798 PROCEEDINGS OF THE AMERICAN ACADEMY, 



for different values of x, as well as of Q t and Q. 2 , where 



} > = - 8S>) md < 29 > 



?.=?• (30) 



Table II contains all of the data. 



It is clearly seen that as long as x < 2 that formula Q x may be 

 used, while if x > 7, formula (?o is valid. In between these points, the 

 calculated values will serve. 



A plot of these three functions on the next page shows still more 

 clearly the relations of the three formulae for different values of x. 



Manner of Using the Curve. 



This curve is to be used in the following manner. We assume that 

 in any coil of a single layer, the falling off of the self-inductance takes 

 place according to equation (22), represented by the full-line curve, and 

 theinaximum ordinate unity is taken to be the maximum change possi- 

 ble of the self-inductance, which is otherwise calculable. For any given 

 dimensions of the coil, the values of x correspond to definite frequencies, 

 and either a table or a plot of corrections may be derived from the above 

 curve. 



For small values of x, and therefore for small values of the frequency, 

 the correction varies proportionately to d 4 , while for very large frequen- 

 cies it is proportionate to \/d by equations (29) and (30). 



As the first case is the more usual, it is important, in order to avoid 

 the necessity of any correction, to wind the coil with wires of small 

 diameter. The size necessary to avoid a correction under a given fre- 

 quency may easily be calculated. As an application of this theory, the 

 following example will be carried out: 



Consider a coil of 27 cms. radius = r x wound with a single layer of 

 wire whose diameter d is .063 cms. Let the conductivity of the wire be 

 taken as 5.9 X 10 -4 . Then the relation between x and n is n = 2630 x' 1 

 from (19) where n = frequency. In the following table, column 2, are 

 the values of x corresponding to the frequencies n in column 1. In 

 column 3 are the values of the ordinates corresponding to these values of 

 x taken from the Plot (I). 



