306 Prof. H. Lamb and Mr. G. Cook on Transmission 



The experiment was tried in this form, and the results were 

 satisfactory so far as they went; but the motion was so 

 rapidly damped that it was difficult to determine the period 

 with any great accuracy. When the oscillations were started 

 it was necessary to wait for some time until the turbulent 

 motion of the water swirling round the sharp edges of the 

 slit had subsided. 



The remaining case is covered by the form uke * 



. . 2tx 

 smh 



<j)=X- 



f=I/ 



. 'ZlT.r 27TU 



cosh —cos 



a a 



. 2iry 

 sin — — 

 a 



, 2lTX 217//' 



cosh cos 



a a 



(16) 



where yjr is the stream-function in the electrical (conduction 

 problem, a denoting as before the breadth of the tank. The 

 stream-lines i/r= Hh-Ja correspond to the sides; for x — we 

 have <f> = 0, and for x = oo , </> — x + \a. The stream-line ^ = 

 consists partly of an oval curve 



. 2777/ 

 61 O Sln 



cosh cos — -=a — , . . . [10 



a a "y / 



which may be taken to represent the section of the obstacle, 

 and partly of the portions of the axis of x which lie outside 

 this oval. By assigning different values to a. we obtain a 

 series of possible forms. 



AVhen the ratio a/a is small, the oval reduces to a circle 



xr + tf = lr, (18) 



approximately, provided 



a = 2irh 2 ja (19) 



This implies that the ratio b/a must be smalt ; but it 

 appears on examination that the circular form is not seriously 

 departed from even when a/a is a considerable fraction. 

 Suppose, for example, that the transverse diameter is one- 

 half the breadth, a ratio not exceeded in the actual experi- 

 ments. If in (17) we put # = 0, y/a = %, we find a/a = ^. 



* Hydrodynamics, p. 514. 



