Early history of Lighthouse lenses, Condorcet, Buffon, Brewster, Fresnel, 239 -- Refraction, 242 -- Lenses, 245 -- Spherical aberration, 248 -- Fresnel’s formulæ for annular lenses, 249 -- Testing lenses, 255 -- Divergence of lenses, 256 -- Illuminating power of lenses, 257 -- Arrangement of lenses in a Lighthouse, 258 -- Pyramidal lenses and mirrors, 259 -- Curved mirrors, 260 -- Cylindric refractors of fixed Lights, 263 -- Application of crossed prisms to cause flashes, 264 -- True cylindric form given to refractors, and other improvements in their construction, 264 -- Catadioptric zones, the mode of computing their elements, &c., 267 -- Testing of zones, 282 -- Framing of zones, 286 -- Mechanical lamp, 286 -- Height of flame of mechanical lamp, 289 -- Position of flame in reference to focus, 290 -- Working of the pumps, 291 -- Choice of focal point for various parts of apparatus, 292 -- Choice of a focal point for zones, 292 -- Application of spherical mirrors to fixed Dioptric Lights, 293 -- Arrangement of Dioptric apparatus, 293 -- Arrangement of Dioptric apparatus in Lightroom, 294 -- Power of Dioptric instruments, 298 -- Orders of French Lights, 298 -- Distinctions of Dioptric Lights, 299 -- Comparison of Dioptric and Catoptric apparatus for revolving lights, 301 -- Comparison for fixed lights, 303 -- Summary of views as to two systems for revolving lights, 306 -- Summary of views as to two systems for fixed lights, 306 -- Advantages and disadvantages of both systems under certain circumstances, 308 -- Distinctions of the Dioptric Lights and the application of coloured media, 311 -- Captain Basil Hall’s proposal for fixed lights, 313 -- Effects of rapid motion on the power of lights, 315 -- Connection of experiments with irradiation, 320. VARIOUS GENERAL CONSIDERATIONS CONNECTED WITH LIGHTHOUSES, 320. Masking Lights, 320 -- Double Lights, 322 -- Leading Lights, 323 -- Distribution of Lights on a coast, 325 -- Height of Lighthouse Tower, and its relation to range of light, 328 -- Diagonal Lantern, 330 -- Glazing of Lantern, 331 -- Ventilation of Lanterns, 331 -- Arrangements and Management of a Lighthouse, 334 -- Cleansing of apparatus, 335 -- Mode of measuring relative power of lights, 336 -- More accurate comparison of intensity of lights, 338 -- Floating Lights, 346 -- Beacons and Buoys, 347. APPENDIX. 1. Table of Co-ordinates of Hyperbolic Column. 2. Notes on the Making of Paraboloïdal Mirrors. 3. Notes on the Grinding and Polishing of Dioptric Instruments for Lighthouses. 4. Table of the Elements of the Catadioptric Zones for Lights of the first order in the system of Augustin Fresnel. 5. Notice to Mariners of the Exhibition of the Skerryvore Light. 6. Detailed Account of the Expense of the Skerryvore Lighthouse.