REPORT ON CAPILLARY ATTRACTION. 2Sl 



Gay-Lussac also observed in a large glass vessel, containing 

 mercury and having its sides vertical, the diflference between 

 the extreme elevation of the fluid and the elevation at the points 

 of contact vfith the sides of the vessel, and found it to be 

 l™'-455 (= -057 in.). The theory gives l'"'-432. 



Laplace concludes his work with some general observations 

 respecting the interior constitution of bodies, and the nature of 

 molecular forces. The viscosity of fluids, he remarks, is a dis- 

 turbing cause in capillary phaenomena, which can be strictly ex- 

 plained by the theory only when the condition of perfect fluidity 

 is fulfilled. To that cause and the friction against the sides of 

 the tube, he considers the differences between the elevations of 

 water in capillary tubes as determined by different obsei'vers, to 

 be attributable. With respect to the variation of pressure from 

 nothing to the quantity K, which according to the calculations of 

 the theory ought to take place within- a space extending from 

 the free surface of the fluid to a small depth below, Laplace 

 observes that it may be attended with a sensible variation of 

 density, and have a perceptible effect on capillary phaenomena. 

 The modification that his theory must undergo if this circum- 

 stance be taken into account, has been fully discussed, as we shall 

 presently see, by M. Poisson. 



There is a good exposition of the leading propositions of 

 Laplace's theory by M. Petit in the Journal of the Polytech- 

 nic School*, 



The work of M. Gauss, entitled Principia generalia TheoricB 

 Figiirae Fliddoriim in statu jEqnilibrii\, has for its main object 

 the correction of the defect already pointed out in Laplace's 

 theory, with regard to the proof of the constancy of the angle 

 of contact. To form the equations of equilibrium, M. Gauss 

 employs the principle of virtual velocities, which he applies to 

 the whole mass of the fluid, and not, as Lagrange has done, to 

 a differential element. This elegant method, which has the pe- 

 culiar advantage of evolving at once the equation of the free 

 surface of the flviid, and that relative to the contour, conducts 

 to a sextuple integral, which extends to the whole mass, and 

 is to be a minimum. By supposing the fluid to be homogeneous 

 and incompressible, the integral becomes quadruple. Byfurther 

 supposing the only forces that act to be gravity and the 

 molecular attractions of the fluid and containing solid, and the 

 sphere of activity of these attractions to be insensible, the 

 quantity (W) to be a minimum, is found to be expressed by 



f^ds -\. «-2U + («2 - 2^3) T, 



/' 



torn. ix. eah. xvi. p. 1. f GottingGn, 1830. 



