50 SURVEY OF MASSACHUSETTS. 
“Having the difference of level of the tops of the signals, that of the copper bolts 
marking the station points is found by applying a correction to H equal to the difference 
in height of the two signals. This correction is + (plus) when 
Fig. 6. the shortest signal is elevated, and — (minus) when it is de- 
pressed, as may be seen in the annexed figure, (Fig. 6,) in 
which B’ R’ = difference of level between tops of signals, and 
A R = difference of level between bolts, but B’ R’ is greater 
than A R by the quantity A a, which is the difference in 
height of the signals A B and A’ B’ above the station marks, 
and which is to be added or deducted, therefore, as indicated 
above. | 
“ Having thus given the formule used where reciprocal observations have been made, I 
here subjoin an example of their application to practice in this survey. 
“At Nahant station, in Lynn, Sept. 14th, 1834, at 41, P. M., the measured zenith dis- 
tance of the top of the signal on Blue Hill, in Milton, was 89° 45’ 35.84. 
Height of the telescope above the copper bolt marking Nahant station, = 4.83 ft. 
Height of top of signal above copper bolt at Blue Hill station,. . . = 31.92 
Semen’ 
a) = 27.09 
“At Blue Hill station in Milton, Oct. 31st, 1834, at 23, P. M., the measured zenith dis- 
tance of the top of the signal at Nahant station in Lynn was 90° 25’ 44’’.58, 
Height of telescope above the copper bolt marking Blue Hill station, = 13.63 ft. 
Height of top of signal above copper bolt at Blue Hill station, . . = 34.98 
a) = 21.80 
By (1.) At Blue Hill station, A = 90° 25’ 44.58 
ob = 21 .80 ft. 
ay = 21.30 log. = 1,38283796 
A = 90° 25’ 44.58 sin = 9.9999878 
ee log. = 5.3144251 
K = 94402.74 ar. co. log. = 5.0250154. 
d= 46'’.54 = 1.6678079 
een nnn oer 
At Nahant station, A = 89° 45’ 35.84 
a) = 27 .09 
a) = 27.09 —_ log. = 1.4828090 
A = 89° 45’ 35.84 = 9,.9999962 
i = 5.38144251 
K ar. co. log. = 5.0250154 
d= 59.19 = 1.7722457 
pocrenence me 
