698 PLATEAU ON THE PHENOMENA OK A FREE LIQUID MASS 



is very slight ; consequently the above conclusion is very pro- 

 bably also true in regard to any of the latter liquids, such for 

 instance as water. 



79. Let us provisionally admit the preceding conclusions as 

 perfectly demonstrated, and let us pass to the other law, i. e. that 

 which governs the length of the continuous portion when the 

 diameter of the orifice is made to vary. I say, in the first place, 

 that, in the case of mercury, this law will coincide with the 

 second of those of Savart, when we give to the common charge 

 the value at which the vein escaping from the largest of the ori- 

 fices employed would begin in reality to satisfy the first of these 

 laws. In fact, let us remark first, that with the charge in ques- 

 tion, and which we shall denote by h^, the veins escaping from 

 all the lesser orifices will exist a fortiori in the effective condi- 

 tions of the first law. Consequently, if for a moment we substi- 

 tute for this charge A, a sufficiently considerable charge to ren- 

 der the velocity of the liquid sensibly uniform throughout all 

 the continuous parts, and if we again pass from this second 

 charge to the preceding, the respective lengths of the continuous 

 parts will all decrease in the same proportion, i. e. in that of the 

 square roots of the two charges. Now, with the largest of the 

 latter, the lengths in question were to each other as the diameters 

 of the corresponding orifices (§ 74) ; it will also be the same 

 with the charge h^ ; consequently with this charge the second 

 of Savart's laws will be satisfied. 



In the second place, I say that with a lower charge than h^ 

 the same will not hold good. To show this, let h^ be this new 

 charge ; and let us denote by h^ the charge which plays the same 

 part with regard to the vein escaping from the smallest orifice 

 as that which A, plays with regard to that which escapes from 

 the larger one. It must be borne in mind that ^3 is less than h^, 

 and let us suppose A^ to be comprised between the two latter. 

 With the charges h^ and h<^ the vein escaping fi'om the smallest 

 orifice will therefore then still exist under the effective conditions 

 of Savart's first law, whilst as regards the vein which escapes 

 from the larger orifice, these conditions wiU only commence at 

 A, ; if then we pass from h^ to hc^, the continuous portion of the 

 first vein will decrease in proportion to the square roots of these 

 two charges ; but that of the latter vein will decrease in a dif- 

 ferent proportion. Now with the charge h■^ these two lengths 

 were to each other as the diameters of the corresponding orifices; 

 with the charge he. then they would exist in another proportion j 



