33 



line end. Now, if we conceive of a half revolution 

 with a ball and socket joint at the junction of the 

 two C C, and at the centre of each, we can suppose 

 the escape of the old curve, and that the alternate 

 diagonal forces, coming immediately into play, ac- 

 cept the central parts of the new C C from the 

 cross-line ends, and, forming the remote parts from 

 the extremities, join in reciprocal counter-action 

 by new cross-lines. 



The reversal of the curvatures would be accom- 

 panied by a spring, in each direction from the 

 cross-line as a point d'appui. 



§ 31. The above gives a spring in two directions, 

 and no advance is made. To accomplish progres- 

 sive or retrogressive locomotion the spring must 

 have place in only one direction with a point of 

 first appui at one of the extremities of the rod, in 

 order to move in the direction of the other. The 

 cross-liae gives the requisite appui for the C remote 

 from the fixed appui (the ground or other basis), 

 and the reaction between this and the cross-line 

 furnishes the spring for the nearer one, and also 

 sustains the spring of the first. 



§ 32. After the upper point of application has 

 formed the general cui'vatures of its winding line, 

 its further action will displace its end of the cross- 



