474 



HYDRODYNAMICS. 



Attraction 

 and the 



Cohesion of 

 Fluids. 



weight.- Dr Young has given the following as the 

 equation of the surface of a drop of water : 



aax x -\-aayy xyy z, when 2 = 0, or 



a 4 * 2 ** 



(a* 



* x* y* i* y* 0. 



Monee'scx. 

 periments 

 on drops. 



Dr Brews- 



ter's expcri 

 merits on 

 drops. 



PLATS 



CCCXV1. 

 Fig. 6. 



^ n o r( ' er * shew that two drops of water do not 

 attract each other when at a distance, M. Monge put 

 some spirit of wine into a cup, and having taken a ca- 

 pillary tube containing some of the same fluid, he allow- 

 ed it to fall from a height of a few lines, drop by drop, 

 into trie cup ; the drops did not immediately mix with 

 the rest of the fluid, but preserved their form, which was 

 nearly spherical ; rolled over the surface with great 

 freedom, like balls over a billiard table, impinged against 

 each other ; changed their form by the force of im- 

 pact ; and, after being reflected from each other, con- 

 tinued to move upon the surface till they were again 

 mixed with the general mass. This experiment does 

 not succeed so well when the spirit of wine is warm. 

 M. Monge explains this phenomenon by supposing that 

 a thin film of air adheres to the drop; and, by dimin- 

 ishing its specific gravity, causes it to float upon the 

 fluid surface ; and hence he concludes that the experi- 

 ment will succeed best with those liquids which are most 

 evaporable, or which have the greatest affinity for the 

 surrounding air. A similar phenomenon, as M. Monge 

 observes, is seen in the drops of water which fall from 

 the oars during the rowing of a boat, and in the drops 

 produced by the condensation of the steam of any warm 

 fluii), such as coffee, &c. These drops are real spheres 

 of fluid, and not spherical vesicles like those formed 

 on the surface of water with heavy rains. These re- 

 sults are hostile to the idea of M. Saussure, who, in his 

 Essays on Hygrometry, has stated that drops of the 

 same liquid cannot be pushed against one another, nor 

 remain simply in contact without instantly uniting; 

 and that only hollow vesicular globules are capable of 

 floating upon the surface of the same fluid with them- 

 selves. 



In repeating the experiments of Monge, Dr Brewster 

 found that the appearances were most beautiful when the 

 capillary tube discharged the drops upon the inclined 

 plane of fluid, which is elevated by the attraction of the 

 edge of the cup. They ran down the inclined plane with 

 great velocity, and sometimes even ascended the similar 

 plane on the opposite side of the vessel. When the drop 

 was discharged at the distance of one or two- tenths of an 

 inch from the surface of the water, they had always the 

 same magnitude when the tube was held in the same 

 position ; but when the point of the tube was brought 

 within a tenth of an inch of the surface of the spirit of 

 wine, this surface, instead of attracting the drop to it 

 instantly, as Saussure would have predicted, actually 

 resisted the gravity or weight of drop, and allowed it to 

 attain a diameter nearly twice as great as it would have 

 had, if it had been discharged in the ordinary manner. 

 This swoln globule floated upon the surface in the same 

 manner as the smaller drops, surrounded with a depres- 

 sion of the fluid surface similar to what is produced by a 

 gl*ss globule floating on mercury, or by the feet of parti. 

 cular insects, that have the power of running upon the 

 surface of water. (See Fig. 5.) The floating globules are 

 often produced even when they are discharged from 

 a height of three or four inches ; and by letting them 

 fall upon the inclined plane of fluid formerly mentioned, 

 they will often rebound from the surface, and fall over 

 the sides of the cup. 

 When a drop of mercury is laid upon glass, it assumes 



a flat spheroidal form, in consequence of its weight. 

 The section of its surface, as M. La Place observed, by Attraction 

 a vertical plane drawn through its centre, is very much 

 curved at its summit. The curvature increases on re- C | ij!? of 

 ceding from that point, till the tangent to the curve is _ __, 

 vertical At this point, the curvature and the width of Korm f a 

 the section will be a maximum. Below that point it <ip of 

 will approach its axis, and will at last coincide with the owcury. 

 plane of the glass, and form with it an acute angle. M. 

 Gay Lussac observed at the temperature of 12.8 of the 

 centigrade thermometer, the thickness of a large drop 

 of mercury, circular, nnd a decimeter in diameter, rest- 

 ing upon a plane surface of white glass perfectly hori- 

 zontal. By a very accurate micrometer, he found its 

 thickness to be 3.378 millimetres. M. Segner had long 

 before obtained nearly the same result, viz. 3.406"! 

 millimetres. 



The cohesion of fluids is beautifully shewn in a phe- r , 



,.,... ' ,. i r f Drrn of an 



nomenon, which is the very reverse of the formation openinftin * 



of a drop, and which was first observed by Dr Brewster. film of fluid. 

 If we take a phial, with a wide mouth, half filled with 

 Canada balsam, and allow the balsam to flow to the 

 mouth of the phial and fill it up, then when the phial is 

 placed on its bottom, a fine transparent film of balsam 

 will be seen extending over the mouth of the phial. If 

 we now take a piece of slender wire, and touch the film 

 near the middle, so as to tear away a little part of it, 

 the remaining part of the film which has been ele- 

 vated by this force will descend to its level position, 

 and the ragged aperture from which the balsam has 

 been torn will be seen to assume a form perfectly cir- 

 cular, having its edge in a slight degree thickened, like 

 a circle with a raised margin turned out of a piece of 

 wood. This fine circular aperture grows wider and 

 wider, and continues to preserve its circular form till 

 the mouth of the phial is again opened. 



The following curious experiment, which was perform- 

 ed by Dr Brewster, is intimately connected with the sub- n) e"ton 

 ject of capillary attraction. Above a vessel MNOP, Fig. piiiary at- 

 6. nearly filled with water, a convex lens LL was placed traction, 

 at the distance of the 10th of an inch, and rays R, R, R, p LATE 

 were incident upon its upper surface. The focus of these CCCXVI. 

 rays was at F, a little beyond the bottom of the vessel, Fig. e. 

 so that a circular image of the luminous object was 

 seen on the bottom of the vessel, having AB for its di- 

 ameter. If the lens is now made to descend gradually 

 towards the surface of the water, and the eye kept stea- 

 dily upon the luminous image AB, a dark spot will be 

 seen at <p in the centre of AB, a little while before the 

 lens attracts and elevates the water MN. Sometimes 

 this spot may be seen playing back and forwards by the 

 slight motion of the hand, so that the lens can even be 

 withdrawn from the fluid surface without having actual- 

 ly touched it. In general, however, the sudden rise of 

 the water to the lens follows the appearance of the black 

 spot. When the water is in contact with the glass, the 

 focus of the rays R, R is now transferred tof, and the 

 circular image on the bottom is now a b, and the inten- 

 sity of the light in this circle is to that in the circle 

 AB, as AB* : a 6*. Now it is obvious, that the darkish 

 spot at <p is just the commencement of the transference 

 of the focus from F toy; or when the dark spot is pro- 

 duced, the progress of the rays is the same as if the fo- 

 cus were transferred to_/l This remarkable effect may 

 arise from two causes. 1. The approach of the lens to 

 the surface MN, may occasion a depression m o n in the 

 surface of the fluid of the same curvature as L / L, which 

 would have the effect of transferring the focus from F 

 to/. This depression may be produced by a film of air 



