Page:Encyclopædia Britannica, Ninth Edition, v. 16.djvu/380

Rh 362 MINERALOGY pleteness and want of symmetry. In the latter case the determina tion of the forms is often difficult. In the albite crystal (figs. 134, 135) P is the basal pinacoid OP ; M the brachydiagoiial pinacoid ooPoo ; s the upper right pyramid P ; I the right hemi- prism oo P ; T the left hemiprism oo P ; and x the hemidome T oo. Figs. 136 and 137 are crystals of axinite, the former from Dauphine, M Fig. 135, Fig. 134. Fig. 136. Fig. 137. the latter from Cornwall, of whose faces the following is the de velopment : r the macropinacoid ooPoo ; P the left hemiprism oo P ; u the left upper quarter-pyramid P ; I the left upper quarter- pyramid 2 P ; s the left upper partial form of the macropyramid 3 P3 ; aiid x the hemidome 2 P oo. The Measurement of the Angles of Crystals. The permanence of the angular dimensions of crystals shows the importance of some accurate method of measur ing their angles, that is, the inclination of two faces to Gonio- each other. Instruments for this purpose are called gonio meters, meters. Two have been specially used for this purpose the common or contact goniometer, invented by Caringeau, and the reflecting goniometer of Wollaston. The former is simply two brass rulers turning on a common centre, between which the crystal is so placed that its faces coincide with the edges of the rulers, and the angle is then measured on a graduated arc. This instrument is suffici ently accurate for many purposes and for large crystals, but for precise determination is far inferior to the reflecting goniometer. This requires smooth and even faces, but these may be very small, even the hundredth of an inch ; and, as small crystals are generally the most perfect, far greater accuracy can be attained. The reflecting goniometer is represented in fig. 138. It con sists essentially of a graduated circle mm, divided on its edge into twice 180, or more frequently into half-degrees, the minutes being read off by the vernier hh. This circle turns on an axis connected with U, so that by turning this the circle is moved round, but it is stopped at 180, when moving in one direction, by a spring at k. The other part of the instrument is intended to attach and adjust the crystal to be measured. The first axis of mm is hollow, and a second axis, aa, passes through it from ss, so that this and all the connected parts from b to / can be turned without moving the circle mm. The axis d passes through a hole in be, so that it can turn the arm dc into any required position ; / is a similar axis turning the arm og, and pq a fourth axis, in like manner movable in g, and with a small knob at q, to which the crystal to be measured is attached. When about to be used, the instrument should be placed on a table, with its base horizontal (which is readily done by the screws in it), and opposite to a window at about 12 or 15 feet distance, so that its axis shall be parallel to the horizontal bars of the window. One of the upper bars of the window, and also the lower bar, or, instead of the latter, a white line on the floor or table parallel to the window, should then be chosen, in order to adjust the crystal. The observer places himself behind the instrument with the side a at his right hand. The crystal is then attached to q by a piece of wax, with the two faces to be measured upwards, and the edge of union of the faces, including the angle to be measured, as nearly as possible in the line of aa. The eye being brought near to the first face of the crystal, the axes aa and p are turned till the image of the window is seen reflected in the face with the horizon tal and vertical bars in their position. The axis d is then turned through a considerable angle (say 60), and the image of the window again sought and brought into its proper place by turning the axis/, without moving p. When this is done that face is brought into its true position, normal to d, so that no motion of d can dis arrange it. Hence the image of the window maj r now be sought in the second face, and brought into its true position, with the horizontal bars seen horizontal, by moving the axes d and a. When this is done the crystal is properly &quot;adjusted.&quot; The angle is measured in the following manner. First bring the zero of the circle and vernier to coincide, and then turn the inner axis a or ss, and move the eye till the image of the upper bar of the window re flected from the more distant face of the crystal coincides with the lower bar or hori zontal line seen directly. Keeping the eye in its place, turn the other axis It till the reflected image of the upper bar in the other face in like manner coincides with the Fig. 138. lower line ; the angle of the two faces is then read off on the divided circle. As the angle measured is not directly that of the faces but of the rays of light reflected from them, or the differ ence between the angle wanted and 180, the circle has the degrees numbered in the reverse direction, so as to give the angle without the trouble of subtracting the one from the other. The apparatus figured is for adjusting the crystal, and is an im provement suggested by Naumann. In the original instrument the axis fo was made to push in or out in a sheath, and had a small brass plate, bent at right angles, inserted in a cleft at o, to which the crystal was attached. The crystal was adjusted as formerly by moving the plate, or the axis fo, and by slight motion of the arm de, which should be at right angles nearly to be when used. A very marked improvement is to have a small mirror fixed on the stand below the crystal, with its face parallel to the axis aa, and inclined at 45 to the window, when the lower line can be dispensed with, and the instrument used for various other purposes of angular measurement. Many more perfect instruments have been intro duced for the purpose of insuring greater accuracy ; but the simple instrument is sufficient for all purposes of determinative mineralogy, and the error from the instrument will, in most cases, be less than the actual variations in the angles of the crystals. Departure from Geometric Simplicity and Loss of Regularity in Crystals. Such departures may be regulated by law, or may result from an undue operation of the force of accretion in certain directions. 1. Regular Departures from Simplicity. There are three varieties of this : parallel groupings, twin forms, hemitrope forms. Parallel Groupings. A plurality of individuals are here Crystal arranged either so that a line which joins their centres groups- becomes a prolongation of one or other of their crystallo- graphic axes, or so that their axes are parallel. Fig. 20 shows the first, where cohesion sufficient for stability requires that the minute octahedra must mutually penetrate some what into each other. Fig. 139 shows the same in baryte. If we suppose octahedra united, the upper left-hand face of the one with the lower right-hand face of the other, there would be parallelism of their axes. Re-entering angles would, in such cases, prove a plurality of individuals, but if a number of cubes were superimposed in similar position, no such angles would occur, an elongated square prism resulting; and such arrangements, if