TRANSACTIONS OF THE SECTIONS. 



and the resulting values of the new constants are — 



247 



An inspection of equation (2) shows — 



1st. That the range of any term P n sin [ 2 n 7r- + E„ J is 2P n , the maximum value 



being +JP»> and the minimum — P n . 



2nd. That the term goes through its cycle of values in the -th part of a year. 



3rd. That any decrease in the value of E„ amounts to a retardation of the epochs 

 of maxima and minima. 



Since the value of any term can never exceed that of its coefficient P n , it is obvious 

 that when P„ is very small the term may be neglected. Generally speaking P n be- 

 comes rapidly smaller as we advance in the series, and for most purposes all terms 

 after that containing P, may be neglected. 



The conducting power of the soil can be found in the following manner. Let x 

 denote the difference in depth of any two of the thermometers ; and let A . E K and 

 A . log, . P„ respectively denote the amounts by which the values of E„ (in circular 

 measure) and log,, P„, for the upper thermometer, exceed the values of the game 

 functions for the lower. Then will 



A . E„_A . log. P„ — 



V 



nitc 

 Tk' 



h being the conductivity of the soil and c its capacity for heat. 



The values of E 1 and E 2 in circular measure, and of log, P 1( log, P 2 , are as 

 follow : — 



And the results of comparing the thermometers two and two in every possible way are, 

 for the term in P x , — 



