170 



In consequence of the remark of Mr. Hassler, that differences of longitude, 

 obtained by the transportation of chronometers, do not possess tho requisite 

 precision for determining the elements for the reduction of the triangulation, 

 and are consequently unfit for geodetic purposes, Mr. Borden was induced to 

 compare the results derived from all the chronometric differences of longi- 

 tudes, with Bessel's mean result from the ten trigonometric surveys hitherto 

 executed. For this purpose, having ascertained that the convergency of the 

 meridians derived from the Massachusetts survey was sufficiently precise, 

 since a change of -f- 2."78 would fit them to Bessel's elements, he proceeds, 

 through the medium of this convergency, to compute the value of the degree 

 perpendicular to the meridian for the latitude of the State House, Boston, 

 42° 21' 30", by means of Mr. Paine's longitudes of those of the principal sta- 

 tions (Nantucket excepted) which were obtained directly from the State 

 House, omitting intermediate stations not directly compared with the State 

 House, and using relative weights proportionate to the polar angle. 



No. 



Stations compared. 



Degree perpen- 

 dicular to me- 

 ridian in feet. 



Relative weight. 



Product in feet. 



1 



2 

 3 

 4 

 5 

 6 

 7 

 8 

 9 

 10 



Boston and Northampton, 

 „ Springfield, 

 ,, Greenfield, 

 ,, Worcester, 

 ,, Barnstable, 

 „ Gloucester, 

 ,, Monomoy, 

 „ Plymouth, 

 ,, Truro, 

 „ Nantucket, 



D 



365119 

 365356 

 365198 

 365904 

 365804 

 365991 

 366382 

 367653 

 366897 

 365329 



W 

 1.00 



0.97 

 0.98 

 0.47 

 0.48 

 0.25 

 0.68 

 0.25 

 0.64 

 0.62 



D X w 



365119 

 354395 

 357894 

 171976 

 175586 



91498 

 249140 



91913 

 234814 

 226504 





Aggregate, 6.34 



2318839 



Paine's mean value, 365747 

 Bessel's do. 365723 







Discrepancy in feet, 24 



By comparing one of the stations, viz. Nantucket, with New Bedford, with 

 which it was actually compared by Mr. Paine, the tenth result becomes 364690, 

 with a weight 0.52. This substituted for No. 10 in the table, gives the mean 

 result, 365701, which falls below that of Bessel as much, nearly, as the former 

 exceeds it, and is preferred by Mr. Borden. 



The conclusion from this examination is, that chronometric com- 

 parisons do afford the means of determining one of the elements of 

 the reduction of a trigonometric survey, viz. the value of a degree 

 perpendicular to the meridian, and that, too, with a degree of uni- 

 formity quite too great to be the result of a happy accident. 



