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THE MOST NOBLE
DUKE OF RICHMOND, AND LENNOX,
MASTER GENERAL OF THE ORDNANCE, &c.
WITH GREAT RESPECT,
BY HIS GRACE's
THOSE who have had much occasion to use the mathematical instruments constructed to facilitate the arts of drawing, surveying, &c. have long complained that a treatise was wanting to explain their use, describe their adjustments, and give such an idea of their construction, as might enable them to select those that are best adapted to their re
This complaint has been the more general, as there are few active stations in life whose professors are not often obliged to have recourse to mathematical instruments. To the civil, the military, and the naval architect, their use must be familiar; and they are of equal, if not of more importance to the engineer, and the surveyor ; they are the means by which the abstract parts of the mathematics are rendered useful in life; they connect theory with practice, and reduce speculation to use.
Monsieur Bion's treatise on the construction of mathematical instruments, which was translated into English by Mr. Stone, and published in 1723, is the only regular treatise * we have upon this subject ;
numerous improvements that have been made in instruments since that time, have rendered this work but of little use.
It has been my endeavour by the following Essays to do away this complaint; and I have spared no pains to render them intelligible , and make them useful. Though the materials,
of which they
are composed, lie in common, yet it is presumed, that essential improvements will be found in almost every part. wholly to the instruments contained in a case of drawing instru*I do not speak of Mr. Robertson's work, as it is confined
cations of Mr. Gale,* and Mr. Milne, here inserted, and which I think will contribute more to the improvement of the art of surveying, than any thing it has received since its original invention.
The reader will, I hope, excuse me, if I stop a moment to give him some account of Mr. Gale's improvements; they consist, first, in a new method of plotting, which is performed by scales of equal parts, without a protractor, from the northings and southings, eastings and westings, taken out of the table which forms the appendix to this work ; of this method is much more accurate than that in common use, because any small inaccuracy that might happen in laying down one line is naturally corrected in the next; whereas, in the common method of plotting by scale and protractor, any inaccuracy in a former line is naturally communicated to all the succeeding lines. The next improvement consists in a new method of determining the area, with superior accuracy, from the northings, southings, eastings, and westings, without any regard to the plot or draught, by an easy computation.
As the measuring a straight line with exactness is one of the greatest difficulties in surveying, I was much surprised to find many land surveyors using only a chain ; a mode in which crrors are multiplied without a possibility of their being discovered, or corrected. I must not forget to mention here, that I have inserted in this part Mr. Break's method of surveying and planning by the plain table, the bear. ings being taken and protracted at the same instant in the field upon one sheet of paper ; thus avoiding the trouble and inconvenience of shifting the paper: this is followed by a small sketch of maritime surveying; the use of the pentographer, or pentagraph;
* A gentleman well known for his ingenious publication on finance.
+ The table is printed separate, that it may be purchased or not as the surveyor sees convenient.