T 
fr. Landen’s Invejligaiwh of 
b' nr + c''a"sfd 1 if 
X 
i- 
l 
7 
v' D nf - Cy" x V D* 2 - By 2 
Dm z -Cd z 
+ 
,22, 22, / 2 
b m c a + « 
x D’ ! /» 
2-4 
A y 
vWf - Cy 2 X V'i,, /•_..}}/ x 
2 2 
//i /i • 
BCoV 
: which, 
■when D/;r is - CL% becomes— 
- <2" ~j- b z . 0 Z y 
e ^BC . a 2 - 
d z 4* b 
It is evident, that X^X hyp. log. of ~~ , the value 'of 
T in that particular cafe, will be infinite when y\$ — a ; and this 
conclufion agrees with what is faid above refpeding the motion 
of the momentary pole along the great circle CR (fig. 2, 
and 3.). 
I have not found, that the value of T will, in general, be 
afligned by the arcs of the conic feci ions ; but my Tables * (hew, 
that it will be fo afligned when Dm 2 is = B a\ and in fome 
other particular cafes. 
We have hill to invefiigate the track -of the momentary- 
pole in the immoveable concave fpherical fur-face, which we 
mu ft conceive to furround our moveable convex fpherical fur- 
face, fuppofing the center of both tiiofe furfaces to coincide 
with the centers of gravity of our parallelopipedon : which 
central point is always in this difquifition fuppofed at reft. 
Let AL be the projection of part of a great circle CL, 
at right angles to the great circle Vp LN ; then will the 
fine of the arc CL be — ; its c-ofine 
Vl) 
z /t z n ~ — BC A/ 2 
J) z ^ D a z m z n 1 ■ 
2 „ 2, 
■ Dm 4 — Cam 
, 22 . 2 
Ca n . y 
V D z 
tn n 
2 BC flV 
and, the fluxion of that fine 
being = 
the fluxion of that arc (CL) will be 
DViV-BCaVi* 
* Mathematical Memoirs, publiflied in 1780 . 
