650 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



Here also, the case in which there are two masses of the small 

 kind to the solid bases is the least frequent, although it occurred 

 twice. Lastly, the different values of the length of a division 

 are more concordant than in the second series 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 which 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 54 

 was 1*05 millim., and the normal length of its divisions was 

 very little less than 6'67 milhms. ; 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*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 

 cyHnder of oil formed in the alcoholic mixture, which may be 

 effected, at least approximatively, with the aid of the result of 

 the experiment in paragraph 4'J. To simphfy the considerations, 

 we shall suppose that the transformation does not commence 

 until the rapidity of transference has entirely ceased. The point 

 of the funnel, on the one hand, and the section by which the 

 imperfect hquid 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 bases of the figure. 

 Now it is evident that, as regards the second of these bases, the 

 last portion of the figure which is transformed should be a con- 

 striction ; for if it constituted a dilatation, there would be discon- 

 tinuity of the curvature at the junction of the respective sur- 

 faces of the latter and the large mass, which is inadmissible. 

 But the same reason does not apply to the other base ; and ex- 

 periment shows that in this case a dilatation is formed, because 

 after the termination of the phaenomenon, we always find at the 

 point of the funnel a mass comparable to the isolated spheres. 



