626 PLATEAU ON THE PHiKNOMENA OF A FREE LIQUID MASS 



versed sine of the small circular segments which we have con- 

 sidered ahove ; consequently these small circular segments heing 

 similar to that of the spherical segment, we obtain for the de- 

 termination of this versed sine, which we shall denote by/, the 



h f 



proportion - = — , which in the case of our liquid figure gives 



f=0'05 millim., whence 



h—f= 9-41 millims. 

 This then is definitively the theoretical value of the quantity 

 which was required to be measured. 



41. Before pointing out the process which I employed for 

 this purpose, and communicating the result of the operation, I 

 must preface a few important remarks. If the densities of the 

 alcoholic mixture and of the oil are not rigorously equal, the 

 mass has a slight tendency to rise or descend, and the height of 

 one of the segments is then a little too great, whilst that of the 

 other is a little too small ; but we can understand that if their 

 difference is very small, an exact result may still be obtained by 

 taking the mean of these two heights. We thus avoid part of 

 those preliminary experiments, which the establishment of per- 

 fect equality between the two densities requires. But one cir- 

 cumstance which requires the greatest attention, is the perfect 

 homogeneity of each of the two hquids. If this condition be not 

 fulfilled with regard to the alcoholic mixture, i. e. if the upper 

 part of this mixture be left containing a slightly greater propor- 

 tion of alcohol than the lower portion, the liquid figure may ap- 

 pear regular and present equal segments ; all that is required for 

 this is, that the mean density of that part of the mixture which 

 is at the same level as the mass, must be equal to the density of 

 the oil ; but under these circumstances the level of the two seg- 

 ments is too low. In fact, the oil forming the upper segment is 

 then in contact with a less dense liquid than itself, and conse- 

 quently has a tendency to descend, whilst the opposite applies 

 to the oil forming the inferior segment*. Heterogeneity of the 

 liquid produces an opposite effect, i. e. it renders the height of the 

 segments too greiit. In fact, the le'ast dense portions rising to 

 the upper part of the mass, tend to lift it up, whilst the most 



* By intentionally producing very great heterogeneity in the alcoholic mix- 

 ture (§9 of the preceding memoir), and employing suitable precautions, a per- 

 fectly regular cylinder may be formed, the bases of which are absolutely plane. 



