June 23, 1887] 



NATURE 



191 



Physical Society, June 11. — Mr. Shelford Bidwell, F.R.S,, 

 Vice-President, in the chair. — A number of Piiluj and other 

 vacuum-tubes were exhibited by Dr. Warren De la Rue. The 

 Puhij tubes consisted of a phosphorescent lamp, and radiometers 

 with phosphorescent vanes and mica disks painted with phos- 

 ]ihorescent substances. The other tubes contained different 

 phosphorescent minerals, such as ma:;nesiam carbonate, calcium 

 silicate, and Iceland spar. When illumined by a large induction- 

 coil, beautiful colour-effects were produced. —The following 

 papers were then read : — Note on beams fixed at the ends, by 

 Profs. Ayrton and Perry. This paper contains a simple method 

 of solving problems relating to liorizontal beams with vertical 

 loads, and fixed at b >th ends. The curve of bending-moment 

 for the given distribution of load is first plotted, supposing the 

 beam ^* sitpportaV at the ends, and the constant c, by which 

 the ordinates of this curve exceed those of the true curye, is 

 determined from the condition that the angle between the end 

 sections must be nought. If M is the bending-moment at a 

 section, I the amount of inertia of the section about its neutral 

 line, and E Young's modulus of elasticity for the material, then 



is the curvature of the beam at that section. If O O' is a 



M 

 EI 



short length of the beam, the angle between the originally 



M 



; allel sections at O and O' is -— - . O O'. Hence, if the 



i>eam be divided into a great number of parts, and the values of 

 M and I determined at the middle of each, then 



sL^ .00' 



I 



(I) 



since E is supposed constant. But M = in - c, where in is 

 the bending-moment at the sams section, suppjsing the ends 

 "supported" ; 



. ~m - c 



or, 



2 _ - 2 _, 



I 



''-\ 



(2) 



The following rule results : Knowing in and I at every point, 



divide the beam into any number n of equal parts, find - 



at the middle of each part, and take their sum ; this gives the 



numerator of (2). Find -at the middle of each part, their sum 



ves the denominator of (2). From this c is determined. 

 . iminiih all the ordinates of the in diagram by c, and we have 

 the diagram of bending-moment for a beam fi.xed at both ends, 

 with any assumed distribution of lo.id and variation of cross- 

 section. Particular cases are worked out in full. Numerous 

 drawings made by students of Finsbury Technical College were 

 exhibited, showing applications of the method to different distri 

 buti^ns of loading. — Note on Messrs. Vaschy and Touanne's 

 method of comparing mutual induction with capacity, by Prof. 

 G. C. Foster. In November last the author describetl a method 

 of cooQparing the mutual induction of two coils with the capacity 

 of a c ondenscr. .Since then he has f nind that a very similar 

 method was used by Messrs. Vaschy and Touanne in July 1886, 

 and published in the Electrician the following minth. The 

 formula; are identical, and the difference consists in inter- 

 changing the galvanometer and the variable resistance /. 

 Messrs. Vaschy and Touanne's arrangement has the advantage 

 that the resistance of the secondary coil need not be known. 

 Prof. Foster's method had been used by one of his students (Mr. 

 Draper) about two years ago, but priority in publication belongs 

 to Messrs. Vaschy and Touanne. — Prof. Perry asked the 

 meeting for suggestions to explain why a stri]3 of steel twisted 

 about its longitudinal axis at a red heat, and allowed to cool, 

 tends to untwist when under tension, and for a formula to 

 calculate the amount. — A note on magnetic resistance by Profs. 

 Ayrton and Perry was postponed. 



Geological Society, June 8.— Prof. J. W. Judd, F.R.S., 

 President, in the chair. — The following communications were 

 read : — A revision of the Echinoidea from the Australian Ter- 



tiaries, by Prof. P. Martin Duncan, F.R.S. After calling atten- 

 tion to a previous p.iper by himself published in the Society's 

 Journal for 1877, and to additions to the fauna made by Prof. 

 R. Tate and Prof. McCoy, the author proceeded to give note^ 

 on the characters, relations, and nomenclature of 29 species of 

 Echinoidea. A few notes were added on the relations between 

 this fauna and that now inhabiting the Australian seas, also on 

 the connexions with the Tertiary Echinoidea of New Zealand, 

 Sind, &c. — On the lower part of the Upper Cretaceous series in 

 West Suffolk and Norfolk, by Mr. A. J. Jukes-BrOwn, and Mr. 

