454 



NA rURE 



[Alarch ii, 1886 



faces of Iceland spar in air, water, and tetrachloride of carbon, 

 the water and tetrachloride of carbon beint; contained by a nearly 

 cylindrical thin glass vessel (a chemical beaker), which stood on 

 the horizontal stage of the goniometer, the tetrachloride being 

 prevented from evaporating by a layer of water floating on its 

 surface. 



The position of the crystal in which the principal section was 

 in the plane of incidence and the obtuse summit nearest the 

 observer was considered the zero position ; when the principal 

 section was in the plane of incidence, and the obtuse summit 

 towards the side from which the light was incident upon it, was 

 therefore azimuth l8o°. The ciystal was rotated clockwise, and 

 the same direction of rotation was considered the positive direc- 

 tion for the Nicol. 



It had been intended to make similar measurements with 

 artificial surfaces cut perpendicular and parallel to the axis of 

 the crystal, and three pieces of Iceland spar cut respectively 

 parallel to a natural face, and perpendicular and parallel to the 

 axis, and all polished with "whiting" were obtained. 



Seebeck states {Fogg. Ann., vol. .xxi. 290) that Iceland spar 

 polished with rouge or putty powder differs in its optical pro- 

 perties from the natural substance, but that an artificial surface 

 polished with chalk behaves very nearly, if not exactly, like a 

 natural one. 



Seebeck's measurements were all made with the crystal in 

 air, and as the changes in the azimuth of the plane of polarisa- 

 tion, and in the value of the polarising angle, for different 

 azimuths of the crystal, when such is the case, are small, it 

 seemed desirable, before making any measurements with the 

 artificial surfaces cut perpendicular and parallel to the axis, to 

 make some determinations with an artificial surface parallel to a 

 natural face of the crystal when the crystal was immersed in 

 water ; this was accordingly done. 



These results differed considerably from those obtained pre- 

 viously with a natural face in water, and it therefore did not 

 appear worth while to make any further experiments with arti- 

 ficial surfaces, as it seemed certain that the results would be 

 untrustworthy. 



The difference between the results obtained with this artificial 

 surface and with a natural surface of the crystal is too great to 

 be explained by supposing that the artificial surface was not cut 

 absolutely parallel to the direction of the cleavage, and must 

 therefore be attributed to some change produced by the polisli- 

 ing, possibly due to the pressure employed (conf. Seebeck, 

 Pogg. Ann. vol. xx., 1S30, 27). 



Prof. Stokes pointed out to me that the experimental results 

 which had been obtained were well suited for reduction by 

 means of the harmonic analysis, and not only explained the 

 method but himself reduced the first set of observations made 

 with a cleavage-face in water. All the observations were accord- 

 ingly reduced by this method. 



Owing to the fact that the principal section of the crystal is a 

 plane of symmetry, the periodic series for the development of the 

 azimuths of the planes of polarisation can contain sines only, and 

 that for the polarising angles cosines only, including the constant 

 term ; therefore the coefficients of the cosines in the former case, 

 and of the sines in the latter, were not calculated, except with 

 the observations made with the artificial surface ; it seemed pos- 

 sible that the process of polishing might occasion some want of 

 symmetr)', and that therefore it was desirable to calculate the 

 values of the coefficients in both sines and cosines. 



Omitting the terms which we know from theoretical reasons 

 ought not to appear, and which at any rate are extremely small, we 

 obtain as the final result the following approximate expressions — 



Azimuths of the Plane of Polarisation of Light Polarised by 

 Reflection 

 Cleavage surface in air - 2° 10' sin 9 -I- 1° 49' sin 29 -I- 0° 2' 

 sin 38 -I- 0° 1' sin 48. 



Ditto, in water - 9°27'sin8-H 5° 29' sin 28 -I- 0° 47' 



sin 38 - 0° 10' sin 48. 

 Ditto, in tetrachloride - 23° 47' sin 8 4- 10° 25' sin 28 -I- 4° 17' 



of carbon sin 38 - 0° 24' sin 48. 



Artificial surface in water — 3° 52' sin 8 -I- 5° 1 1' sin 28 -I- 0° 33' 

 sin 38 - 0° 21' sin 48. 

 Polarising Angles 

 Cleavage surface in air 58° 17' - 1^ 15' cos 28 + 0° 2' cos 46. 



Ditto, in water 52° 2' - 3° 14' cos 28 -H 0° 13' cos 48. 



Ditto, in tetrachloride 53° 9' - 8° 54' cos 28 -|- 1° 12' cos 48. 



of carbon 



.A.rtificial surface in water 48°53'-2° 9' cos 28 -f 0° i' cos 48. 



