356 CAPUT XVI. DE MOTU GYRATORIO

(3 cofjf — x cof 3 ) dM

Q

R

eei fees f

ZF 3

(.v cofj; — y cof£) dM

Eft autem

ZF =r / ((/ cof £ - a;) 1 3 - (/ cos »,- - y) 2 + (x co _ z ) 1 )fcu ob cof ^ + cof») 2 -p cof& 2 = 1 :

ZF — / (xx - 2/**cof£~ tsy cofy,~isz cof$ + xx+yy+zz).Cum autem in corporibus coleftibus diftantia IF = s fit feni per vehemen-ter magna prae ipfo corpore feu quantitabus x t y, z, erit fatis exade ad

3 * cof<? + VJ cof», + 32 co

noftrum inflitutnm

+

ZF 3 x 3 1 s*

Quoniam vero ob I centrum corporis inertiae, et IA, IB, IC ejus axesprincipales habemus fxdM = o, fydM. — o, fzdM — o, atque JxydM= o, fxzdM =z o; fyzdM — 0, prodibit his faiftis fubftitutionibus:

p _ . (3 yy cof»; cof— 3 zz cof») cof3) dM _ 3 ce cof») cof3

_ j ~ 4 “ ~ T 3 ‘

f {yy — 22) dM

• Q= f(?z _ dM . t R _ .»"cr^cor,

X 5 J 5

/ 0* - yy) M

Verum ob data momenta inertiae eft

. ■ fxxdM — 4M ( bb -f cr — aa)', fyydM = ( aa + cc — bV) et

fzzdM = (aa + bb — cc): quocirca erit(rr — /»/») cn(»j cof3

P —

Q =

3Mtr (nti — rr) cof £ cof 3

^_ ^Mrs (bb — t?a) cof£ cof»)

COSOLL. 1.

Si 5 . Haec igitur momenta virium non rigore geometrico funt de-finita, fed tantum valent, quando di flantia putidi attrahentis magnitudi-nem corporis attracfli longe fu pera t. Atque fic commode evenit, ut eaper momenta inertiae tam concinne exprimi potuerint,

COROLL.