WITHDRAWN FROM THE ACTION OF GRAVITY. 683 



be regarded as constant, and equal to that of a section of the 

 imaginary vein ; so that throughout the entire space traversed 

 by the first during this time commencing at the contracted 

 section, the real vein, if it did not become divided, would pre- 

 sence exactly the same diameter, and might be regarded as iden- 

 tical with the imaginary vein, also assumed to be free from 

 divisions. 



Now it necessarily follows from this approximative identity, 

 that during the time 6 the same will apparently occur in like 

 manner in both veins ; consequently the time 6 will be very 

 nearly that which, in the true vein, the liquid section corre- 

 sponding to the neck of a constriction would employ in accom- 

 plishing the modifications which we have considered, and the 

 space which it will traverse during these modifications may be 

 regarded as equal to the distance D relative to the imaginary 

 vein. 



Now as the continuous part of the true vein terminates a little 

 below this space, and is consequently included in the same por- 

 tion of the vein, it follows from the above approximative identity, 

 that this continuous part will be exactly equal in length to that 

 of the imaginary vein, and therefore commencing with the least 

 of the charges considered above, the lengths of the continuous 

 parts of both veins must be very nearly governed by the same 

 law. 



We arrive then, lastly, at this conclusion, that for the same 

 orifice, and commencing with a low but sufficient charge, the 

 length of the continuous part of the true vein must be in pro- 

 portion to the square root of the charge. 



In accordance with the preceding demonstration, the low 

 charge in question is that at which the movement of transference 

 of the liquid begins to remain apparently uniform in all that 

 portion of the true vein which is comprised between the con- 

 tracted action and the point occupied by the middle of each 

 line at the instant of ruptui'e ; but as the extremity of the con- 

 tinuous part is very little distant from this point (§ 72), we 

 may neglect the small difference, and say simply that the low 

 charge in question is that which begins to render the movement 

 of transference of the liquid exactly uniform as far as the ex- 

 tremity of the continuous part of the vein. 



Thus, under the condition of a low charge sufficient to pro- 

 duce this approximative uniformity, which condition is always 



