252 CURVATURES AND MOVEMENTS OF THE 



19. From what has now been stated, it is evident that the 

 two bones return to their original positions as the couple 

 resumes its positive phase. We may, therefore, assume a 

 straight line passing through the surfaces of the couple, or a 

 parallel to such a line, as representing the two bones in their 

 relative positions to one another in the positive phase of the 

 couple. At the commencement of the passage to the negative 

 phase, the line separates into two portions at the point where 

 it passes through the twin-surfaces ; and these two portions 

 thenceforward to their negative position assume a series of 

 relative positions determined by the resultant movements 

 of the twin-elements. These series of relative positions must 

 be similar, but necessarily in inverse order, during the return 

 to the positive phase. 



20. As already stated, the longitudinal and transverse 

 lines of curvature of the twin-elements are curves of double 

 curvature ; and as the resultant movements of the ele- 

 ments themselves must be helical, it follows that the two 

 halves of the line representing the two bones must pass 

 through a series of positions of such a kind that, during 

 action, any given and corresponding point in each of these 

 lines will describe a helical path of similar but opposite cur- 

 vature. 



21. The geometrical character of the generative curves of 

 an articular couple can only be finally determined by means 

 of numerical data. As, however, the forms and movements 

 presented by the twin-surfaces exhibit throughout these 

 strongly marked already described distinctive characters, it 

 becomes a matter of importance to inquire whether the 

 conditions of these characters are fulfilled or supplied by any 

 one geometrical curve. 



22. With this object in view, it is to be observed that 

 during the double gliding of the elements upon one another 

 in their alternate passages from their positive to their nega- 



