498 Mr. Wildbore on 
find with what velocity any great circle on the furface, but 
oblique to that axis, moves along itfelf. 
Let I (Tab. XX. fig. i.) be the centre, and BL b the axis round 
which the globe revolves with a velocity = c meafured along the 
great circle GH, whofe plane is perpendicular to that axis, and 
HSGj any great circle whofe plane is oblique to the axis, ESF 
and esf two leffer circles of the Iphere parallel to the great cir- 
cle GH, and touching HSGr in S and s ; then, as the radius 
BI which may be fuppofed unity : c :: the radius of the lefs 
circle ESF = the fine of the arc BE or BS : the velocity along 
the circle ESF = the abfolute velocity of the point S on the 
furface of the globe : but the point S is alfo upon the great 
circle GSHr, and therefore this is alfo equal to the velocity of 
the point s along the great circle GSRf ; and for the fame 
reafons the point S, which is diametrically oppoliteto S on the 
furface, has alfo the fame velocity. Let P be any other point 
in the great circle GSHj; then, fince as the globe revolves the 
diftances SP and jP always continue invariable, the velocity of 
the point P in the circle HPS in the direction of the periphery 
of the circle itfelf muft be equal to that of S and s ; and is 
therefore the velocity of every point of this circle along its 
own periphery. 
Corollary i. Hence it follows, that in whatfoever manner a 
globe revolves, its velocity meafured on the fame great circle on 
its furface muft be the fame at the fame time at every point of 
the periphery of that circle. 
Corollary 2. Confequently, howfoever the plane of a great 
circle varies its motion, the velocity at any inftant is at every 
point of the periphery equal along its own plane. 
, / ( '■ •• . 
DEFI 
