60 



those effected by Mr. Paine's chronometrical survey of the 

 same state, reported in favour of its publication among the 

 Transactions of the Society, which was ordered accordingly. 



Mr. Borden's paper gives an abstract of the principal results of the 

 Trigonometrical Survey of Massachusetts, begun in the year 1831, 

 and recently brought to a conclusion. It also gives a comparison of 

 these results with those obtained by Robert Treat Paine, Esq., from 

 observations with a Troughton's sextant and mercurial horizon, and 

 chronometers transported to different stations. 



The base line chosen for the Massachusetts survey, was on the 

 Connecticut river, above Northampton ; it was 7.388 miles long. 

 The apparatus with which it was measured, was devised by Mr. Bor- 

 den. It was fifty feet in length, and constructed on compensating 

 principles. The measurement was marked by sections of 1000 feet, 

 and was tested by a remeasurement in an opposite direction. The 

 sum of the discrepancies, without regard to signs, between 25 spaces 

 measured for 1000 feet each from N. to S., and the same spaces 

 measured from S. to N., was 3.567 inches ; making an average dis- 

 crepancy of 0.14268 of an inch; and the first measurement of the 

 entire base exceeded the second in length by 0.237 of an inch. The 

 standard of length first selected, was a scale of two feet, constructed 

 upon compensating principles, and of course unsuitable for subdi- 

 vision. Being afterwards compared at Washington, by Mr. Hassler, 

 Superintendent of the United States' Coast Survey, with his 82 inch 

 scale of Troughton's construction, and which is an exact copy from 

 the well known Troughton scale of Sir George Shuckburgh, it was 

 found to be 0.0018 inches too short, at the temperature of 57°. 5 Fah. 

 But a part of the triangles having been, previous to this comparison, 

 computed according to the Massachusetts scale, it was thought best 

 to complete the calculations in the same manner, and make correc- 

 tion afterwards, when the proper standard should be fixed upon. For 

 this standard, Mr. Borden chose Hassler's 82 inch Troughton at the 

 temperature 62° Fahr. A trial base was not measured, and was not 

 deemed indispensable, as the principal stations will ultimately be con- 

 nected with those of the coast survey, and referred to Mr. Hassler's 

 base. 



The height of the stations above the sea-level was determined from 

 comparison with a principal station on Fay's Mountain, situate in 

 the town of Westboro', about thirty miles nearly west of Boston ; the 

 height of which was ascertained from levels carried forward, by 

 means of vertical triangles, from five points of tide water, viz : at 



