343 
a ane i A,» (6)’ 
in which, by (7), 
H, =H, ¢ (7)" 
It is important to observe, that by the form of these equa- 
tions (6), (which occur in many researches,) we have the 
relation 
n , 
Ryu telat ca 0, (5) 
_ if q be different from 7; and that, by (5) and (5)’, we have 
also the relations 
ae 
21 9 = 1, (8) 
n =e U 
261 iy Ay = 0. (8) 
In the particular integral (4), we may consider Uys. ott 
n 
as arbitrary parameters, of which x, and ¢ are real and ar- 
__ bitrary, while s°. and a, are real and determined functions ; 
and hence, by summations relatively to the index r, and 
_ integrations relatively to the parameters u, employing also 
_ the relations (5) (5)' (8) (8)’, and Fourier’s theorem ex- 
_ tended to several variables, we deduce this general integral, 
. to all arbitrary real values of the initial data: 
(n,,) _du)(e Ey cos+F, , sin) iy % ©, 53 (9) 
n co fea} 
Ty hay =i Ha % sy aA nee, ; (10) 
= Zt AL, (%, cos a, +y'. ity sin t,) 
1 (11) 
a n , ol . i 
F.= =6)1 Any (2, cos ts. + zs, sin ‘s,)3 
