beats per second-secondary beats. Similarly, the intervals 2: 5, 2: 7, if slightly mistuned, will, like the fifth, yield secondary beats. Or, to put it in another way, there may be secondary beats from the (mistuned) beattones that are related (as in our experiment) in the ratio I I, or in the ratios 3: 4,3 5, &c., and even by those of I: 2, 45, 4 : 7, and so forth. I have given you an example of secondary beats now for an example of a secondary beat-tone. This is afforded by one of the previous experiments, in which were sounded ut, and the 11th harmonic of ut3. In this experiment, as in that which followed with the 13th harmonic, two (primary) beat-tones were produced, of 768 and 1280 vibrations respectively. These are related to one another by the interval 35. If we treat these as tones that can themselves interfere, they will give us for their positive remainder the number 256, which is the frequency of ut. As a matter of fact, if you listen_carefully, you may, now that your attention has been drawn to it, hear that note, in addition to the two primary tones and the two beat-tones to which you listened previously. In von Helmholtz's "Tonempfindungen," he expresses the opinion that the distinctness with which beats are heard depends upon the narrowness of the interval between the primary tones, saying that they must be nearer together than a minor third. But, as we have seen, using bass sounds of a sufficient degree of intensity and purity, as is the case with those of the massive forks, beats can be heard with every interval from the mistuned unison up to the mistuned octave. Even the interval of the fifth, ut, to sol, gave strongly-marked beats of 32 per second. When this number is attained or exceeded, the ear usually begins to receive also the effect of a very low continuous tone, the beats and the beat-tone being simultaneously perceptible up to about 60 or 70 beats, or as a roughness up to 128 per second. If, using forks of higher pitches but of narrower interval, one produces the same number of beats, the beat-tone is usually more distinct. Doubtless this arises from the greater true intensity of the sounds of higher pitch. With the object of pursuing this matter still more closely, Dr. Koenig constructed a series of 12 forks of extremely high pitch, all within the range of half a tone, the lowest giving si, and the highest ut. The frequencies, and the beats and beat-tones given by seven of them, are recorded in Table III. The first of these intervals is a diatonic semitone; the second of them is a quarter-tone; the third is an eighth of a tone; nevertheless, a sensitive ear will readily detect a difference of pitch between the two separate sounds. The last of the intervals is about half a comma. These forks are excited by striking them with a steel hammer. Some of the resulting beat-tones will be heard all over the theatre; but, in the case of the very low tones of 40 and 32 vibrations, only those who are close at hand will hear them. The case in which there are 26 beats is curious. Most hearers are doubtful whether they perceive a tone or not. There is a curious fluttering effect, as though a tone were there, but not continuously. We have seen, then, that the beat-tones correspond in pitch to the number of the beats; that they can themselves interfere, and give secondary beats; and that the same number of beats will always give the same beattone irrespectively of the interval between the two primary tones. What better proofs could one desire to support the view that the beat-tones are caused, as Dr. Young supposed, by the same cause as the beats, and not, as von Helmholtz maintains, by some other cause? Yet there are some further points in evidence which are of significance, and lend additional weight to the proofs already adduced. Beats behave like primary impulses in the following respect, that when they come with a frequency between 32 and 128 per second, they may be heard, according to circumstances, either discontinuously or blending into a continuous sensation. It has been objected that, whereas beats imply interference between two separate modes of vibration arising in two separate organs, combination-tones, whether summational, or differential, or any other, must take their origin from some one organ or portion of vibratile matter vibrating in a single but more complex mode. To this objection an experimental answer has been returned by Dr. Koenig in the following way. He takes a prismatic bar of steel, about 9 inches in length, and files it to a rectangular section, so as to give, when it is struck at the middle of a face to evoke transversal vibrations, a sound of some well-defined pitch. By carefully adjusting the sides of the rectangular section in proper proportions, the same steel bar can be made to give two different notes when struck in the two directions respectively parallel to the long and short sides of the rectangle. A