Jets of Liquid issuing from Circular Orifices. 293 



proceeding from external noises and the fall of the liquid into 

 the vessel which receives it, expresses himself thus : — '' No traces 

 of protuberances can be detected in this portion of the jet/^ and 

 in the resume at the end of the memoir, he says, " This first part 

 of the jet is calm and transparent, and resembles a rod of crystal." 

 Nevertheless it is in this same portion of the jet that he has 

 proved, by means of his ingenious contrivance, the presence of 

 expansions the more developed the greater the distance from the 

 orifice at Tvhich they are observed. The non-existence of expan- 

 sions, therefore, cannot be concluded from the quiescent and 

 white appearance of the limpid portion of a jet : this appearance 

 is merely an illusion caused by the small prominency of the ex- 

 pansions in this portion of the jet, and the rapidity of their trans- 

 latory motion. Had Magnus employed Savart^s method, or that 

 of Matteucci*, or one of those of Billet- Selisf^ he would certainly 

 have detected the existence of expansions, even when the jet was 

 protected from external vibratory action ; for seeing that rupture 

 is impossible, the separation of the mass must necessarily be 

 ascribed to the formation of contractions which become more 

 developed as they approach the extremity of the continuous part, 

 and which necessitate expansions whose development passes 

 through the same phases of augmentation. 



By the side of the inherent difiiculties of the hypotheses just 

 discussed, let us place the principles of my theory. 



All physicists are now acquainted with my method of neutral- 

 izing the action of gravity upon a large mass of liquid, and at 

 the same time leaving it free to obey molecular actions. By 

 means of this, and afterwards of another method, I have been 

 able to obtain liquid cylinders and to study their properties. I 

 have thus corroborated the. following, facts (see^myv Second Series, 

 §§ 37 to 68) J : — 'is^do lo-BorLterff 3te':>flob Tgoitr 



1. A liquid cyUnder constitlites'a figure of stable equilibrium 

 as long as the ratio between its length and its diameter does not 

 exceed a certain limit between 3 and 3*6. I will here add, that 

 an a priori method, of which I have hitherto only published the 

 result, gave for exact value of the limit the quantity tt, that is 

 to say, the i:atio bet^eei^t^e.circumferencie^nd; the. diameter of 

 a circle.iii it.'»dirt^fyooi; orft vd baoubn-ci -yim^in \j tu/1) ' 



2. Beyond this limit the cylinder constitutes a figure of un- 

 stable equilibrium, so that it cannot be obtained in a permanent 

 state except by means of certain hindrances. 



3. A liquid cylinder whose length is very great in comparison 

 to its diameter, converts itself, by the spontaneous rupture of 



" '."*" ^ * Comptes Rendus, 1846, vol. xxii. p. 260. 



-anp no^f Annates de Chimie et de Physique, 1851, vol. xxxi. p. 326. /. 



-mil orCvl J Taylor's Scientific Memoirs, vol. v. p. 62|, .!> j/iviioij j,^ Jon 



erioiiom 8it>r "to nomoq hm 



