33° 
Mr. Landen’s Invejligation of 
By)H 
M 
___ 
— * c 
3 a 5 
ST 
Dm 
M 
<l z + b z 
s “ 
3° 3 
ST 
C&yK 
M 
c 2 + b 2 
S ~ 
~ 3 ° 3 * 
ST 
■ B^s/ 3 +^ s .Byr, 
.D/^+pj.W, 
.CeByU^.CfY; 
-y- 
S being ~s/Y) nrn — BC^f 
And, no external force being fuppofed to adt on the body, it fol- 
lows, that the fum of thefe three forces muft be = o: there- 
fore we may infer, that 
■ rf 1 4 
T will be = - x ~ 
e 
c 4 . y ^ |3 — d A — £ 4 , 0 Jy -f 4 — .By$ 
iyp + Dfft — ; which a S ree - 
ing with the value of T found above, the truth of our pre- 
ceding procefs is thus confirmed. 
M 
The force x By <F + D'/3 2 <F + G^jSy, arifing from thofe 
3<PS a 
three forces, is the whole Joint centrifugal force of the particles 
of the revolving body, to turn it about the diameter NAN the 
way it will actually be urged to turn by fuch force ; the value 
whereof fo computed will be (zr X fD 2 m 2 n 2 - BC*z y" rz 
jyi^2g . 
7 ^ 3 -j equal to the value of the force F computed above, both 
being confidered as urging the body to turn in the fame 
direction. And the quantity 
M* ' ~ 1 ’ 7 
3 * 3 ST 
X d 2 q- c" . y$(3 — d z +b z . D/3£y -f c z -\-b z . C/3 yd 
( = JhL x the fum of all the w z X p) is the value of the motive 
aT 
force which, adting in that very direction, is requifite to caufe 
the momentary pole to change its place as above defcribed. 
Thus we fee diffinCtly how the equation arifes, by which the 
value of T is juft now determined. 1 do 
