PREFACE TO THE FIRST EDITION.

AN attempt has been made in the following pages to put
within the reach of all a short and compendious treatise upon
some of the ingenious instruments by which the scientific
practitioner is aided in his observations, and in the delineation
of the results obtained from them.

The instruments treated of have been divided into five
classes, to each of which a part of the work has been devoted.
The first part treats of Mathematical Drawing Instruments;
the second, of Optical Instruments; the third, of Surveying
Instruments; the fourth, of Astronomical Instruments; and
the fifth, and last, of Goniometrical Instruments, for measur-
ing the angles of crystals.

The greater part of the Wood Engravings, and some parts of the Text, of Simms's Mathematical Drawing Instruments, have been pressed into the service of the present work; and the works of the best writers upon the several parts of the subject have been consulted, and much valuable matter has been extracted from them, particularly from Pearson's Astronomy.

The limits of the bulk and cost of the work have forbidden any extensive excursion into the sciences in which the instruments are used; but it is hoped that a large mass of information has here been placed in a small compass without sacrificing perspicuity to undue compression.

ROYAL MILITARY ACADEMY, WOOLWICH,

March, 1849.

J. F. H.

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Problems on the A and B lines

Different modes of construction of the C and D lines.
Squaring Numbers by the lines C and D

Extraction of Square Root

General Rules for Numeration upon the C and D lines
Comparative Merits of the different modes of constructio
Problems on the C and D lines

Uses of the A, B, C, and D lines conjointly

MATHEMATICAL INSTRUMENTS.

PART I.

ON MATHEMATICAL DRAWING INSTRUMENTS.

CHAPTER I.

THE DRAWING-BOARD, PAPER, AND PENS.

THE DRAWING BOARD.

HE first thing to be done, preparatory to the commencement a drawing, is to stretch the paper evenly upon the smooth nd flat surface of a drawing board. The edges of the paper ould first be cut straight, and, as nearly as possible, at ght angles with each other; also the sheet should be so uch larger than the intended drawing and its margin, as to

MR. J. F. HEATHER, M.A., late Mathematical Master at the Royal Military Academy, receives pupils, and undertakes their preparation for the Army, for the Indian Civil Engineering College, for the Civil Service, or for the Universities.

WATERFIELD LODGE,

WATFORD, HERTS.