﻿Solution of Equations. 895 



cosine form of the equation vanishes. Suppose, for instance, 

 that R, R 3 have finite values but that R 2 = 0. The difficulty 

 may be surmounted in the following way (fig. 3). 



Fig. 3. 



A kite in the angular position of that corresponding to R 2 

 is inserted for the purpose of ruling the angular motion of 

 R 3 . It may be of any finite size, and therefore equal in all 

 respects to the kite upon R 3 . It is then necessary to trans- 

 late as it were the third kite until its first point coincides 

 with the second of the first kite. This can be virtually done 

 by supplying the remainder of the links shown. 



Nos. 1, 2, 3, 4, 5, and 6 are each one equal to the shorter 

 side of the third kite, Nos. 7 and 8 to its longer side. No. 5 

 is parallel to No. 3, and attached to the longer side of the 

 third kite so as to secure this, i. e. its point of attachment 

 will be at a distance from the tail of the third kite equal to 

 one of its shorter sides. Should the third kite have R 3 

 negative the case presents no particular difficulty. In these 

 cases some of the sides of the linkage can be dispensed 

 with. In fig. 3 the final two sides of the third kite may be 

 omitted. 



II. The kinematic determination of the roots of an 

 equation, of any magnitude. 

 Suppose the equation to be 



= {A-fCV + E,r 4 + } 



-{Btf+n ( r* + F^ 5 } 



N.r 



