﻿On Electromagnetic Lines and Tul>es. 705 



4. A theoretical derivation for the " exponential formula " 

 is given, which attributes to the exponent 1/n a theo- 

 retical significance which is in qualitative agreement with 

 experience. 



It is not claimed that the theory advanced is a com- 

 plete solution of the problem, or that it is valid in all 

 cases, but the agreement obtained is sufficient to indicate 

 that the mechanism of adsorption suggested may be an 

 approximation to the truth. 



The work contained in this paper was done while the 

 author was " Coutts Trotter" student of Trinity College, 

 Cambridge. 



LXI. On Electromagnetic Lines and Tubes. By S. R. 

 Milner, D.Sc, F.R.S., Professor of Physics, Ihe Uni- 

 versity, Sheffield *. 



IN a recent paper Professor Whittaker t has shown that it 

 is possible to extend the conception of the tubes of force 

 of electrostatic and magnetostatic fields to the general electro- 

 magnetic field, when this is considered as a four-dimensional 

 entity. The differential equations which express the pro- 

 perties of the calamoids, or surfaces from which the tubes 

 are formed, are rather complex, and it is not easy to see from 

 them in their gen oral form a clear picture of what the tubes 

 really are. It is hoped that the treatment of the question 

 contained in the following paper may be of use, as it not 

 only enables such a picture of the position and direction in 

 hyperspace of the tubes to be formed, but it also extends 

 Whittaker's results in certain respects. 



§ 1. TJie Construction of Electromagnetic Lines. 



In an electrostatic field in three dimensions the course of 

 a line of force can be traced out from a given point by first 

 orienting the axes so that % lies along the direction of the 

 electric force at the point, and then continually rotating 

 the axes so that this condition is still obeyed at successive 

 points infinitesimally distant from each other along the 

 curved line which the .r-axis thus forms. The properties 

 of the tubes can be expressed in terms of the curvatures of 



* Communicated by the Author. 



t Proc. Roy. Soc. Edin. xlii. p. 1 (Nov. 1921). 



Phil. Mag. S. 6. Vol. 44. No. 262. Oct. 1922. 2 Z 



