662 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



the mass of each of the divisions, and, on the other hand, the 

 less the curvatures upon which the intensities of the configuring 

 forces depend. It is true that the surface of each of the divisions 

 increases also with the diameter of the cyhnder, consequently it 

 is the same with the number of the elementary configuring forces ; 

 but this augmentation takes place in a less proportion than that 

 of the mass ; this we shall proceed to show more distinctly. Under 

 the above conditions, two cylinders, the diameters of which are 

 different, will become divided in the same manner, i. e. the 

 proportion of the length of a division to the diameter will be the 

 same in both parts (§ 55). Now it may be considered as evident 

 that the similitude in figui'e will be maintained in all the phases 

 of the transformation ; this is moreover confirmed by experiment, 

 as we shall soon see. Hence it follows at each homologous 

 instant of the transformations of the two cylinders, the respective 

 surfaces of the divisions will always be to each other as the 

 squares of the diameters of these cylinders, whilst the masses, 

 which evidently remain invariable throughout the entire duration 

 of the phaenomena, will always be to each other as the cubes 

 of these diameters. Thus, at each homologous instant of the 

 respective transformations, the extent of the superficial layer of 

 a division, consequently the number of the configuring forces 

 which emanate from each of the elements of this layer, change 

 from one figui-e to the other only in the proportion of the 

 squares of the primitive diameters of these figures ; whilst the 

 mass of a division, all tht, parts of which mass receive, 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 corre- 

 sponds to one element of the superficial layer has (§ 59) for its 



expression "5" ( "d + "57 ) • This granted, if, at an homologous 



instant in the transformations of the two figures, we take upon 

 one of the divisions of each of the latter any point similarly 

 placed, it is clear from the similitude of these figures, that the 

 principal radii of curvature corresponding to the point taken 

 upon the second, will be to those corresponding to the point 

 taken upon 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 R and R', those be- 

 longing to the point of the second will be 7iR and tiR' ; whence 



