There is every probability that Mr. Vischer is mistaken in his guess that the sounds are made by the blowing of the wind through a crevice in the rock, as will be seen by a general consideration of the subject, before I attempt to set forth the probable scientific explanation of the phenomenon. It is not confined by any means to the Sahara, or for that matter to desert places.

Near the coast of one of the Hawaiian Islands is an old graveyard. The winds blow ceaselessly across its barren expanse and it is fast being buried by coral sands. Passing fisher boats give this shore a wide berth, for when the wind is right, there arises from the white expanse a strange wail, like the howl of a dog, which is attributed to the restless spirits of the departed.

On the coast of Lower California, there is a locality which emits, at times, a bell-like sound. Here too the winds have piled up fine sand, and the peons declare that under its mounds lie buried the ruins of a convent, the bells of which toll with muffled tones, at the hour of prayer.

The infrequent traveler in the region of Mt. Sinai, camping at the mouth of the Wady el Dér, sometimes hears at sunset, a deep musical, booming sound, descending from the heights above. It is the great wooden gong of a monastery, perched upon the cliff. Such a gong is common in Arabia and is named a "Nagous." On the borders of the Isthmus of Suez stands a hill known as "Jebel Nagous"; that is, the Mountain of the Gong. The Arabs tell of weird sounds heard at this mountain-in storms, loud and wild, audible from a distance; in more quiet weather, low and musical. Jebel Nagous is alluded to in the "Arabian Nights." The American scientist, the late Dr. H. Carrington Bolton, some years before his death, organized an expedition to visit the mountain. After four days' journey from Tor, they went into camp at the base of the hill, which was found to be about 950 feet high. Dr. Bolton heard the music-a song of several notes, rising and falling, with one continuous deep undertone, like an organ note, and was able to ascertain the cause. Here, as in the

other places named above, it is due to singing sands. The winds continuously blow this sand up against the sides of the hill, and impelled by the wind, it rushes up the slopes, emitting a multitude of tiny, tinkling notes, which when combined, make a considerable volume of sound. Then, just as the waves of the sea driven up the beach, rush downwards again, so the sand blown up the steep incline continually slides back, the angle of rest being about. thirty-one degrees. It is the returning flow that gives out the steady undertone, increased by the echo from a sandstone cliff, and varying with the ever-changing wind.

What are singing sands? Every one has noticed the musical note made by the runners of a sleigh on a cold, clear night, which is caused by the impact of the snow or ice particles upon each other under the pressure of the vehicle. No ear could detect the sound made by two ice crystals, but when this is multiplied a thousand-fold, the combined effect is that of an instrument of music, playing one rather shrill note. Something of the kind is observed on parts of many sea beaches or other sand deposits; when they are walked upon, they give forth a note which varies with the locality. Ordinary "singing beaches" or or "musical sands" are rather common, and the phenomenon has often been described and scientifically studied. The sounds are usually like the musical note which may be evoked when the wetted finger is rubbed around the edge of a glass bowl. Up to 1908, seventy-four localities had been noted in this country and eighteen abroad. In spite of this study, the true cause of the phenomenon is not yet certainly understood. It does not seem to make any difference whether the sands have been formed from crystalline or amorphous rocks. They differ widely in different localities in their mineralogical constituents, yet on the same beach, one place will give out a sound when disturbed, while another, a few yards away, is silent though apparently identical in structure. The property may be quickly lost or may be retained for months. When the sand is kept in a paper bag, its quality is best preserved; shaking in a

tin or glass receptacle quickly dissipates it; once lost, it can not be restored. Observers have been able to detect the sound from a New England beach sand over 400 feet away, when a small bagful is suddenly shaken.

While the analogy to the snow crystals may account for part of the phenomenon in some cases, it can not account for the singing of limestone, coral or other non-crystalline sands. Moreover, when one walks barefooted on musical sands, or runs the hand through them, there is felt a distinct tingling sensation. To some, this has suggested an electrical property. The latest and most plausible theory is that upon clean, dry sands, atmospheric gases condense, just as gases will adhere to particles of some metallic minerals and not others, and that the sounds and the sensations described are due to the disturbance of these air cushions. At any rate, the sensation experienced when walking barefoot through a patch of musical sand is very similar to that felt when the hand is immersed in a solution in which nascent oxygen is being generated.

By the way, I wonder if it has ever occurred to any archeologist that a possible explanation of the "Vocal Memnon" which Strabo and other travelers attested some two thousand years ago, might be the presence near the colossi, of musical sands, long since buried by the drift from the Libyan Desert.

ALBERT R. LEDOUX

MODERN INTERPRETATIONS OF

DIFFERENTIALS

TO THE EDITOR OF SCIENCE: Professor E. V. Huntington, in an article entitled "Modern Interpretation of Differentials" (SCIENCE, March 26), states with reference to the definition lim Ay=0, lim N▲y=dy, that, “The inevitable consequence of such a definition is that dy = 0, which is futile." Every school boy in the theory of limits knows that this is not true when N varies.

