226 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



SECOND SERIES. 



PREFACE. 



At the period wlien attacked by the disease which lias entirely deprived me of sight, I had 

 tcriniiiated the greater part of tlie'experinieuts relating to this series, as well as the following. 

 M. Diiprez, correspondent of the Brussels Academy, and M. Donny, had the kindness to 

 undertake those which were still wanting. I constantly directed their execution ; nearly all 

 were made in my presence, and I followed all the details. I have therefore considered 

 myself justified, in order to simplify the description, in expressing myself in the course of 

 this investigation as if I had made the experiments. 



With respect to the theoretical portions, I am indebted to the able assistance of one of my 

 colleagues, M. Lamarle, who has most kindly devoted many long hours to listening to the 

 details of my investigations, and to aiding me in the explanation of several diflicult points. 

 I am also indebted to another of my colleagues, JI. Manderlier, for the execution of a part 

 of the calculations. 



May I ho. pennittcd to express in this place ray gratitude to these devoted friends? 

 Thanks to their generous lielp, science is still an open field for me: notwithstanding the 

 inlirmity with which I am afflicted, I am able to put in order the materials I have collected, 

 and even to undertake fresh researches. , 



Prclhninnr}/ considerations and theoretical principles. General condition to 

 he satisfied, hi/ the free surface of a liquid mass withdrawn from the action of 

 gravitij, and in a state of equilihrinm. Liquid sphere. 



1. The process described in the previous memoir enabled us to destroy the 

 action of gravity upon a liquid mass of considerable volume, leaving the mass 

 completely at liberty to assume the figure assigned to it by the other forces to 

 ■which it is subject. This process consists essentially in introducing a mass of 

 oil into a mixture of water and alcohol, the density of which is exactly equal 

 to that of the oil employed. The mass thouikremains suspended in the sur- 

 rounding liquid, and behaves as if Avithdrawn from gravity. By this means we 

 have studied a series of phenomena of configuration, dependent either simply 

 upon the proper molecular attraction of the mass, or upon the combination of 

 this force with the centrifugal force. We shall now abandon the latter force, 

 and introduce another of a different kind, the molecular, attraction exerted be- 

 tween liquids and solids ; in other Avords, we shall cause the liquid mass to 

 adhere to solid systems, and study the various forms assumed under these cir- 

 cumstances by those portions of the surface which remain free. In this way 

 we shall have the curious spectacle presented by the figures of equilibrium ap- 

 pertaining to a liquid mass, absolutely devoid of gravity and adherent to a 

 given solid system. 



But the figin-es which we shall obtain present another kind of interest. The 

 free jjortions of their surface belong, as we shall show, to more extended figures, 

 which may be conceived by the imagination, and which, in the same condition 

 of total absence of gravity, Avould belong to a perfectly free liquid mass ; thus 

 our processes Avill partially realize the figures of equilibrium of a mass of this 

 kind. I'he latter are far from being confined to the sphere ; but among them 

 the sphere alone is capable of being completely foi'med, the others presenting 

 either infinite dimensions in certain directions, or other peculiarities which we 

 shall point out, and which equally render their realization in the complete 

 state impossible. 



Moreover, the results at which we shall arrive will constitute so many now 

 and unexpected confirmations of tlie theory of the pressures exerted by liquids 

 upon tlicniselves in virtue of the mutual attraction of llieir molecules, a theory 

 upon which the explanation of the plumomcna of capillarity is based. 



Lastly, in our liquid figures wi; .shall discover remarkable properties, which* 

 will lead ua to some important applications. 



