Mr. F. Jenkin on the New Unit of Electrical Resistance. 481 



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 equi- 

 valent 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 measure of resistance is styled - or -, precisely 



second second 



as the common non-absolute unit of work involving the product of 



a weight into a length is styled kilogrammetre or foot-pound. The 



Committee have chosen as fundamental units the second of time, the 



metre, and the mass of the Paris gramme. The metrical rather than 



the British system of units was selected, in the hope that the new 



unit might so find better acceptance abroad, and with the feeling that 



while there is a possibility that we may accept foreign measures, there 



is no chance that the Continent will adopt ours. The unit of force is 



taken as the force capable of producing in one second a velocity of one 



metre per second in the mass of a Paris gramme, and the unit of work 



as that which would be done by the above force acting through one 



metre of space. These points are very fully explained in the British 



Association Report for 1863, and in the Appendix C to that Report by 



Professor J. Clerk Maxwell and the writer *. 



The magnitude of the is far too small to be practically con- 

 second 



venient, and the Committee have therefore, while adopting the system, 



chosen as their standard a decimal multiple 10 10 times as great as 



Weber's unit (the — ), or 10 7 times as great as the . 



\ second / second 



This magnitude is not very different from Siemens' s mercury unit, 



which has been found convenient in practice. It is about the 



twenty-fifth part of the mile of No. 1 6 impure copper wire used as 



* [See pp. 409, 507 of the present volume of this Magazine.] 