 W. Hill. The district described in this paper i; that of West 

 Suffolk and Norfolk, and is one which has never been thoroughly 

 examined ; for no one has yet attempted to trace the beds and 

 zonal divisions which are found at Cambridge through the tract 

 of countiy which lies between Newmarket and Hunstanton. 

 Until this was done the Hunstanton section could not be corre- 

 lated definitely with that of the neighbourhood of Cambridge, 

 It was the authors' endeavour to accomplish this, and the follow- 

 ing is an outline of the results obtained by them. The paper was 

 divided into six parts : (l) stratigraphical, (2) palaeontological, 

 (3) microscopical, (4) chemical analyses, (5) faults and alteration 

 of strike, (6) summary and inferences. In the four first parts 

 separate lines of argument were followed, and each led to the 

 same set of conclusions. The chief interest of the paper pro- 

 bably centres in the gauU, and its relations to the chalk marl and 

 the red chalk. Quite recently the very existence of gault in 

 Norfolk has been disputed, but the authors think the facts they 

 adduce and the fossils they have found will decide that point. 

 The gault at Stoke Ferry is about 60 feet thick, and in the outlier 

 at Muzzle Farm Ammonites interrtiptus occurs plentifully in the 

 form of clay-casts with the inner whorls phosphatized. At 

 Roydon a boring was made which showed the gault to be about 

 20 feet thick, the lower part being a dark blue clay, above which 

 were two bands of limestone incbsing a layer of red marl, and 

 the upper 10 feet were soft gray marl ; the limestones contained 

 Aiiim. rostratus, Atnm. lautns, Inoceramiis sukatus, and Inoc. 

 concentricus {?), while the marls above contained Beleinnites 

 miniintis in abundance. At Dersingham another boring was 

 made which proved the gray marl (2 feet) to overlie hard yellow 

 marl, passing down into red marl which rests on Carstone. The 

 gray marl thins out northward, and as the red marl occupies the 

 position of the red chalk, the authors believe them to be on the 

 same horizon, an inference confirmed by the presence of gault 

 Ammonites in the red chalk. Another point of importance is 

 the increasingly calcareous nature of the gault as it is followed 

 northward through Norfolk. This was regarded as evidence of 

 passing away from the land supplying inorganic matter, and 

 approaching what was then a deeper part of the sea ; this infer- 

 ence is borne out by the microscopical evidence. As regards the 

 chalk marl, it also becomes more calcareous : at Stoke it is still 

 over 70 feet thick, and its ba«e is a glauconitic marl which can 

 be traced to Shouldham and Marham, but beyond this the base 

 is a hard chalk or limestone, which is conspicuous near Grimston 

 and Roydon, and passes, as the authors believe, into the so- 

 called "sponge bed " at Hunstanton. The Totternhoe stone is 

 traced through Norfolk, but is thin at Hunstanton (2 feet) ; its 

 existence, however, enables the limits of the chalk marl to be 

 defined, with the result that some 13 feet of the hard chalk at 

 Hunstanton must be referred to that subdivision. The gray chalk 

 also thins northward, and from 90 feet near Cambridge is reduced 

 to about 30 at Hunstanton. The Belemnite-marls are traceable 

 in Norfolk, but either thin out or are replaced by hard white 

 chalk near Heacham. The Melbourn rock is continuous, and 

 maintains similar characters throughout. The total diminution 

 in the thickness of lower chalk is from 170 feet at Newmarket 

 to 55 feet at Hunstanton, viz. 115 feet. An endeavour was 

 made to estimate the amount and extent of gault removed by 

 erosion from Arlesey and Stoke Ferry. — On some occurrences of 

 Piedmontite-schist in Japan, by Mr. B. Koto. Communicated 

 by Mr. Frank Rutley. 



Mathematical Society, Juneg.— Sir James Cockle, F.R.S., 

 President, in the chair. — The President announced that the 

 Council had awarded the second De Morgan Medal to Prof. 

 Sylvester, F.R.S. — The following communications were made : 

 — Note on the linear covariants of a binary quintic, by A. Buch- 

 heim. — The motion of a sphere in a viscous liquid, by A. B. 

 Basset (the method of solution was by definite integrals analo ^ous 

 to Fourier's solution of equations determining the propagation 

 of heat). — On the reversion of series in connexion with recipro- 

 cants, by Capt. Macmahon, R.A. — Explanation of illustrations 



