520 



Dr. C. Chree. On the Determination of [Dec. 21, 



wall. Denoting the mean value of this tension per unit area by P, we 

 have, since the cross-section of the material is ir(r 2 2 - ri 2 ), 



PTT (r 2 2 - n 2 ) = p&r i 2 , or P = p&JKrf - n 2 ). 



The first limitation above referred to is this : The longitudinal tension 

 exerted on the cylindrical wall by the terminal caps will not in reality 

 be uniformly distributed over the terminal areas 7r(r 2 2 - ?'i 2 ) ; thus the 

 solution is reliable only when the principle of equipollent systems of 

 loading* is applicable. This means that portions of the tube near the 

 ends should be excluded from the solution, the portions being shorter 

 the thinner the cylindrical wall. 



The second limitation is that Mr. Mallock starts by assuming the 

 tube wall very thin, and arrives at a formula which is presumably (5), 

 and which at all events possesses the same limitations.! The formula 

 is applied, however, by Mr. Mallock on his p. 52 to cases in which tjr^ 

 varies from about 1/19 to 1/5. The application of (5) under the 

 circumstances would mean an error of from 2J to 10 per cent, in the 

 value of Jc. 



Case (ii) is parallel in every respect to Case (i) and would apply, 



* Todhunter and Pearson's ' History of Elasticity,' vol. 2, Arts. [8], etc. 

 t The primary formula, to which Mr. Mallock's calculations seem to lead him, 

 as given on his p. 51, is 



from which he apparently derives K = Pr 2 /6e. 



P represents the internal pressure. I do not follow Mr. Mallock's proof of 

 the formulae. But his K and e must, I think, be respectively equivalent to Jc and 

 of the present paper. 



An attempt to ascertain the true significance of Mr. Mallock's r 2 from the 

 numerical results on his p. 52, seemed to show that some errors of calculation 

 must exist, independently of the precise meaning of n>. It thus appeared 

 desirable to recalculate the results from the exact formula (4). They appear 

 in the following table, alongside of the values given by Mr. Mallock. The 

 pressure applied was in all cases " 400 Ibs. per square inch." 



There is an obvious omission of decimals in Mr. Mallock's values for brass, 

 which has been corrected above. 



