636 PLATEAU ON THE PHiENOMENA OF A FREE LIQUID MASa 



words, throughout the duration of the phenomenon the figure 

 remains constantly a figure of revolution. We may add here, 

 that in the horizontal figure the respective lengths of the con- 

 stx-icted and dilated portions appear to be equal ; we shall show, 

 in the following sei-ies, that this equality is rigorously exact, at 

 least at the commencement of the phsenomenon. 



It is now evident that the alteration in the form of these 

 cylinders is really the result of a property which is inherent in 

 them. We shall hereafter deduce this property as a necessary 

 consequence of the laws which govern a more general phaeno- 

 menon. 



It moreover results from the above experiment, that the pro- 

 portion 3-6 is still greater than the limit of stability, so that the 

 exact value of the latter must lie between the numbers 3 and 

 3'6. It is obvious that this method of experiment might be 

 employed to obtain a closely approximative determination of 

 the value in question ; I propose doing this hereafter, and I 

 shall give an account of the result in the following series, when 

 I shall have to return to the question of the limit of stability of 

 the cylinder. 



47. In the unstable cylinders which we have just formed, the 

 proportion of the length to the diameter was inconsiderable ; but 

 what would be the case if we were to obtain cylinders of great 

 length relatively to their diameter ? Now under certain circum- 

 stances, figures of this kind, more or less exactly cylindrical, may 

 be realized, and we shall proceed to see what the results of the 

 spontaneous rupture of equilibrium are. 



A fact which I described in paragraph 20 of the preceding 

 memoir, and which I shall now describe more in detail, affords 

 us the means of obtaining a cylinder of this kind, and of ob- 

 serving its spontaneous destruction. When some oil is intro- 

 duced by means of a small funnel into an alcoholic mixture con- 

 taining a slight excess of alcohol, and the oil is poured in suffi- 

 ciently quick to keep the funnel full, the liquid forms, between 

 the point of the funnel and the bottom of the vessel where the 

 mass collects, a long train, the diameter of which continues to 

 increase slightly from the upper to the lower pai't, so as to form 

 a kind of very elongated cone, which does not differ much from 

 a cylinder*. This nearly cylindrical figure, the height of which 



* This slight increase in diameter depends upon tlie retardation which the 

 resistance of the surrounding liquid occasions in the movement of the oil. 



