will be at hand for the approach of the cardboard to the fork.

§ 30. Experiment 11.-A "Cartesian diver" was made out of a test-tube, a bubble of air, and a beaker-glass of water. This was so nicely adjusted that it rose when near the surface of the water, and sank when the top of the tube was 0.05 metre below the surface. When resting on the bottom of the beaker, the top of the test-tube was below the surface of the water. When the diver was resting on the bottom of the beaker, the tuning-fork A in a state of vibration was presented to the glass in various directions with regard to the tube. The fork was placed sometimes in contact with the water, sometimes in the neighbouring air, and sometimes in contact (towards the base of the fork) with the glass. Although the vibration of the bottom of the beaker caused the diver to leap up, it invariably sank again and showed no sign of undergoing any alteration in specific gravity. If, now, the question in § 29 were answerable in the negative, the equilibrium would have been destroyed, because the atmospheric pressure on the one hand, and the elasticity of the confined air on the other being equal and opposite forces, an alteration in one, caused by its subjection to successive sonorous waves, would have altered the volume of the confined air and so destroyed the equilibrium.

§ 31. I hoped to throw light upon the fundamental experiments of §§ 1 and 21 by varying the nature of the surface of the body which received the vibrations, with the view on the one hand of preserving them, and on the other of dispersing them as much as possible. With this view Experiments 12 to 15 were undertaken.

§ 32. Experiment 12 (fig. 11).—Upon one end of a splinter of wood 0.5 metre long, a cylinder of cardboard 0.03 metre in diameter and 0.04 metre deep, closed at the bottom, was fastened in such a manner that its axis was horizontal and its bottom in the plane V. The cylinder was counterpoised, and the whole was hung from an unspun silk thread. The vibrating fork A was brought near the open end of the cylinder in the three positions already described, and also with one prong inserted into and nearly touching the bottom of the cylinder. In all cases motion towards the fork ensued.

§33. Experiment 13.-A handful of cotton-wool was hung upon the splinter in place of the cylinder of Experiment 12. The cotton moved towards the fork from a distance of at least 0.05 metre, when the latter was presented to it in either of the three positions, § 6.

Muslin and washleather behaved in a similar manner.

§ 34. Experiment 14.-A paper circular drum, 0.25 metre in

diameter, having a rim 0·025 deep, was hung by a silk tape in the same manner as the cylinder of § 32. Parchment was

stretched across the wide end of a funnel 0·20 metre in diameter. The neck of the funnel was placed in the mouth, and the drum of the funnel was brought opposite and parallel to the edged face of the paper drum. Air was rapidly forced into and drawn out of the funnel. The paper drum moved towards the funnel even from a distance of 0.1 metre.

§ 35. Experiment 15.-A sheet of cardboard 0-4 metre square was hung in the plane V from a rod 1 metre long. The cardboard was counterpoised and hung from a silk tape. The paper drum of § 34 was placed 0.05 from the cardboard and parallel to it, and was then tipped. The cardboard moved towards the drum.. § 36. Experiment 16.-A rod of brass 12 metre long, provided at the ends with disks of brass perpendicular to the rod 0.26 metre in diameter, was set in longitudinal vibration by means of resined leather. One of the disks was held during the vibration near to the cardboard of § 35, also near the cottonwool and muslin of § 33. In all cases the suspended body moved towards the disk. By this means it was easy to cause motion when the two were at the distance of 0-2 metre.

§ 37. I have in the preceding paragraphs sought to eliminate systematically secondary and disturbing influences from the fundamental experiment. The experimental results appear to me to point to the following conclusions.

Whenever an elastic medium is between two vibrating bodies, or between a vibrating body and one at rest, and when the vibrations are dispersed in consequence of their impact on one or both of the bodies, the bodies will be urged together.

The dispersion of a vibration produces a similar effect to that produced by the dispersion of the air-current in Clément's experiment; and, like the latter, the effect is due to the pressure exerted by the medium, which is in a state of higher mean tension on the side of the body furthest from the origin of vibration than on the side towards it.

In mechanics-in nature there is no such thing as a pulling force. Though the term attraction may have been occasionally used in the above to denote the tendency of bodies to approach, the line of conclusions here indicated tends to argue that there is no such thing as attraction in the sense of a pulling force, and that two utterly isolated bodies cannot influence one another.

If the ætherial vibrations which are supposed to constitute radiant heat resemble the aërial vibrations which constitute radiant sound, the heat which all bodies possess, and which they are all supposed to radiate in exchange, will cause all bodies to be urged towards one another.

XLVI. Experimental and Theoretical Researches into the Figures of Equilibrium of a Liquid Mass without Weight.-Ninth, Tenth, Eleventh and last Series. By Professor PLATEAU*,

NINTH SERIES.-Secondary causes which affect the persistence of liquid films.-Film-figures of great permanence.-Historical survey of observations relating to liquid films.-Capillary ascension to great heights in tubes of large diameter.-Constitution of a current of gas passing through a liquid.

IN

N the last Series I endeavoured to show that, although cohe→ sion and internal viscosity play the chief part in the development of all liquid films, these causes are not sufficient when we have to do with films which are both large and durable, like those formed by soap-water, and that in such cases other and entirely distinct conditions must concur-namely, great superficial viscosity and a comparatively weak tension. But when such films have been actually produced, their duration is affected by a certain number of secondary causes, which I pass in review in this Series.

