INTRODUCTORY OBSERVATIONS. 15 



When any hollow conducting shell is charged with elec- 

 tricity, the whole of the fluid is carried to the exterior surface, 

 without leaving any portion on the interior one, as may be 

 immediately shown from the fourth and fifth articles. In the 

 experimental verification of this, it is necessary to leave a small 

 orifice in the shell : it became therefore a problem of some 

 interest to determine the modification which this alteration would 

 produce. We have, on this account, terminated the present 

 article, by investigating the law of the distribution of electricity 

 on a thin spherical conducting shell, having a small circular 

 orifice, and have found that its density is very nearly constant 

 on the exterior surface, except in the immediate vicinity of the 

 orifice ; and the density at any point p of the inner surface, is to 

 the constant density on the outer one, as the product of the 

 diameter of a circle into the cube of the radius of the orifice, 

 is to the product of three times the circumference of that 

 circle into the cube of the distance of p from the centre of the 

 orifice ; excepting as before those points in its immediate vicinity. 

 Hence, if the diameter of the sphere were twelve inches, and 

 that of the orifice one inch, the density at the point on the inner 

 surface opposite the centre of the orifice, would be less than the 

 hundred and thirty thousandth part of the constant density on 

 the exterior surface. 



In the eleventh article some of the effects due to atmo- 

 spherical electricity are considered ; the subject is not however 

 insisted upon, as the great variability of the cause which pro- 

 duces them, and the impossibility of measuring it, gives a degree 

 of vagueness to these determinations. 



The form of a conducting body being given, it is in general 

 a problem of great difficulty, to determine the law of the dis- 

 tribution of the electric fluid on its surface : but it is possible 

 to give different forms, of almost every imaginable variety of 

 shape, to conducting bodies ; such, that the values of the density 

 of the electricity on their surfaces may be rigorously assignable 

 by the most simple calculations : the manner of doing this is 

 explained in the twelfth article, and two examples of its use are 

 given. In the last, the resulting form of the conducting body 

 is an oblong spheroid, and the density of the electricity on its 



