254 
MR. S. S. HOUGH OX THE APPLICATIOX OF HARMONIC 
which over sufficiently long intervals of time we may regard as uniform. A simple 
law which will serve for purposes of illustration may be chosen as follows :— 
W = - aPo(p.). 
The equations with which we have to deal will then be 
SU 
-g- + ^- 
0V _ 1 
dfi 
Cyfr 
dt ~ av/(l - /"“) 
“Ps (^) = V 
. (39), 
where, if we neglect the attraction due to the surface-inequalities, we may take 
^ - gC 
To obtain a particular solution of these equations suppose 
^ = — gi= — i/ (Co + U = Uq + Up, \ = Vq + Vp, 
where &c., are all independent of t. 
Substituting these expressions in the equations (39), and equating coefficients of t, 
we find 
1 
0 = 
a 
If h be a function of fx alone, these will be satisfied by 
U. = 0. = 
^ ^ laojfj, Cfx 
provided be also a function of p alone. 
Next, if we equate the terms independent of t in the two members of (39), we 
obtain 
H- i 
1 
U, + 2o,,.V„=-^^y(l-r) 
Ui — 2 w/aUo = — 
a ^{1 - fi-) d<p 
1 r0 
I 
ICfJ. 
«Pa(p) = Ti£{v/(^ - p-)}. * 
