Faraday to Peter Henry Berthon   24 October 1857

Royal Institution | 24 October 1857.

Sir

I am very sorry to trouble the Deputy master¹ & brethren with a further report but having been to the Wharf and carefully examined the situation of the apparatus employed on the 13th & 20th instant I find that my former reports² would convey an erroneous sense without some explanation. Captn. Poulter pointed out to me the position of Hornchurch which he saw at the time in the telescope & knew of his own knowledge. I found that the line from the lamp to it was not that which had been marked down by those who fitted up the apparatus but was more to the north forming an angle with it of 7½ degrees. Hence even if the lights had not been dimmed by mist they could hardly have been seen when employed as fixed lights since the axis of the ray would have been 7½ degrees to the south. This would have taken the great lens light altogether out of sight for its whole divergence is only between 6 & 7 degrees, & it would have taken the 7 lens light nearly out of sight since its whole divergence is 15°, the divergence between the axis or center & the edge of the beam being therefore only 7½ degrees. Happily the revolutions brought all the lights into view at Hornchurch in succession & so we could observe & compare them.

But an error still remained which was serious & really interfered in the comparison of the lenses & reflectors. The reflectors were as I believe properly arranged so that the axis of their rays was horizontal. The place of observation was lifted above the horizontal axes I can hardly say how much but it was assumed in my former report³ for Brentwood as 9’ and equal for all. The lenses ought to have been arranged so that their centers would be ¾ of an inch above the burner that the axis of the whole beams might be horizontal; in place of which I find them on a level with the burner, & as that is only 36 5/16 inches distant the consequence is that the axis of the ray descends forming an angle with the horizontal line of 1° 14’. This is serious with a beam whose divergence is 6 or 7 degrees only especially if to this 1°. 14’ of depression be added the 9’ due to elevations of the observer for at places have 1° 23’ out of the axis of a beam in which there is only 3½°. between the axis & the edge. It is evident therefore that the comparison of the great lens with the 7 reflectors especially as to intensity has not been just to the former & also that the narrower lenses have not been properly compared with the Buchaness three reflectors.

The window frames are only ¾ of an inch thick & would not interfere much. Nothing else but some low railing, affecting the bottom zones, was in the way⁴.

I am | Sir | Your Very Obedient Humble Servant | M. Faraday