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CAPUT V. DE MOTU GUOBORUM,

fin (fx + B) cof(y + C) = fin v y + B) co((fx + C) i

quae ob finivi colN — i fin(M +■ N) -f i fin(M — N) reducitur ad fin(fx — v) cof(B — C); hocque modo redudionem pro aliis formulis infii-tuendo, reperimus:

fm{(x + B) cof(y + C) - fin(y + B) col(// + C) = fin(^„ y)cof(B _ C)

fin(/x + B) fin(y + C) _ fin(y + B) fin(ju + C) — — fin(jw. — y) lin (B _ C)

cof(u + B) cof(y + C) — coi (y + B) cof(^ + C) = — fin (jtf— y) fin (B — C)

ubi fin(/w — y) per formulas ufurpatas datur, efi enim fin — y)cof/

fin m fin»

PROBLEMA. iF.

1184. s> globus ex materia uniformi confiet: vel faltem ita fuerit-comparatus, ut omnia momenta inertiae fint inter fe aequalia, eique ini-tio impreffus fuerit motus quicunque, determinare ejus continuationem,

SOLUTIO.

Cum hic fit aa — bb — cc , feu momentum inertiae refpedu omniumdiametrorum = Mna , prima aequatio integrata praebet aap = Conft,unde p erit quantitas coufians. Statuatur ergo p =: h: et ternae aequatio-nes difterentiales priores induent has formas:

I. — dq cof (A + $ + (p) + q (r/A + dtp) fin (A + B + (p) + —^

aa

dt fin (A + ?• + £) = o

II. — dq co[(/x + 3 - + (p) -f q {dS + dtp) Cm(/x + £• -f <P) + ——

aa

dt fin (/x + <p + |) = o

III. - dq cof(y + B + <P) + q (</$ + dtp) fin (y + & + ©). + iMl

aa

dt fin(y + (p + ^) = o

quarum autem fufficit binas confideralTe, quia inde jam nota efi cqn-clufio p — h. Iam per fuperiores reductiones binae pofieriores itacombinentur:

II. cof(v + & + %)) — III. cof (jx + B + (p') praebet

q (//£