438 PROFESSOR EVERETT OF A METHOD OF REDUCING 
cients in the same manner as above. The agreement as regards the annual term 
is very remarkable, extending, as it does, both in the determination from phase 
and in that from amplitude to the fourth decimal place. 
Note on the Equations 

At. HOOT hme omen 
@ The x 
The differential equation for the conduction of heat through the soil, the 
surface being supposed horizontal and the soil uniform, is 
duv_k d?u 
ditt e da 
This equation is satisfied if we assume 
vsPenea/ Be sin (ne +E, — an/ 270) 
Tk 
—e being the base of Napierian logarithms, and P any constant. 
To show that this integral satisfies the differential equation, put 
The equation then becomes 
u=Pe— sin (B—aa). 
Whence 
1 
z= = . Pe—2* cos (8— ax) = ee . Pe—2t cos (B— aa) 
a = — Pae—2r" { sin (8— ax) +cos (B—aax) } 
Ax i q 
d?u . Viet : 
d= Pave—= sin (8—aa) + cos (B— ax) +cos (8 —aax)—sin (B—axr) \ 
= 2 Pa’e—« cos (B— az). 
Hence 
du_ne 1 dv, but 1_Tk 
di Ta" dat? "8 nee 
Whence ) 
dv valent od? 
z= ar a or the differential equation is satisfied. 
it will be equally satisfied if, instead of a single term, we have a series of a 
terms of the same form as that above assigned to 2, and if we likewise pret a 
constant Ay. Hence we have the general equation 

