278 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



the cjliudcrri are formed in vacuo or in air, and are free from all external resist- 

 ance, or, in other words, free upon tlie wlioTe of their convex gurface. 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 proportion 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 alco- 

 liolic liquid ; but it is clear that in virtue of the similitude of the two figures of 

 oil and that of their movements, the quantities of surrounding liquid respectively 

 displaced will be to each oilier cxactlj', 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 

 circumstance. Ileuce it is very probable that this circumstance Avill no longer 

 exert any infiuence upon the proportion of the durations, except that the abso- 

 lute valnes 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 configuring 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 au homologous instant of the two transformations the 

 alcoholic liquid becomes suddenly 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 configuring 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 those corresponding to two homologous points taken upon both the figures 

 will still be to each other as the configuring forces commencing at these points ; 

 so that in fact the respective resultants of the external and internal actions at 

 these two same points will be to each other in the same proportion as the two 

 internal forces alone. Thus the attractions exerted upon the oil by tbe sur- 

 rounding alcoholic liquid will certainly diminish the absolute intensities of the 

 configuring forces, but they Avill not change the relations of these intensities, 

 consequently they may be considered as not exerting any influence upon the 

 durations. Ikit it is clear that this cause will nevertheless greatly increase the 

 absolute values of the latter. For the two reasons which we have explained, 

 the presence of the alcoholic liquid will then increase the absolute values of the 

 two durations to a considerable extent ; but we may admit that it will not alter 

 the relation of these values, so that this proportion will be the same whether the 

 phenomenon take place in vacuo or in air. We shall, therefore, consider the law 

 which we deduce from our experiments upon short cylinders of oil as inde- 

 pendent of the presence of the surrounding alcoholic liquid, and this will be 

 found to be supported by the nature of the law itself. 



But the exact formation of our short cylinders of oil requires (§ 46) that in 

 these cylinders the ])roportion between the length and the diameter, or what 

 comes to the same thing, between the sum of the lengths of the constriction and 

 the dilatation and the diameter, exceeds but little the limit of stability. Now, 

 in the transformation of cylinders sufficiently long to fuinish several spheres, 

 which would be formed in vacuo or in the air, and free upon their entire convex 

 surface, and the divisions of which have their normal length, the proportion of 

 the sums of the lengths of one constriction and one dilatation to the diameter, 

 which proportion is the same as that of the length of oue division to the diam- 

 eter, Avonkl vary with the nature of the liquid, (§ 59,) and we are ignorant 

 whether the law of the durations is independent of the value of this proportion. 

 The law which we shall obtain in regard to short cylinders of oil can only there- 



