TO LEWIS
CAMPBELL, Esq.
Glenlair, 22d Sept. 1848.
When I
waken I do so
either at 5.45 or 9.15,
but I now prefer
the early hour, as I take the most of my violentexercise at that time,
and thus am saddened down, so that I can do as much still work
afterwards
as is requisite, whereas if I was to sit still in the morning I would
be
yawning all day. So I get up and see what kind of day it is, and
what field works are to be done; then I catch the pony and bring up the
water barrel. This barrel used to be pulled by the men, but
Pa caused the road to be gravelled, and so it became horse work to the
men, so I proposed the pony; but all the men except the
pullers
opposed the plan. So I and the children not working, brought it
up,
and silenced vile insinuators. Then I take the dogs out, and then look
round the garden for fruit and seeds, and paddle about till
breakfast time; after that take up Cicero and see if I can understand
him.
If so, I read till I stick; if not, I set to Xen. or
Herodt.
Then I do props, chiefly on rolling curves, on which subject I have got
a great problem divided into Orders, Genera, Species, Varieties,
etc.
One curve rolls on another, and with a
particular
point traces out a
third curve on the plane of the first, then the problem is:
Order I. Given any two of these curves, to find the third.
Order II. Given the equation of one
and the identity
of the other two,
find their equation.
Order
III. Given all
three curves the same, find them.
In this last
Order I have proved that the equi-angular spiral possesses the
property,
and that no other curve does. This is the most reproductive curve of
any.
I think John Bernoulli had it on his tombstone, with the motto
Eadem
mutata resurgo. There are a great many curious properties of curves
connected
with rolling. Thus, for example,—
If the
curve A when
rolled on a straight line produces
a curve C, and
if the curve A when rolled up on itself produces the curve
B. then the curve B when rolled upon the curve C will produce a
straight
line.
Thus, let the
involute of the
circle be represented
by A,
the
spiral of
Archimedes by B,
and the
parabola by
C, then
the proposition is true.
Thus the parabola rolled on a
straight line
traces a Catenary
with its focus, an easy way to describe the Catenary.
Professor Wallace just missed it in a paper in the Royal Society.
After props come optics, and principally polarised light.
Do you remember our visit to Mr. Nicol? I have got plenty of unannealed
glass of different shapes, for I find window glass will do very
well
made up in bundles. I cut out triangles, squares, etc., with a diamond,
about 8 or 9 of a kind, and take them to the kitchen, and put
them
on a piece of iron in the fire one by one. When the bit is red
hot,
I drop it into a plate of iron sparks to cool, and so on till all are
done.
I have got all figures up to nonagons, triangles of all
kinds,
and irregular chips. I have made a pattern for a tesselated window of
unannealed
glass in the proper colours, also a delineation
of triangles at every principal inclination. We were at Castle-Douglas
yesterday, and got crystals of salt Peter,
which
I have been cutting up into plates to-day, in hopes to see rings. There
are very few crystals which are not hollow-hearted or
filled
up with irregular crystals. I have got a few cross cuts
like
free of irregularities and long [wedge-shaped] cuts for polarising
plates.
One has to be very cautious in sawing, and polishing them, for
they
are very brittle.
I have
got a lucifer
match box fitted up for
polarising, thus.
The rays suffer two reflections at the polarising angle
from
glasses A and B. Without the lid it does for an analysing plate. In the
lid there is set a plate of mica, and so one observes the blue
sky,
and turns the box round till a particular colour appears, and then a
line
on the lid of the box points to the sun wherever he is.
Thus
one can find out the time of day without the sun. [Here
follow
thirteen diagrams of patterns in triangles, squares, pentagons, and
hexagons.]
These are a few of the figures one sees in unannealed glass.
Pray
write soon and
tell when, how, and where
by, you intend to
come, that you may neither on the other hand fall upon us at
unawares,
nor on the one hand break and not come at all. I suppose when you come
I will have to give up all my things of my own devising, and take
Poisson, for the time is short, and I am very nearly unprepared
in
actual reading, though a great deal more able to read it.
I hope
not to write any
more letters till you come. I
seal with an electrotype
of the young of the ephemera. So, sir, I was, etc.
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