Fig. 88.

V

266

CAPUT X. DE VARIATIONE

SOLUTIO.

Transferantur omnia , quae in praecedente problemate funt in-venta ad fuperficiem fphaericam centro inertiae I deferiptam, in quaA, B, C fuit poli axium principalium, eorumque refpechi momentainertiae Maa, M bb, M cc. Tum vero fit 0 polus axis illius, circa queincorpus jam gyratur celeritate angulari — 8 in feufum ABC, Ex C perO dudo circulo maximo COM qui eft quadrans, erunt arcus AM — met MO = m; tum in quadrante BA procludo capiatur AE — y, et dudlo

, r a a (a a — c c) cof;» .

quadrante CE arcus ES = 3, ut fit tangi; — ——---■ feu

1 bb(bb~cc)lmni

bb finiii fn aa cof m cofw . bb finmfy . f aa _ bb) cof»

-- --- atque tangS - - j -—--

aa — cc bb _ cc cc (na — cc)J\i

aa cof m cofi). (aa — bb) co Cn

. His ita definitis ob vires corporis centri-

cc (bb — cc)fn

fugas corpus conabitur circa polum S gyrari in fenfumEe, ita ut tempnfculo

,, , r . . rr ^ , . aa (aa — cc) dt z cof»« f n cof»

at delcripturum eilet angulum da> — _____ t ___

2 bb ft j cofQ-

88 (bb — cc) dt z f m fn cof» ^ ^ %x(aa — bb)dt z fmcofm cofra*

laa cof»; cofB- afffin^

Ducatur ergo arcus circuli maximi OS, qui fit = x, quem deinceps deter-

. aa (aa— bb)fm coLn co{n z

minemus, atque in probi, 02 , erit q —-—--—

2 cc/S

hineque ob motum gyratorium dementarem corpus gyrabitur circa polum

8 (aa - bb) d tfm cof;» cofw z /V

0 , ut fit arculus Oo = --•--: celeritas au-

ccf$

tem angularis g augmentum accipiet da ut fit da —aa (aa — bb)dtfm cof»w co fn z cofi

- . — —-. Nunc igitur pruno quaeri debet

ccf. 9 -

politio arcus OS, feu angulus COS, quo ad arcum CO inclinatur: quemin finem confideretur triangulum OCS, in quo cfiOCt=<}o 0 — CSss yo® — A et angulus OCS = unde reperitur:

COtCOS — cot ~” kangZ- ^ fn cof(wi -f n)

/(*»+«) +

-- , aa(aa — cc) co{ui z + bb (bb — cc) fm z

Eftverotang.(« + >,) = —-—- f--. i—, atque

(aa — bb) (cc — aa — bb) fm colm

cof»