372 CAPUT XVI. DE MOTU GYRATORIO

dx — aNafr cof^ (cof^ cofS- — fin^ cof»;)et xdq — — iNdt col^(fin^ cof9 -f cof^ cofy).

Si jam centro virium F motum quemcunque tribuamus, etiam tamdiu IiJ*formulis uti poterimus, quamdiu arcus AQ =: « manet tam parvus, ut

contractiones adhibitae locum habere polluit.

PROBLEMA . pg.

844. 8! corpus habeat duo momenta principalia aequalia, ac circa

tertium axem lingularem propemodnm gyretur, centrum autem viriumuniformiter in circulo circa centrum inertiae corporis circumferatur, adquodvis tempus /itum et motum corporis determinare.

SOLUTIO.

Fig. io/?. Progrediatur centrum virium per circulum maximum XFY celeritate

angulari = S, ac tempore elnpfo = t ex X pervenerit in F, ut fit XF = F/.In fphaera igitur confideretur circulus fixus XZY, in quo fit Z polus cir-culi XFY, ut fit angulus XZF — St. Nunc autem verfetur axis corporisfinguiaris in A , ponatnrcjue angulus XZA = A, et arcus ZA = p: tumvero corporis quafi primus meridianus fit AB, difians ab arcu ZA anguloZAB = q. Porro gyretur mrac corpus circa axem 10 , ut fit arcus mini-nius A 0 =«, et angulus BAO = celeritate angulari =r e , quoniam jamnovimus eam fore conflantem, ct pundfum A abibit tempufculo dt in a,ut fit A a = edt fin x — xedt ct angulus aAO redtus: quare ob ZAO = q-f £ erit ZAs = q + q — 50°, ideoque demiffo ax perpendiculo ad ZA,

fiet ax = — xedt co i{q + f) et A« = xedt fin {q + q), unde colligimus

npdt coff /J 4 - ai

t t^J '•i

quia ,or-

ww l' - Xrt \ \ / ' ' - UU1«

\\x\p

pus quafi circa polum A gyratur, erit dq edt. Denique in triangulo

AZF ob ZA — p' ZF — 90° et AZF — A — t!'/, reperitur cofFA — cof£= fp cof(A — St)-, et cotZAF = — cofp cot(A — St), Ponamus brevi-

— tan g(A — St)

tatis gratia angulum ZAF — P, ut fit tang@ —

.-, erit BAF

= <p — q', hiucque cofBF — cof(<£» _ q) fin<f = coft; et cofCF = fin(<p__ q) fin g = coi &. Eli vero fin (p fin £ — fin (a — St) et cof£> fin £ = _cofp cofi^A - St),

ideoque cofjj — _ cofp co {q cofjA St) + fin^ fin (A — St)ct cof& = co [q fin (a — St) + cofp fin q cof(A — St),

Unde