flOS PHILOSOPHICAL TRANSACTIONS. [aNNO I768. 



found by equal altitudes of stars, the times were computed when the same or 

 other stars would pass the azimuth of the line pr ; and, at the time computed 

 for any star, the intersection of the cross wires of the transit instrument being 

 brought to cover the star, the telescope was turned down to the horizon, and a 

 land mark was fixed up at the distance of about half a mile, answering to the 

 intersection of the wires. In like manner, by other stars, several other marks 

 were fixed up, and the mean of all was taken. In this direction the line pr was 

 continued ; and though it was at first intended to extend it only to r, to the 

 distance of lO' of a great circle, it was in fact prolonged somewhat further, to 

 s, PS being = 12.312 miles, or lO' 45* of a great circle. Now PC being = 2.991 

 miles, or I' 37* of a great circle, the angle npc is = 89° 58' 55* ; from which 

 NPs = 89° 55' 51" being subtracted, there remains the angle spc or arc = 3' 4" 

 whence ac, or the distance of the parallel pcr at c, south of a, should be 14.1 

 feet. But it having been made a rule, in dividing the provinces of Pennsylvania 

 and Maryland, to trace out the parallels of latitude by the observations taken 

 with the astronomical sector only, the sector was put up at p and s successively 

 (see fig. 3), and the zenith distances of the stars Capella, a. Lyrae, and others, 

 were observed at both places ; whence the point s was concluded to be 43 yards 

 or 129 feet = so, more northerly than p ; and thence it was found by calcu- 

 lation, that the parallel of latitude pa at the point c should be 45-i- feet, := a c, 

 distant from the great circle ps, and to the south of the same ; and the point c 

 was placed accordingly, by laying off 45^^ feet = ac, at right angles to the line 

 pa, from the point a towards the south. 



ca found by the sector being 45^ feet, and found by the azimuth of the line 

 PS, being 14.1 feet only, it follows, that had the position of the point c been 

 determined by the latter method, instead of the former, it would have been 

 placed 3 1 .4 feet more to the northward than it was found by the sector ; and 

 consequently the length of the degree of latitude would have come out 21 feet 

 longer. But the difference is so small, that it only serves to confirm the exact- 

 ness of the work, and renders it unnecessary to enter into any consideration, 

 which of the two methods ought to be preferred. The meridians np, cd, and 

 AM, were found by celestial observations. The method of proceeding was as 

 follows : To find the meridian am, and the angle that the line ab makes with 

 the said meridian : The equal altitude instrument being set up at the point a, 

 with its vertical axis over the said point, equal altitudes of stars were observed lor 

 finding the motion of the clock. The time was next computed when some 

 northern stars would pass the meridian by the clock, at which instant, shown by 

 the clock, the vertical wire in the telescope was brought to bisect the star; 

 and, the vertical axis of the instrument remaining fixed, the telescope was 

 turned down in the same azimuth to the horizon, and a candle placed opposite 



