SURVEY OF MASSACHUSETTS, 37 
Which being further reduced to Mr. Hassler’s standard at 62° of Fahrenheit, and to the 
level of the sea, gives the final adopted length at 39009.73 feet, or 7.388 miles. 
The heights of the north and south ends of the base line, above the mean level of the 
sea, were determined in the same manner as those of the other stations to be mentioned 
hereafter. At the time of measuring the base, however, we found its north end to be 
49.55 feet higher than the south by the following process, namely: For the purpose of 
measuring the line accurately and conveniently, we divided it into a series of hypothe- 
nuses upon which the measuring apparatus was carried; the inclination of these hypo- 
thenuses was determined by precise measures of the depression or elevation of each; and 
the difference in the height of their termini was then computed. The coincidence of the 
difference of level found by the two independent methods serves to test the precision of 
both. Thus the height of the north end of the base above the mean level of the sea was 
found by vertical triangulation to be 220.02 feet, and of the south end by a similar pro- 
cess 169.59 feet; the difference being 50.43 feet, which differs only 0.88 feet from that ob- 
tained by inclination of the hypothenuses. 
For measuring the base line eight persons were employed. This number, which in- 
cluded the principal and assistants, was found necessary to perform the work dexterously. 
Three small tents were used for covering the microscopes when necessary. 
SECT. II].—OF THE TRIANGULATION, AND THE PREPARATION OF THE MAP OF MASSACHUSETTS. 
The instrument used in measuring horizontal angles was a twelve-inch repeating 'Theo- 
dolite, made by Troughton for Mr. Hassler at the commencement of the coast survey, 
and fully described in the second series of the Transactions of the American Philoso- 
phical Society, published at Philadelphia in 1825, page 328. I would refer to that 
paper for a description of it, and will merely add, that I found it necessary to supply the 
instrument with a firmer clamping apparatus, and with a more powerful telescope to be 
used in measuring the azimuth angles. ‘This telescope was forty-six inches in focal length. 
It is now in the hands of Major Graham, upon the north-eastern boundary survey. 
The vertical angles were measured with the small telescope and vertical circle which 
Mr. Troughton made for the instrument, it being difficult to attach the vertical circle 
to the arbour of the large telescope. The clamps of the vertical circle were also insuffi- 
cient for repeating the measures of angles of much magnitude; but as our vertical an- 
gles were for the most part very small, I did not make any change or addition to its 
clamping apparatus. 
After the work fell into my hands, our party never consisted, principal and assistants, 
of more than three persons, while we were employed in making the triangulation; with 
the exception, however, of occasionally employing a person a few hours to assist us in 
putting up a heavy signal, and sometimes for a day or so to assist in felling trees which 
obstructed our operations. 
We had one circular tent, about nine feet in diameter at the upper end of the main 
body, which is about six and a half feet from the ground, and much larger at the lower 
end. The roof or top of this tent was in the form of an obtuse cone, and the sides 
or walls were of four separate curtains, with suitable strings for closing them when 
VOL, IX.—-13 
