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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； 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 wanteda 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 chromatisma subject upon which； I believe； nearly all
our text…books are silent； but one nevertheless of vital
importance to the optician。 I can only p