WITHDRAWN FROM THE ACTION OF GRAVITY. 279 



fore be legitimately applied to cylinders of sufficient length to furnish several 

 spheres supposed to be in the above conditions, in the case where these latter 

 cylinders are formed of such a liquid that they would give for the proportion ija 

 question a value but little greater than that of the limit o{ stability. 



Now this is the case of mercury, (§ GO,) and it is also very probable that of 

 ail other very slightly viscid liquids, (§ CO.) Thus the law given b}' the short 

 cylinders of oil will be exactly or apparently that which would apply to cylin- 

 ders of mercury of sufficient length to furnish several spheres, supposing the 

 latter to be produced in vacuo or in air, free at the whole of their convex surface, 

 and of such length that the divisions in each of them would assume their normal 

 length. Moreover, the same law w. uld be undoubtedly applicable to cylinders 

 formed of any other very slightly viscid liquid, and supposed to be in the same 

 conditions as the preceding. 



The law may possibly be completely general, i. e., it may apply to cylinders 

 formed, always uuder the same circumstances, of any liquid whatever ; but our 

 experiments do not furnish us with the elements necessary to decide this ques- 

 tion. Lastly, the transformation of our short cylinders presents a peculiarity 

 which entails another restriction. The two final masses into Avhieh a cylinder 

 of this kind resolves itself being unequal, the smallest acquires its form of 

 equilibrium considerably before the other, so that the duration of the phenom- 

 enon is not the same. Hence we can only determine its duration iip to the 

 moment of the rupture of the line ; consequently the proportion which we thus 

 obtain for both cylinders will only be that of the durations of two homologous 

 portions of the entire transformations. Moreover, the proportion of these partial 

 durations is exactly that of which we shall have hereafter to make use. 



65. I made the experiments in question by employing two systems of disks, 

 the respective dimensions of which were to each other as one to two; in the 

 former, the diameter of the disks was 15 millimeters, and they Avcre 54 milli- 

 meters apart ; and in the second their diameter was 30 millimeters, and their 

 distance apart 108 millimeters. The cylinders formed respectively in these two 

 systems weie therefore alike, and, as I have previously stated, (§ 63,) these 

 two figures exactly maintained their similarity, as far as the eye was capable of 

 judging, in all the phases of their transformations. It sometimes happened that 

 the cylinder, when apparently well formed, was not at all persistent and imme- 

 diately began to alter; this circumstance being attributable to some slight 

 remaining irregularity in the figure, I immediately re-established the cylindrical 

 form,* and the time was only taken into.accoiint when the figure appeared to 

 maintain this form for a few moments. Another anomaly then sometimes pre- 

 sented itself, Avliich consisted in the simultaneous formation of two constrictions 

 with an intermediate dilatation ; this modification ceased when it had attained 

 a very slightly marked degree, and the figure appeared to remain in the same 

 state for a considerable period ; t then one of the constrictions became gradually 

 more marked, Avhilst the other disappeared, and the transformation afterwards 

 went oft in the usual manner. As this peculiarity constituted an exception to 

 the regular course of the phenomenon, I ceased to reckon as soon as it showed 

 itself, and I again re-established the cylindrical form. The estimation of the 

 time was only definitively continued in those cases in which, after some per- 

 sistence in the cylindrical form, a single constriction only was produced. 



I repeated the experiment upon each of the two cylinders twenty times, in 

 order to obtain a mean result. As soon as one transformation was completed, 



* See the second note to paragraph 46. 



t We shall see, in the following series, to what this singular modification iu the figure id 

 owing. 



