CORPORUM RIGIDORUM A VIRIBUS &c. 343

ydw — zdu — da ((yy + 22) cof « — xy cof§ — xz cofy) — a (yy + 22)det fin # + nxydg fin g -f nxzdy fin y> . + nndt ( fiw — 22) coff cofy + xy cof et cofy — xz cof#

cof£—(finy 2 — fin£ 2 )

Zdu — xdw — da ((xx + 22) cof g — yz cofy _ xy cof ce) — s (xx 4. 23)ag fin f + ayzdy finy + nxyd x fin ce

+ nndt ((22 — xx) eo f# cofy + yz cof et eo fg — xy eo fgcofy — #2 (fince 2 — finy 2 ))

xdv — ydu — da (( xx -f yy) cofy — xz cof ce — y z cofg) _ a(xx -f yy)dy fin y + axzdoe fi» ce 4 - nyzdg fin 5

+ nudi: (_(xx — yy) cof ce cofg -f xz cofg cofy — yz cof#cofy — xy (fin g z - linee 1 )).

... dM

Multiplicentur jam hae formulae per --- , ct per totam corporis mo«

lem integrentur: quem in finem fint Mna, M bb, Mrc, momenta iner-tiae relpedu axium principalium, IA, IB, 1 C, et cum fitfxxdM = \ M (bb + cc — na) ; fyzdM =. ofyyd M = i M (na + cc — bb) ; fxzdM = ofzzdM = i M {ace -f bb - cc) ; fxydM = oobtinebimus terna virium momenta refpecfiu axium principalium, quibusefferius praeferiptus producitur, ita exprefia:

I, Momentum virium refpe&u axis IA in lenfum BC

— (a ad a cof# — actadet fin# -j- an (cc - bb) dt cof£cofy)

II, Momentum virium refpedlu axis IB in fenfum CA

M

-- (bbda cof g — abhdg fin g + an (an — cc) dt cof« cofy)

2 gdt

Ili, Momentum virium refpecflu axis IC in fenfum AB

M

(ccda cofy — nccdy fin y + an (bb — aa) dt cof« cof§).

<xgdt

C O R O L L.

799 * Ut ergo corpus circa eundem axem uniformiter gyretur, ternamomenta virium ob da ~ o, </# = ~o,, dg ~ o, dyz=o, erunt

Myy [cc _ bb) coi g cofy ^ _ M&j# (aa — cc) cof# cofy

' ~ " tg ' 2 g

rrr

1