which need be taken into consideration is a possible variation in the index of the balsam. I assume that it is the hard and brittle balsam used to fasten down the specimen before it is ground thin, and not the soft balsam used to fix on the covering glass. I find that the index of such hard balsam varies but little, and is about 1.54.

As an illustration of what may thus be done, I will describe the results in the case of several different minerals in a section of a dolerite from near Glasgow, which is only about 4 of an inch in thickness. I give the measurements in turns of the head of the fine adjustment.

A colourless mineral containing fluid cavities, filling up cavities between the original minerals, was 207 turn in thickness, as measured in itself, and when compared with the hard Canada balsam the decrease in focal length in the latter was found to be 207-007 •207

=

= 1.49.

007, whence we have μ' 1.54 x In accordance with the principles described in my address at the Mineralogical Society, this clearly shows that this mineral is a zeolite, probably analcime. In a similar manner in the case of a mineral which looks very much like some variety of felspar, the focal length in the balsam was increased, and the index was found 214+025 to be 1.54 x 214

=

= 1·61, which clearly shows that it cannot be any felspar which contains a large amount of alkali, since that would reduce the index very considerably. Theory led me to conclude that the index of labradorite should correspond closely with this. I am not aware that its indices have been previously determined. I found that they are about 1.621, 1.617, and 1.597. The mean of these is about 1.612, which agrees so closely with that of the mineral in the section, that it must almost certainly be labradorite, or some felspar of similar chemical composition.

În like manner I found that the mean index and the focal character of the images given by another colourless mineral closely correspond with those characteristic of calcite. I also found that the mean index of a dark-coloured mineral was 1.79 or 1.80. No common silicate which does not contain much iron has so high an index. Both in this and in other optical characters it corresponds closely with the black augite in the lava of Vesuvius, which has a mean index of 1·785.

The only important objection to this comparison with balsam is that its index may vary. It is, however, always possible to determine what its real index is. Thus, for example, on comparing a * Mineralogical Magazine,' vol. i. p. 193.

4

transparent mineral filling a cavity in an old lava of Vesuvius with fresh soft balsam, having an index of about 1.44, I found that the index of the mineral was about 1 49, which closely corresponds with that of analcime, or some other analogous zeolite.

Very frequently in large sections of rocks some interesting object may occur so far from the edge that direct comparison with the balsam might lead to serious error. This difficulty may be overcome by comparing it directly with some other mineral the index of which is either known or has been previously determined. For this purpose quartz is eminently suitable, since its mean apparent index, which is about 1.55, does not vary materially; it is so frequently met with, and so easily identified. By thus comparing with quartz a reddish mineral having no double refraction, met with in a porphyritic rock from Naddle Fell, I found that its index was about 1 82, which clearly indicates that it is a garnet containing much iron.

To be able thus to determine the index from such thin sections, and from portions of minerals with no solid transparent part more than of an inch in diameter, will for the future make it possible to identify the mineral constituents of rocks in a far more satisfactory manner than heretofore. In order to obtain such good results as those described from very thin sections, it is, however, necessary to take the means of many observations, and thus eliminate the unavoidable errors of individual observations.

I have so far considered almost exclusively the mean indices of refraction and not the separate indices of uniaxial and biaxial crystals. I do not propose to enter at large into this part of my subject, but still I think it is not desirable to omit it altogether.

The meteoric irons of Krasnojarsk and Rittersgrün contain a clear transparent mineral which has been proved to be olivine by the usual methods. I subjoin the values of the three indices, and give for comparison those of olivine, according to Des Cloiseaux:

Such a close agreement clearly shows that the methods I have adopted are correct, and give very satisfactory results when the section is not too thin, and a sufficient number of observations made to eliminate accidental errors.

In the case of the black augite of the lava of Vesuvius I found that the three indices were about 1.80, 1.76, and 1.75. This proves that there are two optic axes, and that the double refraction is positive, in which it corresponds with diopside; but the refractive power is very considerably greater in this black variety of augite

found in lava, no doubt owing to the presence of a larger amount of iron.

TO

It will thus be seen that the study of the indices of refraction in the manner I have described enables us not only to identify with more confidence each particular mineral, by bringing to bear a most important class of optical characters, hitherto unavailable in studying thin sections of rocks, but also in some cases enables us to form a very satisfactory opinion respecting certain variations in chemical composition. Though all this is possible, yet it most certainly requires a far more strict attention to minute details than is ever taken into account in ordinary microscopical research. The accurate measurement of the up and down movement of an objectglass to within rooo of an inch is a very different matter to measuring any such visible quantity with an ordinary micrometer, but then we must remember that by this step we convert the microscope into an all but new physical instrument. However, if some microscopists might not feel disposed to attend to all the minute detail necessary for accurate quantitative observations, the methods now described may easily be employed qualitatively, and many valuable conclusions drawn from what may be seen without any actual measurements. The difference in focal distance and the focal character of the images are easily observed, and much may also be learned from the manner in which the images are separated. This alone may prove that a minute crystal, seen under the microscope, has two optic axes inclined to one another at a greater or less angle. Since this is a fact of some interest, and has I believe not yet been applied to microscopical research, it will be well to notice it in some detail.

