STATICS. 



[225. 



(13) 



The intersections of the surface (13) with the curve (10) give 

 the positions of equilibrium of the particle on the curve. 



The reaction of the curve, or the pressure on the curve which 

 is equal and opposite to this reaction, can then be found from 

 the equations (11). 



225. For a rough curve, the total reaction resolves itself into 

 .a normal component N and a tangential component pN, which 

 represents the frictional resistance. The equations of equi- 

 librium are 



(14) 



ds 



Transposing the third terms, multiplying by dx/ds, dy/ds, 

 ) and adding, we find, since N x dx+N y dy-\-N g dz v, 



as 



as 



as 



(is) 



Multiplying the second of the equations (14) by dzjds, the 

 third by dy/ds, and subtracting, we have 



ds 



ds 



ds 



-11 ^ ^ dx ^ v dz ( \ r dx , r dz\ 



similarly, zZ - 2,X- = (N z - -- N x - 

 ds ds \ ds ds) 



ds 



ds 



,- 



ds ds 



