210 ELEMENTARY LESSONS ON [CHAP. iv. 



257. Electrostatic Units. No special names have been 

 assigned to the electrostatic units of Quantity, Potential, 

 Capacity, etc. The reasons for adopting the following values 

 as units are given either in Chapter I. or in the present Chapter. 



Unit of Quantity. The unit of quantity is that quantity of 

 electricity which, when placed at a distance of one 

 centimetre from a similar and equal quantity, repels it 

 with a force of one dyne (Art. 236). 



Potential. Potential being measured by work done in moving 

 a unit of + electricity against the electric forces, the unit 

 of potential will be measured by the unit of work, the erg. 



Unit Difference of Potential. Unit difference of potential 

 exists between two points, when it requires the expendi- 

 ture of one erg of work to bring a unit of + electricity 

 from one point to the other against the electric force 

 (Art. 242).' 



Unit of Capacity. That conductor possesses unit capacity 

 which requires a charge of one unit of electricity to bring 

 it up to unit potential. A sphere of one centimetre 

 radius possesses unit capacity (Art. 247). 



Specific. Inductive Capacity is denned in Art. 268 as the ratio 

 between two quantities of electricity. The specific 

 inductive capacity of the air is taken as unity. 



258. Dimensions of Units. It has been assumed above 

 that a velocity can be expressed in centimetres per second ; for 

 velocity is rate of change of place, and it is clear that if change 

 of place may be measured as a length in centimetres, the rate 

 of change of place will be measured by the number of centi- 

 metres through which the body moves in a given time. It is 

 impossible, indeed, to express a velocity without regarding it as 

 the quotient of a certain number of units of length divided by 

 a certain number of units of time. In other words, a velocity 



= a a ^l ; or, adopting L as a symbol for length, and T as a 

 symbol for time, V ^, which is still more conveniently written 

 V = L x T ~ . in a similar way acceleration being rate of 

 change of velocity, we have A = ^ "= ~^ = ^ = L x T ~ 2 * 



Now these physical quantities, "velocity," and "acceleration," 

 are respectively always quantities of the same nature, no matter 

 whether the centimetre, or the inch, or the mile, be taken as the 

 unit of length, or the second or any other interval be taken as 



