154 PHILOSOPHICAL TRANSACTIONS, [aNNO 1777. 



And in the very same manner may be explained the motion of a cylinder, 

 whose primitive motion about its proper axis may be disturbed by some percussive 

 force, in like manner as we supposed the spheroid disturbed ; only (instead of 

 the former substitution for f) substituting for the accelerative force arising from 

 the centrifugal force of the particles of the revolving cylinder its proper value 

 - X 2.4.;. (computed in the Appendix) and afterwards proceeding as we have 

 done with regard to the spheroid, h denoting half the length of the cylinder, 

 and r the radius of any section at right angles to its proper axis. 



Seeing that (— X —^ — -rr) the expression for the said accelerative force res- 

 pecting the cylinder vanishes when Zi is ^ ^r\/'6, it is manifest that the cylin- 

 der in that case will (with respect to its own particles) undisturbedly revolve 

 about any axis whatever passing through its centre of gravity, as will a sphere. 

 Which remarkable property of that particular cylinder I believe has not before 

 been taken notice of. And there are also bodies of other forms having the like 

 property. 



The preceding articles lead us to consider the motion of the earth's axis in a 

 light more clear and satisfactory than any in which it has before been considered ; 

 but I must, for want of leisure, defer making the application till some future 

 opportunity : only observing here, that by what is done above it appears, that 

 from the action of the sun and moon on the earth, its axis has a diurnal motion 

 which I have no where seen explained. Which motion is not much unlike that 

 of the axis of the revolving spheroid just now considered, when (2;!') this last 

 mentioned axis is many times longer than (2r) the equatorial diameter of the 



said spheroid, and - very small. 



Appendix. — Showing how the joint centrifugal force of the particles ofasphe- 

 roid or cylinder, having a rotatory motion about any momentary axis, is computed. 



— 1. In fig. 20, let p be a particle of matter firmly connected with the plane 

 DOEFQG, in which the line ocq is situated ; and pq being a perpendicular from 

 p to the said plane, let the distance pq be denoted by u ; also, the line ql being 

 at right angles to o/cQ, let the distance pi be denoted hy h. Then the said 

 plane with the particle p being made to revolve about o/cq as an axis, with the 

 angular velocity e measured at the distance a from the said axis, the velocity of 

 p will be = — , and its centrifugal force from / will (by a well known theorem) 



be = — to make it «^ the expression being — X p. Whence, by resolving that 

 force into 2 others, one in the direction qp, and the other in a direction parallel 

 to Iq, it appears that the force urging p from the plane doefqg, will be = 



— X /), let the distance la be what it will. 



2. The particle J!> being connected with the plane doefqg as mentioned in 



