282 FOURTH REPORT — 1834. 



in which the first term is equivalent to the volume of the con- 

 tained fluid multiplied by the vertical ordinate of its centre of 

 gravity, U is the area of its free surface, and «'^ * a constant de- 

 pending on the intensity of the attraction of the fluid particles 

 for each other, T is the area of the solid surface mth which the 

 fluid is in contact, and j3^ a constant depending on the intensity 

 of the attraction to which the fluid is subject from the particles 

 of the solid. By making S W =0, and in the variation suppos- 

 ing U constant, it is readily found that the mean elevation in a 

 capillary lube varies inversely as its diameter. By again put- 

 ting S W = 0, and making the free surface subject to variation, 

 M. Gauss ai-rives at two equations, one of which, relating to the 

 free surface, is the fundamental equation of Laplace's theory, 

 and the other, relative to the angle of contact, is equivalent to that 

 which Dr. Young obtained. It is not the object of the author to 

 trace the consequences to be derived from these equations in ex- 

 plaining phsenomena, as this was satisfactorily done by Laplace. 



The first published ideas of M. Poisson on the theory of ca- 

 pillary action are contained in a memoir on the Equilibrium of 

 Fluids, read before the Paris Academy November 24, .1828 f. 

 His object in this memoir is to form the equations of the equi- 

 librium of fluids on physical principles, that is, by considering 

 them as composed of distinct molecules, separated from one 

 another by spaces void of ponderable matter. He commences 

 with the following preliminary notions. 



The dimensions of the molecules and of the spaces between 

 them are so small, that a line which may be supposed a great 

 multiple of them is of insensible magnitude. The molecules at- 

 tract each other ; at the same time they mutually repel by their 

 proper heat. For each of these forces the action is equal to the 

 reaction : both decrease with great rapidity as the distances in- 

 crease, and are sensible only at insensible distances. The radii 

 of activity of these forces are nevertheless supposed to be ex- 

 tremely great compared with the intervals between the molecules, 

 and the rapid decrease to commence only at distances which 

 are great multiples of these small intervals. Without this sup- 

 position, in bodies whose molecules are not regularly distributed, 

 the resultant of the molecular forces, that is, the total force 

 which acts on each molecule, might be very different in magni- 

 tude and direction for two consecutive molecules, and conse- 

 quently would not be subject to the law of continuity. It seems 

 necessary therefore to make the above supposition. 



2 



• 4 5t* in M. Gauss's work is the same as tlie — of Laplace. 



cc 



t Memoires dc I'Academie des Sciences, torn. ix. Paris 1830. 



