268 



NATURE 



[7 an. 15, 1880 



L = i, 



= a , £ = b, T = c , 



A A 



We thus ' get for the determinant the 



aud then putting k = o. 

 symmetrical form — 



I ,,2 _ ifi _ f » 2«» , ■ 2 ^ <i , 



2 a b , - a 2 + b" - e 2 , 2b c , 



2 c a , 2 be , - a? - b- + c-, \ 



the value of which is r 3 , and the sum of the terms on the leading 

 diagonal = - r, where r = a 2 + b- + e 2 . The terms of this 

 determinant will be integral if a, b, c are either integral, or of the 

 form integer x -J2, or indeed if they contain any common factor 

 entering under the square root only. It has been shown by 

 Legendre and Gauss that every integer, or its double, is the sum 

 of three squares. It follows that an orthogonal :ransformation 

 of the above symmetrical character can be found for every whole 

 number r. The transformation is, however, nugatory for certain 

 low values of r. The symmetrical transformation means a turn 

 of two right angles about an axis whose direction cosines are 

 proportional to a be. That is to say, if a cube be taken, with 

 the axes for cd^es, and those of rational length, in a cubical 

 system, it is always possible to find one or more axes, inclined to 

 the co-ordinate axes su ch that if we turn the cube about them 

 through two right angles, its points will still rest on points of the 

 system. — Mr. Hammond gave a form for the complementary 

 function in fractional differentiation. Messrs. Cayley, Merritield, 

 Robert-, Glaisher, and Freeman took part in a discussion upon 

 Mr. Hammond's communication. 



Edinburgh 



Royal Society, January 5.— The Right Hon. Lord Moncrieff, 

 president, in the chair. — At the request of the Council an address 

 on the Trigonometrical Survey of Palestine was given by Lieut. 

 Conder, R.E., late in command. Apart from its more technical 

 nature, the paper contained many details of archaeological, 

 ethnological, and geological interest, including the discovery of 

 the positions of not a few historic localities, such as the Cave of 

 Adullam, Bethabara beyond Jordan, the vineyard of Naboth, 

 &c. — Prof. Tait communicated a note on Minding's theorem by 

 Prof. Chrystal. This beautiful theorem in rigid dynamics, the 

 proof of which originally occupied many quarto pages of Crell/s 

 Journal with elaborate analysis, had been proved by Prof. 

 Chrystal by means of Pluck er's congruencies, in a manner almost 

 rivalling in brevity the quaternion demonstration by Prof. Tait. 

 A generalisation of the theorem led to the discovery of a volume- 

 locus, — Prof. Tait then communicated two mathematical notes : 

 (17) on a problem in arrangements ; (b) on a graphical solution of 

 the equation Vp (pp = o. The former was given under the name 

 of The Mad Schoolmaster. A schoolmaster went mad, and 

 began to operate upon his class of boys according to the follow- 

 ing method : — The dux he put down one place, the new dux two 

 places, the next dux three places, and so on till every boy in the 

 class had been shifted at least once. He then began again 

 putting the first dux down one place, the next dux down two, 

 and so on as before. After 306 operations, he found the boys 

 arranged exactly as they had been at the beginning. He then 

 cast one out, and set to work operating similarly upon the re- 

 mainder ; but to his dismay found that he had to operate 1,120 

 times before they were brought back to their old arrangement. 

 The problem is to find how many boys were in the class, and is 

 of course a particular case of a much more general problem in 

 arrangements. Prof. Tait gave a graphical method by which 

 the inverse problem could be solved by a simple inspection for 

 any number. 



Paris 



Academy of Sciences, January 5.— M. Edm. Becquerel in 

 the chair. — M. Wurtz was elected vice-president for 18S0. — M. 

 Daubree gave information as to the Academy's publications and 

 1 hanges in members and correspondents. Two members have 

 died in the year— MM. de Tessan and Gervais— and one corre- 

 spondent—Mr. MacLear.— The following papers were read :— 

 On the motion engendered by diffusion of gases and liquids, by 

 M. Sainte-Claire Deville. The difference of velocity in passage 

 of gases through a porous septum is utilised in raising liquid, a 

 machine being thus produced which apparently does not con- 

 sume heat. M. Debray's diffusion apparatus is used, being 

 changed into a machine simply by adding tubes of discharge and 

 valves. Dutrochet's endosmomeier may be similarly changed to 

 a machine.— On the hydride of copper ; reply t'1 M. Berthelot, 

 by M. Wurtz.— On the heat of formation of hydrate of chloral ; 

 reply to M. Berthelot, by M. Wurtz.— Remarks on a recent 

 communication regarding the photospheric network, by M. 



