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playing, there is no question for instance that a succession of notes, G, G sharp, A and a succession G, A flat, A, are musically distinct, and that each actual sound on the piano is a symbol used to stand in turn for many musical entities. The reformed method would destroy the signs of some of these distinctions and reduce playing at sight to striking a succession of notes with little chance of prevision of the musical meaning.

As to the reformed keyboard there is again an obvious material if no clear ideal loss. However the judgment that the simplification of "physiological reflex" is of much value might be demurred to. One can conceive a psychologist taking the stand that a reflex is a reflex, and a musician saying that he had established the reflexes and forgotten the process. Finally we might have a violinist objecting to the pianist borrowing his G clef and returning it in a damaged condition, for advantages on the keyboard would be disadvantages on the fingerboard where the hand covers an octave diatonically and the accidentals are made by a special finger move

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tion as to whether he published further on this subject. WILLARD J. FISHER



TO THE EDITOR OF SCIENCE: My first experience with the sidewalk mirage described by Professor McNair in your issue of August 27, was on a smoothly paved straight-away between Canton and Alliance, Ohio. The time was three o'clock P.M. of a very hot day in August, 1918, the temperature being just about 100°. We were headed east on a level stretch, while about a mile ahead of us on a slightly higher level was a car apparently submerged in water to a depth of about two feet. A woman crossing the roadway was "in" up over her knees. As none of our party had ever seen such a reflection we got out of the car lest it might be caused by the windshield. At first the vision was lost until we discovered that the angle of vision was so small that we had to hunt for it, when it remained clear and distinct as long as we had the time to watch it.

Since that time I have seen a number of similar reflections, some in warm weather and others in cold; which leads me to conclude that heat is not necessary to produce them. The distance appears to govern the height from the ground as I have seen one within a distance of a square and it was within two or three inches of the surface. The surface reflection mentioned by Mr. Platt in your issue of September 27 is not uncommon, but could never be mistaken for the mirror-like surface of the mirage after you have seen a real one. Such explanations as I worked out in 1918 were upset the following winter and I shall watch with interest for further information that may be offered.



TO THE EDITOR OF SCIENCE: About 11 P.M. on Thursday, November 18, while waiting for a street car, I saw a clearly defined rainbow-a phenomenon which is possibly of sufficiently rare occurrence at night to be of interest to some of your readers.

A drizzling rain was falling overhead, but

stars were shining brightly to the north. The moon, which was very low in the west (about 15° south of west, with an altitude of some 5° or 6°), was hidden from view by buildings, where I stood; and, because of the street lights, I was not even aware that the moon was out until the rainbow in the east caught my eye. None of the prismatic colors could be detected, the bow being merely a yellowish arch of light very well defined at the southern end-rather an odd thing to see at that time of night.





Gli Scienziati Italiani, dall'inizio del medio evo ai nostri giorni. Repertorio biobibliografico dei filosofii, matematici, astronomi, fisici, chimici, naturalisti, medici, e geografi Italiani. Diretto da ALDO MIELI, e compiuto con la collaborazione di numerosi scienziati, storici, e bibliografi. Vol. I., Parte I., Rome, 1921. Pp. viii+236. A. Nardecchia, publisher.

In the issue of SCIENCE of August 30, 1919, pp. 213-214, I called attention to Italian activity in the field of the history of science, evidenced by the new publication Archivio di Storia della Scienza, edited by Aldo Mieli, which journal has now completed its first year. The present work indicates the continued and growing interest in Italy in the history of science.

The first part of this biographical dictionary presents the biographies of thirty-three Italian scientists from the fifteenth to the present century. The list of contributors to the volume shows that the great scholars of Italy are devoting themselves to assure the success of the present work under the able editorship of the distinguished historian of science, Aldo Mieli.

One peculiarity of the work is that neither chronological nor alphabetical order of treatment is pursued in selecting the scientists included. Eventually, of course, the completed work will be provided with all necessary in

dices. Each volume includes also the alphabetical index of names.

The order of treatment of each biography consists of the following: Life; Works, including a critical discussion of the historical and scientific significance; Bibliography, including complete catalogue of all works, with place and date of printing of published works, editions, and translations with precise bibliographical descriptions and also some statement of location in Italian libraries of volumes mentioned; Literature, giving lists of works which discuss the work or life of the scientist in question.

