November 13, 1902] 



NA TURE 



45 



analysis of the courses of study in physics in the different insti- 

 tutions from which data were received. In his circular to labor- 

 atory directors, M. Weinberg tabulated some 910 typical prac- 

 tical exercises in physics and requested that those worked in 

 the laboratories might be underlined. It has thus been possible 

 to institute an instructive comparison between the methods of 

 different countries. About four hundred physical laboratories, 

 having five hundred professors and eight hundred demonstrators 

 or assistants, are recorded for the whole of the institutions for 

 higher education in the world. In about one-fifth of these, 

 practical work in physical manipulations is not carried on ; in 

 the rest, there are about 25,000 students who pass eight hours a 

 week in the laboratories during three semesters. In these four 

 hundred hours passed in the laboratory a student, on the aver- 

 age, performs sixty different experiments, or about two-thirds of 

 the work for which the laboratory makes provision. 



SCIENTIFIC SERIALS. 



American Journal of Science, October — An experimental in- 

 vestigation into the existence of free ions in aqueous solutions of 

 electrolytes, by Julius Olsen. The well-known experiment of 

 Ostwald and Nernst, which has been held to prove experi- 

 mentally the existence of ions in solution, is criticised, and it is 

 held that the conclusion arrived at does not necessarily follow, 

 and that further proof is needed. Experiments are described 

 which show that an electrolyte which has never been acted 

 upon by a current behaves as if it contained particles charged 

 with electricity which are free to move, and these particles have 

 not been produced by a current. This corresponds to the de- 

 finition of free ions. — On the solution of problems in crystal- 

 lography by means of graphical methods, based upon spherical 

 and plane trigonometry, by S. L. Penfield. It is shown that 

 with the addition of certain stereographic scales and protractors 

 to a set of ordinary drawing instruments, the lengthy calcula- 

 tion s usual in determining the crystallographic constants can be 

 avoided or, as an alternative, checked. Several illustrated 

 examples of the mode of application of this method are given. — 

 The estimation of bro'mic acid by the direct action of arsenious 

 acid, by F. A. Gooch and J. C. Blake. It is shown that 

 bromates may be satisfactorily estimated by the direct action of 

 arsenious acid, the few apparent discrepancies which were found 

 being traced to the presence of chlorate as an impurity in the 

 bromate. — Solubilities of some carbon compounds, the densities 

 of their solutions, by Clarence L. Speyers. Seven or eight 

 carbon compounds of different types were examined in various 

 solvents, including water, methyl, ethyl and propyl alcohols, 

 chloroform and toluene. The results are compared with those 

 calculated from Schroeder's formula, but the agreement is not 

 good. 



Transactions of the American Mathematical Society. — Vol. iii. 

 No. 3 (July). — L. E. Dickson, on the group defined for any 

 given field by the multiplication table of any given finite group. 

 The subject of this paper is much the same as that of Burnside's 

 in Proc. L.M.S. xxix. ; the results, however, are obtained by a 

 different method, which does not involve the theory of continuous 

 groups. The paper illustrates the importance of Frobenius's 

 discovery of the group determinant. Two examples are given. — 

 O. Stolz, postscript to a previous article on rectification of 

 curves. A comparison is made with Jordan's treatment of the 

 same theory. — O. Bolza, proof of the sufficiency of Jacobi's 

 condition for a permanent sign of the second variation in the 

 -so-called isoperimetric problems. — H. E. Hawkes, on hyper- 

 complex number systems. The author develops the methods of 

 Peirce, and shows that they give an enumeration of all systems 

 in less than six units which have moduli in more than one 

 idempotent unit. The systems for five units with two idempotent 

 units are worked out in detail. A discussion of nilpotent 

 systems follows.— W. B. Kite, on metabelian groups. — L. P. 

 Eisenhart, on conjugate rectilinear congruences. — D. N. Lehmer, 

 constructive theory of the unicursal plans cubic by synthetic 

 methods. — L. E. Dickson, on the groups of Steiner in problems 

 -of contact (continued from the January number). 



