circles of holes on the siren appear stationary when viewed through the slit, if the velocity of rotation was such that the desired note or notes would be given by the same or other circles of holes. An observer watching the siren through the slit and pressing lightly on the axis with a straw, was able to adjust its speed so that the required combination of sounds was produced for several, and in some cases for many seconds at a time.

We have also projected the image of the row of holes on a screen, the cone of light passing at its narrowest part through the slit in the tinfoil screens carried by the auxiliary fork. When the upper siren was to be used, two semicircles of light mirror-glass were laid on the disk of the lower siren to which the two halves of a paper cog-wheel were fastened. The image of the cogs could thus be projected.

The third method of determining the speed of the siren depended on the use of an instrument first devised by Lord Rayleigh in 1880. A mass of air enclosed in a tube is excited by resonance, and the fact of the excitation is indicated by a light mirror set where the motion is greatest, and inclined at 45° to the direction of the air-currents. In accordance with the general law that a lamina tends to place itself perpendicular to the direction of a stream, the mirror moves when the air vibrates. In the original apparatus the amount of the movement was controlled by magnets. Since that date Professor Boys has modified the instrument by substituting a quartz-thread suspension for a silk fibre, and using the torsion of the thread instead of the directing force of the magnets. He exhibited the apparatus during a lecture delivered before the British Association in Leeds. It may be called a mirror-resonator.

Professor Boys has been good enough to make two of these instruments for us, and it was decided that one of them should respond to 161 vibrations per second. The movement of the spot of light reflected from the mirror informed us when the siren was giving this note, and this fact was utilized in one of the experiments.

Sensitiveness of the Apparatus.

The results were in general improved by laying a small strip of dry blotting-paper upon the prongs. Mere accidental disturbances died out more quickly, and the vibrations of the fork diminished more rapidly, when the notes which had produced them ceased to sound.

A forced movement could be produced in the fork by

blowing directly down the collecting cone, but a small organ-pipe could be sounded, or a König's fork bowed near the opening without producing the least effect if the frequency of the note produced was not near 64 per second. In like manner many notes of two reed wind-instruments, somewhat similar in construction to the harmonium, were sounded simultaneously so that the room echoed with discordant sound, yet without producing the least effect on the steadiness of the bands.

On the other hand, when one of König's forks tuned to €4 vibrations was touched with the india-rubber covered handle of a gimlet, or was struck with a piece of gas-tubing so lightly that an observer with his ear close to the fork could not detect the fundamental note, the bands instantly disappeared.

It was therefore evident that the apparatus could respond to a vibration which was quite inaudible to a person standing by the resonating fork.

When the König fork was weighted so as to give 63.5 vibrations per second, the bands appeared and disappeared at regular intervals of two seconds, thus corresponding to the beats between the exciting and resonating forks. The bands were not disturbed when the beats exceeded 2 or 3 per second unless the exciting fork was bowed very violently. In the experiments with fainter tones, the resonating fork was only disturbed when the frequency of the exciting note agreed very exactly with its own.

As the speed of the siren was gradually increased from rest the bands always disappeared two or three times, the disturbance being no doubt caused by the upper partials as the vibration-frequency passed, in turn, the values 16, 21-3, and 32 per second. No exact measurement was made of the corresponding frequencies, as there could be no question as to whether the partials were produced or as to whether the apparatus could detect them. No such disappearance occurred when the note was higher than C, except in the case of certain spurious effects referred to below.

All the experiments were performed several times on each occasion, and on two occasions at least. The bands were sometimes produced by soda-light, and watched by an observer through a telescope.

Sometimes the electric light was used. The bands could then be projected on a screen side by side with the image of the holes or cogs. In this way information as to the note produced and as to the behaviour of the bands was simultaneously conveyed to all who watched the experiments,

Precautions.

It will not be thought remarkable that so delicate an apparatus requires careful use.

In the first place, it was necessary to be sure that the disturbance ascribed to the joint action of two notes was not produced by one or both of them when acting alone. In all cases, therefore, in which it was possible to determine the pitch of both notes separately, each note was sounded alone and carried slowly past the particular pitch at which the existence of a combination-tone was to be investigated. In general, no effect was produced; but after the apparatus had been in use for some little time, we were troubled by the fact that two notes which did not differ much from 256 and 320 vibrations respectively disturbed the bands when they were produced separately.

