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.