190 



NA TURE 



[December 25, 1902 



compared, but the evidence seems to show that it is much 

 nearer to the latter (gravitational) than to the former 

 (rotational). 



We next consider a number of questions connected with the 

 figure of the earth. It seems to be almost certain that the 

 present elastic constants of the earth are such that a state of 

 spherical symmetry would be one of stable equilibrium. On the 

 other hand, if we look backwards through the history of our 

 planet, we probably come to a time when the rigidity was so 

 small that the stable configuration of equilibrium would be 

 unsymmetrical. At this time the earth would be pear-shaped, 

 and the transition to the present approximately spherical form 

 would take place through a series of ruptures. It is suggesled 

 that the earth, in spite of this series of ruptures, still retains 

 traces of a pear-shaped configuration. Such a configuration 

 would possess a single axis of symmetry, and this, it is suggested, 

 is an axis which meets the earth's surface somewhere in the 

 neighbourhood of England (or possibly some hundreds of miles 

 to the south-west of England). Starting from England, we find 

 that England is at the centre of a hemisphere which is practically 

 all land ; this would be the blunt end of our pear. Bounding 

 the hemisphere we have a great circle, of which England is the 

 pole, and it is over this circle that earthquakes and volcanoes 

 are of most frequent occurrence. Now, if we suppose our pear 

 contracting to a spherical shape, we notice that it would probably 

 be in the neighbourhood of its equator that the changes in 

 curvature and the relative displacements would be greatest, and 

 hence we should expect to find earthquakes and volcanoes in 

 greatest numbers near to this circle. Passing still further from 

 England, we come to a great region of deep seas — the Pacific, 

 South Atlantic and Indian oceans ; these may mark the place 

 where the " waist " of the pear occurred. Lastly, we come, 

 almost at the antipodes of England, to the Australian continent. 

 This may mark the remains of the stalk-end of the pear. 



Physical Society, December 12. — Mr. S. Lupton, vice- 

 president, in the chair. — Mr. S. W. J. Smith exhibited and de- 

 scribed a portable capillary electrometer. This instrument is a 

 modification of the form of capillary electrometer which consists 

 of two wide tubes joined by a cylindrical capillary tube which may 

 be horizontal or inclined. I he apparatus contains mercury and 

 sulphuric ,acid of about maximum conductivity suitably dis- 

 tributed in the tubes. A spring key is commonly used with the 

 instrument, but the author has devised a key consisting of a 

 U-tube closed at one end, communicating at the other with a 

 pneumatic pressure ball and containing mercury in the bend. 

 By squeezing the ball, the same change of contacts can be pro- 

 duced as by pressing the lever of an ordinary spring key. Using 

 this key and a microscope magnifying 50 diameters, a potential 

 difference of 1/10, oooth volt can be detected without difficulty. 

 The instrument, used as a surface-tension galvanometer, is more 

 convenient than an ordinary galvanometer with a magnetic 

 system because there is no suspension, no lamp and scale, and 

 practically no levelling. — A paper on astigmatic aberration was 

 read by Mr. R. J. Sowter. This paper affords a simple ex- 

 planation of some of the shadow phenomena observed by Prof. 

 S. P. Thompson in his experimental researches on the aber- 

 ration of lenses, namely, in those experiments in.which the aber- 

 ration is wholly or in part astigmatic. — Prof. L. R. Wilberforce 

 exhibited apparatus for a lecture experiment on gaseous diffusion. 

 In Graham's experiments on diffusion through porous septa, the 

 gas experimented upon was contained in a vessel inverted over 

 water, and the pressure was kept approximately atmospheric by 

 applying a counterpoise to the vessel. This adjustment, how- 

 ever, is imperfect owing to the weight of the water displaced 

 by the material of the vessel. Prof. Wilberforce showed that, 

 by suspending the vessel from one arm of a balance rendered 

 suitably unstable by a weight above the central knife-edge, a 

 compensating effect could be introduced and the pressure kept 

 sensibly constant for a considerable range of motion of the 

 vessel. He pointed out that this device could also be utilised 

 for the measurement of pressure. — A paper on vapour-density 

 determinations, by Sir W. Ramsay and Dr. Steele, was read by 

 Sir W. Ramsay. This paper gives a detailed account of some 

 accurate experiments on the densities of vapours over a large 

 range of pressure carried out by a modification of Gay-Lussac's 

 method. This method has the advantage that while densities 

 are being determined, compressibilities can, within certain 

 limits, be simultaneously estimated with the same sample of 

 material. From results of experiments, it appears that the 

 densities of certain compounds calculated for zero pressure 



NO. I730, VOL. 67] 



are not proportional to their molecular weights deduced from 

 the atomic weights of the elements which they contain. 

