REPORT OX CAPILLARY ATTRACTIOX. 285 



found by M. Gauss without deviating from the principles of La- 

 place's theory. But this equation is no longer true if it be ne- 

 cessary to take account of the variation of density at the fluid 

 surface ; nor in the same case can the argument hold good by 

 which Clair ai\t showed that the fluid surface is horizontal when 

 its attractive power is double that of the solid*. 



In the next chapter, the equation of the free surface of fluid in 

 equilibrium in a capillary space is obtained by an analysis which 

 takes into account any variation of density that may exist at the 

 fluid surface, although the exact law of variation be unknown. 

 This equation is of the same form as the fundamental equation 

 of Laplace, and involves an analogous quantity H. As M. Poisson 

 infers from it, by assuming an angle w, which is the supplement 

 of that we have hitherto called the angle contact, to be. constant, 



that the weight of fluid raised in a capillary tube is — — ^ cos w, 



which is the expression for the same weight obtained by La- 

 place, it follows that H in the two theories is the same in mag- 

 nitude, though differently represented by the analytical for- 

 mulae. 



The third chapter is employed in finding on the same princi- 

 ples the equation relative to the contour of the capillary surface. 

 The angle of contact, which is found as in preceding theoi'ies to 

 be constant, is assigned by the equation 

 F = H cos o). 



It may be useful to give some idea of the natiu-e and compo- 

 sition of the constants F and H. The following formulae will 

 serve to do this, when the significations of the letters they con- 

 tain have been explained : 



H , F 



ir=? + y/' -77 = ? '^ 



8 »/o 



9i = - 



2 Jo ./o c/o >" 



:!Lr^ r rw'ldudsds' 



Conceive the fluid mass to be divided by a curve siu'face pass- 

 ing through any point M into two parts A and B, and through 

 the sides of a rectangular element of the surface at the point M, 

 let normal planes be erected inclosing a pi'ismoidal element of 



• M. Poisson's theory cannot inform us how far that equation is erroneous, 

 nor whether it is, or not, very approximately true. 



