Mr. landen’s new 'Theory, See. 267 
1. Fig. 1 . Let the fphere adbe, whofe radius is r, re- 
volve uniformly about the diameter acb as an axis, with 
the angular velocity c , meafured at d or e, the motion 
being according to the order of the letters dgeh in the 
fe&ion at right angles to acb, fig. 2. ; and, whilft it is fo 
revolving, let the pole a be impelled by feme inftan- 
taneous percuflive force to turn about the diameter dce, 
from a towards h, with the velocity w. It is propofed to 
find the new axis about which the fphere will revolve 
after receiving fuch impulfe. 
Calling al , parallel to DC, x; cl will be : the 
velocity of the point a (about acb) before the impulfe 
on a will be = — ; and the velocity (about dce) given 
to the fame point (<3) by the faid impulfe will be = 
~ ~ V % . Which velocities of the point a being in con- 
trary directions, if it be fo fituated that they be equal, 
then, one deftroying the other, that point will flop and 
become one of the new poles fought, about which the for- 
mer poles a and b will revolve with the velocity w ; and the 
points d and e will revolve with the fame velocity (c) as 
before the perturbating impulfe on the point a ; but in- 
llead of deferibing the great circle dgeh, their motion 
will be about the new axis ah; about which they (as well 
as the points a and b) will deferibe lefler circles parallel 
M m 2 
