<500 Messrs. Cowley and Levy: Method of Analysis suitable 



If now the value of ty for the deflexion of: the flat plate be 

 identified with the stream-function component yfr 0} it is a 

 simple matter to interpret the boundary conditions in terms 

 of those tor the plate. 



Consider first the determination of ^r . The fundamental 

 equation 



V 4 ^o = o 



indicates that it may be taken to represent the deflexion of 

 an unloaded flat plate. 



Along the curve representing the moving boundary, how- 

 ever, the two component slopes are given — viz., -^— = 0, 



^-° = — 1; and this curve must therefore be clamped to 



have these slopes at each point. Although tlnN determines 

 the relative elevation of each point of *this boundary, it does 

 not fix the elevation of the whole curve with reference 

 to, say, that of the other boundary. This is immediately 

 derived from the interpretation of the remaining condition, 



Prom equation (16) this implies that 



i Kds = 0; 



that is to say, the total shearing force round the curve corre- 

 sponding to the fixed boundary must be zero. Consequently 

 the absolute elevation of the curve corresponding to the 

 moving boundary must be so adjusted that no resultant 

 shearing force is brought fo bear on the curve corresponding 

 to the fixed boundary. The conditions can be realized with 

 comparative simplicity in practice; but for the present it is 

 sufficient to note that under the circumstances described 

 a measurement of the elevations of each point on the plate 

 will determine the function yjr directly. 



By inserting this value for yjr in the expression on the 

 right-hand side of the equation (8 b) an expression is derived 

 which, when interpreted in the light of the parallelism 

 explained above, determines the lateral loading which must 

 be imposed on the same plate as before. The boundary 

 conditions can be interpreted with equal ease and simplicity, 

 and by a direct measurement of the deflexions \jr 1 is at once 

 derived. A repetition of this process leads successively to 

 the evaluation of the functions yjr 2 , ^s, et c» 



