4-02 



NA TURE 



[Feb. 26, 1885 



majority are on the Diadema-type, and the exceptions were 

 recorded. The structure of the triplets of Micropyga is unique, 

 and the arrangements, leaving out the position of the pores, is 

 somewhat like that of Ccelopleurus. Aspidodiadema, as has been 

 explained by A. Agassiz, is like Cidaris in its ambulacra. 



Mathematical Society, February 12. — J. W. L. Glaisher! 

 F.R.S., President, in the chair. — Miss Emily Perrin, Ladies 

 College, Cheltenham, was elected a Member, and Mr. J. Griffiths 

 was admitted into the Society. — Mr. Tucker read the following 

 papers : — " Sur les Figures semblablement Variables," by Prof. 

 J. Neuberg ; on the extension of Ivory's and Jacobi's distance- 

 correspondences for quadric surfaces, by Prof. J. Larmor ; and 

 some properties of a quadrilateral in a circle the rectangles under 

 whose opposite sides are equal, by R. Tucker. Messrs. Jenkins 

 and S. Roberts spoke on the subject of the first paper. A clear 

 idea of Mr. Tucker's communication will be obtained by drawing 

 a figure for the following particular case : — Take a quadrilateral, 

 A BCD, in a circle, with its angles A, B - 5S°, 112' respec- 

 tively, and A B (the unit of length) equal the side (in this case) 

 of the inscribed square. Let B C — A, C D — fi, DA = v ; 

 then if two sets of lines drawn in the same senses with the respec- 

 from the two ends make with those sides (in the par- 

 ticular case) angles of 38 , these lines will intersect in two sets 

 of 4 lines in P, P' (analogous to the Brocard points of a triangle), 

 and in four sets of 2 lines in F, G, //, K. The quantities A, fx, v, 

 are so related that A v = /j, hence w'e see that all such quadrilaterals 

 have the rectangles under their opposite sides equal. The six points 

 lie on a circle which also passes through the circum-centre ( 0), \ 11 lint 

 of intersection (E) of the diagonals AC, B D, and through the 

 mid-points JiJ, L of those diagonals. In fact, since OE is a 

 diameter of this new circle, the mid-points of any chord of the 

 circum-circle which passes through E lies on the small circle. 

 P, P are the foci of an ellipse inscribed in A B C D. 

 Further properties are OP=UP', A P.B P. CP.D P = 

 A P' . B P' . C P' . DP', and many other metrical and angular 

 relations belong to the above collection of points. If instead of 

 38 we take $, then cp is found by the equation cosec -<p = 

 cosec "A + cosec -B. The side A'B subtends at an opposite 

 vertex an i. 8 L , such that cot 8; = cot <f> - cot A - cot B, with 

 similar values for the other angles. The circum-radius (At is 

 found by — 



2R- - (cot 4> - cot A) (cot <p - cot B), 

 and that of the small circle (p) by 



2p ;= A' sec <j> V cos 2<p. 

 Relations connecting the 6 set and <p with the Brocard angles of 

 the 4 constituent-triangles are easily obtained in a neat form. 

 If through E lines are drawn parallel to the sides cutting 

 them in eight points, these points lie on a circumference which 

 has many properties analogous to tho--e of the " T.R. " circle of 

 a triangle. If p' is its radius, then p- + p'- = A' -/„ : the eight 

 points from two equal inscribed quadilaterals similar to thi 

 figure, and whose sides make the same angle <p with the given 

 sides. 



Geological Society, January 28. — Prof. T. G. Bonney, 

 F.R.S., President, in the chair. — Frederick John Cullis, Henry 

 Dewes, Henry Hutchings French, Jacob Hort Player, and the 

 Hon. Donald A. Smith, were elected Fellows, and Prof. F. 

 Fouquu, of Paris, and Dr. Gustav Lindstrbm, of Stockholm, 

 Foreign Correspondents of the Society. — The President called 

 attention to the great loss the Society had sustained in the 

 sudden and unexpected death of Dr. J. Gwyn Jeffreys, F.R.S., 

 •&c, who had been for twenty-one years continuously a Member 

 of the Council, and for fourteen years of that time had performed 

 most valuable services to the Society as Treasurer. — The follow- 

 ing communications were read : — The Boulder Clays of Lincoln- 

 shire : their geographical range and relative age, by A. J. Jukes- 

 Browne, F.G.S. The author commenced by referring to the 

 late Mr. Searles V. Wood's papers on the glacial beds of York- 

 shire and Lincolnshire, and stated, as the result of his own 

 investigations, that two distinct types of boulder clay occur in 

 Lincolnshire : (1) the gray or blue clay ; (2) the red and brown 

 clays, the former undoubtedly an extension of the upper or 

 chalky boulder clay of Rutland and East Anglia, while the 

 second includes the purple and Hessle clays of Mr. S. V. 

