1881.] Mr GreenMll, On height consistent with stability. 71 



which may be written 



72 



^M + 2 |- i M = (1); 



the solution of which is, subject to the conditions that p is finite 



and -r- = when x = 0, 

 ax 



x p= Asin \/{m^) x ®'> 



and therefore the height h is given by 



Sin \/(2^ h = ' 



or 



or 





If 6 be the radius of the base, then 6 2 = 4m^, or 



If & denote the elasticity of volume, and ti the elasticity of 

 figure, or as it is called, the rigidity of the substance, then 



E= dnk 



Sk+n 



(Thomson and Tait, Natural Philosophy, p. 521); and for a sub- 

 stance like jelly, n is small compared with k, and we may put 

 E=3n. 



Now E and n being expressed in gravitation measure, the rate 

 of propagation v of transversal vibrations is given by 



, n Lq 



v = — = ;r- 1 



MJ 



and therefore 



h :i =7T 



s/i • '■''* 



