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 anyt