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TREATISE

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SURVEYING AND NAVIGATION:

UNITING

THE THEORETICAL, PRACTICAL, AND

EDUCATIONAL FEATURES OF THESE SUBJECTS

BY HORATIO N. ROBINSON, A. M.

FORMERLY PROFESSOR OF MATHEMATICS IN THE UNITED STATES NAVY; AUTHOR OF
MATHEMATICAL, PHILOSOPHICAL, AND ASTRONOMICAL WORKS.

THIRD EDITION.

CINCINNATI:

JACOB ERNST, 112 MAIN STREET.

BOSTON:

B. B. MUSSEY & CO.; ROBERT S. DAVIS & CO.; W. J. REYNOLDS & CO.

NEW YORK:

MASON BROTHERS; D. BURGESS & CO.; A. S. BARNES & CO.; NEWMAN & IVISON;

PRATT, WOOdford & co.

PHILADELPHIA:

LIPPINCOTT, GRAMBO & CO.; THOMAS, COWPERTHWAITE & CO.;

E. H. BUTLER & CO.; URIAH HUNT & SON.

1853.

ENTERED, according to act of Congress, in the year 1852,

By H. N. ROBINSON,

in the Clerk's Office of the District Court for the Northern District of New York.

PREFACE.

THIS book is more than its title page proclaims it to be: it is the practical application of the Mathematical Sciences to Mensuration, to Land Surveying, to Leveling, and to Navigation.

Nor is the work merely practical. Elementary principles are here and there brought before the mind in a new light; and original investigations will be found in many parts of the work. To show the reader how a thing is to be done, is but a small part of the object sought to be obtained: the great stress is put upon the reasons for so doing, which gives true discipline to the mind, and adds greatly to the educational value of any book.

We have illustrated the subject of logarithms, and their practical uses, the same in this book as is common to be found in other books, and this is sufficient for the common pupil, or the ordinary practical man, whether surveyor or navigator; but in addition to this, we have carried logarithms much further in this work than in any I have seen. I do not mean by this that we have more voluminous tables than others. Such is not the fact.

Voluminous tables are not necessary for those who really understand the nature of logarithms, and such are mainly intended for those who are not expected to understand principles. To give a more practical illustration of logarithms, and to suggest artifices in using logarithms generally, we have given Table III and its auxilliaries, on page 70 of tables, showing logarithms to twelve places of decimals, a degree of accuracy which practice never demands. By the help of this table combined with a true knowledge of the subject, the logarithm of any number may be readily found true to ten places of decimals, or, conversely, the number corresponding to any given logarithm may be found to almost any degree of accuracy.

Our Traverse Table is not so full as in some other books, but it

is full enough to answer every purpose; and latitude and departure, corresponding to any course and distance, can be found by it, provided the operator's good judgment is awake. Indeed a contracted table, in an educational point of view, is better than a full one; for the former calls forth and cultivates tact in the student, but the latter is best for the unanimated plodder.

In running lines, and computing the areas of surveys, we have endeavored to present the subject in such a manner that the reader must constantly keep Elementary Geometry in view, and the whole is so clear and simple, that many will think it unworthy of the rank that it seems to hold in the public estimation, but there are other reasons for this.

The chapter on surveys and surveyors will be found to be a little peculiar, but the information there given, will be highly useful to all those who are inclined to look upon a survey as a mathematical problem only.

On the compass, and the declination of the needle, we have been very full the subject embraces meridians and astronomical lines drawn on the earth.

The manner in which we should proceed to make a survey, provided no such instrument as the compass existed, and there were no such thing as a magnetic needle, is taken up and illustrated in this work.

The subject of dividing lands is fully discussed and illustrated, and if any one has occasion to complain of mathematical abstrusity in this work, it will be found in this connection; yet there is nothing here above elementary algebra and geometry.

The method of taking levels and making a profile of the vertical section of a line for rail roads, is set forth in this work. The profile shows the necessary excavation or embankment, which it is necessary to cut down or build up at any particular point, to conform to any proposed grade that may be contemplated.

To determine the elevation of any place above the level of the sea, by means of the barometer, has been, and now is, a very interesting problem to all philosophical students, yet very few of them have been able to comprehend it beyond its first great principle, the variation of atmospheric pressure. To trace, or rather to discover the mathematical law which connects the elevation of any locality with the mean hight of the barometer at the same place, has been an obscure problem, and we have taken hold of it with a determination to break open some avenue of light (if such were possible) by which the simplicity of the problem might be brought to the comprehension of the every-day mathematical student, and we believe that we have succeeded in the undertaking.