The mathematician will welcome the fine biographical statement (pp. 4-12) concerning Leonardo Fibonacci, written by Gino Loria; the astronomer will appreciate the excellent account (pp. 45-67) of Schiaparelli, by Elia Millosevich; the geographer and the astronomer will find much of interest in the account (pp. 101-111) of Giovanni Antonio Magini (1555-1617) by Antonio Favaro, who lists no less than 47 printed works (and editions) by Magini; the student of medical history, the botanist and naturalist and the physicist will enjoy a whole series of illuminating articles. Particularly noteworthy is the fact that a photograph and a facsimile of handwriting is given of each scientist, wherever possible.

This publication promises to be a work comparable only to the English Dictionary of National Biography; for America, France or Germany there is no work of this nature. When completed on present plans libraries will find it as indispensable as the above mentioned dictionary.

With the present state of exchange the price of 45 liras for Part I., viii plus 236 pages, is extremely low. Every effort should be made by American scientists, historians, and librarians to encourage the continuation of this publication on the present scale. The effective way to do this is by subscription to the publisher, A. Nardecchia, Via dell' Universita 11-14, Rome, Italy.

The alphabetical list of articles follows: Acri, Francesco (1834-1913), philosopher, by E. P. Lamanna.

Alpino, Prospero (1553-1616) botanist, by Passerini, Giovanni (1816–1893), botanist, by A. Beguinot.

G. B. De Toni.

Piccone, Antonio (1844-1901), botanist, by
G. B. De Toni.

Amici, Giovanni Battista (1786-1863) physicist. naturalist, by G. B. De Toni. Anguillara, Luigi (c. 1512-1570) botanist, by Pontedera, Giulio (1688-1737), botanist, by G. B. De Toni. A. Beguinot. Baranzano, Redento (1590-1622) philosopher, Riva, Giovanni Guglielmo, (1627-1677), phys astronomer, by G. Boffito. ician, by C. Artom.

Bertini, Anton Francesco (1658-1726), phys Schiaparelli, Giovanni Virginio (1835–1910) ician, by A. Corsini.

Bertini, Giuseppe (1772-1845) physician, by
A. Corsini.

Bertini, Giuseppe Maria Saverio (1694-1756),
physician, by A. Corsini.

Biringuccio, Vannoccio (1480-1530?), technician, chemist, by A. Mieli.

astronomer, historian of science, by E. Millosevich.

Silvestri, Francesco (1474-1528), philosopher,
by G. Sestili.

Sterzi, Giuseppe (1876-1919), anatomist, by
G. Favaro.

Valli, Eusebio (1755-1816), physician, by
A. Vedrani.

Cestoni, Diacinto (1637-1718), naturalist, by Zanardini, Giovanni (1804–1878), physician,

G. Stefanini.

Chiarugi, Vincenzo (1759-1820) psychiatrist,
physician, by A. Vedrani.

Cocchi, Antonio (1695-1758), physician, by
A. Corsini.

Corti, Bonaventura (1729-1813), botanist, by
G. B. De Toni.

Cotugno, Domenico (1736-1822), physician,
by G. Bilancioni.

De Visiani, Roberto (1800-1878), botanist, by
A. Beguinot.

Dini, Ulisse (1845-1918), mathematician, by
G. Loria.

Fibonacci, Leonardo (sec. xii-xiii), mathe-
matician, by G. Loria.

Figari, Antonio (1804-1870) traveler, nat-
uralist, by G. Stefanini.

Folli, Francesco (1624-1685), physician, nat-
uralist, by G. Goretti-Miniati.
Ghini, Luca (c. 1490-1556), botanist, by G.
B. De Toni.

Guilandino, Melchiorre (c. 1520-1589), botan-
ist, by G. B. De Toni.
Inghirami, Giovanni (1779-1851), astronomer,
by G. Giovannozzi.

Magini, Giovanni Antonio (1555-1617), as-
tronomer, geographer, by A. Favaro.

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where the ten potentials gik are functions of the four coordinates, in general has a curvature tensor which does not vanish, and therefore defines a curved manifold M of four dimensions. In fact M is flat or euclidean or homodoidal only when there is no actual gravitation. Excluding this trivial case, the question arises what is the flat space of fewest dimensions n, which can be regarded as containing the curved manifold M?