Bulletin of the American Mathematical Society (2) ix. , No. 1 

 (October).— O. Bolza, examples in the calculus of variations — 

 E. R. Hadrick, on the sufficient conditions in the calculus of 

 variations. A convenient summary, based on lectures by 

 Hilbert. — E. B. Wilson, reviews of recent books on mechanics 



NO. 1724, VOL. 67] 



(Foppl, Volkmann, Picard). — E. V. Huntington, on a new 

 edition of Stolz's " Allgemeine Arithmetik," with an account of 

 Peano's definition of number. — E. J. Wilczynski, an obituary 

 notice of Fuchs. 



SOCIETIES AND ACADEMIES. 

 London. 

 Physical Society, October 31.— Prof. S. P. Thompson, 

 president, in the chair. — A paper on the existence of a relationship 

 between the spectra of some elements and the squares of their 

 atomic weights, by Dr. W. M. Watts, was read by Prof. Everett. 

 The author has detected two kinds of relation between the 

 spectra of some allied elements. In the first kind, which is 

 illustrated by comparisons between zinc, cadmium and mercury, 

 and also between gallium and indium, the differences between 

 the oscillation frequencies of certain lines of one element are 

 to the differences between the oscillation frequencies of the 

 corresponding lines of another as the squares of their atomic 

 weights. In the second kind, the relation is not between two, 

 but between three spectra, and is illustrated by the trio potassium, 

 rubidium and caesium, as well as by the trio calcium, strontium 

 and barium. The element of greater atomic weight has the 

 smaller frequency, and, in comparing corresponding lines, one 

 from each of the three spectra, the differences of frequency are 

 proportional to the differences between the squares of the atomic 

 weights. If each of the spectral lines in question is represented by 

 a point the coordinates of which are "frequency" and "square of 

 atomic weight," the three points which represent three corre- 

 sponding spectral lines will lie on one straight line in the diagram, 

 and these straight lines will be parallel for all the components 

 of a given set of corresponding groups. When a similar mode 

 of plotting by points is employed to exhibit the first kind of 

 relation, the joins of corresponding points meet in a point which 

 lies on the axis of frequencies, in other words, on the line of 

 zero atomic weight. This relation was indicated by Ramage 

 about a year ago as holding for corresponding doublets and 

 triplets. — A paper on the size of atoms was read by Mr. H. V. 

 Ridout. This investigation deals with the size of dissociated 

 atoms, or ions, and the results obtained refer to a dissociated 

 atom as the smallest quantity of matter which can take part in 

 an electrolytic action. The element chosen is hydrogen, and 

 the author concludes that, in round numbers, 114! million atoms 

 are necessary to form a line one centimetre long. The method 

 employed consists in finding a pair of spheres which would be 

 charged by the quantity of electricity known to be necessary to 

 electrolyse a given quantity of the body under examination — in 

 this case water — to the known difference of potential of its ions. 

 From this the size of the atoms is deduced, subject to certain 

 assumptions enumerated and discussed in the paper. Lord 

 Kelvin remarked that he had often concerned himself with the 

 size of atoms, and pointed out that the value obtained by the 

 author for the diameter of a hydrogen ion was almost exactly 

 one-half of that which he had obtained for the diameter of a 

 molecule of hydrogen. The fact, however, might be a 

 coincidence. He had dealt with a sphere which would have 

 the same effect as a double atom of hydrogen. While avoiding 

 the assumption that atoms are hard and spherical, it was usual 

 to treat them as such for purposes of calculation. The paper 

 was an important one, but there were many assumptions which 

 required looking into. Lord Kelvin said that, in dealing with 

 the subject of atoms, it was necessary to consider the atoms of 

 electricity. The atomic theory of electricity, now almost 

 universally accepted, had been thought of by Faraday and 

 Clerk-Maxwell and definitely proposed by Helmholtz. The 

 atoms of electricity were very much smaller than the atoms of 

 matter, and permeated freely through the spaces occupied by 

 these greater atoms and also freely through space not occupied 

 by them. An atom of electricity in the interior of an atom of 

 matter experienced electric force towards the centre of the atom. 

 We were forced to conclude that every kind of matter had elec- 

 tricity in it, and Lorenz had named electricity as the moving thing 

 in atomic vibrations. If the electrions, or atoms of electricity, 

 succeeded in getting out of the atoms of matter, they proceeded 

 with the velocity of light and the body was radioactive. It was 

 therefore not surprising that some bodies showed radioactive 

 properties, but rather surprising that such properties were not 

 shown by all forms of matter. Our knowledge of this subject, 



