< Spherical Motion. ^ 20 
alteration mud be caufed by the other motions of the body 
which are referred to the other two permanent axes as iii the 
foregoing folution, and thus produce the forces - , t a „d 1 
t i i ’ 
afting at the nodes S, Q, and R, of the great circles BC, 
CA, and AB. 
If the two great circles DOE, CQA, be continued, they 
will meet in a point of the midcircle 90° from O, and make 
an angle whofe meafure is- the arc OQ , and if Mr. Lan- 
den’s motive force E" be refolved into the diredtion of the 
great circle CA, it will become E" x cof. OQ=E // x^ = 
- x dr — b~ x e 2 / 2 c>, the very fame as inveftigated in the fore- 
going propofition. But Mr. Landen's method, befides the 
force E perpendicular to BO, will like wile give two other 
motive forces perpendicular to AO and CO at O, which re- 
folved into the directions of the great circles BC and AB will 
alfo give the above inveftigated motive forces m thofe circles, 
and thus the two methods prove each other. 
I know then of no objeflion but what is already obviated ; 
1 lhall therefore proceed to the folution of the following pro- 
pofition , fhft, independent of the confideration of a momen- 
ta! y axis, the properties of which fhall be inveftigated after- 
y give the demonftration that the pro- 
perties above fhewn to belong to the parallelopipedon, alfo per- 
tain to any other body ; but as this has been done before by 
Mr. Landed, I fhall take it for granted here. 
Vol. LXXX. 
Z z z 
PRO 
