GRAPHY.
The reflecting goniometers of Dr Wollaston and Dr Brewster were invented nearly about the same time, with out any communication between their respective authors ; but though these instruments resemble one another in so far as they both make use of the principle of reflex ion, yet they chiller very widely in the application of that ciple, and in the mode of measuring the angles of crys!als.
One of the advantages which Dr Brewster's goniouRAer possesses over that of Dr Wollaston's, is, that the former is capable of measuring a hollow angle, such as a b c, re presented in Plate CCLX XVII. Fig. I. and 2. or one in which the crystal a b c, Fig. 3. is imbedded in a stony mass from which it cannot easily be detached. The case repre sented in Fig. 2. is one which actually occurs in measuring the angle which the edge of the interrupting stratum, or crystallised vein of sonic specimens of Iceland spar, forms with the surfaces of the rhomboid. The determination of this angle is of the utmost importance, and is incapable of being measured by any goniometrical instrument with which we are acquainted, excepting that of Dr Brewster's. See Philosophical Transactions for 1815, p. 277.
This goniometer will measure the angles of crystals with great accuracy, and little trouble, if the surfaces are moderately smooth, and reflect the smallest quantity of light. \Vhen the surface has the appearance of being per fectly rough and irregular, the oblique reflection generally gives a very distinct image of a vertical bar, when the image of a horizontal line or of any other object could not possibly be obtained. It frequently happens, however, that the crystal does not reflect sufficient light to form an image, or is so irregular in its surface, or is so incon veniently placed in the specimen, that a variety of different contrivances must be adopted for measuring its angles. In a specimen of Allanite, for example, belonging to Mr Allan, the crystals are situated in such a manner, that their angles could not be measured by any goniometer without breaking off some of the projecting parts of the mineral.
\Vhen the planes of the crystal are smooth, but unpolish ed, a small piece of parallel glass AB, Fig. 4. or any other
reflecting substance, with parallel sides, is successively placed upon the surfaces of the crystal CDE ; the coin cidence of the direct image of a rectilineal object with the image reflected from the piece of glass, is observed as be fore, and the angle found in precisely the same manner. If the two surfaces of the reflector should not be parallel, the aberration will be corrected by reversing its position on the second surface of the crystal.
When the planes of the crystal are covered with as perities which prevent the piece of glass from lying paral lel to these planes, we must make use of the reflector AB, Fig. 5. supported by three slender feet, and so formed that the reflecting plane mn is exactly parallel to the plane o p, passing through the extremities of the three feet. The three feet are then placed upon those points of the surface where there are no asperities, and the coincidence of the images is observed in the reflector : It is then transferred to the other surface of the crystal, the coincidence of the images again observed, and the angle of the planes mea sured as before. As the surface of the crystal may always be brought into a horizontal position when the coincidence of the object and its image is observed, the reflector will stand steadily on the planes of the crystal ; but, in order to secure it from sliding, a drop of varnish or melted bee's wax may be placed round each of its feet. It might be proper to have two or three of these reflecting tripods of different sizes, and with their feet at different distances, in order to accommodate themselves to the smooth parts of the crystal. One of the reflectors might be fixed on each surface with bee's wax, in the way represented in Fig. 6. where C is the crystal, and A, B the two reflecting tripods. If the position of the crystal should prevent us from adopt ing either of these methods, which was the case in the specimen of Allanite already mentioned, we must have recourse to the goniometrical microscope, which is intend ed to measure the angles formed by two lines when the eye is perpendicular to the plane of the angle.