TRANSACTIONS OF THE SECTIONS. 7 



scientific purposes, of so-called " absolute " measurements, instead of mere com- 

 parisons of each quantity to be estimated with a standard magnitude of its own kind. 

 The use of absolute measures constitutes one of the most clmracteristic differ- 

 ences between the Physics of to-day and that of the time when the British Asso- 

 ciation was instituted, and it may even be said to lie at the base of the doctrine of 

 the Conservation of Energy, which implies the principle that every kind of Energy 

 can be reduced to the same denomination. 



Perhaps, after speaking as I have done of the necessity for the cooperation of 

 mathematics in the advancement of physics, it is not inappropriate that I should, 

 in conclusion, refer to the possibility that, by a too implicit reliance upon mathe- 

 matical guidance, the physicist may be led away from the discovery of fresh truth 

 or even into actual error. Mathematics is seen to be so indispensable and usually 

 so powerful an aid in physical investigation, that there is a danger of forgetting 

 that there are, after all, limits to its power. Partly from want of sufficient know- 

 ledge of the physical data on which mathematical discussion must be based, and 

 partly from the imperfection of mathematical methods themselves, it happens that 

 it is not possible to give a thoroughly complete mathematical account of even the 

 simplest physical phenomenon. In all real cases, although some one effect may 

 often predominate so greatly as alone to attract attention on a cursory view, the 

 actual complexity is so great that it is only by deliberately leaving out of consi- 

 deration what we believe to be the accidental accompaniments of a phenomenon, 

 and confining our attention to what seems to be its essential and characteristic 

 part, that it is possible to make it the subject of mathematical calculation. The 

 consequence is that the problems treated of in mathematical physics are not the pro- 

 blems presented by nature, but are problems suggested by these and derived from 

 them by a process of ideal simplification. There is therefore always a possibility 

 that, in the simplifying process, some apparently trivial, but really important, 

 feature of the actual phenomenon, to which the ideal one is meant to correspond, 

 may have been overlooked. When this is the case, the fact will reveal itself sooner 

 or later by the occurrence of discrepancies between the results of mathematical 

 theory and those of experimental investigation. Such discrepancies are the finger- 

 posts pointing to new discoveries ; but the experimenter w r ho forgets the inevitable 

 limitation to the authority of theoretical conclusions, arising from the conditions 

 I have alluded to, is apt to disregard them, and perhaps conscious of laziness and 

 want of care in his method of experimenting, or sometimes from a want of proper 

 self-confidence, he attributes all anomalous results to "the unavoidable errors of 

 observation." 



Two classes of experimenters are safe from falling into this danger. There are, 

 first, those who, the first time they observe any thing that is not provided for in 

 their text-books, conclude that the Law of Gravitation ought to be reconsidered ; 

 secondly, there are those who, with scrupulous care, take account of all the 

 conditions which are known to be able to affect the phenomenon they are investi- 

 gating, and are thus able to say, with well-founded confidence, when they meet 

 with some unforeseen result, that it must indicate the operation of some unrecognized 

 cause. 



A brilliant example of this latter mode of working and of the discoveries to which 

 it may lead has recently been afforded to us by the researches of Mr. Crookes, some 

 of whose results, as embodied in the now well-known instrument which he has 

 called the " Radiometer," have attracted much attention. It has appeared to me, 

 however, that the surprising nature of these results has to some extent called off 

 attention from the remarkable character of the scientific investigation which led to 

 them ; and it was at one time my intention to take advantage of the present oppor- 

 tunity for the purpose of trying, on the one hand, to render to Mr. Crookes the 

 credit which I think his researches deserve, and, on the other hand, to give a con- 

 nected account of the further investigations, both experimental and theoretical, to 

 which these researches have given rise. There seemed to be the more reason for 

 endeavouring to carry out the former part of my intention, inasmuch as an eminent 

 and accomplished scientific man had published, within the last few months, an 

 account of the discovery of the Radiometer, the unmistakable tendency of which 

 was, either intentionally or unintentionally, to depreciate Mr. Crooke's merits, and 



