48 SURVEY OF MASSACHUSETTS. 
turning upon the southerly side of the State, again to Colonel’s Mountain. We there 
compared them, by redetermining the height of the mountain from the returning levels, 
having traversed, in their zigzag course, a distance of several hundred miles. The result 
follows:— 
Mean height of Colonel’s Mountain, obtained from the levels carried directly from tide 
water, - = - - - - - - = 1171.67 feet. 
‘ 13,18 feet, difference. 
From the return levels, = - - - - - 1184.80 feet. 
From the calculation of reciprocal observations, the mean refractions were found to vary 
from one-tenth to one-twentieth of the arc, upon the earth’s surface, contained between the 
two stations from which the reciprocal observations had been made. It may be worthy 
of remark, that, in the western portion of the state, the refractions appeared to be much 
more regular than they were in the eastern,—rarely exceeding one-twelfth, or falling short 
of one-sixteenth of the contained arc. This phenomenon is probably owing to the trigo- 
nometrical stations being much more elevated, above the country which surrounds them, 
in the western portion of the State, than in the eastern. The western portions of the state 
may be said to be mountainous. 
Probably I ought to mention, before I leave this subject, that the ascertaining of the 
heights of the trigonometrical stations was deemed of secondary importance; and, as a 
considerable portion of each day is unsuitable for making accurate observations, our gene- 
ral practice has been to measure the vertical angles at those times,—employing the more 
suitable states of the atmosphere for measuring the azimuthal angles. It is possible that 
mistakes may occasionally have been made in registering our field notes,—such as mark- 
ing an angle as elevated when it should be depressed, and the contrary,—as we did not 
make repeated measurements of the vertical angles. These mistakes, however, can only 
take place when the two stations are near the same level. In other conditions, they can 
be corrected from a knowledge of the apparent or comparative height of the stations, at 
the time of calculating them. 
The following description of the levelling operations has been drawn up, at my request, 
by Mr. Charles Boutelle, one of the assistants in the Massachusetts survey. 
“In order to exhibit the whole matter, in relation to the chain of levels carried across 
this state in the course of the trigonometrical survey, I present herewith some farther 
statements and examples, illustrating the system pursued, and the modes of computation 
employed. I also send a map of the triangles, to show the relative positions of the points 
observed. 
“The zenith distances were observed with the vertical repeating circle of the theodolite 
with which the azimuth angles were measured. It is graduated to 5”, and has four 
verniers. It was customary to make from six to eight repetitions, according to circum- 
stances. Owing to a want of confidence in the accuracy of these observations in the 
early part of the survey, comparatively few observations were taken, and some stations, 
therefore, depend upon single observations only, for their heights. It will be noticed, 
however, that where reciprocal and single observations are brought to bear upon the same 
station, there is generally a close coincidence in the results. 
