HELIOTROPE

In E'. The angles of incidence and reflexion being equal, the angle S' O E' is equal to E' O D: therefore S' E' is to E' D in the ratio of S' O to O D. But S' O and O D ^re constant, therefore the ratio of S' E' to E' D is constant. But D is a given point; therefore by a simple theorem in elementary geometry (Leslie's Geom. Analysis, b. iii. prop. 2.) the locus of E' is a given circle. It follows, therefore, that the axis of the mirror must describe in 24 hours the surface of a cone, the base of which, parallel to the plane of the equator, is a circle determined in magnitude and position by the given direction O D,and the parallel which the sun is describing on a given day of the year. It is easy to conceive a mechanism by which this object may be accomplished. Suppose a clock to be placed with its dial parallel to the equator, or the axis of the index hands parallel to the axis of the earth; and suppose a rod connected with the extremity of the hour hand to meet the axis produced and make with it the proper angle; then a mirror fixed perpendicularly to the rod will have the motion required. For a description of the original instrument see Graves an des' Phys. Element a; but it has been greatly improved by Charles, Malus, . See Journal de VEcole Poly technique, cahier 16.; Biot, Physique Experimcntale, tom.ii. [s. 561]