November 17, 1892] 



NA TURE 



71 



Chamicleon isabdlintis, Rhampkoleon platyceps, and R. 

 brachyurus.—^r. R. Lydekker read a memoir oa some Zeuglo- 

 dont, and other Cetacean remains from the Tertiaries of the 

 Caucasus. — Mr. Martin Jacoby read the descriptions of some 

 new genera and new species of Phytophagous Coleoptera from 

 Madagascar. 



Linnean Society, November 3.— Prof. Stewart, President, 

 in the chair. — The Rev. Prof. Henslow exhibited an instrument 

 used in Egypt for removing the end of the sycamore fig, and 

 gave some account of the mode of cultivation.— Mr. A. Smith 

 Woodward exhibited and made remarks on some supposed 

 fossil lampreys {Pakospondylus gitnni) from the old red sand- 

 stone of Caithness.— The Rev. E. S. Marshall exhibited some 

 hybrid willows from Central Scotland, believed to be rare or 

 new to Britain.— Mr. G. N. Douglass exhibited the train of a 

 peahen which had assumed the male plumage. The bird, which 

 was reared at the Castle Farm, Tilquhillie, near Banchory, N.B., 

 was believed to be about thirty years old at the time of its death, 

 and for some years previously had not laid any eggs. In the 

 opinion of the exhibitor and others present the phenomenon 

 was correlated with disease of the ovarie;. Similar cases had 

 occurred with fowls, pheasants, and black game, but not, so far 

 as was known, with peafowl. — Mr. C. T. Druery exhibited 

 some new examples of apospory in ferns, namely a specimen 

 of Athyrium filix fcemina var c/arissim a wiih pinnae showing 

 development of prothalii by soral apospory, and a seedling 

 Lastrea pseitdomas cristata, showing prothalii developed 

 aposporousiy over general surface of frond (pan-apospory). — 

 Mr. J. E. Harting exhibited some live specimens of the short- 

 tailed fieldvole (Arvicola agrestis), and gave an account, from 

 personal inspection of the serious damage done by this little 

 rodent upon the sheep-pastures in the lowlands of Scotland. — 

 Mr. A. B. Rendle exhibited some seedling plants of the sugar- 

 cane which had been raised in this country by Mr. Veitch. — 

 The discussion on several of these exhibitions having continued 

 untij a late hour, a paper by Prof. Henslow, on a theoretical 

 origin of endogens through an aquatic habit, was by consent 

 adjourned to the next meeting of the Society, which will be held 

 to-day. 



Mathematical Society, November 10.— Prof. Greenhill, 

 F.R.S., President, in the chair.— This was the annual general 

 meeting and after the election of the gentlemen whose names 

 are given on p. 616 (Nature, vol. xlvi.) to serve on the council 

 for the session 1892-93, the new President, Mr, A. B. Kempe, 

 F.R.S., took the chair and at once called upon the retiring 

 president to read his valedictory address. Prof Greenhill took 

 as his subject collaboration in mathematics. — The following 

 further communications were made. Some properties of homo- 

 geneous isobaric functions, by E. B. Elliott, F.R.S. This 

 paper is a sequel to one which the writer communicated at the 

 June meeting entitled a proof of the exactness of Cayley's 

 number of seminvariants of a given type. The earlier part 

 of the present paper supplies omissions in the preceding one 

 and in the remainder the theorem on which Mr. Elliott's 

 argument was oased is transformed, and the result examined for 

 its own sake without reference to the particular application. — 

 On certain general limitations affecting hyper-magic squares, by 

 S. Roberts, F.R.S. The paper does not aim at making any 

 addition to the known ways of constructing magic squares. 

 Hyper-magic squares, as the writer regards them, include those 

 called by M. E. Lucas " carrees diaboliques, " and also treated 

 by Mr. A. H. Frost under the designation of "Nasik squares." 

 The special form is of ancient origin. The second method 

 given by Moschopulus (thirteenth century) is a general one for 

 forming such squares and they have been discussed by various 

 modern authors. The writer's object is to show some limita- 

 tions to which they are subject when the elements are positive 

 or negative integers. Incidentally it appears that hyper-magic 

 squares of oddly even orders cannot be formed of series of con- 

 secutive natural numbers. There is some reason for believing 

 that much ingenuity has been fruitlessly employed in trying 

 to form such squares. We may here mention that a very inter- 

 esting historical essay on the subject of magic squares has been 

 published by Dr. Siegemund Giinther, in his work entitled 

 " Vermischte Untersuchungen sur Geschichte der Mathematischen 

 Wissenschaften " (Leipsic 1876). The subject has also been 

 brought into connection with the " Geometry of Tissues," by M, 

 Lucas and others (see the " Principii Fundamental! della Geo- 

 metria dei Tessuti," par Edoardo Lucas, Torino, 1880). — Note 

 on the equation /- = jr (x» - i) by Prof. W. Burnside.— Note on 



NO. 1203, VOL. 47] 



secondary Tucker circles by Mr. J. Griffiths. The idea of this 

 note sprang from the fact that if G.,^, are two inverse points 

 with respect to the circumcircle (ABC) whose centre is O i.e. 

