;82 



NA TURE 



[February i6, 1905 



percentage of ferric oxide (b.Si). In this respect it was similar 

 to epidotes from Huntington, Mass., and the Zillerthal, and 

 like them showed correspondingly low refractive and double 

 refractive power and large optic axial angle, as compared 

 with epidotes containing higher percentages of iron. — Pre- 

 liminary note on the regular growth of crystals of one 

 substance upon those of another : T. V. Barker. The 

 observations of previous investigators were in general con- 

 firmed with regard to the growths of KI, KBr, KCl and 

 NaNO, upon mica, and of XaNO, upon calcite. In all 

 cases a clean surface is necessary. Attempts to get a 

 regular deposition of NaNOj upon other rhombohedral 

 carbonates of the calcite group and upon dolomite were 

 without any positive result, although the rhombohedral 

 angle of some of them is much nearer to that of NaNO, 

 than is that of calcite. The topic axes, however, are in 

 order: of magnitude as follows : — NaNO,, calcite, rhodo- 

 chrosite, dolomite, chalybite, so that if the regular growth 

 depend on the fitting together of similar structures, the 

 experiments point to the usefulness of the conception of 

 topic axes. The author is continuing his observations. — 

 Apparatus for determining the density of small grains ; 

 K. A. K. Hallowes. The method is by hydrostatic 

 weighing, and the grain is held under water (or prefer- 

 ably alcohol) in a spring-clamp, made of brass wire and 

 tvvo cover-glasses, which is suspended from the beam of 

 the balance by a tine hair. — Exhibits : Specimen of phenacite 

 and one of aurichalcite from Cornish localities : A. Russell. 

 — Specimens of sulphide of lead and oxide of zinc artificially 

 produced in furnaces at Laurium ; H. F. Collins. 



Geological Society, Februaiy i. — Dr. J. E. Mart, 

 F.R.S., president, in the chair. — On the sporangium-like 

 organs of Glossopicris Browniaiia, Brongn. : E. A. Newell 

 Arber. Some specimens from New South Wales, on which 

 scale-fronds of Glossopteris occur, also exhibit impressions 

 of minute bodies, not unlike the sporangia of certain recent 

 and extinct ferns and cycads. They have never been found, 

 except in the closest association with the scale-leaves of Glos- 

 sopteris, and this is regarded as an indication that they may 

 be attributed to that genus, a conclusion supported by the 

 evidence of the scale-fronds, which show scars of attachment 

 and fragments of the sac-like bodies still apparently in con- 

 tinuity. It is impossible to be quite certain that these bodies 

 are sporangia, but there is much to be said for this view. 

 The closest analogy may probably be found in the micro- 

 sporangia of cycads. A historical sketch is given of the pre- 

 sent evidence on the subject of the fructification of Glos- 

 sopteris. If the present conclusion be correct (that the 

 sporangia were borne on the smaller scale-fronds), 

 Glossopteris cannot be included in any recent family of the 

 true ferns. 



Chemical Society. Frbruary 2. — Prnf. VV. A. Tilden, 

 F.R.S., president, in the chair. — The following papers were 

 read : — Camphorylcarbimide : M. O. Forster and H. E. 

 Fierx. The authors described this substance and some of 

 its derivatives and reactions. — Configuration of isonitroso- 

 camphor and its unstable modification : M. O. Forster. 

 It is proposed to represent I'ionitrosocamphor and its unstable 

 isomeride bv the configurations 



/\ 



c/— \c 



N.OH I 



CsHh 



OH.N 



respectively. The evidence for this view is principally based 

 upon the behaviour of the two isomerides towards magnesium 

 methyl iodide. — The determination of molecular weight by 

 lowering of vapour pressure : E. P. Perman. The author 

 has worked out the details of a simple method by which 

 molecular weights can be determined with moderate accuracy 

 from measurements of the lowering of vapour pressure of the 

 solvent in which the substance under investigation is dis- 

 solved. — Note on /3-NH-ethenyldiaminonaphthaIene : R. 

