﻿182 



Sir G. Greenhill 

 dO 



GOC, of magnitude Ay-, and then the resultant impulse 



do 



vector OH describes a curve in a horizontal plane GHK, 

 with velocity equal to the gravity couple gMh sin 6. 



Fig. 2. 



N' 



The radial velocity of H in the horizontal plane is then 



-t— < = gWi sin 6 cos GHK = gWi sin 6-^ , 



and integrating, 



i GH 2 = ?MAA(E - cos 6) = A 2 n 2 (.E - cos 0) 

 = iP(E— costf), iOH 2 = iA: 2 (F-cos^), 



to a geometrical scale, with E, F dynamical constants. 



The component HK is zero in the upper and lower position, 

 where = 6 2 , Z . 



In the general unsteady motion of the top, the impulse 



vector moves from OK to OH with KH = Ay- ; and with 



GC 2 

 sin 2 0' 



OG 2 -2OG.OOcos0 + OC 2 

 sin 2 



KH 2 =OH 2 -OK 2 = OH 2 

 (A^Y=2AV(F-cos0)- 



