CONSTITUTION OF MATTER AND ANALYTICAL THEOEIES OF HEAT. 



25 



Favt II. 

 Discontinnons Tbeory^). 



Formulation of a discontinuous theory of solids. 



25. In the present part I propose to examine tlie phenomenon from the 

 point of view of those theories ivJiich postulate the existence of molecules but take no 

 account of tlieir Constitution. With this end in view, I proceed to formulate a 

 simple and typical discontinuous theory, of solids, in which, for the sake of clear- 

 ness, certain unessential points are detailed. 



Taking a centimetre as the unit of length , snppose that each molecule is a 

 circular cylinder, with its axis parallel to the asis oi x, of length X and cross- 

 section of diameter X ; further, suppose that each molecule oscillates, parallel to 

 the axis of x, about its mean position , the length covered by its axis in any 

 oscillation being less than 2A. Thus the slab consists of rows of molecules, 

 parallel to the axis of x; and the motion in each row is the same. Suppose 

 that the rows are most closely packed; also suppose that the distance between 

 two contiguous molecules in a row is never greater than 21. 



Consider one of these rows. Suppose that it contains r assemblages, 



A^, A^, . . . 



the number of molecules in each assemblage being s. Then with any assemblage 

 A,^ is associated a quantity T^if) which depends only on the molecular motions 

 in A^ at time t and which may be called the temperature of the assemblage at 

 that time. 



The Problem of the linear conduction of heat may now be thus formulated: 



1) lü working out this theory I have received great help from the writings of Lord Kelvin, 

 Larmor, Maxwell, and Poisson. And of these writings the following have been specially 

 useful to me : 



Lord Kelvin's „Populär Lectures and Addresses," Vol. I, The Size of Atoms. 

 Larmor' s „A Dynamical Theory of the electric and luminiferous Medium," Part IIL (Phil. 

 Trans. Vol. 190) Arts. 11 — 12 and 48—51. 



Poisson' s „Theorie Mathematique de la Chaleur," Chapter IV. 



Abhandig. d. K. Ges. d. Wiss. ZQ Göttingen. Math.-Phys. Kl. N. F. Band 2,4. 4 



