1892.] Mr Ghree, On Long Rotating Circular Cylinders. 295 



mined whether these or the speeds assigned by Professor Green- 

 hill's theory are the lowest ; and thirdly, to direct attention to 

 some details of practical interest. 



§ 17. All the methods of determining the limiting speed 

 agree in the conclusion that in cylinders of the same material, in 

 which Ija and a/a have given values, the limiting speed is 

 reached when the velocity aa at the outer surface attains a 

 certain value. Thus coa and not a> is the most convenient 

 quantity to tabulate. 



On the stress-difference theory we assign to S in (22) and (23) 

 a limiting value determined for each material by experiment. 

 The following table is calculated from these formulae, the limiting 

 velocity being termed co t a for the sake of reference. In using the 

 table 8 has to be replaced by the experimental limit found for the 

 material under consideration, and p by its density. 



When less than three decimal figures occur the result is exact. 



On the greatest strain theory the limiting speed is found from 

 (12) and (11) — as s = ha'ja' in the hollow cylinder, — by assigning 

 to s an experimental limit. The value of s like that of E or 

 p varies of course from one material to another. Denoting by &> 2 a 

 the limiting speed allowed by this theory, we obtain the following 

 results : — 



Table VIII. 



Value of co 2 a -r jEsjp. 



•5 2-828 1-069 1066 T057 1-043 1-023 1-0 



All the results are only approximate except those in the last 

 column. 



