Oct 24, 1878] 



NATURE 



685 



adjustment, no matter what maybe their azimuth to the axes of the 

 crystal. We obtain by measurements and calculation one single 

 index of refraction, but this may vary so much in different 

 minerals as to clearly point out what they are. Thus, for 

 example, it varies from 1-43 in fluor to 2-34 in blende. If, how- 

 ever, the crj'stal possesses strong double refraction, the pheno- 

 mena are far more complex, and vary according to the direction 

 in which the section is cut, its azimuth to the hues of thegratino-, 

 and also according as it has one or two optic axes. 



If we look through a parallel plate of a uniaxial crystal with 

 powerful double refraction, like calcite, cut perpendicular to 

 the principal axis, we see two undistorted images of the circular 

 hole, directly superimposed, one over the other, but separated 

 vertically by a wide interval. This doubling of the image is 

 due to the collection by the object-glass of divergent light, silace, 

 for strictly parallel rays passing in the same general direction^ 

 there is no double refraction whatever. Both systems of per- 

 pendicular lines are seen in focus at the same time in each of 

 the images, one of which is due to the ordinary, and the other 

 to the extraordinary, ray. By observing these focal points we 

 obtain two indices of refraction, one being the true index of the 

 ordinary ray (yu), and the other not that of the extraordinary 



»"ay (iu'), but a very low apparent index, equal to — . 



When the section is cut in other directions the images differ 

 very much from one another. That due to the ordinary ray 

 has invariably the same properties. The circular hole is not 

 distorted, and both systems of line are in focus at the same 

 time, so that we may call that image unifocal. The other 

 image, due to the extraordinary ray, instead of thus maintaining 

 a constant character, changes very greatly, the maximum of 

 change being when the section is cut parallel to the principal 

 axis of the crystal. There is no focal point whatever at which 

 the cu-cular hole is seen of its time size and shape, and the 

 entire circumference is never all in focus at once. There are 

 two special foci, widely separated, at which the circle is, as it 

 were, drawn out into a long band, at one focus parallel, and at 

 the other perpendicular to the axis. If the section be strictly 

 parallel to the axis the focal point of the ordinary image is 

 nearly half-way between these two foci of the extraordinary'^ray, 

 and coincides in horizontal position with the point at which the 

 two elongated bands intersect. There is thus no lateral dis- 

 placement of the images. If, however, the section be not 

 parallel to the axis they are displaced laterally, this character 

 being a very delicate test of the accuracy with which the section 

 has been made. In fact, in all cases, if the two opposite sur- 

 faces are parallel, the character and position of the images at 

 once indicate the exact relation between the optic axes and the 

 planes of the plate, whether they be natural or artificial. 



On viewing the rectangular gi-ating through a section cut more 

 or less nearly parallel to the principal axis, no lines whatever 

 can be seen by means of the extraordinary ray, unless one system 

 is nearly parallel to the axis. At one focal point one system 

 of lines is seen, and at the other focal point the other system, so 

 that the image due to the extraordinary ray may be said to be 

 bifocal. On rotating the grating, the lines are seen to become 

 broader, then obscure, and finally invisible. Unhke the image 

 due to the ordinary ray, the bifocal image has thus a special 

 focal axis, and the lines can never be seen in sharp focus if they 

 are not either parallel or perpendicular to this axis. 



On the whole, then, we have three focal points, one for the 

 ordinary, and two for the extraordinary ray ; and by observing 

 these we obtain three different indices of refraction, one being 

 that of the ordinary ray n ; and, provided that the section is 

 closely parallel to the axis, the index derived from the lines 

 parallel to the axis in the extraordinary image is the true index 

 (V) of the extraordinary ray, whilst the third index is of the very 

 abnormally high apparent value t. 



