by Shepherd and by Carpenter and their tensile strength by Lohr (Jour. Physical Chem., XVII, 1). Up to about 36 per cent. of zinc the alloys are homogenous solid solutions (alpha); beyond this point a second solid solution, beta, makes its appearance, and at 47 per cent. zinc the alloy is entirely beta. Carpenter (Jour. Inst. of Metals, VII, 70) has shown that just about 450 deg. C. the beta tends to break down into alpha, and a third solid solution, gamma. The maximum strength is in the beta region at 45 per cent. zinc and is about 31.7 tons per square inch. The copper-tin alloys have been worked out by Heycock and Neville and by Shepherd, and a new transformation in the solid state is recorded by Hoyt (Inst. of Metals, Ghent meeting, 1913). They resemble the brasses in that up to about 10 per cent. of tin the alloys are homogeneous solid solutions, but when the tin is increased a second solid solution, beta, comes in; this beta breaks down into alpha and a third solid solution, gamma, at about 450 deg. C. Hence the properties of the brasses and the bronzes, like steel, can be profoundly modified by heat-treatment. German silver is a white ductile alloy containing 55 to 60 per cent. copper, 15 to 20 per cent. nickel, and 20 to 30 per cent. zinc, and consists of crystals or grains of a single solid solution. Hudson (Jour. Inst. of Metals, IX, 109) has studied the effect of annealing and found that one hour at 800 deg. C. was insufficient to get rid of the "cored" structure, but one hour at 900 deg. C. was sufficient to produce a homogeneous alloy. H. S. and J. S. G. Primrose (ibid., 158) subjected Admiralty gun metal (copper 88, tin 10, zinc 2) to heat treatment and found that simple annealing for 30 minutes at 700 deg. C. gave a maximum increase in strength and elongation, and the homogeneity and other properties were improved. The ternary alloys of nickel, manganese, and copper have been found by Parravano (Gazzetta Chim. Ital.. XLII, ii, 367, 385, 513) to consist of homogeneous solid solutions and het erogeneous structure in these alloys is due to imperfect diffusion. The ternary alloys of iron, nickel, and manganese are similar, while the alloys of iron, manganese, and copper are somewhat more complicated because iron and copper are not completely soluble in each other in the solid. Hence two distinct constituents are found in many of the alloys. Rosenhain and Archbutt (Proc. Institution Mech. Engrs., 1912, 319) have worked out the aluminium-zinc diagram together with the physical properties. They were able to roll and draw an alloy with 25 per cent. zinc. An alloy with 25 per cent. zinc and three per cent. copper gave a hotrolled bar with 30.9 tons per square inch tensile strength and an elongation of nearly 17 per cent. Magnetic Permeability. — In 1903 Heussler prepared alloys of copper, manganese, and aluminium and found them to be magnetic. This magnetism was explained by a ternary compound. Ross (Trans. Faraday Soc., VIII. 185) puts forward the theory that the alloys consist of solid solutions of the binary compounds Cu, Al and Mn, Al, but Rosenhain has shown that the alloys of aluminium and manganese alone are strongly magnetic. - Electric Conductivity. The variation in electric conductivity of alloys is at once made clear when the thermal diagram is considered. Guertler's work (Jour. Inst. of Metals, VI, 135) shows that the conductivity of alloys composed of solid solutions or mechanical mixtures of the metals increases as the temperature rises, while that of intermetallic compounds decreases. Corrosion.-The corrosion of brass has been the subject of a good deal of research. Two causes have been assigned. First, when the alloys are composed of the two constituents alpha and beta, there is a difference of potential between the two, the beta becomes the anode and is destroyed through the zine going into solution, leaving a porous mass of copper behind. Second, when the alloy consits of homogeneous alpha, a difference of potential may be set up by adherent impurities on the surface or by strain, and corrosion begins through electrolysis. When once begun, the presence of metallic copper, which becomes the cathode to the alpha solid solution, hastens the corrosion. XXIV. MATHEMATICS AND ASTRONOMY MATHEMATICS E. B. WILSON somewhat general nature, containing some original articles, many book reviews, and personal notes. This year Prof. M. Bocher (Harvard) has retired from the position of editor-inchief of the Transactions; Prof. L. E. Dickson (Chicago) succeeds him. The management of the Monthly has been completely changed; Prof. H. E. Slaught (Chicago) has been made managing editor and, with the cooperation of his associates, is making a strenuous campaign on behalf of the enlarged and improved Monthly. Annual Production. Many per- est to teachers in the better grade sons believe that mathematics is a of high schools and to undergradudead science and that the mathe- ate students. The Bulletin is of matician, like the teacher of Greek and Latin, does but go over accomplishments of the past. Even those who know that mathematical doctrines are constantly advancing have often but a small idea of the amount of research published. The Jahrbuch über die Fortschritte der Mathematik is an annual publication which lists all the titles of mathematical work coming to the attention of the editors, with brief synopses of most of the original articles. So large is the task of as sembling the material that this authoritative review of mathematical investigation is always three years behind. Volume XLI, covering the year 1910, appeared in 1913; it lists about 3,700 titles and contains 1,054 pages, exclusive of indices and prefatory matter. Path of Falling Bodies.