 Wood. These two types of boulder clay are very rarely in 

 contact with each other. The brown boulder clays of East 

 Lincolnshire rest upon a broad plain of chalk, which appears ti 

 terminate westward in a concealed line of cliff, this cliff-line 

 coinciding with the strike of the slope which descends from the 



chalk wolds to the boulder clay plateau by which they are 

 bordered. The present boundary line of the boulder clay runs 

 along this slope for long distances, though in many places the 

 clay has surmounted the slope and caps the hills to the west of 

 it. From Louth the main mass of the " brown clay " is bounded 

 by a line drawn through Wyham, Hawerby, Laceby, and 

 Brocklesby to Barrow and Barton on Humber, sweeping around 

 the north end of the Lincolnshire wolds and occurring on both 

 sides of the Humber. Previously to the author's inspection of 

 this district no purple or Hessle clay had been discovered west 

 of South Ferriby, and these clays were supposed to be entirely 

 absent on the western side of the wolds. The officers of the 

 Survey have, however, mapped several tracts of such clay in the 

 valley of Ancholme. It occupies the surface at Horkstow, 

 Winterton Holme, Winterton, and Winteringham. It probably 

 underlies the alluvium of the Ancholme near and south of these 

 places, and occurs again at higher levels in the neighbourhood 

 of Brigg. South of Brigg it has been seen at low levels on 

 either side of the valley of the Ancholme, as far as Bishop's 

 Bridge near Glenthara. Beyond this point it was not traceable 

 in the Ancholme valley, but south of Market Rasen patches of 

 reddish-brown clay, mottled with gray, and containing small 

 flints and pebbles of chalk, occur, and cap the low ridges sepa- 

 rating the valleys of the brooks. Another tract of boulder 

 clay, which the author considers to belong to the same series, 

 occupies the western border of the fenland south-east of Lincoln, 

 what is left of it forming a ridge which runs southward for many 

 miles. It passes eastward beneath the fen deposits ; and similar 

 mottled clay was seen in the excavations for the Boston Docks 

 beneath about twenty feet of fen clays, &c, and resting upon blue 

 boulder clay of the "chalky" type. Besides this section at 

 Boston, there are very few places where the two types of clay 

 are in contact, or so near as to afford any evidence as to their 

 relative age. Near East and West Real, and again near Louth, 

 the "brown clays" are banked against the slopes of hills which 

 are capped with the " chalky clay." The same is the case also 

 near Brigg, where the country seems to have been originally 

 covered by a sheet of the chalky clay, through which valleys 

 were eroded into the Jurassic clays, and the brown (Hessle) clay 

 is found only in these valleys. The author concludes, therefore, 

 that the "Brown-clay series" is of much newer date than the 

 " Blue and Grey series." In conclusion the author summed up 

 the inferences drawn in the paper, correlated the Basement clay 

 of Holderness with the Chalky clay of Lincolnshire, and sug- 

 gested that the Purple clay may be confined to the east side of 

 the wolds. The classification he would propose is therefore as 

 follows : — 



Lincolnshire. Yorkshire. 



( Hessle clay. Hessle and upper red clay 

 Newer Glacial. < of coast. 



( Purple clay. Purple clay. 

 Older Glacial = Chalky clay. Basement clay. 

 — On the geology of the Rio Tinto Mines, with some general 

 remarks on the pyrilic region of the Sierra Morena, by J. H. 

 Collins, F.G.S. After briefly describing the geographical posi- 

 tion of the Rio Tinto mines and the occurrence at the same of 

 pyritous ores amongst slates and schists which abut agaii^t 

 gneissose rocks to the north, and pass under Tertiary beds to the 

 southward, the author proceeded to consider the general cha- 

 racters and associations of the pyrites-deposits, and then gave a 

 general account of the Rio Tinto district. The slates were 

 described, and the iossil evidence recapitulated upon which an 

 Upper Devonian age had been assigned to them. Analyses 

 were furnished to show the changes due to weathering and to 

 infiltration. The various intrusive rocks (syenite, diabase, and 

 porphyries) occurring in the schists were described, and analyses 

 of them given. The sedimentary iron ores and their composi- 

 tion were next noticed, and the author ascribed their formation 

 to deposition in lakes. The masses of pyrites which furnish the 

 principal ores of Rio Tinto were then described, their mode of 

 occurrence in fissures between dissimilar rocks explained, and 

 their formation discussed. The different kinds of ore obtained 

 from the mines were noticed in detail, and several analyses 

 added, giving samples both of the mixed ores and of the pure 

 minerals. The manganese lodes were next described, and shown 

 to be parallel to the pyrites fissures, and frequently to be Ana- 

 branches of the latter. A summary of the author's conclusions 

 as to the stratigraphy of the district, the ore deposits, and the 

 surface-geology was appended. — On some new or imperfectly 

 known Madreporia from the Great Oolite of the counties of 

 Oxford, Gloucester, and Somerset, by R. F. Tomes, F.G.S. 



