46 PROFESSOR KELLAND ON A PROCESS 
Which equation is reduced to 

D(D-1).... D—r41) v=a es v (1.) 
he D D— 1 D 
by the condition f (— — +) = pat i (- =) (2.) 
1 
taper f D 
pris 4 
— = Seeeh 
iz 7 
the solution of which equation is 
D 1 
up) ho pease 
(2) 
one as 
[a Dee 
2 St | r, be 
whence i ve pe 
ey el 
| fi 
(RDE 
——+p-1 
=a") L can atl, 
| 
jor 
=( cae Als, aa ~ 
Now ¢ is the solution of equation (1); or, which is the same thing, of 
- 
adv _ nae 
Pcs 
v=Ae*” isa value of v; and hence, finally, 
ae 
Fu 
y=(—) ade 
=B d, e re where B is an arbitrary constant. 
It is evident that any other of the 7 roots of the equation =e" would 
satisfy the conditions, or that any one of the roots of a will produce the same 
result as a itself. 
This example affords an excellent illustration of the process. 
Let us take, in the next place, the equation which occurs in the theory of 
the Figure of the Earth; an equation which has been solved by Professor Boots, 
in his admirable Memoir in the Philosophical Transactions for 1844, p. 251, but 
whose process is necessarily restricted to integral values of 7. 
2 Pu t(it+l1l)u 
Bx, 2. Tang uD #0, 
The equation is— 

