ELECTRICITY. 



547 



Theoretical very near to one another, these series are very eonver- 

 Kkctricity. gent, and as they tend very rapidly to geometrical pro- 

 V "~" Y "~ ' gressions, it is easy to obtain from them sufficiently ac- 

 Resrarches curate values. M'. Poisson has calculated tables in the 

 M. Pois- case Q f two S ph ereS) whose radii are as one to three, and 

 whose surfaces are separated by an interval equal to the 

 smallest of the two radii. These tables contain the 

 thickness of the coating of fluid to less than the 10,000th 

 part, in nine different equidistant points upon each of 

 the two spheres, viz. at the extreme points where the line 

 joining the centres penetrates the surfaces of the spheres, 

 and on other points of the great circles which pass 

 through these extreme points. The simple inspection 

 of these tables shews if the electricity increases or de- 

 creases upon one of the spheres, from the point nearest 

 to the other sphere to the most remote point. They 

 shew also whether the electricity is vitreous or resinous, 

 and through what points passes the line of separation 

 between the two fluids. On these different circum- 

 stances will depend the total quantities of electric fluid, 

 whether vitreous or resinous, with which the two spheres 

 are charged. We may make the electrical densities 

 of the two spheres of any magnitude we choose, and 

 make them either vitreous or resinous ; and if we take 

 one of these quantities equal to zero, we shall have the 

 case where one of the two spheres is electrified solely 

 by the influence of the other, and we shall obtain, at 

 the same time, the reaction of this electrified sphere 

 upon the sphere from which it derives its electricity. 

 When the smallest of the two spheres is electrified by 

 being placed within the atmosphere of the greater one, 

 the Tatter presents a very remarkable circumstance. 

 The electricity will diminish upon its surface from the 

 point nearest the little sphere to a distance of 67 SO* 

 from that point, and will then increase to the point 1 80 

 distant from the point of contact ; so that the thickness 

 f the coating of fluid, without changing its sign 

 upon this surface, reaches its minimum about 67 '>(>'. 



In making equal to one another the thicknesses of 

 the coat of fluid which correspond to two different 

 points upon the same sphere, and in determining by 

 this equation the relation between the quantities of 

 electricity with which the two spheres are charged, M. 

 Poisson could produce at pleasure a similar minimum, 

 which will fall somewhere between the two thicknes- 

 ses which were made equal. By making equal to each 

 other the two extreme thicknesses upon the small 

 sphere, M. Poisson has given another example of this 

 minimum. This particular case is remarkable, as the 

 thickness of the coat is almost constant throughout the 

 whole of the little sphere, and does not vary -fj-th above 

 or below the mean thickness, so that it appears to have 

 experienced no change from its proximity to the great 

 sphere. In this case the electricity upon the surface of 

 the great sphere, passes from positive to negative, and 

 experiences considerable variations of intensity. 



The memoirs of Coulomb do not furnish us with any 

 experiments which could be compared with these re- 

 sults excepting experiments 3d anil 4-th, which we have 

 given in p. 453, col. 2, and which agree with the re- 

 Biilts obtained by \f . Poisson. 



The series which represent the thicknesses of the 

 coat of fluid cease to converge when the spheres are 

 very near each other ; and in order to apply the se- 

 rii> in this case, it is necessary to give them another 

 form, by expressing them in definite integrals. In this 

 way, M. Poisson has transformed them into another -<- 

 rii - , which becomes more convergent as the distance IM-- 

 tween the two spheres diminishes. He has thus been 

 able to explain what happen* during the progressive ap- 



proach of the two spheres before contact, and what hap- 

 pens when they are brought into contact, and then se- 

 parated. 



In the first case, the thickness of the coat of fluid, 

 at the nearest points upon the two surfaces, increases 

 indefinitely, in proportion as the distance of the 

 spheres diminishes. The same thing is true of the 

 pressure which the fluid exercises against the air in- 

 tercepted between the two bodies ; as this pressure is 

 always proportional to the square of the thickness, it 

 ought at last to overcome the resistance of the air, and 

 the fluid in escaping, under the form of a spark, or 

 otherwise, ought to pass, before contact takes place, 

 from one surface to the other. The fluid thus accumu- 

 lated before the spark, is of a different kind, and nearly 

 equal in intensity upon both the spheres : If they are 

 electrified, one vitreously and the other resinously, it is 

 vitreous upon the first and resinous upon the second ; 

 but when they are similarly electrified, positively for 

 example, the sphere, which contains less of the fluid 

 than it ought to have at contact, becomes negative at 

 the point where the spark is preparing itself, and, on 

 the contrary, the sphere which contains more than it 

 ought to have at contact, remains positive over all its 

 surface. 



When the two spheres are brought into contact, and 

 then separated to a little distance, the ratio which ex- 

 ists between their total quantities of electricity, causes 

 to disappear, in the expression of the thickness, the 

 term, which becomes infinitely great for an infinitely 

 small distance. The electricity of the points nearest 

 to each other upon the two surfaces, is then very weak 

 for very small distances: it decreases with the distances, 

 according to a law which M. Poisson has determined. 

 Its intensity is nearly the same upon the two spheres ; 

 but when the spheres are unequal, this electricity is po- 

 sitive upon one, and negative upon the other ; and it 

 is always upon the smallest that it takes a sign contra- 

 ry to that of the total electricity. 



This result is quite conformable to the experiment 

 of Coulomb formerly mentioned, (Exp. 4. p. 453, col. 

 2.) ; and M. Poisson considers it as furnishing an im- 

 portant confirmation of the theory of two fluids. When 

 the two spheres are equal, the electricity during con. 

 tact and after separation, distributes itself in the same 

 manner upon both. Hence it is natural to think, that 

 in this case the fluid is of the same kind over the whole 

 of each surface, however small be the distance which 

 separates the two spheres. This is in reality what is 

 deduced from the formuiz, when the radii of the two 

 spheres are supposed equal. 



M. Poisson next considers what will take place, in the 

 approach of the two spheres, at the most distant points 

 u|K>n their surfaces. The formulae which express for 

 very small distances the quantities of electricity rela- 

 tive to these points, shew that the thickness of the coat of* 

 fluid which corresponds to them, tends towards a con- 

 stant limit, in proportion as the two spheres approach 

 one another ; and that this limit is the thickness which 

 the coats would have had at the same points, at the in- 

 stant of contact. These formula; also shew, that the 

 quantity which they represent, converges very slowly 

 to its limit, so that, for very small distances, the elec- 

 tricity of the most distant points upon the two surfaces, 

 still differs much from what it will be in contact, or 

 after the spurk. Hence M. Poisson concludes, that the 

 spark, when it takes place at a sensible distance, changes 

 the distribution of tiie electric fluid over the whole ex- 

 tent of the two surfaces, and even to points diametri- 

 cally opposite to those where it is produced, (ft) 



