738 



Sir G. Greenhill on Pendulum 



The triangles PpB and OoB are similar, and so are the 

 triangles PHB, P 3 0; so that 



(2) 



Pp_PB 

 Oo ~ OB 



PB 

 PO 



PH 



2PH 



PB" 



an 



d if PRP. is tangent to this circle, 



(3) PR 2 =Pjt) . PB' = 20o . PH, P 1 R 2 = 20o . PA. 



If P and Pj are particles os cillating with the velocity due 

 io the level BB', 



(4) 



vel. of P 

 vel. of P 



/ PH 



PR 

 P,K 



so that, as before in § 4, PP X will continue to touch the 

 circle, centre 0, during the subsequent motion; and the 

 centre has been chosen so as to bring P, to the same level 

 as Qi> and then PQ, P1Q1 will continue to be horizontal, by a 

 suitable arrangement of gravity. 



11. It is desirable to have a geometrical interpretation of 

 the addition formula of (4) and (7), § 8, on the plane in 

 figs. 3 and 6; this is seen by drawing AT, AR to meet DX 

 nnd EX} produced, drawn perpendicular to QQi and PP 1? in 

 W and W x . 



