trious, that few names in the registers of Time will excite more curiosity than that of William Pitt." · Memoirs, Vol. II., pp.

385-388.

ART. VI.1. An Account of the Trigonometrical Survey of Massachusetts. By SIMEON BORDEN, Esq. Published in the Transactions of the American Philosophical Society of Philadelphia. Vol. IX. Part I. 4to. 2. A Topographical Map of Massachusetts, founded on Trigonometrical, Astronomical, and Local Surveys, made by Order of the Legislature. SIMEON BORDEN, Superintendent. Published by the State. Boston.

1844.

THE triangulation and survey of Massachusetts for the purpose of constructing a map of the State, and the publication of the map itself, are matters, which, for various reasons, are worthy of some consideration in our pages. The excellent example which has thus been set, we hope, will soon be followed by some of the sister States, and the experience gained in executing this survey, the first of the kind on a large scale which has been made in this country, may be of use in directing their operations. Mr. Borden's modest account of his highly meritorious labors, and of the many ingenious methods which he contrived in order to insure accuracy in his work, is interesting throughout; but we shall confine our notice chiefly to his details of the history of the survey, and to some of the methods used and the results obtained. The character of the map, and some facts connected with it and its publication, will also be noticed.

The history of the survey, Mr. Borden states, commenced in March, 1830, when the legislature of Massachusetts passed resolves requiring the city of Boston and the several towns in the Commonwealth to make an accurate map, each of its own territory, upon a scale of one hundred rods to an inch, and to deposit the same in the office of the Secretary of State. These resolves gave directions in detail respecting the subject. During the same month, a resolve was passed, authorizing the governor to appoint skilful survey

ors to make a survey of the State upon trigonometrical principles, combining astronomical observations with their work. Some time in the following summer, the governor appointed an astronomical and a topographical surveyor. During the season, most of the instruments were procured, and Mr. Borden was called upon to make an apparatus for measuring the base line. In the autumn, a location for the base line was selected, and the line was partially traced. This was all that was done in 1830. In the course of the ensuing winter, Mr. Borden made the measuring apparatus, and repaired the instruments. The apparatus being ready early in the spring of 1831, astronomical and chronometrical observations were commenced by the astronomical, and the surveys and triangulations by the topographical, surveyor. Mr. Borden was at this time assistant to the latter, and continued to be so for three years; at the termination of that period, the topographical surveyor resigned, and the governor placed the survey under the charge of Mr. Borden.

In 1838, the astronomical surveyor made his final report, and the responsibility of completing the work devolved on Mr. Borden. At this time, the field work was supposed to be completed, and the necessary trigonometrical computations for compiling the map were commenced, when a difficulty was discovered, that might have been expected, considering the great number of individuals who had been employed on the various surveys. This difficulty was caused by the action of the legislature, who wished to save political reputation by saving the funds of the State treasury at the expense of the town treasuries, the expenditures from which would not be so publicly noted. The account before us thus describes the evil.

"After I had completed the field work, and had calculated a sufficient number of the main triangles to cover a section of fifty miles square of the western portion of the State, I commenced the work of compiling the map, when I found that the town maps had been returned to the Secretary so incorrectly drawn as to render it impossible in their actual state to make a satisfactory map from them. I was then obliged to go into the field again, with four or five assistants, to make corrections; and this operation has been one of continual perplexity, and has cost the State, in my department alone, at the least estimation, ten thousand dollars more than it would have done had the towns

executed their portion of the work in good faith. It is my opinion, that, had the work been performed from beginning to end under the direction of a faithful and competent engineer, it might have been executed, at the rate of compensation which has been paid, for many thousand dollars less than it has now

cost.

"Still, the survey of the State of Massachusetts, including eight thousand two hundred and thirty square miles of territory, and having an indented sea-coast of about three hundred miles, has been completed in a little more than ten years, at an expense of only sixty-one thousand three hundred and twenty-two dollars.” p. 34.

To this expenditure must be added about nine thousand five hundred dollars, paid chiefly for engraving and printing about eight hundred copies of the map for distribution among the several towns of the Commonwealth, the members of the legislature of 1844, the State's members of Congress, the president and vice-president, and the several departments at Washington. The whole cost to the State was nearly seventy-one thousand dollars. The act for the publication of the map provided, that the publisher, in return for the sum received by him from the State, and for the copyright of the work, should be obliged, for the term of three years, to furnish copies of the map to any applicant at the price of five dollars each, or about one half the amount for which any private individual could afford to get up such a work.

