78 COHESION or FLUIDS. 



^thesimplest of the least ordinate, and the ordinate is every iv/iere a meant 

 sarfece of a proportional between the greatest height and the same height di- 

 fiwid. minished by twice the versed sine of the angular depression in the 



corresponding circle of curvature. Again, at the vertical point, 

 the square of the ordinafeis equal to the square of the greatest 

 height diminished by the rectangle contained by this heightand the 

 diameter of the correcting circle of curvature, a icciangle which 

 is constant for every fluid, and which may be called the appro- 

 priate rectangle : deducting this rectangle from the square of 

 the ordinate at the vertical point, we have the least ordinate ; 

 ■which consequently vanishes when the square of the ordinate 

 at the vertical point is equal to the appropriate rectangle; the 

 horizontal surface becoming in this case an asymptote to the 

 curve, and the 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 ordi- 

 nate for a diameter, the ch&rd of the angular elevation in this 

 circle will be always equal to the ordinate at each point, and 

 the ordinate mil vary as the sine of half the angle oj elevation 

 twhencver the curve has an asymptote. Mr. J-'uss has demon- 

 strated, in the third volume of the Acta Pctropolitana, some 

 properties of the arch of equilibrium under the pressure of a 

 fluid, which is the same as one species of the curves here con- 

 isi'dcred. The series given by Euler in the second part of the 

 same volume, for the elastic curve, may aiso be applied to 

 these carves. 



IV. Application to the Elevation of particular Fluids. 



Application of The simplest phenomena, which afford us data for detef- 

 the (foe trine to . . , ^ , , . ,. , ,. • , i • - 



particular mming the fundamental properties ot the superficial cohesjon 



^"^- pfjduids, 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 appro- 

 priate rectangle may readily be deduced from the elevation, 

 vceollccting that the curvature in a capillary tube is double, 

 and the height therefore twice as great as between two plates. 



In 



