72 Royal Society. 



of the sun S reflected from the surface of the mirror. This instru- 

 ment has heen constructed on three different principles. In Drum- 

 mond's (Philosophical Transactions for 1826, p. 324), by a simple 

 mechanism, a normal to the mirror is made to bisect the angle 

 between the axes of two telescopes, one of which is pointed to T, and 

 the other to S ; consequently T will receive the light of S reflected 

 from O. In Struve's (Breitengradmessung, p. 49) the mirror is 

 directed by means of two sights attached to its support, which are 

 brought into the line OT. The heliotrope employed in the Ordnance 

 Survey (Ordnance Trigonometrical Survey of Great Britain and 

 Ireland, Account of Observations and Calculations of the Principal 

 Triangles, p. 47) is similar to Struve's, except that a single mark 

 placed at a convenient distance in the line OT is substituted for the 

 two sights. In the two heliotropes invented by Gauss (Astrono- 

 mische Nachrichten, vol. v. p. 329, and v. Z,ach's Correspondance 

 Astronomique, vol. v. p. 374, and vol. vi. p. 65), in Steinheil's 

 (Schumacher's Jahrbuch fur 1844, p. 12), and in Galton's an 

 optical contrivance is connected with the mirror, so as to throw a 

 cone of sunlight in a direction opposite to the cone of sunlight reflected 

 from the surface of the mirror, the axes of the two cones being 

 parallel, and either very nearly or absolutely coincident. Hence any 

 point T, from which a portion of the former cone of light appears 

 to proceed, will receive the light of the sun reflected from the mirror. 



The heliotropes I am about to describe produce two cones of 

 sunlight thrown in opposite directions, like those of Gauss, Steinheil, 

 and Galton, but differ from them in having no moveable parts, 

 and from all but Galton's, and the sextant-heliotrope of Gauss, 

 with a second moveable mirror, in requiring no support except the 

 hand of the operator. 



One of these consists of a plane mirror, to an edge of which are 

 attached two very small plane reflectors, a, c, forming with one an- 

 other a reentrant angle of 90°, and making angles of 90° with the faces 

 of the mirror. If a ray be reflected once by each of the two planes 

 a, c, it is obvious that the first and last directions of the ray will be 

 parallel to a plane containing the intersection of a, c, and will make 

 equal angles with the intersection of a, c, which is also a normal to 

 the face of the mirror. Therefore, if two parallel rays fall, one on 

 the mirror, and one on either of the planes «, c, the direction of 

 the ray reflected from the mirror will be parallel and opposite to 

 that of a ray reflected once at each of the planes a, c. When the 

 small reflectors are made of bits of unsilvered glass, the brightness 

 of the image of the sun is so far reduced after the second reflexion, 

 as not to interfere with the direct vision of T, and the mirror can be 

 pointed without difficulty. 



The other consists of a plate of glass having parallel faces b, d, 

 with two polished plane faces a, c on its edges, making right angles 

 with one another, and with the faces b, d, the face d being silvered, 

 with the exception of a portion at the angle adc not larger than the 

 pupil of the eye. It is easily seen that if a ray of light incident 

 upon b, and refracted through b so as to be reflected internally 



