86 SURVEY OF MASSACHUSETTS. 
FIRST RESULT. SECOND RESULT. 
No. Middle Latitude. Length of Degree, No. ° Middle Latitude. Length of Degree. 
1) 42° 2/44” .05 364313.17 feet, 3) 42° 13’ 19” 20 364348.25 feet, 
2) 42 7 53 .70 389.25 4) 42 15 19 .70 420.25 
6) 41 54 7 .45 253.76 5) 42 17 1 .55 357.10 
2) 41 59 17 .10 340.59 seceding 
8) 42 4 42 .60 279.42 3) 45 40 .45 3) 1125.60 
12) 42 8 26 .95 236.76 
9) 42 8 24 .95 274,76 42 15 13 .48 364375.20 
10) 42 6 43 .10 447.68 
8) 336 32 19 .90 8) 2535.39 THIRD RESULT. 
ineli tti 11) 41 39 39 10 364385.00 
42 4 2 .48 364317.00 
In the absence of the necessary data, to reduce the values thus obtained to the same 
middle latitude, I referred for the occasion to the table in Rees’s Cyclopedia, under the 
article Degree, which purports to give the value of meridional degrees of the terrestrial 
spheroid for every degree of latitude, supposing an ellipticity of ;3,th of the equatorial 
radius; and which indicates fifty-seven feet as the increase in the value of the consecutive 
degrees, from the fortieth to the forty-third degree of latitude. Applying this increase, 
by arithmetical progression, to each of the foregoing values of the meridional degree, I in- 
ferred from them a value corresponding with the middle latitude forty-two degrees; and 
with the values thus reduced, and giving to each value a weight proportionate to the 
number of comparisons on which it was based, I obtained 364334 feet for the length of 
a degree whose middle latitude is 42°. The length of a degree perpendicular to the 
meridian, at the latitude of the Boston State House, was found from the convergency of 
the meridians to be 365511.33 feet, which value also was adopted. Its accuracy was 
tested by applying the results of trigonometrical measurement to the differences of lon- 
gitude ascertained by Mr. Paine’s chronometrical observations. The following values 
of degrees perpendicular to the meridian were attained in the same manner. 
Feet, 
1) From Boston State House and Northampton Church, : : ; ; 365177.60 
2) .# “ “ ss and Plymouth Court House, ‘ d ; -  865653.00 
3) * “ sé ‘sand Amherst College Chapel, . : ; ? 365025.00 
i Ss Springfield Court House and Plymouth Court House, ; ; 3 - 865888.43 
5) « &“ «“ «« and Highland Light, ae Cad, 2s ‘ . 365984,43 
So = Greenfield Church and Gloucester Church, ; ; 4 . 865420.76 
7) ‘ Boston State House and Pittsfield Church, . ; . ‘ ‘ 364193.11 
8) ‘ Plymouth Court House and “ oy ‘ . ‘ : - 864796.00 
9) ‘ Boston State House and Williamstown Church, . , ‘ , 364519.42 
Sum of the first 6 results, : ‘ : - 6) 3149,22 
Mean of the first 6 results, : ‘ : 365525.00 
et a pps 
The last three of these results are rejected on account of their discrepancy from the 
mean. ‘The astronomical observations for determining the longitude at Pittsfield and 
Williamstown are supposed to have been affected by mountain attraction; and I have 
adopted the value of the degree perpendicular to the meridian, as derived from the incli- 
