674 PLATEAU ON THE PH.ENOMENA OF A FREE LIQUID MASS 



the liquid rapidly retires in both directions, still however leaving 

 the masses united two and two by an apparently cylindrical line ; 

 the latter then experiences the same modifications as the cylinder; 

 except that there are in general only two constrictions formed, 

 which consequently include a dilatation between them ; each of 

 these little constrictions becomes in its turn converted into a 

 thinner line, which breaks at two points and gives rise to a very 

 minute isolated spherule, whilst the above dilatation becomes 

 transformed into a larger spherule ; lastly, after the rupture of 

 the latter lines, the large masses assume completely the spherical 

 form. All these phaenomena occur symmetrically as regards 

 the axis, so that, throughout their duration, the figure is always 

 a figure of revolution. 



4. We denominate divisions of a liquid cylinder, those por- 

 tions of the cylinder, each of which must furnish a sphere, 

 whether we conceive these portions to exist in the cylinder itself, 

 before they have begun to be apparent, or whether we take them 

 during the transformation, i. e. wliilst each of them is becoming 

 modified so as to arrive at the spherical form. The length of 

 a division consequently measures the constant distance which, 

 during the transformation, is included between the necks of two 

 adjacent constrictions. 



Moreover, by normal length of the divisions, we denominate 

 that whicli the divisions would assume, if the length of the 

 cylinder to which they belong were infinite. 



In the case of a cylinder which is limited by solid bases, the 

 divisions also assume the normal length when the length of 

 the cylinder is equal to the product of this normal length by 

 a whole number, or rather a whole number and a half. Then, 

 if the second factor is a whole number, the transformation be- 

 comes disposed in such a manner that during its accomplish- 

 ment the figure terminates on one side with a constriction, 

 and on the other with a dilatation ; if the second factor is com- 

 posed of a whole number and a half, the figure terminates on 

 each side in a dilatation. When the length of the cylinder ful- 

 fills neither of these conditions, the divisions assume that length 

 which approximates the most closely possible to the normal 

 length, and the transformation adopts that of the two above dis- 

 positions which is most suitable for the attainment of this end. 



5. In the case of a cylinder of a given diameter, the normal 

 length of the divisions varies with the nature of the liquid, and 