set of such tuned steel bars are here before you. Taking one tuned to the note ut = 2048, with res = 2304, Dr. Koenig will give you the notes separately by striking the bar with a small steel hammer when it is lying on two little bridges of wood, first on one face, then on the other face. If, now, he strikes it on the corner, so as to evoke both notes at once, you immediately hear the strong boom of ut, = 256, the inferior beat-tone. If Dr. Koenig takes a second bar tuned to ute, and sig = 3840, you hear also ut, this time the superior beat-tone. If he takes a bar tuned to ut, and the 11th harmonic of ut, (in the ratio 8: 11), you hear the two beat-tones sol, and mis (in ratios of 3 and 5 respectively) precisely as you did when two separate forks were used instead of one tuned bar. Dr. Koenig goes beyond the mere statement that beats blend to a tone, and lays down the wider proposition that any series of maxima and minima of sounds of any pitch, if isochronous and similar, will always produce a tone the pitch of which corresponds simply to the frequency of such maxima and minima. A series of beats may be regarded as such maxima and minima of sound; but there are other ways of producing the effect than by beats. Dr. Koenig will now illustrate some of these to you. If a shrill note, produced by a small organ-pipe or reed, be conveyed along a tube, the end of which terminates behind a rotating disk pierced with large, equidistant apertures, the sound will be periodically stopped and transmitted, giving rise, if the intermittences are slow enough, to effects closely resembling beats, but which, if the rotation is sufficiently rapid, blend to a tone of definite pitch. Dr. Koenig uses a large zinc disk with 16 holes, each about 1 inch in diameter. In one set of experiments this disk was driven at 8 revolutions per second, giving rise to 128 intermittences. The forks used were of all different pitches from ut, = 256 to ut, = 4096. In all cases there was heard the low note ut, corresponding to 128 vibrations per second. In another series of experiments, using forks ut, and ut, the number of intermittences was varied from 128 to 256 by increasing the speed, when the low note rose also from ut, to utз. From these experiments it is but a step to the next, in which the intensity of a tone is caused to vary in a periodic manner. For this purpose Dr. Koenig has constructed a siren-disk (Fig. 1), pierced with holes arranged at equal distances around seven concentric circles; but the sizes of the holes are made to vary periodically from small to large. In each circle are 192 equidistant holes, and the number of maxima in the respective circles was 12, 16, 24, 32, 48, 64, and 96. On rotating this disk, and blowing from behind through a small tube opposite the outermost circle, there are heard, if the rotation is slow, a note cor responding to the number of holes passing per second and a beat corresponding to the number of maxima per second. With more rapid rotation two notes are hearda shrill one, and another 4 octaves lower in pitch, the latter being the beat-tone. On moving the pipe so that wind is blown successively through each ring of apertures, there is heard a shrill note, which is the same in each case, and a second note (corresponding to the successive beat-tones) which rises by intervals of fourths and fifths from circle to circle. These attempts to produce artificially the mechanism FIG. 1. of beats were, however, open to criticism; for in them the phase of the individual vibrations during one maximum is the same as that of the individual vibrations in the next succeeding maximum; whereas in the actual beats produced by the interference of two tones the phases of the individual vibrations in two successive maxima differ by half a vibration; as may be seen by simple inspection of the curves corresponding to a series of beats. When this difference was pointed out to Dr. Koenig, he constructed a new siren-disk (Fig. 2), having a similar series of holes of varying size, but spaced out so as to corre spond to a difference of half a wave between the sets. With this disk, beats are distinctly produced with slow rotation, and a beat-tone when the rotation is more rapid. Finding this result from the spacing out of apertures to correspond in position and magnitude to the individual wavelets of a complex train of waves, it occurred to Dr. Koenig that the phenomena of beats and of beattones might be still more fully reproduced if the edge of the disk were cut away into a wave-form corresponding precisely to the case of the resultant wave produced by wave-disks corresponding to other intervals lie upon the table; these two will, however, suffice. In the first of these the curve is that which would be obtained by setting out around the periphery a series of 120 simple sinusoidal waves, and a second set of 64 waves, and then compounding them into one resultant wave. In order