666 



ON THE COHESION OF FLUIDS. 



" This theory affords us also an explanation of another 

 remarkable phenomenon, which occurs in experiments of 

 this nature. If a fluid be either elevated or depressed b«- 

 tween two vertical and parallel planes, of which the lower 

 ends are immersed in the fluid, the planes will tend to ap- 

 proach each other. It is shown by calculation, that if the 

 fluid is elevated between them, each plane is subjected to 

 a pressure, urging it towards the other plane, equal to that 

 of a column of the same fluid, of a height equal to the half 

 sum of the elevations of the internal and external lines of 

 contact, of the surface of the fluid with the plane, above 

 the general level, and standing on a base equal to apart of 

 the plane included between these lines. If the fluid is de- 

 pressed between the planes, each of them will be forced 

 inwards, by a pressure equal to that of a column of the 

 same fluid, of which the height is half the sum of the de- 

 pressions of the lines of contact of the external and internal 

 surfaces of the fluid with the plane, and its base the part of 

 the plane comprehended between those lines." 



In another part of his essay, Mr. Laphice 

 asserts, that " this force increases in the in- 

 verse ratio of the distance of the planes ;" 

 if this is not an error of the press, or of the 

 pen, it can only mean that the force in- 

 creases as the distance diminishes : for the 

 magnitude of the force is not simply in the 

 inverse ratio of the distances, but very 

 nearly in the inverse ratio of their squares, as 

 I have already observed. 



" Since it has been hitherto usual with natural philoso- 

 phers, to consider the concavity and convexity of the sur- 

 faces of fluids in capillary spaces, as a secondary effect of 

 capillary attraction only, and not as the principal cause of 

 phenomena of this kind, they have not attached much im- 

 portance to the determination of the curvature of these sur- 

 faces. But the theory, which has been here advanced, 

 having shown that all these phenomena depend principally 

 on the curvature, it becomes of consequence to examine 

 it. Several experiments, which have been made with great 

 accuracy by Mr. Haiiy, have shown, that in capillary tubes 

 of glass, of very small diameters, the concave surfaces of 

 water and of oils, and the convex surfaces of mercury, dif- 

 fer very little from the form of a hemisphere." 



Mr. Laplace informs us that M.M. Haiiy 

 and Tremery made at his request several 

 experiments, in which the mean ascent of 



water, in a tube one thousandth part of a 

 metre in diameter, was 13.37 thousandths, 

 and that of oil of oranges 6.74. The product 

 of the diameter and the height of ascent of 

 water is .039371 X. 534 = .021 E. i., which is 

 little more than half as much as I have 

 assigned for this product from the best expe- 

 riments of many other observers. Probably 

 both these experiments, and those of New- 

 ton or Hauksbee, were made with tubes and 

 plates either a little greasy, or too dry ; and 

 Mr. Haiiy might be the more readily satisfied 

 with the first results that he obtained, from 

 finding them agree nearly with those of 

 Newton, which Mr. Laplace wished to com- 

 pare with them. These gentlemen also found 

 the depression of mercury in a tube of the 

 same diameter .2887 E. i., the product being 

 .01 137, instead of .015, which is the ultimate 

 product inferred from Lord Charles Caven-r 

 dish's experiments of a similar nature. The 

 observation of Mr. Haiiy, on the curvature of 

 the surface of mercury in a tube, is also far 

 from being accurate ; Mr. Laplace himself 

 asserts that the angular extent of the surface 

 must fall short of that of a hemisphere more 

 or less, accordingly as the tube has more or 

 less attraction for the fluid ; and it is easy to 

 show that glass has a very considerable at- 

 traction for mercury. The method that I 

 took to ascertain the angle, formed by the 

 surface of the mercury, with the side of the 

 tube, was to- observe in what position the 

 light reflected from it began to reach the eye, 

 and I have every reason to think, from the 

 comparison of a great variety of experiments 

 of difl'crent kinds, that the angle which I 

 have assigned is very near the truth. 



I have lately repeated my calculations of 

 the depression of mercury, in barometer 

 tubes of considerable diameter, with great 



