Spherical Motion . 5^7 
part of a fecond muft be very near the true quantity ; for, 
though the earth’s figure may not be precifely that of afpheroid, 
it cannot differ from it fo much as to make any fenfible altera- 
tion in this, efpecially now it appears from the foregoing ge- 
neral folution, that the angular velocity about the axis whofe 
pole is Z is always uniform and conftant, let the figure of the 
revolving body be what it will. Neither can the progreffive or 
annual motion caufe any alteration, becaufe it cannot at all 
affedt the rotatory or diurnal one. 
The remarkable property mentioned at the end of the 3d 
of thefe general fcholia, may be more particularly exprefled 
thus: as the f. 7 jq~mb l y : 1 :: y 
mb 
the 
°a- 
Cl 1 
gular velocity at q about the axis whofe pole is Z ; in like 
manner, the angular velocity at r (fig. 4.) about the fame axis — 
vW a + c 4 € z 1 „ + c 4 € z j , . , ~ 
— - ^ , that at ..r= — — , and that at Y zz & coCOZ 
4 - < 4 € 2 
a* --ST xW 
which, being the velo* 
city of the moving fpherical furface at every point of the 
great circle whofe node is Y, and every point of that great 
circle being at the diftance of 90° from Z, the angular ve- 
locity of the body round the axis at ref in abfoluie Jpace whofe 
pole is Z will be always equable , uniform , and confant , not - 
withfanding the other ofcillating , vacillating motions of the 
body : e being the greateft angular velocity about the mo- 
mentary axis. 
This motion, then, is of the moft fimple and evident kind* 
and, together with that of the track under Z above deter- 
mined, limits the whole compound motion under confidera- 
tion, all the others being only necefiary confequences of thefe; 
fa 
