<268 Mr. landen’s new 'Theory of 
to the great circle de , in which the points d and e (de 
Being at right angles to ab) will revolve about the fame 
axis ( ab ) with the velocity Vc 2 + wr. Which being de- 
noted by e , and m and n being put for the fine and cofine 
of the angle Aca to the radius i, me will be = w, ne = c, 
and confequently mne" — cw. 
Now taking — = w '^ r — , in order to- find that new 
axis ah, we have from that equation x— r —-ah 
Moreover it is obvious, that if a fpheroid, a cylinder, 
or any other body, whofe center of gravity is c and pro- 
per axis acb, were, whilft revolving about that axis with 
the fame angular velocity (r), to receive fuch an impulfe 
as inftantly to give the point a the angular velocity w 
about dce ; the axis about which that fpheroid, cylinder, 
or other body, immediately after the impulfe, would re- 
volve, or would have a tendency to revolve, would be 
the fame line ab. 
The great circle de (fig. i.) and any other great circle 
fo fituated with refpedt to the axis of any revolving 
fphere, I fhall denominate the mid-circle.’ 
2 . In the manner above deferibed the polesof the fphere 
are by the iriftantaneous impulfe on the point a inftantly 
changed from a and b to a and b. But if, inftead of fuch 
impulfe, a continued attractive force f (like that of gra- 
vity) 
