624 PLATEAU ON THE PHiENOMENA OF A FREE LIQUID MASS 



convex, as is shown to be the case by experiment ; for as equili- 

 brium requires that the pressure should be the same throughout 

 the whole extent of the figure, these bases must produce a 

 greater pressure than that which corresponds to a plane surface. 

 Our plane figure then fully satisfies theory ; but verification 

 may be urged still further. Theory allows us to determine with 

 facility the radius of those spheres of which the bases form a 

 part. In fact, if we represent this radius by x, the formula (1.) 

 of paragraph 4 will give, for the pressure corresponding to the 

 spheres in question, 



P + A.i 



X 



Now as this pressure must be equal to that corresponding to 

 the cylindrical surface, we shall have 



P + o .r = P + A.-, 



2 X X 



from which we may deduce 



x = 2\. 



Thus the radius of the curvature of the spherical segments con- 

 stituting the bases is equal to the diameter of the cylinder. 



Hence, as we know the diameter, which is the same as that 

 of the solid rings, we may calculate the height of the spherical 

 segments ; and if by any pi'ocess we afterwards measure this 

 height in the liquid figure, we shall thus have a verification of 

 theory even as regards the numbers. We shall now investigate 

 this subject. 



40. If we imagine the liquid figure to be intersected by a 

 meridional plane, the section of each of the segments will be an 

 arc belonging to a circle the radius of which will be equal to 2\, 

 according to what we have already stated, and the versed sine of 

 half this arc will be the height of the segment. If we suppose 

 the metallic filaments forming the rings to be infinitely small, so 

 that each of the segments rests upon the exact circumference of 

 the cylinder, the chord of the above arc will also be equal to 2A, ; 

 and if we denote the height of the segments by h, we shall have 



A=A,(2-V'3) =0-268 .A,. 

 Now the exact external diameter of my rings, or the value of 2X 

 corresponding with my experiments, was 71*4 millims., which 

 gives h=9'5'J millims. But as the metallic wires have a certain 

 thickness, and the segments do not rest upon the external circum- 