 This conclusion involves one, or it may be several, of a series 

 of assumptions enumerated in the paper. These assumptions 

 are fully investigated and discussed, and the authors suggest 

 that it may be possible that the atomic weights of the elements 

 depend on the proportion in which they are present in the 

 compounds which contain them. 



Royal Astronomical Society, December 12. — Dr. 

 J. W. L. Glaisher, F. K.S., president, in the chair. — Mr. 

 Innes presented a paper on some developments in terms of 

 the mean anomaly and also the results of measures of double 

 stars made at the Royal Observatory, Cape of Good Hope, in 

 1902. He made some remarks on the excellence of the 

 McCIean telescope, with which the measures were made, and 

 the great convenience of the rising floor of the observatory. — 

 Mr. Hardcastle re^d a note on binding together reseaux and 

 plates. In measuring some photographs of the moon, on which 

 no reseau had been impressed, the reseau plate and photograph 

 were bound together film to film, but in the course of measure- 

 ment a slight shifting occurred, which it was difficult to prevent. 

 — Mr. Bellamy read a note on preserving negatives. Some 

 developed star negatives which had been placed in envelopes 

 and stacked on shelves were found after a time to have received 

 on the film a faint image of the inscription that had been 

 written on the envelopes. Mr. Knobel remarked that this was 

 certainly not due to the effect described by Prof. Russell, as the 

 writing was only visible on the film by reflected light. — The 

 Astronomer Royal exhibited and described a new measuring 

 machine which had been made by Troughton and Simms 

 for the Royal Observatory, Greenwich, and was intended 

 for the measurement of photographs of Eros. — A paper 

 by Mr. Robinson, of the Radcliffe Observatory, Oxford, was 

 read, on the photographic and visual magnitude of o Orionis. 

 Between March 9, 1901, and October 22, 1902, the photo- 

 graphic magnitude of this star had slightly increased, and since 

 the latter date there appeared a gradual decline in brightness ; 

 both the increase and decrease were confirmed by the visual 

 estimations. — Photographs of the spectra of Jupiter, Saturn and 

 other planets, taken by Mr. Percival Lowell at Flagstaff, Ari- 

 zona, were shown on the screen. — Mr. Hinks exhibited photo- 

 graphs of Mr. Ritchey's series of drawings from the negatives of 

 the nebula surrounding Nova Persei taken at the Verkes Ob- 

 servatory. Mr. f links showed by the aid of diagrams how the 

 apparent motion of the nebula might be explained upon the 

 hypothesis of Prof. Kapteyn, that successive portions of the 

 nebula were illuminated by the star and that there was no real 

 motion of the nebula itself. 



Mathematical Society, December II. — Prof. Lamb, 

 president, in the chair. — The following papers were com- 

 municated : — Prof. L. E. Dickson, (1) The abstract group simply 

 isomorphic with the group of linear fractional transformations in 

 a Galois field ; (2) Generational relations of an abstract simple 

 group of order 40S0. The first paper deals with the abstract 

 group of order i />"(/-" - 1), which is simply isomorphic with the 

 group of all linear fractional transformations on one variable, 

 with coefficients belonging to the Galois field [p"], and with de- 

 terminants equal to unity. It is shown that when n = I, the 

 group may be generated by two operations which are subject to 

 generational relations, and these relations are determined. When 

 n has other values, the generating operations are more numerous, 

 but the generational relations are again determined. The 

 validity of the theorems depends in general on the solution of a 

 problem in the theory of numbers, which can be treated readily 

 in any particular case. In the first paper, p is supposed to 

 be greater than 2 ; the second paper deals with the case p = 2. 

 — Dr. H. F. Baker, (1) On the calculation of the finite 

 equations of a continuous group ; (2) On the integration 

 of linear differential equations; (3) On some cases of matrices 

 with linear invariant factors. In the second paper, use is 

 made of the matrix notation for the systematic study of 

 linear differential equations. This study leads to two inde- 

 pendent problems. One problem consists in the determination 

 of all irreducible types of multiplication tables of sets of matrices 

 of the same order, a problem akin to that of the enumeration of 

 types of discontinuous groups. The other problem consists in 

 the investigation of the properties of a class of functions which 

 arise by repeated integrations from simpler functions. The serial 

 solutions which are obtained converge for all finite values of the 



