ON STANDARDS OF ELECTRICAL RESISTANCE. 149 
varies, this force, f, is inversely proportional to the square of the distance, d, 
between them; hence 
eT i, 
Pages Chet aseatied 4 Phato, CB 
When g and q, are of dissimilar signs, f becomes negative, 7.¢. there is an 
attraction, and not a repulsion. ‘This equation is incompatible with the 
electromagnetic definitions given in Part III., and, if it be allowed to be 
fundamental, gives a new definition of the unit quantity of electricity, as 
that quantity which, if placed at unit distance from another equal quantity 
of the same kind, repels it with unit force. 
34, Electrostatic System of Units—This new measurement of quantity 
forms the foundation of a distinct system or series of units, which may be 
called the electrostatic units, and measurements in these units will in these 
pages be designated by the use of small letters; thus, as Q, C, &c., sig- 
nified quantity, “current, &c., in electromagnetic measure, so g, ¢, ¢, and 7, &e., 
will represent the electrostatic measure of quantity, current, electromotive 
force, resistance, &c. 
The relations between current and quantity, between work, current, and 
electromotive force, and between electromotive force, current, and resistance, 
remain unchanged by the change from the electromagnetic to the electro- 
static system. 
30. Ratio between Electrostatic and Electromagnetic Measures of Quantity. 
—NSince the expression forming the second member of equation (17) represents 
LM L?M? 
a force the dimensions of which are —, the dimensions of q are —T" The 
fie 
dimensions of the unit of electricity, Q, in the electromagnetic system are 
A (25). Hence, since in passing from the one system to the other we 
must employ the ratio ef , this ratio will be of the dimensions 2 that is to 
say, the ratio Z is a velocity. In the present treatise this velocity will be 
Q J Pp 
designated by the letter v. 
The first estimate of the relation between quantity of electricity measured 
statically and the quantity. transferred by a current in a given time was made 
by Faraday*. A careful experimental investigation by MM. Weber and 
Kohlrauscht not only confirms the conclusion that the two kinds of measure- 
ment are consistent, but shows that the velocity v= a is 310,740,000 metres 
per second—a velocity not differing from the estimated velocity of light more 
than the different determinations of the latter quantity differ from each other. 
v must always be a constant, real velocity in nature, and should be measured 
in terms of the system of fundamental units adopted in electrical measure- 
ments (3 and 55). A redetermination of v (46) will form part of the present 
Committee’s business in 1863-64. It will be seen that, by definition, the 
quantity transmitted by an electromagnetic unit current in the unit time is 
equal to v electrostatic units of quantity. 
36. Electrostatic Measure of Currents.—In any coherent system, a current 
* Experimental Researches, series iii. § 361, &c. 
+ Abhandlungen der Konig. Sachsischen Ges. Bd. iii. (1857) p. 260; or, Poggendorff’s 
Annalen, Bd. 99. p. 10 (Aug. 1856), 
