WITHDRAWN FROM THE ACTION' OF GRAVITY. 



701 



in this expression for h and / the values relative to the vein in 

 question, i. e. 47 and 158, we find for the relation between the 

 extreme velocities the value 2*1. Thus, although under a charge 

 of 47 centims., the vein escaping from an orifice of 6 millims. 

 may probably nearly exist under the eflfective conditions of 

 Savart's first law, the velocity at the end of the continuous por- 

 tion is even more than double the velocity at the contracted 

 section, so that the movement of transference of the liquid is 

 still more considerably accelerated. The second conclusion of 

 § 78 therefore appears so far to agree, like the first, with the 

 results of experiment. 



Let us pass to the table relating to the orifice of 3 millims. 

 Here it is evident that the proportion of the length of the con- 

 tinuous portion to the square root of the charge is very nearly 

 the same for all the charges ; whence it follows, that with this 

 orifice the vein already begins to come within the effective con- 

 ditions of Savart's first law under a charge of 4*5 centims. But, 

 according to what we have stated, the orifice being 6 millims., 

 the vein does not satisfy these conditions except under a charge 

 at least equal to 47 centims. ; the charge at which Savart's first 

 law begins to be realized, then, augments and diminishes with 

 the diameter of the orifice, and much more rapidly than this 

 diameter. Now this is the substance of the conclusion of § 78. 



Lastly, if in the general expression of the relation of the extreme 

 velocities found above, we replace h and /by the values 4"5 and 24 

 relative to the first vein of the table under consideration, we shall 

 find for this relation the value 2*5 ; which shows that with the 

 charge 4*5, under which the vein is already placed in the effective 

 conditions of Savart's law, the velocity of transference of the 

 liquid is still very notably accelerated. No doubt can therefore 

 remain of the legitimacy of the second conclusion of § 78- 



Let us now calculate, for each of the four charges, the pro- 

 portion of the lengths of the continuous parts corresponding 

 respectively to the two orifices ; we shall thus form the following 

 table : — 



VOL. V. PART XXI. 



3 B 



