ACTING FACETS OF ARTICULAR SURFACES. 253 



tive, and from their negative to their positive positions, a 

 progressively diminishing or increasing extent of congruence 

 appears to be provided for hy tlic successive fjlidiiuf into ap2)osi- 

 tion, aiid therefore into congruence, of gemnctrically-similar, as 

 well as lincarly-cqual portions of curvature not prcvim/My 

 coincident. 



23. In other words, the geometrical arrangement of the 

 surfaces of the opposite elements appears to be such as will 

 provide, not only for their iKrfcct congruence wlien in tlieir 

 positions, by means of geometrically-similar and linearly-equal 

 longitudinal ami transverse lines of cuirature fitted into one 

 another in tlic o}rpositc elements, but also for an alternating 

 series of jirogressively diminishing and increasing extents of 

 congi'ucncr, by means of corresponding series of geometrically- 

 similar and liiuarly-equal i^ortions of longitudinal and trans- 

 verse curvatures on the opposite elements, and increasing or 

 diminishing in accordance with tlic piositive or negative direction 

 of the movements. These successive coincidences of these 

 similar and equal portions of longitudinal and transverse 

 curvature being brought about by corrcspoiuling gliding move- 

 ments in the negative and positive directions. 



24. The equiangidar spiral, in its more general fonn as a 

 curve of double curvature, is the only geometrical cur\-e which 

 fulfils the conditions of the successive movements and adap- 

 tations of articular curvatures now under consideration. A 

 characteristic property of this spiral, and one which peculiarly 

 adapts it for generating the curvature of the surfaces of organic 

 joints, is the geometrical similarity of all portions of any given 

 example of curve which subtends the same polar angle, how- 

 ever different their linear dimensions may be ; so that, if the 

 spiral be conceived as revolving round its pole, in the plane 

 of two lin(>s diverging from the pole, the lines will inter- 

 cept an infinite number of geometrically-similar portions of 

 the curve, but which become infinitely smaller or greater as 



