. Astronomy for students and general readers . lelto i? P to fall on every part of the first surface of the glass. Afterpassing through it they are all supposed to converge nearly or ex-actly to the same point R. Among all these rays there is one, andone only, the course of vchich, after emerging from the glass at Q,will be parallel to its original direction RF. het R P Q R he thiscentral ray, which will bo completely determined by the directionfrom which it comes. Next, let us take a ray coming from anotherdirection as S P. Among all the rays parallel to 8 P, let us takethat one which, after


. Astronomy for students and general readers . lelto i? P to fall on every part of the first surface of the glass. Afterpassing through it they are all supposed to converge nearly or ex-actly to the same point R. Among all these rays there is one, andone only, the course of vchich, after emerging from the glass at Q,will be parallel to its original direction RF. het R P Q R he thiscentral ray, which will bo completely determined by the directionfrom which it comes. Next, let us take a ray coming from anotherdirection as S P. Among all the rays parallel to 8 P, let us takethat one which, after emerging from the glass at T, moves in a lineparallel to its original direction. Continuing the process, let ussuppose isolated rays coming from all parts of a distant object sub-ject to the single condition that the course of each, after passingthrough the glass or system of glasses, shall be parallel to its originalcourse. These rays we may call central rays. They have this re-markable property, pointed out by Gauss : that they all converge. Fig. 33. toward a single point, P, in coming to the glass, and diverge fromanother point, P, after passing through the last lens. These pointswere termed by Gauss Hauptpunkte, or principal points. Butthey will probably be better understood if we call the first one thecentre of convergence, and the second the centre of must not be understood that the central rays necessarily passthrough these centres. If one of them lies outside the first or lastrefracting surface, then the central rays must actually pass throughit. But if they lie between the surfaces, they will be fixed by thecontinuation of the straight line in which the rays move, the latterbeing refracted out of their course by passing through the surface,and thus avoiding the points in question. If the lens or system oflenses be turned around, or if the light passes through them in anopposite direction, the centre of convergence in the first case be-comes the centre of


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