 Msldola and J. II. Lane. The ethonyldiaminonaphtha- 

 lene, obtained by Pragcr in 1S.S5 by debrominating the 



NO. 1842, VOL. 7 1] 



bromo-anhydro-base prepared by the reduction of 4-bromo : 2 : 

 nitroaceto-a-naphthalide, is now shown to be identical with 

 the anhydro-base obtained from Markfeldt's ethenyltriamino- 

 naphthalene by the diazo-method. 



Mathematical Socitty, Ftbtuaiy 9. — Prof. A. K. Fotsyih, 

 president, in the chair. — The president referred to the loss 

 sustained by the society by the death of Mr. R. Tucker, 

 who was honorary secretary of the society from 1867 to 

 igo2. A resolution of condolence with Mr. Tucker's sur- 

 viving relatives was passed. — The following papers were 

 communicated : — General tlieory of transfinite numbers and 

 order types : Dr. E. W. Hobson. The paper deals with 

 the well-known contradiction which arises in the theory of 

 aggregates, and is expressed in the statements : — The 

 aggregate of all ordinal numbers has an ordinal number 

 which must be the greatest of all ordinal numbers, that is, 

 the last of the series ; but the series cannot have a last 

 element. The source of the contradiction is traced to the 

 assumption that an ordered aggregate necessarilv possesses 

 a definite order-type which can be regarded as an object, 

 viz. the ordinal number coming immediately after all those 

 which are the elements of the aggregate of which it is 

 the order-type. The author proposes to deny this principle, 

 and points out that those parts of the theory of aggregates 

 which are of importance for the general purposes of mathe- 

 matical analysis would not be affected by this denial. — The 

 Maclaurin sum-formula : Rev. E. W. Barnes. The paper 

 contains a new form for the remainder, and a fresh 

 demonstration of the conditions in which certain generalisa- 

 tions of the formula are valid. — The asymptotic expansion 

 of integral functions of finite non-zero order : Rev. E. W. 

 Barnes. The object of the paper is to investigate the 

 asymptotic expansions of functions of the class in question 

 without making any appeal to the theory of divergent 

 series. It is shown that the most general type of integral 

 function of finite non-zero order with a single sequence 

 of non-repeated zeroes admits, when the argument is large, 

 an asymptotic expansion valid everywhere save in the 

 neighbourhood of the zeroes of the function, and all the co- 

 etiicients of this expansion can be built up from the simple 

 Riemann Zefa function. Expansions are also found in 

 the case of integral functions of multiple linear sequence. — 



On the function 2 .v"/«« : G. H. Hardy. — On the re- 



ducibility of covariants of binary quantics of infinite order, 

 part ii. :' P. W. Wood. 



Edinburgh. 

 Royal i>ociety, Janu.iry 23. — Dr. Ttaquair in the chair. — 

 On deep water ship waves ; Lord Kelvin. The waves were 

 supposed to be produced by a floating or submerged body 

 of proper form moving forward with a given speed in a 

 canal of rectangular section. A solution of the appro.xi- 

 mate equations was first obtained for a particular form of 

 surface wave associated with a definite distribution of pres- 

 sure over part of the surface and moving forward with a 

 given speed of propagation. The vanishing of the pressure 

 distribution or " forcive " occurred for a given speed which 

 coincided witli the speed of propagation of the free sinus- 

 oidal wave. When the forcive did not vanish it acted with 

 or against the displacement according as the speed of 

 propagation was less or greater than this critical velocity. 

 By a suitable synthesis of a series of distributed forcives 

 with their associated surface displacements, the solution was 

 put in a form which lent itself towards the elucidation of 

 several important problems. Thus in certain cases it was 

 possible to imagine a cover fitting part of the water surface 

 and moving forward with the proper speed associating this 

 form of surface with a definite forcive, and in this way a 

 solution was obtained of the train of waves accompanying 

 the passage of a suitably shaped pontoon over the fluid 

 surface, .'\gain, by superposition of two exactly equal for- 

 cives half a wave-length apart, the surface outside the 

 region over which the forcive acted was reduced to rest. 

 The disturbed surface within the region of the acting 

 forcive and moving forward with it could then be imagined 

 as fitted with a cover : .Tnd thus was solved the problem 



