WITHDRAWN FROM THE ACTION OF GRAVITY. 255 



42. The instrument best suited for effecting the latter operations in an exact 

 manner is undoubtedly that which has received the name of cathctomctcr, and 

 which, as is well known, consists of a horizontal telescope moving along a ver- 

 tical divided rule. The distance comprised between the summits of the two 

 segments is first measured by the aid of this instrument ; the distance included 

 between the external planes of the two rings (§ 40 ) is then measured by the 

 same means. The difference between the first and the second result evidently 

 gives the sum of the two heights, the mean of which must be taken ; and, con- 

 sequently, this mean, or the quantity sought, h — f, is equal to half the differ- 

 ence in question. 



The determination of the distance between the external planes of the rings 

 requires peculiar precautions. First, as the points of the rings at which we 

 must look are not exactly at the external surface of the figure, the oil inter- 

 posed between these points and the eye must produce some effects of refraction, 

 which would introduce a slight error into the value obtained. To avoid this 

 inconvenience, we need only expose the rings by allowing the liquids, to escape 

 from the vessel by the stop-cock, (note 2 to § 9,) then remove the minute portions 

 of the liquid Avhich remain adherent to the rings by passing lightly over their 

 surface a small strip of paper, which must be introduced into the vessel through 

 the second aperture. The drops of alcoholic liquid remaining attached to the 

 inner surface of the interior side of the vessel must also be absorbed in the 

 same manner. In the second place, as it would be difficiilt for the rings to be 

 rigorously parallel, their distance must be measured from two opposite sides 

 of the system, and the mean of the two valves thus found taken. The follow- 

 ing are the results which I obtained : The mensuration of the distance between 

 the summits gave first, in four successive operations, the values 76.77, 76.80, 

 76.85, and 76.75 milli:neters, the mean of which is 76.79 millimeters. But after 

 the alcoholic liquid had been again agitated for some time, to render its homo- 

 geneity more certain, two new measurements taken immediately afterwards 

 gave 77.05 and 77.00 millimeters, or a mean of 77.02 millimeters. The distance 

 between the external planes of the rings was found, on the one hand, by two 

 observations, which agreed exactly, to be 57.73 millimeters ; on the other hand, 

 two observations furnished the values 57.87 and 57.85 millimeters, or as the 

 mean 57.86 millimeters. Taking, then, the mean of these two results, we get 

 57.79 millimeters as the value of the distance between the centres of the ex- 

 ternal planes. Hence, if we assume the first of the two values obtained for the 

 distance of the summits, 76.79 millimeters, we find 



^ 76.79 — 57.79 ^_ .,,. 

 h — f^^ ^ = 9.50 millimeters ; 



and if from the second result, 77.02 millimeters, we find 



^ 77.02 — 57.79 

 h — j = 2 ^ = 9.61 millimeters. 



These two elevations evidently differ but little from 9.41 millimeters, the 

 altitude deduced from theory, (§ 40;) in the first case the difference does not 

 amount to the y^uth part of this theoretical value, and in the second it hardly 

 exceeds ^^^ths. These differences undoubtedly arise from slight remains of 

 heterogeneity in the liquids ; it is probable that in the first case neither of the 

 two liquids was absolutely homogeneous, and that the two contrary effects 

 which thence resulted (§ 41) partly neutralized each other, whilst in the second 

 case, the alcoholic liquid being rendered perfectly homogeneous, the effect of the 

 plight heterogeneity of the oil exerted its full influence. However this may be, these 

 differences in each case are so small that we may consider experiment as in accord- 

 ance with theory, of which it evidently presents a very remarkable confirmation. 



43. Mathematically considered, a cylindrical surface extends indefinitely in 

 the direction of the axis of revolution. Hence it folloM's that the cylinder 



