52 SURVEY OF MASSACHUSETTS. 
height above the bolts of the signal observed and the telescope at the place of observation. 
This correction is + (plus) when the signal observed is depressed, and — (minus) when 
it is elevated. 
“The refraction, 7, was obtained, in the easterly part of the state, by using .0784 C as 
a mean coefficient, derived from about twenty reciprocal observations. In the interior, 
the mean refraction was found to be less than on the sea-coast, and a mean coefficient of 
06978 C was employed. 
“The following example will illustrate the foregoing remarks :— 
“At Blue Hill station, Oct. 30th, 1834, the telescope standing 13.63 ft. above the cop- 
per bolt, the measured zenith distance of Coddon’s Hill station, in Marblehead, was 
90° 22’ 11.25. Height of signal at Coddon’s above the bolt = 29.83 feet. 
“ By the formula given above, 
i as GO" 22’ 11" 25 
ra 0784 C= + 1 41 62 
90 28 52 .87 
Ci 0 a8 08 
2 
C 
A+r—==90 18 04.78 cot = 7.503348 
K= 181259.69 log. =5.1181314 
H 499.42 log, = 2,6984662 
515.62 ft. 
“ Blue Hill is, therefore, elevated 515.62 ft. above Coddon’s. The height of Coddon’s 
Hill station, above the mean level of the sea, has been ascertained, by levelling, to be 
117.75 feet; therefore, 117.75 + 515.62 = 633.37 feet is the result obtained, by this ob- 
servation, for the height of Blue Hill station above the mean level of the sea. This is 
1.77 feet less than that obtained by the reciprocal observation from Nahant, and giving 
the single observation one third weight, the mean will be 634.55 feet for the height of 
the station. 
“In this manner the levels have been carried over the state, and the results have been 
highly satisfactory, proving sufficiently accurate to warrant the assertion that no point 
is in error more than six feet, and most of them are much nearer. A fair specimen of 
the work may be seen in the following table, in which the levels, taken from the sea at 
four stations distant from each other, are brought to bear upon one station. The four 
stations are Nahant, Telegraph Hill, Hyannis and Bullock’s Neck stations: (the accom- 
panying map of the triangles will show the relative positions of the stations named in the 
following table;) and the point where the levels from them mect is at Copecut station, in 
Fall River. In this table, where the sign + is prefixed to the numbers in the column of 
differences of level, it signifies that the station last named on the same line ig elevated, 
and the contrary sign is used to denote a depression. 
