welcome to those readers who are curious to learn as much as possible about this remarkable star4 ,i am also able to add a further instalment of the #8detective story' which has just come to hand1 the sleuth this time being ,mr4 ,r4 ,h4 ,fowler4 ,the star is between the eighth and ninth magnitude1 so that it is not an excessively faint object4 ,the difficulty in detecting it arises entirely from the overpowering light of its neighbour4 ,at favourable epochs it has been seen easily with an #h-;inch telescope4 ,the period of revolution is #di years4 ,the ,companion is separated from ,sirius by a distance nearly equal to the distance of ,uranus from the ,sun--or twenty times the earth's distance from the sun4 ,it has been suggested that the light might be reflected light from ,sirius4 ,this would account for its whiteness1 but would not directly account for its spectrum1 which differs appreciably from that of ,sirius4 ,to reflect th of the light of ,sirius 7its actual brightness7 the ,companion would have to be #gd million miles in diameter4 ,the apparent diameter of its disk would be #jc1 which1 one would think1 could scarcely escape notice in spite of unfavourable conditions of observation4 ,but the strongest objection to this hypothesis of reflected light is that it applies only to this one star4 ,the other two recognized white dwarfs have no brilliant star in their neighbourhood1 so that they cannot be shining by reflected light4 ,it is scarcely worth while to invent an elaborate explanation for one of these strange objects which does not cover the other two4 ,the ,einstein effect1 which is appealed to for confirmation of the high density1 is a lengthening of the wave-length and corresponding decrease of the frequency of the light due to the intense gravitational field through which the rays have to pass4 ,consequently the dark lines in the spectrum appear at longer wave-lengths1 i4e4 displaced towards the red as compared with the corresponding terrestrial lines4 ,the effect can be deduced either from the relativity theory of gravitation or from the quantum theory2 for those who have some acquaintance with the quantum theory the following reasoning is probably the simplest4 ,the stellar atom emits the same quantum of energy h as a terrestrial atom1 but this quantum has to use up some of its energy in order to escape from the attraction of the star2 the energy of escape is equal to the mass h_/c#b multiplied by the gravitational potential at the surface of the star4 ,accordingly the reduced energy after escape is h7#a - _/c#b72 and since this must still form a quantum h'1 the frequency has to change to a value ' 7#a - _/c#b74 ,thus the displacement ' - is proportional to 1 i4e4 to the mass divided by the radius of the star4 ,the effect on the spectrum resembles the ,doppler effect of a velocity of recession1 and can therefore only be discriminated if we know already the line-of-sight velocity4 ,in the case of a double star the velocity is known from observation of the other component of the system1 so that the part of the displacement attributable to ,doppler effect is known4 ,owing to orbital motion there is a difference of velocity between ,sirius and its ,companion amounting at present to #dc km4 per sec4 and this has been duly taken into account2 the observed difference in position of the spectral lines of ,sirius and its ,companion corresponds to a velocity of #bc km4 per sec4 of which #d km4 per sec4 is attributable to orbital motion1 and the remaining #ai km4 per sec4 must be interpreted as ,einstein effect4 ,the result rests mainly on measurements of one spectral line ,h4 ,the other favourable lines are in the bluer part of the spectrum1 and since atmospheric scattering increases with blueness1 the scattered light of ,sirius interferes4 ,however1 they afford some useful confirmatory evidence4 ,of the other white dwarfs #b ,eridani is a double star1 its companion being a red dwarf fainter than itself4 ,the red shift of the spectrum will be smaller than in the ,companion of ,sirius and it will not be so easy to separate it from various possible sources of error4 ,nevertheless the prospect is not hopeless4 ,the other recognized white dwarf is an unnamed star discovered by ,van ,maanen2 it is a solitary star1 and consequently there is no means of distinguishing between ,einstein shift and ,doppler shift4 ,various other stars have been suspected of being in this condition1 including the ,companions of ,procyon1 #he ,pegasi1 and ,mira ,ceti4 ,if the ,companion of ,sirius were a perfect gas its central temperature would be about #a1jjj1jjj1jjj1 and the central part of the star would be a million times as dense as water4 ,it is1 however1 unlikely that the condition of a perfect gas continues to hold4 ,it should be understood that in any case the density will fall off towards the outside of the star1 and the regions which we observe are entirely normal4 ,the dense material is tucked away under high pressure in the interior4 ,perhaps the most puzzling feature that remains is the extraordinary difference of development between ,sirius and its ,companion1 which must both have originated at the same time4 ,owing to the radiation of mass the age of ,sirius must be less than a billion years2 an initial mass1 however large1 would radiate itself down to less than the present mass of ,sirius within a billion years4 ,but such a period is insignificant in the evolution of a small star which radiates more slowly1 and it is difficult to see why the ,companion should have already left the main series and gone on to this 7presumably7 later stage4 ,this is akin to other difficulties in the problem of stellar evolution1 and ,i feel convinced that there is something of fundamental importance that remains undiscovered4 ,until recently ,i have felt that there was a serious 7or1 if you like1 a comic7 difficulty about the ultimate fate of the white dwarfs4 ,their high density is only possible because of the smashing of the atoms1 which in turn depends on the high temperature4 ,it does not seem permissible to suppose that the matter can remain in this compressed state if the temperature falls4 ,we may look forward to a time when the supply of subatomic energy fails and there is nothing to maintain the high temperature2 then on cooling down1 the material will return to the normal density of terrestrial solids4 ,the star must1 therefore1 expand1 and in order to regain a density a thousandfold less the radius must expand tenfold4 ,energy will be required in order to force out the material against gravity4 ,where is this energy to come from8 ,an ordinary star has not enough heat