684 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



realizable, the law indicated by Savart as establishing the rela- 

 tion between the length of the continuous part and the charge, 

 necessarily follows from the properties of liquid cylinders. To 

 discover whether this law is also true when weaker charges are 

 employed, we must start from other considerations ; but it is 

 evident so far, that if in the latter case the law is different, it 

 must at least necessarily converge towards the proportionality in 

 question, in proportion as the charge increases. 



We must remark here, that in the case of a given liquid, the 

 charge with which the vein begins to exist under the condition 

 which we have determined, must be as much less as the diameter 

 of the orifice is smaller. In fact, since, all other things being- 

 equal, the transformation of a liquid cylinder occurs with a 

 rapidity proportionate to the diminution in size of the diameter 

 of the cylinder, it follows that the value of 6 will diminish with 

 the value of the orifice ; and therefore the smaller the latter 

 is, so much the less will the value of h become to allow of the 

 term (/6 in the expression V 1gh-\ g9, placed at the commence- 

 ment of this section, being neglected in comparison with the 

 term V2gh, and consequently for the vein to exist under the 

 condition in question. 



Moreover, as the time 6 varies with the nature of the liquid, 

 the same will necessarily apply to the charge under consideration. 



74. Let us now investigate the second law, namely that which 

 establishes the approximative proportion of the length of the 

 continuous part of the vein and the diameter of the orifice, when 

 the charge remains the same. 



Let us resume, for an instant, the imaginary case of an abso- 

 lutely uniform movement of transference. The vein, leaving its 

 divisions out of consideration, will then constitute a true cylinder 

 commencing at the contracted section (§ 72), which cylinder will 

 be formed in the air, and the entire convex surface of which will 

 be free ; moreover, as the movement of transference of the liquid 

 does not exert any influence upon the effect of the configuring 

 forces (§ 72), and as there is no extraneous cause tending to 

 modify the length of the divisions, the latter will necessarily 

 assume their normal length. It is evident, therefore, that ex- 

 cepting that the formation of its divisions is not simultaneous 

 (§ 69), our imaginary vein will exist under exactly the same cir- 

 cumstances as the cylinders to which the laws recapitulated in 

 section 68 refer ; consequently, if we consider in particular one 



