298 Prof. "VV. H. Miller on Two New Forms of Heliotrope. [May 18, 



reflected from the surface of the mirror. This instrument has been con- 

 structed on three different principles. In Drummond'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 Tri- 

 angles, 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 (Astronomische Nachrichten, vol. v. 

 p. 329, and v. Zach's Correspondance Astronomique, vol. v. p. 374, and 

 vol. vi. p. 65), in Steinheil's (Schumacher's Jahrbuch fur 1844, p. 12), 

 and in Gallon'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 Gallon, 

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

 Gallon'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 another 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 a, 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 excep- 

 tion 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 



