100 LECTURES TO SCIENCE TEACHERS. 



on one link and a recess upon the other link gear together at a 

 point corresponding to the point of contact of the centroids. 

 The teeth G and H are virtually formed upon the centroid 

 of b, and the recesses E and F upon that of d. At the 

 points where these come into gear, the two centroids are com- 

 pelled to roll upon one another, just as the pitch circles of 

 two toothed wheels are compelled to roll on one another, and 

 in this way the mechanism is carried over its only indeter- 

 minate point, and the cranks remain continuously anti- 

 parallel and revolve in opposite directions. 



This antiparallel chain gives us two different mechanisms. 

 Fig. 13 shows us (C'^Cy. In the other mechanism 

 (CJ2!^s)* ^ e ^ wo cran ks revolve in the same direction with 

 very varying velocity ratios. 



Returning again to the chain (4), it will be seen at once 

 that we may substitute for the pair of elements at 4 a slot 

 and a sector concentric with it, as in Fig. 14. The motions 



FIG. 14. 



remain entirely unaltered. By adopting this construction, 

 however, it becomes possible to construct the mechanism 

 without covering with it the centre of the pair 4, i.e., the 

 point of intersection of the links c and d. "W e can therefore 

 lengthen these links without making the mechanism incon- 

 veniently large. The only constructive alteration is that 

 the slot becomes flatter as the links are lengthened. If 

 we lengthen them little by little until they become infinitely 

 long, the curved slot becomes straight, and its centre line will 

 pass through the point 1. The mechanism modified in this 

 fashion takes the extremely familiar form, already shown in 

 Fig. 8. It now contains three cylinder pairs with parallel 

 axes; the fourth cylinder pair has become a straight slot 

 with a block working in it, namely, a prism pair (see page 



