grovee: calculation of force between currents 457 



two parallel circular coaxial coils, one fixed, and the other at- 

 tached to one end of the beam of a balance, the distance between 

 the planes of the coils having been adjusted until the force 

 exerted between the currents in the coils is a maximum. From 

 the observed weights, which must be added to the other arm of 

 the balance to restore equilibrium, the value of the current flow- 

 ing through the two coils in series may be calculated, provided 

 the ratio of the radii is known. The latter may be determined 

 experimentally by an electrical method, without measuring the 

 individual radii, and with an accuracy not attainable from direct 

 measurements of the dimensions of the coils. 



The calculation of the constant of the balance is based on the 

 theory for two circular filaments to which the coils may be re- 

 garded as equivalent. The corrections necessary to be taken 

 into account, because of the finite cross section of the coils, have 

 been derived by Rayleigh, Lyle, and others, and reference may 

 be made to the paper on the "Determination of the International 

 Ampere in Absolute Measure," by Rosa, Dorsey, and Miller, 

 for a treatment of this question and for other details concerning 

 the theory and methods of manipulation of the balance. 



The force between two parallel, circular coaxial currents of 

 given radii, situated with any desired distance between their 

 planes, may be calculated by the formula of Maxwell in elliptical 

 integrals, or by the formulas of Nagaoka which involve q series. 



Previously, the value of the maximum value possible of 

 the force between any two such circular currents, of given radii, 

 has been obtained bj^- calculating the force directly (by means 

 of the formulas just mentioned) for a number of chosen distances 

 of the coils in the neighborhood of the critical distance, which 

 was supposed to have been approximately determined before- 

 hand. The final value of the maximum force was determined 

 by interpolation from this series of calculated values. This 

 process is indirect and laborious. 



In the detailed paper to be published a formula is derived for 

 calculating the value of the critical distance from the assumed 

 ratio of the radii. By substituting the distance thus found in 



