CRYSTALLOGRAPHY. 



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GAtilome* gee, from the mirtake into which he has fallen in the 

 v (e r< ' case of calcareous spar, that not even the most sedu- 

 """ cing and numerous mathematical analogies are to be 

 relied on in all cases. For nothing- can be more con- 

 clusive in appearance, than his reasons for fixing' upon 

 a particular angle for the inclination of the faces in 

 this crystal, yet they have led him to an inaccurate 

 conclusion. Hence it would not be at all surprizing, 

 if the measures which lie assigns for a very consider- 

 able number of his primitive forms, should turn out ul- 

 timately nothing more than approximations. 

 Dr Wollas- It was an object of great importance, therefore, to 

 ton's gonic. get a goniometer capable of measuring with a greater 

 meter. degree of accuracy. Dr Wollaston, to whose mecha- 



nical inventions the philosophical world lies under such 

 obligations, has contrived one upon optical principles, 

 susceptible of as great a degree of accuracy as is 

 thought requisite. The original instrument of Dr Wol- 

 laston only measures angles within five minutes of the 

 truth ; but we have seen the same instrument made so 

 as to come within half a minute ; and Malus, by con- 

 Verting it to a repeating circle, has made it susceptible 

 of as much accuracy as the experimenter chuses. But 

 the truth is, that in the greater number of crystals it 

 is not possible to measure the angles with perfect ac- 

 curacy, from some imperfection in the crystal itself. 

 The faces are often rough, and do not reflect the light 

 equally. The best crystals for measuring with Dr 

 Wollaston's goniometer, are those which are very small. 

 When they are very small, and transparent, with 

 smooth feces, we may arrive at any degree of precision 

 we think proper. 



Fig. 1. represents Dr Wollaston's goniometer, as ori- 

 ginally constructed. It consists of a brass circle, gra- 

 duated on its edge, and mounted on a horizontal axle, 

 supported by an upright pillar. This axle being per- 

 forated, admits the passage of a smaller axle through 

 it, to which any crystal of a moderate size may be at- 

 tached by a piece of wax, with its edge, or intersection 

 of the surfaces, horizontal and parallel to the axis of 

 motion. This position of the crystal is first adjusted, 

 so that, by turning the smaller axle, each of the two 

 surfaces, whose inclination is to be measured, will re- 

 flect the same light to the eye. The circle is then set 

 to zero, or to 1 80°, by an index attached to the pillar 

 that supports it. The small axle is then turned, till 

 the further surface reflects the light of a candle ( or the 

 bar of a window) to the eye ; and, lastly, the eye be- 

 ing kept steadily in the same place, the circle is turn- 

 ed by its larger axle till the second surface reflects the 

 same light. This second surface is thus ascertained 

 to be in the same position as the former surface had 

 been. The angle through which the circle has moved, 

 is, in fact, the supplement to the inclination of the sur- 

 faces ; but as the graduations on its margin are num- 

 bered accordingly m an inverted order, the angle is 

 correctly shewn by the index without need of compu- 

 tation. The best way of using the instrument, is to 

 place the eye within about an inch of the face of the 

 crystal, and to turn it by means of the small axle, till 

 a bar of the window, or some other distant object, be 

 brought exactly to correspond with the bottom of the 

 window. You then turn the circle till the other face 

 is in the same position. The index now points out the 

 size of the angle measured. 



In Fig. 1, a b is the principal circle of the goniome- 

 ter, graduated on its edge ; cc the axle of the circle ; 

 d a milled head, by which the circle is turned ; ee the 

 small axle for turning the crystal without moving the 

 circle ; f a milled bead on tjbe small axle ; g a brass 



plate supported by the pillar, and graduated as a ver- 

 nier to every five minutes ; h tiie extremity of a small 

 spring, by which the circle is stopped at 180°, without 

 the trouble of reading off; it and kk are two centres 

 of motion, the one horizontal, the other vertical, for 

 adjusting the position of the crystal ; one turned by 

 the handle /, the other by the milled head m. 



The crystal being attached to a screw-head at the 

 point n (in the centre of all the motions), with one of 

 its surfaces as nearly parallel as may be to the milled 

 head m, is next rendered truly parallel to the axis by 

 turning the handle /, till the reflected image of a hori- 

 zontal line is seen to be horizontal. By means of the 

 milled head^j the second surface is then brought into 

 the position of the first ; and if the reflected image from 

 this surface is found not to be horizontal, it is rendered 

 so by turning the milled head w ; and since this mo- 

 tion is parallel to the first surface, it does not derange 

 the preceding adjustment. See Phil. Trans. 1809, 

 Part II. 



Another goniometer, upon optical principles, has 

 likewise been invented by Dr Brewster. Fig. 2. ex- 

 hibits a view of this goniometer. AB is a circle 

 about six inches in diameter, divided into 360°. It 

 moves round OO as a centre, and is supported by 

 two upright bars M, N, fixed with screws into the 

 stand SS. To the ring OO, supported by these bar% 

 is fixed the arm G, that carries the vernier scale E. 

 This scale remains stationary, while a rotatory motion 

 is communicated to the divided circle AB, by means of 

 a pinion moved by the milled head Q, which works in 

 the teeth cut upon the circumference of the circle AB, 

 A rectangular piece of brass L is fixed by two screws 

 to one of the radii R of the graduated circle, so that 

 the slider ss may move upon it, and be placed at dif- 

 ferent distances from the centre of motion, by laying 

 hold of the pin below s. A thin plate b c, forming 

 part of the cock tbcC on the top of this slider, carries 

 the crystal, and by means of its projecting extremity b 

 this plate has a motion round the screw c, in a plane per- 

 pendicular to that of the divided circle. Below this is 

 another plate, which is seen at a, and which may be 

 raised and depressed round an axis, one end of which ap- 

 pears at x, by turning the screw /, which works in the 

 plate below a. Below the plate a, and fixed to it by the 

 screw C, is another piece of brass fastened to the top of 

 the slider by the screw above C, and moveable, by means 

 of the lever t, round that screw as a centre, in the same 

 plane with the circle. When the handle b is employed 

 to move the plate b c, it is pushed to or from the plane 

 of the circle AB. When the lever t is used to give the 

 whole cock b cC a rotatory motion about the screw C, it 

 is moved in a plane parallel to tliat of the circle AB ; 

 but when t is used to raise or depress the plates b c, 

 and a, it is turned round like a screw. By the com- 

 bination of these motions, the common section of the 

 surfaces of the crystals is brought into a position paral- 

 lel to the axis of the instrument. This adjustment is 

 effected by placing the graduated circle in such a posi- 

 tion, that a vertical window bar, or any other straight 

 line, is nearly in the plane of the circle. A motion of 

 rotation is then given to the crystal by the lever t ; and 

 if the reflected image of the window bar forms one 

 straight line with the object itself, when examined in 

 each surface of the crystal, the adjustment is complete, 

 or the plane of the graduated circle is paraUel to a 

 plane at right angles to the edge or common section 

 of the surfaces of the crystal. The instrument is then 

 placed in such a position, that the plane passing 

 through the eye and the window bar is perpendicular 



Dr Brew- 

 ster's go- 

 niometer. 

 Plate 

 CC'XXIV, 

 Fig. 2. 



