OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 435 



PROBLEM LXXI. 



551. If two smooth plates of glass be inclined to each other at 

 a very small angle, having their lower sides brought in contact 

 with a fluid, to the surface of which the coincident edges are 

 vertical : 



It is required to determine the nature of the curve which 

 the fluid forms upon the plates, by rising up in virtue of the 

 attraction. 



Let ABEF and CDEF be the smooth plates of glass, having their 

 edges coinciding in the line EF, and 

 their planes inclined to each other 

 in the angle BED; and suppose the 

 edges BE and DE to be coincident 

 with the fluid, while EF the line in 

 which the plates are brought toge- 

 ther, is perpendicular to its surface, 

 which is represented by the plane 

 BED; then shall FTWOB and FW^D, 

 be curves described by the particles 

 of the fluid upon the surface of the 

 plates. 



Take any two points t and r in 



the line DE, and in the plane CDEF, draw tn and rp perpendicular 

 to DE, and meeting the curve FW^D in the points n and p ; the lines 

 tn and rp are therefore parallel to EF the line of coincidence, and 

 perpendicular to BED the surface of the fluid. 



Again, from the same points t and r, and in the plane BED co- 

 incident with the fluid's surface, draw the straight lines ts and rq 

 perpendicular to DE, and consequently, parallel to each other; then, 

 from the points s and q, in which the lines ts and rq meet BE the 

 lower edge of the plane ABEF, draw sm and qv respectively parallel 

 to tn and rp, and meeting the curve FWOB in the points m and o; 

 these lines are consequently parallel to EF and perpendicular to the 

 plane BED. 



552. Since by the supposition, the angle BED which measures the 

 inclination of the planes, is very small, the fluid in each section may 

 be conceived to be elevated by the attraction of parallel planes, and 

 consequently, by an inference under the preceding problem, the 

 altitude of the fluid at any two points, will vary inversely as the 

 distances between the planes at those points ; therefore, we have 



2r2 



