706 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



from the contracted section equal to about 6 times the diameter 

 of this section, the number of vibrations corresponding respect- 

 ively to the sounds produced by each of the veins of the series 

 will necessarily satisfy the first of the two laws discovered by 

 Savart. 



2. When a series of veins, formed of a very slightly viscid 

 liquid, escapes under a conimon charge and from orifices of dif- 

 ferent diameters, if the common charge is sufficient for the same 

 condition to be fulfilled with regard to the vein which escapes 

 from the larger orifice, the number of vibrations corresponding 

 respectively to the sounds produced by each of the veins of the 

 series will necessarily satisfy the second law. It now remains 

 for us to show that the above condition was satisfied in the ex- 

 periments from which Savart deduced the two laws under con- 

 sideration. 



In the series relating to the first of these laws, the diameter 

 of the common orifice was 3 millims., and the smallest charge 

 was 51 centims. ; and in the series which refers to the second 

 law, the value of the common charge was the same, 51 centims., 

 and the diameter of the largest orifice was 6 millims. For our 

 condition to be fulfilled with regard to both series, it was there- 

 fore evidently sufficient that it was so in the vein which escaped 

 under the charge of 51 centims., and fi-om the orifice the dia- 

 meter of which was 6 millims. Now on multiplying this diameter 

 by 0*8, we obtain for the approximative value of that of the con- 

 tracted section of the vein in question 4'8 millims., and 6 times 

 the latter quantity gives us 28'8 millims., or nearly 3 centims. 



Now if in the expression V/ ' , which gives the general value 



of the relative proportions of the velocities of transference at 

 a distance I from the contracted section and at this section 

 (§ 80), we make h = 51 and 1=3, we obtain for this proportion 

 the value 1"03 ; whence it is evident, that from the contracted 

 section to a distance equal to about 6 times the diameter of this 

 section, the velocity of transference of the liquid of the vein in 

 question only increased 3 centims. more than its original value. 

 83. Let us imagine a vein of water, and let us call a division 

 considered immediately after its passage to the contracted sec- 

 tion, i. e. at the instant at which its upper extremity passes this 

 section, the nascent division. It follows from what we have de- 

 tailed in the preceding section, starting with a sufficient charge, 