To take his figure of a graph of a function y= f(x), it is logically correct to denote a point on the graph by P(x, y) without subscripts, and P(x+▲x, y + Ay) is any other point on the graph, where PQ = ▲x, QP' =▲y.

Professor Huntington asserts that S′(x+ A'x, y+A'y) inevitably approaches coincidence with P(x, y) when Ax, Ay, approach zero, although it is obvious that it may, if N increase appropriately, approach any chosen point S(x+dx, y+dy) on the tangent at P(x, y), so that lim A'xdx, lim A'y=dy. Variation in the first ratio is therefore upon the tangent.

Professor Huntington should also have investigated the historical questions involved before venturing to assert that the above theory of differentials would prove highly misleading to the modern student." It is a sad commentary on the present state of the calculus in respect to its fundamental ideas, when we note the variety of explanations of these ideas by authors with little historical knowledge, all of whom, no doubt, would term their productions "modern," though most explanations will be found to date back several centuries, if they be anything more than vaporizing.

Sir William Rowan Hamilton in his Elements of Quaternions (Bk. III., p. 392) states that ordinary definitions by derivative methods do not apply in quaternions, and that after a careful examination of the Principia, he would formulate and adopt Newton's definition as follows:

Simullaneous Differentials (or Corresponding Fluxions) are Limits of Equimultiples of Simultaneous and Decreasing Differences.

As we have seen, Newton also made this definition in "Quadrature of Curves," essentially as Hamilton gathered it from the "Principia." Many better mathematicians than myself, or than Professor Huntington, have, in fact, examined this definition carefully, and have found it to be rigorous, simple, and of great generality.

The infinitesimal method of Leibniz is to be found essentially in Newton's first tract De analysi per aequationen .," which Newton himself later rejected as illogical. A third method of explanation is that of Lagrange, which consists in assuming (for independent variables), dx = Ax, dy = Ay, and for a dependent variable z dz= principle part of Az, which Lagrange proposed to determine as the terms of first degree in the expansion of z+Az in ascending powers of Ax, Ay. Newton's dz is the same, if we put dx Ax, dy: Ay. The adoption of the derivative method, led to devices to obtain the same significance of dz by derivatives, without assuming expansions in series. These involve various logical difficulties, especially when there are several independent variables. Also the differentials appear to change their values by changing the independent variables, whereas, Newton's method shows that for every equation between the variables, there exists (if differentiation be possible) a definite corresponding equation between their differentials, irrespective of the choice of independent variables. Unquestionably, there has been a long continued propaganda, fostered at bottom to protect the claims of Leibniz, and aided by the inertia of established usage, to keep the methods of Newton in abeyance. Imagine, if the nationalities of these men had been reversed, the number of pamphlets that would have exploited the matter, and the number of textbooks in that method which would years ago have been published.

ARTHUR S. HATHAWAY ROSE POLYTECHNIC INSTITUTE

CARBON DIOXIDE AND INCREASED CROP
PRODUCTION

TO THE EDITOR OF SCIENCE: In 1912, at the International Congress of Chemists held in New York, Professor Ciamician, of the University of Bologna, presented a paper on the "Photochemistry of the Future," in which, among other things, the suggestion was made that crop production might be increased by increasing the concentration of carbon dioxide in the air. Of course, the idea underlying such a suggestion is that since the carbon dioxide of the air is a necessary constituent in the synthesis of carbohydrate by the plant, and since, furthermore, the percentage of the gas in the air is comparatively small, any increase in the amount of carbon dioxide may tend to increase the amount of carbohydrate produced.

That such is actually the case has been found by a number of German chemists, according to the Berlin correspondent of the N. Y. Tribune (April 4). Working in greenhouses attached to one of the large iron companies in Essen, and utilizing the carbon dioxide (freed from impurities) obtained from the blast furnaces, the yield of tomatoes was increased 175 per cent. and cucumbers 70 per cent. Further experiments in the open air, on plots around which punctured tubes were laid, and through the latter of which the carbon dioxide was sent, gave increases of 150 per cent. in the yield of spinach, 140 per cent. with tomatoes and 100 per cent. with barley. BENJAMIN HARROW

STRUCTURAL BLUE IN SNOW

TO THE EDITOR OF SCIENCE: The recent blizzard began here with a heavy downpour of rain on the evening of March 5, which later turned into a glistening snow that was shattered by the furious wind and formed a crystallinelooking glittering coherent mass whose structure was maintained by the low temperature (about 20° F.).

