( 26 ) 



radius curvaturae hujus curva? , semper exprimetur per 



t/ d LJ \ a "i L 

 l + (~dT)\* (i+n^'tfT 



d'U dn 



eff 



ponendo dU = wcTT: jam heec expressio ope coefficientium duTerentia- 

 lium superficiei , est exprimenda : hujus quaestionis solutio requirit rela- 

 tiones (a5) in sectione priore evolutas: mutando x' ,y' , in T, U , fiunt 



x = Tcos<p Usincp cosQ 



y Tsin<p -j- Ucoscp cosj 



z = Usinj) 



notandoper ty angulum (T, x") et per 6 angulum inter plana TU et 

 unde concluditur 



dx =r dTcos(p crtJsin^ cosQ 

 dy = dTsin(p -]- dUcos(p cosd 



quos valores scribendo in aequatione difFerentiali superficiei , 



dz = pdx -\- qdy 

 prodibit 



f/Usin9 = p [cTTcosfp </Usin(|) cos9 ] -\- q [fZTsin0 -f dUcosQ cos0 } 

 tinde 



pcosty -f- ^sincp 



+ psin(p cosfl 



f" (sin9 4-/ >cos 9 sm $ ycosflcoscp) (dpcosty + c?^sin<J) )-i 

 , (pcostp -\-qsin(p} (dpcosfts'axp dqcosQ cos(f)} J- 

 (sinfl -\- psinQ cosft qcostycosft )* 



jam loco ^p et dq substitui deberent 



dp = rdx -{- sdy, dq = sdx -{- ^rfj' , 



scriptis in his pro dx et dy illorum valoribus supra inventis. Calculus vero 

 brevior reddi potest, supponendo planum xy tangens in dato puncto , axem 

 z normalem ad punctum M superficiei , planum xz per circulum maximi 

 radii curvaturae et planum yz per circulum minimi radii utrumque due- 

 turn. His positis, et simul p = o, q o, s o ( Gamier, calc. 



