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FIG. 1.-Resultant curves formed by compounding together the wave-for ns of a har.non.c series of simple tones of equal intensity but differing in phase.

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F G. 2.-Resultant wave-form for odd members of series of upper partial tones when there is no difference of phase.

In the second of the row, each of the separate component waves begins with a negative ordinate of maximum amplitude, or differing in phase by one quarter from the first case. In the third the difference is half a

wave-length, and in the fourth case three-quarters of a wave-length. It will be noticed how very different these curves are to the eye, though compounded of the same elements. It will also be observed that the curves for

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difference of phase is a reversed copy of that for which the difference of phase = 0; while the curves for phase-difference and are reversed copies of one another. Now, according to Helmholtz's theory. all these forms of vibration should yield identical sounds in the ear. Koenig finds, on the contrary, the startling result that the sounds are perceptibly different in quality. His proof is extremely simple. The curve, calculated graphically with great care, is set off upon the circumference of a cylindrical band of thin metal, the edge being then cut

away leaving the shaded portion, the curve being repeated half a dozen times, and meeting itself after passing round the circumference. For convenience the four curves to be compared are set out upon separate rims of metal, all of which are mounted upon one axis to which a rapid motion of rotation can be imparted. Against the indented edges of these rims wind can be blown through an appropriate slit; the whole combination forming a variety of the Wave-Siren described a few months ago in the columns of NATURE (p. 358, vol. xxiv.). It will be

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FIG. 3.-Resultant wave-form for old members of series of upper partial tones when the difference of phase is a . obvious that as these indented curves pass in front of the slit the maximum condensation will result when the slit is least covered, or when the point of greatest depression of the curve crosses the front of the slit. The negative ordinates of the curves correspond therefore to condensations, the positive ordinates to rarefactions. Now, according to Koenig's experiment, the sound is louder and more forcible, with a difference of phase of, than in any other case, that with difference being the most gentle and soft in tone; whilst the curves of phase

o and yield intermediate qualities of tone. Koenig also finds that by combining simply a note and its octave, the loudest resultant sound occurs when the phase of combination is, a difference of phase of again yielding the feeblest resultant. In Fig. 1, b, four curves are shown corresponding to the combination of the odd members, 1, 3, 5, 7, 9, of the harmonic series, taken as before as of equai intensity. In this case the form of the waves is identical for the phases o and and also for the phases and . The latter yield a loud and strident tone as com

pared with the former, though according to Helmholtz's theory their tones should be alike. It may be objected to these illustrations that in all natural sources of tone one never finds a whole series of partial tones every member of which is equally loud as the fundamental tone. It is more nearly true for most musical instruments that the higher up one goes in the series of partial tones the feebler are they in comparison with the fundamental

tone.

Accordingly, Koenig has combined, as in Fig. 2, a series of partial tones corresponding to the respective frequencies 1, 3, 5, 7, 9, making the amplitude of each partial tone inversely proportional to its frequency. The separate curves are shown in Fig. 2, both grouped about a horizontal line, and also as successively superposed upon the fundamental. The uppermost of the set of curves exhibits the final resultant; which, in this case, where the difference of phase is taken as nil, and all the components rise from zero together, is seen to consist of bold, wellrounded sinuosities. In Fig. 3, curves identical in wavelength and amplitude, but differing in phase by, are compounded together; but the final resultant shows a wave-form that is practically a zig-zag. Now if these bold sinuosities and zig-zags be cut out in thin metal and curled up into circumferences so as to adapt them to use as wave-sirens in the manner before-mentioned, it is again found that the zig-zags corresponding to differences of phase and yield always harsher and louder tones than the rounded sinuosities that correspond to o and

These observations are very remarkable, and have important bearings that must be left for discussion in the next article on Koenig's work.

For the present we will conclude by observing that more than once it has been pointed out that a certain perception of difference of phase did exist. Sir W. Thomson has suggested that there is evidence of this in the phenomenon of slow beats which by a curious acoustic illusion almost always suggest the idea of something revolving. The writer of this notice had also previously pointed out that in certain cases where a compound sound was led separately to the two ears a difference of phase between the components could be detected.

