6io 



NATURE 



[April 25, 1895 



the simplest and most interesting yet described. The 

 accuracy depends entirely upon the closeness of the ap- 

 proximation of the refractive index of the liquid to the 

 3 index of the crystal. Of course it will rarely happen 

 that coincidence of these values will occur for all colours 

 of the light employed, the dispersion of the crystal and 

 the liquid in general being diti'erent. So that although 

 the values may be coincident for sodium light, they would 

 in all probability be different for other colours. But if 

 the obsen-ations are only conducted for sodium light, a 

 process which is frequently sufficient for the purpose in 

 view, then this objection entirely disappears. Moreover, 

 the errors introduced by the discrepancy for different 

 wave-lengths of light would not be sufficiently large in 

 most cases, if observations for other colours were made, 

 to materially reduce the value of the method for the 

 purposes for which it was designed. 



A consideration of the simple formulje connecting the 

 optic axial angle with the ,i refractive index and the 

 refractive index of an immersion liquid will at once 

 render the value of the method, within the above speci- 

 fied limits, clear. Representing as usual the real semi- 

 acute angle between the optic axes within the crystal by 

 A'a, the semi-obtuse angle by \'o, and the apparent semi- 

 acute and obtuse angles in the immersion liquid by Ha 

 and Ho respectively, the refractive index of the medium 

 for light of the same wave-length being n, then : 



Sin Va 



3 



sin Ha and sin Vo 



- sin Ho. 



These two equations are of the same kind, for both 

 \'a and \'o are less than 90' ; and the only variables are 

 n sin Ha and n sin Ho, for i^, sin \'a, and sin \'o are 

 constant quantities for this wave-length of light. If, now, 

 the sum of the angles 2Ha and 2H0 is greater than iSo% 

 the common factor n must, in order to bring the sum of 

 these angles down equal to iSo', be increased, that is, a 

 liquid of higher refractive power be employed. Conversely 

 if the sum is less than iSo the refractive power of the 

 liquid must be diminished in order to bring the sum of 

 the an>;Ies up to iSo'. For the specially interesting 

 intermediate case where » = /3, the sum of 2 Ha and 

 2H0 will be exactly 180% and sin Va = sin Ha and sin 

 A'o = sin Ho, when also \a = Ha and V'o = Ho. 



From the above theoretical considerations one can 

 immediately deduce the course to be taken to render the 

 immersion liquid exactly equal to the ,-i index of the 

 crystal ; if the measured values of 2Haand 2H0 add up 

 to over 180' a liquid of higher refraction must be 

 obtained, and vice versa if the sum is less than iSo . 

 There are, however, several ways of determining the 

 closeness of approximation of the indices without going 

 to the trouble of actually making preliminary measure- 

 ments. In the first place the crystal will disappear in 

 the liquid, that is to say, will be invisible, provided 

 that it is colourless, when its refractive power is 

 equal to that of the surrounding medium, especially 

 when the line of the observer's vision lies in the plane of 

 the optic axes. This is very beautifully observed when 

 calcite is immersed in monobromnaphthaline, and parti- 

 cularly when it is arranged so that the observer looks 

 along the direction of the vertical axis of the crystal ; 

 under these conditions the latter is completely invisible. 

 In the second place, instead of hyperbolic curves passing 

 through the positions occupied by the optic axes, the 

 brushes will take the form of almost straight lines when 

 the refraction of crystal and liquid is about the same. 



In choosing crystals for observation by the new method, 

 I'rof Klein recommends that individuals or fragments 

 should be selected which arc equally thick in two perpen- 

 dicular directions in the plane of the optic axes, that is, 

 such as are almost cylindrical in appearance, and not 

 too thick to prevent the interference figures being ob- 

 served. When immersed in the liquid, it is as if at each 



NO. 1330. VOL. 51] 



moment, and for every position during rotation of the 

 cn'stal, a parallel section-plate were being examined, the 

 natural faces of the crystal — however rich in faces the 

 zone may be — not entering into consideration whatever. 



The advantages of the use of an immersion liquid of 

 equal refractive power in the examination of crystals 

 have been pointed out by several previous observers, as 

 Prof Klein is careful to state. So long ago as \%i,\ Biot, 

 in his memoir concerning lamellar polarisation, describes 

 the use he made of it. The method has long remained 

 dormant, however, as far as is known from the literature 

 of this branch of study. In the oiijhth edition, however, of 

 the Lcltrbuch der Physik tind Mitcorologic of Joh. 

 Miiller, edited by L. Pfaundler in 1S79, it is stated that 

 if the refractive index of the liquid in which a plate per- 

 pendicular to one of the medium lines is immersed is 

 equal to that of the crystal, the true angle between the 

 optic axes is at once afforded. Latterly, however, the 

 evident advantages of the method have sug£;ested them- 

 selves to several crystallographers. ^L Fouquo men- 

 tions it in his memoir in the Bulletin of the French 

 Mineralogical Society of 1S94 on the felspars. 



The writer of this article has frequently made use of 

 the method for certain specific purposes, and it may be 

 of use to other workers to give a brief indication of one 

 or two modes of extending its sphere of usefulness not 

 touched upon by Prof Klein. In the course of the in- 

 vestigation of the noriral sulphates of potassium, rubi- 

 dium, and caesium, the results of which were laid before 

 the Chemical Society last year (Journ. Chein. Soc. 1894, 

 62S, and Zeitscliri/t fiir Kryslallographie, 1894, xxiv. l), 

 a difficulty was fountl in determining the true optic axial 

 angle of rubidium sulphate by means of the very accu- 

 rately orientated section-plates prepared by use of the 

 new grinding goniometer described to the Royal Society 

 {Phil. Trans. 1S94, Series A, SS7) earlier in the same 

 year. The difficulty, which is one not uncommonly met 

 with, was owing to the fact that the extremely low double 

 refractir n, necessitating the use of very thick section- 

 plates, combined with the slight separation of the optic 

 axes, rendered it impossible to measure the obtuse angle 

 in monobromnaphthaline, and so to calculate the true 



angle by means of the formula tan \'a = ,. ,, . The 



Sin Ho 



difficulty was surmounted, as fully described in the 

 memoir referred to, by measuring the .acute angle by 

 means of section-plates perpendicular to the first median 

 line immersed successively in two liquids, benzene and 

 cedar oil, whose refractive indices were nearly, and the 

 mean of them exactly, equal to the mean refractive index 

 of rubidium sulphate. The two series of values obtained 

 for six wave-lengths of light (the monochromatic light 

 producer recently described by the writer, Phil. Trans. 

 1S94, Series A, 913, being employed) were almost iden- 

 tical, differing only by a very few minutes, and the mean 

 for each wave-lenj^th was taken as representing the true 

 angle of separation of the optic axes for that particular 

 wave-length. The method is applicable to all cases 

 where it is found impossible to see the hyperbolic brushes 

 through a section perpendicular to the second median 

 line on account of the slight separation of the optic axes. 

 The suggestion to employ it was made to the writer by 

 Mr. Miers, of the British Museum, who has had a gonio- 

 meter constructed for the express purpose of studying 

 the use of an immersion liquid. 



Another case in whichobservations in such a lic|uid are 

 of great value is when it is found desirable to confirm, in 

 some independent manner, the mode of dispersion of the 

 optic axes for different colours indicated by the calcu- 

 lated values of 2\'a. obtained from the formula last 

 quoted. Several of the compounds which the writer has 

 lately been engaged in studying exhibit very low dis- 

 persion of the optic axes, and the calculated values of 



