55 o 
Mr. WlLDBORE on 
crofles BA, both O and Z ftill enter the odant ABC together, 
both pafs over it in the fame time, and both quit it or crofs CA 
together ; but in this cafe the track for Z upon the moving 
furface is lefs than, or within, that of O, Z eroding BA at a 
point nearer to A than that where O erodes it ; and O in both 
thele cafes fnifts its place on the moving fpherical furface 
making one revolution in the time that the whole curve 
WV / W'V takes in paffing under Z ; both curves being fuch 
^riat in the cafes above defcioed where the projedion of 
WV'W'V is a conic fedion, that of the track of O projected 
upon the fame plane will be a conic fedion alfo, that is, 
where it is Ihewn above that the projedon of WV'W'V is an 
hyperbola, that of the track O will be an hyperbola, and an 
ellipfis where that of the other is an ellipfis. 
And when Aa 2 = C£ 2 or£ 2 : a 2 :: A : C :: S 1 : /3% the track 
of O as well as Z is a great circle of the lphere, lince 
and f. CQ = — x f. AQ when O crofles CA at Q 
(fig. 4.); and when Z crofles CA cof. AZ 2 = f. CW 2 = 
, and 1. CQ ~ = - x — ^ nnr ] f c W 2 — 
^ a a c + a’ anai,L ' w — 
I 
I -f 
c*A 
LC + 
a* A 
i 
, confequently, a being, by hypothefis, greater 
a 
than c\ the fine of CW mud be greater than f. CQ or than 
f. CO when O crofles CA ; and therefore the point where O 
crofles CA muft be nearer C than the point where Z crofles it 
tne lame inflant, in the cale where both the tracks are great 
circles of the fphere, palling through the fame point B. 
2. It is now well known, that the momentum of inertia of 
the body round the axis whofe pole is O, is = Ma 2 /3 2 + M^y + 
MeT, and if this be drawn into » 2 , the produd Ms 2 x (a z 0 2 + 
