resultant of a component of the known solar motion with reference to the stars

19.5

29-76

× cos 574°=·352, × 10-*c, in direction 270°-46)

compounded with a true drift in plane of ecliptic

1.78 × 10-4 c in direction 162°.

I really do not know whether astronomers could pass, as at all possible, outstanding perturbations such as those last tabulated. Comparing Tables V. and II. they are clearly not of orthodox size; they are too big for Earth and Venus, and too small for Mars. But I suppose that the recognized values are in reality dissected out from a group system of small discrepancies of which the total is more certain than the precise distribution among individual members.

I submit also that even the forced agreement for Mercury is not to be wholly set aside as mere algebra; for the postulated solar drift is of a not unreasonable order of magnitude, and the figures are got from it absolutely by a theory which if not in the least degree valid might have given them millions of times wrong. So the fact that absolute values not quite hopelessly discordant with observation can be thus reckoned ought to be taken into account.

Assuming that astronomers will not pass them, however, we must face the question why not. Full gravitational influence on the extra inertia might halve the necessary values of k, but would not otherwise improve things. Total absence of solar drift is unlikely; so in order to explain the hypothetical absence of perturbations which ought to occur but do not, we may be driven to conclude that the gravitationconstant itself is a function of the speed of the attracting masses, in some such way as that suggested in Part I. above: thus adding to the evidence for an uncompromising Principle of Relativity.

PART III.-Suggested Possibilities.

In support of the idea that gravitative attraction may be a function of speed, I may point out that if the attraction were of an electrical order, such dependence on speed would be reasonable, and even the amount of the dependence would

be appropriate; for the attraction between two charges

moving together in parallel lines is K(1-"); while if

one charge is revolving round another, the attraction between them presumably has for its main term

(See J. J. Thomson's "Report on Electrical Theories," British Association volume for Aberdeen, p. 110 (1885).) Hence if

then, u being in this case far larger than any probable V,

and the terms involving sin 0, which are responsible for the cumulative terms in the solution of the differential equation quoted in paragraph 1, cancel.

Were it not so, some curious consequences could be deduced for an electron revolving at immense speed inside an atom round a nucleus under the inverse-square law, especially when such an atom is shot away at high speed; for the angle or 2πn is enormous.

Assuming it possible, then, that a quantitatively similar law holds in the case of gravity, the force of attraction F=ymM/2 will diminish as m increases (M the central body, moving steadily at speed V, will not change its value whatever it is), and accordingly the product Fm (involving ym2) will remain constant at whatever varying speed m moves through the æther the variation of the gravityconstant just compensating for the double variation of

mass m.

But it will be very remarkable if such compensation really occurs; and if such a fact is established it may begin to throw some light on the family relationship of the force of gravity.

XVII. On the Lubricating and other Properties of Thin Oily Films. By Lord RAYLEIGH, O.M., F.R.S.*

HE experiments about to be described were undertaken to examine more particularly a fact well known in most households. A cup of tea, standing in a dry saucer, is apt to slip about in an awkward manner, for which a remedy is found in the introduction of a few drops of water, or tea, wetting the parts in contact. The explanation is not obvious, and I remember discussing the question with Kelvin many years ago, with but little progress.

It is true that a drop of liquid between two curved surfaces draws them together and so may increase the friction. If d be the distance between the plates at the edge of the film, T the capillary tension, and a the angle of contact, the whole force is t

A being the area of the film between the plates and B its circumference. If the fluid wets the plate, a=0 and we have simply 2AT/d. For example, if d=6 x 10-5 cm., equal to a wave-length of ordinary light, and T (as for water) be 74 dynes per cm., the force per sq. cm. is 25 x 103 dynes, a suction of 2 atmospheres. For the present purpose we may express d in terms of the radius of curvature (p) of one of the surfaces, the other being supposed flat, and the distance (x) from the centre to the edge of the film. In two dimensions da2/2p, and A (per unit of length in the third dimension) = 2x, so that the force per unit of length is SpT/x, inversely as x. On the other hand, in the more important case of symmetry round the common normal A=2, and the whole force is 4πpT, independent of x, but increasing with the radius of curvature. For example, if T=74 dynes per cm., and p=100 cm., the force is 925 dynes, or the weight of about 1 gram. The radius of curvature (p) might of course be much greater. There are circumstances where this force is of importance; but, as we shall see presently, it does not avail to explain the effects now under consideration.