That these effects were spurious was evident from two facts. Firstly, the same notes had previously been sounded for a long time with the special object of determining whether they produced any effect, and had produced none. Secondly, the disturbances were evidently forced. When the fork has been disturbed by a vibration of frequency 64, it continues to oscillate for several seconds after the disturbing note has ceased. The bands alternately appear and disappear several times before the final state of rest is attained. In the case of a "spurious" effect, the bands reappear instantaneously with absolute clearness the moment the disturbing note ceases, thereby indicating a forced vibration. It was, however, a more difficult task to discover the cause than to determine the character of these disturbances. Finally, it was found that since the apparatus was first set up some cracks had opened in the wooden pyramidal collector. A tap on the side of this will disturb the bands; and when one of the cracked sides was loaded with weights the disturbance due to the 320 note was much reduced. The cracks were then cut out, the defects made good; and since that time this disturbance has entirely ceased.

The effect produced by the 256 note was due to another cause. When the pyramid was removed, the open ends of the resonance-boxes of various tuning-forks (256, 320, 384) were held near the square of wood which was attached to the fork F. It was found that the 256 fork was the only one which affected the bands, and that it only produced any result when the sounding-box was held near that part of the wood which projected beyond the end of the prong. It was therefore.

evident that the two ribs attached to this were not sufficient to prevent a certain flapping of the projecting part, and that this responded to a note of about 256 vibrations. The end of the collecting pyramid was then shifted a little so that the waves of sound impinged only on the more rigid part of the wooden square, and the spurious effect immediately and completely disappeared.

Of the notes which caused these troubles, the lower one was decidedly lower than the c' of 256; the other corresponded very accurately with the e' of 320. The fact that both these numbers are multiples of 64 may legitimately give rise to the doubt whether the fork F can be set in motion by disturbances which are multiples of its own frequency.

Even if it be admitted that such forced vibrations would be especially easy to produce, we must insist-(1) that we can distinguish (as above described) between forced and natural vibrations; (2) that when the apparatus was properly arranged such notes could be produced by the siren for long intervals of time without the least effect on the bands; (3) that two tuning-forks, of 256 and 320 vibrations respectively, have been placed within the wooden pyramid with their sounding-boxes resting on and supported by, the lower side, yet no effect was produced on the bands even when they were both sounding loudly at the same time; (4) that one of König's large forks, with a frequency of 128, was placed in front of the collecting cone and produced no effect when sounding loudly, though the slightest tap on the 64 fork caused the bands to vanish for many seconds; (5) that the 320 and 384 forks produced no effect when the pyramid was removed and they were held as above described close to the receiving prong of the fork; (6) and, lastly, that in two out of the five experiments on the difference-tones, and in all those in which the interference apparatus was used to detect summation tones, the frequencies of the notes employed were neither multiples nor sub-multiples of 64.

As in all the above experiments the resonator was in position, they also sufficed to prove that tones of 64 vibrations were not manufactured in it by the primary notes when acting singly.

If the objection is raised that, although neither note disturbed the bands when sounded alone, the effect might be due to the double disturbance produced by the two sounds, we think it sufficient to answer that we have always carried the two notes above the pitch at which the difference-tone might be expected to affect the instrument, then lowered the pitch again till the notes were too flat, and repeated this

operation several times. The disturbances were only produced when the pitch was nearly, or very nearly, correct. As soon as a few beats per second were heard the bands became visible.

Having thus described the various tests which were applied to the apparatus, we may proceed to describe the experiments without dwelling further on the necessary precautions. It is sufficient to say once for all that they were adopted in each

case.

The main object of the enquiry was to obtain evidence as to the objective reality of the combination-tones, and for this purpose the following experiments were arranged.

Each box of the siren had four circles of holes which could be used separately or together. The number of openings in the upper box were 9, 12, 15, and 16, and in the lower 8, 10, 12, and 18. It will be convenient to refer to these as the 9 row of holes, and so on.

Experiment I.

The 12 and 15 rows of holes in the upper box were opened, and the pitch was raised until the upper note gave slow beats with a fork of 320 vibrations per second. The lower note was then the C of 256 vibrations. The difference or beat tone of 64 vibrations affected the instrument powerfully. The experiment was tried both by night and by day. It was difficult to keep the siren exactly at the true pitch, but when the beats were very slow the bands continually disappeared, sometimes for many seconds at a time, then appeared for a moment and then disappeared again. As soon as the pitch was lost by a few beats per second, the bands remained steady and clearly visible.

The experiment was repeated with the 9 and 12 rows of holes. When the upper note was C of 256 vibrations, the lower note was 192 vibrations. The difference-tone of 64 vibrations affected the fork very powerfully.

The experiment was also modified by opening the 10 and 12 rows of holes. When the notes corresponded to 320 and 384 vibrations respectively, the bands disappeared as before.

Experiment II.

In experiment I. the frequencies of the difference-tone and of König's first lower beat-tone were identical. The experiment was therefore varied by using 8 and 18 rows of holes. The frequency of the difference-tone was thus proportional to 10, while that of König's lower beat-tone would be 18-2×8=2, When the siren was revolving at the rate of