466 



NA TURE 



[September 6, 1S94 



Section E. 



Mr. Sowerbatls said that the Manchester Geographical 

 Society had come to the conclusion that geography would 

 never be taught satisfactorily in primary schools unless it was 

 made a compulsory subject. Progress had been made in some 

 primary schools by the instituti m of school-museums. It was 

 a s:ngular fact that at an examination in geography of the 

 primarj' schools of Cheshire, Lancashire, and Yoikshire, the 

 girls had won all the prizes in Yorkshire, and the boys in 

 Lancashire. His Society had for the last two or three years 

 published an analysis of the chief geographical papers which 

 had appeared in English and ioreign journals. 



Sectio.n H. 



Ethnographical Survry. — Mr. Brabrook remarked that during 

 the past year their list of suitalil: villages had been con- 

 siderably increased, and now numbered 367. At Ipswich a 

 sub-committee had been formed to assist theui, and at Liverpool 

 the keeper of the museum had given most valuable help. In 

 Wales their sub-committee had met and had done good work, 

 and the same remark might be made of Ireland. In Scotland 

 they had a promise of assistance from the Gla-gow Archa;ological 

 Society. They had been told that their instructions about 

 photographing were too minute, but they had been drawn up by 

 Mr. Francis Gallon with reference to his system of composite 

 photographs, and any departure from them would make the 

 application of that system comparatively difficult. 



Mr. Sowerhults stated that old people in his district objected 

 to be photographed and measured. 



Dr. Garson said that as regards photographs it was not 

 necessary to get all the appliances Mr. Galton had mentioned 

 It was desirable to have a seal which co Id be raised or lowered 

 like a piano-sto^l, so that each person might have his head in 

 the same plane, whatever his height might be. It was well, also, 

 to have chalk lines on the floor at right angles to each other, 

 the sitter being directed to look along either one line or '.he other. 

 They did not want measurements of people more than fifty 

 years old. 



Mr. Brabrook added that a set of instruments for measure- 

 ments might be had for £\ 6., and a more expensive set for 

 ;^3 y. And Dr. Garson remarked that the cheaper set was 

 quite good enough. 



A vote of thanks to the chairman closed the proceedings. 



SCIENTIFIC SERIALS. 



Proceedings of the Edinlnirgh Mathematical Society, vol. xii. 

 (William^ and Norgate, 1894.)— The geomclro.;raphy of 

 Euclid's problems, by IJr. J. S. Mackay, is a mndific.ition of 

 M. E. Lemoine's La Gcomelrographie ou r.iri des cunsiructinns 

 Giomctriqucs (the subject ot iwn memoirs read at the Oran 

 (1S88) anil Hau (1892) meetings of the Eicnch Associ.uinn for 

 the .-Vdvanccment ol the Science>), and an ai>|ilication of it 10 

 the problems in the fir>l si» books of Euclid's " Elcmenls." 

 The restric(ion> arc those of Euclid, viz. ihat the cunstruciioiis 

 should be effected by means o( the slramhr-eilgc ami Clll1l)la^se^ 

 only. It is an interesting inlroducti n of M. Lcmoinc'.^ mcth.ils 

 to English readers. The same auihor cuniiiliuies foinmla: con- 

 nccteu with the -radii of the incircle ami the excircles ul a 

 triangle. This is on ihe lines of the woik «e reci nlly no iceii 

 by the same writer (vol. i. EJin. Maih. Soc. I'roieeditixs). Ii 

 is founded ui^in a t-bk given in the Lady's ana Cetiiteman's 

 Diary for 1871. Ncaily all of ihe eighiy loimula- are .isMghed 

 to the authors who first puhlishcil them : pu^»ibly iho>e un- 

 assigned arc due to I)r. .Maci~ay himself. M. Paul Aniieri, in 

 hn "Coordonnt-cs Tangcniielles," apjilies them to the dis- 

 cuvsioii of a number of general problems relating to surfaces of 

 the second order. — Dr. Sprague writes on the geometrical in- 

 lerprclation of <■ ; his investigation was suggested by a result 

 given in Hayward's " Vector Algebra and Trigonometry."— Mr. 

 G. A. Gibson, in a proof of the uniform convergence of the 

 Fourier Serici, with notes on the difTercnliation of the seiies, 

 discusses a point which has not, apparently, been considered in 

 the Kngli-.h leti-books. — In addnion to the above paper> there 

 arc scvcial short notes : Prof. Crum llrown gives an abstract 

 of a pa[)e' (to appear) in the 1 raniactiom of the Rnyal Society 

 of E(liiiburi;h, un ihc division o( a parallelepiped inio lelra- 

 hedra ; note.- on factoring, J. W. Butlers ; on a problem in 



NO. I 297, VOL. 50] 



tangency, G. E. Crawford ; on certain maxima and minima, G. U 

 Duihie ; on solutions of certain diflerential equations, F. H. I 

 J.ickson ; on E. Carpenter's proof of Taylor's theorem, R. F. 

