MOTVS FLVIDORVM. 



291 



quibus vaioribus fubftitutis tres illae aequationes abibunt 

 in has : 



^WTT)-+<Ty)+^+('-I"(L+»)+^-H-Nr:o 

 ^ Hh( ^ )+< ^ )+ ^ )+(x . nx . l+(/)+/ix . bM: - 



("Sr^^fj+^^J+^V^M^+^^-Nfc» 

 60. Manifefium iam eft, his tribus aequationibus 

 fatisfieri fequentibus tribus valoribus : 



/mM ; X = N; \k-zzn 

 quibus continetur criterium , quod confideratio follicita- 

 tionum fuppeditat. Hinc ergo iequitur fore recepto 

 defignandi modo 



du 



d v 



du 



d 1» d v 



div 



dy — d x 7 dz — d x 1 dz — dy ■ 



hae autem ipfae ftjnt illae conditiones , quae requirun- 

 ttir , \'t haec formula udx-\-vdy-\-wdz fit differen- 

 tiale completum. Ex quo hoc criterium in eo con- 

 fifiit , vt ternae celeritates n, v et w eiusmodi efle de- 

 beant fun&iones ipfarum x,y et z vna cum /, vt pofi- 

 to tempore confiante formula udx-\-vdy-\-ivdz in- 

 tegrationem admittat. 



61. Cum ergo pofito tempore l conftante, feu 

 W?z=o, fit 



du— Ldx-i-Mdy-hNdz 



d v zr M dx -\-mdy -+- vdz 



div — N dx -+- n dj -+- v dz 

 valores autem pro R, r et g fiant : 



R=-2(L«+M« + N«;+ g) 

 r zz:—2.(Mu-\-mv -+ kw+^) 

 f = — 1 — z(Nu-\-nv-\-vw-\-ffl) 

 Tom.VI.Nou.Com. Pp pro 



