New-York daily tribune. [volume] (New-York [N.Y.]) 1842-1866, 1851-07-26
NEW PUBLICATIONS.

from the French Of UGUsTB CoHrE oy !" ~ N III
IyspfH Professor 10 Union College sVo PIP N"' MAI
ger < Brothers.
II speaks well for the devotion to science
in this country tina, the present admirable anaiy-
ais of the primary principles of mathematics
.bould be issued from the American press under
such worthy auspices. Prot. Gillespie has thus
rendered service TO the cause OF inteiiec'uai
culture, which we are bound to acknowledge
with grateful emphasis. The work, although
not intended nor adapted for popular reading
addressing the highest faculty OF abstraction
which the intellect can exerclse,-assuming a
conversancy with the most recondite details OF
mathematical calculation,-and clothed IN the
austere language of logical deductlon,-cannot
fail TO win the attention of thinking men, and to
he classed among the few standard treatises OF
science which are read for the pure gratihcatioh
which they afford to the reflective powers. Inc
mere practical student, who seeks IN mathemat-
ical science nothing but the utility oil It's various
and significant applications looks Tor I'M
mediate results which shall tell on sbip-buildlng,
ON the arrangement of machinery, on the con-
struction OF canals and rallroads,-who Is wholly
absorbed in the concrete elements, which are so
much the order Of the day In modern times, and
especially with the eager, restless, proJectlle
American.-wiIl no doubt find this tough bone
TO pick OF hot afternoon, and will be apt to
wish that Prof Gillespie had confined himself
10 his legitimate function Of throwing light on
the duties OF the engineer and roadmaker ln-
stead of perplexing the brain OF his readers
with the subtle hair-splittng of the French
transcendentalist.
The work is designed for persons Of different
order OF intellect. II aims to solve similar
problem in regard to mathematics, with that pro-
posed in Humboldt's Cosmos in relation to the
material universe, that is, the detection of the
principle of unity amid the variety OF phenomena.
Accepting the established processes OF mathe-
mates as fact, COmte endeavors to trace them
to the ultimate principle of thought IN which
they had their origin, and thus enters difficult
but highly attractive sphere OF the transcenden-
tai philosophy. With what success he has &C
compllshed his task, must be decided by the
reader after a studious pemsal of his analyses.
For ourselves, believing that all such attempts,
in the present state of knowledge, can only be
approximative we still recognise the compre-
hcnsivc wisdom, the mastery power of general
ization and the exquisite critical keenness with
which Comte has performed the task of contrib
utlng toward an ultimate solution of the problem
In the commencement OF the volume the author
engages in very curious investigation, IN order
10 determine the true object OF mathematical SCI
ence. This is one OF the most characteristic
portions of the work, and gives favorable spe-
cimen of Comte's method.
l-c. e t,nc ia pn
by naming it "the science OF magnitudes.' This
is entirely loose, affordmg no additional idea.
and containing no exact description OF the Oh
lect to be explained. We gain step by calling
i, "the science which has for its purpose the
measurement of magnitudes." But this does not
90 to the bottom of the matter We suppose IN
every process of measurement, comparison OF
the magnitude in question, with another similar
magnitude which is supposed to be known and
which is adopted as the unit OF reference.
Hence, this definition reduces mathematics to a
simple mechanical method, which gives the
ratio of the quantities to be measured to those by
which we wish to measure them. The error IN
the case consists in supposing that the measure
ment of magnitude is always direct, whereas, IN
the great majority OF cases, 1t is not only not d.
rect, but impossible. If there were no other
means than direct comparison for determining
magni,udes, we could make no progress IN this
department of knowledge
Ii is obvious that the simplest case which we
can imaeine--the measurement of one strait line
by another-is encountered with great difficult
ties The conditions necessary to measure a
line can seldom be realized at the same time
Even the most probable of all these conditions
that of being able to pass over the whole line
from end TO end in order 10 apply the unit OF
ACKNOWLEDGEMENTS be fulfilled IN the most
important distances For example, all the dis
tancos from one celestial body to another, or from
any one of them to the earth, are inaccessible IN
this way. Even the greater number oiterrestrlal
distances are In the same predlcament. o.
course, they are excluded by the definition. Still
further a direct measurement requires that the
length be neither too great nor too small, and
also that it be suitably sitaated-for a horizontal
line which could be easily measured in its natu-
raj position, if turned into vertical position,
would become inaccessible. These difficulties
are greatly increased in the measurement OF sur
faces, velocities, times, forces, and the like
which are less susceptible of direct measurement
than is frequently the case with lines. We art
accordingly thrown back on new definition o.
mathematics. its precise object Is clearly to
ascertain magnitudes which do not admit OF q
direct measurement, by connecting them with
others which we can determine Immediately, and
then discovering the frs, through the relation.
which subsist between the two.
This definition is presented IN still more com
prehensive aspect, when we consider that the
indirect determination OF magnitudes may be In
direct in very different degrees, In great many
cases, the magnitudes OF comparison, by means
of which we determine the principal magnitudes
cannot be measured directly themselves. They