704 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



principally arising from the periodical shock of the isolated 

 masses of which the discontinuous portion is composed against 

 the body upon which they fall, and this sound may be made to 

 acquire great intensity by receiving the discontinuous portion 

 upon a tense membrane. On comparing the sounds thus pro- 

 duced by veins of water under different charges and with orifices 

 of different diameters, Savart found that, for the same orifice, the 

 number of vibrations made in a given time is proportionate to the 

 square root of the charge ; and that for the same charge, this 

 number is in inverse proportion to the diameter of the orifice. 

 We shall now see that these two laws also result from our 

 principles. 



Let us again have recourse to imaginary veins. In these the 

 length of the divisions is equal, as we have seen (§ 74), to the 

 normal length of those of a cylinder of the same liquid, formed 

 under the conditions of our laws, and having for its diameter 

 that of the contracted section of the vein ; thus this length de- 

 pends only upon the diameter of the orifice and the nature of the 

 liquid, and does not vary with the velocity of the flow. Now 

 it follows from this, that for the same liquid and the same ori- 

 fice, the number of divisions which pass in a given time t o the 

 contracted section is in proportion to this velocity, i. e. to s/lgh, 

 consequently to V h. But each of these divisions furnishes 

 lower down an isolated mass, and each of these subsequently 

 strikes the membrane ; the number of impulses produced in a 

 given time is equal then to that of the divisions which pass in 

 the same time to the contracted section, and is consequently 

 proportionate to the square root of the charge. 



In the second place, as the normal length of the divisions of 

 a cylinder, supposed to exist under the conditions of our laws 

 and composed of a given liquid, is proportionate to the diameter 

 of this cylinder, it follows, that for any liquid, the length of the 

 divisions of the imaginary vein is proportionate to the diameter 

 of the contracted section, and therefore exactly proportionate to 

 that of the orifice. Now for a given velocity of escape, the 

 number of divisions which pass in a given time to the contracted 

 section is evidently in inverse ratio to the length of these divi- 

 sions ; if then the liquid remains the same, this number is exactly 

 in inverse ratio to the diameter of the orifice. 



Thus the two laws which, according to Savart, regulate the 

 sounds produced by the veins, would necessarily be satisfied 



