616 PLATEAU ON THE PH.ENOMENA OF A FREE LIQUID MASS 



plate of iron, the sides of which are of the same length as the 

 edges of the metallic frame, is introduced into the vessel ; and 

 that a mass of oil equal in volume to that which is lost hy one 

 of the faces of the cube is placed in contact with one of the faces 

 of this plate ; I say that the liquid, after having become ex- 

 tended upon the plate, will present in relief the same figure as 

 the face of the modified cube presents in intaglio. Then, in fact, 

 in passing from the hollow surface to that in relief, the radii of 

 curvature corresponding to each point will only change their 

 signs without changing in absolute value; consequently (§8) 

 since the condition of equilibrium is satisfied as regards the first 

 of these surfaces, it will be equally so with regard to the second. 

 Now let us imagine a plane passing through one side of the 

 plate, and tangentially to the surface of the liquid which adheres 

 to it at that point. As long as this liquid is in small quantity, 

 we should imagine, and experiment bears us out, that the plane 

 in question will be strongly inclined towards the plate ; but if 

 we gradually increase the quantity of liquid, the angle comprised 

 between the plane and the plate will also continue to increase, 

 and instead of being acute, as before, will become obtuse. Now 

 so long as this angle is less than 45°, the convex surface of the 

 liquid adhering to the plate will remain identical with the con- 

 cave surfaces of the mass attached to the metallic frame, and 

 suitably diminished ; but beyond this limit, the coexistence in 

 the frame of the six hollow identical surfaces with the surface 

 in relief becomes evidently impossible, for these surfaces must 

 mutually intersect each other. Thus when the withdrawal of 

 the liquid from the mass forming the cube is continued, a point 

 is attained at which the figure of equilibrium ceases to be 

 realizable in accordance with the ordinary law of pressures. We 

 then meet with a new verification of the principle enunciated in 

 § 28, i. e. that the formation of layers commences. These layers 

 are plane ; they commence at each of the wires of the frame, 

 and connect the remainder of the mass to the latter, which con- 

 tinues to present six concave surfaces. In fact, we can imagine, 

 that by this modification of the liquid figure, the existence of 

 the whole of this in the metallic frame again becomes possible, 

 as also the equilibrium of the system ; for there is then no fur- 

 ther impediment to the concave surfaces assuming that form 

 which accords with the ordinary law of pressures ; and, on the 

 other hand, in supposing the layers to be sufficiently thin, the 



