The Torsion of Closed and Open Tubes. 569 



This result and formula (32) have been used in the design 

 of the spars of the tail-planes of aeroplanes which are under 

 torsion from the king-posts carrying the control wires. 



I also showed in paper B that formula (32) could be used 

 to solve the general (St. Venant) problem of torsion by con- 

 sidering a solid shaft as made up of tubes of shear. This 

 method gives the same results as the St. Venant theory, 

 without involving the use of the equations of elasticity or of 

 conjugate functions. 



The approximate formulae used in engineering practice for 

 elliptical and rectangular tubes often give results which are 

 greatly in error. This matter is considered in paper B § 7. 



Yours faithfully, 

 Dept. of Civil Engineering (J # BathO. 



and Applied Mechanics, 

 McGill University, Montreal, 

 November 30th, 1920. 



To the Editors of the Philosophical Magazine. 



Gentlemen, — 

 The results in my paper on " The Torsion of Tubes " 

 were worked out about last March in connexion with a 

 book I am writing. I had not then seen or heard, of any of 

 Professor Batho's work on the subject, and I thought my 

 results were quite new. After I had decided to publish my 

 results in the form of a paper I saw in ' Engineering ' the 

 paper (A) mentioned above, but this paper had so little in 

 common with my own that I saw no reason lor withholding 

 publication. It was only after I had sent off the final proofs 

 of my paper that Professor Batho's paper (B) came to my 

 notice. If I had seen this paper earlier I should probably 

 not have published my results in a separate paper. How- 

 ever, I now think that it was worth while to publish my 

 results because our methods are so different, and especially 

 as the correspondence in ' Engineering ' shows that there 

 were people who did not believe in Professor Batho's 

 methods. Moreover, as he points out above, my formula for 

 an open tube (or thin strip) applies to strips of variable 

 thickness, whereas his applies to strips of constant thickness 

 only. 



Professor Batho's claim that he does not use the equations 

 of elasticity cannot be upheld for his work on the thin strip, 

 since, for this purpose, he borrows St. Venant's results for a 

 prism of rectangular section. 



J. Prescott 



Jan. 7th, 1921. 



