PROCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH. 
VOL. XLII. 
1921 - 22 . 
I. — On Tubes of Electromagnetic Force. By Professor 
E. T. Whittaker, F.R.S. 
(Read November 7, 1921. MS. received November 11, 1921 . •••9 
§ 1. Introduction. 
The object of the present paper is to introduce certain surfaces, which 
will be shown to play the same part in the general electromagnetic field 
as Faraday’s tubes of force do in electrostatic and magnetostatic fields. 
The value of Faraday tubes in electrostatics and magnetism has led 
many investigators to seek for them a wider application, in connection 
with variable electromagnetic fields. In such investigations it has 
generally been assumed that the tubes are to be defined in much the 
same way as in static fields, but that instead of being at rest they are in 
motion. It cannot be said, however, that researches on these lines have 
led to completely satisfactory results : and the reason for this comparative 
failure is supplied by the Principle of Relativity. For, in the case of a 
purely electrostatic field, we can imagine an observer who is at rest 
relative to the electric charges : the electric force, as measured by this 
observer, depends only on the charges and their position, so that the 
Faraday tubes based on his measurements furnish a representation of the 
field which does not involve any arbitrary foreign element. If, however, 
we consider a field in which a number of charges and magnets are moving 
independently of each other, it is not possible for an observer to be at 
rest relative to all of them, and therefore all observers are on a footing 
The results of this paper were communicated to Section A of the British Association 
at its meeting in Edinburgh on September 8, 1921, 
VOL. XLII. 
