A. — MATHEMATICS AND PHYSICS. 45 



star, and not forced from outside, the density must be the leading factor 

 in detei-mining the period. If the star is contracting so that its density- 

 changes appreciably, the period cannot remain constant. Now, on the 

 contraction hypothesis the change of density must amount to at least 

 1 per cent, in 40 years. (I give the figures for d Cephei, tlie best- 

 known variable of this class.) The corresponding change of period 

 should be very easily detectable. For 8 Gephei the period ought to 

 decrease 40 seconds annually. 



Now 8 Cephei has been under careful observation since 1785, and 

 it is known that the change of period, if any, must be veiy small. 

 S. Chandler found a decrease of period of -^^ second per annum, and in a 

 recent investigation E. Hertzsprung has found a decrease of yL second 

 per annum. The evidence that there is any decrease at all rests almost 

 entirely on the earliest observations made before 1800, so that it is not 

 very certain ; but in any case the evolution is proceeding at not more 

 than fiy of the rate required by the contraction hypothesis. There 

 must at this stage of the evolution of the star be some other source 

 of enei'gy which prolongs the life of the star 4'00-fold. The time-scale 

 so enlarged would suffice for practically all reasonable demands. 



I hope the dilemma is plain. Either we must admit that whilst the 

 density changes 1 per cent, a certain period intrinsic in the star can 

 change no more than^fi^ of 1 per cent., or we must give up the con- 

 traction hypothesis. 



If the contraction theory were proposed to-day as a novel hypothesis 

 I do not think it would stand the smallest chance of acceptance. From all 

 sides — biology, geology, physics, astronomy — it would be objected that 

 the suggested source of energy was hopelessly inadequate to provide the 

 heat spent during the necessary time of evolution ; and, so far as it is 

 possible to interpret observational evidence confidently, the theory would 

 be held to be definitely negatived. Only the inertia of tradition keeps 

 the contraction hypothesis alive — or rather, not alive, but an unburied 

 corpse. But if we decide to inter the corpse, let us frankly recognise 

 the position in which we are left. A star is drawing on some vast 

 reservoir of energy by means unknown to us. This resei-voir can 

 scarcely be other than the sub-atomic energy which, it is known, exists 

 abundantly in all matter; we sometimes dream that man will one day 

 learn how to release it and use it for his service. The store is well-nigh 

 inexhaustible, if only it could be tapped. There is sufficient in the Sun 

 to maintain its output of heat for 15 billion years. 



Certain physical investigations in the past year, which I hope we 

 may hear about at this meeting, make it probable to my mind that some 

 portion of this sub-atomic energy is actually being set free in the stars. 

 F. W. Aston 's experiments seem to leave no room for doubt that all the 

 elements are constituted out of hydrogen atoms bound together with 

 negative electrons. The nucleus of the helium atom, for example, 

 consists of 4 hydrogen atoms bound with 2 electrons. But Aston has 

 further shown conclusively that the mass of the helium atom is less 

 than the sum of the masses of the 4 hydrogen atoms which enter into 

 it ; and in this at any rate the chemists agree with him. There is a 

 'oss of mass in the synthesis amounting to about 1 part in 120, the. 



