700 PLATEAU ON THE PHENOMENA OP A FREE LIQUID MASS 



This being established, let us now begin by examining the 

 table relating to the orifice of 6 millims. It is evident that the 

 proportion of the length of the continuous portion to the square 

 root of the charge diminishes considerably from the first charge to 

 the last ; whence it follows, that in the case of a vein of water 

 escaping from an orifice 6 millims. in diameter, if the charge be 

 not made to exceed 47 centims., Savart's first law is far from being 

 satisfied. Thus the first conclusion of § 78 is conformable with 

 experiment. Moreover, the diminution of the proportion deter- 

 mines the direction in which the true lawdiffers from that of Savart, 

 within the limit at which this begins to be sufficiently approxi- 

 mative ; it is evident that the length of the continuous portion 

 then augments less rapidly than the square root of the charge. 

 In the second place, as the proportion in question increases, we 

 find that the latter converges towards a certain limit, which 

 must be a little less than 23, i. e. the value corresponding to the 

 charge of 47 centims. In fact, whilst the charge receives suc- 

 cessive augmentations of 7'5, 15 and 20 centims., the proportion 

 diminishes successively by 14, 8*9 and 4'5 units, and the latter 

 difference is still tolerably slight in regard to the value of the 

 latter proportion ; whence we may presume, that if the charge 

 were still further increased, the further diminution of the pro- 

 portion would be very small, and that a sensibly constant limit 

 would soon be attained, at which limit Savart's first law would 

 be satisfied. 



Let us now find the proportion of the velocity of transference 

 of the liquid at the extremity of the continuous part to that at 

 the contracted section, in the case of the vein escaping under a 

 charge of 47 centims. We shall disregaid here the small alter- 

 nate variations which have been treated of in § 77? and shall 

 therefore consider the velocity of transference of a horizontal 

 section of the liquid of the vein as being also that which this 

 section would have if it had fallen freely and in a state of isola- 

 tion from the height of the level of the liquid in the vessel. 

 Then, on neglecting the small interval comprised between the 

 orifice and the contracted section, we shall have for the velo- 

 city in question, at any distance I of this section, the value 

 \/2g .{h + l)\ if then I denotes the length of the continuous 

 portion, the proportion of the velocity at the end of this length 

 to that at the contracted section will be expiessed generally by 



y , or more simply by /\/ -- — . On now substituting, 



