112 UNIVERSIIT OF COLORADO STUDIES 



8a, _ A,0, .^. Sa, ^ A,0, 2^ 



from which follows 



Sa, 



Now 



A,0, _6in yS, 



(3) 



B,0, sin 7 B,02 sin 7 



where angle OAjB,=:«w^Z<j OA2B,=:7. Consequently, 



ottj oa2 



sin /3, sin ^^ 



(*) 



As there is only one degree of freedom, the angles ;9„ yS^* «iy 

 and ttj may be regarded as functions of the same independent variable. 

 From triangle OAjQ follows 



cosa, = J 



29\e 



and by differentiation 



sin a, • <7a, : 



?•,(? 



But sin a,= — J(f{s—'f\){s—e){s—p,), 



7\ey 



where .s = , or 



sin a - 1 -[P?-(^'»+^)n[Pt-(^-.-^)'] 

 sm a,_ — , 



hence dai= ' 



In the triangle A,B,0, 



