parts, 6cc. 



Y^ COHESION OF FLUIDS. 



i='prtn of the the atmosphere, or, whea'c the atmosphere is excluded, th? 



MiWaceofa equivalent pressure arising from the \vei2;ht of the particles 



fluid, as mcdi- ' ' * • \ • ■ \ 



lied by the co- suspended from it by means of their cohesion, in the same 



^ll'^^^i^^^ manner as, \vhen water is supported by the atmospheric 

 pressure in an inverted vessel, the outside of the vessel sustains 

 a hydrostatic pressure proportionate to the height ; and this 

 pressure must remain unaltered, when the water, having been 

 sufficiently boiled, is made to retain its situation for a certain 

 time by its ^cohesion only, in an exhausted receiver. When, 

 therefore, the surface of the fluid is terminated by two right 

 lines, and has only a simple curvature, the curvature must be 

 every wh'MC as the ordinate; and where it has a double cur- 

 vature, the sum of the curvatures in the dilTcrent directions 

 must be as the ordinate. In the first case, the cui-ve may be, 

 constructed by approximation, if we divide the height at 

 which it is either horizontal or vertical into a number of smalt 

 portions, and taking the radius of each portion proportional to, 

 the reciprocal of the height of its middle point or below the 

 general surface of the fluid, go on to add portions of circles 

 joining each other, until they have completed as much of the 

 Curve as is required. In the second case, it is only necessary 

 to consider the curve derived from a circular basis, which is a 

 solid of revolution ; and the centre of that circle of curvature." 

 which is perpendicular to the section formed by a plane passing 

 through the axis, is in the axis itself, consequently in the point 

 w'hcre the normal of the curve intersects the axis; we must 

 therefore here make the sum of this curvature, and that of the 

 generating curve, always proportional to the ordinate. This 

 may be done mechanically, by beginning at the vertex, where 

 the two curvatures are equal, then, for each succeeding por- 

 tion, finding the radius of curvature by deducting the proper 

 reciprocal of the normal, at the beginning of the portion, 

 from the ordinate, and taking the reciprocal of the remainder. 

 In this case the analysis Teads to fluxional equations of the 

 second order, .which appear to afford no solution by means 

 Hitherto discovered ; but the cases of simple curvature may 

 ^c wore easily subjected to calculation. 



HI. Jiialj/si-s of the simplest For?)is. 



On tTie simplest - Supposing the curve to be described with an equable ?mgu^ 

 forms of the • 



surface of a 

 fluid. 



^F 



