8 REPORT — 1901. 



with a large measure of success, by means of an imaginary machine, 

 which shared with a map or diagram the characteristic that it was in 

 many ways unlike the things it represented, but might be compared to a 

 model in that the behaviour of the things represented could be predicted 

 from that of the corresponding parts of the machine. 



We might even go a step further. If the laws of the working of the 

 model could be expressed by abstractions, as, for example, by mathe- 

 matical formulae, then, when the formulae were obtained, the model 

 might be discarded, as probably unlike that which it was made to imitate, 

 as a mere aid in the construction of equations, to be thi'own aside when 

 the perfect structure of mathematical symbols was erected. 



If this course were adopted we sliould have given up the attempt to 

 know more of the nature of the objects which surround us than can be 

 gained by direct observation, but might nevertheless have learned how 

 these objects would behave under given circumstances. 



We should have abandoned the hope of a physical explanation of the 

 properties of inanimate Nature, but should have secured a mathematical 

 description of her operations. 



There is no doubt that this is the easiest path to follow. Criticism is 

 avoided if we admit from the first that we cannot go below the surface ; 

 cannot know anything about the constitution of material bodies ; but 

 must be content with formulating a description of their behaviour by 

 means of laws of Nature expressed by equations. 



But if this is to be the end of the study of Nature, it is evident that 

 the construction of the model is not an essential part of the process. 

 The model is used merely as an aid to thinking ; and if the relation of 

 phenomena can be investigated without it, so much the better. The 

 highest form of theory — it may be said— the widest kind of generalisa- 

 tion, is that which has given up the attempt to form clear mental pic- 

 tures of the constitution of matter, which expresses the facts and the 

 laws by language and symbols which lead to i-esults that are true, what- 

 ever be our view as to the real nature of the objects with which we deal. 

 From this point of view the atomic theory becomes not so much false as 

 unnecessary ; it may be regarded as an attempt to give an unnatural 

 precision to ideas which are and must be vague. 



Thus, when Rumford found that the mere friction of metals produced 

 heat in unlimited quantity, and argued that heat was therefore a mode of 

 motion, he formed a clear mental picture of what he believed to be occur- 

 ring. But his experiments may be quoted as proving only that energy 

 can be supplied to a body in indefinite quantity, and that when .supplied 

 by doing work against friction it appears in tlie form of heat. 



By using this phraseology we exchange a vivid conception of moving 

 atoms for a colourless statement as to heat energy, the real nature of 

 which we do not attempt to define ; and methods which thus evade the 

 problem of the nature of the things which the symbols in our equations 

 represent have been prosecuted with striking success, at all events 