Abstractly considered the possible values of n are 5, 6, 7, 8, 9, 10; that is, any M can surely be immersed in a flat space of not more than 10 dimensions. But if we take into account

Maranta, Bartolomeo (c. 1500-1511), phys- Einstein's differential equations of gravita

ician, botanist, by G. B. De Toni.

Moletti, Giuseppe (1531-1588) astronomer, cosmographer, by A. Favaro.

tion, Rik=0, or Gik0, we find that the simplest case, n=5, is actually impossible. That is to say:

An Einstein four-dimensional manifold, defining a permanent gravitational field, can never be regarded as immersed in a flat space of five dimensions.

This applies in particular to the solar field (defined say by the Schwarzschild form), in which the earth and the other planets are moving. The appropriate value of n must therefore be greater than 5 and less than 11. A brief discussion shows that actually n=6. Therefore:

The solar gravitational field can be represented by a curved manifold of four dimensions situated in a flat space of six dimensions.

This manifold can be written in finite form and gives what may be called a geometric model of the field in which we are living.

The proofs of these theorems and the actual equation of this model are appearing in current numbers of the American Journal of Mathematics, together with the full discussion of the general results connecting light rays. and orbits in any field stated in SCIENCE, October 29, 1920, pp. 413-414.






F. B. Carpenter, chairman
H. C. Moore, secretary

Kelp as a basis of an American potash industry: J. W. TURRENTINE.

Relationships of chemistry and the fertilizer industry: C. H. MACDOWELL.

A perfect fertilizer law: E. G. PROULX. Boron in relation to the fertilizer industry: J. E. BRECKENRIDGE.

The quantitative estimation of borax in mixed fertilizers: J. M. BARTLETT.

Note on the determination of nitrogen in fertilizers containing both organic and nitric nitrogen: F. B. CARPENTER. Notwithstanding the fact that the modified Kjeldahl and Gunning methods have been in use for a number of years, the results obtained by these methods in the hands of different analysts on samples containing mixtures of organic and nitric nitrogen are far from satisfactory.

This is probably largely due to a wrong interpretation of the official method. From the standpoint of the manufacturer this is quite a serious matter and it seems desirable that the Association of Official Agricultural Chemists should take such action as is necessary to modify or at least change the reading of the modified methods so that there may be no misunderstanding of how they should be carried out.

Dicyanodiamide. A rapid, direct method for its determination in cyanamid and mixed fertilizers: ROLLA N. HARGER, presented by Oswald Schreiner. The method depends upon the fact that when a solution of silver picrate is added to a solution of dieyanodiamide, the latter is quantitatively precipitated as a double compound of silver picrate and dicyanodiamide, CH, (NO,),OAG, CH,N.. This new double compound we have named silver picratemono-cyanoguanidine. It forms in small crystals which quickly settle out of the solution and can be separated upon a Gooch crucible very rapidly, so that the analysis can be carried out in a very short time. Neither cyanide nor urea give any precipitate when their solutions are treated with silver picrate, and determinations of dicyanodiamide carried out in the presence of these compounds showed that they have no effect upon the analysis. The molar weight of the compound is 420.22, five (4.991) times that of dicyanodiamide, a fact which greatly enhances the accuracy of the method, since an error of 1 mg. in the precipitate weighed will mean an error of only 0.2 mg. of dicyanodiamide or 0.13 + mg. of nitrogen.

The changes taking place in cyanamid when used in mixed fertilizers: ROLLA N. HARGER, presented by Oswald Schreiner. (1) When cyanamid is placed in a mixed fertilizer containing acid phosphate and 5-10 per cent. of moisture, the cyanamide content decreases with great rapidity. (2) This change is represented principally by, and in many cases quantitatively by, the formation of dicyanodiamide. (3) A given quantity of moist acid phosphate is able to transform a limited amount of calcium cyanamid. (4) Cyanamid is not affected by dry acid phosphate. (5) Moisture alone is able to cause the conversion of cyanamid to dicyanodiamid, but the change is much slower than when acid phosphate is present. Since it has been repeatedly shown that dicyanodiamid is valueless as a fertilizer material and, moreover, is toxic to many plants, the formation of this compound in fertilizer materials seems undesirable. From the results of this study it would seem that

