266 FOURTH REPORT — 1834. 



not only accounts for the attraction of the planes towards each 

 other, but gives the measure also of the pressures which urge 

 them. By an exact consideration of all the forces concerned in 

 these phaenomena, he finds that when the fluid is raised between 

 the planes, each plane experiences, from without to within, a 

 pressure equal to that of a column of the contained fluid, of 

 which the height is half the simi of the elevations above the or- 

 dinary level, of the points of contact of the interior and exterior 

 surfaces of the fluid witli the plane, and whose base is the part 

 of the plane comprised between two horizontal lines drawn 

 through these points. The value of the pressure is similarly 

 stated when the fluid is depressed between the planes. Hence, 

 neglecting the small exterior elevation or depression, the pres- 

 sure varies as the square of the elevation or depression between 

 the planes, and consequently inversely as the square of the in- 

 terval between them. 



Laplace also enters into a consideration of the proposition 

 first announced by Clairaut, viz. that if the law of the attraction 

 of the matter of the tube upon the fluid, differs only by its in- 

 tensity from the law of the attraction of the fluid on itself, the 

 fluid will be raised so long as the intensity of the former of these 

 attractions surpasses the half of the intensity of the other. He 

 arrives at the following conclusions*. If the one intensity be 

 exactly half the other, there is neither elevation nor depression. 

 If the intensity of the attraction of the tube for the fluid be in- 

 sensible, the fluid will be depressed, and the depressed surface 

 will be convex and hemispherical. If the two intensities be 

 equal, the surface of the elevated fluid will be concave and hemi- 

 spherical. When the intensity of the attraction of the tube is 

 the greater of the two, the fluid, by attaching itself to the tube, 

 forms an interior tube to which alone the capillary elevation is 

 due, and which being of the same matter as the raised fluid, acts 

 with the same intensity, and causes the surface to be still con- 

 cave and that of a hemisphere. This appears to be the case with 

 water and oils in capillary glass tubes. M. Haiiy found by ex- 



* These conclusions appear to be correct, but the reasoning of Laplace in 

 this part "of his theory is liable to a serious objection, first pointed out by 

 Dr. Young. For in art. 12, he obtains the following equation, 



Q cos {■7r — d)=. (2 g' — ?) K sin 6, 

 in which 5' and ^ are respectively proportional to the intensities of the attrac- 

 tion of the solid for the fluid, and the fluid for itself; 2 j K is equal to the re- 

 sultant of the molecular attractions on a superficial particle of all the fluid 

 particles within the sphere of its activity ; but ^ the resultant of the attractions 

 of only a portion included between a tangent plane and surface passing through 

 the particle. This equation, therefore, could scarcely be true unless 2 j' = j . 

 The source of the error that occurs here will be elucidated as we go on. 



