Page:Scientific Memoirs, Vol. 2 (1841).djvu/462

the word conductibility occurs without any closer definition, the absolute conductibility is always to be understood.

Hitherto we have left out of consideration the change which the disk suffers from the adjacent atmosphere. This influence may easily be determined. If, for instance, we designate by $c$ the circumference of the disk belonging to the abscissa $x$, then $c\,dx$ is the portion of its surface which is exposed to the air; consequently, according to the experiments of Coulomb, mentioned in § 9,

$bcu\,dx\,dt$

is the change of the quantity of electricity which is occasioned in the disk $M$ by the passing off of the electricity into the atmosphere during the moment of time $dt$, where $b$ represents a coefficient dependent on the cotemporaneous nature of the atmosphere, but constant for the same atmosphere. It expresses a decrease when $u$ is positive, and an increase when $u$ is negative. But in accordance with our original supposition, this action cannot occasion an inequality of the electroscopic force in the same section of the body; or at least, this inequality must be so slight that no perceptible alteration is produced in the other quantities; a circumstance which may nearly always be supposed in the galvanic circuit.

Accordingly, the entire change which the quantity of electricity in the disk $M$ undergoes in the moment of time $dt$ is

$\chi \omega {\frac {d^{2}u}{dx^{2}}}dx\cdot dt-bcu\,dx\,dt,$

in which the portion is comprised which arises from the motion of the electricity in the interior of the body as well as that which is caused by the circumambient atmosphere.

But the entire change of the electroscopic force $u$ in the disk $M$ effected in the moment of time $dt$ is

${\frac {du}{dt}}dt,$

consequently the total change in the quantity of electricity in the disk $M$ during the time $dt$ is

$\omega {\frac {du}{dt}}dx\,dt,$

where, however, it is supposed that under all circumstances similar changes in the electroscopic force correspond to similar changes in the quantity of electricity. If observation showed that different bodies of the same surface underwent a different