VOL. LVIII.] PHILOSOPHICAL TRANSACTIONS. S/l 



■ the line ad. At a and n marks were placed, and 3 or 4 feet north of n, which 

 was 4- of a mile from A, the instrument was set up; then, in the same manner 

 as above, the vertical wire in the telescope was brought in a line with a and n, 

 and the vertical axis made fast; the telescope was then turned to point to the 

 northward, and a third mark placed, &c. &c. In this manner the line a n was 

 continued to b. Having continued the line to b, it fell 22 cha. 31 1. west of 

 the point d: we then returned and laid off eastward ofF-sets from the line ab, 

 at every 5th mile from B, proportional to the distance from a, and at the end 

 of every off-set placed a post, to form the line ad. 



/■about lOi miles = ab,"j 

 Off-setswere measured very correct at < the 10"" mile = fc, >and at the 3 points, b, c, d, 3 



I about the9"d» = hdj 

 marks were placed. At b the instrument was set up, to see if the 3 marks were placed in a right 

 line; when it appeared they were not exactly so; but, on moving the middle one -J- an inch 

 east, they then made a right line. 



In this direction we continued the lines b, c, d, to a, which fell 2 feet 2 inches 

 west of the point a, at q. The distance a q being so small a quantity, gradually 

 rising, in 10 miles, we thought it would be superfluous to change the direction, 

 and therefore returned to the point b, and extended the line northward, 

 proceeding in the same manner as before. Having continued the line to e, 

 it fell l6 feet 9 inches east of the point d. Hence the off-sets from this line 

 to the true line ad. And as we passed by the off-set posts made from ab, we 

 measured the distance of this line ae from the said off-set posts. 



These measures give the difference of the results of the two lines ab and ae ; 

 that is, the off-set posts from the line ab, which form the true line ad: And the 

 off-set posts from the line ae traced last, that also form the said line ad, will be 

 distant from each other, at every 5th mile, as was set down; which was a sufficient 

 proof that the line ab is the arch of a great circle; but, as a further confirmation 

 that no error could arise, they observed at different points in the line the right 

 ascensions of the meridian when the star S ursae minoris passed an azimuth 

 corresponding to the direction of the line, bfeing in the upper part of its circle. 

 The method of proceeding was in the same manner, as described before, for 

 finding the angle bam. 



Then are set down, as they were observed, with their reductions, at length, 

 a great number of observations of several stars, with the plane of the sector 

 turned both to the east and west, to determine the magnitudes, in degrees, 

 minutes, and seconds, of the celestial arcs, answering to the several parts 

 measured of the terrestrial meridian. 



Remarks on re-measuring the lines ivilh two rectangular levels or measuring 

 Jrames. — The levels used in this work were each 20 feet in length, and 4 feet 

 in height. They were made of pine, an inch thick, and in form of a rectangle; 



4 D 2 