-Since the time of Gauss and Laplace, a century ago, the question of the path followed by a body falling from a moderate height above the surface of the ground has been subject to theoretical and experimental investigation. A body released at a In the United States the Trans- height does not follow an exactly actions of the American Mathemati- vertical path; for, as the earth turns cal Society, the Bulletin of the So- on its axis, a point such as the top ciety, the American Journal of of the Eiffel tower, being farther Mathematics, the Annals of Mathe- than the base from the axis, and matics and the American Mathe- having the same angular velocity as matical Monthly, are the five lead the base, is moving faster than the ing periodicals devoted exclusive point on the surface of the ground ly to mathematics; they print in the immediately beneath. Hence a body neighborhood of 2,000 pages annually. released from the top has an easterly The Transactions and the Journal velocity in excess of the velocity of appeal only to the highly trained the point vertically underneath, and professional mathematician inter- consequently falls to the east of the ested in advanced research. The vertical. This chief part of the Annals aims to provide material in phenomenon has long been known telligible to a large range of gradu- both theoretically and experimentate students and teachers of ordinary ally. The question has been raised collegiate courses in mathematics. whether the body does not also deviThe Monthly is still less technical ate slightly either to the north or and contains much that is of inter- south. The earlier mathematicians found a slight deviation toward the subject has been given by Professors equator, and some experimenters E. B. Wilson and G. N. Lewis (Masshave thought they corroborated this finding, though many persons have felt that the experimental data were insufficient to establish a definite conclusion. The calculation of the deviation has to be effected by approximations, an exact solution being too intricate for even modern mathematical science. For the sake of simplicity it has been customary to retain only the expressions for the first approximation, and it has been assumed that the terms expressing the second approximation would be insignificantly small. R. S. Woodward, President of the Carnegie Institution, has treated the problem in the Astronomical Journal for Aug. 4, 1913, taking into account the previously neglected terms of the second order which he finds are not negligible, and has shown that there is an appreciable deviation away from the equator. (See also Astronomy, infra.) Origin of Planets. In the Memoirs of the American Academy of Arts and Sciences, XIV (1913), Prof. Percival Lowell (Massachusetts Institute of Technology) discusses mathematically the "Origin of the Planets." He finds that each planet has formed the next one in order outward from the sun, that the positions of the planets are not haphazard, and that the solar system forms an articulated whole evolved in definite order. Theories of the origin of the solar system and explanations of its evolution into its present form have a great fascination for astronomer, mathematician, and the general public. As we really are acquainted only with the present status of the system, all discussions of its origin are largely hypothetical and many of them differ widely among themselves. It is particularly interesting, however, to have a theory developed which offers an explanation of the distribution of the planets in distance from the sun. Theory of Relativity. The theory of relativity has been mentioned in all previous volumes of the YEAR Book (1910, pp. 601, 602; 1911, pp. 567, 632; 1912, p. 658). A technical mathematical treatment of the achusetts Institute of Technology) in Foundation of Mathematics Logic. The attempt of the pure mathematician is ever to reach a greater degree of rigor in his demonstrations, a greater degree of certainty for his propositions. This led during the last century to the arithmeticization of mathematics, that is, to the attempt to lay the ultimate foundations of mathematical science in the properties of the ordinary integers of arithmetic, which are probably as well known as any mathematical objects. Later the attempt has been made to go further back and to found mathematics upon the very laws of logic. This programme has been systematically carried out by B. Russell and A. N. Whitehead in their three-volume work Principia Mathematica (Cambridge University Press). The work is very technical and difficult reading, and most mathematicians will be content to admire it without going quite so deeply into the fundamentals as far as their own work is concerned. ASTRONOMY HENRY NORRIS RUSSELL wich, has been adopted in Brazil. The present summary deals neces- | four and five hours slow of Greensarily with the published work of the year, and hence, in many cases when the reduction of observations is laborious, with observations of the previous year. The Sun. The solar surface at the beginning of the year was very quiet, and on most days no spots were visible. Most of the few spots observed Observatories and Instruments.- were in low latitudes, but small The great tower telescope of the groups appeared about 30 deg. north Solar Observatory on Mount Wilson and south of the solar equator, the is now completed, and gives very precursors of the new cycle of activsatisfactory results. The figuring of ity now commencing. Hale has the mirror for the 100-in. reflector taken advantage of this absence of of the same observatory is in prog- local disturbances to detect and inress, and the chief difficulties of the vestigate the general magnetic field problem seem to have been overcome. of the sun. The existence of a strong A reflector of six-foot aperture is magnetic field in sun spots is proved planned for the new observatory by the breaking up of certain lines which the Canadian Government pro- in the spectrum into doublets, whose poses to erect in British Columbia. components are circularly polarized On the other hand, the completion in opposite directions, so that by of some of the large refractors now under construction has been very seriously delayed by the extreme difficulty of getting suitable disks of glass for the objectives. a placing a Nicol prism and a quarterwave plate in front of the slit of the spectrograph, either one of them can be extinguished at will. With weak magnetic field the components Longitude and Time.