1892.] Mr Ghree, On Long Rotating Circular Cylinders. 297 



and s, when ij is given, vary simply as S/E, it is most convenient 

 to attach a value to this ratio and not to 8 itself. This has the 

 further advantage that S/E is a purely numerical quantity, inde- 

 pendent of the system of units adopted. It is taken in Table IX. 

 to be '001. This value is selected principally owing to the facility 

 with which it lends itself to the deduction from the table of 

 numerical values in other special cases. It is not intended to 

 imply that this is the true ratio of the greatest allowable stress- 

 difference to Young's modulus in any actual material. 



Table IX. 

 S/E = -001 ; v = -25. 



n S v h A a'/a = 2 -4 "6 '8 10 



Cylinder ' 



(-81/1) x 10 s = S7 5 150 155 169 190 -218 25 



O/a)xl0 3 = -562 -225 -262 -369 '537 -753 1-0 



§xl0 3 = -875 -975 -976 -980 -985 '992 1-0 



The results, with one or two exceptions, are only approximate. 

 In the hollow cylinder s = Sa'/a', so the table gives also the increase 

 in the radius of the inner surface. 



§ 20. The velocity ma, as may be seen by reference to equa- 

 tions (22) and (23) or to Table VII., varies as Js/p. So in calcu- 

 lating it the absolute values of S and p, or rather their ratio, and 

 not the value of S/E, is wanted. 



Since British engineers seem accustomed to measure velocity 

 in feet per second and stress in tons weight per sq. inch, these 

 units have been adopted in Table X. Two special cases are there 

 dealt with, in both of which rj is taken as "25. The first case, in 

 which the velocity is styled w^a, answers to 8 = 12 tons wt. per 

 sq. inch, p — 7*5 times the density of water. This selection is 

 made so as to fit in with the case treated in Table IX. For if, as 

 there, we suppose S/E—'OOl, then E = 12 x 10 3 tons wt. per sq. 

 inch, i.e. approximately 18'90 x 10 8 grammes wt. per sq. cm. Now 

 this value of E and a specific gravity of 7 "5 may fairly be taken as 

 representing steel or wrought iron, though rather low values for 

 good material. The second case in Table X., where the velocity is 

 styled ro/a, answers to 8 = 1 ton wt. per sq. inch, p = the density 

 of water, or more generally to 8 — n tons wt. per sq. inch, 

 p = n times the density of water. This selection is made with a 

 view to facility of application to other special cases. The results 

 are all approximate. 



