Spherical Motion, 5 % 1 
forces of the particles being no longer in equilibria , becaufe it 
is not a permanent axis (except in particular cafes) this oblique 
motion of the particles will in time alter the velocity %■. To 
determine then the value of the motive force caufing fuch alte- 
ration of z, let ML — 2d be a line parallel to the fide of the 
parallelogram which is a feftion of the folid perpendicular to 
the axis Cl, q the middle point of ML, p any other point 
therein, pm and qn two perpendiculars to the plane which is 
perpendicular to BCI and pafles through SI ; and from B let 
fall BN perpendicular to the axis SI : then, the point n muft 
neceffarily fall upon SI, becaufe the plane BSCI produced bi- 
fe&s the folid, join pn which is the perpendicular diftance of 
p from the axis SI ; let v— the velocity of the body at B per- 
pendicular to BI and to the plane BCI ( which is the fame in- 
variable one in the body, and that wherein the permanent axes 
BI and Cl are fituated) ; then, as BN ; v 1 : the angular 
velocity of the body about the axis SI = ^, and by the nature 
of all motion, as BN t v :: x v - the velocity of the 
point p round n, or of a particle of the body at p in the circle 
whofe radius is pn, confequently the centrifugal accelerating 
force, which is always equal to the fquare of the velocity di- 
vided by the radius of motion, is there = x v afting in the 
direction pn upon the axis SI, which may De refolved into two 
others, the one parallel to the plane SmJ, which can have no 
effect in a direction perpendicular to that plane, and the others 
■hi x pm = ^ - 2 x qn perpendicular to that plane, which drawn 
into a particle^ of the body at p gives p x qn x g^-, — the motive 
Yol. LXXX, Y y y * orce 
