632 



NATURE 



[July 15, 1920 



form for at least 60 per cent., and in most cases 80 to 

 90 per cent., of the whole action. The interpretation 

 of the mechanism of the action which the authors 

 deduced from the work on unsaturated glycerides thus 

 receives experimental confirmation.— H. Jeffreys: 

 Tidal friction in shallow seas. In a recent paper 

 G. I. Taylor has shown that the friction of the tidal 

 currents in the Irish Sea over the bottom causes 

 enough dissipation of energy to account for about 

 one-fiftieth of the known empirical secular accelera- 

 tion of the moon. This suggests that other and 

 larger shallow areas within strong tidal currents will 

 contribute a still greater amount to the dissipation 

 of energy, and in the present paper the chief shallow 

 seas of the earth are treated separately. The greatest 

 dissipation is found to take place in the Bering Sea, 

 the Yellow Sea, and the Strait of Malacca. Alto- 

 gether, enough is found to account for about 8n per 

 cent, of the secular acceleration, leaving a balance 

 to be explained by currents in fjords and along the 

 open coast.— Prof. J. C. McLennan, J. F. T. Young, 

 and H. J. C. Ireton : Arc spectra in vacuo and spark 

 spectra in helium of various elements. (i) The 

 vacuum arc spectra of antimony, bismuth, calcium, 

 magnesium, silver, and copper, and the spark spectra 

 in helium of antimony, bismuth, aluminium, 

 cadmium, lead, magnesium, thallium, and tin, have 

 been investigated in the region below A=i85o A.U. 

 (2) The measurements of the arc spectra of antimony, 

 bismuth, calcium, and selenium, and the spark 

 spectra of antimony and lead, appear to be the first 

 recorded for these elements in this region. (3) The 

 work with the vacuum grating spectrograph has 

 resulted in the extension of the vacuum arc spectrum 

 of copper to about A=i2i6 A.U. — Prof. J. C. 

 McLennan and A. C. Lewis : Spark spectra of various 

 elements in helium in the extreme ultra-violet. In 

 this investitration the spark spectra in helium of the 

 elements silicon, tellurium, molybdenum, and zir- 

 conium have been determined for the spectral region 

 between A^igoo A.U. and A=i6oo A.U. — K. H. 

 Kingdon : Low-voltage ionisation phenomena in 

 mercurv vapour, fi) By the use of a masfnetic field 

 experimental proof has been given that when 

 mercurv-vapour atoms are bombarded with electrons 

 possessing volt-velocities greater than 4-9, the atoms 

 mav be ionised bv these collisions. (2) An attempt 

 has been made to explain the experimental results of 

 Davis and Goucher on the basis of the results ob- 

 tained. (3) Arguments are presented for showing 

 that the production of ions in mercury vapour at this 

 voltage is not so definitely at variance with the Bohr 

 theory as might at first be thought. (4) The experi- 

 ments go to show that the low-voltage ionisation is 

 not due to ionisation by successive impacts, but that 

 perhaps, in order that a 4-9-volt collision should pro- 

 duce ionisation, the velocity of the impinging electron 

 must bear some definite orientation with regard to 

 the orbit of the electron which is to be ejected from 

 the atom.^ — Sir Geotge Greenhill : Electrification of 

 an insulated lens and allied problems treated by the 

 stream function. — C. Chree : Simultaneous values of 

 magnetic declination at different British stations. A 

 comparison is made of corresponding diurnal varia- 

 tions of magnetic declination at Eskdalemuir and 

 Kew observatories. Mean monthly, daily, and hourly 

 values of declination at Eskdalemuir, Stonyhurst, 

 Falmouth, and Kew are compared. The results are 

 also given of the measurements of a large number of 

 irregular declination changes at the several stations. 

 It is found that the differences between different 

 stations increase with the amount of magnetic dis- 

 turbance, and that if accurate information is desired 

 as to magnetic declination anywhere in the field, 



NO. 2646, VOL. 105] 



observations taken on disturbed days should not be 

 relied on. It is thus important that observatory 

 records should be consulted before the results of field 

 observations are accepted. A number of results are 

 obtained as to the relative amplitudes of irregular 

 declination chani^es at the several observatories. — 

 J. Mercer : Symmetrisable functions and their expan- 

 sion in terms of biorthogonal functions. The purpose 

 of this communication is to announce certain results 

 relative to the expansion of a symmetrisable function 

 K (s, t) in terms of a complete system of fundamental 

 functions corresponding to k (s, t), regarded as the 

 kernel of a linear integral equation. An expansion 

 of the function of positive type by which k (5, t) is 

 symmetrisable is obtained and applied in two im- 

 portant cases.— W. F. Sheppard : Reduction of error 

 by linear compounding. The paper deals with the 

 general problem of improving an observed quantity 

 which contains an unknown error bv adding to it a 

 linear compound (linear function) of other observed 

 quantities, called auxiliaries, the coef^cients in the 

 added portion being chosen so as to make the mean 

 square of error of the whole a minimum. This is a 

 generalisation of the special problem of finding the 

 improved value when the auxiliaries are the differ- 

 ences of suflficientlv high order of a set of quantities. 

 The treatment of the problem is simplified bv a brief 

 statement of general theorems, and by a theory of 

 conjugate sets of quantities. The object is to arrive 

 at formulae suitable for numerical calculation. — G. B. 

 Jeffery : Plane stress and plane strain in bipolar co- 

 ordinates. The solution is given for a flat, elastic 

 plate bounded bv two circles when under stresses 

 applied over its boundaries. Curvilinear co-ordinates 

 are emoloyed, for which the co-ordinate curves form 

 a double set of orthogonal coaxial circles. Important 

 particular cases are : (i) A circular plate with an 

 eccentric circular hole : (2) a semi-infinite plate 

 bounded bv a straight edge with a circular hole : and 

 C-?) an infinite plate containing two circular holes. 

 The differential equation of the stress function is 

 solved for these co-ordinates, the stress function 

 is obtained for given arbitrary stresses applied over 

 the boundaries, and expressions are deduced for the 

 stresses and displacements produced at anv point of 

 the plate.— R. O. Street : The tidal motion in the 

 Irish Sea : Its currents and its energy. Certain 

 general relations are obtained from the Laplacian 

 dynamical theory connecting the form of the tidal 

 wave and the magnitude of the surface current on a 

 sea of limited extent rotating with the earth. In 

 continuation of a former paper, these are applied to 

 the recorded data for the Irish Sea, and the agree- 

 ment is found to be fairly satisfactory. A second 

 approximation to the hydrodvnamical problem for a 

 rotating tidal basin is then effected, and by means of 

 the relations thus obtained the mean rates of transfer 

 of water and of energy across certain vertical sec- 

 tions placed transverse to the direction of the flood- 

 stream in the Irish Sea are computed from the exist- 

 ing hvdrographical data. The results show that 

 there is a residual flow of water northwards through 

 this region of such magnitude that the Irish Sea 

 would empty itself through the North Channel about 

 three times a year, while the tidal flow of energy 

 from all causes which takes place into this area is at 

 the mean rate of about 6 x 10" ergs per second. The 

 result of this estimate of the flow of energy into the 

 area is in general agreement with an independent one 

 made recently by Mr. G. I. Taylor (Phil. Trans., A, 

 vol. ccxx., 1919. pp. 1-33). H we could assume that 

 this energy is all dissipated, the result would be about 

 2qo times the viscous dissipation calculated directly 

 bv the writer in a previous paper (Roy. Soc. Proc, A, 



