458 WOLFF, SHOEMAKER, BRIGGS : RESISTANCE STANDARDS 



one of the above general formulas for the force, the maximum 

 value of the force can at once be determined. In some cases 

 the maximum force can be calculated directly from a formula 

 given here in which this substitution has been made once for all. 



The formula for the critical distance is, unfortunately, not 

 simple enough to allow of the direct calculation of the critical 

 distance from the given ratio of the radii. It is, however, not 

 difficult to obtain the desired value with great accuracy by a 

 method of successive approximation, provided a first approxi- 

 mation is at hand. 



The latter part of the paper is devoted to the development of 

 methods for facilitating this process. The formulas derived are 

 fully illustrated by numerical examples, and tables are given of 

 the critical distance and the value of the maximum force for such 

 values of the ratio of the radii as are likely to occur in practice. 

 It is further shown how the constants for coils, whose dimensions 

 differ slightly from one of the exact ratios given in the table, 

 may be derived from the latter values with little trouble and labor. 



To test the new formulas ' the complete calculations of the 

 constants of the coils of the Bureau of Standards current balance 

 have been carried through, and the results were found to be in 

 agreement with the values obtained by the interpolation method 

 within less than a part in a million. . 



PHYSICS. — On the construction of primary mercurial resistance 

 standards.'^ F. A. Wolff, M. P. Shoemaker, and C. A. 

 Briggs, Bureau of Standards. 



This paper deals with the construction of four one-ohm mer- 

 cury standards of resistance in accordance with specifications 

 adopted by the International Conference on Electrical Units and 

 Standards (London, 1908). The London Conference defined the 

 international ohm as the resistance offered to an unvarying elec- 

 tric current by a column of mercury at the temperature of melt- 

 ing ice, 14.4521 grams in mass, of a constant cross-sectional area 

 and of a length of 106.300 cm. 



' To be presented in full as a Scientific Paper of the Bureau of Standards. 



