NUMERICAL LAWS AND MATHEMATICS 157 



atom) is quite as marvellous. But of these I could not give, 

 even if space allowed, even such an explanation as I 

 have attempted for Maxwell's. And the reason is this : 

 A theory by itself means nothing experimental we 

 insisted on that in Chapter V it is only when something 

 is deduced from it that it is brought within the range of 

 our material senses. Now in Maxwell's theory, the 

 symbols, in the alteration of which the characteristic 

 feature of the theory depends, are retained through the 

 deduction and appear in the law which is compared with 

 experiment. Accordingly it is possible to give some idea 

 of what these symbols mean in terms of things experi- 

 mentally observed. But in Sommerfeld's or Einstein's 

 theory the symbols, which are necessarily involved in the 

 assumption which differentiates their theories from 

 others, disappear during the deduction ; they leave a 

 mark on the other symbols which remain and alter the 

 relation between them ; but the symbols on the relations 

 of which the whole theory hangs, do not appear at all 

 in any law deduced from the theory. It is quite impos- 

 sible to give any idea of what they mean in terms of experi- 

 ment. 1 Probably some of my readers will have read the 

 very interesting and ingenious attempts to " explain 

 Einstein " which have been published, and will feel that 

 they really have a grasp of the matter. Personally I 

 doubt it ; the only way to understand what Einstein did 

 is to look at the symbols in which his theory must 

 ultimately be expressed and to realize that it was reasons 

 of symbolic form, and such reasons alone, which led him 

 to arrange the symbols in the way he did and in no other. 

 But now I have waded into such deep water that it is 

 time to retrace my steps and return to the safe shore of 

 the affairs of practical life. 



1 The same is true really of the exposition of the Newtonian 

 assumption attempted on p. 151. It is strictly impossible to state 

 exactly what is the assumption discussed there without using 

 symbols. The acute reader will have guessed already that on that 

 page I felt myself skating on very thin ice. 



