On the Dimensions of Physical Quantities. 235 



indeed proved by the relation 



0*] = (L- 2 T 2 )*, 

 then the fact that the dimensions of electrical and magnetic 

 quantities are different in the two systems arises only from 

 our ignorance of the dimensions of fi and k, which must be 

 such as to bring the two systems into accord when ultimately 

 expressed in terms of L, M, and T. Prof. Pucker therefore 

 suggested that yu and k should be admitted into the formulae 

 along with L, M, and T, and that, since nothing is definitely 

 known as to their physical nature, they should be regarded as 

 secondary fundamental units, additional to L, M, and T, but 

 which must be ultimately expressed in terms of them. There 

 is thus, in each formula, an indication that the irrational and 

 unsuggestive dimensions are not absolute as they stand ; each 

 formula is made to express a physical reality, and each con- 

 tains in the proper form the factor necessary to render the 

 formula absolute. This system has been adopted, among 

 others, by Prof. Gray in his smaller edition of 'Absolute 

 Measurements in Electricity and Magnetism,' and by Prof. 

 Everett in his last edition of ' Units and Physical Constants.' 



Prof. Fitzgerald has pointed out (Phil. Mag. April 1889) 

 that if a system be taken" in which the dimensions of /j, and k 

 are the same, and of the dimensions of a slowness, that is the 

 inverse of a velocity (L _1 T), then the two systems become 

 identical as regards dimensions, and differ only by a numerical 

 coefficient just as centimetres and kilometres do." But 

 although fju and k are quantities of the same order, both being 

 capacities, their dimensions need not necessarily be the same, 

 unless electrification and magnetization be phenomena of the 

 same order as well. If, however, these be different orders — 

 as they almost certainly are — the one possibly a strain, the 

 other a vortex motion, then it is unlikely that k and fi, bearing, 

 as each does, similar relations to two dissimilar phenomena, 

 should have identical dimensions. 



In one of the Appendices to ' Modern Views of Electricity ' 

 Dr. Lodge develops a system in which fi and k~ l have re- 

 spectively the dimensions of density and rigidity. It is then 

 found that the dimensions of all the other quantities become 

 unique, and capable of purely dynamical interpretations. 

 Thus, magnetic moment becomes linear momentum; magnetic 

 induction, linear momentum per unit volume; magnetic force, 

 velocity; electrical force, pressure ; current, displacement x 

 velocity; self-induction, "inertia per unit area," &c. In a 



* See also " On the Dimensions of a Magnetic Pole in the Electrostatic 

 System of Units," Dr. Lodge, Phil. Mag. Nov. 1882. 



