CORPUSCUL. A VIRIBUS QUIBUSC. &c. S9

unde fit = c et s = ct. Revocentur vires a tubo exertae ad easdemdt

ternas directiones, fintque SP = X, SQ^= Y et SR — L, et ob celerita-

ttem immutabilem Xdx + Ydy + 'Ldz — o. Deinde quia dt — -£i-, loco

dt confians erit elementum ds, ex quo formulae principales eruntA ccddx — igXds 2 ; A ccddy — igYds 2 et A ccddz — 2gLds 2exifiente dx 2 + dy 2 + dz 2 — ds 2 . Tota ergo vis, quam tubus in cor-pufculum exercet, fiet

AccS (ddx 2 + ddy 2 -f ddz 2 )

/(X* + Y* + Z*) = igdi - - = V,

X

cujus directio inclinata erit ad rectam SP angulo cujus cofinus — --- —

JJ — ; , ~r~ ' 2d 80 angulo cujus cofinus -3 =r

/{ddx 2 + ddy 2 -f ddz 2 ) ^ & V

ddy z

“ ., ,-■' et ad SR angulo cujus cofinus —- =

/{ddx 2 + ddy 2 + ddz z ) 6 1 V

ddz

—-—----. Huic autem vi aequalis et contraria eft

/(ddx 2 + ddy 2 + ddz 2 ) 1

preflio, quam corpufculum vicifiim in tubum exerit,

CO ROLL. I.

229. Si radius ofculi curvae in 8 ponatur = r, ob vim normalem

Ace

: V et celeritatem — c erit r = -—, ideoque

ds 2

2gV

• - fumto ds conflante*

y f {ddx 2 + ddy 2 + ddz 2 ')

C O R O L L, 2 ,

230. Radii ofculi autem politio cum directione vis V, qua cor-pufculum a tubo urgetur, congruit, inclinabitur igitur is ad rectam

SP angulo, cujus cofinus = —- , ,, , — JJ ——> - , ad SQ angulo.

/(ddx 2 + ddy 2 + ddz z )

cujus cofinus =

ddy

/ {ddx 2 + ddy 2 + ddz 2 )

et ad SR angulo, cujus co-

finus efl =

ddz

y/'{ddx 2 q. ddy 2 q. ddz 2 )

M

SCHO-