246 Intelligence and Miscellaneous Articles. 



it for a new class of condensers, that of concentrical spherical con- 

 densers. 



The problem which I proposed to solve was as follows : — Given 

 two concentrical spheres, suppose that the inside sphere, whose 

 radius is r, is placed in contact with a constant source of electricity, 

 and that the external sphere whose radius is H, is placed in contact 

 with the ground ; it is required to express the charge of the inside 

 sphere in terms of the radii r and R. 



In order to obtain the corresponding question of propagation, it 

 is sufficient to suppose that the insulating substance, which sepa- 

 rates the two spheres in the case of condensation, is replaced by a 

 medium which is a conductor, but to a far less extent than the 

 substance of which the spheres consist. The problem then con- 

 sists in finding an expression for the intensity of the current 

 transmitted from the internal sphere to the external one ; and this 

 latter question is easily solved. 



Suppose two concentric spheres very near each other, and having 



the radius x and x-\-dx {x being less than R and greater than r) ; 



the resistance of the medium comprised between these two spheres 



Izdx 

 will be expressed by — — , k being a constant coefficient ; and this 

 x 



resistance will be the differential of the total resistance of the sphe- 

 rical ring comprised between the spheres of the radii r and x. This 



total resistance will thus have the value kl — J , that of the ring 



comprised between the spheres of the radius r and radius R will be 

 expressed by k( - ~ -^- J, and consequently the intensity of the cur- 

 rent transmitted will be proportional to R . Now, from the prin- 

 ciple which I have adduced at starting, the charge expressed in the 

 case of condensation ought to be proportional to this same expres- 

 sion. It was necessary to ascertain experimentally if this were so. 



To do this I have compared, two by two, six concentrical spherical 

 condensers, the armatures of which had the following dimensions : — 

 Internal sphere. External sphere. 



Diameter in Diameter in 



millimetres. millimetres. 



No 1 61'5 890 



2 61-5 118-5 



3 61-5 161-0 



4 90-5 118-5 



5 90-5 161-0 



6 120-0 161-0 



I charged these six apparatus successively by placing them in 

 communication with the same source, and 1 determined the charge 

 accumulated on the sphere by the methods described in my pre- 

 ceding Notes. Through a circular aperture, 30 millims. in diameter, 



