Faraday to Frederick Madan   9 November 1852

R Institution | 9 Novr. 1852

My dear Sir

My letter¹ with its reservations does mean what the Deputy Master² understands “- that one lamp & its reflector would probably be equal to one Second Order lens.” Your note³ seems to me to imply that you think one first order lens sends forwards as much light as ten lamps & reflectors. In reference to this point you no doubt remember the experiments made at Purfleet and Blackwall I think in September 1840⁴, when both the French & English first class refractors were compared with a single lamp in its reflector, and the latter was found to surpass both. Now the refractors though they had concentrated the rays from above & below had not done so for the horizontal line and therefore to get an idea of what might be the increase of effect in that respect we may assume that as each of the eight refractors receives 45˚ horizontally of the light issuing from the lamp; & that as this light in the lens form is reduced from a divergence of 45˚ to that of 15˚, so such a lens would be equal to three such lamps & reflectors. But the lamp then used and was one of four wicks burning above 7 1/2 pints of oil (7.625) in 8 hours[.] Whereas the 2nd order or three wicked lamp as Mr. Wilkins now tells me burns only 4 pints per 8 hours⁵. Therefore one of the eight lenses of the 2nd order might be expected to equal about 1 1/2 such lamps & reflectors - and one of twelve lenses only 1 such lamp i.e a lamp & reflector not so good as compared with the refractors at Purfleet[.]

I think the lenses generally, especially the excellent ones of France, compress the chief part of the beam into a less divergence than 15˚ at certain distance: & then of course the effect on the axis of the beam is brighter but that means the edge of the 15˚ dimmer than the mean: But I have not seen a second class lens and therefore my reply⁶ to Mr Herberts letter⁷ is worded with much diffidence & reservation. Still you will perceive that the above mode of viewing the question founded on experiment & observation does not lead to a result much different from the former, and in the absence of a more direct comparison, I dare not venture to go farther[.]

Yours Very Truly | M Faraday

Captn Madan | &c &c &c