Faraday to Jacob Herbert   26 October 1852¹

Royal Institution | 26 Octr 1852.

My dear Sir

In reference to the matter of the Caskets lights² I wrote some time since to M. Lepaute³ for any experimental results he could supply me with as to the relative power of the beams of light sent forth by lenses of the 2nd order. He was so kind as to answer my letter, and stated that 2nd order lights, revolving in one minute, had 8 lenses, and those revolving in 30 seconds had 12 lenses; both kinds having the same radius of 70 centimeters:- but he did not give me their area or their power; both of which I had asked for. I wrote to him again for the latter data on the 27th Septr. but have received no answer. Probably he is not in possession of experimental comparisons of the beams from the two different sized lenses. I enclose his letter that you may see exactly what he says.

I therefore venture some considerations which are necessarily imperfect, since I have not had the opportunity of examining a 2nd order light with either 8 or 12 lenses: you will easily see how far they offer safe suggestions to the mind. The quantity of light evolved by combustion will be, with equal care, nearly as the oil consumed; as former experiments have shewn. I have tried to ascertain the quantity of oil burnt in a second order lamp, but Mr Wilkins has not been able to supply me with the result[.] I therefore take the proportion of cotton in the burners as my guide; and I find that the cotton in a 2nd order lamp is six times that in a reflector lamp, whilst the cotton in a 1st order lamp is ten times that of the reflector lamp. I think I have never seen the light of the first order lamp exceed that of fourteen argand lamps: and though the 2nd order lamp may not give so intense a light in proportion, as the 1st order, yet, taking that proportion, then its light will be eight times (or a little more) that of the Argand.

Of the light thus generated, probably 3/4 falls on the surrounding lenses; but as I have not the area or measurement of the lenses I cannot be sure; the rest go off above & below:- indeed less than this must be intercepted by the lenses, because much that would proceed to the lower part of the lenses, is intercepted by the burner. About the same proportion of light is also received by the reflectors. The quantity of light extinguished respectively by the lenses and the reflectors, I do not know: it was in reference to that point that I wished to know the experimental results as to the power of the beams, but judging (from the comparison at Purfleet of a good reflector & a first order lens) that the loss was about equal: then it would seem probable that eight lamps and their reflectors, would give beams of equal power to a 2nd class light with eight lenses; or might probably surpass it. I have no doubt they would much surpass the same 2nd class light with twelve lenses. It is needless for me to say that sixteen lamps & reflectors would (in my opinion) far surpass any arrangement of the 2nd class lights⁴.

I am My dear Sir | Most truly Yours

Jacob Herbert Esq | &c &c &c