Relations between Electrical Measurements. 509 



surements in these units will in these pages be designated by 

 the use of small letters : thus, as Q, C, &c, signified quantity, 

 current, &c, in electromagnetic measure, so q, c, e, and r, &c, 

 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 electrostatic system. 



35. Ratio between Electrostatic and Electromagnetic Measures 

 of Quantity. — Since the expression forming the second member 

 of equation (1 7) represents a force the dimensions of which are 



LM . . IJ?M 2 



7p§-, the dimensions of q are — ^ — . The dimensions of the 



unit of electricity, Q, in the electromagnetic system are L 2 M 2 (25). 

 Hence, since in passing from the one system to the other we 



must employ the ratio ~) this ratio will be of the dimensions 



fp ; that is to say, the ratio ~ is a velocity. In the present 



treatise this velocity will be designated by the letter v. 



The first estimate of the relation between quantity of electri- 

 city measured statically and the quantity transferred by a cur- 

 rent in a given time was made by Faraday*. A careful experi- 

 mental investigation by MM. Weber and Kohlrauschf not only 

 confirms the conclusion that the two kinds of measurement are 



consistent, but shows that the velocity v= gr 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 con- 

 stant, real velocity in nature, and should be measured in terms 

 of the system of fundamental units adopted in electrical mea- 

 surements (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 elec- 

 tromagnetic unit current in the unit time is equal to v electro- 

 static units of quantity. 



36. Electrostatic Measure of Currents. — In any coherent sys- 

 tem, a current is measured by the quantity of electricity which 

 passes in the unit of time (15); if both current and quantity 



* Experimental Researches, series iii. § 361, &c. 



f Abhandlungen der Kbnig. Sdcksischen Ges. vol. iii. (1857) p. 260 j 

 or Poggendorff's Annalen, vol. xcix. p. 10 (Aug. 1856). 



