a second it would, in the interval taken by sound to pass from one strip to the next, rotate through about 33°; the displacement of the image produced by a rotation one thousandth part of this could easily be detected.

When the phosphorescence was produced by the discharge of an ordinary induction-coil, the images seen in the telescope after reflexion from the revolving mirror were drawn out into very faint ribands of light without definite beginnings or ends; so that it was impossible to say whether or not there was any displacement of one image relative to the other.

I tried a considerable number of phosphorescent substances in the hope of obtaining sharp images, but without success. The substances I tried were ordinary German-glass, uraniumglass, lead-glass, the cyanide of magnesium and platinum, asaron, æsculine, and Schuchardt's "Leucht-farbe."

The gradual fading away of the phosphorescence after the exciting cause has been removed, is one reason why one of the edges of the image formed by the revolving mirror should be indistinct this cannot be remedied unless some substance can be found which ceases to phosphoresce immediately the incidence of the negative rays ceases. I was unable to find any substance possessing this property of the substances I tried, uranium-glass was the one whose phosphorescence died away most quickly.

I tried several experiments with a specimen of asaron. This substance was found by Lenard to cease to phosphoresce so quickly after the cessation of the phosphorogenic rays that he could not detect its duration in his very sensitive phosphoroscope. My specimen of asaron must, I think, have been impure, as it phosphoresced a coral-pink instead of violet as described by Lenard, and its phosphorescence showed a very appreciable duration; in addition to this, it did not give out nearly enough light to be of any use in experiments of this kind.

But even though the images of the phosphorescent strips have one edge (that corresponding to the end of the phosphorescence) indistinct, we can get the information we require about the velocity of the cathode-rays if we can get the image of the edge corresponding to the beginning of the phosphorescence sharp and distinct.

After unsuccessful attempts with several methods, I found that this could be done in the following way, using the oscillatory currents produced by the discharge of a Leyden jar :The electrodes of the discharge-tube were connected with the ends of the secondary coil of a transformer, whose primary

circuit consisted of a coil of wire with the ends connected to the outside coatings of two Leyden jars, the inside coatings of which were connected with the extremities of an inductioncoil: the secondary coil of the transformer had about 30 turns for each turn of the primary coil. It was heavily insulated, and both primary and secondary were immersed in an oilbath. This transformer easily gave sparks 7 or 8 inches long in air, and when connected to the terminals of a dischargetube made of uranium-glass produced a very vivid phosphorescence. When the phosphorescence was produced in this way, the images after reflexion in the rotating mirror had one edge quite sharp and distinct, though the other edge was indeterminate in consequence of the duration of the phosphorescence.

When the images of the two bright phosphorescent strips were observed in the telescope, after reflexion from the rapidly revolving mirror, their bright edges were seen to be no longer in the same straight line: if the images came in the field of view from the bottom and went out at the top, then the sharp edge of the phosphorescent strip nearest the electrode was lower than the edge of the other image; if the direction of rotation of the mirror was reversed so that the images came in at the top of the field of view and disappeared at the bottom, then the bright edge of the image of the phosphorescent strip nearest the negative electrode was higher than the bright edge of the image of the other strip. This shows that the luminosity at the strip nearest the cathode begins to be visible before that at the strip more remote ; and that the retardation is sufficiently large to be detected by the revolving mirror. This retardation might be explained, (1) by supposing it due to the time taken by the cathode-rays to traverse the distance between the phosphorescent patches; or (2) we might suppose that, though the cathode-rays reached the two phosphorescent patches almost simultaneously, it took longer for the rays falling on the patch at the greater distance from the cathode to raise the patch to luminosity. In other words, there may be an interval between the incidence of the cathode-rays and the emission of the phosphorescent light; this interval being greater the further the phosphorescent patch is from the cathode. This latter supposition cannot, however, explain the displacement of the images for the following reasons:-The sharpness and brightness of the edge of the image show that the phosphorescence, when once it is visible, must attain its maximum brilliancy in a time very small compared with the time taken by the mirror to rotate through an angle large enough to produce the

observed displacement of the images. Again, the two phosphorescent patches are as nearly as possible of equal brightness, so that there can be very little difference in the intensity of the cathode-rays falling upon them: it was for this reason that both the phosphorescent patches were taken some distance down the tube. Again, I took a tube which was bent so that that the cathode-rays fell more directly upon the patch farther from the cathode than upon the other patch, so that in this case the phosphorescence of the more remote patch was brighter. The displacement of the images with this tube was just the same as for the previous, i. e. the phosphorescence commenced at the patch nearest the cathode sooner than at the other patch; whereas if the displacement of the images was due to the interval between the arrival of the rays and the beginning of the phosphorescence it should have commenced at the patch furthest from the cathode, as this was the most exposed to the cathode-rays and phosphoresced with the greatest brilliancy.

