May 19, 1904] 



NA TURE 



71 



Challenger Society, A| ril 27. — Sir ]-\\n Mirray in tlie 

 chair. — Prof. Minchin exhibited specimens of the new 

 sporozoan, Lynnphocystis johnstoni. — Mr. E. T. Browne 

 showed MedusEe from Valencia. — Dr. G. H. Fowler ex- 

 plained some graphic diagrams of the distribution of 

 Biscayan Cha^tognatha, and announced that he had detected 

 Krohnia hamaia among specimens obtained at the Falk- 

 land Islands by Mr. \allentin within six fathoms from the 

 surface. — Mr. \'. H. Blackman read a paper on the meta- 

 bolism of the ocean, dealing with the close analogy between 

 the circulation of nitrogen on land and that in the sea ; 

 this was followed by an interesting discussion. — Mr. G. P. 

 Farran described the copepods of the north-east Atlanti.; 

 slope ; of these rather less than half present a wide .la 

 often tropical distribution, occurring also in the Indian or 

 Pacific Oceans. The remainder are only known as Atlantic 

 or .\tlanto-Mediterranean species, many being bottom 

 haunting forms, the recorded range of which is likely to 

 be extended. About 12 per cent, of the total copepod fauna 

 extends north to the Arctic regions. 



British Academy, April 27.— Lord Reay, president, in the 

 chair. — Prof. I. Gollancz read a paper on Shakes- 

 peariana, 1598-1602. A theory was put forward explan- 

 atory of Shakespeare's use of the name Polonius for the 

 counsellor of the King of Denmark in place of Corambis, 

 or Corambus, found in the first quarto, evidently the name 

 of the character in the old play, which belonged to about 

 the year 1587. Corambus, being discarded by Shakes- 

 peare, was used bv him as a passing name in the play of 

 "All's Well." 



Physical Society, May 6. — Mr. J. Swinburne, vice-presi- 

 dent, in the chair. — Some instruments for the measurement 

 of large and small alternating currents : W. Duddell. The 

 author, after some preliminary remarks on the available 

 means for measuring alternating currents, proceeded to 

 describe three thermal instruments which he has constructed 

 for this purpose. The first instrument is essentially a 

 sensitive Ayrton-Perry twisted strip ammeter which is very 

 quick in action for a thermal instrument, and has been used 

 for observing and recording P.D.'s and currents which 

 varied as rapidly as one per second. The second instru- 

 ment exhibited was a very sensitive thermal galvanometer 

 called in the paper a " thermogalvanometer. " It consists 

 of the combination of a radio-micrometer of the " Boys " 

 type with a very small resistance which is heated by the 

 current to be measured, and in turn heats the thermo- 

 junction of the radio-micrometer by radiation and con- 

 vection. The third instrument described was a switchboard 

 instrument which works on the same principle as the last. 

 — Mr. F. E. Smith exhibited and described the following 

 instruments from the National Physical Laboratory : — (i) 

 a mercury-resistance standard ; (2) a lo-ohm build-up resist- 

 ance-box ; (3) an astatic galvanometer. 



Mathematical Society, May 12. — Dr. E. W. Hobson, 

 vice-president, in the chair. — The following papers were 

 communicated : — On the evaluation of certain definite 

 integrals by means of Gamma functions, and generalisations 

 of Legendre's formula KE' — (K — E)K' = ^5r : A. L. Dixon, 

 It has been shown by E. B. Elliott that Legendre's re- 

 lation may be regarded as a particular case of a relation 

 by which a certain sum of products of what are really 

 hypergeometric functions can be expressed in terms of 

 Gamma functions. In the Weierstrassian form of 

 Legendre's relation, a certain determinant of the second 

 order having elliptic integrals as its elements is shown to 

 be a constant. In the generalisation the determinant is of 

 order higher than the second, the elements are hyperelliptic 

 integrals, and the constant is expressed as a product of 

 Ganmia functions. The ratio of two such determinants, of 

 suitable orders, is expi essed in a similar form. Weierstrass's 

 relations between hyperelliptic integrals of the first and 

 second kinds are deduced. The results are extended to in- 

 clude a certain class of integrals which are not integrals of 

 algebraic functions. — Perpetuant syzygies : A. Young and 

 P. W. Wood. The perpetuants considered are linear in the 

 coefVicients of each quantic concerned, that is to say, they 

 are " perpetuant types." All possible products of irreducible 

 forms of a given degree and weight are arranged in a pre- 

 determined sequence so that any product may be identified 



NO. 1803, VOL. 70] 