As previously named, if a parallel plate of any doubly refracting mineral be cut in the plane of any two of the focal axes, the two images, polarized in opposite planes, are not separated horizontally. When cut obliquely, the results vary with the direction of the section and the character of the crystal. If it have one optic axis, and therefore only one focal axis, the line along which the images are separated is in all cases parallel to this axis, and therefore parallel to the plane of polarization of one of the images. If it have two optic axes, and therefore three focal axes, and the section be cut obliquely to two of them, the images will be separated in relation to both of them, and the resultant line of maximum separation will not be parallel to the plane of polarization of either image. These facts will be better understood by means of Figs. 9, 10, and 11.

In both cases the planes of polarization of the two images are supposed to be parallel to one or other of the two systems of perpendicular lines of the grating (Fig. 9). This is easily arranged practically. The plane of polarization of a polarizer under the

stage is arranged parallel to one set of lines, and the analyzer over the eye-piece crossed so as to give rise to a naturally dark field. The object is then introduced and rotated until it is in such a position that it does not in any way depolarize the light. The polarizer and analyzer are then removed, and the microscope so adjusted that the lines of the grating are seen in good focus through the crystal. If both systems of lines are doubled, as in the case of the olivine of the Rittersgrün meteorite, shown by Fig. 11, the crystal must have two optic axes, inclined to one another at a considerable angle. If, however, only one system is doubled, as in Fig. 10, it may be a two-axed crystal, cut obliquely only to one focal axis; but if on examining a number of different crystals, scattered in various positions through the thin section of rock, only one system of lines is invariably doubled, the mineral must either have only one optic axis or two which are inclined to one another at a small angle, two of the three indices of refraction being very nearly equal.

A little care is sometimes necessary in order to see the lines well separated. Frequently they lie in different planes, so that they cannot be seen in focus at the same time, especially if too high a magnifying power is used. On the contrary, the horizontal separation may be so small that they cannot be seen separately, unless a high power is employed. The extent of this separation varies directly as the intensity of double refraction, and as the thickness of the section, but also, as previously named, depends on the direction in which it is cut. With a object-glass and a powerful eye-piece, there is no difficulty in seeing that one set of lines is divided by calcite, even when it is only 4000 of an inch thick, since its double refraction is so strong, but a much greater thickness of some minerals would be necessary. Care must be taken not to confound this true separation with any duplication of the lines due to accidental reflexions, which are distinguished by varying with slight movements of the object.

If any individual crystal be so cut that its optical characters cannot be determined by means of this visible horizontal separation of the lines, it must necessarily be cut in such a direction as to enable us to determine them by means of the focal character of the images, the one method being the most applicable just when the other breaks down.

As a practical example, I will describe what I observed in a section of lava from Vesuvius about 3 of an inch thick. It contains a few scattered crystals of what I believed to be olivine. In some cases neither system of lines was sensibly divided, but both images were bifocal, and I obtained for the three indices about 1.77, 1.72, and 1.64. In some examples only one system of lines was divided, but in others both, one being separated by

about 1200 of an inch, and the other by about 2000, the former being readily resolved by a object-glass, but the other requiring a. It will thus be seen that both classes of facts clearly prove that the mineral has two optic axes, and that the three indices of refraction differ very considerably, but have a mean value of about 1.71. This is 03 higher than that of the variety met with in the meteorites previously mentioned, probably owing to a variation in the amount of iron, though at the same time it is only fair to say that in measuring only once the indices in a section of an inch in thickness, we cannot be sure that the second place of decimals is perfectly correct. On the whole, there can be very little doubt that it is olivine, since, so far as I am aware, no other common mineral has corresponding optical characters.

In this section of lava are also scattered crystals of augite, their mean index of refraction being 1.80. By using a , I could just separate one system of lines, but the section is too thin to enable me to separate the other system. In the case of another section, which is nearly three times as thick, I found that the indices were about 1.80, 1.76, and 1.75, and I could just see that the second system was also double, but the lines much less separated than the others, which agrees with what would result from two of the indices being nearly equal. We thus prove most completely that the mineral has two optic axes inclined at a small angle, and has positive double refraction. In all these characters it differs so much from the olivine, that they could not possibly be confounded together, even if they were not otherwise well distinguished. I am not yet quite certain whether the above-described characters enable us to distinguish augite from hornblende. As far as my present observations go, the mean indices of refraction of the dark varieties of hornblende and of augite are nearly the same, but all my sections of hornblende show the lines very decidedly less separated horizontally than in the case of augite of equal thickness, as though the double refractions were less intense.

6

The principal difficulty in at once applying this method of study is that our knowledge of the indices of refraction of even some of the commonest minerals is so imperfect. Des Cloiseaux, in the Annuaire du Bureau des Longitudes' for 1877, gives what appears to be a very complete summary of what was then known. The minerals in this list are all but exclusively those which can be obtained in comparatively large and transparent crystals, since the indices could not be determined by the old method if they were small and somewhat opaque. In many cases also only the mean index of biaxial crystals is known, and not their three different indices. What we ought to know is the value of all the indices of the commoner and more opaque varieties of the constituent minerals of rocks. By the methods I have described these indices could soon

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