A. — MATHEMATICS AND PHYSICS. 35 



But it is far better if we can deal with matter in that state known 

 as a perfect gas, which charms away difficuhies as by magic. Where 

 shall it be found? 



A few years ago we should have been puzzled to say where, except 

 perhaps in certain nebulae ; but now it is known that abundant material 

 of this kind awaits investigation. Stars in a truly gaseous state exist 

 in great numbers, although at first sight they are scarcely to be dis- 

 criminated fi-om dense stars like our Sun. Not only so, but the 

 gaseous stars are the most powerful light-givers, so that they force 

 themselves on our attention. Many of the familiar stars are of this 

 kind — Aldebaran, Canopus, Arcturus, Antares; and it would be safe 

 to say that three-quarters of the naked-eye stars are in this diffuse 

 state. This remarkable condition has been made known through the 

 researches of H. N. RusselP and E. Hertzsprung; the way in which 

 their conclusions, which ran counter to the prevailing thought of the 

 time, have been substantiated on all sitles by overwhelming evidence », 

 is the outstanding feature of recent progress in stellar astronomy. 



The diffuse gaseous stars are called giants, and the dense stars are 

 called dwarfs. During the life of a star there is presumably a gradual 

 -ncrease of density through contraction, so that these terms distinguish 

 the earlier and later stages of stellar histoiy. It appeal's that a star 

 begins its effective life as a giant of comparatively low temperature — 

 a red or M-type star. As this diffuse mass of gas contracts its tem- 

 perature must rise, a conclusion long ago pointed out by Homer Lane. 

 The rise continues until the star becomes toO' dense, and ceases to 

 behave as a perfect gas. A maximum temperature is attained, depend- 

 ing on the mass, after which the star, which has now become a dwai'f, 

 cools and further contracts. Thus each temperatui'e-level is passed 

 through twice, once in an ascending and once in a descending stage — 

 once as a giant, once as a dwarf. Temperature plays so predominant 

 a part in the usual spectral classification that tlie ascending and 

 descending stars were not originally discriminated, and the customary 

 classification led to some perplexities. The separation of the two series 

 was discovered through their great difference in luminosity, particularly 

 striking in the case of the red and yellow stars, where the two stages 

 fall widely apart in the star's history. The bloated giant has a far 

 larger surface than the compact dwarf, and gives correspondingly 

 greater light. The distinction was also revealed by direct determina- 

 tions of stellar densities, which are possible in the case of eclipsing 

 variables like Algol. Finally, Adams and Kohlschiitter have set the 

 seal on this discussion by showing that there are actual spectral differ- 

 ences between the ascending and descending stars at the same tem- 

 perature-level, which are conspicuous enough — when they are looked 

 for. 



Perhaps we should not too hastily assume that the direction of 

 evolution is necessarily in the order of increasing density, in view of 

 our ignorance of the origin of a star's heat, to which I must allude 

 later. But, at any rate, it is a great advance to have disentangled what 



' Nature, vol. 93, pp. 227, 252, 281. 



