456 grover: calculation of force between currents 



From considerations of bimetallic wires as two circuits in par- 

 allel, formulas are obtained which permit the computation of 

 effective resistance and inductance of the wires. The core is 

 treated as one circuit and the shell as another; the self inductance 

 of each is computed, as well as the mutual inductance of one on 

 the other. Assuming no skin effect in the shell and introducing 

 the effective resistance and inductance of the core for a given 

 frequency, the resistance and inductance of the whole wire can 

 be computed for that frequency from the expressions for the 

 equivalent resistance and inductance of two circuits in parallel. 

 The measured values of the copper-clad wire for low current 

 strengths are compared with the computed values, and the agree- 

 ment is very satisfactory. The formulas are also used in com- 

 puting wire tables for copper-clad steel wire. Values of effec- 

 tive resistance and inductance are tabulated for the even sizes 

 from No. to No. 12 A. W. G. for conductivities of 30, 40, and 

 50 per cent of hard drawn copper and for frequencies up to 1000 

 or 3000 cycles per second. 



PHYSICS.- — The calculation of the maximum force between two 

 parallel, coaxial, circular currents.^ Frederick W. Grover, 

 Bureau of Standards. 



The force of attraction or repulsion between two currents 

 flowing in parallel, coaxial, circular paths of unequal radii, 

 increases as the distance between their planes is increased, until 

 a maximum value of the force is reached, and then, as the dis- 

 tance is indefinitely increased, decreases toward zero as a limit. 



It was shown by Maxwell that the distance for which the force 

 is a maximum bears a ratio to either of the radii, which is a func- 

 tion of the ratio of the radii alone, and depends in no way on their 

 absolute values. Further, the maximum value of the force, 

 with unit current in each circuit, is also a function of the radii 

 alone. 



These facts have been utilized in the current balance, first 

 used by Lord Rayleigh, in which is measured the force between 



^ Detailed paper to appear in the Bulletin of the Bureau of Standards 



