302 Mr Chree, On Long Rotating Circular Cylinders. [Feb. 8, 



the magnitude of S/E or s is known for any one value of a/l, it is 

 a simple matter to obtain its magnitude for any other value of ajl 

 supposing 77 and a'/a unaltered. The following table gives the 

 approximate numerical magnitudes of S/E and 5 when I = 10a, 

 the value of 77 in the material being "25. 



Table XIV. 



Solid 



a'ja 



cylinder '2 -4 '6 -8 10 



(£/#) x 10 3 = -261 -652 -683 780 -950 1-206 1-564 

 8 x 10 s = -228 -635 -667 -764 -936 1-196 1*564 



§ 27. By assigning a given value to S/E or s in equations 

 (26) to (29) we obtain a value of l/a which gives the shortest 

 cylinder in which so large a value of S/E or s would be reached 

 when the velocity was kept within the range prescribed by the 

 Greenhill formula (24). If this value of S/E or s be the extreme 

 limit of safe working in the material considered, the corresponding 

 value of l/a determines the shortest cylinder in which the safe 

 speed can properly be assigned by (24). Suppose for instance 

 t] = 0, the case in which the stress-difference and greatest strain 

 theories agree, and let S/E = s = -001 denote the safe working 

 limit, then the values of l/a for the shortest cylinders in which it 

 is legitimate to determine the safe speed by means of (24) are 

 those given in the following table : — 



Solid 



Table XV. 



a'/a 



cylinder -2 '4 *6 -8 TO 



l/a = 7-36 8-75 8-87 920 9 72 1039 1118 



For the limiting case a'/a = 1 the result is independent of 77, 

 and in fact the value of 77 is of comparatively little importance 

 except in the case of the solid cylinder or when a'/a is small. 

 The difference between the limiting values of l/a allowed to the 

 application of (24) in a solid cylinder and in a hollow cylinder in 

 which a'/a is vanishingly small is least when 77 = 0. It is greatest 

 when 77 = "5, in which case we find for l/a in a solid cylinder 

 answering to S/E ='001, and to s=*001 the respective values 

 6'65 and 5-59; while for the hollow cylinder a'/a = the cor- 

 responding values are no less than 940 and 910. 



