The Portland daily press., 1876-11-14
WI. G. MI. A. COURSE.
Lecture by Rev. DIR. Hill.

The course of free lectures given under the
auspices of the Maine Charitable Mechanic AS
ISOLATION, was opened last evening by Rev. DIR.
Hill, who delivered an admirable lecture upon
Geometry and Politics." Owing to the small
size of the Llbraryroom, which has formerly been
used, it was found necessary to move into the
hall of the Association. The change was time
ly, for last evening the hall was packed and
some were turned away for want OF standing
room. The lecture contained much more OF
Geometry than of Politics. Indeed, he inti-
mated that at time when all his hearers were
wearied with the strain of political excitement,
he should attempt to rest and refresh them by
turning their thoughts to something which
should give an entire change.
He began by leading his hearers to the def
milton of curved line, line that constantly
but steadily bends from its course, as the path
of a yacht before the breeze, while she sweeps
steadily round to new course. Such line
has no straight places in it, no places at which
it is not bending; yet there is nc point at which
it bends, for if there were there would be an an
gle there a corner; no matter how slight bend
ing; still blunt corner. Thus our idea of
line bends, and does not bend at each point
The geometer affirmed that all four PROPOSE
tions are true, it does and does not bend, either
both or neither, just as you please: and from
either proposition you might draw conclusions
that were false, or conclusions which would
stand every test of reason and experiment.
Hence the politician and theologian might
learn that both of apparently contradictory
propositions might be true. Both church and
state, on both sides the Atlantic, were troubl-
ed by obstinate conservatives, aud by fanaticaI
radicals, who argued from one or two premises,
and denied all conclusions drawn from other
equally valid although apparently contradicto-
ry premises. Would that they could learn
from geometry that logic must be distrusted
and its conclusions revised, whenever those
conclusions affronted common sense and gen.
eral experience.
The lecturer then passed to the distinction
between curves and mere curved lines. curv-
ed line could be made of pieces of curves, join
ed smoothly together; but true curve could
not be made in that way any more than an ami
NAL can be made Of the dissected parts of other
animals. true curve is the path of point
which is moving always under one and the same
law, or intellectual condition of position; so
for example point keeping the sum of its dis
tances from two centres constant, moves in an
e!ilpse. Every curve can generate innumera-
Bile lnvolutes; each point of strug kept taut
and wrapped and unwrapped from the curve gen.
crates an involute. Each curve has an evolute
OF which the curve is an involute. Now If you
give to geOmeter the exact shape of never SO
small a fragment of curve, he will not only
reproduce the whole curve, even of infinite
length, but its evolute and evolutes of evoutes,
and its involutes of involutes, od intinit,no.
Here was the prophecy and pledge of Ovens |
reconstruction of the Moa, and of Agassz's re-
construction of the fish. 1t was the prophecy |
and pledge of craftsmanship, a political and |
social economy, that should not guess at hap |
hazard, but foretell with accuracy the effects of |
policy and the issue of events.
The true law of curve might be grasped by |
the artist and by the artisan, as really as by |
the mathematician; and although they might |
fail to express the curve in the artificial Ian
guage OF the calculus, they could easily show |
their grasp of its law by simply drawing dia- |
gram OF it. Now the external world was full |
of diagrams of curves. AL sorts of mathe- |
NAUTICAL laws were illustrated in tine forms and |
movements OF the universe. How could the |
theoogian avoid seeing, in this fact, natural |
confirmation of the Scrptural doctrine that |
man was made in the image of God; and that
in our pr5ori, geometical curves we are only |
expressing ideas which were clear to Him from
before eternity. After abiding to several in |
stances OF the discovery in nature of what had |
been invented by pure geometrical fancy, the
lecturer passed to the curve made by one point |
of an imaginary pair of shears, in which the |
other blade was held stationary, and the blade |
whose point made the curve grew longer in ex-
act proportion to the closing OF the shears. This
curve constantly recedes, although at dimin-
ishing rate, from the line of the stationary
blade, and approaches line called the asymp- |
totes, parallel to that blade. 1t illustrated the
approach of finite being toward perfection;
and DR.. Hill expressed his hope that the United
States would ever approach the asymptote of |
perfect state.