234 MR. HARRIS ON SOME ELEMENTARY LAWS OF ELECTRICITY. 



before (14.), the respective capacities were found to be in a simple inverse ratio of the 

 areas. Thus, when the area m ?i\ fig. 20, was doubled, so as to become equal 

 area 7n n, whilst at the same time m h -\- h n equalled m K -{- K n\ the intensity was 

 only one half as great. 



57. Since, then, the intensity of a rectangular plate, is inversely as its perimeter 

 when the area is constant, and inversely as its area, when the perimeter is constant, it 

 follows that the intensity must vary inversely with those quantities jointly ; or calling 

 I the intensity, A the area, and P the perimeter, we have 



1 



Ice 



AP 



This, however, is on the supposition that the quantity of electricity is constant ; but 

 if the quantity varies, whilst the form and size of the conductor remain the same, 

 then from the results obtained (20.) the intensity, is as the square of the quantity ; 

 therefore, if .r represent the number of measures of electricity (12.), we have 



I 



AP 



Now the capacity of a conductor, is measured, by the quantity of electricity it can re- 

 ceive under a given intensity ; and from the above formula we have 



x2 a I A P 



If, therefore, we take the intensity constant, x will represent the capacity, and we 



shall have 



Capacity a -v^ A P 



To obtain, therefore, rectangular plane conductors, having capacities, double, treble, &c., 

 of a given conductor, we must construct them so, that the areas and perimeters shall 

 be also, double, treble, &c., of the first respectively ; a deduction which is in a great 

 measure confirmed by the following experiments. 



(</.) A circular plate a, fig. 2, being placed in connexion with the electrometer, a 

 given quantity of electricity was transferred on it by means of a well insulated plate 

 of given dimensions. The intensity being observed, a second equal quantity, trans- 

 ferred as before, was added to the former, when, according to the general law (16.), 

 the resulting intensity amounted to just four times the first. 



The electricity of the different bodies was now neutralized, and a transfer-plate 

 applied to the jar, the area and perimeter of which, was just double that of the for- 

 mer. This plate being deposited on the circular area in contact with the electrometer, 

 the intensity was found to be exactly the same as that produced by two contacts of 

 the first plate (14. h.). In a similar manner, a transfer-plate of a treble area, and 

 treble linear boundary, abstracted from the jar as much electricity at one contact, as 

 the first did by three successive contacts ; but this result could not be obtained under 

 any other disposition of the areas of the respective plates. 



It may perhaps be requisite to observe, that slight differences may occasionally 



