90 SURVEY OF MASSACHUSETTS. 
In consequence of a remark of Mr. Hassler, that differences of longitude obtained by 
transportation of chronometers do not possess the requisite precision for determining the 
elements for the reduction of the triangulation, and are consequently unfit for geodetic 
purposes, I was induced to compare the results derived from all the chronometric differ- 
ences of longitude, which, according to the plan pursued, would produce a weight worth 
noticing, (except Williamstown and Pittsfield stations, which stations, as I have before 
noticed, are presumed to be affected by a deflection of the plumb line,) with Bessel’s 
latest mean result from the ten trigonometric surveys hitherto executed. For this pur- 
pose, I first ascertained that the meridians of the Massachusetts survey were sufficiently 
accurate, since a change in their convergency of — 2".94, in latitude 42° 21 30", fora 
difference of longitude of 1° 58’ 30”.27, would fit them to Bessel’s elements. I then pro- 
ceeded to compute the value of the degree perpendicular to the meridian for the latitude 
of the State House at Boston, (namely, 42° 21’ 30”,) by means of Mr. Paine’s longitudes 
of the principal stations, which were obtained directly from the State House, and omit- 
ting those intermediate stations which were not directly compared therewith, excepting 
Nantucket, which, by Mr. Paine’s report, appears to have been compared directly with 
New Bedford. But, as I have presumed there might exist a difference of opinion respect- 
ing Nantucket, that is, whether it should be compared with Boston or New Bedford, I 
have compared it with both, and have taken a mean of the results; presuming, further, 
that Mr. Paine frequently hastened his journey as rapidly as possible from Boston to 
Nantucket, and from Nantucket to Boston, by the way of New Bedford, and that there- 
fore both comparisons would be equally entitled to consideration. Throughout the whole 
of these comparisons a relative weight, proportionate to the polar angle subtended, has 
been given to each value obtained. 
Degree perpendicular| 
No. Stations compared. to ge Relative Weight.) Product in Feet. 
Dz. Ww. 2D ow, 
1 |Boston and Northampton, . . . 365119 1.00 865119 
2 66 SMOLIN RHE as as Ee 365356 0.97 354395 
3 “6 Greene, 4 7s 365198 0.98 357894. 
4. se HOW OICOneh. 4 a 8 365904 0.47 171976 
5 “6 fe Bamisiable,. ya eti cs 365804 0.48 175586 
6 66 fe Gipucenicn, «34. s 365991 0.25 91498 
7 " H SMPOHOMOY, et 6 os 366382 0.68 249140 
8 os HERI Oth, 4a bs 367653 0.25 91913 
9 “ DATING i 366897 0.64 234814 
10 “  INAMMICKey os 4 rk. 365329 0.62 226504 
Aggregate, 6.34 2318839 
Paine’s mean value, 365747 
By comparing the Nantucket station with New Bedford, the tenth result becomes 
364690 feet, with a weight of 0.52. This, substituted for No. 10 in the table, gives a 
mean result 365701, which, added to the result before obtained, and divided by 2, gives 
365724 feet for the value of the perpendicular degree. This value I have adopted in 
computing the succeeding elements, which are compared, in the following table, with 
corresponding elements obtained by Bessel. 
