WITHDRAWN FROM THE ACTION OF GRAVITY. 'JO'J 



that the proportion of the length of the nascent divisions of the 

 vein in question to the diameter of the contracted section will 

 assume a constant value, i. e. independent of the charge, and 

 that this value will very probably differ but little from 4. 



Now the results obtained by Savart in the experiments relative 

 to the laws which we have just discussed, allow us, as we shall 

 see presently, to verify the consequences of our principles. 



The two opposite causes which tend to modify the length of 

 the divisions, are also those which exert an influence upon the 

 velocity of transference, or, more precisely, upon the velocity of 

 the transference of the necks which terminate them (§ 76). Now 

 in the case under consideration, these same causes both remain- 

 ing very small throughout the extent corresponding to a nascent 

 division, their resulting action upon the velocity of transference 

 of the necks will be insensible throughout this extent; conse- 

 quently the velocity with which a neck descends may be i-egarded 

 as exactly uniform and equal to the velocity of the flow V2gh, 

 from the contracted section to a distance equal to the length of 

 a nascent division. 



If, then, for an orifice of a given diameter. A, denotes the 

 length of a nascent division, and i the time occupied by a neck 

 to traverse it, we shall have 



Moreover, let n represent the number of divisions which pass to 

 the contracted section in a second of time ; as the time t evi- 

 dently measures the duration of the passage of one of them, we 



shall have, taking the second as the unit of time, ^=-, and 



therefore ^ 1 , 



Lastly, let k denote the diameter of the contracted section cor- 

 responding to the same orifice ; to represent the proportion of 

 the length of the nascent division to this diameter, we shall have 

 the formula 



^ = ;^^^- («) 



Now to obtain, by means of this formula, the numerical value 

 of the proportion -r relative to a determined charge and orifice, 

 we have only to ascertain by experiment the number of vibra- 



