^44' 



(12) 



i{l3) 



*^,o-V2W v\o\J-.oo g^iJ^g^Jho'' V (01 » ^'V 



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 

 ii^i.,.u , of values of the n arbitrary quantities u ,.,.u , 



we deduce a corresponding set of coefficients h" , h'^^ ., by 

 the formulae (7) and (7)', and represent by s\^ and by 

 ^ 1,1' * • • ^h,V • • • ^^« 1 ^0^6 o"e corresponding system of 

 quantities which satisfy the equations 



n s2 



we shall then have, as a particular integral system, that 

 which is thus denoted : 



x\ and Bi denoting here any arbitrary real quantities. If 



