382 Prof. R. Clausius on the different Systems of 



England as correct throughout, but also to be adopted un- 

 altered in the works of writers belonging to other nations. In 

 regard to the latter, I will mention only Mascart and Joubert's 

 valuable Legonssur V Electricite et le Magndtiame (Paris, 1882), 

 and Herwig's useful book, Physikalische Begriffe und absolute 

 Maasse (Leipzig, 1880). 



Nevertheless I think I can show that Maxwell has committed 

 an error in his development, by which several of his formula? 

 have been rendered incorrect. The correction of this mistake 

 appears to me to be especially necessary just now, since at the 

 present time -the attention of wider circles than formerly is 

 directed to this subject by the decisions of the Congress of 

 Electricians at«Paris upon the electrical units of measurement, 

 and hence an error remaining uncorrected might be mis- 

 chievously disseminated and fixed. It also appears to me 

 that Maxwell's exposition of the subject (which is not all col- 

 lected together in one passage of his book, but appears in 

 portions in different parts of it) presents some difficulty to the 

 understanding. Hence I think that a connected presentation 

 of the thing, as simple and distinct as possible, will not be 

 unwelcome. 



§ 1. The Fundamental Units and the first General Equation of 

 each System. 



As already mentioned above, the units of mass, length, and 

 time are employed as fundamental units. After Maxwell, it 

 is usual to denote them by enclosing in square brackets 

 the letters which are generally employed to represent those 

 three kinds of quantity. Thus the unit of mass is [M] , the 

 unit of length [L] , and the unit of time [T] . 



From these are immediately obtained the units of various 

 other quantities. That velocity with which a unit of length 

 is passed through in the unit of time is employed as the unit 

 of velocity; hence, for its representation, we have to divide the 

 unit of length by the unit of time, and we get the formula 

 [LT -1 ] . The unit of force is that force which imparts the unit 

 of velocity to the unit of mass in the unit of time; hence we 

 obtain the formula which serves to represent it, if we divide 

 the product of the mass-unit and the velocity-unit by the time- 

 unit, whence arises [MLT -2 ] . The unit of mechanical work 

 is that work which is done by the force-unit along a path 

 equal to the length-unit ; and therefore, in order to represent 

 it, we need only to multiply the force-unit by the length-unit, 

 by which we get [ML 2 T~ 2 ]. 



Now, for the measurement of electricity we must employ 



