146] 



PLANE REPRESENTATION OF DYNAMICAL PROBLEMS. 



135 



but we showed, in the article referred to, that A l varies inversely as the 

 acquired twist velocity, whence the theorem is proved. 



Fig. 27. 



This is, in one respect, the simplest construction, for it only involves the 

 chord A A and the homographic axis. 



The chord A A must envelop a conic having double contact with the 

 circle (Fig. 28), for this is a general property of the chord uniting two corre 

 sponding points, A and A , of two homographic systems. Let / be the 



Fig. 28. 



point of contact of the chord and conic (Fig. 28). Then A A is divided 

 harmonically in 7 and T ; for, if ZFbe projected to infinity, the two conies 

 become concentric circles, and the tangent to one meets it at the middle 

 point of the chord in the other ; the ratio is therefore harmonic, and must 

 be so in every projection ; whence, 



AI _^AT 



A I A T 



but the last varies as the square of the twist velocity acquired, and hence we 

 see that 



