38 Mr Larmor, On Rigidly connected Points, [Jan. 27, 



form is given by (7) possesses this property, the movement being 

 a screw of pitch — /3" 1 (1 + B~ l ) round the axis of x, eased off in 

 a way that retains one degree of indeterminateness. 



We proceed to investigate the trajectory of any point of the 

 solid by the aid of this cubic. 



Through any point, as is well known, one and only one chord 

 of the cubic can be drawn. We may regard this chord as a line 

 of constant length moving with its extremities on two fixed 

 lines, which may be considered straight so far as the determi- 

 nation of accelerations and curvatures is concerned. 



Consider two consecutive positions of it, BG and B'C; let 

 BP = B'F = p, and CP = C'P' = p, and let p + p' = a. Complete 



Fig. 1. 



the parallelogram C'CBA, and draw P'M, P'N parallel to A B', 

 AC, as in Fig. 1. The circumstances of the motion are given 

 by the velocities of the extremities of BG ; let then 



BB' = bt+±bt 2 \ 8) 



cG' = ct + yf\ { 



so that b, c are the velocities, and b, c the accelerations of B and G 

 along their straight trajectories. 



The point Q moves in a fixed plane which is parallel to both 

 BB' and GG', being parallel to the plane ABB'. The coordinates 

 of Q referred to axes of x and y parallel to BB' and GG' are the 

 same as the coordinates of N referred to axes BB' and BA . They 

 are therefore given by 



BB'=-x=bt + ibf] 



9 (9). 



CG'= p -y=ct + ±c? I 



