WITH AN APPENDIX BY PROFESSOR A. LODGE. 



95 



In the table of coefficients it will be observed that the highest entry occurs at 

 n = 10, in accordance with an anticipation expressed in a former paper. 



As will readily be understood, the multiplication by P,, and the summations involve 

 a good deal of arithmetical labour. These operations, as well as most of the 

 preliminary ones, have been carried out in duplicate with the assistance of 

 Mr. C. BOUTFLOWER, of Trinity College, Cambridge. 



kc = 10. 



The results are recorded in the annexed table and in curve B, fig. 1. The 

 intention had been to limit the calculations to intervals of 1 5, but the rapid increase 

 in (F~ + G 2 ) between 165 and 180 seemed to call for the interpolation of two 

 additional angles. This increase, corresponding to the bright point in POIWSON'S 

 experiment of the shadow of a circular disc, is probably the most interesting feature 

 of the results. A plot is given in fig. 1, showing the relation between the angle ft, 

 measured from the pole, and the intensity, proportional to F- + G 2 . It should, 

 perhaps, be emphasised that the effect here dealt with is the intensity of the pressure 

 variation, to which some percipients of sound, e.y., sensitive flames, are obtuse. 

 Thus at the antipole a sensitive flame close to the surface would not respond to a 

 distant source, since there is at that place no periodic motion, as is evident from the 

 symmetry. 



I now proceed to consider the case where the source, as well as the place of 

 observation, are situated upon the sphere ; but as this is more difficult than the 

 preceding, I shall not attempt so complete a treatment. It will be supposed still 

 that kc =10. 



