If we now place before the other half of the object glass a second prism equal to the first, but moveable in a contrary direction, the two images of Q will be both seen by reflexion; and by the continued move ments of the two prisms we can carry the measure of an angle to the double of the greatest angle measured by one prism alone, that is to 204°, if the prism is or common glass.
From this theory of the new sextant, its construc tion and use will be readily understood. In the per spective drawing of it in Fig. 9, ABD is a sector, greater than a quadrant, of four inches radius. It is divided intd 10', which by a vernier is subdivided in to 10". Round the centre C revolves the index CE, which carries the vernier at one end, and the isosceles rectangular prism F at the other, with its edge SC directed to the centre, and perpendicular to the plane of the limb. The other prism H, similar to the first, is fixed on the instrument, so that when the index marks zero, the larger faces of the two prisms are perfectly parallel, and nearly in contact. A telescope N on the arm IL is moved about the centre C, and on the plane of the sector. The divisions are read off by a microscope M. By this double motion of the teles cope parallel to the limb, the object glass can receive a greater quantity of rays from one prism than from the other, so that we may by this means render the images of two objects equally luminous when they happen to be of different brightnesses. This effect is similar to what is obtained in Hadley's sextant by the elevation or depression of the telescope on the limb. If an equality of light is not thus obtained, we must apply to the object glass of the telescope the cover A', half of the aperture of which remains un covered, while the other half is filled with a plain co loured glass. This glass being turned towards the prism which reflects the most luminous object, will enable us to obtain the necessary equalization of the light.
The error of collimation may be detected in this instrument in three different ways.
1. By the coincidence of the two images of the same object, the one direct and the other reflected. The sun's disk is the best object, but any terrestrial object will answer if more than 100 yards distant, for at this distance the parallax becomes visible.
2. By the coincidence of two images of the same object externally reflected from two small faces of the prism, for when the two isosceles and rectangular prisms having their greater sides parallel at zero, have their smaller sides parallel so as to give coincident ima ges, we have an angle of 90'.
3. By measuring two angular distances of two ob jects diametrically opposite to each other. The ex cess or defect of the sum of these two angles upon 180', will give half the angle to be added to or sub tracted from the zero point given by the vernier, in order to have the true zero or the error of collimation.
If we compare this last verification with the first, and find a difference, it must arise from an error in the division of the limb.
If the telescope is inclined to the common section of the reflecting planes of the prisms, the fourth part of the trangle will have for its sine, the sine of the fourth part of the angle given by the instrument mul tiplied by the cosine of the inclination of the axis, Let SR, ST be the two reflecting planes, whose common section is SQ; let SV bisect the angle of the two planes, let AB be perpendicular SQ and AD = AB From D let fall DH perpendicular to BA, and from D and B the perpendiculars DE and BC upon SB, and draw EA, CA, and HF parallel CB. Now if BA is the axis of the telescope, the angle formed by two coincident objects by reflexion, is qua druple the angle CAB, or twice the motion of the in dex. But if the angle has the obliquity DA, the true angle is the quadruple of the angle DAF, although the index gives the same angle as it had marked before. To find the error then, it is sufficient to determine the value of the angle DAE by means of the known angles CAB and BAD. By this construction we have AH : HE = AB : BC, or since IIF = DE cos DAH : sin. DAE = 1 : sin. CAB, we have sin. DAE = sin. CAB cos. DAH. From this formula it appears that the greatest error must take place when CAB is In this case, if the axis of the telescope is inclined 1°, the angle observed will be 179', 57', 56", instead of 180'; but this error, produced by a defective position of the telescope, is reduced to nothing, if we make the observation in that part of the field of the telescope where the slightest contact of the objects takes place.