670 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



must act with energy ; moreover, as the transformation ceases 

 to take place immediately above the limit of stability, the dura- 

 tion of the pheenomenon may then be considered as infinite, 

 whence it follows that when this limit is exceeded, the duration 

 passes from an infinite to a finite value, consequently it must 

 decrease rapidly as it deviates from this limit ; lastly, this is 

 also confirmed by the results of observation, as we shall show 

 hereafter. Thus, even if it were possible to form in vacuo or in 

 air one of our very short cylinders of oil, consequently to elimi- 

 nate the two causes of retardation due to the presence of the 

 alcoholic liquid, the duration relative to the cylinder would still 

 exceed that which would relate to a cylinder of oil of the same 

 diameter formed under the conditions we have supposed. 



I have said that the principle above established is confirmed 

 by experiment, i. e. for the same diameter, the same liquid, and 

 the same external actions, if any exist, when from any cause, the 

 sum of the lengths of a constriction and a dilatation augments, 

 the total and partial durations of the transformation become less. 

 We shall proceed to make this evident. In the experiments of 

 the preceding section, the partial duration relating to the cylinder, 

 the diameter of which was 15 millims., was for instance about 

 30 seconds, the mean, as shown by the table. Consequently, if 

 we were to form in the alcoholic liquid a similar cylinder of oil, 

 the diameter of which is 4 millims., the partial duration of this, 

 in virtue of the law which we have found, would be nearly equal 



30" X 4 

 to = 8". Now, in the nearly cylindrical figure of oil of 



§ 47, which figure is also formed in the alcohohc liquid, the mean 

 diameter was (56) about 4 millims. In this and the preceding 

 figure, the diameter, the liquid and the external actions then are 

 the same; but in the former, the sum of the lengths of the con- 

 striction and the dilatation would only be equal to 4 millims. 

 X 3-6 = 14-4 millims., w^hilst in the second, this sum, which is 

 equivalent to the length of a division, was (§ 56) appi'oximatively 

 66*7 millims. ; now on observing this latter figure, we recognise 

 easily that the duration of its transformation is much less than 

 8". In ti'uth, from the nature of the experiment, it is impos- 

 sible with regard to this same figure, to fix upon the commence- 

 ment of the formation of a given constriction or dilatation, so 

 that the complete duration should considerably exceed that which 

 would b deduced by the simple inspection of the phasnomenon j 



