the Rotatory Motion of Bodies. ytg 
If we refolve each of the three forces H, I, K, into two 
others ; the one to turn the body about the diameter NAN, and 
the other to turn it about the momentary axis PAP, at right 
angles to that diameter ; the forces to turn it in the laft men- 
tioned diredion, arifing from the faid forces H, I, K, will be 
1 ^ 
HH 
11 
M 
d z + c z 
a 
3 
« 4 T 
vl_ 
M 
d z +b z 
’ a 
IT 
a 4 T 
M 
A+ b z 
— m 
© 
a 
3 
«fr 
Xj3 flux, of ej3 
3 a 
X y flux, of + 
X $ flux, of e l - — e 
ID e “/3 y 5, 
C e^yl 
The fum of thefe forces, it is obvious, muft be = o ; the di- 
redion wherein they are fuppofed to ad being at right angles 
to that in which the body will be adually urged to turn by the 
joint centrifugal force of its particles, and that being the only 
force whereby the motion of the body is fuppofed to be affeded : 
which fum (B + C - D being = o) is, when divided by -^ 7 - , 
3 a ' 
_ ~T ‘ ■+? . tfe +¥+¥ . ye+e + V- . Pe 
d~ -p c . e (3 (3 4 - d “ -f* b z . eyy + c z -\-b~ « eh^ 
But + being before found = o, we have 
d z + c~ + b z x/3j8 + yy + ^=o ; and b z f$-\-c~yy + d z fl being 
alfo found — o ; It evidently follows, that 
d z + c z • jGjS + d z + b z , yy + c z + b z . will be = o. 
Therefore d z ^ r c z , (3 z e + d z + b z . ye + c z + b z . Ve will be = o : 
confequently e will be = o, and £ 'invariable ; which agrees with, 
what is faid above refpeding the momentum of rotation. 
The other forces arifing by refolution from the forces H, I, 
K, to turn the body about the diameter NAN, will be 
X X 2 