 such that OG x Og = R^, then the pedal triangles DEF, def of 

 G,^, with regard to ABC are similar. Taking G to be one of 

 the Brocard points, then (DEF) is a Tucker circle and {def) a 

 secondary circle.— On a group of triangles inscribed in a given 

 triangle ABC whose sides are parallel to connectorsof any point 

 P with A,B,C, by Mr. Tucker. If DEF, D'E'F', are a pair of 

 such triangles they are readily seen to be in perspective. Their 

 properties are considered with reference to the principal points 

 and lines of the modem geometry of the triangle. — A note on 

 triangular numbers by Mr. R. W, D. Christie. 



Paris. 

 Academy of Sciences, November 7.— M, de Lacaze- 

 Duthiers in the chair. — Letter addressed to the President by the 

 committee formed to celebrate the seventieth birthday of M. 

 Pasteur. — Influence of the distribution of manures in the soil upon 

 their utilization, by M. H. Schloesing. — Note on the reply of M. 

 Berthelot to my note of October 24, by M. Th. Schloesing.— 

 Comparison of ihe magnetic observations of General Pevzoff in 

 Central Asia with the data of the English magnetic charts, by 

 M. Alexis de TiUo. General Michael Pevzoff, in his last ex- 

 ploring tour in Eastern Turkestan, made some careful determi- 

 nations of magnetic declinations and inclinations. If these are 

 compared with those published by M. Creack in the report of 

 the Challenger expedition, it appears that in declination an 

 average correction of -f i°7 has to be applied to the latter, 

 while the inclinations are practically identical.— On the new 

 triangulation of France, by M, L. Bassot. This work was 

 commenced in 1870. It comprised the establishment of a 

 continuous chain between the Spanish frontier and Dunkerque, 

 supporting the net on three base lines, and attaching it as far as 

 possible to each of the parallel chains of the old triangulation. 

 Also a new determination of the co-ordinates of the Pantheon, 

 the fundamental point of the triangulation, the measurements 

 of base-lines in terms of the international metrical standard, 

 and the calculation of the new arc of meridian. It was found 

 that, starting from the Paris base-line, the network was verified 

 at Perpignan, at a distance of 6", to within i in 250,000. 

 Where the French system meets the English, Belgian, and 

 Italian systems, the correspondence is found practically perfect, 

 but on the Spanish frontier there exists a difference of I in 

 65,000 at present unexplained. The arc between Dunkerque 

 and Carcassonne, a# now calculated, exceeds that of Delambre 

 by 447m., or I in 20,000. — Essay on a general method of 

 chemical synthesis, by M. Raoul Pictet. — On the fifth satel- 

 lite of Jupiter, by M. E. Roger. From the empirical formula 

 for the distances of Jupiter's satellites 



log hyp a = 8 



_ 3'« _ 



003 cos _ -f e 

 2^ 5 



the probable distances of any satellites yet undiscovered can be 

 calculated. It appears that there may be one at distance I "97, 

 two others at i "61 and i '27, or a single one at i "425, and others 

 beyond the outermost satellite. The distances of those already 

 known are 2*50, 6-05, 962, I5'3S, and 27-00.- On the trans- 

 formations of dynamical equations, by M. Paul Painleve. — 

 Lenticular liquid microglobules and their conditions of equili- 

 brium, by M. C. Maltezos. The smallest drops of a liquid jet 

 falling upon another liquid often assume a lenticular shape, one 

 surface of which is more curved than the other. These are called 

 microglobules. Their diameters were measured, and their 

 volumes and masses calculated. The production of micro- 

 globules in all the liquids in Quincke's table was experimented 

 upon. — Effects of weight on fluids at the critical point, by M. 

 Gouy. — Dilatation of iron in a magnetic field, by M. Berget. 

 An elegant experiment to exhibit the lengthening of an iron bar 

 on magnetization, on the principle of Newton's rings. The bar 

 in question, provided with a cap of black glass, presses against 

 the flat side of a plano-convex lens screwed to the same stand. 

 The bar is surrounded by a coil, which can be excited by a 

 battery of accumulators. Magnetization is at once indicated by 

 the expansion of the rings. On the dissipation of the electric 

 energy of the Hertz resonator, by M. V. Bjerknes (see Wiede- 

 mann's Annalen, No. 9).— On the equality of potential at the 

 contact of two electrolytic deposits of the same metal, by M. G. 

 Goure de Villemontee. — On the rotating power of the diamine 

 salts, by M. Albert Colson. — Volumetric determination of the 

 alkaloids, by M. E. L^ger,— On the fixation of free nitrogen by 



