14 ROSA and grover: inductance formulas and tables 



ELECTRICITY. — Formulas and tables for the calculation of mutual 

 and self inductance. (Revised.) E. B. Rosa and F. W. 

 Grover. To appear in the Bulletin of the Bureau of 

 Standards, 8: 1-237. 1911. 



With the increase in the precision demanded in electrical 

 measurements, and in the standardization of electrical apparatus, 

 and more especially in the determination of the fundamental 

 units in absolute measure, there has arisen the necessity for more 

 and more precise standards of mutual and self inductance, whose 

 values may be calculated from their dimensions. 



For example, in the calibration of working standards of self and 

 mutual inductance, the values are very conveniently referred 

 to those of absolute standards, consisting of windings of bare or 

 enamelled wire wound uniformly on accurately turned forms 

 of marble or other suitable non-magnetic material. The formulas 

 for the calculation of the constants of such standards from their 

 dimensions should be capable of at least the precision attainable 

 in the measurement of the dimensions of the coil and the pitch of 

 its winding. 



In the most accurate methods employed for the absolute meas- 

 urement of resistance and for the absolute measurement of 

 current by means of a current balance, it is required that the 

 value of a standard of mutual inductance may be calculated to 

 about one part in one hundred thousand. 



In magnetic measurements and in wireless telegraphy, a knowl- 

 edge of the calculated value of a mutual or self inductance is 

 often requisite, although in these cases a smaller degree of pre- 

 cision is sufficient. 



The problem of the calculation of inductance received consider- 

 able attention as early as Maxwell's time, with the result that the 

 constants of the simpler forms, such as circles, solenoids, and coils 

 whose cross-section is not too large relatively to the radii, were 

 calculated with fair precision. Some of these solutions are abso- 

 lute formulas, involving elliptic integrals; others are expressed 

 as infinite series, the number of terms requisite being governed 

 by the precision desired, and the degree of convergence of the 

 formula for the case in question. 



