"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."