I have been impressed for some time with the unsatisfactory character of the present fog signals. We must recognize that powerful siren signals are sometimes inaudible at distances but little exceeding a mile. It is true that these worst cases of inaudibility may not recur during fogs—as to this there seems to be insufficient evidence. But even when a sound-in-air signal is audible, the information conveyed is far from precise. The bearing of the source cannot be told with much accuracy, indeed some say that it cannot be told at all. The distance is still more uncertain. I should say that no system is satisfactory which does not give either the one or the other element, bearing or distance.

The system of synchronous signalling explained by Prof. Joly claims to give the distance with sufficient precision, and the American and Russian trials show that the claim is justified, as might indeed have been expected with some confidence, provided both signals themselves are well defined in time. The wireless electric signals are easily made sharp. Submarine signals from a bell, or explosive, would also be sharp enough. So probably would be explosive signals in air. The case of siren signals is more doubtful. Possibly the end might be sharp enough. Even so, the objection of the uncertain carrying of air signals remains.

I do not know whether there is already sufficient experience of submarine signals. If it be true that they can be depended upon up to distances of at least 4 or 5 miles, the case is strong for a combination of them with electric signals.

When reading O. Reynold's description of the sounds emitted by water in a kettle as it comes to the boil, and their explanation as due to the partial or complete collapse of bubbles as they rise through cooler water, I proposed to myself a further consideration of the problem thus presented; but I had not gone far when I learned from Sir C. Parsons that he also was interested in the same question in connexion with cavitation behind screw-propellers, and that at his instigation Mr S. Cook, on the basis of an investigation by Besant, had calculated the pressure developed when the collapse is suddenly arrested by impact against a rigid concentric obstacle. During the collapse the fluid is regarded as incompressible.

In the present note I have given a simpler derivation of Besant's results, and have extended the calculation to find the pressure in the interior of the fluid during the collapse. It appears that before the cavity is closed these pressures may rise very high in the fluid near the inner boundary.

As formulated by Besant, the problem is—

“An infinite mass of homogeneous incompressible fluid acted upon by no forces is at rest, and a spherical portion of the fluid is suddenly annihilated; it is required to find the instantaneous alteration of pressure at any point of the mass, and the time in which the cavity will be filled up, the pressure at an infinite distance being supposed to remain constant.”

Since the fluid is incompressible, the whole motion is determined by that of the inner boundary.

In the summer of 1907, in connexion with my experiments upon reflexion from glass at the polarizing angle, I made observations also upon the diamond, a subject in which Kelvin had expressed an interest. It was known from the work of Jamin and others that the polarization of light reflected from this substance is very far from complete at any angle of incidence, and my first experiments were directed to ascertain whether this irregularity could be plausibly attributed to superficial films of foreign matter, such as so greatly influence the corresponding phenomena in the case of water. The arrangements were of the simplest. The light from a paraffin flame seen edgeways was reflected from the diamond and examined with a nicol, the angle being varied until the reflexion was a minimum.

In one important respect the diamond offers advantages, in comparison, for instance, with glass, where the surface is the field of rapid chemical changes due presumably to atmospheric influences. On the other hand, the smallness of the available surfaces is an inconvenience which, however, is less felt than it would be, were high precision necessary in the measurements. Two diamonds were employed—one, kindly lent me by Sir W. Crookes, mounted at the end of a bar of lead, the other belonging to a lady's ring. No particular difference in behaviour revealed itself.

The results of repeated observations seemed to leave it improbable that any process of cleaning would do more than reduce the reflexion at the polarizing angle. Potent chemicals, such as hot chromic acid, may be employed, but there is usually a little difficulty in the subsequent preparation.

In T. 749, Major Taylor presents some calculations which “shew that the chief cause of the dissipation of sound during its transmission through the lower atmosphere must be sought for in the eddying motion which is known to exist there. The amount of dissipation which these calculations would lead us to expect from our knowledge of the structure of the lower atmosphere agrees, as well as the rough nature of the observations permit, with the amount of dissipation given by Mr Lindemann.”

The problem discussed is one of importance and it is attended with considerable difficulties. There can be no doubt that on many occasions, perhaps one might say normally, the attenuation is much more rapid than according to the law of inverse squares. Some 20 years ago (Scientific Papers, Vol. iv. p. 298) I calculated that according to this law the sound of a Trinity House syren, absorbing 60 horse-power, should be audible to 2700 kilometres!

A failure to propagate, so far as it is uniform on all occasions, would naturally be attributed to dissipative action. I am here using the word in the usual and narrower technical sense, implying a degradation of energy from the mechanical form into heat, or a passage of heat from a higher to a lower temperature. Although there must certainly be dissipation consequent upon radiation and conduction of heat, it does not appear that these causes are adequate to explain the attenuation of sound sometimes observed, even at moderate distances. This question is discussed in Phil. Mag. XLVII. p. 308, 1899 (Scientific Papers, Vol. IV. p. 376) in connexion with some observations of Wihner Duff.