It may not be generally known that Dr. Koenig has quite recently republished under the title of "Quelques Expériences d'Acoustique" the most important of his recent researches, including those on the Wave-Siren and on the Beats of Imperfect Consonances. The figures herewith presented, and those which will accompany the continuation of this notice, are taken by Dr. Koenig's courteous permission from this his very valuable contribution to experimental acoustics. S. P. T.

THE RAINFALL OF THE GLOBE

PROF. LOOMIS has recently contributed a paper on this subject to the American Journal of Science of no small interest and value. The paper gives the mean annual rainfall at 713 places in all parts of the globe, and the results are graphically represented on a map of the world as closely as can be done by five tints of one colour. These tints represent respectively annual amounts of rain under 10 inches, from 10 to 25 inches, 25 to 50 inches, 50 to 75 inches, and above 75 inches. It is stated that the map is merely a provisional one, it being Prof. Loomis's expressed intention to publish a list of additional observations with a revised edition of the map; and in the meantime he invites the assistance and criticism of meteorologists in furtherance of the work.

The map shows unquestionably the broad features of the geographical distribution of the rainfall of the globe, so that any changes that will be made in a future issue, however interesting and important these may be locally, will only be rectifications of the iso-hyetal lines in some of their subordinate details.

Leaving out of consideration all exceptionally heavy rainfalls confined to limited spots, such as those of Cherapunji, in Assam, which amounts to 492 inches annually, and the Stye, in Cumberland, which is about 190 inches, the heaviest rainfall is met with in the rain-belt, which surrounds nearly the whole globe lying between the northeast and south-east trade-winds. Absolutely the largest rainfalls over large regions are to be found where the trade-winds, after having traversed a great breadth of ocean, are forced against and over a breadth of land, of some elevation and extent which lie across their path. Of these the best examples are the highlands of Java, Sumatra, and Assam, in the Old World, and parts of the north of South America, and of the steep slopes of Mexico facing the Gulf of Mexico in the New World, over which the trades or monsoons discharge their moisture so copiously as to raise the rainfall over large tracts up to, and in cases considerably above 200 inches annually. influence of height is well illustrated by the rainfall of Mauritius; thus, while at the observatory it is 46 inches, it amounts at Cluny to 149 inches on a mean of the same 19 years. Similarly in St. Helena, while near the sealevel it is only 5 inches, at a height of 1764 feet it is 48 inches. In Ascension, no part of which rises to any considerable height, the annual rainfall is only 3 inches, and the whole island is little else than a burned-up desert.

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The rainfall is particularly large in mountainous regions in both hemispheres above lat 40°, situated on the eastern shores of the great oceans, and consequently in the full sweep of the strong westerly winds of these high latitudes. Thus large portions of Scotland north of the Clyde, one or two small patches in England, a few spots in Ireland, large tracts between California and Alaska, the south of Chile, and the west coast of the south island of New Zealand have an annual rainfall exceeding 80 inches. Nay, even at Bergen, lat. 60° 23′ N., bathed in the warm, moist, westerly winds of the Atlantic, the rainfall is 73 inches annually, which is the largest rainfall yet observed anywhere at so high a latitude. Those headlands, even though of comparatively small height, which ran out into the sea, meeting the moist oceanic winds, have rainfalls very considerably above the average-owing doubtless largely to the greater friction of land than water on the winds, thus partially arresting their progress, and inducing a more copious precipitation.

As causes of deficient rainfall, Prof. Loomis enumerates five, viz.: (1) a uniform direction of the winds during the year, such as prevails within the regions of the trades. illustrated by the rainfall of Ascension, Sahara, and South California; (2) the prevailing wind having crossed a mountain range, thence descends on the leeside, illustrated by desert of Gobi, Chili, and large tracts in Spain; (3) ranges of mountains so high as to obstruct the free movement of the surface-winds towards the interior, as parts of Central Asia and California; (4) remoteness from the ocean measured in the direction from which the wind proceeds, illustrated by the gradual diminution of the rainfall on advancing eastward into Europe; and (5) high latitudes, since beyond lat. 60°, at a little distance from the ocean, it seldom exceeds 10 inches, and there are apparently large tracts in North America and Asia, where the rainfall is less than 10 inches. As regards this last statement, observation scarcely bears it out, since in Europeo-Asiatic continent, only two stations in latitude the above 60°, viz. Kola in Russian Finland, on the Arctic Sea, and Yakutsk, show rainfalls less than 10 inches, and these are doubtful owing to the short periods over which the observations extend.

