344 
a oe ay! ag We le Y= 2a Ane Bo? 
(12) 
= Eat Bar Fh, 0? ee Say a ae 
n 
me yale) (a I), “Vout ) & Eh, 0° cos(2 (il a :)s 3 
n 
rE’ i =(5-)" (a (ny os, Nes (31 u. , i) 
, as vals 
ah =(5-) (n'a "2, Re! »sin(3 1 (1 * St 
, 1 \n nee , 1 Ba .& :) . | 
* 0 — (55) ae sa gt eho AG a 
This general solution involves multiple integrals, of the 
order 2n; but many particular suppositions, respecting the 
initial data, conduct to simpler expressions, among which the 
following appear worthy of remark. 
Suppose that having assumed some particular set 
w',...u, of values of the » arbitrary quantities w,,...w,, 
by 
we deduce a corresponding set of coefficients H' 
the formule (7) and (7)’, and represent by s‘\? and by 
pe: 
‘ 
i? he? 
‘ ‘ ‘ . 
de vale : ng system of 
Ayr, ree) Some one corresponding sy 
quantities which satisfy the equations 
et i SS ee 1 ‘ 
2a 4n1 7 | (5) 
n 
a = gh Bay his 
we shall then have, as a particular integral system, that 
which is thus denoted : 
aoa ‘ ‘ ‘ ed Be ang Fy \ 
ont] Ay Cos(e, +s t 214 5% i) 3 (4) 
x‘, and «, denoting here any arbitrary real quantities. If 
