CONSTITUTION OF MATTER AND ANALYTICAL THEORIES OF HEAT. 



65 



P»art JTV. 

 Snmmary. 



The Relation of Mathematical Analysis to Physics. 



60. In the present part I propose to discuss briefly the theories expounded 

 in the preceding pages. With this end in view, I proceed first to consider the 

 nature of the relation of mathematical analysis to physics. Like grammar, 

 mathematical analysis helps the physicist to express his thoughts with clearness 

 and precision. Its chief characteristic is that it makes use of Symbols which 

 are not mere counters but represent Operations involving complex processes of 

 thought. Thus the language of mathematical analysis possesses the desired 

 quality of conciseness which is necessary for the proper concentration of attention; 

 but the mind falls to grasp its füll meaning without considerable efFort. 



61. The appUcation of mathematical analysis to phijsics consists in describing 

 the results of obseriation in analytical language; and, of course, in order that the 

 description may have any meaning, it is necessary that it be consistent: this is 

 the first requisite of the analytical description of a physical phenomenon. The 

 second requisite is that the description should be tme ^) ; and the third requisite 

 is that the description should be so simple that it can be recognised as a true 

 one with the least possible expenditure of thought. 



The object of the essay. 



62. The object of this essay is to shew how , in the present state of 

 mathematical analysis , it is fully possible to work out analytical theories of 

 the linear conduction of heat in a homogeneous solid; each theory being based 

 on definite suppositions as to the Constitution of the solid, and the description 

 furnished by it being, in all the cases that can possibly come under Observation, 

 not only consistent and the simplest possible but also true. I have thus worked 

 out three analytical theories. Of these the first treats the solid as a continuum 

 with the same properties in all its points, and is exact ; the second postulatea 

 the existence of molecules but takes no account of their internal Constitution, 



1) The sense in which the word „true" is used here is made fully clear by the example in 

 Art. 63. 



Abliandlg. d. K. Ges. d. Wiss. zu Göttingon. Ilath.-Phys. Kl. N. F. Band 2,4. 9 



