FERROMAGNETIC DISTORTION OF A WAVE 345 



Recapitulation of Principal Results 



General formulae have now been made available for calculating the 

 flux density over a wide range of conditions of two-frequency mag- 

 netization. For many ordinary purposes a table or graph of some of 

 the results is convenient ; useful ones are therefore included. 



The hypergeometric expansions in the coefficients of case 1 can be 

 put to further use to examine the behavior of the induction for special 

 ratios of fundamental amplitudes and frequencies. When k <^\ and 

 /c <^ 1 the coefficients of the several frequencies in the induction reduce 

 to simple, rational, algebraic expressions of the amplitudes. These 

 coefficients likewise reduce when k = \ and k = 1, since 



^ '^'^'^ r(7 - «)r(7 - /3) 



Third order coefficients for case 1 with restricted parameters, and 

 also those for case 2 are tabulated in the accompanying table through 

 terms in the lowest power of the smaller amplitude. Underlined sub- 

 scripts distinguish lower side frequencies ; a bar under a digit indicates 

 it is to be taken with a negative sign. 



When the ratio of amplitudes is unrestricted, graphs of the coef- 

 ficients which specify the induction enable their magnitudes to be 

 determined most readily. The strongest products are found to be the 

 third order lower side frequencies; Fig. 3, calculated by A. G. Tynan, 

 may be used to get both components of either of these. The corre- 

 sponding upper side frequencies are almost as strong ; their amplitudes 

 can be found from the figure by virtue of the relations Ci2 = C12 and 

 C21 = C21, since their other components are zero. 



By interchanging P and Q and likewise p and q in either the table or 

 the graphs, the subscripts are also reversed. In the table the inequal- 

 ities restricting the columns are reversed thereby, since the inter- 

 changed quantities are arbitrarily assignable. This procedure does 

 not extend the applicability of either case, but does permit the appli- 

 cation of case 1 directly to both extremes of the amplitude ratio and 

 the use of the oiirves to evaluate the amplitudes of both lower side 

 frequencies. The scope of the table and curves given has been 

 extended in this manner. A field of usefulness sufficiently extensive 

 for most purposes of present-day communication is thereby achieved. 



