680 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



time which a division of the vein will occupy in effecting any 

 one and the same part of its transformation, will be as much longer 

 as the vein is thicker ; whence it follows, that if the rapidity of 

 the flow does not change, the space which the division will tra- 

 verse during this time will be as much greater as the diameter 

 of the orifice is greater ; consequently, for the same charge, the 

 length of the continuous part must increase with the diameter of 

 the orifice, and this is also verified by the observations detailed 

 in the memoir quoted. 



With regard to the laws which regulate these variations in the 

 length of the continuous part, Savart deduces from his observa- 

 tions, which were made by employing veins of water, that for 

 the same orifice this length is nearly proportional to the square 

 root of the charge, and that for the same charge it is nearly in 

 proportion to the diameter of the orifice. 



Let us now examine whether these two laws also emanate 

 from our explanation. 



72. Imagine for a moment that gravity ceases to act upon the 

 liquid as soon as the latter passes the contracted section. Then, 

 commencing at this section, the rapidity of translation will sim- 

 ply be that which is due to the charge, and the value of which, 

 as we know', is \/ 2gh, g denoting gravity and h the charge. 

 This velocity will be uniform ; consequently, if the vein had no 

 tendency to divide, it would remain exactly cylindrical through- 

 out any extent (§ 69). Now all parts of the liquid being actu- 

 ated by the same velocity of transference, this common move- 

 ment cannot exert any influence upon the effect of the configuring 

 actions ; so that, for instance, the gradual modifications which 

 each of the constrictions undergoes, and the time which it takes 

 in their accomplishment, will be independent of the rapidity of 

 transference. 



This admitted, let us consider the infinitely thin section which 

 constitutes the neck of a constriction, at the moment at which 

 it quits the contracted section. This section will descend with 

 a constant velocity, and at the same time its diameter will con- 

 tinually diminish until the constriction to which it belongs 

 becomes transformed into a line, and then the section in ques- 

 tion will occupy the middle of this line ; the line will become 

 disunited, to be converted into spherules. As we have shown 

 above, the time employed in the accomplishment of these phae- 

 nomena, and during which the liquid section we have con- 



