420 Mr. A. Russell on the Magnetic 



condenser charge, as follows from Maxwell's theory and from 



Lorentz's method, is proportionate to — ^ — , where K denotes 



the dielectric constant. And this is in perfect accord with 

 the experimental result that the magnetic force is pro- 

 portionate to the fraction — ^ — . 



Now any theory which yields this coefficient for the Eontgen 

 current, leads to the same coefficient called FresneFs coefficient 

 for the Fizeau experiment. Evidently according to Maxwell 



T ^ equals 1 „ where n is the refractive index, if we 



K 1 n z 



disregard dispersion effects. I intend working out a complete 



theory of the Fizeau experiment on the basis of the principle 



of relativity. 



I hope to have shown by this short survey that this 

 principle can account for all the known facts of electro- 

 magnetism. 



Bonn Univeisity, 



January 1907. 



XXXIII. The Magnetic Field and Inductance Coefficients 

 of Circular, Cylindrical, and Helical Currents. By 

 Alexander Russell, M.A., M.I.E.E* 



Table of Contents. 



1. Introduction. 



2. Mathematical Formulae. 



3. Formulae for the magnetic force at any point due to the current in a 



circular filament in rectangular, polar, and bipolar coordinates. 



4. Applications of the Formulae. 



i. Force in the plane of a circular current, 

 ii. The mutual inductance of two coaxial circular currents, 

 iii. Approximate formula for the self-inductance of a circular 

 current. 



5. Applications to Hydrodynamics. 



6. The magnetic force due to a cylindrical current sheet. 



7. Formulae for the mutual inductance between two coaxial cylindrical 



current sheets. 



8. Formulae for the mutual inductance between a helical current and a 



coaxial cylindrical current sheet. 



9. Formulae for the self-inductance of a helical current, when the pitch 



of the helix is small. 



1. Introduction. 



SERIES formula? f are usually given for the components 

 of the magnetic force at a point in the neighbourhood of 

 a current flowing in a circular filament. They are generally 



* Communicated by the Physical Society : read February 8, 1907. 

 t E. Mascart and J. Joubert, Lecons sur VElectvicite et le Magnetisme, 

 vol. ii. § 566 (1897). 



