of an Elastic Plate under Normal Pressure. 119 

 corrugations on the sheet, and the maximum amplitude is, 



/ 2 



as for a plane sheet, crh\/ ^ ^-. 



In a paper read before the London Mathematical Society 

 (Proceedings, vol. xxi. p. 142), Professor Lamb. has obtained 

 results for the bent cylinder which differ only in one respect 

 from the results I have just indicated. The difference is 

 that his results do not show the relation between A and the 

 amplitude of the corrugations, and this is due to his tacit 

 assumption that (b — a) is small in comparison with b, a 

 restriction which is quite unnecessary. He has a boundary 

 condition which, written in terms of the symbols of this 

 paper, has the form 



d\ P -b) p-b 

 df + b 2 U ' 



If this had been written in the more correct form 



and if, then, p had been replaced in the second term by its 

 approximate value a, the condition would have been 



+ 



•(H)-* 



dif 2 



and this would have given the results indicated in the 

 present paper. 



In a later paper, read before the Manchester Literary and 

 Philosophical Society *, Professor Lamb worked out the 

 problem of the flat plate bent into a surface of revolution by 

 using an elementary method which has the advantage of 

 showing clearly the physical actions taking place. His 

 method was, however, a special one which did not show the 

 connexion between this problem and the general theory in 

 which the stretching of the middle surface is taken into 

 account. 



Problem 4. — The stretching of a circular membrane by a 

 uniform pressure p over its area. 



If the terms having a factor It are omitted from equation 

 (14), we fall back on Poisson's equations. If, however, the 

 term containing the factor /i 3 were omitted, this would 

 amount to nssuming that the plate is much more effective in 

 supporting pressure by means of its stretching than by 



* See also Phil. Mag. [5] vol. xxxi. p. 182. 



