62 



Rejecting the four last results in consequence of their difference 

 from the mean, the others give the value of a degree of the meridian 

 in English feet at the several middle latitudes as follows: 





FIRST RESULT. 





SECOND RI 



]SULT. 



No. 



Middle Latitude. 



Length of Degree. 



No. 



Middle Latitude. 



Length of Degree, 





o ' " 



Feet. 





o ' " 



Feet. 



1) 



42 2 44.05 



364313.17 



3) 



42 13 19.20 



364348.25 



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 



7) 

 8) 



41 59 17.10 



42 4 42.60 



340.59 

 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 

















THIRD RF S 



8) 



336 32 19.90 



8) 2535.39 



It) 



41 39 39.10 



364385.00 





42 4 2.48 



364317.00 





In the absence of the necessary data, to reduce the values thus ob- 

 tained to the same middle latitude, Mr. Borden referred for the occa- 

 sion to the table in Rees's Cyclopaedia, under the article Degree, 

 which purports to give the value of meridional degrees of the terres- 

 trial spheroid for every degree of latitude, supposing an ellipticity of 

 •j-y^th of the equatorial radius ; and which indicates 57 feet as the 

 increase in the value of the consecutive degrees, from the 40th to 

 the 43d of latitude. Applying this increase, by arithmetical progres- 

 sion, to each of the foregoing values of the meridional degree, he 

 inferred from them a value corresponding with the middle latitude 

 42° ; and with the values thus reduced, and giving to each value a 

 weight proportionate to the number of comparisons on which it was 

 based, he obtained 364334 feet for the length of a degree whose mid- 

 dle latitude is 42°. The length of a degree perpendicular to the me- 

 ridian, at the latitude of the Boston State House, he found from the 

 convergency of the meridians to be 365511.33 feet, which value also 

 he adopted. Its accuracy was tested by applying the results of trigo- 

 nometrical measurement to the differences of longitude ascertained 

 by Mr. Paine's chronometrical observations. The following values 

 of degrees perpendicular to the meridian were attained in the same 

 manner : 



