294 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If the harmonics are to be expressed in terms of time and the period of 

 the e. m. f. wave, which is the same as the period of the secondary 

 oscillation, the substitution 



2a; = 2irnt or 



x= — -— IS to be made. 



Then ^2 = ^ (-43 sin 27rl ^j^ + .50 sin 27r«^ + .26 sin 2;r[^ 1^ — .061 

 sin 27r \^\t + .028 sin 27rl -^ 1^ — .017 sin 27T[^Ji5 + . .j 



The results for I. C. F. equal to 3 and 4 are given below. 

 I. C. F. = 3 



es = E(.2l sin 27rr| |i + .33 sin 2^1^ 1^ + .33 sin S'rl^ |^ + 



.24sin2Trr ^ U+.lOsin 27r ^ U-.04sin 2it\ ~ \t-. . . j 



LC. F. =4 



^4 = ^^.12 sin 277 J p + .21 sin 2tt\ ^ K+ -26 sin 2-k\ '^ \t + 



.25 sin 2n?it + .20 sin 277 '^ U + .13 sin 27r ^ r + • • • • ) 



A classification of the harmonics is given in the adjoining table, 

 where the columns are headed according to the I. C. F. 



The coefficients of the various terms in the developments mean very 

 little, but the existence of most of the harmonics, given in the table, 

 has been verified by wave meter readings. 



A much more beautiful proof of the existence of the harmonics is 

 presented by Braun tube oscillographs. If, in addition to the arrange- 

 ment of circuits shown in Figure 13 for obtaining the primary wave 

 form, another adjustable secondary circuit be used, excited by the 

 primary current, and having a deflecting coil also about the Braun tube 

 and parallel to the primary deflecting coil, the pattern observed on the 

 fluorescent screen is the resultant of the deflections of the first sec- 



