1891.] Fluxes of Energy in tlie Electromagnetic Field. 127 



uttermost. Practical forms are considered. In the electromagnetic 

 application the flux of energy has a four-fold make-up, viz., the 

 Poynting flax of energy, which occurs whether the medium be 

 stationary or moving ; the flux of energy due to the activity of the 

 electromagnetic stress when the medium is moving ; the convection 

 of .electric and magnetic energy ; and the convection of other energy 

 associated with the working of the translational force due to the 

 stress. 



As Electro- magnetism swarms with vectors, the proper language 

 for its expression and investigation is the Algebra of Vectors. An 

 account is therefore given of the method employed by the author for 

 some years past. The quaternionic basis is rejected, and the 

 algebra is based upon a few definitions of notation merely. It may be 

 regarded as Quaternions without quaternions, and simplified to the 

 uttermost ; or else as being merely a conveniently condensed expres- 

 sion of the Cartesian mathematics, understandable by all who are 

 acquainted with Cartesian methods, and with which the vectorial 

 algebra is made to harmonise. It is confidently recommended as a 

 practical working system. 



In continuation thereof, and preliminary to the examination of 

 electromagnetic stresses, the theory of stresses of the general type, 

 that is, rotational, is considered ; and also the stress activity, and 

 flux of energy, and its convergence and division into translational, 

 rotational, and distortional parts ; all of which, it is pointed out, may 

 be associated with stored potential, kinetic, and wasted energy, at 

 least so far as the mathematics is concerned. 



The electromagnetic equations are then introduced, using them in 

 the author's general forms, i.e., an extended form of Maxwell's 

 circuital law, defining electric current in terms of magnetic force, 

 and a companion equation expressing the second circuital law ; this 

 method replacing Maxwell's in terms of the vector potential and the 

 electrostatic potential, Maxwell's equations of propagation being 

 found impossible to work and not sufficiently general. The equation 

 of activity is then derived in as general a form as possible, including 

 the effects of impressed forces and intrinsic magnetisation, for a 

 stationary medium which may be eolotropic or not. Application of 

 the principle of continuity of energy then immediately indicates that 

 the flux of energy in the field is represented by the formula first 

 discovered by Poynting. Next, the equation of activity for a moving 

 medium is considered. It does not immediately indicate the flux of 

 energy, and, in fact, several transformations are required before 

 it is brought to a fully significant form, indicating (1) the Poynting 

 flux, the form of which is settled ; (2) the convection of electric and 

 magnetic energy ; (3) a flux of energy which, from the form in which 

 the velocity of the medium enters, represents the flux of energy due 



