"I then went on with Algebra and Euclid, and took up plane trigonometry; but I devoted most of my time to electricity and magnetism. I constructed various scientific apparatus--a syren, telephones, microphones, an Edison's megaphone, as well as an electrometer, and a machine for covering electric wire with cotton or silk. A friend having lent me a work on artificial memory, I began to study it; but the work led me into nothing but confusion, and I soon found that if I did not give it up, Ishould be left with no memory at all. I still went an sketching from Nature, not so much as a study, but as a means of recruiting my health, which was far from being good. At the beginning of 1881 I obtained my present situation as assistant master at the Yorebridge Grammar School, of which the Rev. W. Balderston, M.A., is principal.
"Soon after I became settled here, I spent some of my leisure time in reading Emerson's 'Optics,' a work I bought at an old bookstall. I was not very successful with it, owing to my deficient mathematical knowledge. On the May Science Examinations of 1881 taking place at Newcastle-on-Tyne, applied for permission to sit, and obtained four tickets for the following subjects:-- Mathematics, Electricity and Magnetism, Acoustics, Light and Heat, and Physiography. During the preceding month I had read up the first three subjects, but, being pressed for time, I gave up the idea of taking physiography. However, on the last night of the examinations, Ihad some conversation with one of the students as to the subjects required for physiography. He said, 'You want a little knowledge of everything in a scientific way, and nothing much of anything.'
I determined to try, for 'nothing much of anything' suited me exactly. I rose early next morning, and as soon as the shops were open I went and bought a book on the subject, 'Outlines of Physiography,' by W. Lawson, F.R.G.S. I read it all day, and at night sat for the examination. The results of my examinations were, failure in mathematics, but second class advanced grade certificates in all the others. I do not attach any credit to passing in physiography, but merely relate the circumstance as curiously showing what can be done by a good 'cram.'
"The failure in mathematics caused me to take the subject 'by the horns,' to see what I could do with it. I began by going over quadratic equations, and I gradually solved the whole of those given in Todhunter's larger 'Algebra.' Then I re-read the progressions, permutations, combinations; the binomial theorem, with indices and surds; the logarithmic theorem and series, converging and diverging. I got Todhunter's larger 'Plane Trigonometry,' and read it, with the theorems contained in it;then his 'Spherical Trigonometry;' his 'Analytical Geometry, of Two Dimensions,' and 'Conics.' I next obtained De Morgan's 'Differential and Integral Calculus,' then Woolhouse's, and lastly, Todhunter's. I found this department of mathematics difficult and perplexing to the last degree; but I mastered it sufficiently to turn it to some account. This last mathematical course represents eighteen months of hard work, and I often sat up the whole night through. One result of the application was a permanent injury to my sight.
"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!
