XXVI INTRODUCTION. 



quantities of magnetism is taken as the basis. In this system the quantities force, 

 quantity of magnetism, and length are connected by an equation of the form 



r mm, 



where m and m^ are in this case quantities of magnetism, and the other symbols 

 have the same meaning as before. In this case it has been usual to assume the 

 magnetic inductive capacity of air to be unity, and to express the magnetic induc- 

 tive capacity of other media as a simple number representing the ratio of the in- 

 ductive capacity of the medium to that of air. These numbers, by analogy with 

 specific inductive capacity for electricity, might be called specific inductive capac- 

 ities for magnetism. They are usually called permeabilities. {^Vide Thomson, 

 " Papers on Electrostatics and Magnetism," p. 484.) In this case, also, like that 

 for electricity, the unit quantity of magnetism is obtained by making m ^=^ m^, and 

 /, a, and / each unity. 



In both these cases the intrinsic inductive capacity of the standard medium is 

 suppressed, and hence also that of all other media. Whether this be done or not, 

 direct experiment has to be resorted to for the determination of the absolute val- 

 ues of the units and the relations of the units in the one system to those in the 

 other. The character of this relation can be directly inferred from the dimen- 

 sional formulae of the different quantities, but these can give no information as to 

 the relative absolute values of the units in the two systems. Prof. Riicker has 

 suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist- 

 ence of the suppressed properties by putting symbols for them in the dimensional 

 formulae. This has the advantage of showing how the magnitudes of the different 

 units would be affected by a change in the standard medium, or by making the 

 standard medium different for the two systems. In accordance with this idea, the 

 symbols K and P have been introduced into the formulae given below to represent 

 inductive capacity in the electrostatic and the electromagnetic systems respectively. 

 In the conversion formulae k and/ are the ordinary specific inductive capacities 

 and permeabilities of the media when air is taken as the standard, or generally 

 those with reference to the first medium taken as standard. The ordinary for- 

 mulae may be obtained by putting K and P equal to unity. 



ELECTROSTATIC UNITS. 



1. Quantity of Electricity. — The unit quantity of electricity is defined as 

 that quantity which if concentrated at a point and placed at unit distance from an 

 equal and similarly concentrated quantity repels it, or is repelled by it, with unit 

 force. The medium or dielectric is usually taken as air, and the other units in ac- 

 cordance with the centimetre gramme second system. 



In this case we have the force of repulsion proportional directly to the square 

 of the quantity of electricity and inversely to the square of the distance between 

 the quantities and to the inductive capacity. The dimensional formula is there- 

 fore the same as that for [force X length^ X inductive capacity]* or M*L'T~^K\ 

 and the conversion factor is mHH~^k^, 



