6o2 



NA TURE 



[Al'RIL 24, 1902 



This is shown for a 2 per cent, alloy (except in the case of 

 carbon) in the second cohimn of the accompanying table, along 

 with the specific heats and atomic weights of the elements 

 named in the first column. 



The author ventures to think that the correspondence shown 

 in columns 2 and 3 of the foregoing table is something 

 more than a chance coincidence. He states, however, that it is 

 necessary to have exact determinations of the resistivity of a 

 larger number of alloys of iron before any definite conclusions 

 can be reached. 



A series of experiments is in progress for the measurement 

 of the relative thermal conductivity of the foregoing alloys. 

 About forty determinations have been made, and so far the order 

 of thermal conductivity has been found to be the same as that 

 of their electrical conductivity. 



As regards the magnetic permeability of these alloys, the 

 author states that the order is very^ifferent from that of their 

 electric conductivity. The most highly permeable alloys are 

 those formed of aluminium and silicon with iron. In fact, the 

 magnetic permeability of an alloy of iron with 2J per cent, of 

 silicon exceeds that of the best and purest annealed iron up to a 

 field of 10 CG.S. units. Still more remarkable is a similar 

 alloy of aluminium and iron ; although it contains i\ per cent, 

 of non-magnetic elements, its magnetic permeability and maxi- 

 mum induction up to a field of 60 units exceeds the best and 

 purest annealed iron, a specimen of Swedish charcoal iron 

 containing 99-9 per cent, of iron, all the specimens having been 

 subjected to a precisely similar annealing process. 



It is possible the increased magnetic susceptibility given to 

 iron by aluminium, and to a less extent by silicon, may be due 

 to the strong chemical affinity which these elements have for 

 oxygen, whereby any of this gas which might be dis.sociated in 

 the molten iron would be removed, and the texture of the metal 

 thus rendered closer and more uniform. In the same way, by 

 combining with the oxygen, they would remove traces of oxide 

 of iron, more or less diffused through all iron, and the presence 

 of which would certainly lower the magnetic susceptibility. 



The remarkable magnetic properties of these two alloys, 

 especially of the aluminium-iron alloy, is a matter, not only of 

 considerable theoretical interest, but obviously is also of great 

 practical importance in electrical engineering. 



Note added by the Author April 21. 



In connection with the increased magnetic permeability pro- 

 duced by alloying iron with a small percentage of aluminium. 

 Principal Hicks draws attention, in the last number of N.Mt'RE, 

 to the interesting fact — of which I was unaware, and which I 

 believe has not hitherto been published — that some years ago 

 he noticed this property of aluminium ; and he attributes it " to 

 the increased size of the iron crystals" produced by the foreign 

 body. This may be the explanation, but I am disposed to 

 think it is closely allied to the one I have suggested, and with 

 the known metallurgical effect of aluminium on iron, to which 

 Prof. Wilson has drawn attention in his contribution to the 

 discussion at the Institute of Electrical Engineers. W. F. B. 



March 20. — "The Equilibrium of Rotating Liquid 

 Cylinders." By J. H. Jeans, B.A., I.saac Newton Student 

 and Kellow of Trinity College, Cambridge. Communicated 

 by Prof. G. H. Darwin, E U.S. 



The most serious obstacle to progress in the problem of 



1 For a I per cent, alloy. The molecular weight of carbon would appear 

 to be at least four times its atomic weight if this analogy holds true. 



-^"^ grapkitc ; zf. diamond ihc specific heat of carbon is 0-113, according 

 to H. F. Weber. 



NO. 1695, VOL. 65] 



determining the equilibrium configurations of a rotating liquid 

 lies in the difficulty of determining the potential of a mass of 

 homogeneous matter of which the boundary is given. 



The present paper deals only with two-dimensional problems, 

 and for these a method is developed enabling us to write down 

 the potential by transformation of the equation of the boundary. 

 The method is not of universal applicability, but is adequate to 

 the problem in hand. 