to permit of a comparison being made with the simple component sounds, two concentric rings of holes have been also pierced with 120 and 64 holes respectively. Regarding these two numbers as the frequency of two primary tones, there ought to result beats of frequency 8 (being the negative remainder corresponding to the superior beat). An interior set of 8 holes is also pierced, to enable a comparison to be made. To experiment with such wave-disks they are mounted upon a smoothly running whirling-table, and wind from a suitable wind-chest is blown against the waved edge from behind, through a narrow slit set radially. In this way the air-pressures in front of the wave-edge are varied by the rush of air between the teeth. It is a question not yet decided how far these pressures correspond to the values of the ordinates of the curves. This question, which involves the validity of the entire principle of the wave-siren cannot here be considered in detail. Suffice it to say that for present purposes the results are amply convincing. On The wave-disk (Fig. 3) has been clamped upon the whirling-table, which an assistant sets into rotation at a moderate speed. Dr. Koenig blows first through a small pipe through one of the rows of holes, then through the other. The two low notes sound out separately, just a major tone apart. Then he blows through the pipe with a slotted mouth-piece against the waved edge; at once you hear the two low notes interfering, and making beats. increasing the speed of rotation the two notes become shril, and the beats blend into a beat-tone. Notice the pitch of that beat-tone: it is precisely the same as that which he now produces by blowing through the small pipe against the ring of 8 holes. With the other wave-disk, having 184 and 64 holes in the two primary circles, giving a wave form corresponding to the interval 8: 23, the effects are of the same kind, and when driven at the same speed gives the same beat-tone as the former wave-disk. It will be noted that in each of these two cases the frequency of the beat-tone is neither the difference nor the sum of the frequencies of the two primary tones. THE To be continued.) DR. HENRY SCHLIEMANN. 'HE death of Dr. Schliemann comes on his friends not only as a sorrow but as a surprise, for though he had tried his constitution, his strength was so great that it seemed equal to many more labours. He was essentially a self-made man, not merely as the architect of his own fortunes, but as having at an early age deliberately adopted certain purposes in life, and having acomplished them with astonishing success. These deliberate purposes made his career brilliant, and his character manly and sturdy. In the preface to "Ilios" (1880) Schliemann gives a sketch of his early life and his excavations which reads like a romance. Before he was ten years old, he had made up his mind that the mighty walls of Troy could not have entirely disappeared, but must have been only buried by the dust of ages, and that he would himself some day bring them to light. But a romantic boyhood ended in a bitter struggle with poverty, until at one time he had to sell his last coat, and after shipwreck arrived at Amsterdam a penniless outcast. Obtain ing there a post worth £32 a year, he spent the half of that sum on living, and the other half on self-education, his dinner costing him twopence, and a fire being an unknown luxury. By sheer business talent he rose from this poverty to great wealth; but this has been done by hundreds of uninteresting men: the interesting thing about Schliemann is that he never looked on wealth save a means for accomplishing his darling purposes. While never ceasing to pray that some day he might have the happiness of learning Greek, he began on modern languages, which he mastered one after another in an incredibly short space of time, learning not merely to read, but to write and speak fluently, Swedish, Polish, Russian, Arabic, and many other tongues. as In 1871, he began his career as an explorer by an attack on the hill of Hissarlik, where he expected to find the remains of the Troy of his early dreams. In the art of excavation he seems to have had no teacher, and there can be no doubt that he has opened a new era in that art through his scientific genius. Literary genius may be erratic and incalculable, but genius works in science through clear discernment of means and by infinite pains. Schliemann's method was simple-to remove all the earth of a site and pass it through a sieve, taking care that, though hundreds of hands were at work, every one worked as an immediate organ of his own intelligence and design. The quality of insight came in principally in the choice of sites. Splendid as were the results of Schliemann's excavations at Hissarlik, at Mycenæ, and at Tiryns, both as regards the recovery of antiquities, and as regards the advancement of knowledge, scholars recognize that he was