478 



NA TURE 



[March 19, 190J 



a succession of wash-bottles containing water and placet 

 in a thermostat. The water carried off by the air was 

 absorbed by means of concentrated sulphuric acid am 

 weighed. The results obtained show in every case a close 

 agreement between the calculated vapour-pressure and that 

 commonly accepted. Experiments were made at temper- 

 atures varying from 20° to 90' C. It may he concluded 

 from this that in air saturated with moisture (under the 

 conditions used in the experiments) the pressure of the 

 aqueous vapour is the same as the vapour-pressure of water 

 when no other gas is present, also that the density of the 

 aqueous vapour in the mixture is normal. It follows also 

 that the density of saturated aqueous vapour, without ad- 

 mixture of any other gas, is approximately normal. This 

 conclusion is confirmed by calculations of the density from 

 the thermodynamical equation L = T/J(s' — s)dp/dT, using 

 Griffiths's values of I. and J and the latest determinations 

 of vapour-pressure at the Reichsanstalt for the values of 

 dp/dT. 



Mathematical Society, Match 12. — Dr. E. W. Hobson, 

 vice-president, in the chair. — Mr. G. H. Hardy, On the con- 

 vergence of certain multiple series. The paper contains an 

 investigation of the analogue for multiple series of a theorem 

 (due to Abel) concerning the partial summation of simple 

 series. Most of the ordinary tests of convergence for simple 

 series are founded on this theorem. Proofs of convergence 

 of certain classes of multiple series are obtained, in par- 

 ticular of the class in which the general term is of the type 

 (^r-j + 6 2 r 2 + . . . + d„>- n )-" exp 1 (a,?-j + o 2 »- 2 + . . . + a„>-„). 



— Mr. S. M. Jacob, On certain sequences for determining 

 the nth root of a rational number. The paper contains a 

 systematic development of a method used by Dedekind (in 

 the case of the square root) to obtain sequences of the kind 

 in question. If D is any rational number, and x is a rational 

 approximation by excess or defect to the nth root of D, it 

 is shown how to construct a rational number y which lies 

 between * and the itth root of D. — Prof. H. Lamb, Note on 

 the approximate calculation of the frequencies of a vibrating 

 circular plate. The method of Rayleigh (" Theory of 

 Sound," § 88) is applied to calculate the frequencies of the 

 gravest modes of vibration of a plate by means of the 

 assumption of very simple hypothetical types. The agree- 

 ment of the results with those calculated by Kirchhoff from 

 the exact equation for the frequencies is remarkably close. — 

 Prof. A. R. Forsyth, On surfaces which have assigned 

 families of curves as their lines of curvature. The paper 

 contains a new method of investigating the conditions that 

 a given family of curves may be the lines of curvature of a 

 surface, and of determining the character of the surface 

 from that of the lines. The method is illustrated by the 

 example of Dupin's cyclide. — Mr. E. T. Dixon, Note on a 

 point in Hilbert's " Grundlagen der Geometric" — Mr. J. H. 

 Grace, Extension of two theorems on covariants. — Prof. 

 T. J. I'A. Bromwich, Note on double limits and on the in- 

 version of a repeated infinite integral. The object of the 

 note is to determine the conditions which are necessary and 

 sufficient for the change of order of integration in an in- 

 tegral with infinite limits, and for the existence of a double 

 integral with such limits. The continuity of a definite 

 integral with infinite limits, considered as a function of a 

 parameter contained in the subject of integration, is dis- 

 cussed. — Prof. \Y. Burnside, On the representation < .f a 

 group of finite order as an irreducible group of linear sub- 

 stitutions, and the direct establishment of the relations 

 between the group characteristics. The paper deals with 

 the representation in question from a self-contained point 

 of view, without introducing considerations which are 

 foreign to the conceptions of an abstract group of finite 

 order and of a group of linear substitutions. The arrange- 

 ment of the subject from this point of view is materially 

 different from that in previous discussions of it. The com- 

 plete reducibilitv of a group of linear substitutions of finite 

 order is taken first, the number of distinct irreducible re- 

 presentations and the composition of them follow, and the 

 group-characteristics and their properties occupy the last 

 place. 



Geological Society, February 20. — Prof. Charles Lapworth, 

 F.R.S., president, in the chair. — Annual General Meeting. — 

 In hi- anniversary address the president dealt with the rela- 



NO. 



