257, 258] EQUATIONS OF ELECTROMAGNETIC FIELD. 557 



258. Other Systems of Units. The systems of units that 

 have been explained in this book are those in universal use. The 

 electromagnetic system is the one altogether used in practical 

 measurements, but as we have seen when considering the mutual 

 effects of electrical and magnetic phenomena the Gaussian system 

 is least liable to produce confusion. When only electrostatic 

 phenomena are under consideration the electrostatic system is 

 most convenient. 



A change of units has been proposed by Heaviside, who would 

 define the unit of electricity and magnetism in such a way that 

 the flux of force due to unit charge out from a closed surface in 

 air should be unity in value, instead of 4?r. This would have the 

 convenient effect of causing the disappearance of the factor 4?r 

 from many of our equations, for instance from the equation 



while the energy per unit volume would be 



A practical advantage would be the disappearance of 4?r in 

 the formula connecting current-turns with magnetomotive-force. 

 On the other hand the quantity 4?r would be introduced in certain 

 places where it is now absent. For instance the force at a distance 

 r from a charged point m would be 



ra 



It is rather singular that Maxwell adopted this method in his 

 definition of electrical displacement, making the density equal to 

 the divergence of the displacement, but did not do it in the case 

 of the magnetic induction, nor even of the electric force. He was 



therefore obliged to make the displacement equal to -- times the 



force, and his equations have an unfortunate appearance of dis- 

 symmetry. This has been avoided by Hertz, and in the present 

 book, and it therefore seems merely a matter of convenience in 

 writing whether we adopt Heaviside's proposition or not. Heavi- 

 side has called the new units rational, probably not because they 

 are more reasonable than the old ones, but because of their avoid- 

 ance in the majority of cases of the irrational number 4?r. Of the 



