224 PIERCE. 



B- B^ B^ 



cosB=l-^+~--^ , (78) 



5^ B^ 

 BsinB = B^--f^+~ - (79) 



Equations (77), (78) and (79) substituted in (76) will give 



where Fn (-B) is a polynomial in fi", B-, B*, etc., where the coefficients 

 of the several powers of B are contained in the table of page 225. 



In this table the bottom row of terms gives the coefficients of the 

 powers of B, when the summation indicated in (80) is performed 

 with ?? = 2, 4, 6- • • • 03 . The various terms in the colunuis were 

 employed in obtaining the last row by addition. 



The coefficient of B^'^ is not contained in the table, because of its 

 numerous terms, but its value when summed up is 



255?t^ + 6084/1^ + 51396n^ + 177264ri + 193536 



10 ! (w + 1) (w + 3) {n + 5) (» + 7) {71 + 9) 



Substituting the values of the coefficients multiplied by the corre- 

 sponding powers of B and summing up as indicated in equation (80), 

 we obtain for the power the expression 



P 



P = 



' \ B' _ n^ 135^ _ B'^ ) 



'" ) 60 3780 • 56700 93555 ) 



_ \ B" _ ^ , ^ B^ I 



) 1120 6480 83160 77395500 \ 



\. W R^ 7B^ I 



i 7.6 } ^ ^ L '^ '- (81) 



^ / 45360 24960960 6134720 \ ^ ' 



This cquaiion gives the average jjou-er radiated in the aerial hemisphere 

 from the flat-top of the antenna regarded as a separate radiator with the 

 distribution that it has under the fundamental assumptions of the problem. 

 The current is to be measured in absolute electrostatic units, and the power 

 is in ergs per second. 