the method of applying cyanamid, commonly employed, which consists in adding the cyanamid to fertilizer mixtures containing acid phosphate, which mixtures almost always contain several per cent. of moisture, is a very questionable practise. Moreover, the use of cyanamid as a "conditioner'' for "green" acid phosphate is very probably at the expense of most of the nitrogen in the cyanamid. On first thought it would appear that this conversion of cyanamid into dicyanodiamide could be avoided by simply employing dry fertilizer mixtures, but this overlooks the fact that when such mixtures are added to the soil moisture conditions are at once provided and the transformation may possibly then take place. Preliminary experiments carried out in this laboratory indicate that under certain conditions at least this is the case.

Some results of the determination of potash by the Lindo-Gladding method, using alcohol of various strengths in the presence of sodium salts: R. D. CALDWELL and H. C. MOORE. When potash is determined by the official method of the A. O. A. C. but slightly lower results are obtained when 80 per cent. alcohol is used than when 92 or 95 per cent, is used in case of sample of pure potassium chloride, but when sodium chloride or sulfate is added the results with 80 per cent. alcohol are lower. Tests with a sample of potassium platinic chloride showed it to be but slightly soluble in 80 per cent. alcohol alone, but the solubility increases with the increase of sodium salts added but with 95 per cent. alcohol sodium salts have no effect.

Injurious effects of borax on field crops: F. B. CARPENTER. It has long been known that certain chemical substances are poisonous to plant life. While certain compounds of copper, zinc and arsenic are exceedingly poisonous, compounds of manganese and boron are far less deleterious. Most of the experiments which have been made with these compounds have been made on plants grown in pots or water cultures; in case of borax, however, considerable knowledge has been gained during the past few years on field crops from the use of Searles Lake potash, which contained an excessive amount of this compound. The first large scale borax poisoning in this country occurred in Indiana in 1917 on corn. In 1919 considerable damage was reported on potatoes and tobacco in different localities. Many conflicting reports were made in regard to amount of borax required to produce injury. While in some instances as little as two pounds per acre has been reported to have slightly injurious effects, one report was noted

where as much as 400 pounds per acre was used with apparently no bad results. Experiments made by the writer on corn, beans, cotton, Irish potatoes, sweet potatoes and tobacco showed no bad effects where 8 pounds anhydrous borax per acre were used, but there was slight injury with sixteen pounds. It is evident, therefore, that the character of soil, amount and time of rainfall, the manner of application, etc., influence to a large degree the amount of borax which can be used without poisonous effect.

The "blank" in the Kjeldahl process; its analytical and commercial significance: B. F. ROBERTSON. Potash shales of Illinois: M. M. AUSTIN and S. W. PARR. (1) Shales occur in at least two localities in Illinois which contain five per cent. or more of potash. (2) Shale outcropping in several places near Jonesboro in Union County which contain five per cent. of potash would be suitable, so far as can be determined from its chemical composition and physical character, for use in the manufacture of Portland cement. (3) By using this material in the manufacture of cement and by applying the known methods of potash recovery, a yield of 5.3 pounds of potash, representing a value of 70 to 80 cents per barrel of cement could be obtained. (4) The constitution of the southern Illinois shale is complex. The shale contains free oil, bituminous matter, pyrite, undecomposed potassium bearing rock, feldspathic in character and potassium bearing material of the nature of glauconite or greensand. (5) Shale from Dixon, Lee County, contains 5.8 per cent. of potash which is held for the most part in a more stable condition than that in the southern Illinois shale. (6) Extraction of the potassium from shale of either the southern Illinois or Dixon type by means of solid or liquid reagents would seem to be impracticable, because of the incomplete reaction of these reagents on the shale and because of the cost of leaching and recovering potash from material where it is present in such small amounts. (7) The plant availability of the potash in the southern Illinois shale is probably characteristic of all of the material of this type outcropping in that locality. (8) That part of the potassium in the southern Illinois shale which is soluble in sulphuric acid, is shown to be in a combination of the glauconite type. (9) In southern Illinois shale having a potash content of 5.0 per cent. in the raw condition or 5.6 per cent, when ignited, 62 per cent. of the total potash is glauconitic in character and is available as plant food. Potash situation in Germany: H. A. HUSTON.

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