694 PLATEAU ON THE PHENOMENA OP A FREE LIQUID MASS 



diminution of the volume of its divisions. Since a cylinder, 

 supposed to exist under the conditions of our laws and formed 

 of a given liquid, becomes transformed with rapidity propor- 

 tionate to the smallness of its diameter, it necessarily follows 

 that as the volume of its divisions is smaller, the gradual 

 diminution in the volume of the divisions of the vein tends to 

 render the velocity of their transformation more accelerated 

 than it would be in the imaginary vein of the same liquid 

 if it flowed under the same charge, and from an orifice of the 

 same diameter. Under the isolated influence of this modification 

 of the volume, the time which the portion of the phaenomenon 

 corresponding to the course of the continuous portion requires 

 would therefore be shorter, consequently the length of this 

 portion would be less than in the imaginary vein. Now if the 

 charge under consideration were replaced by a charge very nearly 

 sufficient to annihilate the acceleration of the movement of trans- 

 ference of the liquid in the continuous part, this portion of the 

 vein would then be equal in length to that of the corresponding 

 imaginary vein (§ 73) ; therefore in passing from the first charge 

 to the second, the continuous part of the true vein would aug- 

 ment more than that of the imaginary vein, i. e. would conse- 

 quently augment in greater proportion than that of the square 

 roots of the two charges. Thus the gradual diminution in the 

 volume of the divisions tends to render the law regulating the 

 length of the continuous part of the vein, when the charge is 

 made to vary, more rapid than that of Savart. 



Let us pass on to what relates to the length of the divisions. 

 As the acceleration of the velocity of the transference of the 

 liquid forms an obstacle to the free shortening of the divisions, 

 the latter must be gradually extended in the direction of their 

 length, in proportion as they descend upon the continuous part. 

 Now this gives rise to an influence exerted in the same direction 

 as the preceding; for in consequence of their less thickness, the 

 constricted portions will yield more readily to this traction than 

 the dilated portions, which will necessarily increase the rapidity 

 with which the former become diminished in thickness, and will 

 therefore tend to produce, in each of them, the formation and 

 rupture of the Ime sooner than in the corresponding imaginary 

 vein. But the difference of the laws which the divisions and the 

 liquid follow in their respective movements of transference, en- 

 genders an influence which acts in a contrary direction to the two 



