484 Dr. J. Robinson on Konig's Theory of the 



experienced the same velocity. In applying this to the case 

 when they do not have the same velocity, it was assumed 

 that the force of one sphere on the other was a function of 

 the velocity at the former sphere. 



The present investigation shows that this assumption was 

 not well founded. 



The law cos*- j showed only that the experimental results 



given in the paper quoted agreed qualitatively with Konig's 

 theory. The law here found gives also what may be taken 

 as a quantitative agreement, and so the experimental results 

 quoted give another verification of Konig's theory. 



The following calculation shows how well the law just 

 developed agrees with the experimental results. In the 

 paper quoted above, the mean distance between two ripples 

 was given at different places between two nodes. This latter 

 was divided into three equal parts, left, middle, and right, and 

 the mean distance between two consecutive ripples in each 

 part measured. Hence the distance between two ripples was 

 measured at the antinodes and near the nodes. The ratio of 

 these distances was found as follows : — 



Using fine iron powder and a frequency of 3208, the 

 distances between the consecutive ripples in the three parts 

 were found to be 1*01, 1'25, and 1*07 mm. respectively. 

 The mean distance at the sides was thus 1*04 mm., and at 

 the centre 1*25 mm. The ratio of the mean distance at the 



1*04 

 sides to that at the centre thus was -=-^z, ="83. 



12 5 



In this way this ratio was found, for the different powders 

 used, to be 



0-941, n ■ , 



rv.no >-ior tine iron powder. 



0-80 

 0-70 



coarse 



0-781 , 



0-89 f " emei T powder. 



0-661 

 0-70 J " ' 



sand. 



The two values for each powder are for two different 

 frequencies. The mean ratio is 0*78. 



