802 PROCEEDINGS OF THE AMERICAN ACADEMY. 



correction is 0.3 of the maximum change. The value of the correction 

 may be best obtained by reading down from the ordinate unity. 



These computations also show that equation (29) 



x 

 9i = 1 ~ 7^ 



i 

 630 



may be employed up to frequencies of 10,000 for this particular coil, and 

 that equation (30) 



3 



X 



may be used for frequencies beyond 120,000 per second. As the max- 

 imum correction is 0.2 per cent of the total, if frequencies under 4000 per 

 second are used, the error will not be over 0.2 per cent X 0.005 = 0.001 

 per cent, which is practically negligible. 



If, however, other things being equal, the diameter of the wire were 

 four times larger than it is, the same corrections would correspond to 

 frequencies 16 times less, or an error of 0.001 per cent is now obtained 

 at a frequency of only 250. 



This suggests, if large currents must be carried, that to wind the coil 

 with flat wires would diminish the effect of the frequency upon both the 

 changes in self-inductance and resistance. 



The Plots I and II, just derived, show how the self-inductance of a 

 circular current sheet falls off with the frequency. In other words, the 

 coil is assumed to be wound with wires of rectangular cross-section. 

 This may cause a doubt as to the applicability of the curve in question. 



In the first place, the method of its use does away with the necessity 

 of knowing the constant multiplier of the function Q, as explained above ; 

 and in the second place, the following two reasons go to show the entire 

 correctness of the deductions. 



Sornmerfeld finds that his results agree to a constant pres with those 

 of Max Wien, which were deduced for circular wires, and both formulae 

 agree remarkably well with the experimental data at hand ; this for the 

 increase of resistance with the frequency. We should, therefore, fairly 

 expect the results for the decrease in self-inductance to also be correct to 

 within a constant factor. As there are no data available for the decrease 

 in self-inductance, we have not been able to verify this conclusion. To 

 further assure ourselves, however, we have worked out the problem of 

 the change of self-inductance with the frequency in an infinite straight 

 circular-ring conductor, using the approximation formulae for the Bessel's 