The truth is there are other causes powerfully influencing the distribution of the rainfall than these, which an examination of the rainfall of the individual months, notably January and July, best discloses. These causes have their explanation in the systems of low and high pressures, which appear and disappear with season. Of these the most

prominent are the low pressures which occupy the centres of continents in the summer months, and the northern portions of the Atlantic and Pacific Oceans in the winter months; and on the other hand, the high pressures which fill the centres of the continents in the winter months, and the high pressures in the oceans immediately to the west sides of the great continents, about lat. 36°, as shown by the Admiralty's physical charts of the Atlantic, Pacific, and Indian Oceans.

To take, as an example, the great summer barometric depression of Central Asia with the winds, flowing in upon it on all sides vortically, carrying with them the moisture of the ocean from which they come. Thus East Siberia is then swept by south-east and east winds, which distribute to westward as far as Irkutsk, in July, a monthly rainfall of 3 inches and upwards. Now since the annual rainfall of this region is all but wholly determined by the rains of the summer months, the extension of these rains inland wholly determines the position of the annual iso-hyetal lines. Again, to westward of long. 100° in Siberia, the rains have their origin in the Atlantic and Arctic seas, and since west and north-west winds prevail from Archangel to Central Asia, they bring with them comparatively so large a share of moisture from the ocean, as to raise the annual rainfall over the greater part of these northern regions to about 20 inches, or even more. On the other hand, on the east side of the Ural Mountains, which drain these winds of much of their moisture, the summer rainfall is much less. From north of the Caspian and Aral Seas, southward to the Persian Gulf, and eastward to the Indus, the summer winds are north-west, and since they thus advance over regions rapidly rising in temperature, little if any moisture is deposited in their train, thus rendering this extensive region one of the largest arid tracts of the globe.

These, with other considerations, indicate that the courses of several of the iso-hyetal lines, where observations are sparse, should be regulated to a greater extent than has been done in the map before us, by the positions of river-basins and mountain ranges in their relations to those seasonal winds, which really determine the annual amounts of the rainfall.

One of the most important points to which attention is drawn by Prof. Loomis, is that more rain falls on the eastern than on the western sides of continents. This remark holds good everywhere, until we reach the higher latitudes of both hemispheres, where the predominating winds become westerly. Thus the rainfall at San Francisco is only from a half to a third of the amount which falls on the coast of Pennsylvania in the same latitude; and about the same proportions, or even proportions still more striking, are seen on comparing Morocco with the Chinese coast, and the west with the east coasts of South Africa, Australia, and South America. The explanation is to be found in the portions of the areas of low and high pressures, with their accompanying winds, during the season whose rainfall determines the annual amounts. On the east side of the continents the prevailing summer winds are south-west, south, or south-east, which having traversed a large extent of ocean, and constantly advancing into higher and colder latitudes, spread a copious rainfall over the regions they traverse. But on the other hand, since the west side of continents in the same latitude lies between the region of abnormally high pressure in the ocean immediately to westward, and the low pressure of the interior, north-west winds in the northern, and south-west winds in the southern hemisphere prevail there; and as they advance into lower latitudes or over regions of a constantly increasing temperature, they deposit little or no rain in their course. Hence, owing to the failure, more or less complete, of the summer rains, it follows that the annual rainfall of these portions of the continents is small.

In preparing the second issue of the map, attention should be directed, in addition to the regions already

indicated, to the rectification of the lines of equal rainfall over Iceland, the south-east of Norway, the Gulf of Guinea, the temperate regions of South America, and Northern, Central, and Western Australia, and we feel assured meteorologists will heartily co-operate with Prof. Loomis, and give him all possible assistance in completing the important work he has so successfully begun.

NOTES

THE name of Prince Leopold (Duke of Albany) has been added to the General Committee of the Darwin Memorial Fund, subscriptions to which, we may remind our readers, are still being received at the Royal Society, Burlington House, by the Hon. Secretaries, Prof. T. G. Bonney and Mr. P. Edward Dove.

