de nova methodo iritrgrandi. 



1 1 1 



dt = tdr + Ttla-f- 



il u = U tl V 4" « ^ '"> + •••• • 

 dp == JP (1 V rt-, -yj! a j+r . . . .^ . 



dq=ö,dv4-<J<la+- 



dr = 9?dv -\- rda -f 



ds = (Bdv-}-gda + \ 



Sit porro, w considerando tanquam functionem datam rariabilium et reli- 

 quomm quotiyniiutn difFeientialium , 



«Iw 



_ (w'dx+w"dy+w"'dz + w"dt + w''dv-fw^'du + -«"'dp 



-fAv'""dq + w'^'dr + wMs. 

 Tum aequaiio dv = pdx-j-qdy-|-rdz-j-sdt-j--\vdv, in hanc aljit: 



db + .... 



Quo nunc ex haec aequatione dv et v exearit, ponendum est 

 i) pX+ qY+ rZ + rZ+ st + w=U 



_., -,■ d'(p%-t- qn+ r^+ ST — u) 



Deinde debet esse 



, p% -»- q>I + r^ 4- ST — u 



"1' fp:*j' -+- q»' -4- r{' + st' — u) 



= etc. 



VX + qn + r^ -4- 5T — U 

 F.'^t auLcm d" (p% + qn -H r^ -H st — ti) 



= pi^'% + qd >j -+- rd"^ 4- sd'T — du 4- %d"p 4- «d' q 4- ^d' r 4- t d's 

 = pd'X4- qd'y4-id'Z4- sd^'J — d'U 4- :^d'p + >,,lNi -4- <d'r -f Td's 

 Id' (pX 4- qY 4- rZ 4- s"i — U) 



(— Xd'p • Yd'q - Zd"i- — $d's 4- ■;^a''p+ »d'q + ^d^i -f Td\* 

 = d'w~Xd'p— Yd^q-Zd'r — Td»s + a^d'p + »d'q + ^d'r-f-Td's 

 1' f piirro d'prs-n-, d'qssq, d"r=:r, d's = ö; 



_ j M (1-' X -f- w' d- y + w"'d ' 7. + V,-'-' d' t 4- w ^^ d' u -f « ' " d' p 

 *' ^'^ "~ / rf iv"" d' q 4- w '" d' r + W" d»"» 



= !' 



