610 PLATEAU ON THE PH^ENOMENA OF A FREE LIQUID MASS 



this same molecule, and let us consider a second molecule 

 situated at some other point of this right line. The little sphere 

 which belongs to the second molecule in question may again 

 be intersected by the two surfaces of the layer ; but then the 

 two suppressed segments will be unequal; the molecule will 

 consequently be subjected to a preponderating attraction, evi- 

 dently directed towards the thickness of the layer. The mole- 

 cule will then exert a pressure in this direction, and it must be 

 remarked that this pressure will be less than if the hquid had 

 any notable thickness, the molecule being situated at the same 

 distance from the surface ; for in the latter case the little sphere 

 would only be cut on one side, and its opposite part would be 

 perfectly full of liquid. It might also happen that the little 

 sphere belonging to the molecule in question in the thin layer is 

 only cut on one side ; the molecule will then still exert a pressure 

 in the same direction, but its intensity will then be as great as 

 in the case of a thick mass. It is easy to see that if the thick- 

 ness of the layer is less than the simple length of the radius of 

 the molecular attraction, the little spheres will all be cut on both 

 sides ; whilst if the thickness in question is comprised between 

 the length of the above radius and twice this same length, a por- 

 tion of the minute spheres will be cut on one side only. In both 

 cases, the pressure exerted by any molecule being always di- 

 rected towards the middle of the thickness of the layer, it is 

 evident that the integral pressure corresponding to any point of 

 either of the two surfaces will be the result of the pressures in- 

 dividually exerted by each of those molecules, which, com- 

 mencing at the point in question, are arranged upon half the 

 length of the small perpendicular. Now each of the two halves 

 of the small perpendicular being less than the radius of the sphere 

 of activity of the molecular attraction, it follows that the num- 

 ber of molecules composing the line which exerts the integral 

 pressure is less than in the case of a thick mass. Thus, on the 

 one hand, the intensities of part or the whole of the elementary 

 pressures composing the integral pressure will be less than in 

 the case of a thick mass, and, on the other hand, the nuinber of 

 these elementary pressui-es will be less ; from this it evidently 

 follows that the integral pressure will be inferior to that which 

 would occur in the case of a thick mass. P always denoting the 

 pressure corresponding to any point of a plane surface belonging 

 to a thick mass (§ 4), the pressure corresponding to any point of 



