"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, I had 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. I bought 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, I thought 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, I consider 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.
"In astronomy, I have really done very little beyond mere algebraical working of the fundamental theorems, and a little casual observation of the telescope. So far, I must own, I have taken more pleasure in the theory and construction of the telescope, than in its use."
Such is Samuel Lancaster's history of the growth and development of his mind. I do not think there is anything more interesting in the 'Pursuit of Knowledge under Difficulties.' His life has been a gallant endeavour to win further knowledge, though too much at the expense of a constitution originally delicate. He pursues science with patience and determination, and wooes truth with the ardour of a lover. Eulogy of his character would here be unnecessary; but, if he takes due care of his health, we shall hear more of him.[11]
More astronomers in humble life! There seems to to be no end of them. There must be a great fascination in looking up to the heavens, and seeing those wondrous worlds careering in the far-off infinite. Let me look back to the names I have introduced in this chapter of autobiography. First, there was my worthy porter friend at Coupar Angus station, enjoying himself with his three-inch object-glass. Then there was the shoemaker and teacher, and eventually the first-rate maker of achromatic instruments. Look also at the persons whom he supplied with his best telescopes. Among them we find princes, baronets, clergymen, professors, doctors, solicitors, manufacturers, and inventors. Then we come to the portrait painter, who acquired the highest supremacy in the art of telescope making; then to Mr. Lassell, the retired brewer, whose daughters presented his instrument to the nation; and, lastly, to the extraordinary young schoolmaster of Bainbridge, in Yorkshire. And now before I conclude this last chapter, I have to relate perhaps the most extraordinary story of all—that of another astronomer in humble life, in the person of a slate counter at Port Penrhyn, Bangor, North Wales.