296 



ON CAPILLARY ACTION. 



Hence the preceding expression of the resistance the disk 

 opposes to its separation from the fluid, or, which comes 

 to the same thing, of the weight necessary to raise it, be- 

 Attraction of a comes 2 *x i * X s/ g D x $. " For disks of the same dia- 

 fluid determina- meter therefore, and different substances, the squares of 

 ble from its these weights, divided by the specific gravities of the fluids, 

 surface;" ° are proportional to the value of ?." Accordingly, by very 

 accurate experiments on the resistances opposed by disks 

 to their separation from the surfaces of fluids, we may de- 

 termine their respective attractions for those fluids. 



Two important observations are here to be made : the 

 first is, that ? expresses the action of a plane of a sensible 

 thickness on a fluid plane of a sensible thickness parallel 

 to it, and touching it by the right line, that terminates 

 one of its extremities ; whatever be the laws of the at- 

 traction of the molecules of the fluid for those of the 

 plane, and for each other, even in the case where these 

 laws are not expressed by the same function of the distance. 

 But if this function be the same, then the values of f and %' 

 are proportional to the respective intensities of the attrac- 

 tions ; or, which comes to the same thing, to the constant 

 coefficients, which multiply the common function of the 

 distance, by which the law of these attractions is repre- 

 sented ; but these values are relative to equal volumes. 



To show this, let us conceive two capillary tubes of the 

 same diameter and different substances, but in which a fluid 

 rises to the same height. It is clear, that, if in these tubes 

 we take two equal volumes, infinitely small, and similarly 

 placed, with respect to the interior fluid, their action on 

 this fluid will be the same, and one may be substituted for 

 the other. But to have their attractions in equality with 

 the masses, the attractions of equal volumes must be 

 divided by the specific gravities : the values of? and / there- 

 fore must be divided by the respective densities of the dif- 

 ferent substances. 



The second observation is, that the preceding results 

 suppose f less than q f : for, if ? exceeded ?', the fluid would 

 unite intimately with the disk with which it was in contact, 

 and thus form a new disk, the surface of which in contact 

 with the fluid would be the fluid itself. But as by the pre* 

 ceding formula we may determine the resistance, that such 



a disk 



