Ripple Formation in Kundt's Tuhe. 485 



This -ratio can be calculated for the law cost— - as 

 follows :— 2 l 



If 21 is the distance between two nodes then the middle 



part of the distance between the two nodes extends - to 



o 



each side of an antinode, and the sides extend from 



I 



o to I. Thus we need to plot the curve y = acosi0, and 



then the ratio required is the ratio of the mean ordinate of 

 this carve from 30° to 90° to its mean ordinate from 0° to 

 30°. 



The curves y =■ a cost 9 



and y = a cost 



were drawn, and from them the required ratios were calcu- 

 lated. The results are shown in the following table. Now 

 as the ripples generally do not extend as far as the nodes it 

 is not correct to take the mean ordinate from 30° to 90°. 

 Thus in the following table this has been calculated for three 

 different cases, 30° to 90°, 30° to 80°, and 30° to 70°. 





cos 5 9. 



coa 8 0. 



Mean ordinate from 30° -90° 

 Mean „ „ 0°-30° 



0'60 



043 



Mean ordinate from 30° -80° 

 Mean „ „ 0° -30° 



0-65 



045 



Mean ordinate from 30° -70° 

 Mean „ „ 0°-30° 



0-76 



0-56 



Now the mean value of this ratio from the experimental 

 results is 0'79. Hence considering the ripples to extend 

 only from 0° to about 70°, which is frequently the case, we 

 see that there is a very good agreement between the experi- 

 mental results and the law costd deduced from Konig's 

 theory ; in fact these results furnish another quantitative 

 agreement between experiment and this theory. 



Armstrong College, Newcastle-on-Tyne, 



December 17, 1909. 



