SECT. IV.] UNIFORM LINEAR MOVEMENT. 4.5 



supposed that the initial temperature of the first point, which was 

 a, became a at the end of the first instant ; hence if this initial 

 temperature had been 2 a, and if all the other temperatures had 

 been doubled, it would have become 2 a . The same would be the 

 case with all the other molecules b, c, d, and a similar result 

 would be derived, if the ratio instead of being 2, were any number 

 whatever g. It follows then, from the principle of the communica 

 tion of heat, that if we increase or diminish in any given ratio 

 all the initial temperatures, we increase or diminish in the same 

 ratio all the successive temperatures. 



This, like the two preceding results, is confirmed by observa 

 tion. It could not have existed if the quantity of heat which 

 passes from one molecule to another had not been, actually, pro 

 portional to the difference of the temperatures. 



64. Observations have been made with accurate instruments, 

 on the permanent temperatures at different points of a bar or of a 

 metallic ring, and on the propagation of heat in the same bodies 

 and in several other solids of the form of spheres or cubes. The 

 results of these experiments agree with those which are derived 

 from the preceding propositions. They would be entirely differ 

 ent if the quantity of heat transmitted from one solid molecule to 

 another, or to a molecule of air, were not proportional to the 

 excess of temperature. It is necessary first to know all the 

 rigorous consequences of this proposition; by it we determine the 

 chief part of the quantities which are the object of the problem. 

 By comparing then the calculated values with those given by 

 numerous and very exact experiments, we can easily measure the 

 variations of the coefficients, and perfect our first researches. 



SECTION IV. 

 On the uniform and linear movement of heat. 



Go. We shall consider, in the first place, the uniform move 

 ment of heat in the simplest case, which is that of an infinite 

 solid enclosed between two parallel planes. 



We suppose a solid body formed of some homogeneous sub 

 stance to be enclosed between two parallel and infinite planes; 