I conclude, therefore, that the displacement of the images is due to the time taken by the rays to travel from one patch to the other. This displacement enables us to measure the velocity of the cathode-rays. The amount of displacement observed through the telescope is not constant: even though the mirror is turning at a uniform rate, there are quite appreciable and apparently irregular variations in the amount of the displacement of the images seen in the course of a few minutes. I think these are due to irregularities in the sparks discharging the jar, and the consequent irregularities in the electromotive force acting on the discharge-tube.

When the mirror was rotating 300 times a second, the bright edges of the two patches were on the average separated by the same distance as the image of two lines 1.5 millim. from each other placed against the discharge-tube. Since the distance of the discharge-tube which contained hydrogen from the mirror is 75 centim., the mirror must, in the time taken by the cathode-rays to pass from one patch to the other, have

turned through the angle whose circular measure is

1.5

2 × 750' Since the mirror makes 300 revolutions per second, the time it takes to rotate through this angle is

and since the distance between the patches is 10 centim., the

This velocity is small compared with that with which the main discharge from the positive to the negative electrode travels between the electrodes (see J. J. Thomson, Proc. Roy. Soc. 1890). I verified this by inserting an electrode into the far end of the tube used in the previous experiment, and observing the images formed when a bright discharge passed down from the electrode at the beginning to the electrode at the end of the tube. The light from the luminous gas shines through the places where the lampblack has been scraped from the tube, and we get two images, which when the mirror is at rest coincide in position with the images of the two phosphorescent patches in the previous experiment. These images, however, unlike the phosphorescent one, remained in the same straight line when the mirror was rotating rapidly, thus proving that the velocity of the main discharge is very large indeed compared with that of the cathode-rays.

The velocity of the cathode-rays is very much greater than the velocity of mean square of the molecules of gases at the temperature 0° C. Thus, for example, at 0° C. the velocity of mean square of the molecules of hydrogen is about 1.8 × 105 centimetres per second: the velocity of the cathode-rays about one hundred times as great. The velocity of the cathode-rays found from the preceding experiments agrees very nearly with the velocity which a negatively electrified atom of hydrogen would acquire under the influence of the potential fall which occurs at the cathode. For, let v be the velocity acquired by the hydrogen atom under these circumstances, m the mass of the hydrogen atom, V the fall in potential at the cathode, e the charge on the atom; then we have, by the conservation of energy,

mv2=2Ve.

Now e has the same value as in electrolytic phenomena, so that e/m=10*.

Warburg's experiments show that V is about 200 volts, or 2 × 101o in absolute measure. Substituting this value, we find

A value almost identical with that found by experiment,

The very small difference between the two is of course accidental, as the measurements of the displacement of the images on which the experimental value of v was founded could not be trusted to anything like 5 per cent.

The action of a magnetic force in deflecting these rays shows, assuming that the deflexion is due to the action of a magnet on a moving electrified body, that the velocity of the atom must be at least of the order we have found.

Consider an atom projected parallel to the axis of the tube which is situated in a uniform field of magnetic force, the lines of magnetic force being at right angles to the axis of the tube. Let H be the intensity of the magnetic force. Then, if m is the mass of the atom, v its velocity, and p the radius of curvature of its path, we have

where e is the charge on the atom; since e/m for hydrogen is 10*, we have v=pH x 10".

I cannot find any quantitative experiments on the deflexion of these rays by a magnet; but ordinary observation shows that it would require a strong magnetic field to make p as small as 10 centim., which would mean clearing the tube of phosphorescence except within about 10 centim. of the cathode. If v were 2 × 107, this would give H=200, which is not extravagant.

XLI. On the Amplitude of Aerial Waves which are but just Audible. By Lord RAYLEIGH, Sec. R.S.*

THE

HE problem of determining the absolute value of the amplitude, or particle velocity, of a sound which is but just audible to the ear, is one of considerable difficulty. In a short paper published seventeen years ago I explained a method by which it was easy to demonstrate a superior limit. A whistle, blown under given conditions, consumes a known amount of energy per second. Upon the assumption that the whole of this energy is converted into sound, that the sound is conveyed without loss, and that it is uniformly distributed over the surface of a hemisphere, it is easy to calculate the amplitude at any distance; and the result is necessarily a superior limit to the actual amplitude. In the case *Read at the Oxford Meeting of the British Association. Communicated by the Author.

† Proc. Roy. Soc. vol. xxvi. p. 248 (1878).