6G4 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



discs and their diameters is the same in both parts, in order 

 that similitude may exist between the two Hquid figures, at their 

 origin and at each homologous instant of their transformations. 

 Before giving an account of the employment of these figures 

 of oil for the determination of the law of the durations, we 

 shall take this opportunity of making several important re- 

 marks. We shall only require to make use of the law in ques- 

 tion, in that case, which in other respects is the most simple, 

 where the cylinders are formed i?i vacuo or in air, and are 

 free from all external resistance, or, in other words, free upon 

 the w^hole of their convex surface. Now our short cylinders of 

 oil are formed in the alcoholic liquid, and it might be asked 

 whether this circumstance does not exert some influence upon 

 the proportion of the durations corresponding to a given pro- 

 portion between the diameters of these cylinders. At first, a 

 greater or less portion of the alcoholic liquid must be displaced 

 by the modifications of the figures, so that the total mass to be 

 moved in a transformation is composed of the mass of oil and 

 this portion of the alcoholic liquid ; but it is clear that in virtue 

 of the similitude of the two figures of oil and that of their move- 

 ments, the quantities of surrounding liquid respectively displaced 

 will be to each other exactly, or at least apparently, as the two 

 masses of oil ; so that the relation of the two entire masses will 

 not be altered by this cii'cumstance. Hence it is very probable 

 that this circumstance will no longer exert any influence upon 

 the proportion of the durations, except that the absolute values 

 of these durations will be greater. On the other hand, the 

 mutual attraction of the two liquids in contact diminishes the 

 intensities of the pressures (§ 8), and consequently the con- 

 figuring forces ; but it is easy to see that this diminution does 

 not alter the relation of these intensities in the two figures. 

 For let us imagine that at an homologous instant of the two 

 transformations the alcoholic liquid becomes sudden'y replaced 

 by the oil, and let us conceive in the latter the surfaces of the 

 two figures as they were at that instant. The configuring forces 

 will then be completely destroyed by the attraction of the oil 

 outside these surfaces, or, in other words, the external attraction 

 will be at each point equal and opposite to the internal configu- 

 ring force. If we now replace the alcoholic liquid, the intensities 

 of the external attractions will change, but they will evidently 

 retain the same relations to each other ; whence it follows that 



