268 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS. 



paragraph ; tlic?e two longtlis aro thereforo, in fact, in tlie proportion to each 

 other otilhe diamntcrs of the two cylirtder.s. 



A? tlie perfectly roguhir result of the above table has given a mass of the 

 larger kind to each ba;^c, it follows, that to enable the divisions of the cylinder 

 itself to assume their normal length, or the nearest possible length to this, the 

 transformation has necessarily ensued according to tlie former method ; whilst 

 in regard to a cylinder the diameter of which is a half less, and the total length 

 of Avhich is the same, I'OO millimeters, the transformation ensued according to 

 the second method, (§ 54.) 



Ucrc, also, the case in which there are two masses of the small kind to the 

 solid bases is the least I'rcquent, although it occurred twice. Lastly, the differ- 

 ent values of the length of a division are more concordant than in the second 

 scries relating to the first diameter, and consequently show the tendency towards 

 a constant value better; we also see that the normal length is that which is 

 most frequently reproduced. 



56. According to the law Avhich we. have just established, when the nature of 

 the liquid and external circumstances do not change, the. normal length of the 

 divisions is proportional to the diameter of the cylinder; or, in other words, the 

 proportion of the normal length of the divisions to the diameter of the cylinder 

 is constant. 



As we have seen, the diameter of the cylinder in paragraph 5i was 1.05 mil- 

 limeters, and the normal length of its divisions was very little less than G.G7 

 millimeters ; consequently, when the liquid used is mercury and the cylinder 

 rests upon a plate of glass, the value of the constant proportion in question is 

 6.67 , , 



-j-rrp ^^ 6.35, which approximates closely. 



To ascertain whether the nature of the liquid and external circumstances 

 exert any influence upon this proportion, we shall now determine the value of 

 the latter in the case of a cylinder of oil formed in the alcoholic mixture, which 

 may be effected, at least approximatively, with the aid of the n^sult of tho 

 experiment in paragraph 47. To simplify the considerations, we shall suj^pose 

 that the transformation does not commence until the rapidity of transference has 

 entirely ceased. The ])oint of the funnel, on the one hand, and the section by 

 which the imperfect liquid cylinder is in contact with the mass which collects 

 at the bottom of the vessel, on the other hand, may then be regarded as playing 

 the part of the two buses of the figure. Now it is evident that, as regards the 

 second <,f these bases, the last portion of the figure which is transformed should 

 be a constriction ; for if it constituted a dilatation, there would be discontinuity 

 of the curvature at the junction of the respective surfaces of the latter and the 

 large mass, which is inadmissible. But the same reason does not apply to the 

 other base ; and experiment shows that in this case a dilatation is formed, be- 

 cause after the termination of the phenomenon we always find at tho point of 

 the funnel a mass comparable to the isolated spheres. Hence in this experiment 

 the transformation ensues according to the second method. Therefore, as the 

 whole length of the figure is about 200 millimeters, and as the transformation 

 constantly yields two isolated spheres, the mean length of the divisions has 



(§ 53) for its approximative value — — ■ millimeters = 66.7 millimeters ; I say 



th*^ mean length, because, as the diameter of the figure increases slightly from 

 the summit towards the base, the divisions are probably not exactly equal in 

 length. It must be added here, that the transformation ensues under circixm- 

 stances which are always identical, and consequently, in the absence of acci- 

 dental disturbing causes, the above quantity ought to represent the normal 

 length of the divisions, or the nearest possible length to the latter. Now, 1 



