ACTING FACETS OF ARTICULAR SURFACES. 259 



generatinp; curve of ai-ticular couples is in each instance a 

 special equian^nilar spiml, we may conceive the two constitu- 

 ent couples of an articular combination to be simultaneously 

 generated by two similar and equal equiangular spirals placed 

 tangentially on opposite sides of a common axis, but with the 

 polar extremity of the one, and the antipolar extremity of 

 the other, in contiict with it, so that all tangeutially-con-e- 

 sponding parts in the generative curN'es of the two couples 

 shall be parallel, while they at the same time glide along the 

 axis and revolve aroiuid it in the same direction, increasing 

 their dimensions by successive increments in a given ratio at 

 thofr antipolar extremities, by revolving round their poles in 

 the direction of these poles. Tlie two couples thus generated 

 would be respectively aodal and antcuvial, the former ha\ing 

 the pole of its generative spiral towards, the latter turned 

 away from, the common axis. During the passage of a com- 

 bination of this kind from its positive to its negative phase, 

 the opposite elements of both of its couples would respectively 

 glide in the same direction along their threads, because 

 the proximal and distal — i.e., the polar and antipolar — ex- 

 tremities of the couples are symmetrical. But as by construc- 

 tion the one couple is axial, and the other antaxial, their 

 margins are not symmetrical, for the polar margins of the 

 axial couple are on the concave, those of the antaxial on its 

 convex side. But this as}numetrical arrangement of the 

 margins of the two couples of the combination neces.sarily 

 co-ordinates their gliding acro.ss their threads. Their com- 

 bined movements across their threads and their inclination in 

 relation to the axis being simultaneous, and all their geo- 

 metrical relations being similar and equal — c.fj., all tangents 

 of corresponding points in their cur\'aturcs being parallel, 

 as the same relations obtain during the passage of the com- 

 bination from its negative to its positive phase — it follows tliat 

 a combination of this kind could be screwed and unscrewed 



