1892.] Mr Chree, On Long Rotating Circular Cylinders. 305 



Let the limiting speeds in a long solid cylinder and in a 

 complete disk, both of radius a and of the same isotropic material, 

 be denoted by w x and 12, respectively on the stress-difference 

 theory, by &> 2 and fl 2 respectively on the greatest strain theory. 

 Then by reference to my previous paper, we easily find 



ov/H^l + 77 (2-^/(3-4^) (30), 



<yn 2 2 = I+17 2 (1 + ^/(3 -5*7) (31). 



Hence eoj/fli and o)Jfl 2 both vary from 1 when w = to J 7/4, 

 or 13229 approximately, when r/ = '5. For w = '25 we have 

 approximately 



6)^ = 1-104, 6) 2 /n 2 = 1-022. 



For a hollow cylinder and an annular disk of the same 

 isotropic material, with the same values of a and a, we find, 

 distinguishing the results from those given above by dashed 

 letters : 



(a^'/n/) 2 = 1 - V 2 (1 - a' 2 /a 2 ) -=- {3 - 2 V + (1 - 2?) a' 2 /a 2 } . . .(32), 

 (<y 2 '/n 2 ') 2 = 1, for all values of 77 and of a /a (33). 



Thus the limiting speeds on the greatest strain theory are 

 here identical, and on the stress-difference theory the difference 

 between the speeds is extremely small for ordinary materials, 

 especially when 1 — a'ja is small. It is worth noticing that 

 according to the stress-difference theory the limiting speed is 

 less in the long hollow cylinder than in the corresponding thin 

 disk, whereas it is greater according to both theories in the long 

 solid cylinder than in the complete disk of the same radius. 



Monday, Feb. 22, 1892. 

 Professor G. H. Darwin, President, in the Chair. 



The following communications were made to the Society : 



(1) Some jyreliminary notes on the anatomy and habits of 

 Alcyonium digitatum. By Sydney J. Hickson, M.A., Fellow 

 of Downing College, Cambridge. 



Alcyonium digitatum is one of the most difficult Coelenterates 

 to kill in a fully expanded condition. In the first place it is only 



