286 FOURTH UEPORf — 1834. 



the portion A. Let m and m' be two molecules of the fluid, 

 one in the prismoid, the other in some part of A. Then r is the 

 line joining them, u is its projection on the tangent plane at M, 

 and * s' are the perpendiculars from the molecules on the same 

 plane, so that r^ = ^<^ + (*—*')'-. R, R;, and R' are functions 

 of r, which are insensible for every sensible value of this varia- 

 ble, and express the mutual action referred to the units of volume 

 of the fluid molecules at the distance r from each other. R re- 

 lates to the interior of the fluid, R, to its superficial stratum, and 

 R' to the stratum adjoining the side of the tube. With respect 

 to R^ the surface through M is parallel to the free surface of the 

 fluid at a distance I from it, and A answers to the fluid contained 

 between these two surfaces. So with respect to R', the surface 

 through M is parallel to the surface of the tube at a distance 

 which may also be called /, and A answers to the fluid contained 

 between this surface and the tube. Ry and R' vary very rapidly 

 with A' and s', and confound theiiiselves with R so soon as 

 these variables exceed the radius of the molecular activity. The 

 quantity /, which is the limit of the integrals with respect to s 

 and si , is greater than this radius, yet of insensible magnitude. 

 It is shown that q, and •or do not change sensibly with the mag- 

 nitude of I. 



As the forms of the functions R, R^, and R' are quite un- 

 known, the values of q, qp and •cy cannot be calculated a jjriori. 

 Neither are there any means known at present of determining 

 them experimentally. But experiment can assign the numeri- 

 cal values of H and w, and consequently that of F. Hence if 

 the ratio of q^ to q should become known, the three quan- 

 tities wovdd be determined. The knowledge of this ratio is the 

 chief desideratum of the theory. M. Poisson has shown that if 

 there be no variation of density near the surface of the tube, 

 which will happen when the molecular action of the tube is the 

 same as that of the solid, ct = 2 y. In this case cos «j = — 



— - — . He shows also, according to what might be expected 



from experience, that cosco = — 1, when the molecular attrac- 

 tion of the tube exceeds that of the fluid, but assigns no limit- 

 ing value of the excess at which this value of cosw begins. It 

 seems, therefore, reasonable to conclude that when the forces 

 are equal, cos w is nearly equal to — 1, and consequently that 

 qi is a small quantity compared to q. Also, as the density in the 

 thin superficial stratum of the fluid varies from to the density 

 of the interior, the state of dilatation near the surface would 

 naturally lead us, as M. Poisson observes, to make this inference 

 with respect to the value of q^ . 



