T)t Pietro FRANOfiiNi . a8i 



dine fra quattro variabili Qdx^ -+- l\dx\ìy-h Sdx^dzA-ldx^du 

 -f- \dxdy -h Zdxd's -+- Xdxdu ^V{\)dxdy'- -\- ^{^\)dxds' -^ 

 Y^.{l)dxdu,'■-\- S( 1 )dxdydz -f- T(. l )dxdyda -+- V( ) )dxdudz 4- Z( i )/^«?=_; 

 4- Y{\)dyd'z -4- P(a;/y/^/ + ^(2)4^ 4- R(3)«'ys' + .S(a)//yz^' -+■ 

 T(ayy=-///</^ -^V(aX)lV2 + Z{,^)dy'du -4- \{'2)d'ydz -+- ¥{6)d'ydu, 

 H- Q(-J/'^> +- RC^) ^-'^ - ♦• S(3)/fe//'7i + T(3yWzi -+- \{?,)dz'du -h 



e posto che il suo integrale piimo completo sia kdx^ H-- Bdxdy 

 H- Cd dz -X- \)dA du H-- E^' ~+- Ydydz H- G^yfl'z-; -4- ì^d^y -f- I//^' 4- 

 L(/'s -f- M^«^;s^-i- N^M*4-0<:/*z^ = ct/x-*. Differenziando e parago- 

 nando i tti-jiiini sinjiili si deduce 



B=V- ^«i, C=Z-^^^', D=Y--'^, Q= ^i , r.= §^ + f 



dx dx dx dx dy dx 

 dk dC dÀ. dD 

 ^ = dz -^ 7x' ^ = du-^ dx^^'^ 



dx dx 



p / JS(4) X -, 1 



j T-d yt - -j^ \ j du\ espressione esatta, perchè dalle condì- 



In seguito si trova E = - / Z(i) - '^\ F-Yfr) - '^— 



a \ dy / ^ ' dv ' 



^ = ^(^) - 'l!7' " = ^(•^)' ' = I (/^^3y-. M y L=p(4), 



Tomo A'/. N n M = 



