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LVII. On the Dimensions of a Magnetic Pole in the Electro- 

 static System of Units. (Second Article.) By Prof. J. D. 

 Evebett*. 



MY appeal for an explicit statement of Maxwell's definition 

 of the unit pole in the electrostatic system has brought 

 me several communications from correspondents; and the diver- 

 sity between them is a sufficient proof of the necessity for such 

 an appeal. My correspondents do not refer me to any explicit 

 definition by Maxwell himself, but give investigations which 

 they regard as substantially his and which lead to his result. 

 Two of these investigations seem quite satisfactory, and show 

 that Maxwell's result can be obtained with as much simplicity 

 as that of Clausius. They are given under the heads I., II., 

 below. 



Before entering on the points in dispute with respect to the 

 electrostatic system, I may premise that the definitions of the 

 unit quantity of electricity, the unit current, the unit electro- 

 motive force (or difference of potential), and the unit resist- 

 ance (all of which may be called purely electrostatic defini- 

 tions), are not in question, but are accepted by all parties. 

 The divergence begins Avhen we attempt to express magnetic 

 quantities in an electrostatic system; and different results may 

 be obtained according to the particular relation between mag- 

 netism and electricity which we select as the guiding principle 

 in our definitions. In a strict sense there is no such thing as 

 an electrostatic unit of any magnetic quantity; since magne- 

 tism and its relations to electricity lie outside the domain of 

 electrostatics. 



There are three- laws of nature any one of which may be 

 used to connect electrical with magnetic units. 



I. The galvanometer law, as I may for brevity call it, 

 because it is the law which determines the force which a cur- 

 rent passing through the coil of a galvanometer exerts upon 

 either pole of the needle. This law, stated without any assump- 

 tion as to units, is that the force varies directly as the length 

 of the wire, the strength of the current, and the strength of 

 the pole, and inversely as the square of the distance of the wire 

 from the pole. We must therefore, in every system, have 



Force = k x x Current x Pole x Length -r (Distance) 2 , (1) 

 &x being a factor which depends on the system employed. 

 Maxwell's unit pole may be defined by making l\ = l. This 

 gives, for determining the dimensions of a pole, 



MLT- 2 = Current x Pole x IT 1 . 



* Communicated by the Author. 

 2K2 



