March 24, 1892] 



NATURE 



503 



This division into filaments of waves, along whose course the 

 energy of the radiation is propagated, is the true objective ana- 

 lysis of the light ; and it also, on Sir VV. R. Hamilton's prin- 

 ciples, leads to more compact and comprehensive treatment than 

 the ordinary analysis into linear rays. It is shown that the 

 effect of the medium on any filament following the given path 

 is exactly equivalent to that of a certain pair of thin astigmatic 

 lenses with a common axis, on a beam passing across them ; 

 and a method is given for constructing these lenses from obser- 

 vations made at the two extremities of the actual optical path. 

 It is shown, in continuation, that conjugate pairs of focal lines 

 at the two ends of a filament are given by a 2 to 2 correspond- 

 ence, whose general relations are exhibited graphically by the 

 aid of a pair of conies, and various developments are made in 

 this direction. There are, in general, no points which have con- 

 jugate foci ; but, if a certain condition hold, there exist two 

 transverse planes of points which have conjugate planes of focal 

 points. This occurs only when the equivalent astigmatic pair 

 of lenses have their principal sections parallel, so that the com- 

 ponent refractions in these principal sections are independent of 

 each other. It is only in this special case that the emergent 

 filament can be constructed by means of rays, in Moebius's 

 manner, by aid of the two conjugate pairs of focal planes. If 

 a certain other condition is also satisfied, there is complete 

 symmetry round the axis, except as regards a possible con- 

 stant rotation of the filament ; and then the optical path is 

 equivalent to refraction by a single ordinary thin lens. — The 

 President communicated a paper, by Prof. W. Burnside, on I 

 cases in which a hyper-elliptic integral of the first order can I 

 be expressed as the sum of two elliptic integrals. — Mr. Tucker 

 read abstracts of the following notes : — On the analytical j 

 theory of the congruency, by Prof Cayley, F. R.S.— On certain i 

 curves of the fourth order, and the porism of the inscribed and ' 

 circumscribed polygon, by Mr. R. A. Roberts.— Notes on dual- 1 

 istic differential transformations, by Mr. E. B. Elliott, F.R.S. [ 

 A perusal some time ago of De Morgan's paper in the Cam- ' 

 bridge Transactions on the subject of the principle of duality in 

 differential equations which bears his name led Mr. Elliott 

 to notice a short note thereto, in which the author an- 

 nounced that after writing his paper he had found a note 

 by Chasles, in which the method had been anticipated. Upon 

 this, referring to Chasles's work (" Apercu Historique," note 

 XXX ), he found that Chasles had stated arid to a certain extent , 

 developed a theory on the subject of much wider generality. 

 It occurred to Mr. Elliott that some further consideration 

 might with advantage be given to Chasles's conclusions and 

 their extension ; and a portion of this paper is the result. 

 It had previously occurred to the author that recent theories as 

 to the transformation of differential expressions by interchange , 

 of dependent and independent variables, and in particular the ] 

 theory of reciprocants, had a bearing on the more restricted or \ 

 De Morgan duality, and even more on its simpler analogue as 

 to ordinary differential equations, which had probably escaped '•■ 

 notice. Another portion of these notes is devoted to the elucida- 

 tion of this idea.— Prof. M. Hill made a few remarks on ' 

 singular solutions ; and the President spoke on the rectification 

 of the Cartesian oval. It has been shown by Prof. Genocchi, of ■ 

 Turin [Annalidi Matematica, 1864), and by Mr. Samuel Roberts 

 (Proc. L. M.S. iii.), that the arc of a Cartesian oval can be 

 expressed as the sum of three elliptic arcs. Taking a fixed 

 oval (i.) and its conjugate oval (ii.) in a triconfocal system of 

 Cartesians, then as a variable orthogonal oval traces out by its 

 intersection with (i.) a certain arc, us conjugate oval traces out 

 on (ii.) another arc ; the sum of these arcs can be expressed ' 

 by a single elliptic arc. while the difference is expressible as 

 the sum of two elliptic arcs ; thus leading to the theorems of 

 Prof. Genocchi and Mr. S. Roberts. 



Anthropological Institute, March 8.— Edward B. Tylor, 

 F.R. S., President, in the chair. — Mr. J. Allen Brown read a 

 paper on the continuity of the Palaeolithic and Neolithic periods. 

