278 FOURTH REPORT — 1834. 



ai*e shown to be the same for the two planes, and their actions 

 on each other by the intervention of the fluid to be equal and 

 opposite. The theory leads to the singular result that the re- 

 pulsion will change into attraction by making the planes ap- 

 proach very near each other, and experiments by M. Haiiy show 

 that such is the fact. 



(2.) When a disc is applied to the surface of standing water, 

 on being raised it draws, by capillary action, a portion of the 

 fluid with it, which detaches itself when the disc is raised above 

 a certain elevation. At this limit the suspending force must 

 plainly be equal to the weight of the disc and of the portion of 

 fluid raised above the horizontal level of the water. As this force 

 may be accurately determined by experiment, we are furnished 

 with means of putting the theory to a test, because the surface, 

 and consequently the volume of the raised column, can be found 

 from the fundamental equation of the theory. When the calcu- 

 lation is made, the expression for the volume involves a quantity 



2 2 H 

 which Laplace calls — , and which is, in fact, the same as 



a . 5" 



Now, as was said above, the weight of fluid raised in a capillary 



tube is — i- cos 9, or — ^ if the fluid perfectly wets the tube ; 



and this weight in a cylindrical tube is also equal to ^r c hg g,if r 

 be the radius of the cylinder, and h the mean elevation of the fluid ; 



2H 



so that = 2r A = diameter of the tube x mean elevation of 



the fluid *. If, then, the diameter of a cylindrical capillary tube, 

 and the elevation in it of a fluid which perfectly wets it, be ob- 



2 

 served, the value of- for that fluid is found experimentally. The 



2 

 following numerical values of — are deduced by Laplace from 



the experiments of Gay-Lussac, after correcting for the tempe- 

 rature f, M'hich was 8°"5 of the centigrade thermometer, and for 

 the difference of one sixth of the diameter between the mean 

 elevation, and the observed elevation of the lowest point of the 



* This equality is also readily deduced from the fundamental equation. 



f " The elevation of a fluid which wets completely the sides of a capillary 

 tube is, at different temperatures, in the direct ratio of the density of the fluid, 

 and in the inverse ratio of the interior diameter of the tube." This is shown at 

 p. 38 of the iiupplement. An increase of temperatui'e diminishes the elevation 

 both by diminishing the density of the fluid and increasing the capacity of the 

 tube. Admitting that H varies as q, it will be seen from the equation above 



thai h varies as — . 



