

518 Mr. E. C. Rimington on Luminous 



this gives 



("dc 12V . ' f <te U*+e>-, P* +*),*, \ 



| — . at = rr- sm < e b + e b + e* + &c. > . 



The series in the bracket is a geometrical progression, in 



a 



which the constant factor is e^ n ; and, since a is negative, 

 this is less than unity. 



Hence 



J. 



*dc , 2Vsin<9 e& 

 at 



n dt bL , « 



and 



to^^/^^orsin^^/! 



4L 



NT T7D; 



tan «;= /y KR2 > or sm t7= V 

 also 



/4L-KR 2 , sin (9 ,r— 

 b= V 4KL 2 ' and ~F" = KL; 



j>-«v 



K g 



L 'i-* 



2V \/ 



fty/ KR * -fa-fl), / KR2 



6 v 4L-KR2 — £ V 4L _ KR 2 



Let ^ /"gg" sf and t^ /" 1 ^*— = 

 V 4L-KR 2 V 4L--KR 2 y 



Then the denominator =e x — e x -y, and 

 e*= 1 +#+ j- + jg- + &c, 



c i-t-ci y+ g |2 |2 + |3 |3 



|3 |3 + ' 



* e y+ |2 |2 + |3 |3 + |3 



4- terms of the 4th, 5th, &c. powers, 



