254 CURVATURES AND MOVEMENTS OF THE 



the curve advances in the direction of its pole or away 

 from it. 



25. Now we may conceive the opposite, similar, and equal 

 curved surfaces of an articular couple to be generated simul- 

 taneously by a given equiangular spiral. This spiral, in 

 successive stages of development, represents corresponding 

 successive transverse lines of curvature of the twin-elements ; 

 its primitive extent or dimension being assumed as equal to 

 that of the first opposite transverse lines at the proximal 

 extremities of the elements. The proximal extremities of the 

 transverse lines of curvature, which collectively constitute the 

 proximal margins of the elements, are assumed as representing 

 the polar portion of the generating curve ; while the distal 

 extremities of the transverse lines of curvature, which collec- 

 tively constitute the distal margins of the elements, are as- 

 sumed as representing the anti-polar portion of the generating 

 curve. The primitive dimension of the given curve having 

 been assumed equal to the first proximal transverse curvature 

 on each element, the successive greater transverse curvatures 

 are geometrically conceivable as being produced by successive 

 rotations of the generating curve round its pole and in the 

 direction of the pole, so that successive additions are made 

 to its anti-polar extremity, and consequently to the distal 

 extremities, of the transverse lines of curvature of the 

 anti-polar elements. 



But it is evident, on inspection of the articular surface of 

 an acting couple, that the transverse lines of curvature are 

 arranged in series along the lines of longitudinal curvature, 

 and that the series therefore sweeps in a heUcal or screwed 

 direction round a central axis of the entire combination. We 

 must assume, therefore, in addition, that the generating spiral, 

 while increasing its dimensions by revolving round its pole 

 in the direction of that pole, also revolves tangentially roimd 

 a fixed axis, while it glides along that axis in the direction of 