Janssen. The reticulated aspect produced by faculoe round 

 spots has been long known, but has nothing in common 

 with the photospheric network revealed by photographs. This 

 is formed by the totality of points where the solar granu- 

 lation is disturbed by upward currents of hydrogen, while 

 the faculse are due to gaseous masses above the granulated 

 region. The former is in the photospheric layer, the latter 

 above it ; the network seen chiefly in the central parts, the 

 faculae only easily visible at the border. M. Lamey seems to 

 have confounded the phenomena. The network is only visible 

 in photographs C25 m. to C30 m. in diameter. — On treatment 

 of phylloxerised vines, by M. Maren. — M. Perry was elected 

 Member in Geography and Navigation in room nf the late M. 

 de Tessan. — Carbonic acid in the air in its relations with the 

 great movements of the atmosphere, by M. Marie-Davy. A 

 discussion of daily mid-day analyses (April, 1876, to June, 

 1879) at Montsouris, by MM. Levy and Allaire. The quantity 

 of C0 2 in 100,000 parts of air in volume varied between 

 twenty-two and thirty-six. Winds blowing from Paris con- 

 tained, on an average, less CO a than those from the country. 

 This might be explained by CO« occurring more largely in air 

 below than above the layer of clouds. Three periods are noted : 

 in the first, to November, 1877, the C0 2 was below the mean, 

 and sometimes very low; in the second, to September, 1S79, 

 it was considerably above the mean ; the third, commencing in 

 October, 1879, showing very little CO a . The second period 

 was one of wet weather, and comprised two bad harvests ; the 

 equatorial current was predominant in France. This current 

 had less extension in the first, which was also less wet, and gave 

 better harvests. A complete change in the atmospheric circula- 

 tion seems to have occurred since October. — On an application 

 of the pre-existence of Ampere's currents in soft iron, by M. 

 Treve. With iron solenoids he gets much better effects than 

 with copper. — On new luminous tubes, by M. Treve. Into a 

 large Geissler tube he introduces a Fizeau condenser, and fixes 

 the electrodes (connected with the two poles of the induced 

 current of a Ruhmkorff coil) to the eleventh and twelfth tin 

 sheets. On reducing the pressure to 0'003m. or so, sound is no 

 longer heard, but a brilliant white light springs in pearls from 

 the sheets of the condenser, quite distinct from the common light 

 of Geissler tubes. — Action of acetic anhydride on some phenol- 

 aldehydes, by M. Barbier. — On a new synthesis of saligenine, by 

 M. Greene. This is by reaction of chloride of methylene with 

 phenate of sodium in presence of hydrate of sodium. — On the 

 preparation of iodised and bromised derivatives of benzine, by 

 M. Greene. — On the comparative value of monochromatic im- 

 pressions in invertebrates, by M. Chatin. In arthropods, deca- 

 pod crustaceans, and some insects, Dewar's current of the retina 

 is well marked, and varies with different rays, reaching a maxi- 

 mum in the yellow-green region. In molluscs, and especially in 

 pulmonated gasteropods, the differences are still more pro- 

 nounced. — Histology, development, and origin of the testicle 

 and ovary of Campanularia angulata (Hincks), by M. Fraipont. 

 M. Touchiinbert presented a photograph of forms of snow 

 (resembling small roses) observed at Poitiers. 



CONTENTS Page 



Erasmus Darwin 2 45 



North American Ethnology. By W. L. Distant 247 



Letthrs to the Editor : — 



Sunshine Cycles.— Prof. Piazzi Smyth ^S 



Cranial Measurements.— Prof W. H Flower. F.R S. . . . . 249 

 '■ Why the Air at the Equator is not Hotter in January than in 



July"— Freezing of the Neva— A. Woeikof :4a 



Hearing through the Mouth.— W11. Chappell 250 



Intellect in Brutes.— Commander J. P. Maclear; Francis E. 



Colenso • • • • ■ • 2 5° 



Notes on the Papuans of Maclay Coast. New Guinea.— V. Ball . 251 



The Word " Telegraph."— Richard B. Prosser 251 



Stags' Horns.— Dr. F. Buchanan White . . . ... . • • =5" 



Visualised Numerals. By Francis Galton, F.R.S. (With 



Diagrams) ' 252 



On a Modk of Explaining the Transverse Vibrations of Light. 



By S. Tolvek Preston ■ ... 256 



The Natural History of the Transit of Venus Expedition . . 259 



Artificial Diamonds =°° 



The Times on British Birds 200 



Edison's Electric Light "J* 



Notes - 



Our Astronomical Column: — ^ 



Winnecke's Comet *2j 



Meteorological Notes 



Gbogkaphical Notes " 6 J 



Physical Notes ;. 



Scientific Serials J' 



Societies ano Academies - ' 



