106 



LECTURES TO SCIENCE TEACHERS. 



complex, as is shown by dotted lines. For such a chain we 

 may use the formula (C" 3 P^) b. The process of reduc- 

 tion can be carried on in this way until only two links are 

 left, which then become really a pair of higher elements. 

 It is constantly employed in machinery, mostly in the case 

 of compound chains, or chains in which some links contain 

 more than two elements. 



The chain which we have been examining has been applied 

 more often than any other to the leading trains of engines 

 and pumps. "We shall in conclusion look at a few of these 

 machines, in order to notice the constructive disguises which 

 often appear in them and render their kinematic identity 

 almost unrecognisable. 



Fio. 20. 



Fig. 21 shows a rotary engine which has been patented 

 several times, and which is founded on the same mechanism, 

 (C" 3 jP- 1 -)*, as the common direct-acting engine. The letters 

 and figures placed upon it correspond to those on Fig. 8, so 

 that the identity of the mechanisms may be the more easily 

 traced. The extraordinary change of form undergone by the 

 connecting-rod b is worth special notice. It has become a 

 bar having a cross-section like a half-moon. It still consists 

 however, kinematically, of two cylinders or portions of them, 

 one described about the axis of 2 (the centre of the disc), 

 the other about the axis of 3. The element 2 is expanded 

 so as to include 1, the crank a becoming therefore a disc. 

 The mechanism is so proportioned that the virtual length of 

 the connecting-rod the distance, that is, between the centres 



