WITHDRAWN FROM THE ACTION OF GRAVITY. 27? 



these figures; whilst the mass of a division, all the parts of which mass receivei 

 under the action of the forces in question, the movements constituting the 

 transformation, changes in the proportion of the cubes of these diameters. As 

 regards the intensities of the configuring forces, we must remember, first, that 

 the measure of that which corresponds to one element of the superficial layer 



has (§ 59) for its expression "5 f tT + tt, |- This granted, if, at an homologous 



instant in the transformations of the two figures, we take upon one of the divi- 

 sions of each of the latter any point similarly placed, it is clear from the simili- 

 tude of these figures that the principal radii of curvature corresponding to the 

 point taken upou the second will be to those corresponding to the point taken. 

 uj)on the first in the proportion of the diameters of the original cylinders, so 

 that if this proportion be n, and the radii relating to the point of the first figure 

 be 11 and R', those belonging to the point of the second will be «R and nW ; 

 whence it follows that the measure of the two configuring forces corresponding 



• A / 1 1 \ T A / 1 1 \ 

 to these pomts will be respectively ^ I fi + ^ /• ^"^^ ~^\~v "^ P' / ^^ 



- . — • I v^ + t;-: y Thus, in passing from the first to the second figure, the 

 n 2 \ll IV / r o 



intensities of the elementary configuring forces in all the phases of the trans- 

 formation will be to each other in the inverse proportion of the diameters of 

 the cylinders. 



I have convinced myself, by means of cylinders of mercury 1.05 millimeters 

 and 2.1 millimeters in diameter, (§ 54 and 55,) that the duration of the phe- 

 nomenon increases, in fact, with the diameter : although the transformation of 

 these cylinders is effected very rapidly, yet we have no difficulty in recognizing 

 that the duration relating to the greater diameter is greater than that which 

 refei's to the least. 



64. As regards the law which governs this increase in the duration, it would 

 undoubtedly be almost impossible to arrive at its experimental determination in 

 a direct manner, i. e., by measuring the times which the accomplishment of the 

 phenomenon would require in the case of two cylinders of sufficient length 

 to allow of their being respectivel}' converted into several complete isolated 

 spherules, and of their sati.'^fying the conditions indicated at the commencement ■ 

 of the preceding section. In fact I can hardly see any method of realizing such 

 cvlinders without giving them very minute diameters, like those of our cylindei-s 

 of mercury, and then their duration is too short to allow of our obtaining the 

 proportion with sufficient exactness. 



But we may be able to arrive at the same result, but with certain restrictions, 

 which we shall mention presently, by means of two short cylinders of oil formed 

 between two disks, {§ 46 ;) there is nothing to prevent these cylinders from 

 being obtained of such diameters as to render the exact measure of the durations 

 easy. In the transformation of a cylinder of this kind, only a single constric- 

 tion and a single dilatation are produced ; but as in the transformation of cyl- 

 inders which are sufficiently long to furnish several complete isolated spheres, 

 the phases through which the constrictions and the dilatations pass are the same 

 for all, we need only consider one constriction and one dilatation. "VVe can 

 understand that the relative dimensions of .the two solid systems ought to be 

 such, that the relation between the distance of the disks and their diameters is 

 the same in both parts, in order that similitude may exist between the two liquid 

 figures at their origin and at each homologous instant of their transformations. 



Before giving an account of the employment of these figures of oil for the 

 determination of the law of the durations, we shall take this opportunity of 

 making several impoftant remarks. We shall only require to make iise of the 

 law in question in that case, which in other respects is the most simple, where 



