the Heat-conductivity of Stone. 253 



From these the mean value of N was found to be 84*29 ; and 



since 



sin « — a cos a N" 



a — sin a COS a I v Q 



= 0-784, 

 it follows that 



a = 125° ; 54; 

 so that 



K = 0-00609, 

 and 



E = 0-00226. 



Fourth method. — We now come to the last and most impor- 

 tant method, to use which, however, requires a certain amount 

 of experience in curves of this kind. If the stream of water 

 outside the ball had been kept exactly at the lowest tempera- 

 ture (16°'4 (J.) all the time, then the centre would have cooled 

 more quickly at the beginning, and the last observation would 

 have been less than it is. A curve for the cooling of the centre 

 when the external temperature is kept perfectly constant we 

 shall call, for brevity, an exisothermal curve. We see there- 

 fore that the exisothermal curve for 16°*4 C. will be altogether 

 below the curve AAA, and the exisothermal curve for 19°*9 

 will be below AAA for some distance at the beginning, and 

 that it then cuts AAA and remains above it. 



If there are two exisothermals for the external temperatures 

 x l and x 2 with the same initial temperature of the centre T, 



v v 



then, since at any moment — of the one equals — of the other, 



v o < v o 



it follows, if Y" A and P /X B (fig. 3) are the exisothermals in ques- 

 tion, and if OA" represents x x and OB" represents x 2 , that 



so that if the point P is given and we want to find PQ, we 

 have the equation 



Now it will be observed from this formula that all the exiso- 

 thermal curves that we can draw from 19°*9 to 16°'4 C. almost 

 coincide with one another for small values of the time, and 

 even at 2700 seconds their distance asunder is not very great. 

 With practice it is not difficult to see between what exiso- 

 thermal curves lie the different parts of the curve obtained 



