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truly unifocal and the other bifocal, unless the section is nearly perpendicular to the optic axis; and crystals having two optic axes give two images, both of which are bifocal, unless the section is nearly parallel to four different planes much inclined to the plane of the optic axes. The separation of the focal points in bifocal images varies directly as the intensity of the double refraction and the thickness of the specimen; and if the double refraction be weak and the section too thin, the bifocal character of the image may not be recognizable with an object-glass of too low power. Sometimes, however, as in orpiment, the difference in the focal distances amounts to more than one-fifth its thickness. As a general rule, all the more important facts may be observed qualitatively, no matter what may be the direction of the section, though it may not be suitable for determining the true value of the indices. The natural planes of crystals belonging to all those systems in which the axes are rectangular, are, however, often in the proper direction; and, unless their surfaces be very irregular, perfectly satisfactory results may be obtained by mounting the specimens on glass and fixing over them a thin glass cover with Canada balsam, or by using oil of cassia or some other liquid of nearly the same refractive power as the specimen under examination, if it be desirable not to use balsam.

Applying this method to the study of various minerals, the difference between them is found to be very great. We can, usually, at once see whether they give a single unifocal image or one or two bifocal images, and form a very good opinion respecting the intensity of the double refraction, and easily determine whether it is positive or negative. There can never be any question as to the index of the ordinary ray since the observed index is always true, and in many cases the index or indices of the extraordinary ray can also be determined. All these facts combined furnish data so characteristic of the individual minerals, that it would usually be difficult to find two approximately similar. In any case we have data which may often be of the greatest assistance in identifying the different species. Of course this method cannot be employed if the specimens are opaque, or have such a fibrous or laminar structure as to prevent our distinctly seeing the lines of the grating; but the presence of a vast number of fluid cavities and minute crystals or granules may not signify much.

The above sketch of some of the leading principles involved in this method of research would be very inadequate if on the present occasion it were desirable to fully explain its application to the study of crystals sufficiently large to be cut in a proper direction, and to make it possible to determine the indices with considerable accuracy. It will, however, I hope, be enough to indicate what we might expect to be able to learn by applying the method to the

study of thin sections of rocks. For some time I feared that it never would be possible to obtain satisfactory results with sections sufficiently thin to be useful for ordinary microscopical examination, since it appeared probable that the errors of observation would be as great as the differences between the indices of the various minerals usually met with in rocks. In order to identify these with confidence, there ought to be no considerable error in the second place of decimals of their measured indices. I, however, now find that it is possible to make sufficiently accurate measurements with sections less than 1 of an inch in thickness, which had been prepared many years ago, and ground down as thin as was thought desirable for ordinary microscopical examination. Though my apparatus is still far from perfect, I have been able to obtain satisfactory results with sections only of an inch in thickness, and even less.

Application of the above Method to the study of thin Sections of Rocks.

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When first I commenced to apply this method with thin sections, I very naturally dealt with them in the same manner as I had previously adopted in the case of thicker specimens, and determined the values of t and d by means of the scale attached to the body of the microscope. The next step was to determine their values by means of the rotation of the roughly graduated circular head of a well-constructed, fine adjustment screw. I found that with a object-glass of small aperture a difference in adjustment corresponding to of a revolution was just certainly apparent, which corresponds to about Too of an inch. cutive measurements may vary by several such divisions, but by taking the mean of a number of observations it appears to me possible to measure to at all events Too of an inch, and probably less. Since the true value of each revolution gradually diminishes from the top downwards, the mean value of d must be determined from observations made both at the upper and lower limits of the range of the adjustment required to determine the value of t. If, however, the range be small, no such precaution need be taken. Of course when thus employing a microscope for such extremely accurate quantitative observations it is absolutely necessary that all the movements should be thoroughly well made, and that no other part but the fine adjustment should by any accident move to such an extent as even rooo of an inch. A general construction, which would do well enough for mere magnifying purposes, might thus be totally unfit for such refined quantitative observations.