-A prelimi- would not be separated; but with mary determination of the difference the apparatus just described first one of longitude between Paris and Ar- side and then the other of the broadlington, Va., by means of wireless ened line may be extinguished, caustelegraphy, has been made by French ing a shift in its apparent position astronomers, with very encouraging to the right or the left in successive results, the transmission time of the strips of spectrum photographed on signals across the Atlantic being the same plate. Displacements of only 0.03 sec. (C. R., CLVII, 165). this character have been observed in An extensive series of observations the case of several faint lines of iron for the same purpose is to be carried out during the winter of 1913-14. Any observatory within several hundred miles of Washington may determine its longitude at the same time by using these radio-signals. Standard time, in three zones, three, and nickel. They are excessively St. John, studying the radial motions in sun spots discovered by Evershed in 1909, has shown that in the lower layers of the sun's visible atmosphere there is an outward flow of material from the spot, while in the highest layers the flow is inward, the rate of motion varying from one kilometer per second outward in the lowest layers to 1.5 km. inward at the top. A sun spot may be compared with a terrestrial tornado, seen from above the clouds. There is a whirling upward rush of material in the deep-seated layers, which at the visible surface spreads out radially with rapidly decreasing velocity. The inward motion in the highest layers is a secondary effect (Ap. J., XXXVII, 322). meter Abbot, summarizing the results of eight years' work of the Smithsonian Astrophysical Observatory in Volume III of its Annals, gives the value of the solar constant of radiation as 1.932 cal. per square centithat is, the per minute; energy in a beam of sunlight, outside our atmosphere, of this cross section would suffice to raise the temperature of one gramme of water at the rate of 1.932 deg. C. per minute, and that in a beam one meter square would be equivalent to. 1.8 h. p. Simultaneous measurements at stations in California and Algeria seem to prove conclusively that the radiation of the sun is subject to a variation, occurring irregularly in periods of a week or ten days, whose fluctuations are irregular in magnitude, but usually within the range of seven per cent. It appears also that the sun sends us most heat when sun spots are most numerous, the solar constant increasing by 0.07 cal. when the sun spot numbers increase by 100 units, which is about the usual change from minimum to maximum. From the distribution of energy among the different wave lengths in the solar spectrum, Abbot concludes that the effective absolute temperature of the radiating layers of its surface great ly exceeds 6,000 deg. C. and may exceed 7,000 deg. with the profile of the moon's limb and the track of the shadow on the earth's surface. The Earth.-The variations of latitude in 1912 showed a range of about 0".35, a decrease from that of 1911, but with little further diminution during the year (A. N., 4665). Those for 1913 will not be computed until the middle of 1914. Hagen has continued his study of experimental proofs of the earth's rotation, using Atwood's machine (two unequal weights connected by a wire passing over a pulley), to study the eastward deviation of falling bodies. The top of a tower, being farther from the earth's center than the bottom, is carried eastward faster by the earth's rotation. A falling body retains this more rapid eastward motion, and strikes the floor to the east of a plumbline hung from its original position. With a fall of 75 ft., the obdeviation served agreeing with theory within one per cent. Woodward, discussing the theory of such experiments (A. J., 651), concludes that in addition to the eastward deviation there should be a smaller one away from the equator, to the north in northern latitudes. (See also Mathematics, supra.) 0.90 was mm., Fabry and Buisson have shown that the abrupt termination of the solar spectrum toward the ultraviolet at about 13000 is probably due to the absorption of the light beyond this limit by ozone in the upper layers of the earth's atmosphere (C. R., CLVI, 782). The great eruption of Mt. Katmai in Alaska (A. Ỹ. B., 1912, p. 612) filled the upper air with fine dust, which took months to settle, and spread all over the world. The effect of this upon climate has been discussed by Abbot and Fowle (Smithson. Misc. Coll., LX, No. 29) and by Humphreys (Jour. Franklin Inst., CLXXVI, 131). The amount of solar heat which directly reached the earth's surface was diminished about 20 per cent. by the volcanic haze. After allowance for the increased brightness of the sky, there remains a net loss of ten per cent. in the heat available to warm the earth. If such a change should be permanent, it would be dealing largely enough to bring on a new glacial Eclipses. The three partial solar eclipses, and two total lunar eclipses of the year were of little importance. Many observations of the solar eclipse of April 17, 1912, were published during 1913, |