Faraday to Jacob Herbert   21 November 1849

Royal Institution | 21 November 1849

My dear Sir,

My call yesterday was only to say that as Mr Wilkins was about to send to the Needles¹ to day or tomorrow & would be a fortnight engaged in the business I prepared to leave town on the 3rd or 4th of Decr. & might be at the Portland Lighthouses on the 5th or 6th². You wished me to let you know & said you said you would either give me a note or write to the Principal keeper.

Meeting Captain Madan yesterday I endeavoured to refer him to some observations which I thought I had made in reply to a letter of yours of the 9th Decr. 1847³ requesting me to examine Mr A. Gordons Catadioptic arrangement at the Trinity House on the Tuesday following. The observations were to the following purport. Mr Gordons object is, to use an Argand lamp of the same size & power as that in use by the Trinity house but by means of a different reflector & a ring lens, to send far more light forwards towards the sea horizon than is so sent by the Trinity reflector. The Trinity reflector gathers & disposes of the light of 235˚ (measured on a great circle passing through the lamp flame & the axis of the reflector) & allows 125˚ to pass unused. Mr. Gordons reflector & lens together gather up & dispose of 320˚ & allow only 40˚ to escape[.] This I conclude is the chief foundation of the hope which is entertained by the inventor that it will practically surpass the Trinity reflector but there is at the same time another ground of expectation built upon the fact that in Mr Gordons reflector most of the impinging rays are reflected at a much smaller angle with the reflecting surface than in the Trinity house reflector & will therefore (according to a supposed law of reflexion which holds good indeed with such bodies as glass water marble &c) be more abundantly reflected.

With respect to this second point of a more abundant reflexion as the incident ray forms a smaller angle with the reflecting surface Newton⁴ believed that to be the case with metals as it is with ordinary bodies and most writers on optical science including Herschell⁵ & others have since his time repeated⁶ the statement probably on his authority but Mr Potter⁷ a few years ago showed that it was not true for metals for that they reflected at least as much if not more light when the ray was incident perpendicularly upon their surface as when incident at very small angles. Upon the occasion of your letter to which I have already referred I had two silvered reflecting surfaces prepared & observed & confirmed the quantity of light reflected at the same time at very high & very small angles⁸ & could find no difference: in that respect therefore I am satisfied that any point of a Trinity House reflector acts upon the light as perfectly as any point of Mr. Gordons reflector.

With respect to the first point:- Mr. Gordons arrangement takes up a far greater number of rays of the sphere of light from the lamp than the

Trinity reflector calling the whole quantity of light is 100 the Trinity reflector leaves about a fourth or rather more untouched whilst Mr. Gordons only allows about a thirty second part to escape and there can be no doubt that if all the rest were sent forward in the required beam of 15˚ of divergence the effect ought to surpass that of the simple Trinity arrangement[.] It is the province of trial & experiment only to decide whether these are so sent forward, but even theoretically it does not follow from the construction that they should go in the desired or expected direction & for the following reasons. The centre of the Argand lamp flame is in the Trinity arrangement 3 1/2 inches distant from the nearest point of the reflector that being the focal distance. Now the divergence of the whole beam of light depends upon this distance & the size of the flame & they are such as to give the required 15˚ of divergence or thereabouts. In Mr Gordons arrangement the flame has the same size but is only 1 1/2 inches distant from the reflector which gives a divergence so great that if the reflector alone were used the light would be spread over a space of 5 or 6 times as large as that covered by the Trinity reflector & would be proportionately feeble. It only requires the removal of the ring lens from Mr. Gordons arrangement (which I had done in my trial examination), and then the inferiority of Mr Gordon’s reflector to the Trinity House reflector from this cause is even in a room at once manifest though it receives from the lamp a much greater number of rays. It is true that the ring lens gathers up much of this outstanding light, but it cannot correct the large dispersion and also in its action of bringing these rays nearer to parrallism [sic] with the axial ray it cannot be correct at one & the same time for the light from the reflector & for the light which it receives directly from the lamp. Trial & observation therefore only can decide how far this gathering up has been done and an observation near at hand cannot shew by its effect what would be the result at a distance. A very powerful light might be produced at 100 or any other number of feet or yards by the collecting & crossing of the rays at that spot and yet at a point further out as 2, 3, or 4 miles a comparatively poor effect be obtained. Trial only & at different distances can give a true comparison with the simpler & so far more correct apparatus of the Trinity house⁹[.]

I am | My dear Sir | Ever truly Your | M. Faraday

Jacob Herbert Esq | &c &c &c