ROSA AND GROVER: INDUCTANCE FORMULAS AND TABLES 15 



For numerical calculation, the absolute formulas have the dis- 

 advantage that the inductance is given by the difference of two 

 nearly equal terms, each of which is many times larger than 

 the desired quantity. In such cases, each term must be calculated 

 with greater precision than is required in the result. Series for- 

 mulas, on the other hand, exhibit a satisfactory degree of conver- 

 gence over a more or less limited range only, two or more series 

 formulas being, as a rule, necessary to cover the same ground as a 

 single absolute formula. 



It thus occurs that several formulas are available in almost 

 every case, and the question naturally prssents itself as to what 

 criterion may be applied to aid in the selection of a suitable for- 

 mula for the solution of a given problem, and which is the more 

 reliable when their results do not agree. 



It was to furnish an answer to these questions that Messrs. 

 Rosa and Cohen undertook, in 1906-07, a critical examination 

 of all the existing formulas which had come to their notice. In 

 the course of this investigation, certain formulas were found to be 

 in error or capable of giving approximate values only, others were 

 extended by them so as to give more accurate results, and in 

 addition many new formulas were derived. These results ap- 

 peared in a series of papers in the Bulletin of the Bureau of 

 Standards. 



At the conclusion of the work, a compilation was made of all 

 those formulas which had been shown to be suitable for numerical 

 calculation, together with auxiliary tables of elliptic integrals and 

 other constants useful in such calculations. The work was 

 divided into nine sections, treating of the mutual and self induc- 

 tance of coaxial circles, solenoids, and coils of rectangular cross- 

 section and of linear conductors, together with a chapter on 

 geometric and arithmetic mean distances. A special feature 

 was a collection of examples so chosen as to provide an illustra- 

 tion of the various formulas, and to show the agreement and rela- 

 tive degree of convergence of the different formulas applicable 

 to the same problem. 



Since the appearance of this collection of formulas in 1907, 

 a number of new formulas have appeared, and the edition becom- 



