CE^TRIFUGA CORP. SPHAERICI &c. 15, 



fph.ierici GL?SG —p(n—g)f dudiim in tcrminos feqq. 



(m -»- - "■'^-f- : r.x ) — m _(w-f-x) (m. -+-:m a-4--rjc) 2 — m 



3.v'M-i) 2»i_+-r — — — 



2 -"-H3 in-HI 



i_(m -4-2 mx-t- 2 r«) : — m 



'' '"'(;n-+-i m' 2'M-3 )(nM-r j 



§. 10. liudcni methodo prodit vis totius 

 fcgmenti fphacrici li iWi^W U=p(a-i-f) f du- 



2 n-Hi ;n-f-2 



(Jlum in terminos rcquentcs (? — 2?^-i-2r-») -5 



' 2(»l-+-i ) 



2 2n -f-l Zn-+-2 2 -"-+-3 2n-+-3 



[<}-V'(q ~2qv- ^ -2rv) ': — 7 (q —2jv-i-2rv] - -^ 



2n-f-i (;n-f-"i ) ( 2n-H 3 ) (?— r) 



Cafas S ectuidus. 



$.11. Pro Vi Segmenti GLP. Diftantia Arcns 

 GSYP eiidem efl a ccntro vorticis, fed mociificatio 

 virium uiuerfa. Itaque \t habeas vim pundli S, 



21 — « 



mafla eius non cfl duccnda in OS fed in OZx 



OS fit OS~^jquoniam conflans cfl: in Arcu GSP, 

 ct YZ~f , adeoquc Zz—dt. Annuhis fphaericae 

 fuperficici ab clemento S/circa Zz rotato defcrip- 

 tac, cnt znpbdt. Igitur Maffa cius —i' a-g)pbr/t, 

 et Vis centrifiiga huius annuli —{a-g^pbdt.O^Z. 

 OS^'^-—(!i-g)pb-''-'(b-t)dt, et integrando, Vis 

 ccntrifui^a totius fuperficiei fphacricae, ab arcu YS 

 circaYZ rotato, genitae =z:/'(^-?)(/'="'-4^'"''~'/^). 

 Si iam YZ=YX—b-m-x , ct YS=i;YG ,^ erit Vis 

 totins luperficici fphaericae, per Arcum GSYP re- 

 prjcfentatae , —p(ei—g)U^''^*(h'^—m-—2tnx—x^) 



21 — 1 2 " 



^Pi^^-S)^^ CjX . Fiat nunc OS variabilis, 



