c j 2 Mr . Wildbore on 
will come to the fame as a cafe occurring hereafter, when 
_. 0 y — % = — where A is fome conftant quantity ; 
for then x = o = e^ + f-e ee - xx +yy + zz=yy + z^ = eyy -f eoz, 
e = yy + Sz= + ^ = £ * -7& + 7& S = 0 > therefore <? is 
conftant, and i = — = 4 ^= 4~* and fince e~o, and x = e& + 
7 xy e py etfy 
£e = 0 = e@; therefore /3 = o, /3 conftant, and y=\/ b"' -f \ 
therefore i = ~ » and * = 3 g * arc EO ; confequently, 
the velocity with which O Ihifts its place in the arch EO is = 
‘It . which is a conftant quantity. 
a ’ 
proposition V. 
The fame being given, as in the laft propofition, it is pro- 
poled to illuftrate the manner in which the furface moves with 
refped to a point at reft in abfolute fpace. 
Let Z (fig. 4 .) be a point touching the furface, but at reft 
in abfolute f^ace whilft the furface moves under it in any man- 
ner whatfoever. In any one pofition of the oCtant ABC 
through Z draw the great circles As, By, and Cr, which by 
the property of the fphere muft be perpendicular to BC, CA, 
and AB, refpe&ively ; then muft the velocities of the fpheri- 
cal furface at s , y, and r, in directions perpendicular to each 
of the circles As, By, and Cr, be x, y , and s, the angular 
velocities therefore about Z, with which the furface paffes 
under s, q, and r, muft be — , JL-, and f -^-; throughZand 
O draw the quadrant of a great circle ZY ; then, as/3 : x : : f. OY 
