U. x' d' z-\-^' X' ddz+^' X dz + (^ z-{-ot.i x^ d dy 

 •\-y' X dy -\- i' y — o, 



ex quibus per triplicem difterendationem fequentes pro- 

 venient aequationes : 



III. X' d' y -\- {:i + ci) X' d\y -\- {2. a + y) X d dy 



-\-{y-\-?.)dy-\-^x'.d'z + {2^ + Z)xddz 

 + (^4 ^)dz — o, 



IV. X' d'z\-{:i -h^')^'- d'z \-{^^<-\-^')xddz 



^l^' ^^')dz\-a.' x' d'y -\.{zaJ -\-y')x ddy 

 -f (V + £')<>' =0, 



V. x'' d' y ^ {6 -\- a.) X' d' y -\- {6 -\. i^ ci -\- y) X d^ y 



H- ( 2 a + 2 y + e) d dy -\ ^ x^ d\z 



+ {^(i-\S)xd'z-\ {2 (i+ 2^ + ^)ddzZZ0y 



VL X' d' z -\ {6 -^ (^y) x' d' z + {6 + ^(^1 + 6') X d' z 

 -+- ( 2 (3' + 2 5' + /' ) r/ // 2; •+ a' .V d^y 

 4-(d. a' -{- y') X d' y -\ {2 a' -f 2 y' -\ s') dd y:zo, 



VII. X' d'y -i-{9 4-a)-v' ^/^ J + ( i 8 4 ^ a + y) Jf ^^ 



+ ( 6 + ^ a + 3 y + £ ) ^' / + p .V' rf' 2; 



+ ( 6 |3 + 5) X ^/^ xr + ( 6 (3 + 3 J + 2;) ^' 2=: o , 



VIII. x'd' z-i-{9-i- 13') Jf' ^" 2; + (; r 8 + 6 j3' + 5') xd'z 



+ {6 \ 6 p' + 3 5' + <^') ^^ 2: + a' X' ^^ j/ 



+ (6 a' + y') X d'y + (6 «'+ 3 y'+ e') tf^j/ - o. 



Pro aequatione autem inuenienda , quae fola difFerentialia 

 ipfins j' inuoluat, fcquens fiat combinatio: 



VII. X'-\-y.X x\-{- VI. V X' 4- III. |Jl A- +- IV. {JL'' X "^ 



tumque in aequatione refultante coefficientes differentia-*-' 

 lium ipfius y nihilo aequales ponantur 



x' d" 



