IS BRLL SYSTEM TECHXICAL JOURNAL 



AlM'KNDIX 



Equation (5) is 



I II 



.IB(\ - cos ul) 



S = A -\- B 



A -^ B 



III IV 



y4 2^2(1 _ cos utY ylVi'(l - cos ut) 



2{A -{- By 2iA -\- By 



To expand tliese terms we write 



1 1 



{A -{-By (E -\- e -\- ME COS pt-\- me COS qty 



1 / 11 {ME cos pt + me cos qt) 



C^) 



{E + ey \ E^e 



}i(ii-\-\){ME cos pt-{-})ie co^qt)^ 



, , ,, v(n^\)(tJ + 2)---(}i-\-r-\)( ME cos pt-\-nie cos qt)'\ .. . 



It is evident there are present in S an infinite number of frequencies 

 and it is necessary to select those which are of appreciable magnitude 

 relative to that of the desired frequency of amplitude £.1/. Fortu- 

 nately these are not very numerous. 



In deciding whether or not a given term should be retained there 

 are two points to be considered: (1) whether all the terms of a given 

 frequency total to a value sufficiently large to call for the presence of 

 this term in the final result; (2) what per cent accuracy should be 

 required in the frequencies which are retained. Thus if it is desired to 

 retain all frequencies the relative amplitude of which is greater than 

 0.01 we cannot arbitrarily retain all individual terms which make a 

 contribution of 0.01 or greater and neglect those of relative importance 

 of less than 0.01. Thus if a term of a given frequency has a relative 

 amplitude of 0.01 and another term of the same frequency a relative 

 amplitude of 0.009 the second term should be retained. Otherwise we 

 should have a large percentage error in the value of the amplitude of 

 this frequency. On the other hand it is not desirable to maintain 

 the same degree of accuracy for the case of retained frequencies of 

 slight relative importance as for those of large importance. As a 

 compromise all individual terms have been retained which, after 

 division by EM, are of a magnitude greater than 0.005 for any values 

 of M , m and e'lE which are here dealt with. An exception is made in 



