246 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1933 



de Sitter. The interest of Professor de Sitter's theory for us is that 

 any particles introduced into it would tend to run away from an 

 observer stationed at the origin; and the light from distant objects 

 would give a spectrum shift toward the red. In a sense, therefore, 

 the notion of an expanding universe is to be found in Professor de 

 Sitter's theory. 



But it was not until 1922 that the theory as strictly understood 

 was founded. A. Friedmann then jx'inted out that the Einstein 

 universe was unstable, so that if once disturbed it must go on ex- 

 panding or contracting. Although he published his proof in one of 

 the best-known German scientific periodicals, it fell completely 

 unnoticed. Independently the Abbe Lemaitre was developing a simi- 

 lar theory, and in 1927 he published his results, only to find that 

 they also were unnoticed. But in 1930 the ground was better pre- 

 pared, chiefly owing to the growing evidence for the recessive mo- 

 tions of the nebulae. Sir Arthur Eddington expressed the wish that 

 a certain mathematical result had been worked out; Lemaitre, who 

 had previously been a pupil of his, wrote to say he had already ob- 

 tained it. From that moment the theory of the expanding universe 

 leaped into prominence. Sir Arthur Eddington has himself been no 

 mean contributor to it. Although most men of science do not believe 

 he has completely justified his particular form of the theory, all are 

 forced to admire it by its extraordinary elegance and power. He 

 obtains by pure theory a value for the expansion of the universe 

 which does not differ so very much from the observed value of the 

 recession of the nebulae. In the course of the w^orlving he obtains 

 a quadratic equation whose roots are in the ratio 1,846 to 1, which 

 is the ratio of the mass of the proton to that of the electron. And he 

 is able to prove that on his theory the total number of particles in the 

 universe is 10'^ (10 followed by 79 noughts). 



Dr. McVittie and Dr. McCrea have done some valuable investi- 

 gation of the effect of condensation in the matter filling the Einstein 

 universe. But the most original contribution to the theory recently 

 has been that of Professor Milne, of Oxford. At first it seemed to 

 knock the bottom out of theories of expanding space, because Pro- 

 fessor Milne explained the recession of the nebulae by using ordinary 

 kinematics and Euclidean space. Consider a number of billiard balls 

 moving on an indefinitel}'^ large table. If any point be taken on the 

 table, there comes a time when all the balls will seem to be moving 

 away from it. Some will always have been moving away ; others will 

 first come near the point and then pass away; but given sufficient 

 time all will appear to be moving outwards, and the fastest-moving 

 will naturally be farthest away. Professor Milne seemed to have hit 

 on an absurdly simple explanation of the recession of the nebulae, 



