162 THEORY OF HEAT. [CHAP. III. 



satisfied, it is evident (Art. 170) that the quantity of heat which 

 determines the temperature of each molecule can be neither 

 increased nor diminished. 



The different points of the same solid having received the 

 temperatures expressed by equation (a) or v = &amp;lt;f*(x,y), suppose 

 that instead of maintaining the edge A at the temperature 1, the 

 fixed temperature be given to it as to the two lines B and C ; 

 the heat contained in the plate BAG will flow across the three 

 edges A, B, C, and by hypothesis it will not be replaced, so that 

 the temperatures will diminish continually, and their final and 

 common value will be zero. This result is evident since the 

 points infinitely distant from the origin A have a temperature 

 infinitely small from the manner in which equation (a) was 

 formed. 



The same effect would take place in the opposite direction, if 

 the system of temperatures were v = (f&amp;gt; (x, y), instead of being 

 v = (j) (x, y) ; that is to say, all the initial negative temperatures 

 would vary continually, and would tend more and more towards 

 their final value 0, whilst the three edges A, B, C preserved the 

 temperature 0. 



202. Let v = $ (x, y) be a given equation which expresses 

 the initial temperature of points in the plate BA C, whose base A 

 is maintained at the temperature 1, whilst the edges B and C 

 preserve the temperature 0. 



Let v = F(x, y} be another given equation which expresses 

 the initial temperature of each point of a solid plate BAG exactly 

 the same as the preceding, but whose three edges B, A, G are 

 maintained at the temperature 0. 



Suppose that in the first solid the variable state which suc 

 ceeds to the final state is determined by the equation v = (f&amp;gt;(x, y, t\ 

 t denoting the time elapsed, and that the equation v = &amp;lt;3&amp;gt; (x, y, t) 

 determines the variable state of the second solid, for which the 

 initial temperatures are F(x, y}. 



Lastly, suppose a third solid like each of the two preceding: 

 let v =f(x, y) + F(x t y) be the equation which represents its 

 initial state, and let 1 be the constant temperature of the base 

 A y and those of the two edges B and C. 