The above results were obtained with my ordinary condenser

and object-glasses. I find that they can be greatly improved by using a condenser of shorter focal length, specially constructed so that it can be adjusted for different thickness of glass. The objectglasses should also possess special characters. It is more important that the spherical aberration should be well corrected, than that the aperture should be large, or the image achromatic, since red light is generally used for illumination.

When the thickness of a section is considerable it may be allowable to assume that the polished surfaces are in contact with the thick glass plate on which it is mounted, and with the thin glass cover; and we may disregard the thickness of the intervening Canada balsam; but when we come to deal with very thin sections this would lead to very great errors. It is also necessary to bear in mind that both the thick and the thin plate glass are not of uniform thickness, so that measurements made in any one part would apply only to closely adjacent parts. It is also very necessary to remember that the thickness of any transparent substance measured in the manner described, by looking through itself is not the same as its real thickness, but is approximately equal to its real thickness divided by its index of refraction. In accordance with these principles the most legitimate process appeared to be to measure the total thickness of the mineral, of the upper and lower balsam, and of the covering glass, and to deduct from it the true thicknesses of the balsam and of the glass, calculated from their apparent thickness; and also to determine the displacement of the focus due to the mineral alone, by similar means. Such a process is, however, very tedious, and the chances of error are greatly increased by the large number of measurements required, and I have therefore been led by degrees to greatly simplify and improve it. My experience so far leads me to recommend three different methods, one or other of which appears to be the best, according to circumstances. If the specimen be somewhat thick, and the indices of the minerals to be observed not so different from that of Canada balsam as to make a slight error in its thickness of importance, the balsam between the glass slide and the covering glass should be carefully cleaned out along one edge of the section. Fig. 7 shows what would then be the general relation of the different parts as seen in section. The thickness and effect of the covering glass (g) may then be entirely neglected, since the true distance between it and the glass slide is easily measured, and so is the total displacement of the focus due to the mineral (m) and the upper and lower balsam (b, b'). Unless the balsam be relatively very thin its apparent thickness must be measured and due allowance made for it in calculating the results. The mineral observed ought to be as near to the edge as possible, to avoid any errors due to varying thickness.

As an illustration of the use of this method, I give the particulars in the case of a section of the pitchstone of Arran which is about of an inch in thickness. The space between the glasses was 2.54; the apparent thickness of the upper balsam 12, and of the lower 22. The total displacement of the focus was 89, from which must be deducted 19 for the balsam. Hence the 2.03

2.03-70

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1.526. This corrected for

mean apparent index is the effects of the aperture of the object-glass would be about 1·52. One image was very decidedly bifocal, and the other very nearly unifocal, as though the crystal had two optic axes, but two of the three indices nearly equal. In all these characters this mineral corresponds most closely with adularia, so that its general composition cannot differ much from that variety of felspar. only question is whether the double refraction be not positive, instead of negative, which it does really seem to be.

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The only serious objection to this direct method of comparison is the chance of error in measuring the thickness of the balsam used in mounting, and when this is relatively great, it is better to adopt one or other of the following systems, in which the thickness of the balsam may be entirely neglected.

It can easily be shown that if parallel plates of two transparent substances be of exactly the same thickness, their apparent thickness (t and t') as measured through themselves, varies inversely as their indices of refraction (u and μ). If then the index of one of them (μ) be known, that of the other can easily be calculated, thus

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These relations enable us to ascertain the approximate value of the indices of refraction of minerals in very thin sections without any special preparation, by making only a few simple measurements.

Fig. 8 shows the section of the edge of a thin plate of rock covered with a thin glass which projects beyond it, the space between the two glasses being filled with hard Canada balsam (b), as shaded. Now in this case, if we measure the apparent thickness of any mineral near the edge, by focussing first to its upper and then to its lower surface, and also observe the difference in the focal position of the lines of the grating, as seen through the mineral and through the balsam alone, we can at once calculate the index of refraction. A moment's reflection will show that the thickness of the balsam over and above the thin slice need not be taken into account, since the displacement in the focal length only corresponds to a thickness of balsam equal to that of the mineral, whatever it may be. The only source of material error

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 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 207-007 007, whence we have μ' 1.54 × =

to be 1.54 x

*

.214

=

.207

= 1·49. 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 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.

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