"Wanting some object on which to apply my newly-acquired mathematical knowledge, I determined to construct an astronomical telescope. I got Airy's 'Geometrical Optics,' and read it through. Then I searched through all my English Mechanic (a scientific paper that I take), and prepared for my work by reading all the literature on the subject that I could obtain. Ibought two discs of glass, of 6 1/2 inches diameter, and began to grind them to a spherical curve 12 feet radius. I got them hollowed out, but failed in fining them through lack of skill.
This occurred six times in succession; but at the seventh time the polish came up beautifully, with scarcely a scratch upon the surface. Stopping my work one night, and it being starlight, Ithought I would try the mirror on a star. I had a wooden frame ready for the purpose, which the carpenter had made for me.
Judge of my surprise and delight when I found that the star disc enlarged nearly in the same manner from each side of the focal point, thus making it extremely probable that I had accidentally hit on a near approach to the parabola in the curve of my mirror.
And such proved to be the case. I have the mirror still, and its performance is very good indeed.
"I went no further with this mirror, for fear or spoiling it. It is very slightly grey in the centre, but not sufficiently so as to materially injure its performance. I mounted it in a wooden tube, placed it on a wooden stand, and used it for a time thus mounted; but getting disgusted with the tremor and inconvenience I had to put up with, I resolved to construct for it an iron equatorial stand. I made my patterns, got them cast, turned and fitted them myself, grinding all the working parts together with emery and oil, and fitted a tangent-screw motion to drive the instrument in right ascension. Now I found the instrument a pleasure to use; and I determined to add to it divided circles, and to accurately adjust it to the meridian. I made my circles of well-seasoned mahogany, with slips of paper on their edges, dividing them with my drawing instruments, and varnishing them to keep out the wet. I shall never forget that sunny afternoon upon which I computed the hour-angle for Jupiter, and set the instrument so that by calculation Jupiter should pass through the field of the instrument at 1h. 25m. 15s. With my watch in my hand, and my eye to the eye-piece, I waited for the orb. When his glorious face appeared, almost in a direct line for the centre of the field, I could not contain my joy, but shouted out as loudly as I could,--greatly to the astonishment of old George Johnson, the miller, who happened to be in the field where I had planted my stand!
"Now, though I had obtained what I wanted--a fairly good instrument,--still I was not quite satisfied; as I had produced it by a fortunate chance, and not by skill alone. I therefore set to work again on the other disc of glass, to try if I could finish it in such a way as to excel the first one. After nearly a year's work I found that I could only succeed in equalling it.
But then, during this time, I had removed the working of mirrors from mere chance to a fair amount of certainty. By bringing my mathematical knowledge to bear on the subject, I had devised a method of testing and measuring my work which, I am happy to say, has been fairly successful, and has enabled me to produce the spherical, elliptic, parabolic, or hyperbolic curve in my mirrors, with almost unvarying success. The study of the practical working of specula and lenses has also absorbed a good deal of my spare time during the last two years, and the work involved has been scarcely less difficult. Altogether, Iconsider this last year (1882-3) to mark the busiest period of my life.
"It will be observed that I have only given an account of those branches of study in which I have put to practical test the deductions from theoretical reasoning. I am at present engaged on the theory of the achromatic object-glass, with regard to spherical chromatism--a subject upon which, I believe, nearly all our text-books are silent, but one nevertheless of vital importance to the optician. I can only proceed very slowly with it, on account of having to grind and figure lenses for every step of the theory, to keep myself in the right track; as mere theorizing is apt to lead one very much astray, unless it be checked by constant experiment. For this particular subject, lenses must be ground firstly to spherical, and then to curves of conic sections, so as to eliminate spherical aberration from each lens; so that it will be observed that this subject is not without its difficulties.
"About a month ago (September, 1883), I determined to put to the test the statement of some of our theorists, that the surface of a rotating fluid is either a parabola or a hyperbola. I found by experiment that it is neither, but an approximation to the tractrix (a modification of the catenary), if anything definite;as indeed one, on thinking over the matter, might feel certain it would be--the tractrix being the curve of least friction.