by its place in the sequence. A syzygy expresses one of the 

 products that enters into it, viz. the one that comes earliest 

 in the sequence, in terms of others which come later in the 

 sequence. In consequence of the existence of the syzygy 

 this earliest product is "reducible." It is possible to 

 enumerate the actually irreducible forms for degree 5 by 

 means of a generating function. When the irreducible pro- 

 ducts have been identified for any degree, all the independent 

 syzygies of this degree will have been identified, there being 

 one such syzygy for each reducible product of irreducible 

 forms. The work can be completed as far as degree ti, but 

 a large class of products have been discussed in general. A 

 generating function for all irreducible products and types of 

 degree 5 is suggested in the form 



.0^ 



^it) 



and this form is proved to hold for k=i, k = 2 and k^jS. — 

 Note on the integration of linear differential equations : Dr. 

 H. F. Baiter. — Some properties of the function Fp : Rer. 



F. H. Jacl(son. — Informal communications were made as 

 follows : — On the geometrical representation -of imaginaries : 



G. B. Mathews. — A collation of Kessler's and Hertzer's 

 tables'of the residue-index {i>} of 10 (mod p) with Shanks's 

 table of the Haupt exponent (f ) of 10 (mod p) : Lieut. - 

 Colonel A. Cunningham. The numbers f and £ are 

 defined by the congruence 10^=1 (mod />= i/|-|-i). Twenty- 

 nine errors were found in Kessler's table, 3 in Hertzer's, 

 107 in Shanks's. 



Cambridge. 

 Philosophical Society, May 2. — Dr. Baker, president, in 



the chair. — Early development of the unfertilised egg of the 

 sawfly Nemaitis ribesii : L. Doncaster. In the unfertilised 

 egg the two maturation divisions give rise to four nuclei, 

 the outer two of which are the halves of the first polar 

 body, the third is the second polar nucleus, and the inner- 

 most the egg-nucleus. The second polar nucleus unites 

 with the inner half of the first, giving the " copulation 

 nucleus." This divides into two groups of chromosomes, 

 which persist without important change until the blasto- 

 derm begins to form, beyond which stage their fate has 

 not yet been followed. The egg-nucleus soon begins to 

 divide, and gives rise to the embryo, the chromosomes re- 

 maining at the reduced number. The outer nucleus of the 

 first polar body rapidly disappears. These results are very 

 similar to those obtained by Petrunkewitsch in the bee, 

 where, as in this case, virgin eggs produce males, and 

 fertilised eggs females. It was pointed out that a com- 

 parative study of the development of sawflies which pro- 

 duce males and females respectively from virgin eggs would 

 provide a test of Castle's hypothesis of sex-determination. 

 — Metallic " passivity " in relation to time and temperature : 

 Dr. W. A. Mollis. — (i) On partial fractions; (2) note on 

 plane unicursal curves ; (3) on the order of certain systems 

 of conditions : Dr. A. C. Dixon. 



Paris. 

 Academy of Sciences, May 9.— M. Mascart in the chair.— 

 The president announced to the academy the death of M. 

 Duclaux, member of the section of rural economy, and gave 

 a short account of his life work. — Remarks on the use of 

 alternating currents in chemistry and on the theory of re- 

 actions which they set up : M. Berthelot. Remark's on the 

 recent work of M.M. Brochet and Petit concerning the solu- 

 tion of platinum in a solution of potassium cyanide by the 

 action of an alternating current. The author directs attention 

 to a similar reaction with glucose studied by him in 1879. 

 The bearing of these experiments on the action of the silent 

 discharge is also discussed. — The cooling power of a feebly 

 conducting liquid current on an indefinite cylinder, the axis 

 of which is normal to the current : J. Boussinesq. — On a 

 new method of preparation of alkyl and alkylidene deri- 

 vatives of cyclic ketones. The application to the prepar- 

 ation of alkyl-menthones : A. Waller. By treating certain 

 cyclic ketones, such as menthone, with sodium, the corre- 

 sponding alcohol is formed besides the sodium derivative, 

 and in preparing alkyl derivatives this leads to undesirable 

 secondary products. The formation of the alcohol is 

 avoided if sodium amide is used instead of sodium, and the 