THE communication from Greenwich which appeared in our last number, p. 175, showed that in the double magnetic storms of April, the Greenwich times of commencement of disturbance were, for Greenwich, April 16, 11h. 32m., and April 19, 15h. 35m.; and for Toronto, Canada, April 16, 11h. 34m., and April 19, 15b. 34m. The communication in question was followed by one from M. Dechevrens, reporting the magnetic disturbance as commencing suddenly also at Zi-ka-wei, China, at 7h. 36m. on the morning of April 17, and as being as suddenly renewed at 11h. 40m. on the morning of April 20; equivalent to April 16-11h. 30m., and April 19, 15h. 34m. Greenwich time. The outbursts thus occurred at the same absolute time at Toronto, Greenwich, and Zi-ka-wei.

THE Prince and Princess of Wales opened the handsome new Technical School at Bradford on Friday. The Prince, in the various speeches he gave showed that he has a real appreciation of the necessity for scientific training in this country, if we are to keep on a level with the other great nations in our industry and commerce.

THE Commission appointed by M. Ferry to report on the construction of the rotating dome for the large refractor of the Paris Observatory, has held numerous meetings at the Conservatoire des Arts et Métiers, Col. Laussedat, director of the establishment, being in the chair. Only two projects have been reserved for final choice. M. Eiffel proposes to use a saline diminish the weight of the rotary roof. solution in a horizontal circular channel placed on the wall to

WE are glad to learn that owing to the exertions of Admiral Mouchez, magnetical observations will soon be resumed at the Paris Observatory, in subterranean chambers which have been excavated in the newly annexed grounds. These observations will be self-registering by photography, in conformity with the instruments established by M. Mascart at the Collège de France. Direct observations will also be conducted with the old instruments which were used by Arago, which were famous for his prognostications of Aurora, at a period when, the electric telegraph not having been invented, many days must elapse before the arrival in Paris of news from the northern parts of Europe.

IN the course of a few weeks all the International circumpolar observatory parties will have arrived at their different destinations, or be on their way thereto, and on August I the observations will commence simultaneously on the common plan framed by the different conferences held in Hamburg in 1879, in Bern in 1880, and in St. Petersburg in 1881. By the present arrangement Russia has three stations, the United States and Germany two each, whilst England, Austria, Sweden, Norway, Denmark, France, Holland, Italy, and Finland maintain one each, of which three-the French, the Italian, and one German will be established in the Antarctic regions. The total number

of stations will thus be sixteen, with a complement of some 150 men. The work will be carried on continuously for thirteen months, and the expeditions will leave their quarters on September 1, 1883. On their return an International Conference will assemble-it is suggested in London-in order to examine the material collected, which will, it is hoped, give important results, particularly as regards meteorology.

"LA LAMPE SOLEIL," or the sun lamp as it is called, from the likeness of its rays to solar light, was successfully tried on Saturday last in the vaults of the Royal Exchange. This lamp is the invention of MM. Clerc and Bureau of Brussels, and is so simple in its action as to require no regulating mechanism. It consists of a square block of marble or dry limestone, having two holes pierced into it from above. The holes slant together until they nearly meet just within the base of the block. Into these holes are inserted the two carbon rods forming the poles of the arc, and the current traversing the partition of calcareous stone between their points heats it to incandescence, and thus a soft white light is emitted from the bottom of the block. This light is remarkably steady, and is very suitable for picture galgalleries. It was used to light the picture gallery in the recent Paris Electrical Exhibition, and is now employed in the foyer of the Grand Opera House, Paris. The limestone is calcined by the current, and the carbons feed themselves by gravity as they are consumed. The ugly shape of the lamp is certainly against its use, unless it be sufficiently well screened from view, but its simplicity is decidedly in its favour.

THE new Report (1880) of the Smithsonian Institution contains among other valuable material, a Bibliography of Sir W. Herschel's writings, a list of his published portraits, and a long and very careful synopsis of his scientific writings. This last occupies nearly 100 pages, and its value to the student is evident. Appended there is a subject-index to the scientific writings of Herschel. The same volume contains the first results of the attempt of the Institute to issue a yearly report of the work done at observatories all the world over; the report covers upwards of 100 pages.

Of the Smithsonian Report, upwards of 200 pages are occupied with a Record of Recent Scientific Progress, in which Prof. Baird writes the Introduction, Prof. Holden, Astronomy, Dr. G. W. Hawes, Geology and Mineralogy, Prof. G. F. Barker, Physics and Chemistry, Prof. Barlow, Botany, Prof. Theodore Gill, Zoology, and Mr. O. T. Mason, Anthropology. Mr. Mason also contributes a separate Bibliography of Anthropology, in which (p. 412) we find the following curious entry—“ Vikin's (A.) ship."

