A.— MATHEMATICAL AND PHYSICAL SCIENCES 27 



ing to Einstein had to be composed of arrows, whereas a hundred years 

 eariier Fresnel had proved that it was a system of waves ? What does 

 a rational being do when faced with two mutually contradictory but both 

 indubitable pieces of evidence ? It was a nice test for the critical spirit, 

 and it revealed a wide divergence of choices. In making a historical 

 judgment long after the event, one of the hardest things to do is to recall 

 the relative scale of importance which contemporaries were inclined to 

 attach to the different branches of their subject. 



The statistical theory of matter had already been well established by 

 the work of Maxwell, Boltzmann and Gibbs, but it was not regarded 

 as an essential part of a general mathematical-physical education. For 

 example, in the various courses I was advised to undertake during my 

 undergraduate career, no one at any stage ever suggested to me that I 

 should learn anything about the kinetic theory of gases. I think that 

 that period was one when the Cambridge mathematical school was not 

 at its best, and very probably a little more was done at other places, but, 

 to judge by the available text-books in any language, statistical theory 

 was not regarded as one of the prime subjects of study, as it would be 

 now. The period was essentially dynamic, and as such it was moderately 

 easy for it to take in the new ideas of relativity, to which indeed the 

 experimental work of the last century had been leading. But there was 

 no common habit of thought on statistical lines, and so there was a 

 sharp separation of opinion. The seniors, impressed with the vast mass 

 of successful physics of the nineteenth century, with only a rather 

 general knowledge of statistical theory but no facility of thought in it, 

 found the new ideas completely contrary to their convictions. Such 

 men would think that these ideas depended on the difficult and un- 

 familiar conceptions of statistics and would be inclined to judge that 

 there must be a fallacy in the statistics which would be cleared up later. 

 On the other hand the laboratory workers, dealing with atoms and electrons 

 from day to day, could not fail to be more impressed with the discontinuous 

 phenomena and the beautiful way these could be explained by the 

 quantum. Such men would cheerfully accept the Bohr orbits as a com- 

 plete explanation of the hydrogen spectrum, and certainly in many cases 

 would be actually ignorant of the difficulty, the monstrous absurdity, 

 of supposing that a sharp jump from one orbit to another could be 

 responsible for a train of waves shown by the spectroscope to be lasting 

 for quite a long time. So the majority of rational beings behaved in 

 the natural human way of managing to forget all the disagreeable facts. 

 But not every one, for there were Bohr and the other leaders who 

 recognised the difficulties on both sides but could still maintain an attitude 

 of balance and could believe that from somewhere there would come a 

 higher synthesis by which everything would be fitted together. 



As time went on the quantum got obviously stronger and stronger, 

 and began to invade more fields. The nuclear atom in the hands of Bohr 

 showed itself capable of giving all the broad details of the periodic table 

 of chemistry, still with nothing done to meet the awful difficulties of 

 optical theory. But about 1925, guided by the Correspondence Principle, 

 things were moving towards a tentative theory of the refractive index, 

 and it was this that finally suggested the break in the contradictions. 



