44 SURVEY OF MASSACHUSETTS. 
happens;) that the azimuth of station, 6 No. 2, determined from station 5, No. 1, is South 
40° 10’ 22" West, and the azimuth of station b, No. 1, determined from station b, No. 
2 is North 40° 10’ 20” Hast. As these are not exact reverse courses, a mean course 1s 
taken, and applied in tlie Calculations as the azimuth of the line. Thus: 40° 10’ 29" 
+ 40° 10’ 20”==80° 20’ 42” and ae ==40° 10' 21”, which is taken ag the bearing 
or azimuth from 6, No. 1, to 4, No. 2, reversing the names of the points as before ex- 
plained: hence station 2, No. 2, bears from 3, No. 1, South 40° 10’ 21” West, and b, 
No. 1, bears from 0, No. 2, North 40° 10’ 21” East. The same principle has been 
carried through the whole work. Having thus determined the azimuthal bearings of 
one station from another throughout the whole of a section, (the distances also from one 
Station to the other, having been previously calculated according to the method of Legen- 
dre,) we proceed to make upon the principles of plane trigonometry, a table of Northings, 
Southings, Hastings, and Westings, as the case may require, of each station in the section, 
or any other station in the survey to which we desire to know the bearing and distance 
from station a, of the section. The whole calculated and summed up from station a, 
through which, as before stated, the true meridian passes. ‘I'he station a, we shall there- 
fore call the zero point. Then, with the Northing or Southing, Easting or Westing, of a 
point to which our table has been carried, (which in fact constitutes two sides or legs of 
a right angled triangle,) we calculate on the principles of plane trigonometry, the angle 
at the zero point, which gives the bearing or azimuth of the distant station from that point. 
And in a similar manner, the azimuth of any point within the scope of the table, may be 
determined from said zero point. To determine an azimuth or bearing from any other 
station than the zero point, it becomes necessary to calculate a meridian for that station, 
and for that purpose we must know the value of the meridional and perpendicular degrees. 
The method of managing these calculations will become apparent, when we show the 
method of determining the value of a degree perpendicular to the meridian, from the in- 
clinations or convergence of two observed meridians. It will therefore be unnecessary to 
go further into an explanation of this subject in this place. 
For the purpose of testing the accuracy of the main triangulation, I have made several 
double computations of the latitude and longitude of points situated in different parts of 
the state. In the first place, I computed the latitude and longitude of our primitive sta- 
tion, upon French’s Hill, in the town of Peru, and upon the top of the Green Mountain 
ridge. Ithen computed the latitude and longitude of Tuft’s Hill, from the French’s Hill 
station, and also from the State House, which, if the triangulation had been accurately 
performed, and no mistake made in our calculations, should have both given the same po- 
sition to the Hill. The table shows a discrepancy in latitude of 0” .05==6 feet, and in 
longitude of 0” .08==6 feet. This is not a greater error than might arise, in calculations of 
this kind, by using tables carried to only seven places of decimals; and, as I possessed no 
better tables, I could not make the computations with greater accuracy. ‘The latitudes 
and longitudes of the other points given in the table were calculated, in a similar manner, 
from the stations named against them ; and-as the object of the table cannot be misunder- 
stood, it will be unnecessary to give further explanations. 
