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own practice having been unusually large and diversified, probably the examples given will prove adequate, directly or indirectly, to all contingencies.

No attempt has been made to swell the bulk of the volume with imaginary cases; the object being, not to provide barren mathematical exercises, but to teach useful knowledge.

Problems, also, affecting location in its economical aspects, -- the balancing of physical and financial conditions, equating of alternative lines, and the like, – do not come within the scope of the work, and are therefore not treated.

Considerable pains have been spent on the tables. However far the young engineer way eventually outgo his teacher as regards the text of the book, these are inplements of his art which never become antiquated, and can never fall into dis..

Those herein contained which are original will, it is boped, be esteemed worthy of place with their well-approved associates.

The author invites friendly criticism: he would be pleased 1:7 receive suggestions, both for the improvement of the book, and for the correction of possible errors in it, should another edition be called for.

In dismissing the work from his hands, the precarious snatches of time occupied in its preparation, by day and by night, during the past two years, which might have been inore agreeably spent in reading, talking, or musing, recur to the writer's mind; and the thought arises, To what end or from what motive do people undertake these technical labors? Why should Forney and Bourne toil to simplify steam for our apprehension; Nystrom 10 compile mechanical, Molesworth and Trautwine tv epitomize civil engineering; Henck to prepare his elegant manual of field mathematics; Box to itłustrate hydraulics; and Shreve, with lucid pen, to make clear for us the strains in truss or arch? The ordinary motives to endeavor here have no place. There is neither faine nor profit

to his book; he remains impersonal, – known but indirectly, and but to a class. How, then, shall we account for his labors? I take it, the Father of mankind has not only made our minds to hunger for knowledge as our bodies for food, but has also imposed upon 11.4 kindly law of communion, by virtue whereof we cannot 'do otherwise, without violence to generous nature, than share with our fellows whatsoever we have learned that seems new and useful. Under this law these beneficial works would appear to have had their being, and thus pure are they from the stain of selfishness.

Though the present writer would not arrogate equal fellowship in the eminent brotherhood named, yet he inay justly claim like pureness from unworthy motive, and certainly feels like comfort at heart to that which they must know, for having discharged, in what measure it has been laid upon him, the divine obligation.

WM. F. SHUNK. RAHWAY, N.J.

PREFACE TO THE NINTH EDITION.

ALTHOUGH the writer has thanked individually all who have sent him errata from time to time, he cannot regard this enlarged edition of the “FIELD ENGINEER” as complete without a general salutation to them. Thanks, too, for pleasing . evidences, received from many hands, that the book has been helpful to those for whom it was intended.

He would make special acknowledgment to Mr. T. C. Mendenhall, Supt. U. S. Coast and Geodetic Survey, and to his assistant, Mr. C. A. Schott, for the new astronomical tables herein first printed, which were kindly computed for this edition in response to a call for much less.

He would also express his obligation to Mr. Fred. Brooks, C.E., Boston, Mass., whose critical suggestions for the better ment of the text have in the main been adopted.

knows them only by good report, and by these personal courtesies. He had no claim on them but that of Saint Paul's one blood." He can pay back thanks alone, -a residual debt being left over to do the like by others as they have done by him, to the extent of his limited ability. Thus good turns go round, and we civilize by mutual service.

W. F. 8. HARRISBURG, PA., March, 1890.

ABBREVIATIONS.

a

+ Increased by.

Diminished by. X Multiplied by. • Divided by.

Equal to. ::: Since, or seeing that. .Hence, or therefore.

: Indicates the quotient of one divided by the other of the quantities it connects, called sometimes the ratio of the quantities.

:: Indicates an equality of ratios, and connects equal ratios in a proportion. Thus, a :b :: :d indicates that a = b=0 • d; or it may be read, a is to b as c is to d.

( ) Brackets indicate that the operations embraced by them shall first be performed, and the result treated as a single term in the remaining processes required by a formula. Thus, a X b = (a + b) requires that the product of a and b shall be divided by their sum. This expression may also be written ab

6
or a x or b +

If the brackets be omitted a +6

ab the expression a x b = a + b would mean

+6.

a AA small secondary figure annexed thus to an expression is called its exponent. It requires the principal to which it is attached to be used as many times in continued multiplication as there are units in the exponent. Thus, A2 = A X A; A3 = A XA X A, which is called the cube, or third power, of A.

✓ This is called the square root sign: it signifies that the square root of the quantity covered by it is to be taken.

If preceded by a small secondary figure, called the inder, as in the marginal figure, it indicates that the cube root of the quantity covered by it shall be taken; and so on.

Al. If an exponent be fractional, as in the marginal figure, it requires that the square root of the third power of the quantity covered shall be taken, the numerator indicating the power and the denominator the root. B. M. Bench-mark: any fixed reference point for the level,

ix

a +6

at b'

as outcropping ledge, water-table of building, or other permar bent object. Usually a blunt conical seat for the rod, hewni on a buttressed tree-base, having a small nail sometimes driven flush in the top of it, and a blaze opposite, on which the elevation is marked with kiel.

T. P. Turning-point: usually marked in the field-book.

P. I. Point of intersection : as of tangents, which are to be connected by a curve.

A. D. Apex distance : e., the distance from the P. I. to the point where a curve merges in the tangent.

P. C. Point of curve : the stake-mark at the beginning of

a curve.

P. T. Point of tangent: the stake-mark at the end of a curve.

P. C. C. Point of compound curvature: the stake-mark where a curve merges in another of different curvature, turning in the same direction.

P. R. C. Point of reverse curvature: the stake-mark where a curve merges in another turning in the opposite direction.

B. S. Backsight, in transit work; or the reading of the rod to ascertain the instrument height in levelling.

F. S. Foresight, in transit work; or the reading of the rod to ascertain elevations in levelling.

H. I. Height of instrument : elevation of the level above the datum or zero plane.

H. W. High water.
L. W. Low water.

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