WITHDRAWN FROM THE ACTION OF GRAVITY. 241 



that we tlius obtain a diverging lens, the curvature and action of wliich are 

 variable. 



23. Now let us suppose that we have increased the curvatm-es of the lens 

 until the two surfaces nearly touch each other by their summits.* We might 

 presume that if the removal of the liquid were continued, the mass would be- 

 come disunited at that point at which this contact took place, and that the oil 

 would recede in every direction towards the metallic baud. This is, however, 

 not the case ; Ave then observe in the centre of the figure the formation of a 

 small sharply defined Circular space, through which objects no 'longer appear 

 diminished, and we easily recognize that this minute space is occupied by a 

 layer of oil with plane faces. If the removal of the liquid be gradually con- 

 tinued, this layer increases more and more in diameter, and may thus be ex- 

 tended to within a tolerably short distance of the solid surface. In my experi- 

 ment, the diameter of the metallic cylinder was seven centimetres, and I have 

 been enabled to increase the size of the layer until its circumference was not 

 more than about five millimetres from the solid surface ; but at this instant it 

 broke, and the liquid of which it consisted rapidly receded towards that which 

 still adhered to the metallic band. The fact which we have just described is 

 very remarkable, both in itself and in the singular theoretical consequences to 

 which it leads. In fact, that part of the mass to which the layer adheres by its 

 margin pres(jnts concave surfaces, whilst those of the layer are plane ; now the 

 existence of such a system of surfxces in a continuous liquid mass seems in op- ' 

 position to theory, since it appears evident that the pressures cannot be equal 

 in this case. But let us investigate the question more minutely. 



24. According to theory, the pressure corresponding to any point of the sur- 

 face of a liquid mass, as we have seen, (§ 3,) is the integral of the pressures 

 exerted by each of the molecules composing a rectilinear line perpendicular to 

 the surface at that point, and equal in length to the radius of the sphere of 

 activity of the molecular attraction. The analytical expression of this integral 

 contains no other variables than the radii of the greatest and of the least curva- 

 ture at the point under consideration, (§ 4,) consequently the pressure in 

 question varies only.Avith the curvatures of the surface at the same point. This 

 is rigorously true when the liquid is of any notable thickness ; but we shall 

 show that in the case of an extremely thin layer of liquid there is another 

 element which exerts an influence upon the pressure. Let us conceive a liquid 

 layer, the thickness of which is less than twice the radius of the sphere of sen- 

 sible activity of the molecular attraction. Let each molecule be conceived to 

 be the centre of a small sphere with this same radius, (§ 3,) and let us first 

 consider a molecule situated in the middle of the thickness of the layer. The 

 little sphere, the centre of which is occupied by this molecule, will be intersected 

 by the two surfaces of the layer, consequently it will not be entirely full of 

 liquid; but the segments suppressed on the outside of the two surfaces being 

 equal, the molecule will not be more attracted perpendicularly in one direction 

 than in the other. Now let a small right line, normal to and terminating at the 

 two surfaces, pass through 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 at- 

 traction, evi^lently directed towards the thickness of the layer. The molecule 

 will then exert p, pressure in this direction, and it must be remarked that this 

 pressure will be less than if the liquid had any notable thickness, the molecule 



* To effect this operation, the point of the syringe must not be pliiced in the middle of the 

 figure, as in the case of the doubly convex ions; but, on the contrary, near the metallic 

 band, as this is now the point whore the greatest thickness of the liquid exists. 

 16 S 



