Page:Philosophical Transactions - Volume 095.djvu/84

70 square of the greatest ordinate being equal to twice the appropriate rectangle, and the greatest ordinate to twice the diameter of the corresponding circle of curvature: so that, if we suppose a circle to be described, having this ordinate for a diameter, the chord of like angular elevation in this circle will be always equal to the ordinate at each point, and the ordinate will vary as the sine of half the angle of elevation, whenever the curve has an asymptote. Mr. has demonstrated, in the third volume of the Acta Petropolitana, some properties of the arch of equilibrium under the pressure of a fluid, which is the same as one species of the curves here considered. The series given by in the second part of the same volume, for the elastic curve, may also be applied to these curves.

The simplest phenomena, which afford us data for determining the fundamental properties of the superficial cohesion of fluids, are their elevation and depression between plates and in capillary tubes, and their adhesion to the surfaces of solids which are raised in a horizontal situation to a certain height above the general surface of the fluids. When the distance of a pair of plates, or the diameter of a tube, is very minute, the curvature may be considered as uniform, and the appropriate rectangle may readily be deduced from the elevation, recollecting that the curvature in a capillary tube is double, and the height therefore twice as great as between two plates. In the case of the elevation of a fluid in contact with a horizontal surface, the ordinate may be determined from the weight required to produce a separation; and the appropriate rectangle may be found in this manner also, the angle of contact being