The characteristic peculiarity of crystals like aragomte, which 

 have two optic axes, is that, when the section is so cut that the 

 images are directly superimposed without lateral displacement 

 they give two bifocal images, and four apparent indices. When 

 cut in particular directions one of these images may become uni- 

 focal, but then there is a more or less considerable lateral dis- 

 placement of the two images. When the section is cut perpen- 

 dicular to the line bisecting the acute angle between the optic 

 axes, so as to give two very bifocal images, the images of the 

 curcular hole are crosses at two different foci, and not, as in the ca^^e 



of calcite, two circles. Biaxial crystals have three true indices 

 ot retraction {/^, ^u', ;u"), and, if the section be accurately cut in 

 the plane of any two of the axes of elasticity, so that there is no 

 lateral displacement of the images, the four apparent indices 

 observed from the lines of the gi-atings are as follows •— 



From lines perpendicular to the plane 

 of polarisation 



From lines parallel to the plane of 

 polarisation 



Polarised in 



the opposite 



plane. 



Calling thes^observed indices a, b, c, and ^respectively, we thus 

 have /x" = Va; c or si h d- It follows from this that we can de- 

 termine the value of all tliree indices by very simple observation^ 

 made by employing a single section cut in the plane of any two 

 of the three axes of elasticity. Absence of lateral displacement 

 in the images at once shows us that the specimen in its natural 

 state, or as artificially cut, is sufficiently parallel to one of these 

 planes to be suitable for the determination of the indices ; but 

 even if it is not such as to give all three indices absolutely true, 

 one at least may be correct, and the others may be determined 

 approximately. In any case the character and position of the 

 images at once shows in what direction the section is cut, or the 

 relation which any parallel planes of a natural crystal bear to 

 the optic axes, though the phenomena are more complex than in 

 the case of uniaxial minerals. 



It would occupy far more time than can be allowed on the 

 present occasion to describe in detail the curious and anomalous 

 appearance due 'to dichroism or to the laminar structure of 

 particular minerals which gives rise to complex internal reflec- 

 tions. My chief aim has been to call attention to the very valu- 

 able facts which may be learned by viewing a circular hole or 

 rectangular grating with a microscope through a parallel plate of 

 any crystalline mineral. The data thus obtained are so remark- 

 ably characteristic that they alone would amply suffice to identify 

 a large proportion of natural minerals. In many cases all the 

 necessary observations can easily be made with small crystals in 

 their natural state, which alone is of course a very great gain for 

 practical mineralogy. The chief value of the method is, how- 

 ever, that it enables us to identify portions of minerals of micro- 

 scopic size in sections of rocks as thin, or even thinner than 

 Tcirth of an inch with an amount of certainty which leaves little 

 to be desired. 



When examining specimens of such a size that their thickness 

 must be measured by means of the scale attached to the body of 

 the microscope, I find that an object-glass of about | inch focal 

 length, combined with a somewhat highly magnifying eye-piece, 

 gives the best results. When, however, we come to study the 

 minerals in moderately thin sections of rocks, it is impossible 

 to measure the thickness and the displacement of the focus suffi- 

 ciently accurately by means of the scale and vernier. The fine 

 adjustment screw of the microscope may then be employed alono' 

 with a I or I- object-glass, and, if properly constructed and used^ 

 the requisite measurements may be made to within ^^^nrth of an 

 inch. We may thus approximately determine the indices in sections 

 only TWD- of an inch in thickness. It is, however, necessary to 

 adopt a system which reduces the number of separate measurements 

 and to a great extent eliminates several sources of error. Instead 

 of attempting to measure the absolute thickness of any particular 

 crystal, and the actual displacement of the focal length due to 

 it, the apparent thickness of the mineral, as seen through itself 

 {t), is measured by means of the rotation of the graduated 

 circular head of the fine adjustment by focussing, first to the 

 top and then to the bottom, of some appropriate specimen. In 

 each particular substance this apparent thickness is equal to the 

 true thickness divided by the index of refraction. The thin 

 glass cover is made somewhat larger than the section, so as to 

 project beyond it, and inclose a layer of the hard and brittle balsam 

 used to fasten down the piece of rock. Selecting for observation 

 a specimen as near as possible to this balsam, so as to avoid any 

 error due to unequal thickness, the difference {d') in the dis- 

 placement of the focal length due to the mineral and the balsam 

 is ascertained by focussing through each the lines of the grating. 

 This value is positive or negative, according as the index 



