120 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



differences of temperature. In accordance, then, with the results 

 we reached in 45 7, both these types of co-ordinates must be 

 subject to the law that the value assumed by one of them at a 

 given moment can be regarded as an expression of the " notice " 

 taken by the system or a part of the system of two previous 

 configurations. 



56. 



The consideration of this example may suffice to illustrate 

 the fact that the sphere of operations of the method can only 

 include a given co-ordinate when it is possible, in the assumed 

 absence of other co-ordinates, to express the whole of the 

 energy of the system in terms of the former. Consequently 

 when Professor Thomson approaches questions in which 

 temperature effects are involved* it is necessary for him to 

 form and to justify some definite concept of the relation of the 

 whole energy of a body to its temperature, when the body is 

 merely hot, and is not the seat of an electric charge, of elastic 

 strain, etc."f Thomson follows Hehnholtz in assuming that 

 the quantity analogous to temperature is the kinetic energy 

 due to the molecular or unconstrainable co-ordinates. It is 

 unnecessary, therefore, to do more than quote Professor Bryan's 

 criticism, that in Professor Thomson's argument " properties of 

 temperature are assumed which . . . have not hitherto been 

 satisfactorily deduced from dynamical principles.''^ 



57. 



In face of mathematical difficulties that have baffled even 

 such giants of analysis as Helmholtz, Maxwell, and Thomson, 



* Op. cit., Ch. VI 



t So long as the specific heat of a body is constant the rise of tem- 

 perature may be (at constant volume) a measure of the energy given to it 

 in the form of heat. This fact alone does not enable us to express as a 

 function of the temperature the whole energy of the body. 



+ Bryan, loc. cit., p. 121. 



