120 Lord Rayleigh. On the [Dec. 13, 



v = a 30 = B s z cos 50") 



> ................ (). 



w = cr = sB s z sin s0 J 



Another disk, attached where z has a finite value, would render the 

 cylinder rigid. 



Instead of a plane disk let us next suppose that the cylinder is 

 closed at z = by a hemisphere attached to it round the circum- 

 ference. By (1) the three component displacements at the edge of the 

 hemisphere (9 = JTT) are of the form 



v = a = a cos s0. 

 u = a cO = a sin s0. 

 w = fir = sa sin s0. 



Equating these to the corresponding values for the cylinder, as given 

 by (23), (24), (25), we get 



so that the deformation of the cylinder is now limited to the type 

 v = (a + sz) cos s0 "*) 



w = s (a+sz) sin 



u = a sin s0 J 



in which we may, of course, introduce an arbitrary multiplier and an 

 arbitrary addition to 0. If the convexity of the hemisphere be turned 

 outwards, z is to be considered positive. 



In like manner any other convex additions at one end of the 

 cylinder might be treated. There are apparently three conditions to 

 be satisfied by only two constants, but one condition is really re- 

 dundant, being already secured by the inextensibility of the edges 

 provided for in the types of deformations determined separately for 

 the two shells. Convex additions, closing both ends of the cylinder, 

 render it rigid, in accordance with Jellet's theorem that a closed 

 oval shell cannot be bent. 



It is of importance to notice how a cylinder, or a portion of a 

 cylinder, can not be bent. Take, for example, an elongated strip, 

 bounded by two generating lines subtending at the axis a small 

 angle. Equations (31) [giving cfiw/dr' 2 ' = 0] show that the strip 

 cannot be bent in the plane containing the axis and the middle 

 generating line.* The only bending symmetrical with respect to this 



* This is the principle upon which metal is corrugated. 



