IN THK NEIGHBOURHOOD OF A CAUSTIC. 



ms 



APPENDIX. 



On the numerical computation of the definite integral /„ cos - {uf - m.w), 



between the limits and - . 







The simplicity of the form of this differential coefficient induces me 

 to suppose that the integral may possibly be expressible by some of the 

 integrals whose values have been tabulated. After many attempts how- 

 ever, I have not succeeded in reducing it to any known integral : and 

 I have therefore computed its value by actual summation to a consider- 

 able extent and by series for the remainder. 



The summation was continued jfor each of the values of m in the 

 table given in (17)}, as far as w = 2. This extent was divided into 

 eight sections, corresponding nearly to quadrants of the circular func- 

 tion when m = 0, as follows : 



These sections were divided into small intervals corresponding to 

 uniform increments in the value of w, as follows : 



In the 1st section the increment of w was 004, 



2nd -02, 



3rd 018, 



«h 014, 



5th 012, 



6th 010, 



7th 010, 



8th 008. 