1742, VOL. 67] 



tion of geology to its fellow-sciences. In the course of the 

 address the president remarked that the study of geology 

 shows that the corporate geological organism has three 

 necessary functions — research, practice and education. So 

 1' rig as all three functions are nalurallv and healthfully 

 performed, so long will geology live and flourish. The work 

 and influence of Werner and De la Beche show that the 

 progress of the science is at its swiftest and surest when 

 none of the three functions suffer from disuse. 



February 25. — Prof. Charles Lapworth, F.R.S., presi- 

 dent, in the chair. — On the occurrence of Dictyozamites in 

 England, with remarks on European and eastern floras, 

 by Mr. A. C. Seward, F.R.S. The specimens described as 

 a new species of Dictyozamites were obtained from a bed 

 of ironstone on the northern face of the Upleatham outlier, 

 near Marske-by-the-Sea. The genus is also found in the 

 Rajmahal Series of India, in Central Japan and at Born- 

 holm. Its probable taxonomic position is best expressed 

 by placing it as a member of the Cycadophyta. A com- 

 parison of the Bornholm, Indian, Japanese and English 

 floras is made, and a special list of these floras has been 

 prepared, in which, while the names at present in use are 

 indicated, it is pointed out where obscured identities or re- 

 semblances exist. The author concludes that there was a 

 greater similarity between the vegetation of eastern and 

 western regions, during part at least of the Mesozoic era, 

 than is usually admitted. The most noteworthy exceptions 

 are afforded by the Mesozoic representatives of the two 

 isolated recent ferns Matonia and Dipteris ; these two 

 families — each with a surviving genus — played a con- 

 spicuous part in the vegetation of the Rha^tic and succeeding 

 Jurassic epochs in Europe, and to a less extent in North 

 America, but there are no satisfactory records of their 

 existence in India or Japan. — The amounts of nitrogen and 

 organic carbon in some clays and marls, by Dr. N. H. J. 

 Miller. Analyses of soils are given to show that decaying 

 vegetable matter in soil tends to become more nitrogenous, 

 on account of the greater ease with which gaseous com- 

 pounds are formed with carbon than with nitrogen. Hil- 

 gard's experiments throw light on the effects of extreme 

 conditions of climate, the amount of soluble humus being 

 much greater in soils in humid than in arid climates. The 

 large areas of peat-land known as " Hochmoor " contain 

 larger proportions of carbon and nitrogen at depths of seven 

 and fourteen feet than at the surface. The organic matter 

 of soils is of two kinds — the humous portion and the bitu- 

 minous, the latter being regarded as belonging to the 

 original deposit from which the soil is derived. Analyses 

 of soils and subsoils are given to illustrate this point. 

 Further light on this subject is derived from the analysis 

 of specimens obtained through the kindness of Sir A. Geikie 

 from borings in the possession of the Geological Survey. 

 Apart from the interest due to the great depths from which 

 the samples were obtained, and the evidence which they 

 afford of the enormous accumulations of combined nitrogen, 

 they possess the further and greater value of representing 

 the materials out of which large areas of soils have been 

 derived. It would be important to determine, in the case 

 of these older deposits, whether any of the organic matter 

 at all is in the form of humus. 



Zoological Society, March 3.— Mr. G. A. Bou'enger, 

 F.R.S., vice-president, in the chair. — A communication was 

 read from Mr. E. R. Sykes on the operculate Land-Mollusca 

 collected during the " Skeat Expedition " to the Malay Pen- 

 insula in 1899-1900. Fourteen genera were represented in 

 the collection by examples of twenty-three species, eight of 

 which were described as new. — Mr. R. Lydekker com- 

 municated a paper on the callosities of the limbs of the 

 Equidae, in which it was urged that the view of the callosi- 

 ties being vestigial foot-pads was untenable. The author 

 maintained that they were probably decadent glands, and 

 that possibly the one on the hind limb might correspond 

 to the tarsal gland of deer. — Mr. Rudolf Martin read a 

 paper on some remains of the ostrich, Struthio karathco- 

 doris, found in the Upper Miocene deposits of Samos. The 

 author stated that the existence of an ostrich in Samos was 

 "t interest, because a comparison of the fauna of Samos and 

 that of the Siwalik Hills showed that the latter was younger, 

 and consequently S. karatheodoris was of a greater geo- 

 logical age than 5. asiaticus. The hypothesis, therefore, 



