+ 
d z +b- 
hence, 
Spherical Motion . 
' 2 C Z 
/Z Z - 
tf 2 + C 2 
xr 
: 2 ~£ 2 
f 2 + £ J 
X f 
* prpr . C % £« 2 
: % » or, putting - 2 — 
g L -t - ^ 
S 2 7 
y . 
~ ~2 * 
£ 
^ 2 + ^ + t a +^ Xy “^Z+7 2 Kg:: 
~~Z 7- 2 Tz 2 2 
o — c . c — b . a — c 
*. ,£ = ivrx^^ + ? r^i and — — -h 
r 2 — 
C 2 + £ 2 
,2 2 / 2 • 
£ — yy . 0 — Ci 
= N 2 x 4 — 2 4 -Vtti + 
2 , 2 
2 * 
y/' ‘{-c z c + b d z -J- b 
PP 9 
ss : — 2 : : j • - 
g 
: i — N 2 g : 
or 
jj 
J — lVi 
M 2 
—^4- ; but when g= i, j = and the fluents 
— N £ 4 
«t a -M a 
corrected accordingly, give the equation § log, of 
j 2 — M 2 
i log. of q— - log. of 
i-NY 
i — iS 
2 J 
consequently, ^ 
I ud • — 
M a 
i 2 — M 2 
r- N ~g 
i-^ 
2 2 
2 2 ? 
, and »r x i - N 2 g 2 - M 2 = s z g 2 x i - iV - M 2 ^ 2 ; but 
sg — S, therefore m z - S x » — N 2 = M 2 — N 2 ot 2 x y 2 ; or, expung- 
ing M aud N, m - $ = ===== X y -my x ? — — ^ is 
the equation of the curve whichis the locus of O upon the moving 
Ipherical furface ; or, if 
d x ±c % 
d z -c z 
a ^ 2 + ^ 2 p j r + b z „ 
A, Ta 72 = b and, = C, 
a z ~~b 2 
? 2 '2 
c — zr 
r> 2 2 2 
*^ 2 _ J 2 = _h - HI- . Which conclufion may be brought out 
with much more facility, by means of the three original equa- 
tions above inveftigated, which eXprefs the values of the three 
accelerating forces 4,4, and 4 , as will be (hewn hereafter. 
But it is of importance to have proved here, that this different 
method when rightly treated comes to the fame as the other. 
scholium 
