Faraday to Frederick Madan   c24 August 1842¹

My dear Sir

I have always thought that in the case of high lighthouses as the Needles &c the middle ray should not be sent strictly horizontally as respects the place where the lighthouse stands but be depressed so as to touch tangentially the sea horizon. In the case of the Lundy light there is no doubt but that under the first arrangement far more light would go over the sea than would fall on to it and as the intensity of light diminishes from the middle ray upwards & downwards those vessels which may be comparatively near the lighthouse would not receive their due quantity & those within about 3/4 of a mile would have no light at all at the sea's surface except that due to the inaccuracy of workmanship. I should have thought that in misty or foggy weather the latter circumstances might be important[.]

The calculated divergence of the beam is about 5˚ according to the size of the flame but inaccuracy of workmanship in grinding the glasses makes it often more. You say that the depression or dip of the Sea Horizon is for a lighthouse of 550 feet in height about a degree by the tables. Whether this takes in any effect of refraction or other circumstances I do not know; by mere calculation I think it is about 30' (is 24'.8) or half a degree. I should like to see the tables some day when I am at the Trinity House[.]

If the apparatus be adjusted to throw its medium or principal beam on to the sea horizon it should be done by observation. It would be very easy by raising the lamp a certain quantity to throw the beam that passes through the lenses downwards by the quantity required but the same alteration of the light would throw the beam reflected by the mirrors upwards or in the contrary direction[.] The mirrors therefore ought in such a case to be adjusted after the lenses and according to instructions which would be very simple[.]

I am My dear Sir | Your faithful Servant | M. Faraday

Capt F. Madan | &c &c &c