From these expressions the values of the ordinates of the 

 curves representing the phenomena were calculated, and the 

 curves plotted from the values so obtained. 



These curves correspond very closely with the smooth curves 

 drawn from the points given by the observations, the values of 

 the ordinates for those portions of the curve corresponding to 

 azimuths o°-40° and 320°-36o°, being rather greater than the 

 values given by the smooth eye-drawn curve. The curves for 

 the artificial surface in water show clearly, when compared with 

 the corresponding curves for the natural surface, how greatly 

 these two surfaces differed in their optical behaviour. 



Brewster, in his paper in the Philosophical Transactions for 

 1819, says: — " In any given surface when A and A" are the 

 maximum and minimum polarising angles, viz. in the azimuths 

 of 0° and go", the polarising angle A' at any intermediate azi- 

 muth a may be found by the formula A' — A + sin-a(.J "-.-/)." 



This expression is the same as that given by the harmonic 

 reduction of the observations set forth in this paper, if 

 we assume that the smaller terms are due to errors of observa- 

 tion, as in that case the expression for the polarising angle in 

 air (B) becomes 58° 17'- i 15' cos 28. 



Brewster's formula also appears to hold good for the case of 

 Iceland spar in water, as the harmonic series for the value of 

 the polarising angle {D) may be taken as 52° 02' - 3" 14' cos 28. 

 But with the spar in tetrachloride of carbon the agreement no 

 longer holds, as the coefficient of cos 48 becomes too large to be 

 neglected, being 1° 12'. The determinations made in this 

 strongly refracting liquid were less satisfactory than the others, 

 but there is hardly sufficient ground for assuming that the 

 value of the coefficient of cos 48 is merely due to errors of 

 observation. 



The experiments, of which an account had been given, confirm 

 the accuracy of Brewster's observations made with a surface of 

 Iceland spar in contact with media other than air, and show 

 moreover that, as .Seebeck pointed out, the change in the value 

 of the azimuth of the plane of polarisation of the reflected 

 light also occurs, though to a far less extent, when the crystal 

 is in air, and further, as the refractive index of the medium 

 increases, the change in both these values is greatly augmented. 



The harmonic analysis affords a means of expressing approxi- 

 mately at least both these changes as functions of the azimuth 

 of the principal section of the crystal, and further shows that, 

 when the crystal is in air or water, Brewster's formula for the 

 angle of polarisation expresses the facts of the case. 



Linnean Society, February 18. — Dr. St. George Mivarf, 

 F. K.S., in the chair. — Prof. II. Macaulay Posnett, N.Z., was 

 elected a Fellow of the Society. — Mr. W. Joshua exhibited over 

 130 species of Lichens from Jamaica, collected by Mr. J. Hart 

 in the Blue Mountains near Gordon Town, and after- 

 wards determined by Dr. J. Miiller (Arg.) of Geneva ; 

 many of these were of great interest. — Mr. T. Christy ex- 

 hibited some flowers preserved by a new chemical process ; 

 he also called attention to a hitherto unknown Cinchona bark 

 from South Africa ; and besides showed a living plant of 

 Erytho.xylon coca in fruit. — Mr. H. Goss made remarks on 

 specimens of the Wild Parsnip (Pastinaca sativa) gathered by 

 him on the Thames side, Moulsey, Surrey. — Mr. A. D. Michael 

 read a paper on Acari of the genus Glycifhagus, discovered in 

 moles'-nests. In G. platygaster the male, although slightly 

 differing from the female, as is usual in the genus, still can 

 easily be recognised as of the same species ; but in G. dispar, 

 while the female closely resembles that of G. platygaster, the 

 male, on the contrar)', is totally unlike in size, form, markings 

 of body, and arrangement of the legs, &c. G. dispar also 

 affords evidence of the retro-anal position of the bursa copulatrix, 

 and its being the posterior median projection characteristic of 

 the females of the genus. Mr. Michael speculates wherefore 

 the above divergence of the male form of G. dispar, seeing 

 that its habitat and other conditions are the same as 

 its female, and the closely-allied species. — Mr. John Ball 

 gave a communication on the botany of Western South 

 America. He introduced the subject with reflections on the 

 climatal relations of the western seaboard, which have such 

 a remarkable influence on the development of vegetable life, 

 lie then describes his collection of plants from Buena Ventura 

 in Columbia, from Payta in Northern Peru, from Caldera in 

 Northern Chili, and Lota in Chili, from the neighbourhood of the 

 Ch.annels of Western Patagonia, andStraitsof Magellan, through- 

 out interspersing reflections and brief summiiries of the peculiari- 

 ties of the floras in each of the districts in question. He infers 



