﻿894 Mr. T. H. Blakesley: A Kinematic 



is a root of the equation, or the projection of H 1 upon Ox 

 divided by Rj is a root. 



It may be pointed out that the projection of AB upon Oy 

 in any position of the linkage is 



R 1 sin^ + R 2 sin2(9-f , + R„sin??<9. 



This plan is obviously applicable only to roots which are 

 less than unity numerically. The roots which exceed unity 



might be found by writing x= - in the original equation, 



and solving the resulting equation for y in a similar manner. 

 Should the coefficient of a term in the cosine form of the 

 equation be negative, the corresponding kite must be turned 

 in its plane through 180° from the position it would have 

 occupied had the coefficient been positive, round the point of 

 junction with the preceding kite. The sides adjacent in the 

 two kites concerned will still be continuous, and the bars 

 incorporated as before, as shown in fig, 2, where the dotted 



Fijr, 2, 



outline represents the position the second of the two kites 

 would have occupied if the coefficient had been a positive 

 one. It may here be noticed in regard to the position of 

 all the kites, positive or negative in their chords, that if an 

 observer traverses the series of chords in order from end to 

 end, he will always have the similar ends of all kites on the 

 same side of him. 



An important point arises if one of the coefficients in the 



