APPLICATIONS OF ELLIPTIC FUNCTIONS TO PROBLEMS OF CLOSURE 111 



Assume in Fig. 5, the links 0A, = 0A2=ri, A,Bj=BiA2=A2B,' 

 =B/A,=r2, QB,=K, and 0Q=«. The points O and Q are fixed, 

 while all the others are movable. During the motion B, describes a 

 circle having Q as a center and QBj as a radius. Now, according to 

 the properties of Peaucellier's Inversor OBi.OB/ =rf— r|=constant; 

 consequently the point B,' also describes a circle, which is inverse to 

 the circle described by Bj in an inversion having O as a centre and 

 ^r,—rl as a radius. Further let Ba„ Sa^, BjS^ be the infinitesimal 

 displacements of the points Aj, A2, Bj in a virtual displacement of 

 the cell; a„ a^ the angles which the links OAi, OA2 include with the 

 positive part of the axis OQ ; ^„ ^^ ^^^ angles which the links A,B, 

 and BjAj include with the link QBi; Oj and O^ the points of inter- 

 section of the link QBj with the links OAj and OAj respectively; 

 and, finally, the variable distances pi = QA, and pr^=QA2. The points 

 Oj and O, are evidently the \irtual centres of rotation of the links 

 A,B, and BjAj respectively. Hence, from Fig. 1, the relations : — 



