9 Park Square
Wednesday night
My dear Sir
I am at a loss to understand how your demonstration could have depended on supposing the effect of light on the retina proportional to the simple velocity: and not to the square: since all the combinations of the medium, and almost all the calculable parts of the problem depend on the additions and subtractions of the simple velocities and not of their squares –
But in truth I should almost suspect the effect on the retina to be as some much higher power than the square rather than a lower power: there are so many cases of apparently abrupt termination of lights and shadows where the tints are in reality very gradually shaded off that I think it is quite impossible to suppose the effect to be as the simple velocity only –
The intensities to be combined seem to follow something like this order cos x + cos 2x + cos 3x + cos 4x + … cos nx, n being the number of pairs of lines in the grating: and I suppose that this gives a strong line of light in the middle where x = 0, declining very rapidly on each side probably also each successive term is weakened a little by the obliquity of the diffraction
Must not the irregularity of the images depend on the want of uniformity in the form of the striae of the grating? But I rather think my formula will give you a sufficient variety of cycles when x is not an aliquot <1> part of a circle
There n may be about 100, and the sum of the series will continue to increase by the addition of its terms till 100x becomes 180° 90°, and the cosines become negative: though they continue to decrease from the first by slow degrees: but when 100x is 180° the whole sum must vary by the effect of the negative cosine, and it will never acquire any value at all comparable to the initial 100 again: so that the practical effect will be that of a narrow line of the breadth of 1.8° terminating abruptly
This is only a first impression – but I think it will succeed on further examination –
Yours very truly
Thomas Young
H. Fox Talbot Esq
31 Sackville Street
Notes:
1. Aliquot: a mathematical term for an exact divisor, especially of an integer.