510 



In the particular problem, let z be measured vertically downwards 

 from the plane of the table, then Z=^r, and repeating for the parti- 

 cular case the investigation ab initio, the general equation of motion is 



Let s be the length in motion, or, what is the same thing, the z co- 

 ordinate of the lower extremity ; and suppose also that the mass of a 



unit of length is taken equal to unity, we have Iz = ls, - ?, 



at* at 



dmdz, and the summation or integration with respect to z is from 

 z=0 to z=$, whence 



ePz \ , fcPs \ ^ 



s? -*) ** dm= (*? - ff ) * = - * 



which is of the form 



d dT dT dV 



where the bar is used to denote exemption from differentiation, but 

 ultimately is to be replaced by . Considering now the second 



term here =0, but =&, and thence -2 = '. Moreover, dp = 



s'dt, and thence finally the second term is *' 2 , which is of the form 



dK {f 



M' K=|7.A 



the bar having the same signification as before, but after the differ- 

 entiation '='. The resulting equation is 



(->+()'= 



which may be written in the form 



and the first integral is therefore 

 sds 



