276 FOURTH UEt'OUT 1S34. 



As it appears that the weight of the elevated column varies as 

 the periphery of the transverse section of the tube ; and as, for 

 tubes of like peripheries, the weights are as the products of the 

 heights and the squares of homologous lines, it follows that the 

 heights are inversely as homologous lines. This proportion, 

 says Laplace, is true also if the contour be not continuous, but 

 of the form, for instance, of a rectilinear polygon ; for the error 

 that would be occasioned by the angles of the polygon would 

 be of insensible magnitude, by reason of the small extent of 

 the sphere of activity of the particles. Gellert has made some 

 experiments on the elevation of water in glass prismatic tubes, 

 with rectangular and triangular bases *. They confirm the law 

 according to which the heights are inversely as the homologous 

 lines of like bases. He thinks also that the elevation is the same 

 for a rectangular as for an equal triangular base ; but the experi- 

 ments do not appear to be decisive of this point. Laplace calcu- 

 lates theoretically that the diiference would be one eighth be- 

 tween the elevations in a prism Avith a square base, and in one 

 whose base is an equilateral triangle of equal area. 



One of the most interesting of the questions considered by 

 Laplace in the Supplement, relates to the capillary action 

 which takes place when two or more fluids are contained in the 

 same tube. Suppose a prismatic tube to be plunged vertically 

 in a vessel containing any number of fluids lying horizontally 

 one above another ; then " the excess of the weight of the 

 fluids contained in the tube above the weight it would have con- 

 tained without capillary action, is equal to the weight of fluid 

 which would have been raised above the exterior level, in case 

 the vessel contained only that fluid in which the loAver extremity 

 of the tube is immersed." For, in fact, the action of the prism 

 and of this fluid on the column of it in the tube, is plainly the 

 same as in this case, the action of the tube on each of the other 

 fluids being equal in opposite directions, and the mutual action 

 of the fluids being destroyed just as if they were supposed to 

 form a solid mass. The surface of the uppermost fluid is the 

 same as if that alone were in the tube. 



When only two fluids are contained in a cylindrical tube, the 

 theory determines the common surface of their junction to be 

 spherical, and gives for the angle of contact f of this surface a 



* Memoirs of the Academy of Petershiirgh, vol. xii. p. 302. 



t It ought to be observed that the angle which is here and elsewhere called 

 the angle of contact is, strictly speaking, not the angle which the fluid surface 

 makes with the surface of the solid at the points of their junction, but the angle 

 which a tangent plane to the surface of the fluid at the limit of the sphere of 

 activity of the solid's attraction makes with the surface of the solid. 



