WITHDRAWN FROM THE ACTION OF GRAVITY. 625 



ference of the rings, it follows that the chord of the meridional 

 arc is a little less than 2\, and that consequently the true theo- 

 retical height of the segments is a little less than that given by the 

 preceding formula. To determine it exactly, let us denote the 

 chord by 2c, which will give 



h = 2\— 'v/4X2_c2. 



Now let us remark, that the meridional plane intersects each of 

 the rings in two small circles to which the meridional arc 

 of the spherical segment is tangential, and upon each of M'hich 

 the chord of this arc intercepts a small circular segment. The 

 meridional arc being tangential to the sections of the wire, it 

 follows that the above small circular segments are simila • to 

 that of the spherical segment; and as the chord of the latter 

 differs but very slightly from the radius of the circle to which 

 the arc belongs, the chords of the small circular segments 

 may be considered as equal to the radius of the small sec- 

 tions, which radius we shall denote by r. It is moreover 

 evident that the excess of the external radius of the ring over 

 half the chord c is nothing more than the excess of the radius r 

 over half the chord of the small circular segments, which half 



chord, in accordance with what we have stated, is equal to -r. 



Thence we get \—c=—r, whence c=.\—-r, and we have only to 



substitute this value in the preceding formula to obtain the true 

 theoretical value of h. The thickness of the wire forming my 



rings is 0"74 millim., hence — r = 0'18 millim., which gives as 



the true theoretical height of the segments under these circum- 

 stances, 



A = 9'46 millims. 



I may remark, that it is difficult to distinguish in the liquid 

 figure the precise limit of the segments, i. e. the circumferences of 

 contact of their surfaces with those of the rings. To get rid of 

 this inconvenience, I measured the height of the segments, com- 

 mencing only at the external planes of the rings, i. e. in the case 

 of each segment, commencing at a plane perpendicular to the axis 

 of revolution, and resting upon the surface of the ring on that 

 side which is opposite the summit of the segment. The quantity 

 thus measured is evidently equal to the total height minus the 



