SURVEY OF MASSACHUSETTS. 87 
nation of the meridians, in preference to the mean result given by this last table, in con- 
sequence of the discrepancies among its single results. 
With the values of the meridional and perpendicular degrees thus found, I calculated 
the equatorial radius, polar semi-axis, and ellipticity of the terrestrial spheroid, and the 
differences in value of the meridional degrees of 41° 21’ 30", 42° 21' 30”, and 43° 21’ 30”. 
The results are as follows:— 
Meridional degree for the latitude of the State House, 364356 feet. 
Perpendicular degree for the same latitude, 365511 feet. 
Equatorial radius, 20914728 feet = 3961.123 miles. 
Polar semi-axis, 20854128 feet = 3949.646 miles. 
Iillipticity, 345 nearly of the equatorial radius.* 
Length of meridional degrees, the latitude of whose middle point corresponds to 
Feet. Difference. 
41° 21’ 30” = 364300.96 
+ 55.04 feet. 
42 21 30 = 364356.00 
+ 55.22 « 
43 21 30 = 364411.22 
From the calculated differences in the value of these meridional degrees, it was appa- 
rent that the increase of 57 feet to the degree, which I had adopted when preparing to 
deduce the value of the meridional degree from a combination of my proximate results, 
was not strictly accurate. But as the effect of the resulting error would scarcely have 
been appreciable, I did not deem it necessary to recalculate the work. 
With the data already mentioned, I proceeded to determine the latitude of a Cardinal 
point, namely, the State House at Boston, by comparison with several of the principal 
stations, as follows :— 
No. Place compared with Boston State House. torneo ead 
1) New Bedford Mariners’ Church, ‘ : ‘ 42° 21' 29” 84 
2) Harris Street Church in Newburyport, —. ‘ ‘ 29 .95 
3) Salem East India Marine Hall, ; ‘ . 30 .38 
4) Saint Ann’s Church in Lowell, . ; ‘ ‘ 20 .82 
5) Barnstable Court House, ‘ ‘ ‘ ‘ 31 ,23 
6) Sandwich Church in Sandwich, . . ‘ ‘ 29 .91 
7) Highland Lighthouse, Cape Cod, ‘ . . 28 84 
8) Nantucket South Tower, . : : : : 29 .38 
9) Holmes’ Hole Windmill, ‘ : : ‘ 30 .43 
9) 270.78 
Mean latitude of the State House, ‘ » 42° 21’ 307.08 
Mr. Paine’s Astronomical Result, . ‘ 42 21 28 .08 
Discrepancy, : : ‘ 7".05 
The results arrived at from these data, on the final reduction of the triangles of the 
Survey, using for the latitude of the State House 42° 21’ 30”, and for its longitude, that 
which is given by Mr. Paine, 4" 44" 16.6 west of Greenwich, are compared with the 
* Combining the meridional degree measured in Peru, in latitude 1° 80’, with the meridional degree measured in Mas. 
sachusetts, they give an ellipticity of 1-313th nearly of the equatorial radius. 
