[71] See also M. LEONOR FRESNEL’S _Instructions sur l’organisation et la surveillance du service des Phares et Fanaux de France_. Paris, 1842, pp. 12, 13, 14, and 15. ~Choice of Focal Point for various parts of the apparatus.~ The focal point for the lenses and refractors is in the centre of the flame and on the level of its brightest film, as shewn in Plate XXV. The choice of a focus for the zones naturally formed a most important practical consideration in their arrangement; and the judicious remarks of M. LEONOR FRESNEL on that subject, already noticed, would alone have induced me to discard my former calculations in favour of his. For the upper zones, M. FRESNEL had adopted a point in the centre of the flame 10 millimètres above the focus of the lenses, so that all the light _below_ that point necessarily falls between the horizon and the Lighthouse; but for the lower zones, it was necessary, owing to their arrangement for convenience in a cylindric form, to adopt a separate focus for each zone in the direction of the centre of gravity of that part of the flame which would light each zone. In this manner (fig. 86) the foci of the zones recede upwards from _a_ to _f_ in proportion to the depression of the zones _a_, _b_, _c_, _d_, _e_, _f_, so that the line joining each zone and its focus, must revolve as a _radius vector_ round some point O between them. The details of this arrangement are shewn in Plate XVIII.; and are also given in the Table of the Catadioptric Zones in the Appendix. [Illustration: Fig. 86.] ~Application of Spherical Mirrors to fixed Dioptric Lights.~ [Illustration: Fig. 87.]