As applied to the determination of equilibrium configurations, 

 the method is as follows. Starting from the general equation 

 (in polar coordinates) 



r'^ = a^ + za^r cos9-\- za^r- cos 26+ . . ., 



we transform by the substitution { = «■', Tj = r-^-'*, and attempt 

 to solve the resulting equation explicitly for | in the form 



i = bi + b„ri + i-,V-+ ■ ■ ■ +-+-: + -'+ ■ ■ ■, 

 1 I" v' 



this solution being such that the right haiid° shall give the true 

 value of I at every point of the surface. Subject to certain 

 limitations, the condition that the surface shall be an equili- 



brium surface under a rotation 

 system of equations 



is found to be given by the 



*» = «„(, -?^\ (,, = 1,2,3....). 

 n \ 27rp / 



The linear series of circles and ellipses (corresponding to the 

 Maclaurin spheroids and Jacobian ellipsoids) are investigated 

 without difficulty, and the points of bifurcation on these series 

 are found. The first point of bifurcation on the latter series is 

 shown to lead to a pear-shaped curve, similar to that of 

 Poincare, and it is shown that an exchange of stabilities takes 

 place at this point. The linear series of which this pear-shaped 

 figure is the starting point is now investigated, the equation 

 being expanded in an ascending series of powers of a para- 

 meter 9. 



After passing through various pear-shaped configurations, the 

 fluid is found to assume a shape similar to that of a soda-water 

 bottle with a somewhat rounded end. Beyond this the con- 

 figuration is found to be suggestive of a tennis-racquet with a 

 very short handle. A " neck" gradually forms at the point at 

 which the handle joins the racquet, and this becomes more 

 pronounced, until ultimately the curve separates into two parts. 

 As we proceed along this series the rotation steadily increases. 

 At the point of bifurcation the value of oj-'/aTrp is 0-375 ; when 

 separation takes place this value is about 043. It is tolerably 

 clear (although not rigorously proved) that when separation 

 takes pkce the primary may be regarded as the Jacobian ellipse, 

 corresponding to "rotation w-l2Trp — 0'4^^ distorted by the tidal 

 influence of the satellite. The linear diameters of primary and 

 satellite are in a ratio of about 4 : I. 



The points of bifurcation on the Poincare series are not 

 investigated. Since the Jacobian ellipse is known to be stable, 

 there is ground for supposing that the series remains stable up 

 to the point of separation. It therefore appears probable that 

 the primary moves through a cycle of configurations in which 

 Jacobi's and Poincare's figures alternate. The angular mo- 

 mentum is decreased by about 30 per cent., at the ejection of 

 each satellite. 



Royal Astronomical Society, April 11. — Dr. J. W. L. 

 Glaisher, F. R.S , president, in the chair. — Among the presents 

 announced, special attention was called to Circular No. 9 of 

 the Paris Astrographic Conference, by M. Lcewy, dealing with 

 the accuracy of measures of sl.ar images on photographs, and 

 with the planet Eros. — In a third paper on stationary meteor 

 radiants. Prof. Turner considered the possible effect of atmo- 

 spheric retardation of ineteors passing near the earth, concluding 

 that such effect would be so small as to be negligible. — Prof. 

 Turner also read a paper on the relative number of star images 

 photographed in different parts of a plate. Counts of star 

 images on plates taken at Oxford, Paris, Algiers, Toulouse and 

 San Fernando showed that the density of star images in different 

 parts of a plate varied by about 50 per cent. The region of 

 greatest density is not in the centre, but a ring of 35' to 60' 

 radius, plates taken at different observatories giving different 

 results. On the other hand, the photographic doublet used for 

 the Cape Photographic Durchmusterung gave sensibly uniform 

 density ; it was therefore suggested that the doublet may be 

 the best instrument for star charting. — Ur. Kambaut read a 

 paper by Mr. W. II. Robinson on k Persei and 36 Persei, 



