MAXWELL'S METHOD. 101 



CL X (ft 



If the ratios - , and are of the same order, we get to the 

 cb 0* 



same degree of approximation. 



(44) 



X = T_l_ + 3_(__ll 



b 2 b* 8 r { 70 - " 



2 b* 16 



743. MAXWELL'S METHOD. In passing from the action of a 

 single current to that of a coil, instead of using quadratures as in the 

 preceding paragraph, it is sometimes more advantageous to use the 

 following method employed by Maxwell.* 



Let P be a function of two variables x and y it is desired to 

 calculate the function P defined by the equation 



(45) P-- 



that is to say, the mean value of P within the limits of the 

 integration. 



If P is the value of the function P for x = and y = 0, Taylor's 

 theorem gives 



Replacing P by this value in the above expression, and integrating 

 between the limits in question, all the uneven terms of x and y 

 vanish ; the final result, divided by xy^ is the desired value of P. 



X 2 () 2 P 



The term -r for instance, gives 



1 



2' ~ 



We have finally, 



* MAXWELL. Electricity and Magnetism, Vol. u., p. 304. 



