354 ON THE MOTION OP 



coordinates x" downward from the horizontal plane of x and x 

 and observing that we have 



X t = - ga", V = - gb", Z ,- - gc . 



Sxfim = o , Syfim = o , Sz t Dm = o . 



the other quantities remaining as before.) 



d%-+-6L, = ga", 

 d\^BM t = gb", 

 d% + 6N, = gc"; 



U+Q{Ny-M,z) = o, 

 V-^%{L,z-N^ = o, 

 W+B{Mp, — L iy ) = o: 



from which 6 being eliminated, there will remain five equa- 

 tions, which along with the equation of condition comprehend 

 and determine all the phenomena of the motion. The first 

 three of the above equations may by means of formulas (8) 

 and (11) be presented in this form (2S) 



d*g -\-6L = o , 

 W+6L' = o , 

 dT + eL" = g; 



which are in appearance simpler than the others, more espe- 

 cially as the accelerations are now complete. It will however 

 be found necessary to have recourse to the former, except 

 when the supporting surface is a plane, or the supported body 

 is a homogeneous sphere. 



Let us now suppose that the surface of the moving body 

 and the surface of support are both of the second degree. For 

 the sake of greater simplicity, let us suppose also that the rec- 

 tangular diameters of the surface of support coincide with the 

 axes in space, and that the centre of the moving body when 