not to be followed in his interpretation of his own discoveries. His individuality was too strongly marked, his imagination too fervent, to allow him to walk safely in the narrow ways of archæological science. And as a man who was born a fighter, and thoroughly carried out the old rule as to loving one's friends and hating one's enemies, he could not be impersonal in the choice of theories. To the judgment of his allies he often gave way with a delightful simplicity and modesty, but to attack he was impervious. One of his most interesting appearances in London was when he came in hot haste from Athens, accompanied by Dr. Dörpfeld, at the invitation of the Hellenic Society, to meet in open debate the objections, which he characteristically called “calumnies," which some archeologists had brought forward against his theory in regard to the prehistoric palace at Tiryns. Though Schliemann was a decided believer in Providence, there was in him an immense force of tough old Teutonic heathenism. 66 Yet he was a man of the world, and cosmopolitan in a sense in which few can claim to be so, for in almost any country he could have made himself at home as an active citizen. His ideal was Greece, and he succeeded in a very difficult task by finding in modern Greece the materials for a splendid ideal, when worked up with traditions of ancient glory. In this respect he was a greater poet than Byron, who spoke of some modern Greeks as craven crouching slaves." Athens has indeed good reason for the gratitude which has assigned him a public grave at Colonus. At Athens he will leave a great gap. His palace, reflecting in every corner his career and his enthusiasms, was a place where the most open hospitality was accorded to men of all nations. In the living-rooms were Homeric texts; the servants bore high-sounding Greek names; the basement rooms were full of the spoils of Troy; while on the summit stood replicas of celebrated Greek statues. The host poured forth the simplicity of his heart and the overflowings of his enthusiasm, talking with an unconventional plainness sometimes disconcerting to Western ladies. Not even Madame Schliemann, long as she has shared her husband's labours seen by various persons in the south-western part of the Government of Perm, and in the Government of Viatkaprincipally in the districts of Perm, Oschansk, Kungur, Osoo, and Sarapul. Between Perm and Oschansk, according to an inhabitant, it appeared about 12.30 p.m. in a clear sky, leaving behind it an almost horizontal train of great brilliancy. Detonations were heard, resembling a discharge of musketry rather than thunder. A little afterwards it fell in a shower of incandescent stones, which buried themselves more or less deeply in the earth. They were very numerous, and weighed from one to 330 kilogrammes. Fig. I represents the meteor as it was seen by M. Selivanof, a professor of the seminary of Perm. This observer writes: On August 18, a little before one o'clock p.m., I returned to the seminary. The weather was calm, and the sky covered with small fleecy clouds. Just as I was about to cross the threshold, I happened to look towards the south, and saw a brilliant body like a shooting-star, or, rather, like a piece of iron glowing at the forge, gliding from east to west in a direction almost horizontal or slightly inclined towards the earth. The meteor made scarcely more noise than a rocket, and at first I believed it was one. Its course was sufficiently rapid, and during two or three seconds I followed the bolide over the space of a small number of degrees. It left a luminous train, which was very rapidly extinguished. Perhaps this train resulted simply from the persistence of the luminous impression upon the retina. The case, however, was otherwise with a pale nebulous band, which persisted about five minutes." The majority of the meteorites brought by this fine meteor have certainly been lost. Only six of them have been found-five at Oschansk, one at Tabor. At the moment of the fall, M. Nagibine was in a street of Oschansk, and heard the noise which announced it. About half a minute after the cessation of this noise, he observed a blackish stone which hissed through the air as a cannon-ball might have done. Several workmen ran and found the meteorite at the bottom of a hole-about 50 centimetres deep-which it had hollowed in the ground. It was as large as a child's head, and was still hot; it weighed 1.790 kg. At Tabor the phenomenon was noticed by two peasants who were working in a field. Surprised by the detonations and the rumbling sound, they looked up, and saw the bolide, of a dark red colour, followed by a white smoke, which the wind agitated; and sending forth an odour of sulphur (Fig. 2). The mass seemed to be at a height of about 200 metres, and by the shock of its fall raised a column of dust. One of the peasants, who was mounted on a corn-rick, was thrown to the ground by the |