A goniometer, upon another principle, has recently been invented by the Rev. E. J. Burrow, fellow of Magdalene College, Cambi idgc. The following is the description of it, given by himself : " BG (Fig. I I.) is a steel bar of about of an inch square, chamfered off to the point 11. On I3G is taken exactly an inch, BA, and A is made the centre of motion of the legs DE and d e, of which DE is also brought to a point D, to correspond with B. To the other end of these legs is attached, by the pin I'', a moveable quadrant, pass ing through the bar BG at C, and graduated to read to wards the side of the shorter leg d e. The handle Gil is made to project on the opposite side to that on which the legs move, that it may not interfere with the use of a brass degree divided into minutes, to he attached to the centre A upon longer radii. The leg All is divided accurately into tenths, and the two nearest the point B into twentieths, and these again into fortieths. The whole instrument is about four inches and a half long.
Now if the crystal, the angle of which is to be measur ed, be detached, it is obvious, that, if an acute one, by ap plying it to the angle BAD, the vertical and equal angle EAC will be given on the quadrant; if obtuse, by apply ing it to the angle E and B, we obtain its supplement EAC. But if the crystal be embedded in the matrix, so that with the common goniometers having the moveable vertex, it is difficult to procure a mechanical measurement of the protruding angle, we take any distance from the vertex of the crystal measured upon the scale of tenths, Ste. ; and placing one point of the instrument, (ex. gr.) on x (Fig. 12.) and the other on z, so as to snake the triangle x y z isosceles, we get upon the quadrant the angle which the base x z subtends at the radius one inch ; and we have the side x y, measured. As, therefore, when the object is giv 1 en, the angle it subtends, and —, we have the proportion rad.
x y : AB: : angle found : angle sought. And as the whole radius is one inch divided into tenths, this proportion is easily made in the head.
The short bar is added for the better carrying of the quadrant, and renders the instrument useful in geological observations, to ascertain the inclination of strata. This is done by hanging a small plummet to a hook at A, and hav ing made the angle which it forms at BC a right angle, and moving the outer bars, till their upper line coincides with the stratum, the angle of inclination will be given on the quadrant." We shall now conclude this article with the description of a goniometrical telescope, and a goniometrical micros cope, invented by Dr Brewster, and described in his Trea tise on New Philosophical Instruments.
This instrument is represented in Fig. 13, where TT is the eye-tube of the telescope, which carries the graduated circle All, divided into 360 degrees. By means of the milled head which surrounds the eys-glass at E, this circle has a motion of rotation about the axis of the eye-tube. The vt ruler V has likewise a motion round the axis of the instrument, and may be set to the zero of the scale, when the level L, fixed to the plane surface of the graduated cir cle, is adjusted to a horizontal line. On the same surface,
parallel to the axis of the level, there arc fixed two screws, (one of them is seen at s,) on which the arm DF may slide to or from the eye-glass E. This arm is bent into a right angle at D, and carries a frame, in which the small reflect ing plane 0, made of black glass, is fitted so as to have a rotatory motion about the axis a b.
When an angular object appears in the field of the teles cope, the arm D F is pushed backwards or forwards, till the mirror 0 is near the centre of the eye-glass, and it is then turned round its axis a b, by means of the lever h, till the observer, by looking through the eye-glass, and into the mirror at the same time, perceives a distinct reflected image of the field of view, and the angular object which it contains. The graduated circle AB is then moved round its centre, till the reflected image of one of the lines which contains the angle is continuous with the line itself, and the degree pointed out by the index is noted down. The circle is again made to revolve till the image of the other line is continuous with the line itself, and the place of the index is again marked. The arch of the circle intercepted between these positions, is the measure of the angle re quired. To save the trouble of reading off a second line, the vernier may be placed at the zero of the scale, when the first coincidence has been observed.
In order to explain the theory of this instrument, let ABC, Fig. 14. be a plane angle seen in the field of the te lescope, and MN the section of a reflecting mirror, which moves along with the graduated circle. 'When the side BC is in the same straight line with its image CE, BC is pea pendicular to AIN ; and when, by the motion of the divided circle, the mirror MN is brought into a posi tion in n perpendicular to the other side AB, the arch de scribed by the moveable circle is evidently a measure of the angle formed by the lines AB BC. The angular mo tion of the mirror, in passing from the position MN to m n, is not measured by the angle AOC, formed at the centre 0 by AO and CO, but by the angle FOG, which is equal to ABC. This will be evident from considering, that the lines AB, CB are parallel to FO, GO, and that the same angle would have been obtained, by taking the reflected image of the lines FO and GO.
When the instrument is required to measure the appa rent angle which any right line makes with the horizon, the index of the vernier should point to zero when the level is adjusted to the horizon ; and then, by turning round the graduated circle till the coincidence between the direct and reflected image of the right line is observed, the index will point out the angle required.
The goniometrical microscope is represented in Fig. 15, and is nothing more than the application of the preceding contrivance to a microscope. See Nicholson's Journal, Jan. 1809, vol. xxii. p. 1. and Brewster's Treatise on Xev., Phil. Instruments, p. 97-106, 110.