July 15, 1897] 



iVATC/R£ 



261 



deviation), the skewness, and the modal frequency were found 

 to be the constants, which described a local barometric frequency 

 with the smallest probable errors. 



They have next discussed the chief physical features of a 

 barometric frequency distribution. 



(a) The modal height and the modal frequency are found to 

 possess certain advantages over the mean height and the mean 

 frequency. \'arious methods are considered for approximately 

 determining the position of the mode. 



{b) The variability of the barometric height and the skewness 

 of the distribution are discussed at some length. 



((•) A test of the accuracy of the observations for the twenty 

 coast stations is made by attempting an interpolation of the 

 frequency constants of London and Cambridge between those of 

 Southampton, Ilillington, and St. Leonards. 



In the second part of the memoir the subject of correlation is 

 dealt with. It is shown that within the limits of the British 

 Isles there is a very high degree of correlation (as high as o 9824 

 between Babbacombe and Churchstoke), and only sinking to 

 07572 if we take practically the utmost reach of the British 

 Isles. It is pointed out that the gradual change of correlation 

 with direction and distance, combined with change owing to the 

 interval of time between observations, enables the meteorologist 

 to find systems of stations with almost every variety of corre- 

 lation coefficient. 



The probable height and probable deviation from that height 

 at any given station, based on a knowledge of the heights, con- 

 temporaneous or not, at one, two, three, or more other stations, 

 are considered. It is indicated that with proper arrangement 

 of times and distribution of stations it must be possible to make 

 the probable deviation zero or nearly zero, and hence to predict 

 with very great accuracy the height at one station from a know- 

 ledge of heights at other selected stations. The suggestion is 

 made that this principle might very possibly be applied to 

 closely predict future barometric heights at a given station from 

 antedated observations at other selected stations. 



Various theorems are deduced from the general principles of 

 correlation : thus, it is shown that — 



{a) There is a balance height for every pair of stations, such 

 that when the barometer stands above this height at one station 

 it will usually stand below it at the other, and vice versd. 



(d) That for a very considerable number of triplets of stations 

 which are positively correlated together, so that a high baro- 

 meter at one means usually a high barometer at a second, it can 

 still be predicted that if the barometer be steady at one, a rise 

 or fall at the second denotes a fall or rise respectively at the 

 third member of the triplet. 



The writers hope that their paper may draw attention to the 

 importance of rendering the large amount of barometric ob- 

 servations now made, available for the easy calculation of the 

 variation and correlation coefficients. They consider that if a 

 chain of stations round a large continental area could have 

 their correlation for a series of intervals of time worked out, 

 much might be done in the way of very close prediction of baro- 

 metric changes. 



" On the Theory of the Magneto-Optic Phenomena of Iron, 

 Nickel, and Cobalt." By J. G. Leathern, Fellow of St. John's 

 College, Cambridge. Communicated by Sir Robert S, Ball. 

 F.R.S. 



In this paper the fundamental equations of a particular type of 

 magneto-optic theory are taken in a general form on the lines of 

 Mr. Larmor's recent papers on electro dynamics, and developed 

 so as to obtain the solutions of the problems of magnetic reflec- 

 tion and of transmission throvigh films. The formulae so ob- 

 tained are compared with the available experimental results. 



The notation differs slightly from that of Maxwell : c denotes 

 the velocity of radiation, and (/", /', A") corresponds to Max- 

 well's total electric displacement ; this has components (/, ^, k) 

 and (/', g', h'), of which the former is the displacement involved 

 in the ether strain, and the latter that involved in the polarisa- 

 tion of the matter. It being assumed that for light oscilla- 

 tions the magnetic permeability is unity, the fundamental 

 equations of the theory are as follows : (i.) The circuital rela- 

 tions dcjdy - dbjdz = 4^11 and dR/dj/ - dQ/dz = - da/d/. (ii. ) 

 The equations of the current « = <rP + g^Q - _^^R + df jdt, 

 where the vector (^1,^2,^3) represents the Hall effect, (iii.) 