energy inside it to be able to expand against gravitation to this extent2 and the white dwarf can scarcely be supposed to have had sufficient foresight to make special provision for this remote demand4 ,thus the star may be in an awkward predicament--it will be losing heat continually but will not have enough energy to cool down4 ,one suggestion for avoiding this dilemma is like the device of a novelist who brings his characters into such a mess that the only solution is to kill them off4 ,we might assume that subatomic energy will never cease to be liberated until it has removed the whole mass--or at least conducted the star out of the white dwarf condition4 ,but this scarcely meets the difficulty2 the theory ought in some way to guard automatically against an impossible predicament1 and not to rely on disconnected properties of matter to protect the actual stars from trouble4 ,the whole difficulty seems1 however1 to have been removed in a recent investigation by ,r4 ,h4 ,fowler4 ,he concludes unexpectedly that the dense matter of the ,companion of ,sirius has an ample store of energy to provide for the expansion4 ,the interesting point is that his solution invokes some of the most recent developments of the quantum theory--the #8new statistics' of ,einstein and ,bose and the wave-theory of ,schrdinger4 ,it is a curious coincidence that about the time that this matter of transcendently high density was engaging the attention of astronomers1 the physicists were developing a new theory of matter which specially concerns high density4 ,according to this theory matter has certain wave properties which barely come into play at terrestrial densities2 but they are of serious importance at densities such as that of the ,companion of ,sirius4 ,it was in considering these properties that ,fowler came upon the store of energy that solves our difficulty2 the classical theory of matter gives no indication of it4 ,the white dwarf appears to be a happy hunting ground for the most revolutionary developments of theoretical physics4 ,to gain some idea of the new theory of dense matter we can begin by referring to the photograph of the ,balmer ,series in ,fig4 #i4 ,this shows the light radiated by a large number of hydrogen atoms in all possible states up to ,no4 #cj in the proportions in which they occur naturally in the sun's chromosphere4 ,the old-style electromagnetic theory predicted that electrons moving in curved paths would radiate continuous light2 and the old-style statistical theory predicted the relative abundance of orbits of different sizes1 so that the distribution of light along this continuous spectrum could be calculated4 ,these predictions are wrong and do not give the distribution of light shown in the photograph2 but they become less glaringly wrong as we draw near to the head of the series4 ,the later lines of the series crowd together and presently become so close as to be practically indistinguishable from continuous light4 ,thus the classical prediction of continuous spectrum is becoming approximately true2 simultaneously the classical prediction of its intensity approaches the truth4 ,there is a famous ,correspondence ,principle enunciated by ,bohr which asserts that for states of very high number the new quantum laws merge into the old classical laws4 ,if we never have to consider states of low number it is indifferent whether we calculate the radiation or statistics according to the old laws or the new4 ,in high-numbered states the electron is for most of the time far distant from the nucleus4 ,continuous proximity to the nucleus indicates a low-numbered state4 ,must we not expect1 then1 that in extremely dense matter the continuous proximity of the particles will give rise to phenomena characteristic of low-numbered states8 ,there is no real discontinuity between the organization of the atom and the organization of the star2 the ties which bind the particles in the atom1 bind also more extended groups of particles and eventually the whole star4 ,so long as these ties are of high quantum number1 the alternative conception is sufficiently nearly valid which represents the interactions by forces after the classical fashion and takes no cognizance of #8states'4 ,for very high density there is no alternative conception1 and we must think not in terms of force1 velocity1 and distribution of independent particles1 but in terms of states4 ,the effect of this breakdown of the classical conception can best be seen by passing at once to the final limit when the star becomes a single system or molecule in state ,no4 #a4 ,like an excited atom collapsing with discontinuous jumps such as those which give the ,balmer ,series1 the star with a few last gasps of radiation will reach the limiting state which has no state beyond4 ,this does not mean that further contraction is barred by the ultimate particles jamming in contact1 any more than collapse of the hydrogen atom is barred by the electron jamming against the proton2 progress is stopped because the star has got back to the first of an integral series of possible conditions of a material system4 ,a hydrogen atom in state ,no4 #a cannot radiate2 nevertheless its electron is moving with high kinetic energy4 ,similarly a star when it has reached state ,no4 #a no longer radiates2 nevertheless its particles are moving with extremely great energy4 ,what is its temperature8 ,if you measure temperature by radiating power its temperature is absolute zero1 since the radiation is nil2 if you measure temperature by the average speed of molecules its temperature is the highest attainable by matter4 ,the final fate of the white dwarf is to become at the same time the hottest and the coldest matter in the universe4 ,our difficulty is doubly solved4 ,because the star is intensely hot it has enough energy to cool down if it wants to2 because it is so intensely cold it has stopped radiating and no longer wants to grow any colder4 ,we have described what is believed to be the final state of the white dwarf and perhaps therefore of every star4 ,the ,companion of ,sirius has not yet reached this state1 but it is so far on the way that the classical treatment is already inadmissible4 ,if any stars have reached state ,no4 #a they are invisible2 like atoms in the normal 7lowest7 state they give no light4 ,the binding of the atom which defies the classical conception of forces has extended to cover the star4 ,i little imagined when this survey of ,stars and ,atoms was begun that it would end with a glimpse of a ,star-,atom4 ,printed in ,england at the ,,oxford ,,university ,,press by ,john ,johnson ,printer to the ,university