problem can be put in this quite simple mathematical way. After finding the types or varieties by such or such process of substitution, we can form a table of existing varieties and find some general expression, some mathematical formula to express it. I do not know if I make clear enough my idea, but I think it is possible indeed to deal with the question in a purely experimental way. It is an experimental fact that there exist three compounds of chlorine and benzene and their substitution by another element will result in only three isomeric compounds and no more. By just expressing these experimental facts, it seems to me we get the same result, and freed at the same time from all hypotheses; we would be dealing with facts alone.

I can only repeat that I think it would take much work to carry out this idea, i. e., to develop it so far as to cover all our actual knowledge of organic chemistry, but I feel rather sure that something in this line, free from all hypothesis, could be developed. And that by it we could substitute for hypothetical organic chemistry a rational one, unsaturated with this discussion of the theory of atoms. You know of course, that the whole difficulty is how to account for the fourth valence; for the fourth valence of carbon is indeed a nuisance. If we could get rid of it, all would be in good order, all discussion would cease at once. Then we could say such and such a variety is brought about by such and such a chemical change.

Sections V. and VI. will appear in the next number of the QUAR

TERLY.

THE DETERMINATION OF MINERALS IN CRUSHED
FRAGMENTS BY MEANS OF THE POLAR-
IZING MICROSCOPE.

BY

AUSTIN F. ROGERS.

Our knowledge of the optical characters of minerals is confined almost entirely to the following classes of minerals: (1) Rockforming minerals, of which many detailed characters useful in identification are known. (2) In oriented sections of nearly all transparent minerals the optical constants, index of refraction, axial angle, etc., have been determined. I believe it is also possible to use the detailed optical and microscopic characters of the non-rock-forming minerals in identification as well. The polarizing microscope should have a place in every mineralogical laboratory and supplement the blowpipe in the determination of minerals.

While preparing cleavage plates of minerals to illustrate for class use some of the optical characters of crystals, it occurred to the writer that possibly minerais might be determined in crushed fragments by means of the polarizing microscope. The results obtained in the last year or so have more than exceeded my expectations.

The method in general consists in reducing the mineral to coarse powder* and examining the fragments on the stage of a polarizing microscope. The powder is placed on a glass slip, the coarse fragments removed by tapping the slip with the finger, then tapping off the medium-sized ones on to another slip. Some liquid, such as oil of cloves or bromoform is added and the shape, color, index of refraction, extinction, elongation, specific gravity, etc., determined. The remaining fine powder is tested as to solubility, and if soluble microchemical tests are employed.

The orientation is not haphazard as in rock sections. Because of cleavage there is in many cases a constancy in orientation. For example, in ten fragments of hornblende the extinction angles only varied from 15° to 17%.

Even if the method is not used in the identification of minerals

* A small square anvil and blowpipe hammer are convenient. Pounding gives better results than grinding as the fine particles adhere to the larger fragments and render them somewhat opaque.

it furnishes a convenient method of illustrating the optical characters of minerals without the use of thin sections which are rather expensive when required for large classes.

In a general course in mineralogy some attention ought to be paid to the optical side and every student should know something of the meaning of such terms as pleochroism, index of refraction, extinction angle, etc. (as an introduction to petrography, if for no other reason). With this end in view, the following suggested outline has been prepared. It serves the double purpose of furnishing a convenient method of studying the optical characters of minerals and as an introduction to the use of the scheme, as the slides may all be made from crushed fragments or cleavages.

SUGGESTED OUTLINE OF SLIDES TO ILLUSTRATE THE OPTICAL PROPERTIES OF MINERALS.

Ordinary Microscope, Common Light. (Both nicols out,* medium power objective.)

Index of refraction varies with direction - calcite, aragonite.

Crossed Nicols and Convergent Light. (Both nicols in, high power objective, condenser

and Bertrand lens in.)

Interference figures.

Uniaxial positive.

Alunite crystals.

Brucite cleavage.

Uniaxial negative.

Calcite, basal parting.

Wulfenite, tabular crystals.

Biaxial positive, small axial angle.
Clinochlore cleavage.

Biaxial positive, large axial angle.

Topaz and heulandite cleavages.

Biaxial negative, small axial angle.

Biotite, phlogopite and talc cleavages.

Biaxial negative, large axial angle.

Muscovite, lepidolite, margarite and cyanite cleavages.

Biaxial, to optic axis, showing axial bar.

Pyroxene, basal parting (|| 001).

Epidote, basal cleavage (001).

Form is due to cleavage, and is fairly constant. The fragments, of course, lie on the broadest surfaces. One can easily distinguish seven groups, designated by Roman numerals.

Can easily be made by shaving down a cleavage flake and cutting away part of the under side.

I. Triangular plates.

II. Square or rectangular plates.

III. Rhombic plates

IV. Prismatic plates with uneven ends, more or less striated.

V. Very long fragments grading into needles.

VI. Flat plates not belonging to foregoing, rhomboidal or

irregular in cross section.

VII. Irregular, but not plates, as shown by non-uniformity of interference colors.

IV. and VII. are the large groups.

Some minerals fall in two or three divisions. For example, gypsum is found in IV., V and VI.

་

Index of Refraction. This, one of the most important characters of minerals, is easily determined by means of the so-called "Becke test." * The fragments to be tested are embedded in various liquids of known refractive indices. Focus sharply on edge of a thin fragment with lower nicol down and raise objective slightly when a bright line appears on the side of the substance having the greater index of refraction. For instance, if quartz is embedded in Canada balsam, and the objective is raised, the bright line appears on the side of the quartz, its refractive index being greater than that of balsam.

Twenty or more liquids might be used, but in this study it was found that seven were all that are ordinarily needed, and in many cases three suffice.

1.50 Benzol.

1.54 Oil of cloves.

1.58 Bromoform.

1.62 Mono-iodo-benzene.

1.65 a-monobromnaphthalin.

1.74 Methylene iodide.

1.83 Sulphur in methylene iodide.

If permanent slides are wanted, Canada balsam in xylol, with index of refraction about equal to oil of cloves, is used. Bromoform is perhaps the best liquid to start with. Determine whether index of refraction (designated by letter n) is higher or lower, then try liquid next above or below bromoform, and so on until is known within certain limits.

* Becke, Sitz. der k. k. Akad. d. Wiss. Wien., I. Abt., p. 358, 1893. Abstract by Luquer; SCH. MIN. QUAR., 23: 127, 1902. Also in Minerals in Rock Sections, 2d edit., 1905.