Dear Sir,
Dr Adamson <1> is much pleased that you think so well of his pictures, and is going on with double energy. I enclose you Five which are tolerably good.
I have tried to see the Direct Positive Calotype which you have sent to Mr Furlong, <2> and have always missed him. I deliver my Annual Lecture on the subject on Saturday first; <3> and if you have one by you I should like to be able to shew it.
When do you Leave England? I may possibly trouble you with a letter. If you see Mr Merz <4> at Munich I will thank you to say to him that his Large Prism <5> is all that I could wish. It is oxidated, however, on the surface. Perhaps he could advise me how to remove it with safety to the Prism.
I have just solved the Problem of the Form of the Image of the Sun at any distance from a Quadrilateral Aperture.
It consists, (that is the Figure of the illuminated Space) of 4 straight lines which are portions of a quadrilateral image similar to the aperture, and eight portions of a Spiral whose Equation is curious. The straight lines are ab, cd, ef, gh [illustration] and the Spirals am, gm, cn, kn, bp, cp, do, fo. This is the true geometrical form of the luminous space, & it never becomes a circle, for when the distance is infinite ao, cd, &c? are infinite.
Calling aba¡äb¡ä (equal to the projection of the aperture by a luminous pt of the [circled dot operator U2299] 's disc) the generating square, MNOP whose radius NC is the Tang. of the [circled dot operator U2299] 's true diameter, the generating circle, then if the semidiagonal aN is always as it is parallel to the axis mo of the spiral the radius of the Spiral is equal to aC the third side of a triangle whose angles sides are the constant quantities aN, NC and angle NaC=aCm the angular distance of a from the axis.
The Red Curve is the spiral drawn by the corner a of the generating square. Every other Corner describes a spiral, the portions RS of each form the outline of the Figure of Equal Illumination while the portions am, bn &c form the figure curvilineal part of the Figure of general illumination. And what is very interesting the illumination or the intensity of the Sun's light at any one part of the whole illuminated Space is equal to the area of the generating Square included within the generating Circle MNOP. The investigation is exceedingly simple, & the results curious & unexpected. I am ashamed to send you such a hurried notice of it, but the Post is about to depart.
Believe me to be Ever Most Faithfy yrs
D Brewster
St Leonards St Andrews
March 29th 1842
Notes:
1. Dr John Adamson (1809-1870), physician and pioneer of photography. See A. D. Morrison-Low, "Dr John Adamson and Robert Adamson: An Early Partnership in Scottish Photography¡" The Photographic Collector, v. 2, 1983, pp. 198-214.
2. See Doc. No: 04440 from William Holland Furlonge, sometimes William Holland Furlong (1826-1881), Irish born chemist, photographer and Assyriologist.
3. But 1 April was a Friday in 1842.
4. Georg Merz (d. 1867).
5. See Doc. No: 04339.