of Aerial and Electrical Waves hij a Grating. 307 



The half-breadth of the oval in the direction of x is found by 

 putting f/ = ; thus 



cosh— = 1 + *tt, (20) 



a tj 



whence l r/a = , 2537. The two diameters therefore agree 

 within 1£ per cent. 



The cylinders used were of circular section, and the value 

 of a was calculated from the formula 



a = 25tan— , {21) 



where b denotes the radius ; this is obtained by putting 

 x — O^y — b in (17). The theoretical period was then obtained 

 from (b*), with l+a. written for /. 



The tank used in the experiments was 5 feet long, 8*95 in. 

 wide, and about 12 in. deep. A series of observations was 

 made with different depths of water, in the case of each 

 cylinder, and the period compared with that obtained when 

 the cylinder was removed. In order to ensure an exact com- 

 parison a hook gauge was used, and the level of the water 

 adjusted so as just to reach the sharp point. 



The oscillations were started by alternately raising and 

 lowering one end of the tank, in an approximately simple- 

 harmonic manner, by means of a lever, the period corre- 

 sponding as nearly as might be to that of the free oscillations. 

 In this way the production of minor surface waves was 

 discouraged ; but it was found impossible, when the obstacle 

 was present, to avoid altogether the simultaneous generation 

 of the second normal mode of oscillation, whose period is 

 (very nearly) half that of the fundamental mode which was 

 the object of study. The effect of this was, however, com- 

 pletely eliminated by the method used for counting the 

 oscillations. This consisted in observing, by means of a 

 telescope with cross-wires set up at one end of the tank, the 

 reflexion of a sharply defined object on a distant building, 

 the axis of the telescope being directed to a point on the 

 central transverse line of the water surface. The second 

 mode of oscillation referred to affects the level, but not the 

 inclination, of this part of the surface ; and the modes of 

 still higher frequency subsided too rapidly to affect the 

 observations, which were of course only begun after a short 

 interval. 



It was found possible in this way to observe as man} as 

 200 oscillations with an initial vertical amplitude of about 

 ^ in. at the end of the tank ; but it was found that greater 



