Jets of Liquid issuing from Circular Orifices, 295 



obtained, though by an entirely different method ; that is to say, 

 he finds for the exact value of the limit of this stability the 

 quantity tt. This calculation, therefore, which fully corroborates 

 mine, sanctions one of the principal results of my observations ; 

 it shows the absolute necessity of it, and gives the precise mea- 

 sure of the phsenomenon. 



Now a jet of liquid issuing in any direction whatever, fulfils 

 the condition expressed in 5; that is to say, it constitutes a 

 liquid figure whose length is considerable when compared with 

 its transversal dimensions. It should then of necessity alter its 

 form, in order to transform itself gradually and in a continuous 

 manner into a series of isolated spheres with interposed spherules; 

 and the phsenomenon ought to manifest itself by the formation 

 of contractions and expansions which develope themselves more 

 and more without changing their nature, until the generation 

 and rupture of the threads take place as above described. But 

 the liquid of the jet having a motion of translation, which carries 

 with it the expansions and contractions, it is during this journey 

 that each of them completes all its progressive modifications ; so 

 that each protuberance leaving the orifice in its rudimentary 

 state, does not attain to that of an isolated mass until at a greater 

 or less distance from the orifice. Further, a fresh quantity of 

 hquid being always supplied, the transformation must be inces- 

 santly repeated. Hence the continuous and discontinuous parts 

 of the jet ; hence also the origination of expansions and contrac- 

 tions scarcely perceptible near the orifice, but becoming more and 

 more developed as they move onwards with the liquid, until the 

 expansions arriving one after another at the extremity of the 

 continuous part, successively detach themselves and pursue their 

 course as isolated masses, which assume, or tend to assume, a 

 spherical form; hence, too, the spherules interposed between 

 these masses ; and lastly, the laws discovered by Savart, con- 

 necting the length of the continuous part, as well as the tone 

 produced by the shock of the jet, with the charge and the dia- 

 meter of the orifice. To render this last deduction evident, 

 however, it would be necessary to have recourse to facts, which, 

 fearing to extend this note too much, I have not here stated. 



It will be seen that the fundamental part of my theory con- 

 sists, not of hypotheses, but of facts and their inevitable con- 

 sequences ; which consequences are so strict, that, had not the 

 admirable research of Savart revealed to us the true constitution 

 of jets of liquid issuing from circular orifices, we might have pre-^ 

 dieted the same with all its details and laws from my experiments. 

 My theory does more : it shows that the laws indicated by Savart 

 are only the limits, which are more and more approached the 

 stronger the charges and the smaller the orifices, a deduction 



