thing was wanting in their clearness. This instrument proves to be an excellent syren, and all the facts illustrated by the apparatus of Cagniard de la Tour and others can be equally illustrated by it. Moreover, it forms the basis of a new musical instrument which there has been no time as yet to mature. 18. In the hope of getting more perfect definition, another machine was now made upon which disks were fitted, whose peripheries were cut in exact copy of the curve produced by the synthetic curve machine. These curves were transmitted by vibration to the receiving diaphragm of a phonograph, and really formed an "automatic phonograph." The automatic phonograph consists of an axle A, fig. 9, about 6 inches long, one end of which carries a fly-wheel B, and the other end a grooved pulley C, round which a band or gut passes from a driving wheel D, fitted with a crank handle E. On rotating the driving wheel, the long axle is caused to make about three revolutions to one of the wheel. On the long axle are placed, in such a manner that they can easily be removed and replaced by others, a number of brass wheels or disks, a, a, a, a, the circumferences of which have been cut by a machine especially devised for that purpose into the different curves corresponding exactly to the curves obtained by the synthetic curve machine, but on a much reduced scale. A diaphragm G with spring and frame H, similar to that in a phonograph, is so fitted that it can be shifted from one disk to another, and the sounds produced by the different curves can be readily compared. The number of periods or resultant vibrations recurring on each wheel or disk has for convenience been taken at thirty. Thus, when the driving wheel is rotated about twice per second, 180 to 200 vibrations are caused, resulting in a note at f or g in the musical scale. A number of combinations of curves has been cut on the circumferences of the brass disks, representing each vowel sound with certain variations of the partials, as experience determined. These disks were then placed on the axle, and the sounds most resembling the vowel sounds of the human voice were easily recognised. 19. In this way it was found that from about f to b in the musical scale, the sound oo consists mainly of the first partial or prime. But to maintain the oo character descending the scale, the second and third partials became slightly necessary. 20. The prominent partial in the vowel sound O at the same pitch is the second, while the first can be reduced considerably. The third and fourth partials have to be used as the sound descends the scale, otherwise what is O at say b flat, will become oo an octave lower. 21. The vowel sound ah is the easiest to reproduce. It consists chiefly of the third, fourth, fifth, and sixth partials at the above pitch, the first and second partials being only slightly represented. A little more prominence to the second, third, and fourth partials will result in aw, while a bright ah is obtained by increasing the amplitude of the fifth and sixth partials. 22. A very good and full ah is obtained by having all the partials equally represented, from the first to the eighth; and this really probably takes place when the human voice pronounces this vowel, as, in so doing, the mouth cavity is fully opened, so as to favour most of the partials. 23. The vowel sounds à and ee, when reproduced by most of the ordinary phonographs, resemble respectively more o and oo. Also the curves for a and ee, obtained by the phonautograph, fig. 2, resemble those for o and oo. This shows, in the first instance, that neither instrument is sensitive to the higher upper partials; and, secondly, that the lower partials for a must be similar to those in O, and the lower partials for ee must be the same as in oo. To prove this, two disks were cut, one with a curve composed of the first, second, and eighth partials, and the other of the first, third, and eighth partials. The former, when sounded, produced a sound like ee, and the latter more like a. 24. The best ee has been obtained from a curve composed of the best first, second, eighth, and sixteenth partials; and a from a curve composed of the first, third, and sixth or eighth partials; but this last curve can hardly be called satisfactory. 25. Diagram 10 graphically illustrates the above facts, and the following table gives them in a tabulated form : Hence, although the reproduction of vowels was good, it was imperfect. This is due probably to the absolute impossibility of reproducing the noises that accompany the last two vowels. 26. One very curions result arising from the experiments with the automatic phonograph was to show that, by varying the pitch, the vowel sounds could be shifted, i.e., the curve which produced oo at a low velocity becomes approximately O at a higher velocity. O similarly becomes ah, ah becomes a, and ā, ēē. 27. It follows from this investigation as far as it has gone, that our knowledge of vowel sounds is not perfect. The principal proof of this is the fact that vowels cannot be reproduced exactly by mechanical means. Something is always missing-probably the noises due to the rush of air through the teeth, and against the tongue and lips. 28. The curves (fig. 10) arrived at synthetically do not differ very materially from those arrived at analytically by Helmholtz (fig. 6). They principally differ in the prominence of the prime. But the prime can be dispensed with altogether. Curves produced by the synthetic machine, compounded of the different partials without their prime, show that there exist beats or resultant sounds. A vowel sound of the pitch of the prime may be produced by certain partials alone, without sounding the prime at all. The beat in fact becomes the prime. This point is clearly illustrated, orally, by the automatic phonograph, and graphically by the sketch (fig. 11), drawn by the synthetic curve machine. In fact, every two partials of numbers indivisible by any common multiple, if sounded alone, reproduce by their beats the prime itself. Thus, the third and the fifth partials, or the second and the third, &c., will result in the reproduction of the prime. In fact, fig. 11 illustrates not only this, but it shows that when the number of partials introduced is increased, the beats become more and more pronounced. II.-The Loudness of Sound. 