686 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



Moreover, as this alteration is attributed to the influence which 

 the thickness of the edges of the orifice, although very slight, 

 exerts, it is probable that it may be rendered still less by em- 

 ploying, as Savart has done, orifices expanded outwardly, and 

 which may be shaped so that their edges may be very sharp. 

 Thus, with properly made orifices, we may undoubtedly admit, 

 without appreciable error, that commencing with a diameter 

 equal at most to a millimetre, the diameter of the contracted 

 section is proportional to that of the orifice. 



Hence, as the length of the continuous part of our imaginary 

 vein is in proportion to the diameter of the contracted section, 

 it will also be in proportion to the diameter of the orifice, at least 

 starting from a low value of the latter, which must not be much 

 less than a millimetre. 



We have only considered the case of mercury ; but the prin- 

 ciple with which we set out, i. e. the proportionality between 

 the partial duration of the transformation of a cylinder and the 

 diameter of the latter, very probably applies also, as we are 

 already aware, to all other very slightly viscid liquids ; conse- 

 quently, in the case of any of the latter liquids, it is very probable 

 that the length of the continuous part of the imaginary vein 

 will also be in proportion to the diameter of the orifice. The 

 law may also be true in regard to all liquids ; but it may be the 

 case that this general application does not hold good. 



If we now pass from the imaginary to the true vein, we have 

 only to suppose that the value of the constant charge is suffi- 

 ciently considerable to allow of the condition assumed in the 

 preceding section being satisfied throughout the entire extent 

 which we assign to the variations in the diameter of the orifice ; 

 so that, for each of the values given to this diameter, the con- 

 tinuous part of the true vein is apparently of the same length as 

 that of the corresponding imaginary vein. The law which regu- 

 lates this length may then be regarded as the same in both kinds 

 of veins. In accordance with the two remarks terminating the 

 preceding section, it is evident that if the common charge fulfills 

 the condition in question with regard to the greater value as- 

 signed to the diameter of the orifice, it will a fortiori fulfill it 

 with regard to all the others. 



10 niillims., the mean proportion of the diameter of the contracted section to 

 that of the orifice is 0*78 ; that in passing from 10 millims. to 1 millim., the 

 proportion only increases 083 ; and lastly, when the diameter is equal to 0*55 

 millim., the proportion becomes 0*88. 



