OF SMALL FLOATING BODIES. iQj 



suitable manner the respective intensities of their electricity, 



and their distance. 



By means of the two following theorems, we may calcu- Calculation of 



late the tendency of the planes toward each other, or their thc att " ctlon 



1 ' or repulsion, 



mutual repulsion. 



Whatever be the substances of which the planes are form- Theorem I. 

 ed, the tendency of each of them toward the other, is equal 

 to the weight of a parallelopipedon of the fluid, the height 

 of which is the elevation of the extreme points of contact of 

 the fluid with the interior plane, minus the exterior eleva- 

 tion 4 the depth half the sum of these elevations; and the 

 breadth that of the plane in a horizontal direction. We 

 must consider the elevation as a negative quantity, when it 

 is changed into depression below the level. If the product 

 of the three preceding dimensions prove negative, the ten- 

 dency become repulsive. 



When the planes are very near together, the elevation of Theorem II. 

 the fluid between them is the inverse ratio of their mutual 

 distance; and is equal to half the sum of the elevations, that 

 would have taken place, if we suppose the first plane to be 

 of the same substance as the second, and then the second 

 plane to be of the same substance as the first. We must ob- 

 serve too, that the elevation must be put as negative, when 

 it changes into depression. 



We see by these theorems, that in general the repulsive The repulsion 



force is much weaker than the attractive, which displays itself * eaker than 



- ^ •> the attraction. 



when the planes are brought very close together, and must 

 then carry them toward each other with an accelerated mo- 

 tion. In this case the elevation of the fluid between the 

 planes is very great, relatively to its elevation near the same 

 planes exteriorly. If therefore we neglect the square of the 

 latter elevation, with respect to the square of the former, 

 the fluid parallelopipedon, the weight of which expresses the 

 tendency of one of the planes toward the other, inyirtue of 

 the first of the preceding theorems, will be equal to the 

 product of the square of the elevation of the interior fluid, 

 by half the breadth of the plane in the horizontal direction. 

 This elevation being, by the second theorem, reciprocal to 

 the mutual distance of the planes ; the parallelopipedon will 



be 