Among the many remarkable anticipations contained in T. Young's Lectures on Natural Philosophy (1807) is that in which he explains the effect of what is now commonly known as the sand-blast. On p. 144 he writes:—“There is, however, a limit beyond which the velocity of a body striking another cannot be increased without overcoming its resilience, and breaking it, however small the bulk of the first body may be, and this limit depends on the inertia of the parts of the second body, which must not be disregarded when they are impelled with a considerable velocity. For it is demonstrable that there is a certain velocity, dependent on the nature of a substance, with which the effect of any impulse or pressure is transmitted through it; a certain portion of time, which is shorter accordingly as the body is more elastic, being required for the propagation of the force through any part of it; and if the actual velocity of any impulse be in a greater proportion to this velocity than the extension or compression, of which the substance is capable, is to its whole length, it is obvious that a separation must be produced, since no parts can be extended or compressed which are not yet affected by the impulse, and the length of the portion affected at any instant is not sufficient to allow the required extension or compression.

In a recently published paper I have examined, with the aid of a new manometer, the behaviour of gases at very low pressures, rising to 1·5 millims. of mercury, with the result that Boyle's law was verified to a high degree of precision. There is, however, a great gap between the highest pressure there dealt with and that of the atmosphere—a gap which it appeared desirable in some way to bridge over. The sloping manometer, described in the paper referred to, does not lend itself well to the use of much greater pressures, at least if we desire to secure the higher proportional accuracy that should accompany the rise of pressure. The present communication gives the results of observations, by another method, of the law of pressure in gases between 75 millims. and 150 millims. of mercury. It will be seen that for air and hydrogen Boyle's law is verified to the utmost. In the case of oxygen, the agreement is rather less satisfactory, and the accordance of separate observations is less close. But even here the departure from Boyle's law amounts only to one part in 4000, and may perhaps be referred to some reaction between the gas and the mercury. In the case of argon too the deviation, though very small, seems to lie beyond the limits of experimental errors.

The expression of Prof. Larmor's views in his paper “On the Constitution of Natural Radiation” is very welcome. Although it may be true that there has been no direct contradiction, public and private communications have given me an uneasy feeling that our views are not wholly in harmony; nor is this impression even now removed. It may conduce to a better understanding of some of these important and difficult questions if without dogmatism I endeavour to define more clearly the position which I am disposed to favour on one or two of the matters concerned.

On p. 580, in comparing white light and Röntgen radiation, Prof. Larmor writes: “Both kinds of disturbance are resolvable by Fourier's principle into trains of simple waves. But if we consider the constituent train having wave-length variable between λ and λ + δλ, i.e. varying irregularly from part to part of the train within these limits, a difference exists between the two cases. In the case of the white light the vibration-curve of this approximately simple train is in appearance steady; it is a curve of practically constant amplitude, but of wave-length slightly erratic within the limits δλ and therefore of phase at each point entirely erratic. In the Fourier analysis of the Röntgen radiation the amplitude is not regular, but on the contrary may be as erratic as the phase.” This raises the question as to the general character of the resultant of a large number of simple trains of approximately equal wave-length.

Speculations on tidal questions are much hampered by our ignorance of the peculiar influence of the earth's rotation in any but the simplest cases. The importance of this element was first appreciated by Laplace, and he succeeded in obtaining solutions of various problems relating to a globe completely covered with water to a depth either uniform throughout, or at any rate variable only with latitude. His work has been extended by Kelvin, G. Darwin, and Hough. For an excellent summary, reference may be made to Lamb's Hydrodynamics, which includes also important original additions to the theory.

But it must not be overlooked that a theory which supposes the globe to be completely covered with water has very little relation to our actual tides. Indeed, in practice, tidal prediction borrows nothing from Laplace's theory, unless it be to look for tidal periods corresponding with those of the generating forces. And this correspondence, although perhaps first brought into prominence in connection with Laplace's theory, is a general mechanical principle, not limited to hydrodynamics. If the theory of terrestrial tides is to advance, it can only be by discarding the imaginary globe completely covered with water and considering examples more nearly related to the facts, as was done in some degree by Young and Airy in their treatment of tides in canals.

I suppose that everyone is familiar with the system of oblique waves advancing in echelon from the bow of a ship which travels through smooth water. What is not so easily observed from on board is the corresponding wave-profile, i.e. the deviation of the water-surface at the side of the ship from the position which it would occupy in a state of rest. Sketches, both of the whole system of waves and of various wave-profiles, have been given by W. and R. E. Froude, and the influence of the various components of the wave-system in contributing to the aggregate wave-resistance has been discussed. Attention has perhaps tended to concentrate upon the directly advancing waves—those whose crests are perpendicular to the ship's motion—and upon the remarkable interaction between the systems originating at the bow and stern. But, apart from its interesting geometrical features, the oblique part of the wave-system also impresses an observer with its mechanical importance as probably contributing in no mean degree to the total wavemaking resistance.

From the time of my first acquaintance with drawings of wave-profiles I have been struck with their significance as indicating that the usual form of bow (and perhaps of stern) is not well adapted to minimise the forces of resistance. At the stem and immediately behind, the water is raised above the normal level, and this elevation is undoubtedly the principal feature.