652 PLATEAU ON THE PH/ENOMENA OF A FREE LIQUID MASS 



below would be -— r millims. = 57"1 millims., which would cor- 



respond 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 iso- 

 lated spheres formed, and the transformation always ensues ac- 

 cording to the second method, we must conclude that the normal 

 length of the divisions approximates more closely to the length 

 found, 66-7 millims., than the length 57'1 millims.; if then the 

 normal length is greater than the first of these two quantities, it 

 must at least be more than their mean, i. e. 61*9 millims.; con- 

 sequently the relation of the normal length of the divisions and 



61'9 

 the diameter of the cylinder is necessarily greater than — — 



= 15*5 ; now this latter number considerably exceeds the number 

 6*35 which cori'esponds 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 circum- 

 stances, at others according to both these elements. 



57. But I say that there is a limit below which this pro- 

 portion 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 re- 

 gularity. Suppose, for the sake of clearness, that the phteno- 

 menon ensues according to the second method, or in other 

 words, that the terminal portions of the figure consist 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. e. 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 phaenomenon at which it still presents constrictions and di- 

 latations, 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 portion ; the solid base upon which this 

 i-ests, and which constitutes the first of the sections in question, 

 will occupy, as we have shown, the origin of the constriction 

 itself; we shall then have a second section at the origin of the 