The first of these causes consists in the small disturbances communicated to the films by the movement of the surrounding air and by the vibrations conducted by the ground. These small disturbances no doubt act by overcoming the inertia and frictional resistance of the molecules; they thus hasten the descent of the molecules, and consequently the attenuation of the film; and besides this, they cause the breakage of the parts that are very thin. It is partly on this account that the films generally last longer in closed vessels; for then one of the causes of disturbance (namely the movement of the air) is got rid of.

A second cause is evaporation (when the liquid constituting the film is susceptible of it). From the experiments described in the last Series, I conclude that in the case of liquids which do not admit of being blown into bubbles, evaporation is favourable rather than hurtful to the permanence of the films. I try to account for this singular fact, and I show that the contrary is true in regard to liquids that are easily blown out into bubbles; that is to say, in the case of these the persistence of the films is diminished by evaporation. For instance, hemispherical bubbles about a centimetre in diameter, formed at the surface of a solution of Marseilles soap, last for several hours in an atmosphere

* Translated from the Author's abstract, in the Annales de Chimie et de Physique, S. 4. vol. xix. p. 369 (March 1870), of the complete memoir published in the Mémoires de l'Académie de Bruxelles, vol. xxxvii. For abstracts of the preceding Series see Taylor's Scientific Memoirs, vol. iv. p. 16, vol. v. p. 584; and Phil. Mag. (§. 4.) vol. xiv. p. 1, vol. xvi. p. 23, vol. xxii. p. 286, vol. xxiv. p. 128, vol. xxxiii. p. 39, and vol. xxxviii. p. 445,

saturated with aqueous vapour, but only for a few minutes when they are freely exposed to the air. The glycerine-solution not only does not emit vapour, but, on the contrary, absorbs the moisture of the surrounding air; and it is partly because of this that films of this liquid last so long even when exposed to the air. In the third place, since gravity constantly causes the liquid to descend towards the base of the films, it is plain that, by getting rid of or lessening the action of this force, the duration of the film must be increased. Hence it evidently follows that, other things being equal, a horizontal film will last longer than one which is inclined or vertical. I have made this comparison in the case of films of soap-water formed upon rings of iron wire 7 centims. in diameter and exposed to the air, one being horizontal and the other vertical. The average persistence of the first was 25 seconds, and that of the latter 13 seconds. Hence the position, or, more accurately, the greater or less degree of inclination, of the film must be reckoned as one of the secondary causes that we are considering.

In the fourth place, combinations of films always last a much shorter time than figures formed of a single film. This is because the highly concave surfaces of the small masses of liquid which form the liquid edges, and especially those which exist at the points of junction of these edges, produce a continual drain upon the liquid of the films and thus tend powerfully to make them thinner. The combination of films into systems is therefore likewise one of the secondary causes which modify their per

manence.

In the fifth place, films generally last longer in proportion as they are of smaller size. For instance, if systems of films are produced upon two skeletons of similar shape but of different sizes, the one on the smaller skeleton lasts the longest.

If the persistence generally diminishes when the size of the films is increased, this is, I think, simply because the greater a film is, the greater is the chance that one point or another will yield to some cause of rupture. Under certain circumstances this effect of size does not show itself; for instance, films of soapwater formed upon rings 10, 7, 2, and 1 centim. in diameter lasted on the average for the same length of time. This last fact may be explained by the consideration that the drain of liquid caused by the great concave curvature of the small quantity of liquid which connects the film with the whole of the inner circumference of the ring, tends to make the smaller films last a shorter time, and thus the effects of size and curvature may neutralize each other.

Lastly, it is needful, in the sixth place, to take account of the nature of the solid to which the film adheres, and of the condi

tion of its surface. For instance, we know that films formed upon rings or frames made of iron wire that has not been oxidized break immediately, or last only for a very short time; and according to the Abbé Florimond, soap-bubbles of a much larger size can be blown with a glass pipe than with a clay one &c.

From this examination of all the accessory circumstances, it follows that a film of given size will last longest if it is a plane horizontal film, attached all round to the side of a glass vessel, entirely shielded from evaporation, and protected from the motion of the surrounding air, and, as much as possible, from the tremors conducted along the ground. Now all these conditions were fulfilled in the case of a film 7 centims. in diameter mentioned in my Seventh Series, formed of the glycerine solution and placed inside a bottle: accordingly this film lasted eighteen days.

I next pass to another subject. The beauty of the film-figures of the glycerine-solution naturally gives rise to the wish to have them entirely permanent. In the case of one of them (the sphere) this object is attained, as every one knows, by means of molten glass; but the production of other figures in this material, especially of such as are formed by an assemblage of films, would present difficulties, and in any case it would not be convenient. The first idea that suggests itself is to employ a liquid which produces films that become solid by simple evaporation in the cold, such as collodion, solution of albumen, &c.; but with liquid of this kind no result can be obtained except by limiting our attempts to figures of very small size.

Hence, in order to succeed in producing figures of tolerable size, we are obliged to have recourse to substances which, like glass, are liquid only at high temperatures, and to seek for one which fulfils the double condition of not requiring a very high temperature to melt it, and of being capable of extension, in the molten state, into films of sufficient size. I succeeded almost completely with a mixture of one part of pure gutta percha and five parts of resin, kept at a temperature of about 150° C.; the frame employed was a cube measuring 5 centims. along the edge. The system of films that was produced was very firm, and lasted, I think, more than two years, when a slight blow reduced it to fragments from which we must conclude that the constitution of the films had undergone a gradual change. I think one would succeed still better, and that the gradual alteration would be less, if a somewhat larger proportion of resin were employed.

I conclude the part of my work which is specially devoted to liquid films by a succinct account of every thing that, as far as my knowledge goes, has been published in relation to such films independently of my own researches.