MOTVS FLVIDORVM. 34.9 



elicinmus , aj tioftrum inftitutum plurimum con- 

 ducet has formulas difFerentiales ad (blum elemen- 

 tum dx reuocare quod facile fit , dum ex illius 

 fbrmae integrabilitate eft 



^dJJ — ^cT^^ ■> ^dr^^ — \Tlef ^' ^JT^ — dHl 



vnde confequimur : 



U =«(ii)+t,(i^)4-^(i^)+(i|) fimilique modo 



d j ■' ' ^d y d y ' d y 



yN=u(y^)+v('^)+w{^)+(t^). 



Cum iam pofita virium acteleratricium P, Q,, R 

 a«flione : 



/(P dx ^- Q^dy -\-Kdz) — S 



et in fluidi elemento , quod confideramus preflione 

 — p et denfitate — ^, hanc inuenerimus aequa- 

 tionem : 



'-^cz^LgdS-l^dx-Vdy-Wdz 



in qua tcmpus t conftans afflimitur , quoniam ia 

 hac hypothefi eft : 



dx('^)+dj('^) + dz{^f) = d(^ 



erit hac redudione in reliquis membris obferuata' 



\}dx-^Vdy--^W dz—udu-^-vdv-^-ivdiv-^d^^- 



qnae forma cum fit inte?,rabilis habebimus : 