 The displacement relations, and the elastic relations between 

 electromotive force and polarisation, viz./'=/-f /', /=P/4irc2, 

 and /' = (K - i)/4irc» . P -f b^i^ldt - b.^Rld(, the vector 



NO. 1446, VOL. 56] 



(*i, K b^) representing, in transparent matter, the whole 

 magneto-optic effect. 



The vector {{b^d^/di'-^ +g,), {b^fdt^ -f g^), l,b.^ldfi + ^3)' is 

 assumed equal to Co^- («„, /3«, 7„), where («„, /S,, y,) is the in- 

 tensity of magnetisation ; and Q^^ is the single magneto-optic 

 constant of the theory. =» t> p 



The principal experiments made use of are those of Drs. 

 bissingh and Zeeman on magnetic reflection, their observations 

 being measurements of the phase m and amplitude ^ of the 

 " magneto-optic component " of the reflected light for various 

 angles of incidence. 



The following table will serve to indicate what sort of agree- 

 ment is found to exist between the theory and the experiments. 



Eijuatorial Reflection from Iron. 

 Angle of incidence. Observed value of w. Calculated value of w. 



86 o ... 209 26 ... 272 35 -X 



82 30 ... 204 22 ... 265 19 -X 



76 30 ••• 194 49 ••■ 256 31 -X 



71 25 ... 190 3 ... 251 13-X 



61 30 ... 181 49 ... 244 i8-jr 



55 22 ... 179 o ... 239 48 -A- 



36 10 .. 174 9 ... 235 27-jir 



If the value of jr is afcout 62°, the agreement shown is remark- 

 ably good. Experiments on polar reflection from iron point to 

 almost exactly the same value for x. 



If we suppose the value of Co to be given by 



-Co = 7-283 X 10-", 



the ratios of the calculated to the observed values of /t for the 

 above angles of incidence are found to be respectively 1-13, 

 096, 0-99. 0-97, I 01, 1-03, and 097; so that in the case of 

 the amplitudes also there is good agreement. 



The theory gives a satisfactory account of a phenomenon 

 which has only recently been discovered, namely, an effect of 

 the component of magnetisation perpendicular to the plane of 

 incidence. Good agreement is also found to exist in the case of 

 the experiments on transmission through films. 



It is to be noticed that, as b-^, b.^, 6^ are necessarily real, the 

 imaginary part of Co«'^ must be entirely accounted for by the 

 Hall effect. Hence the present theory involves the suppo.sition 

 that the Hall effect is very much greater for rapidly alternating 

 currents than for steady ones. 



" On the Change of Absorption produced by Fluorescence." 

 By J. Burke, M.A. (Dub.). 



A careful series of experiments which have led to the result 

 that certain fluorescent substances — notably uranium glass — 

 absorb the rays which they give out whilst fluorescing differently, 

 according as they are in a state of fluorescence or not ; so that 

 if a body, A, of some fluorescent substance, such as uranium 

 glass, be transmitting light from a similar body, B, which is 

 fluorescing the amount of light transmitted by A from B, is quite 

 different, according as A is fluorescing or not. 



If o and are the coefficients of transmission in the two cases 

 for uranium glass i cm. thickness, the mean values obtained by 

 eye observation are a =0*47 ; =079. 



The ratio —~ was also independently determined, the mean 



value of which =0-507. The values of a and ^8 determined 

 photographically were 



a <o'48 >o75 



>o-43 <o-89 



In the determinations of a and 0, a null method has been 

 employed, by which any appreciable want of uniformity in the 

 illumination could be detected. 



The source of illumination was almost invariably the spark 

 discharge of a Leyden jar between cadmium electrodes, being 

 one of the richest sources of the fluorescence exciting rays, and 

 the photometer one specially constructed for the purpose. 



The phenomenon has been exhibited directly by obtaining 

 two photographs side by side upon the one plate : one the 

 effect of the fluorescence due to two layers of the fluorescent 

 substance ; the other the result of superposing the effects due 

 to the fluorescent light from a single layer according as it came 

 directly or through a non-fluorescing layer of equal thickness. 

 The exposures being equal in each of the three cases, the super- 

 posed photographic effect was greater than the other one, 