My first experiments were very simple ones, with a slab of *Communicated by the Author.

See for example Maxwell on Capillarity. Collected Papers, vol. ii.

p. 571.

Phil. Mag. S. 6. Vol. 35. No. 206. Feb. 1918.

N

thick plate glass and a small glass bottle weighing about 4 oz. The diameter of the bottle is 44 cm., and the bottom is concave, bounded by a rim which is not ground but makes a fairly good fit with the plate. The slab is placed upon a slope, and the subject of observation is the slipping of the bottle upon it. If we begin with surfaces washed and well rubbed with an ordinary cloth, or gone over with a recently wiped hand, we find that at a suitable inclination the conditions are uniform, the bottle starting slowly and moving freely from every position. If now we breathe upon the slab, maintained in a fixed position, or upon the bottle, or upon both, we find that the bottle sticks and requires very sensible forces to make it move down. A like result ensues when the contacts are thoroughly wetted with water instead of being merely damped. When, after damping with the breath, evaporation removes the moisture, almost complete recovery of the original slipperiness recurs.

In the slippery condition the surfaces, though apparently clean, are undoubtedly coated with an invisible greasy layer. If, after a thorough washing and rubbing under the tap, the surfaces are dried by evaporation after shaking off as much of the water as possible, they are found to be sticky as compared with the condition after wiping. A better experiment was made with substitution of a strip of thinner glass about 5 cm. wide for the thick slab. This was heated strongly by an alcohol flame, preferably with use of a blowpipe. At a certain angle of inclination the bottle was held every where, but on going over the surface with the fingers, not purposely greased, free movement ensued. As might have been expected, the clean surface is sticky as compared with one slightly greased; the difficulty so far is to explain the effect of moisture upon a surface already slightly greased. It was not surprising that the effect of alcohol was similar to that of water.

At this stage it was important to make sure that the stickiness due to water was not connected with the minuteness of the quantity in operation. Accordingly a glass plate was mounted at a suitable angle in a dish filled with water. Upon this fully drowned surface the bottle stuck, the inclination being such that on the slightest greasing the motion became free. In another experiment the water in the dish was replaced by paraffin oil. There was decided stickiness as compared with surfaces slightly greasy.

The better to guard against the ordinary operation of surface tension, the weight of the bottle was increased by inclusion of mercury until it reached 20 oz., but without

material modification of the effects observed. The moisture of the breath, or drowning in water whether clean or soapy, developed the same stickiness as before.

The next series of experiments was a little more elaborate. In order to obtain measures more readily, and to facilitate drowning of the contacts, the slab was used in the horizontal position and the movable piece was pulled by a thread which started horizontally, and passing over a pulley carried a small pan into which weights could be placed. The pan itself weighed 1 oz. (28 grams). Another change was the substitution for the bottle of a small carriage standing on glass legs terminating in three feet of hemispherical form and 5 mm. in diameter. The whole weight of the carriage, as loaded, was 73 oz. The object of the substitution was to eliminate any effects which might arise from the comparatively large area of approximate contact presented by the rim of the bottle, although in that case also the actual contacts would doubtless be only three in number and of very small area.

With oz. in pan and surfaces treated with the hand, the carriage would move within a second or two after being placed in position, but after four or five seconds' contact would stick. After a few minutes' contact it may require 1 oz. in pan to start it. When the slab is breathed upon it requires, even at first, 3 oz. in the pan to start the motion. As soon as the breath has evaporated, oz. in pan again suffices. When the weight of the pan is included, the forces are seen to be as 1:3. When the feet stand in a pool of water the stickiness is nearly the same as with the breath, and the substitution of soapy for clean water makes little difference.

In another day's experiment paraffin (lamp) oil was used. After handling, there was free motion with 1 oz. in pan. When the feet stood in the oil, from 2 to 3 oz. were needed in the pan. Most of the oil was next removed by rubbing with blotting-paper until the slab looked clean. At this stage oz. in pan sufficed to start the motion. On again wetting with oil 2 oz. sufficed instead of the 23 oz. required before. After another cleaning with blotting-paper oz. in pan sufficed. From these results it appears that the friction is greater with a large dose than with a minute quantity of the same oil, and this what is hard to explain. When olive oil was substituted for the paraffin oil, the results were less strongly marked.

Similar experiments with a carriage standing on brass