THE KINEMATICS OF MACHINERY. 



89 



at last the distances PP V P^P^ QQ V &c., be taken infinitely 

 small, each corner of the polygon will be infinitely clo*e to 

 the next one. That is to say the two polygons will become 

 curves, and of these curves " infinitely small parts of equal 

 length continually fall together after infinitely small rotations 

 about their end points." In other words the two curves 

 roll on one another during the continuous alterations in the 

 relative position of the two figures. Instead of finding 

 points now by the intersection of normal bisectors, they 

 are found by intersection of normals to the paths of P and Q 



Fio. 5. 



(Fig. 5). The turning about each point now occurs not 

 (in general) for a finite period, but for an instant only. 

 Each point is therefore called an instantaneous centre. The 

 curve containing all the instantaneous centres, or the Locus 

 of instantaneous centres, is called a centroid. Without giving 

 them any special name, several writers on Mechanics have 

 made more or less use of these curves. Among these I 

 may mention Dwelshauvers-Dery, Schell and Prbll. Eeuleaux 

 has, however, given them a name (Polbahnen), and has made 



