120 Mr. R. Moon on the Integration of the General Linear 



Substituting this value of/ in (8), and also the above value of 



V 



rp, and observing that 



we shall get 



-(ct + mi (3)p-(3.f a -y.z-S; 



and since / involves x, y, z only, the terms involving p must se- 

 parately = 0. Hence we shall have simultaneously 



<>=«■/» -/»' (y) -/. y.'(*)-/S •/«- ?*-S, ■ (10) 



0=fm o -m 1 )/»-(« + m 1 ^)+m 2 ^-^,} . (11) 



"2 



both of which must be satisfied by/„. 

 Integrating (11), we get 



=A* ar +/ft(^ 2/) suppose. 

 Substituting this in (10), observing that 



we shall get 



o=m 2 /» -/,%) +( m * 1 - f-)*-(^+/ 4 )(/*+/3) -y*-«! 



And since /^ contains a? and ?/ only, the terms involving z must 

 vanish ; hence we must have simultaneously 



o=™ 2 /» -f b '(y) - (/* + W 4 -S, 



