4IO 



NATURE 



[February 21, 1901 



of Bessel's spheroid, of which the compression is i/299'2 ; that 

 is, one more closely approaching a sphere. 



In the present state of our knowledge there is no reason to 

 suppose that the curvature of the northern part of America 

 differs any more from that of a general spheroid derived from 

 arcs of all kinds so far measured than local ones in either hemi- 

 sphere differ among themselves. A comparison of a number of 



such locally adopted spheroids will bring to evidence the local 

 deformities in the shape of the earth's equilibrium surface and 

 furnishes the geodesists endless material for the study of the 

 earth's actual figure. 



The manuscript concludes with a comparative table of the 

 dimensions of several spheroids which of late have come more 

 into prominence. It is as follows : — 



Spheroid of 



Equatorial radius, 

 a, in metres. 



Bessel, 1841. From ten arcs of the meridian and total amp- 

 litude 50" 34' 6,377,397 



Clarke, 1858. Special spheroid for surface of Great Britain 

 and Ireland ; range of latitude 12°, the same in longitude ; 

 seventy-five astronomic stations 6,378,494^90 



Clarke, 1866. From five meridional arcs, of total amplitude 



76° 35' .••; 6,378,206 



Clarke, 1880. From five meridional arcs and longitudinal 



measures, total amplitude 88° 59'S' (equatorial degrees) 6,378,249 



United States Coast and Geodetic Survey, 1900. Eastern 

 oblique arc of the United States ; total length, 23° 31', and 



eighty-four astronomic stations 6,378,157^:90 



Harkness, 1891. From "The Solar Parallax and Related 

 Constants," Washington, 1891, p. 138. From a variety of 

 sources 6,377,972+125 



Polar semi-axis. 

 h, in metres. 



6,356,079 



6,355>746 

 6,356,584 

 6,356,515 



6,357,210 

 6,356.727±99 



a-h. 



21,318 



22,748 

 21,622 



21,734 

 20,947 

 21,245 



Compression 

 (a.-b)la. 



i/299-i5±3-i5 



i/28o-4±8-3 

 1/295-0 

 1/293 '5 



1/304 •5± I '9 

 1/300-2 + 3 "O 



N.B. — The i Indicates probable errors. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Cambridge. — A valuable collection of Greek papyri from 

 Oxyrhyncus and the Fayum has been presented to the University 

 library by the Egypt Exploration Fund. 



Dr. A. C. Haddon, F. R.S , University lecturer in ethnology, 

 and professor of zoology in the Royal College of Science, Dublin, 

 has been elected to a junior fellowship at Christ's College. 



The King's Speech to the Commons at the opening of 

 Parliament on Thursday last contained the announcement that 

 " Legislation will be proposed to you for the amendment of the 

 law relating to education." 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, February 7.— "The Integration of the 

 Equations of Propagation of Electric Waves." By A. E. H. 

 Love, F.R.S. 



The equations of propagation of electric waves, through a 

 dielectric medium, involve two vector quantities, which may be 

 taken to be the electric force and the magnetic force. Both the 

 vectors are circuital ; and the several components of them 

 satisfy the partial differential equation of wave propagation, viz. 

 ^ =i:-V^(/), c being the velocity of radiation. 



Owing to the circuital relations, certain known solutions of 

 the partial differential equation of wave propagation are not 

 available, for representing the components of the vectors. A 

 very general system oiparlictilar solutions, which are available for 

 this purpose, is obtained. These include solutions corresponding 

 to two types of sources of electric radiation : — The sources of 

 one type are similar to infinitesimal Hertzian vibrators, being 

 related in the same way to an axis, but the dependence of the 

 emitted radiation on time is arbitrary ; the sources of the other 

 type are obtained therefrom by interchanging the roles of the 

 electric and magnetic forces. 



The general integrals of the equations would express the values 

 of tbe vectors, at one place and time, in terms of their values, 

 at other places and times. To find such integrals, we require 

 (i) sets of particular solutions, which tend to become infinite, 

 in definite ways, in the neighbourhood of chosen points ; (2) a 

 theorem of reciprocity, connecting the values, on any chosen 

 surface, of two sets of solutions ; (3) the limiting form, assumed 

 by the theorem of reciprocity, when the solutions of one 

 system have the assigned character of infinity at a given point. 

 The solutions required for the first step are among those already 



NO. 1634. VOL. 63] 



found ; the theorem of reciprocity is obtained by a modification 

 of the process by which the fundamental equations can be 

 deduced from the Action principle ; and the limiting form of the 

 theorem is found by adapting a process due to Kirchhoff. The 

 result is that the radiation which arrives at a chosen point may 

 be regarded as due to a distribution of imagined sources of 

 radiation upon an arbitrary closed surface, separating the point 

 from all the actual sources of radiation. The imagined sources 

 are of the two types previously specified ; and the directions of 

 their axes, and the intensities of the radiation sent out from 

 them, are determined simply and directly by the values, on the 

 surface, of the vectors involved in the propagation of the 

 waves. 



The general theorem is applied to the problem of the passage 

 of radiation through an aperture, and the result is utilised to 

 determine the rate of decay of the vibrations of a condensing 

 system. The example of a condenser, with concentric spherical 

 conducting surfaces, the outer conducting sheet being perforated 

 by a small circular aperture, is worked out in detail ; and the 

 results suggest that the maintenance of the vibrations depends 

 on the screening action of the outer conductor rather than on 

 the largeness of the capacity of the condenser. 



Anthropological Institute, February 4. — Annual General 

 Meeting. — Mr. C. H. Read, president, in the chair. — On a ballot 

 the following were elected to office for the ensuing year : — 

 President : Prof. A. C. Haddon, F.R.S. Vice-presidents: A. J. 

 Evans, W. Gowland, Prof G. B. Howes. Hon. Treasurer : 

 A. L. Lewis. Hon. Secretary : J. L. Myres. Council : SirT. H. 

 Holdich, Sir C. E. Peek, Messrs. G. M. Atkinson, H. Balfour, 

 W. Crooke, Prof. D. J- Cunningham, W. L. H. Duckworth, 

 R. W. Felkin, H. O" Forbes, J. G. Garson, E. S. Hartland, 

 T. V. Holmes, E. F. im Thurn, A. Keith, R. B. Martin, M.P., 

 R. H. Pye, E. G. Ravenstein, Prof. W. Ridgeway, W. H. R. 

 Rivers and F. C. Shrubsall. After reading and discussion of the 

 reports of the treasurer and council, the retiring president pro- 

 ceeded to give his address. After alluding to the death of Her 

 Majesty Queen' Victoria and paying a tribute to Lieut. -General 

 Pitt-Rivers, an ex-president of the Institute, Prof. Max Miiller, 

 Miss Kingsley and other distinguished Fellows who had been re- 

 moved by death, he went on to call attention to the progress made 

 by anthropology, more especially in the British Empire, during the 

 past year. A joint memorial of the Folk-lore Society and the 

 Institute had been presented to the Government, urging the 

 theoretical and practical importance of an inquiry into the status 

 of native races in South Africa. In India, in combination with 

 the census, a scheme for a partial ethnographical survey had been 

 called into existence, over the working of which the Hon. H. H. 

 Risley would preside. He hoped that in England we should 

 soon have chairs of anthropology at all the important teaching 



