1893.] 



On the Three-Bar Motion of Watt. 



T A 



473 



-"good" values, i.e., they give the path of P nearly rectilinear; but 

 they are all subject to the relation d?r 2 = Z 2 . The curve above is 

 one of this class ; in these the tangent at the origin lies wholly out- 

 side the curve, and has the closest possible contact with it, while at 

 the moment the tracing point P passes through the origin, the arms 

 are at right angles to the link. The question arises, may there not 

 be better values of d and r (not subject to the relation d z r z = Z 2 ) 

 which give a more nearly rectilinear motion to P than any of the 

 Watt values ? 



The equation to the curve traced by P, in common polar coordin- 

 ates, is (taking CO initial radius vector) 



-r sn 



(A) 



Willis (' Principles of Mechanism,' p. 401) says that the full equation 

 is so exceedingly involved and complex as to be of no use in obtain- 

 ing the required practical results. And Willis accordingly follows 

 the preceding writers in " approximate methods." 



The present paper takes up the subject at this point, and the general 

 substance of the paper and its results may be stated under three 

 heads, viz. : 



1. The nature and properties of the curve (A) are worked out so 

 that a complete idea of it for all values of d and r is obtained. 



2. Hence are derived numerous values for d and r which give 

 good results ; the deviation in these from the right line is calculated, 

 and in some of them shown to be less than in any of the arrangements 

 given by Watt. 



3. The more complex arrangements, where the radii are not equal 

 or where the tracing point divides the rod unequally, are also dealt 

 with. 



In the first head, large use has been made of plotting the para- 