After the history of the survey, Mr. Borden enters into some details respecting the instruments and methods used, and then describes very fully the results obtained from his arduous and skilful labors with them. The first work was measuring the base line for the system of triangulation throughout the State, a work entitling him to the greatest credit. The apparatus by which the base line was measured was of his own invention and construction, and so accurate did it prove, that two separate and independent measurements of a line over seven miles in length differed only 0.237 of an inch, a result showing a degree of perfection in the instruments and their use which we think has never been surpassed. A correct base line is so important an element of a trigonometrical survey, that we deem it of sufficient interest to transcribe from Mr. Borden's second

paper as perfect a description of the instruments used as can be made intelligible without reference to his diagrams; and we give the account more in detail, because it has not yet been published.

The standard of length first selected was a scale two feet in length, constructed upon compensation principles, and of course unsuitable for division. When afterwards compared at Washington, by Mr. Hassler, of the United States coast survey, with his eighty-two-inch scale of Troughton's construction, which is an exact copy from the well known Troughton scale of Sir George Shuckburg, it was found, at the temperature 57° Fahrenheit, to be 0.0018 inches too short. The Massachusetts scale was used to complete the calculations with, and the corrections were made after a proper standard was fixed upon, which was Hassler's eightytwo-inch Troughton, at 62° Fahrenheit.

The apparatus with which the line was measured is fifty feet in length, and is contained within a strong and firmly soldered tin tube, eight and one-fourth inches in diameter, by which it is supported. It consists of two rods, three eighths of an inch in diameter, one of steel, the other of brass. These rods project six inches at both ends of the tube. They are each in four pieces, of nearly equal lengths, and are united, as it were, into two continuous rods, by what machinists call coupling-boxes. These are cylindrical in shape, about three inches long, and seven-eighths of an inch in diameter, with a hole passing through their centres longitudinally, of the size of the rods. A hole also passes transversely through the middle of the coupling cylinder, through which the observer may see that the ends of the rods are free from dirt or extraneous matter. The end of one of the rods having been inserted into the couplingbox until it makes its appearance in the centre of the transverse orifice, a hole of proper size is drilled through the box and the centre of the rod, in which a pin is inserted, and its ends riveted, so as firmly to bind the rod and coupling-box together. The end of the next rod is provided with a thin mortise, of a size proper to receive a suitable key; the coupling-box, also, has a mortise to correspond to that in the rod. The mortised end of this rod is then inserted into the box, until it comes in contact with the end of the rod to which the coupling-box has already been secured. Then,

by examining the ends as seen in the transverse orifice, they may be made to meet each other properly. The key is then driven into the mortise, and keeps the ends of the rods firmly in contact with each other. The couplings belonging to the steel rods, as well as the pins and keys, are made of steel; those belonging to the brass rod are made of brass. These rods are supported within the tube by nineteen supports of cast-iron, each held in its place by five screws, to keep them in a single plane, and the rods straight when in their place.

Near the centre of each sheet of tin of which the tube is composed is soldered a ring or flange of tin, one inch deep, which serves to stiffen the tube and prevent it from collapsing while in use; the nineteen supports are placed near these flanges. The tube is about forty-nine feet long, made in four pieces of nearly equal length; they are attached to each other by small screw bolts passing through strong brass flanges, which are soldered into the ends of the several parts. These flanges are cast of sufficient length and strength to serve as bearings, to rest in the Y's of the trestles and support the tube. Each end of the tube, considering all the pieces as one, is tapered to about the size of the inside of the flanges placed within it, and has a cast-iron end fitted to it. Through these iron terminations the brass and steel rods project, and are attached to couplings similar in construction and principle to those which have been described. These couplings are fastened by movable joints to arms or indices; and at one end of the measure the index is made to stand at a constant angle with the axis of the tube by a stirrup-like apparatus screwed to this index and the iron end of the tube.

The arrangements at the other end are quite different, though the projection of the rods beyond the tube and their attachment by coupling-boxes to the index are the same. Within the end of the tube is placed a stiff spiral spring, capable of exerting an expansive force equal to several hundred pounds. There are two circular pieces of cast-iron, with flanges projecting in such a manner as to retain the spiral spring between them; and another piece of circular iron closes the end of the tube. The inner plate of iron is held in its position by two screws, which pass through the iron end of the tube, through a loop or projection of the centre plate, and through this inner plate, and is secured by screws