29. Another point remaining for investigation arising out of this inquiry, is the true theory of the loudness of sound. It is thought by the authors that loudness does not depend upon amplitude of vibration only, but also upon the quantity of air put into vibration; and, therefore, there exists an absolutely physical magnitude in acoustics analogous to that of quantity of electricity or quantity of heat, and which may be called the quantity of sound. This can be shown experimentally by constructing three disks like those in fig. 1, whose diameters increase in arithmetical ratio. When these disks are vibrated by the same curve by the automatic phonograph, or when they are thrown into vibration by tuning forks, it will be found that the intensity of sound increases in a surprising ratio. The amplitude remains just the same; the area under vibration alone increases. Thus, in the automatic phonograph, for two notes, one of which is an octave higher than the other, the area ought probably to be diminished one-half for the higher to produce equal loudness. Similarly for the same note, if we increase the area to be vibrated in its reproduction, it will be found that, as the area increases, so does the loudness of the sound emitted. In fact, in the automatic phonograph the diameter of the sounding disk ought, if it were possible, to vary with the pitch of each note, to produce equal intensity of sound. The authors are now engaged in pursuing this inquiry into the consonantal sounds. II. "On the Reversal of the Lines of Metallic Vapours." No. V. By G. D. LIVEING, M.A., Professor of Chemistry, and J. Dewar, M.A., F.R.S., Jacksonian Professor, University of Cambridge. Received February 20, 1879. Since our last communication we have continued our experiments, using the electric arc as a source of heat, in lime and in carbon crucibles as described before. Success depends on the getting a good stream of vapour in the tubular part of the crucible. This is easily attained in the lime crucibles, which quickly reach a very high temperature, but are very soon destroyed; not so certainly in the carbon crucibles, which are good conductors of heat. The latter, however, last for a very long time. In our experiments with tubes heated in a furnace we used a small spectroscope with a single prism, which gave a good definition and plenty of light; but in the experiments here described we have used a larger spectroscope by Browning, with two prisms of 60° and one of 45°, taking readings on a graduated circle instead of on a reflected scale. Both in the lime and in the carbon crucibles we have found that the finely channelled spectrum, extending with great uniformity from end to end, always made its appearance so long as the poles were close together. A few groups of bright lines appear on it. We have not at present investigated this remarkable spectrum further. In several cases we have observed the absorption lines of the metals put into the crucibles on this channelled spectrum as a background, but generally when the vapours in the crucibles become considerable, the channellings give place to a spectrum of bright lines on a much less bright continuous background; we have used generally thirty cells in the galvanic battery, sometimes only twenty-five, once forty. The calcium line with wave-length 4,226 almost always appears more or less expanded with a dark line in the middle, both in the lime crucibles and in carbon crucibles into which some lime has been introduced; the remaining bright lines of calcium are also frequently seen in the like condition, but sometimes the dark line appears in the middle of K (the more refrangible of Fraunhofer's lines H), when there is none in the middle of H. On throwing some aluminium filings into the crucible, the line 4,226 appears as a broad dark band, and both H and K as well as the two aluminium lines between them appear for a second as dark bands on a continuous background. Soon they appear as bright bands with dark middles; gradually the dark line disappears from H, and afterwards from K, VOL. XXVIII. 2 D while the aluminium lines remain with dark middles for a long time. When a mixture of lime and potassium carbonate (to produce a stronger current of vapour in the tube) was introduced into a carbon crucible the calcium (?) line with wave-length 4,095 was seen strongly reversed, and the group of three lines with wave-lengths 4,425, 4,434, and 4,454 were all reversed, the least refrangible being the most strongly reversed, and remaining so the longest, while the most refrangible was least strongly reversed and for the shortest time. Besides these reversals, which were regularly observed, the following were noticed by us as occurring in lime crucibles but with less certainty, perhaps only at the highest temperatures. Dark bands appearing for a short time and dwindling into sharp dark lines with wave-lengths about 6,040 and 6,068 (perhaps due to the oxide); a dark line replacing the most refrangible of a well-marked group of several bright lines with wave-length 5,581 (or possibly the brighter line 5,588); and the lines with wave-lengths 6,121 and 6,161 reversed simultaneously for an instant and reappearing bright immediately; and the line with wave-length 5,188 reversed. When aluminium was put into the crucible only the two lines of that metal between H and K were seen reversed. The lines at the red end remained steadily bright. When some magnesium was put into a lime crucible, the b group expanded a little without appearing reversed, but when some aluminium was added, the least refrangible of the three lines appeared with a dark middle, and on adding more magnesium the second line put on the same appearance; and lastly, the most refrangible was reversed in like manner. The least refrangible of the three remained reversed for some time; and the order of reversibility of the group is the inverse of that of refrangibility. Of the other magnesium lines, that in the yellowish-green (wave-length 5,527) was much expanded, the blue line (wave-length 4,703), and a line still more refrangible than the hitherto recorded lines, with wave-length 4,354, was still more expanded each time that magnesium was added. These last two lines expanded much more on their less refrangible than on their more refrangible sides, and were not seen reversed. The bright blue line (wave-length 4,481) seen when the spark is used, was not visible either bright or reversed; and this seems to be in agreement with Capron's photographs, which show this line very strong with the spark but not with the arc. The following experiments were made in carbon crucibles: When strontia was put in the lines with wave-lengths 4,607, 4,215 and 4,079 were all seen with dark lines in the middle, but no reversal of strontium line less refrangible could be seen. any After adding some aluminium and some potassium carbonate to increase the current of vapour, no reversal of any strontium red line could be detected, though momentary cloudy dark bands were seen in the red when |