J 66 ATTRACTION AND REPULSION 



interior of the other plane, as it is depressed below it at the 

 exterior. Thus the repulsion is changed into attraction at 

 the same moment in each plane. On bringing them still 

 nearer, they attract each other, and proceed to unite with 

 an accelerated motion. These planes therefore exhibit the 

 remarkable phenomenon of an attraction at very small dis- 

 tances, that is changed into repulsion beyond certain limits ; 

 a phenomenon which nature presents likewise in the inflexion 

 Case of con- °f Ught near the surfaces of bodies, and in the attractions 

 Want repulsion of electricity and magnetism. There is one case, however, 

 m which the planes repel each other, however small their 

 distance may be ; and this is where the fluid is depressed 

 near one of them as much as it is raised near the other. Here 

 the surface of the fluid has constantly an inflexion in the 

 The equation middle of the interval between them. 



of the curve of The integration of the differential equation of this surface 

 the suriace not . * 



obtainable in in general depends on the rectification of conic sections, and 



finite terms, consequently it is impossible to obtain it in finite terms. 



except within -^ ut ** becomes possible, when the planes are at the distance 



a certain dis- where repulsion is changed into attraction ; as this distance 



can then be determined in a function of the elevation and 



depression of the fluid at the exterior of the planes. Thus 



we find, that it is infinite, if the depression of the fluid on 



the exterior of the plane incapable of being wetted, be infi- 



nitel} r small : whence it follows, that the two planes never 



repel each other then. This may take place too even in the 



Modified by case where the fluid is perceptibly depressed at the exterior 



friction. • f the latter plane : as it is sufficient, if friction keep the 



fluid a little more elevated at the interior of the plane, than 



it would be if this friction did not exist ; an effect analogous 



,_„, , to that daily perceived in the barometer, when the quicksil- 



^\ henthesur- . J r , . .^ 



face ir, wetted Vf; r 1S falling. \\ e find too by this analysis, that, if the sur- 



it attracts at a f ace f th e plane capable of being wetted come to be made 



greater dis- 



tance. W€ h the two planes will begin to attract each other at a very 



perceptible distance, greater than that at which they began 

 to attract eqch other before. It is not the truth therefore 

 to say, that two planes, one capable of being wetted, the 

 other not, always repel each other. The same thing happens 

 here as with two balls having the same kind of electricity, as 

 -these attract each other notwithstanding, when we vary in a 



suitable 



