On the Physical Units of Nature. 53 



It is easy to ascertain the relation of this metric electrine to 

 the B.A. (British Association) standards for electrical measure- 

 ment, which are those most in use. The B.A. units are electro- 

 magnetic units based on the following fundamental units — the 

 second for unit of time, the metre-seven (the quadrant of the 

 earth, or lO'' metres) for unit of length, and the eleventh-gramme 

 (or gramme divided by 10") for unit of mass. These were so 

 chosen as to furnish a connected body of systematic units with 

 such values that the practical electrician could conveniently use 

 them. Now the ' dimension ' of electromagnetic quantity of elec- 

 tricity is [■\/LM] (see B.A. Report for 1863, p. 159).* Hence and 

 from the foregoing values of the lengthine and massine of the 

 B.A. series — 



e, : One Ampere = 1 : ^jqTi 

 Therefore ej = 100 Amperes. 



The term Ampere is here used to designate the B.A. unit of 

 quantity, corresponding to the Ohm (the B.A. electromagnetic 

 unit of resistance), the Volt (the corresponding unit of electro- 

 motive force), the Weber (unit of current), and the Farad (unit of 

 capacity). The electrostatic units of the B.A. series might with 

 great advantage be called the static-Ampere, static-Ohm, static- 

 Volt, and static-Farad. 



Units like the above, whether of the metric or of the B.A 

 series, of which three are fundamental and all others derived 

 from them in such a way as will exclude unnecessary coefficients 

 from our equations, are called systematic units. In forming the 

 existing artificial series of systematic units it has been usual to 

 regard the units of length, time and mass as fundamental and the 

 rest as derived, but there is nothing to prevent our regarding any 

 three independent members of the series as fundaviental and 

 deriving the others from them. It is the aim of the present paper 

 to point out that Nature presents us with three such units ; and 

 that if we take these as our fundamental units, instead of choos- 

 ing them arbitrarily, we shall bring our quantitative expressions 

 into a more convenient, and doubtless into a more intimate, rela^ 

 tion with Nature as it actually exists. I will then approximate 



* This follows at once from the fundamental equations of electromagnetism, viz. : — 



^ EE- ^ „, ^ CM ^ MM- 



Foe -^, E Ci, F = — ^, F = —T- 