 Muirhead ; notes on the number of numbers less th.in a given 

 number and prime to it, and on the pedal triangle. Prof. 

 Sieggall ; five notes, vii. two circular notes, geomeirical note 

 (ii. ), two triplets of circum-hyperbolas, three parabolas con- 

 nected with a plane triangle, and notes on an orthocenlric 

 triangle, R. Tucker ; and a note, by \V. Wallace, on a third 

 mode of section of the straight line. Of the other communica- 

 tions that were made to the Society during the session the titles 

 only are given. A list of members and of the presents made to 

 the library close the volume, which contains a good deal of 

 matter of interest to mathematical teachers. 



SOCIETIES AND ACADEMIES. 



London. 



Royal Society, June 7. — "On the Recurrent Iai.iges 

 following Visual Impressions." By Shelford Bidwell, F. K.S. 



The earliest recorded observation of a certain curious pheno- 

 menon associated with optical after-images is that of Prof. C. .\. 

 Young, who published a note on the subject in the year 1872, 

 and proposed that the phenomena should be called "recurrent 

 vision." (Phil. Mai;, vol. xliii. 1872, p. 343). He noticed 

 that when a powerful Leyden jar discharge took place in a 

 darkened room, any conspicuous object was seen twice at least, 

 with an interval of a little less than a quarter of a .second ; often 

 it was seen a third time, and sometimes even a fourth. 



A few months later an account of two experiments on the 

 same subject was published by Mr. A. S. Davis. (Phil. .Ma«. 

 vol. xliv. 1872, p. 526). In the first, a piece of charcoal, one 

 end of which was red- hot, was waved about so as to describe an 

 ellipse or circle a few inches in diameter. A blue image of Ihe 

 burning end was seen following the ch-ircoal at a short distance 

 behind it, the space between the charcoal and its image being 

 absolutely dark. The other experiment was made with a jiiece 

 of apparatus resembling a photographic instantaneous shutter. 

 The shutter was interposed between the observer's eye and the 

 sky, and was covered with pieces of coloured glass, through 

 which momentary fl.ishes of light were allowed to pass. It was 

 found that e.tch fl.ish was, after a short interval, generally 

 succeeded by a recurrent image, the colour of which was nearly 

 complementary to that of the glass. 



In 1885 the author called attention to a very simple and effec- 

 tive method of exhibiting a recurrent image (Nature, vol. 

 xxxii. 1885, p. 30). If an ordinary vacuum tube, illuminated 

 by an induction coil discharge, is made to rotate slowly upon a 

 horizontal axis fixed at right angles 10 the middle of ihe tube, 

 the lube is seen to be followed at a distance of a few degrees 

 by a ghost-like image of itself, the ghost exactly imitating the 

 oiigmal in form, but having a uniform steel grey colour. In 

 the same paper the following observation is noted : — " The 

 v,icuum lube being at rest in a feebly lighted room, I concen 

 tra cd my gaze upon a certain small portion of it while the dis- 

 charge was passing. The current was then interrupted, anl 

 the luminous image was almost instantly replaced by a corrc- 

 spoi ding image which appeared to be intensely black upon a 

 less dark background. After a period, which I estimated at 

 from a qu.-irter to half a second, Ihe black im.igc again bccanir- 

 luminous ; this luminous impression lasted but for a small 

 fraction of a second, and the series of |)henomena terminated wiih 

 ils disappearance .... It was also found desiratile In 

 make the preliminary illumination as short as possible, a single 

 Hash being generally sufficient to ]iroduce the phenomena." 

 The following comment was added: — " The series of pheno 

 mena seem to be <lue to an affection of the optic nerve which 

 is of an oscillatory character. Abnormal darkness follows as a 

 reaction after the luminosity, and again after abnormal dark- 

 ness there is a rebounti into (cebler luminosity." 



The subject has recently atir.icled much attention in connec- 

 tion with the experim- nts of M. Aug. Cliar[)entier. The 

 account of them given by M. Charpenlior in a paper on 

 " Kclinal Oscillations " ' is l>rielly as follovts: — If a bl.ick disk 

 having a white .sector is illuminated by a strong bghl, and 

 slowly turned round while the observer's eye is fixed upon ils 



' Olc.tlationR rdtiniennes," Comf>lfs Ri-Hiiits, vol. cxiii. ]<!qi, p. 147. 

 il»o " Kiiaciion oscillatuirc dc U Kcliric,'* Arcli. tie Phyuiitogie,iii)i^ p. 



