602 Messrs. Cowley and Levy: Method of Analysis suitable 



tlie contours of the plate. On general grounds it is clear 

 that these will be of the nature .shown in tig. 1, where points 

 A and B, the positions of maximum and minimum deflexion, 



Fi2. l. 



are stationary points at the instant relative to the walls of the 

 channel. If the body be considered at rest and the planes 

 be supposed in motion past it, the problem can be reproduced 

 by tilting the whole system in the previous case until the 

 section of the cylinder is once more in a horizontal plane. 

 If the cylinder is symmetrical about a plane perpendicular 

 to the axis of the channel, for example, a circular or elliptical 

 cylinder, the system of stream-lines obtained above would be 

 symmetrical about the lengthwise and crosswise plane. A 

 consideration of the next term in the expansion, however, 

 indicates how asymmetry about the crosswise plane arises. 

 This is due to the fact that the expression on the right-hand 

 side of (8 b) is of the same s"gn in opposite quadrants. The 

 result of this is, that whereas the loading still maintains 

 symmetry about the x axis, asymmetry occurs about the 

 y axis. The stationary points A and B are thus, as can be 

 seen by a simple inspection, similar to that already indi- 

 cated, moved further back towards the rear of the body, the 

 extent depending upon the value of YL/c with which yjr l 

 is associated. It is evident that the exact expressions for 

 the various functions could be obtained by experiment, and 

 until that is carried through, no general conclusions can be 

 drawn, but the general nature of the stream-lines is clearly 

 indicated in the foregoing discussion. It is hoped in a 

 future paper to indicate how the system of equations (8 b), 

 (8 c), etc. can be solved graphically. 



§ 7. Simple cases for verification. — As a check on the 

 analysis the case of a cylinder rotating in a viscous fluid 

 inside a concentric cylinder is here worked out. It should 

 be noticed that in this case the body is not moving forward 

 with constant speed but rotating with constant angular 

 velocity; but the necessary modifications and boundary 



