272 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



The intensities of the configuring forces corresponding to different liquids 

 may be compared numerically for the same curvatures. In fact, let us first 

 bear in mind that the pressure corrcKponding to one element of the superficial 

 layer, and reduced to unity of the surface, is expressed by (§ 4,) 



--tG-0 



Now, the value of the part P of this pressure being the same for all the elements 

 of the superficial layer, and the pressures being transmitted throughout the 

 mass, this i)art P will always be destroyed, whether equilibrium exists in the 

 liquid figure or not; so that the active part of the prest^ure (that which consti- 

 tutes the configuring force) will have for its measure simply "^ I "tT + i77 Y 



Hence it is evident that when the curvatures are equal, the intensity of the 

 configuring force arising from one element of the superficial layer is propor- 

 tional to the coefticiont A. Now, this coefiicicnt is the same as that which 

 enters into the known expression of the elevation or depression of a liquid in a 

 capillary tube : consequently the measures relating to this elevation or depres- 

 sion M'ill give us, in the case of each liquid, the value of the coefiicient in ques- 

 tion. Hence we may also say that the proportion of the normal length of the 

 divisions to the diameter of the cylinder will be greater as the liquid is more 

 viscid and as the value of A which corresponds to the latter diminishes. For 

 instance, oil is much more viscid than mercury ; on the other hand, it Avould 

 be easy to show that the value of A is much less for the first than for the 

 second of these two liquids ; lastly, this value must be much diminished in 

 regard to our figure of oil by the presence of the surrounding alcoholic liquid, 

 the mutual attraction of the molecules of the two liquids in contact diminishing 

 the inteiisities of the pressures, (§ 8.) This Is why the proportion belonging to 

 a cylinder of oil formed in the alcoholic mixture considerably exceeds that be- 

 longing to a cylinder of mercury resting upon a plate of glass, notwithstandmg 

 the slight external resistance to which the latter is subjected. 



60. It follows from this discussion concerning the resistances that the 

 smallest value Avhich the pi'oportion of the normal length of the divisions to 

 the dii^meter of the cylinder could be supposed to have corresponds to that 

 case in Avhicli there is simultaneously complete absence of external resistance 

 and of viscidity; and, after the demonstration given in § 57, this least value 

 will be at least equal to the limit of stability. Now, as all liquids are more or 

 less viscid, it follows that, even on the hypothesis of the annihilation of all ex- 

 ternal resistance, the proportion in question will always exceed the limit of 

 rttability ; and since this is more than 3, this proportion will, a for lion, be 

 always more than 3. 



It is conceivable that the least value considered above, ^. c, that which the 

 proportion would have in the case of complete absence of resistance, both 

 internal as well as external, would be equal to the limit of stability itself, or 

 woukl very slightly exceed it. In fact, on the. one hand, the proportion ap- 

 proximates to this limit as the resistances diminish, and on the other hand, if it 

 exceeds it, the transibrmation becomes possible, (§ 57;) hence we see no reason 

 why it sliouhl differ sensibly from it if the resistances were absolutely null. 

 The results of our experiments, moreover, tend to confirm this view. First,. 

 since the proportion belonging to our cylinder of mercury descends from 10.29 

 to C.35, passing from that case in which the cylinder touches the glass at two 

 lines to that Avhere it touches it at a single one only, (§ 58,) it is clear that if 

 this latter contact itself could be suppressed, which would leave the influence 

 of the viscidity alone remaining, the proportion would become much less than 



