Semi-weekly standard. [volume] (Raleigh, N.C.) 1853-18??, 1857-07-15


PLICATIONS, By CHARLES PHILLIPS, Professor
Of Civil Engineering in the University Of North
Carolina. RALEIGH: PRINTED BY w. D. Cooke.
We rejoice to see that Wheeler's History and
Wiey's Alamance are not the only representatives
of North Carolina in the world of letters. The
above work, written by North Carolinian for the
use of the students of our own University printed,
and we'll printed, in the City OF Raleigh, on paper
made at Neuse Mandatory, and bound by North
Carolina hands, has appeared among u.s. and reflects
credit the author and the Institution for which
he labors
Prot. Phillips has been for many years a Jealous
and successful teacher, and therefore knows the
wants of young student In this work he not
only shows that he is acute and clear-headed
mathematician, but has exhibited good taste and
Judgment in the selection and arrangement of
Trigonometric principles. The work may be diff
cult to beginner unaccustomed to close reading as
every word has a use-every sentence conveys a
distinct truth. But the STYLE though concise is
clear; the language accurately expresses the mean
ing intended to be conveyed the notation is SIMPLE
and the pupil, if he has any brightness, will soon
take pleasure in the study Of this treatise than
of one the style of which is more diffuse.
Besides this general commentator of the work
as whsle, we propose to point out some of the
particulars which, Think give it an air of novel
ty, and improvements the treatises generally
used.
Many writers move smoothly on, drawing the
careless learner in their wake, and suddenly with
dark " &c" or a mysterious $50 it will be perceiv-
pupil to founder in hopeless bog. Prof Phillips
has avoided this inconsistency. His Algebraic and
Geometrc processes uniformly concise yet clear
not duting too freely, yet leaving gaps in the
reasoning so large as to bewilder the learner
In the second place, our authors definitions
admirable-in some cases altogether new. For
instance, those Of Snes. Tangents, &C., comprehend
the cases of all angles, acute as we'll as obtuse, while
even that of Mr.. Peirce, who rarely fails in this
particular, (or any other,) will apply only to an
acute angle The general properties Of these func-
tons too, are collected in groups and become more
securely liked in the pupils mind than when he is
forced to pick them up best he can, scattered
here and there over the surface of many pages.
In Algebra We learn that the positive sign means
greater, the negative sign less than zero. As
advance in our studies, to our establishment, and
often mystcaton, discover that the former often
right left of object, and the latter signifies the
reverse. The pupil will thank author for rea-
sonaby calling his attention to this change. Similar
thanks will be due for full exposition of the dis
tinction between Circula, and angular functions
we'll the difference between the NeridianaI Parts
Of the Latitude of place. and the Latitude ITSELF
and the advantages and disadvantages of Mercators
sailing.
graduate at the University ten years ago
will remember the uncouth strangeness presented
by Peirces Analytical Geometry and Diferential
Calculus to his despairing eyes on his first entrance
on those studies The manual before US has such
descriptions, incidentally but naturally thrown in,
of Functions, Co-ordinates Projections of Auxiliary
Angles-has too, clear and beautiful notation
of the latest invention that the learner will almost
feel among familiar friends his first arrival in the
hostile territory And so we notice that the trape.
zoid, instead Of the triangle, is selected as the
primary figure in Surveying. As in the Calculus,
the diferential of any area has that figure; the
pupil, when he mounts so high, will be already &C.
customed to its use.
We think, too, that Prof Philips, while his book
evnces scientific spirit, has very happily increas.
ed its value and kinded the zeal of the learner by
occasional donations of truths applicable to the
wants of every day life. Note, for instance, the
method of finding the feet inches, &c., in given
arc-vauable in laying down Railroad curves. The
transformation of French Grades into English Degrees
comes in OPPORTUNITY in these days of French
alliances and the mode of laying out land in given
figures and of dividing fields into proportional parts
will be appreciated by those DESTROYS of becoming
practical surveyors So, too, in Parallel Sailing
is problem taken from Cookies new map of North
Carolina-useful in the construction of charts; and
we notice also a full explanation of some problems
important in photography.
No pupil can keep his mathematical knowledge
distinct in his mind, or become an accurate and
rapid computer without much study and practice
in the solution of problems He may well under
able glibly to tell others what to do but unless he
employs his fingers in the active operation, his in
formation will be of little practical value, and in
short time will fade from his mind altogether. Our
author has been fully aware of this truth, and has
interspersed his work with many examples of the
application of his principles. They are we'll select
ed often convey some incidental benefit, are some
times easy Of solution, occasionally difficult to
be handled by those bountifuy gifted with analytic
and inventive talent
1t rejoices us to perceive that Prof Phillips has
had the kindness of heart to recall from exile our
old friend, the Rhum6 and the Versed.sine And
though he has been at some pains to show that the
former is not important parsonage in the scen-
tific household the Arc of Great Circle we are
convinced that the offices which both he and the
versedsi sine are made to perform, will permanently
reinstate them.
1t has not been attempted to mention all the par
ticulars which make this manual valuable acqusi.
ton to the teacher and the pupil Containing full
and lucid discussions Of all the subjects usually en-
braced in elementary works on Plane and Spherical
Trigonometry, it gives the former ample foundation
which to base his instructions while the latter
unassisted, might by its aid become respectfully
learned in the principles of the science The rea.
tons of angles in themselves without regard to
their utility, most worthy of careful attention. and
the fond devotee of abstract investigation might de-
light in their study. Our author would teach his
pupils, as is remarked in the preface, Ito take
pleasure in whatever is beautiful and true even if
they know not where it will be useful" But Trig-
onometry is of the highest practical importance. It
points to Navigators their route on the ocean; it
guides ships safe among sunken rocks on dangerous
stars; it is the hand-maiden of the land-surveyor
the engineer and the Mechanic .-,.-5Esst4 So n