INTERCHANGE OF HEAT — -VON BEZOLD 405 



It we write equation (23) in the form 



H H 



u 2 = C f 6 2 dh - C f 6 t dh + u x 

 



and choose / t as the initial point for counting the time so that t t = o 

 we may write 



H 



u 2 = C J 2 dh + K 







or briefly, by omitting the index 



H 



u = C f Odh + K (24) 







where K is a constant whose value depends on what we adopt as 

 the zero of energy. Theoretically it would be most correct to adopt 

 for this the absolute zero, but frequently it will prove advan- 

 tageous to start from the zero point of the ordinary thermometer 

 scale. Of course by doing this one may in certain cases obtain 

 negative values for the energy, but this will not be objectionable 

 so long as we are clear as to the meaning of this result. 

 The last given equation can also be written in the form 



H 



u = CH. - I ddh + K =CH 6 +K 

 H 



where we put 



// 



1 f dh = 6 (25) 



But this value 6 is simply the average temperature of a prism cut 

 out of the ground to the depth H beneath the unit of surface, while 

 CH is the so-called water equivalent of this prism if we adopt the 

 expression used in calorimetry. 



If now we designate by 8 t and d 2 the values of 8 corresponding 

 to the times t t and t 2 we obtain 



u 2 -u 1 = CH (6> 2 -BJ. (26) 



This equation may be interpreted thus: 



