is described as a bright fixed light, 21 feet above high water, and visible from an altitude of 10 feet at the distance of 12 nautical or 14 statute miles. The altitude of 10 feet would place the horizon at the distance of 4 statute miles from the observer. The square of the remaining 10 statute miles multiplied by 8 inches will give a fall or curvature downwards from the horizon of 66 feet. Deduct from this 21 feet, the altitude of the light, and we have 45 feet as the amount which the light ought to be _below the horizon_! By the same authority, at page 39, the Bidston Hill Lighthouse, near Liverpool, is 228 feet above high water, one bright fixed light, visible 23 nautical or very nearly 27 statute miles. Deducting 4 miles for the height of the observer, squaring the remaining 23 miles and multiplying that product by 8 inches we have a downward curvature of 352 feet; from this deduct the altitude of the light, 228 feet, and there remains 124 feet as the distance which the light should be _below the horizon_! Again, at page 40:--“The lower light on the ‘Calf of Man’ is 282 feet above high water, and is visible 23 nautical miles.” The usual calculation will show that it ought to be 70 feet _below the horizon_! At page 41 the Cromer light is described as having an altitude of 274 feet above high water, and is visible 23 nautical miles, whereas it ought to be at that distance 78 feet _below the horizon_! At page 9 it is said:--“The coal fire (which was once used) on the Spurn Point Lighthouse, at the mouth of the Humber, which was constructed on a good principle for burning, has been seen 30 miles off.” If the miles here given are nautical measure they would be equal to 35 statute miles. Deducting 4 miles as the usual amount for the distance of the horizon, there will remain 31 miles, which squared and multiplied by 8 inches will give 640 feet as the declination of the water from the horizon to the base of the Lighthouse, the altitude of which is given at page 42 as 93 feet above high water. This amount deducted from the above 640 feet will leave 547 feet as the distance which the Spurn Light ought to have been _below the horizon_! The two High Whitby Lights are 240 feet above high water (see page 42), and are visible 23 nautical miles at sea. The proper calculation will be 102 feet _below the horizon_! At page 43, it is said that the Lower Farne Island Light is visible for 12 nautical or 14 statute miles, and the height above high water is 45 feet. The usual calculation will show that this light ought to be 67 feet _below the horizon_! The Hekkengen Light, on the west coast of Norway (see page 54), is 66 feet above high water, and visible 16 statute miles. It ought to be sunk beneath the horizon 30 feet! The Trondhjem Light (see p. 55), on the Ringholm Rock, west coast of Norway, is 51 feet high, and is visible 16 statute miles; but ought to be 45 feet below the horizon!