Diffraction of an Annular Aperture. 7 



By means of this series I have computed the value of E for 

 every value of e, proceeding by steps of 02 from 0-0 to 10;0. 

 Ahhough the series does in all cases ultimately converge with 

 great rapidity, yet for large values of e it commences by di- 

 verging rapidly. Thus for e = lO'O the successive terms are 

 1-0, 



- 25-0, 

 + 156-25, 



— 434-0277, 



+ 678-168, &c. 

 and for this value it was necessary to proceed as far as e^. 

 The calculations have been made to six places of decimals, 

 but I have thought it prudent to retain only four places. I 

 may add, that the calculations have not been examined with 

 great care, but that, from the care with which they were made 

 and the general regularity of progression among the numbers, 

 I am confident that there is no large error in the results. 



Table of the values of E = -^J(^ cos (e cos 0), the limits 

 of the integral being and 2 -n. 



It nppears from this table that E vanishes for the values of 



