That these experiments may succeed well, the air must be very dry; else the electricity of the large globe, escaping through the air, will tend directly to neutralize the weak electricity of the opposite kind, which is developed at the point a of the little globe, and the phenomena will become much less sensible, if not entirely disguised.
We have hitherto supposed the two globes to have been brought into contact before being submitted to their mutual influence. This condition establishes between the quantities of electricity, which they possess, a relation that limits the generality of which the problem is susceptible, and to embrace it entire ly, we must consider two spheres charged, in any proportion whatever, with electricity of the same or of a different nature; and that they gradually ap proach each other until they come into contact.
Here the analysis of M. Poisson has anticipated the results of experiment ft is from thence that we shall draw the details into which we are to enter; and which, if they should come one day to be ob served, will furnish the severest test to which this analysis can be submitted.
When two electrified spheres are made gradually to approach each other, and when there does not exist between the species and the quantities of elec tricity which they possess, the particular relation which would be established by their contact, the thickness of the electric stratum at the points near est each other, on the two surfaces, becomes greater and greater, and increases indefinitely as their dis tance diminishes. It is the same with the pressure exerted by the electricity against the mass of air in. tercepted between the two spheres ; since the pres sure, as we have mentioned above, is always pro portional to the square of the thickness of the elec tric strata. It must at last then overcome the re sistance of the air, and the fluid, in escaping under the form of a spark or otherwise, must pass, previous to the contact, from the one sUrflice to the other. The fluid thus accumulated, before the spark takes place, is of a different nature, and of nearly equal intensity on each of the spheres. If they are elec trified, the one vitreously and the other resinously, it is vitreous in the first and resinous in the second; but when they are both electrified in the same man ner, vitreously for example, there arises a decompo sition of the combined electricity upon the sphere which contains less of the vitreous fluid than it would have in the case of contact; the resinous electricity, resulting from this decomposition, flows towards the point where the spark is preparing, and, on the con trary, the other sphere, which contains more vitre ous electricity than it would have after the contact, remains vitreous over its whole extent.
The phenomena are no more the same after the two spheres have been brought in contact together, and are then removed, however little, from each other. The ratio which then exists between the total quantities of electricity with which they are charged, causes to disappear in the expression of the thickness, the term which before became infinitely great for a distance infi nitely small, and no spark takes place. The electricity
of the points nearest each other upon the two spheres is then very feeble, for very small distances, accord .
ing to a law which calculation determines, and its intensity is nearly the same on both spheres ; but when they are unequal, this electricity is vitreous on the one, resinous on the other; and it is always upon the smallest that it becomes of a nature con try to the total electricity, which is conformable to the observations related above.
In general, all the varieties of these phenomena depend on the relation which we establish between the radii of the two spheres, and also between the quantities of electricity with which they are charged. We may even determine these proportions in such a ' manner, that, at a certain distance, the thickness of the electric stratum on the small sphere may be al most constant, so that this sphere may remain near the other, almost as if it were not exposed to any action, not from the weakness of the electricity on the other sphere, but in consequence of a sort of equilibrium which is then established between its action upon the smallest, and the re-action of this upon itself. In this case, the electricity diffused over the large sphere is vitreous in certain parts, re sinous in others, and its thickness in different points presents very considerable variations. M. Poisson has determined the proportions of volume and of electric charge necessary to produce these phenome na ; and, in this respect, as we have formerly observed, his analysis has anticipated the observations, To complete the case of two electrified spheres placed in presence of each other, M. Poisson has calculated the changes which the greater or less dis tance produces on the state of the points most dis tant from those where the contact takes place. In this respect he has found, that, in proportion as the two spheres approach each other, the thicknesses of the electric stratum in these points tend more and more towards the values which they would have at the instant of contact. As they arrive at this limit, however, but very slowly, it hence follows, that even at very small distances, they differ yet much from what they would be if the contact or the spark ac tually took place. Hence we conclude also, that the spark, when it takes place at a sensible distance, changes suddenly the distribution of the electricity over the whole extent of the two surfaces, from the point where it is produced even to that which is dia metrically opposite. This re-action is easily verified by experiment ; we have only to fix, at certain dis tances from each other, along an insulated conduc tor, couples of linen threads, with pith balls suspend ed to them, and to communicate to this conductor a certain quantity of electricity, by which the threads may be made to diverge ; if we then draw succes sively several sparks by the contact of an insulated sphere, whose volume is not too small, all the threads will be observed to be disturbed, and shaken in a manner by each explosion, in whatever part of the conductor it is produced.