98 LECTURES TO SCIENCE TEACHERS. 



(which we have supposed to be longer than a), we have the 

 entirely different mechanism (C" 4 ) e , (Fig. 12). The two arms 

 no longer revolve but only swing, and the link a turns right 



round once in every double swing of d and 6. This mechanism 

 is occasionally used in part of its stroke in parallel motions 

 with some modifications, but is not so well known as the 

 others. 



The four inversions of this one chain therefore give us 

 three different mechanisms. Looked at separately it is hard 

 to see the relation in which these stand to each other ; from 

 the point of view which we have taken their mutual relation- 

 ship has become at once evident. 



Without altering the pairing at all, we can greatly alter 

 the chain by changing the relative length of its links. If 

 we made all the links equal we should have a square, of 

 which all four inversions would give similar mechanisms. 

 If we make 6=d and c=a we get a mechanism which is 

 perfectly familiar in the couplings of locomotives and many 

 other cases. All four mechanisms are again similar, each 

 one consisting of "a pair of cranks revolving with equal 

 velocities and connected ]by a link which moves always 

 parallel to itself. 



These mechanisms are among those which have the 

 peculiarity to which I alluded yesterday, that in one of their 

 positions their motions are not determinate. This occurs at 



