302 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
ad 
Diameter of the orifice, 6 millimetres. | Diameter of the orifice, 3 millimetres. 
1 Saat Te ce 1 
Charges. Length of the con- | Proportion to the Charges. Lengthofthecon-| Proportion to the 
tinuous portion. square root of tinuous portion. square root of 
the charge. | the charge, 
4.5 40 18.9 4.5 16 7.9 
12 59 17.0 12 25 tee, 
27 82 15.8 27 Al 78 
47 112 16.3 47 5d 8.0 
and the first shows that, with an orifice of 6 millimetres, the proportion of the 
length of the continuous portion to the square root of the charge appears to 
have attained its limit even with a charge of 27 centimetres; the slight in- 
crease manifested in the case of the succeeding charge is undoubtedly due to 
the causes of irregularity which I have mentioned. 
Let us further calculate, for these two series, the proportions of the lengths 
corresponding respectively to the two orifices, which gives us the following 
table: 
Charges. Proportions, 
Ais atere «| ciao dete ein Shsinla mieia acbible ys sles crgte SOS GGO. UL Sa 2.50 
WD ipereswts ah) siete els fl SSPE a teielh Paha eI, farciths «me ye teevatalel ars 2.36 
2d pin bial e SIRS eae) s a Hladalm =: 3,22 a Wary TSE RIEL iis i PSI ORS SS 2.00 
Arle, (isiats< ah F sia ofetstje HOSE 2-GE ERIGD, AL DOC Saat ht cee tere 2.04 
Tt is, therefore, also under the charge of 27 centimetres that the proportion of 
the lengths of the continuous portions attains that of the diameters of the 
orifices, which completes the establishment of the conformity of the conelu- 
sions of § 79 to the results of observation. 
Lastly, with an orifice of 3 millimetres, Savart has made a series of obser- 
vations corresponding to four larger charges than the preceding, and the pro- 
portion of the length of the continuous portion to the square root of the charge 
still appeared pertectly constant; the first of these new charges was 451, and 
the last 459 centimetres. 
82. Thus, as we have been taught by Savart’s investigations, the vein gives 
rise to the production of a continuous sound, principally arising from the peri- 
odical shock of the isolated masses of which the discontinuous portion is com- 
posed 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 produced 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 hay- 
ing for its diameter that of the contracted section of the vein; thus this length 
depends 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 orifice the number of divisions which pass in a 
given time to the contracted section is in proportion to this velocity, 2. e., to 
V2ch, consequently to Vhs. But each of these divisions furnishes lower down 
an isolated mass, and each of these subsequently strikes the membrane; the 
