158 Mr. F. Jenkin Report on the New Unit [April 6, 



reproduction, which are by no means contemptible, arbitrary material 

 standards, whether of mercury, gold, silver, platinum, or any other mate- 

 rial, would be heterogeneous isolated units without any natural connexion 

 with any other physical units. The unit proposed by Weber, on the other 

 hand, forms part of a symmetrical natural system, including both the fun- 

 damental units of length, time, and mass, and the derived electrical units 

 of current quantity and electromotive force. Moreover it has been shown 

 by Professor W. Thomson*, who accepted and extended Weber's proposal 

 immediately on its appearance, that the unit of absolute work, the con- 

 necting link between all physical forces, forms part of the same system, 

 and may be used as the basis of the definition of the absolute electromag- 

 netic units. 



The full grounds of the choice of the Committee could only be explained 

 by a needless repetition of the arguments given in the reports already made 

 to the British Association. It will be sufficient here to state that, in the 

 absolute electromagnetic system, the following equations exist between the 

 mechanical and electrical units : 



W=C 2 Itt, (1) 



where W is the work done in the time t by the current C conveyed 

 through a conductor of the resistance R. This equation expresses Joule 

 and Thomson's law. 



c =l <*> 



where E is the electromotive force. This equation expresses Ohm's law. 

 Q=C*, (3) 



expressing a relation first proved by Faraday, where Q is the quantity of 

 electricity conveyed or neutralized by the current in the time t. Finally, 

 the whole system is rendered determinate by the condition that the unit 

 length of the unit current must produce the unit force on the unit pole 

 (Gauss) at the unit distance. If it is preferred to omit the conception of 

 magnetism, this last statement is exactly equivalent to saying that the unit 

 current conducted round two circles of unit area in vertical planes at right 

 angles to each other, one circuit being at a great distance D above the 

 other, will cause a couple to act between the circuits of a magnitude equal 

 to the reciprocal of the cube of the distance D. This last relation expresses 

 the proposal made by Weber for connecting the electric and magnetic 

 measure. These four relations serve to define the four magnitudes R, C, 

 Q, and E, without reference to any but the fundamental units of time, 

 space, and mass ; and when reduced to these fundamental units, it will be 

 found that the measurement of R involves simply a velocity, i. e. the 

 quotient of a length by a time. It is for this reason that the absolute 



* Phil. Mag. Dec. 1851, 4th series, vol. ii. p. 551. 



