WITHDRAWN FROM THE ACTION OF GRAVITY. 269 



estimate the mean diameter of the figure before the transformation at about 4 



.„. 1,1 , , 66.7 



millimeters; we should consequently have —-—= 16.7 as the approximative 



value of the proportion between the normal length of the divisions and the 

 diameter of the cylinder. This is, therefore, approximativcly the constant pro- 

 portion sought in the case of a cylinder of oil formed in the alcoliolic mixture ; 

 now this proportion, as is evident, is much greater than that which belongs to 

 the case of a cylinder of mercury resting upon a plate of gla^s. 



In fact, the length 66.7 millimeters may. differ somewhat materially from the 

 normal length ; for if on the one hand, the whole length of the figure of oil is 

 considerable in regard to its diameter, on the other hand, the number of divisions 

 which form there is very small. Let us then see, for instance, what is the least 

 value which the normal length of these divisions may have. We must in the 

 first place remark, that in this case, notwithstanding the absence of disturbing 

 causes, the third method of transfer nation is possible; in fact, as the lower 

 constriction is adherent to a liquid base, nothing can prevent the oil which it 

 loses from traversing this base to reach the large mass, so that in the third 

 method, also, the direction of the movements of transport may be the same in 

 regard to all the constrictions, (§ 52.) This granted, as the denominator of the 

 expression which gives the length of one division can only vary by half 

 units, (53,) and as the length which we have found resulted from the division 

 of 200 millimeters by 3, it follows that the length immediately below would be 



200 



— — millimeters =: 57.1 millimeters, which would correspond to three isolated 



spheres and a transformation disposed according to the third method. But as 

 matters do not take place in this manner, since there are never more than two 

 isolated spheres formed, and the transformation always ensues according to 

 the second method, we must conclude that the' normal length of the divisions 

 approximates more closely to the length found, 66.7 millimeters, than the length 

 57.1 millimeters. If, then, the normal length is greater than the first of these 

 two quantities, it must at least be more than their mean, ^. c, 61.9 millimeters ; 

 consequently the relation of the normal length of the divisions and the diameter 



61.9 

 of the cylinder is necessarily greater than — — -= 15.5; now this latter num- 

 ber considerably exceeds the number 6.35, which corresponds to the mercurial 

 cylinder. 



Thus, the proportion of the normal length of the divisions to the diameter of 

 the cylinder varies, sometimes according to the nature of the liquid, sometimes 

 according to external circumstances, at others according to both these elements. 



57. But I say that there is a limit below which this proportion cannot descend, 

 and that this is exactly the limit of stability. Let us imagine a liquid cylinder 

 of sufficient length in proportion to its diameter, comprised between two solid 

 bases, and the transformation of which is taking place with perfect regularity. 

 Suppose, for the sake of clearness, that the phenomenon ensut-s according to the 

 second method, or, in other words, that the terminal portions of the figure con- 

 sist one of a constriction, the other of a dilatation ; then, as we have seen, (§ 52,) 

 the regularity of the transformation will extend to these latter portions ; i. c, the 

 terminal constriction and the dilatation will be respectively identical with the 

 portions of the same kind of the rest of the figure. Let us then take the figure 

 at that period of the phenomenon at which it still presents constrictions and 

 dilatations, and let us again consider the sections, the diameter of which is equal 

 to that of the cylinder, (§ 52.) Let us start from the terminal constricted por- 

 tion ; the solid base upon which this rests, and Avhich constitutes the first of the 

 sections in question, will occupy, as we have shown, the origin of the constric- 