When the sun finally came out on Saturday afternoon, I noticed that the shadows of the trees and the shadow masses of the distant snow, appeared unusually blue, and that the

snow itself looked blue-white, like paper or sugar "blued" with ultra marine. Evidently the snow, because of its structure, reflected a larger proportion of the short wave-lengths of blue; and we have here another illustration of a structural blue color, which, according to Wilder D. Bancroft may be obtained when we have finely divided particles of liquid or solid suspended in a gaseous medium (blue of the sky) or a liquid medium (blue of the eye or of the tree-toad); or when we have finally divided air-bubbles suspended in a liquid or solid medium (blue feathers).1

Incidentally there is some justification for the somewhat brilliant blues used by the artists in painting snow scenes, especially in the shadows; and we recall the story told of Whistler, who, when a lady visitor at his exhibition remarked, "I've never seen a sunset like that, Mr. Whistler," promptly replied, "Well don't you wish you could?"

RIDGEFIELD, CONN.

JEROME ALEXANDER

SCIENTIFIC BOOKS

How to Make and Use Graphic Charts. By ALLAN C. HASKELL, B.S., with an introduction by RICHARD T. DANA. 539 pages. First edition. Price $5.00.

The last years have seen a tremendous progress in the application of graphic methods and while these methods must be regarded as means rather than as ends they nevertheless play a most important part of scientific analysis.

To most persons except the trained engineer, biologist or statistician the principles of analytic geometry which are the basis of most graphic methods appear too difficult and intricate as that they would be used for practical problems of every-day life.

Mr. Haskell's book fills therefore a distinct demand when it contributes to a clear understanding and wider application and recognition of the graphic method. The treatment is written from the standpoint of the practical engineer who comes daily in contact with such 1 See "The Colors of Colloids," VII., J. Phys. Chem., Vol. 23, pp. 365-414.

problems which will lend themselves to the application of this form of analysis.

The 539 pages of the richly illustrated book are divided into 18 chapters which go exhaustively into every phase and detail of the possibilities and applications of graphic analysis. Special consideration is given to the current engineering problems of to-day. One whole chapter is devoted to the nomographic or alignment chart. This subject is treated in Chapter VIII. and taken up again in Chapter XVI., "Computation, arithmetical and geometrical" which devotes some thirty pages to this interesting subject.

The author deserves much praise for faithfully collecting the manifold material on this subject. On page 348 however I think it would be worth while to mention the graphic calculation of the polytropic curve based on the equation

(1 + tgẞ) = (1+tga)n.

The lack of space prevents a longer explanation but for the rapid design of isothermal and adiabatic curves in connection with combustion engine design, this method1 is extremely valuable on account of its accuracy, rapidity and range covering all exponents n1.10 (isothermal) to 1.41 (adiabatic).

Chapter VII. would have had room for the smelting diagrams of Stead and Saklatwalla2 and of Shepherd.

Chapter XVII. is devoted to the graphic methods of designing and estimating. The civil engineer will find much of value and interest here. I think however the chapter could be extended to the advantage of the mechanical engineer and his problems.

The wealth of references relating to the graphic methods which are given at the end of each chapter and which have been collected by Mr. Haskell make the book valuable as a source of information, in short the author has responded to a vital demand for a practical book, "How to make and use graphic charts." The practical man will find much material ready for use and easily understandable and 1 E. Braner, Z. d. v. d., I., 1885, p. 433.

2 Journal of the Iron and Steel Institute, 1908, No. 11, p. 92.

2

The F2 generation gave a very interesting result-only three out of 183 mice grew the tumor. At that time the results were explained on the basis of multiple Mendelizing factors whose number was estimated at from twelve to fourteen. Simultaneous presence of these factors, themselves introduced by the Japanese waltzing race, was considered necessary for progressive growth of the tumor. The analogy between this case and that of coat color in wild mice, dependent upon the simultaneous presence of at least five known Mendelizing factors was at that time pointed

1

twenty-three susceptible, to sixty-six non-susceptible animals. It was previously estimated that from five to seven factors were involved. In order to determine more closely the number of factors, new experiments were devised as follows: F, hybrid mice themselves susceptible were crossed back with the non-susceptible parent race. This has recently given a back cross generation whose susceptibility would depend upon the factors introduced through the gametes received from their F, parent. If one factor was involved, the ratio of gametes containing it formed by the F1 animal, to those lacking it would be 1:1, if two factors, 1:3; if three factors 1:7; if four factors, 1:15; if five factors, 1:31; if six factors, 1:63; and if seven factors, 1:127. Susceptible and non-susceptible individuals would occur in the back cross generation in similar proportions.

The actual numbers obtained were twenty one susceptible to 208 non-susceptible. This result may be compared with expectations on three, four, five, and seven factor hypotheses, as follows:

The observed figures fall between the three and four factor hypothesis. The numbers are not large enough to give a definite test, but the F, generation already mentioned is interesting as a supporting line of evidence. If we compare this with the expectation, we find that the observed figures lie between the

2

Expected 3 factor... Expected 4 factor. Observed.... Expected 5 factor.

four and five factor hypothesis. In both cases the four factor hypothesis figures are close and the three and five factor hypothesis