 The deductions of the author are based on the large number of 

 flint implements of Palaeolithic type which have been discovered 

 during recent years at PLasibourne, East Dean, Cuckmere, and 

 in other combes and dry valleys in England ; at East Dean, &c., 

 they are associated with compact aggregated deposits of flints 

 and chalk rubble, evidently due to the erosion of the valleys and 

 combes by underground water, as seen at Birling Gap, near 

 Eastbourne. The valleys of Sussex have been subject to many 

 changes during the concluding episodes (bo'.h glacial and sub- 

 aerial; of the Quaternary period, and in many cases the older 



NO. I 169, VOL. 45] 



forms of flint implements have been covered up and preserved 

 by the deposit of loam and chalk rubble resulting from the waste 

 of the surface of the land. Intermixed or associated with the 

 flint implements of older types are others of transition form, to 

 which he desired to see the term " Mesolithic " applied. The 

 East Dean Valley appeared to contain flint implements forming 

 a series ranging from the late Palaeolithic age to the polished 

 stone period of true Neolithic. The old mining-shaft at Ciss- 

 bury has furnished analogous specimens. Similar implements 

 of the Palaeolithic type have been found in chalk rubble far 

 awny from the sea-board, and associated with the bones of the 

 mammoth, tichorine rhinoceros, hippopotamus, and other Qua- 

 ternary Mammalia, as well as the remains of various animals of 

 species still living, showing that man Was present in Southern 

 Britain not only in the plateaux and river-drift periods, but also 

 continuously into the so-called Neolithic epoch. The author 

 alluded to the evidence derived from caves and rock-shelters and 

 peat-beds, both in this country and in France, which pointed in 

 the same direction. A large series of flint implements of Pdlceo- 

 lithic form from East Dean, &c., were exhibited, with specimens 

 of corresponding forms from the river-drift ; also a series showing 

 the evolution of the axe or celt form from the simply chipped 

 nodule of the plateaux drift, through the valley drift and transi- 

 tional types to the highly finished celts of the Neolithic age, of 

 which the forms were continued in the earliest stages of the age 

 of copper and bronze. Other series were exhibited, showing in 

 like manner the evolution of the spear-head and knife, &c. 



Zoological Society, March i.— Dr. A. Giinther, F.R.S., 

 Vice-President, in the chair. — The Secretary read a report on 

 the additions that had been made to the Society's Menagerie 

 during the month of February 1892, and called attention to two 

 Short-winged Tyrants (Machetoruis rixosa) purchased February 

 15, being the first examples of this bird that have reached the 

 Society, and to a female Beatrix Antelope {Oryx bealrix) from 

 Arabia, presented by Lieut. -Colonel Talbot, February 18. — Mr. 

 J. Graham Kerr gave a short account of the expedition up the Rio 

 Pilcomayo in 1890-91, which he had accompanied as naturalist. 

 Mr. Kerr made remarks on the animals met with on the banks of 

 the Pilcomayo, and exhibited a series of photographs illustrating 

 the vegetation of the district and its native Indian inhabitants. 

 — Mr. G. F. Hampson read a paper on stridulation in certain 

 Lepidoptera, and on the distortion of the hind-wings in the 

 males of certain OmmatophorirtcB. The author attributed the 

 clicking sound described by Darwin as produced by various 

 species of the South American genus of Butterflies, Aitgerona, 

 and confirmed by Wallace and other observers, to the presence 

 of a pair of strong corneous hooks on the thorax, which play on 

 a pair of curved hooks with spatulate ends attached to the inner 

 margin of the fore-wing close to the base, and surrounded by a 

 membranous sac which acts as a sounding-board. An account 

 was given of a similar sound produced by the males of a Burmese 

 moth of the family Agaristidas and of a buzzing sound in an allied 

 Australian form, both of which have a patch of ribbed hyaline 

 membrane below the costa of the fore-wing. The sound was 

 attributed to the friction of spines, attached in the former to the 

 first pair of legs, in the latter to the second pair, on the ribbed 

 membrane. A description was then given of the transformation 

 of the costal half of the hind-wing in the Noctuid genus Patida 

 into a large scent-gland, and of the manner in which this had 

 distorted the neuration. The still greater distortion of the neura- 

 tion in the allied genus Argida was attributed to its once having 

 possessed a similar scent-gland, now become rudimentary by dis- 

 use. — A communication was read from Prof. W. N. Parker, on 

 the retention of functional gills in young Frogs [Raita temporaria), 

 which he had succeeded in producing in specimens reared in his 

 laboratory. Prof. Parker described ihe method employed with 

 this object, and made remarks on the way in which the fore- 

 limbs are protruded. — Prof F. Jeffrey Bell read a paper entitled 

 " A Contribution to the Classification of Ophiuroids," to which 

 were added descriptions of some new and little-known forms of 

 this group. — Mr. M. F. Woodward gave an account ot an 

 abnormal Earthworm {Ltimbricus terrestris) possessing seven 

 pairs of ovaries situated on the eighth and following souiites to 

 the fourteenth. 



Oxford. 



University Junior Scientific Club, March 4. — Mr. J. A. 

 Gardner, of Magdalen College, President, in the chair. — Some 

 investigations of the action of dry hydrochloric acid gas on dry 

 carbonates were brought forward by Mr. F. R. L. Wilson, 