ON the recommendation of the Agricultural Chamber in Stockholm the Swedish Government has accepted the invitation to participate in the International Fishery Exhibition to be held in London next year, and granted a sum of about 3c00l. towards the expenses of representation. The Norwegian Government has also accepted the invitation, and a small sum has been voted by the Storthing.

AT a recent meeting of the Smoke Abatement Committee, held at 44, Berners Street, Mr. Ernest Hart in the chair, jurors' reports were handed in from Col. Festing, C. B., Prof. Chandler Roberts, F.R.S., Mr. Atchison, Mr. D. Kinnear Clark, Mr. Harris, and others, on behalf of the various juries, discussing the results obtained and tabulating the figures shown by the various tests. Great satisfaction was expressed at the excellent results which these reports show to have been achieved by some of the leading exhibits in the economy of fuel and abatement of smoke in open grates, as well as the satisfactory action of open grates and kitcheners intended for burning anthracite or smokeless coal. The hon. secretary (Mr. W. R. E. Coles) announced

that the Manchester Exhibition of Smoke-Abating Apparatus, carried out partly under the auspices of this Society, had proved highly successful, and had attracted great interest among the practical men in the Lancashire district, and would, it was believed, be fruitful in good results. The arrangements were discussed for converting this committee into a permanent institution for smoke abatement, under the provisions of the law. It was announced that the Duke of Westminster would preside at a meeting to be held at Grosvenor House on Friday, July 14, for the purpose of distributing the awards, when it was expected that all the reports and tabulations would be ready in the form of a volume for public information.

THE President of the Italian Antarctic Expedition has received, at Genoa, a letter from Lieut. Bove, announcing the arrival of the expedition at Punta Arenas, on April 24 from Staten Island. Staten Island has been thoroughly examined as to its fauna, flora, topography, hydrography, and commercial utility.

THE Hope, commanded by Sir Allen Young, left the Thames last week to search for and succour the Eira, under Mr. Leigh Smith, missing in the Arctic regions for about a year. The Hope is 450 tons register, is fortified for ice work, well equipped, and with provisions for two years, and a year's supply

for the Eira. Sir Allen, while he will doubtless use his discretion, has been instructed to avoid entering the ice, if possible. It has certainly been a peculiar Arctic season, so far as ice condition are concerned, and Sir Allen may find when he gets on the ground that all his calculations and arrangements are at fault.

MR. C. HOLCOTT BROOKS, Secretary of the Californian Academy of Sciences, sends us the following note on a meteor in Wyoming, which he states is "well authenticated in all respects." "May 11, at 4 p.m., in Weber Cañon, Wyoming Territory, while the sun was shining brightly, a sudden and steady glow in the sky attracted attention to an immense meteor, whose brilliant colours were beautiful beyond description. Its track across the heavens was marked by a large red belt, which after its brightness had died out, left a column of clearly defined white smoke in its place. It fell in a south-easterly direction, and was observed by a scientist who recently arrived in this city, and who attended the meeting of the California Academy of Sciences last evening."

NEW seismic apparatus for indication of earthquake-motions on Etna have been devised by the brothers Brassart, at the instance of Prof. Tacchini. From an illustrated account in the Rivista Scientifica Industriale, we gather that the indicator for undulatory shocks is in form as follows: a funnel grooved interiorly (and looking like a small inverted umbrella) is fixed at one end of a pivoted horizontal bar having a counterpoise; it has an aperture at the bottom, which allows of its oscillating a little way with the bar on a vertical column, on which is placed a vertical style with weight at top (this latter act being facilitated by a sliding brass tube). This weight, by its fall (contrary to the direction whence the shock comes), into one of the eight lettered grooves of the funnel (N, E, &c.), indicates the direction, and, depressing the bar, closes a circuit, making an electro-magnet, the result being that the pendulum of a small clock on the base-board is liberated. Thus if the clock had been set at 12, and it indicated 5 when looked at, this would show that the liberating shock had occurred five hours before. An electric bell may be introduced; also the liberation of the pendulum may be effected without electricity. In an arrange ment for vertical shocks, a spiral of fine wire, with platinatipped weight, is suspended vertically over a cup of mercury;

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