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It is with the greatest pleasure that we acknowledge
the receipt from that gifted author, of the
“Analysis of Rotary Motion, as applied to the
Gyroscope,” by Major J. G. Barnard, A. M.,
Corps of Engineers, U. S. Army. The “Gyroscope”
has always been with us a favorite instrument.
Of beautifully simple construction, easily
managed, and exceedingly gratifying in its results,
we know of no machine equally adapted to household
use, or more eminently fitted for the amusement
or instruction of a small family. It has remained
for Professor Barnard, in the interesting
treatise alluded to above, to explain, in a simple
style, easily comprehended by the merest child, the
operation of this instrument, and to show by a

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clear and beautiful analysis the principle upon
which its results depend. There are certain
points in “the Analysis,” however, on which, with
all due humility, we must venture to differ with
Professor Barnard; for instance, on page 545 we
have the following: “Knowing this fact, we may
assume that the impressed velocity n is very great,
and hence cos θ — cos a exceedingly minute, and
on this supposition obtain integral of equations 6
and 7, which will express with all requisite accuracy
the true gyroscopic motion.” We doubt
very much the propriety of making these assumptions;
the Mathematics is properly an exact
science, and we are by no means prepared to admit
the exceeding minuteness of the cos θ — cos a,
until it is demonstrated to us unmistakably.
Again, on page 545, the Professor says: “By developing
and neglecting the powers of u superior
to the square, we have:

“sin θ 2a — u sin 2 a + u 2cos 2 a, etc.”

Allow us to inquire the object of developing the

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powers of u, provided they are to be subsequently
neglected? Can Professor Barnard answer this
question? Or, how do we know that u, or its
powers, are superior to the square, which, as
every school-boy knows, is next to the sphere, the
most perfect of figures? But we have no wish to
be hypercritical; our remarks are merely made
with the object of discovering the truth, which result
deep research only can obtain; as Cicero
beautifully remarks, “De profundis clamavi,” or
“out of the deep have I procured a clam;” showing
in a figurative manner the necessity that he
felt of thorough investigation on the most ordinary
occasions. The analysis of Professor Barnard is
written in a playful, humorous style, admirably
adapted to popular comprehension, and, like the
chaste works of Professor Bache, formerly noticed
favorably in this journal, contains nothing that
could bring a blush on the cheek of the most fastidious,
the whole subject being treated in the most
delicate manner, and all unpleasant allusions carefully
avoided. We cordially recommend to each

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of our readers to purchase the work for himself
and Mrs. Smith, and a copy for each of the children,
satisfied that they will be well repaid by its
perusal.

p548-217

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