Intelligence and Miscellaneous Articles. 175 



perpendicular to each other, if the angular mirror which they con- 

 stitute makes the two images (produced by double reflection) of the 

 cross-wires of one of the telescopes coincide with the cross-wires 

 themselves. 



If the axes of the telescopes 1 and 2 are, through reflection of 

 the illuminated cross-wires, set normal to the two faces of the 

 mirror, they make exactly an angle of 90° with each other. Different 

 positions of the angular mirror then determine every four points 

 of the circle-division which are 90° distant from each other. 



Two plane glasses make exactly an angle of 120° or 60° with 

 one another, if two telescopes, placed each normal to one of them, 

 show simultaneously, through double reflection, the cross-wires of 

 telescope 1 in the cross-wires of telescope 2, and vice versa. 



By putting, with different positions of the angular mirror of 

 120° or 60°, the two telescopes normal to the respective faces of 

 the mirror, we obtain, by reading-off the circle, points exactly 60° 

 or 120° distant from one another. 



If the two plane glasses make an angle of 180°— 20, and the 

 telescope-axes, normal to them, an angle 2p with each other, a 

 third plane glass can be fastened with wax upon the turntable in 

 the centre of the graduated circle in such manner as to reflect the 

 rays proceeding from the cross-wires of telescope 1 upon the cross- 

 wires of telescope 2. Plane glass 3 is then inclined at the angle 

 to plane glass 1 or 2 ; and the angular mirror formed of 1 and 3 

 or 2 and 3 can be used to set the telescope-axes perpendicular to 

 the mirror-faces, and to determine points in the circle whose 

 distance from one another is measured by the angle (p. 



From the angles 90° and 60° we thus obtain with this third 

 plane mirror angles of 45° and 30° — and from these, angles of 22 J° 

 and 15°, &c. 



Should there be any difliculty in bringing the plane glasses into 

 correct position with wax and the free hand, it can be readily 

 obviated by a simple arrangement with screw and pressure-spring. 



The method of reflection of the cross-wires permits us also to 

 compare the angles of glass prisms with those of the angular 

 mirrors, and, with the unalterable angle of a glass prism of exactly 

 90°, 60°, 30°, 20°, 10°, &c, to measure and calibrate the divisions 

 of the circle. The latter I have not been able to carry out, as 

 the prisms long since ordered for the purpose are not yet in my 

 possession. 



The method above described is most convenient, and accurate to 

 the extent of the magnifying-power of the telescopes and as far 

 as the distinguishing of the ocular-threads is possible — that is, as 

 nearly as one can in general see with the apparatus in question. 

 As, also, the perfectness of the plane glasses can be easily con- 

 trolled with the telescope, it is probably applicable to the produc- 

 tion of a new and accurately graduated circle. 



Wiirzburg, June I, 1873. 



