ON CAPILLARY ACTION. 



the fluid. W.e shall also have Q / =z^'xc; / being propor- 

 tional to the intensity of the attraction of the fluid for it- 



self. Therefore V= — j which is the algebraic ex- 

 pression of the theorem to be demonstrated. 



The constant quantity -4 — —may be determined by means 



of the observed elevation of the fluid in a very narrow cy- 

 lindrical tube. Let q be the height, to which the fluid rises 

 in this tube, and / the radius of its cavity : putting t for the 

 semicircumference of which the radius is unity, we shall 

 have nearly Vzzvxl x q , c=2 Inr: the preceding equation 



then will give — == — 5 and consequently we shall 



» In 



have Vz= — -xc. 

 2 



If g exceed 2f, q will be negative; and consequently, 

 the elevation of the fluid changing to depression, V will be 

 negative. 



Let us put h for the mean height of all the fluid columns, 

 that compose the volume F, and b for the interior base of 

 the parallelopipedon : then we shall have V=hb^ and con- 

 sequently h - lqXC . 

 2 b 



Proportions of When the bases of different parallelopipedons are similar 

 bases, if similar figures, they are proportional to the squares of their ho- 

 mologous sides, and their circumferences are proportional 

 to these sides. 

 If re ular ol - ^ these bases be regular polygons, they will be equal to 

 gems, the products of their circumference multiplied into half the 



radius of the inscribed circle: the heights h therefore Will 

 be reciprocals to these radii. Denoting these radii by r, 



we shall have h = — — 



r • 



A square and a Thus supposing two equal bases, one of which is a square, 



and the other an equilateral triangle; the values of r will 



be to each other as 2 to 3 4 , or nearly as 7 to 8. 



The law con- Mr. Gellcrt has published some experiments on the ele- 



b^Gellert. 6Se vat i° u of water in rectangular and triangular prismatic tubes 



of 



