The Portland daily press., 1874-12-18
Re cent Publications.

GEOMETRY AND FAITH. A Fragmentary Supple
ment to the Ninth Bridgewater Treatise. By
Thomas Hill. New York: G. P. Putnam's Sons.
1874. For sale by Loring Short and Harmon.
While graphing with the dense definitions
in the first chapter of this little book the
reader will recognize gratefully that law of
compensation by which density and bulk are
in inverse proportion; no will be glad that,
since the book must be so thick, it could be
made so thin. But, once out of those entan-
clements and fairly embarked upon the course
of the authors thought, he will be likely to
exchange that momentary satisfaction for an
increasing regret that his journey with the
author is to be so brief.
For the views unfolded in these seventy
pages of generous type will engage the inter
est, if not the assent, Of all thoughtful readers.
Under the competent guidance of skilled
mathematician we are led TO the discovery
that even in the relations of forms and num-
bers are contained revelations of God. Men
play with comic sections and evolve certain
laws of form which have no known applica
ton in nature, either in the heavens above, or
on the earth beneath; and. afterwards discover
them to be the laws by which the heavens
WcIC uldu6! LII OtHCL 4AIhu uao ICio a
certain language recorded in the forms and
orbits of the heavenly bodies, and Mind again
independently of that record, writes the same
language upon the students slate! A ''math
ematical demonstration Of kinship between
Designer and learner; or. more than that,
proof that Mind is one. So, then, it is no mele
dream of credulous desire that, in kind. at
least Gods thoughts are as our thoughts, and
His Word is not far from any one of u.s.
To confine these remarks, however, strictly
to the contents of the volume. The first chap
ter treats of Symmetry in Space, and is made
especially interesting By an exposition of the
aw of extreme and mean ratio and of it's en-
bodiment in plants and planets,-in the rela-
tive position of leaves upon the stems of plants
and in the relative periodic times of plants.
In other chapters similar illustrations Of
Woodworking in the determination of the
relations of things are drawn from manifold
observations. ''Space has three dimensions,
time but one. Yet, in some respects, time is
richer in its contents for man than is Space
From Symmetry in Time we have color, heat,
and music, the information given through the
spectroscope by rays of hight from distant stars,
and the harmony of tlnts in landscape
'.Number is an impress of thought it is a
pure creation of spirit; and its constant sug
gestion in the forms and periods of nature, is
clear demonstration that nature is the work of
an Intellect which controls both time and space
in thought. "***"And the increasing knowledge
of the physical world, in our nineteenth cen
fury, brings US increasing proof that God, who
planned heaven and earth, was acquainted
with numbers; made all things in number,
weight and measure, and adopted the smaller
numbers, either out of preference for them, or
in cOndescension to the minds of his children,
whom he has placed here for their preparatory
education" A reason is given for the mystic
charms that cluster around the numbers three,
five, seven and nine.
The Calculus enables the human mind to
carry its native element of time into the do.
main of space. 1t puts into the hands Of the
geometer comprehensive language and gives
Elasticity to infinitely rigid space. Under this
head the author shows the singular mathemat-
isal relation which the elasticties of gases,
rods, and vibrating strings, bear to tie force
of gravity, of which force, however, they are
entirely independent.
In the chapter on Applied Mathematics the
relation of mathematical science to physical
science is considered. Also the gradual proc
ess by which, in the great textbooks Of ma
ture, the education of man, is Conducted. 'The
circle and the ellipsa are among the simplest of
figures, defined by the simplest laws. Accord
ingly, the Creator has strewn examples of the
circular form around US on every.side: and. by
the pictured alphabet of the heavens, called
our attention to the consideration of ellipticaI
orbits. When, in the course of ages, some of
the comparatively easy problems of astronomy
had been successfully solved, problems of more
difficulty were gradually brought into view;
and phenomena which were not obvious, not
pictured alphabet, but the fine print of crea-
ton, led men into the hidden knowledge Of op.
tics, electricity, chemistry, and other forms Of
molecular physics"
Other special topics are,-Motion, Muscular
Action. Geometrical Instincts, Motion Eternal
in Duration Motion Omnipresent in Space, the