VOL. LVIII.] PHILOSOPHICAL TRANSACTIONS. 573 



foot for a variation of 180° of Fahrenheit's thermometer; whence the expansion 

 answering to 4 times the length of the brass standard, or 20 feet, or the length 

 of one level, would be ,\V6 of an inch for the same difference of the ther- 

 mometer; and T-^'-Zj-g- of an inch for 1° of the same thermometer. Therefore, in 

 order to find the correction of column 7th, the constant quantity ,00258, was 

 multiplied by the difference of 62, and the degree of the height of the ther- 

 mometer; and that product, again multiplied by the number of levels measured, 

 gave the correction required in inches and decimal parts of an inch : which was 

 additive or subtracive, according as the thermometer was higher or lower than 62 

 degrees. 



These geographical measurements are then all set down very particularly. 



Hence the line ab = 21696.47 levels -|- 892.34 inches -f- 94.51 inches 

 =. 43401 1.64 feet. The breadth of the rivers was found by measuring a base, 

 and taking angles with a Hadley's quadrant. 



Note. — ^The reckoning was kept by stretching a rope in the line to be 

 measured, in general =12 levels, which was often proved: and it was almost 

 impossible that an error could arise; as they always began tlie rope with the 

 same level, and ended it with the other; the rope not being removed till the last 

 level was set. The person that stretched the rope, sometimes Mr. Dixon, and 

 sometimes Mr. Mason, kept the count of the number of ropes measured: 

 though the mile posts in the lines ab and dc were sufficient for that purpose, 

 as the lines had been so often measured before. In the line np tliere were no 

 mile posts, but 2 or 3 intermediate marks, which they found to agree in a 

 general law with the levels. Supposing the levels exactly = 20 feet each; 

 then in the line np a mile per chain measure = a mile and 9.44 feet by the 

 levels; and in the line cd a mile per chain measure = a mile and 9.86 feet 

 by the levels. They took notice of these differences as they measured from b 

 to A, always finding the miles greater by the chain measure; which shows that 

 the chain was continually extending itself by use; as they had direct proof ofj 

 being obliged to contract it every day, and re-adjust it to its proper length by 

 means of the standard chain. — For observations of several stars, they found the 

 latitudes of the points a and n; viz. the mean lat. of n 39° 56' 18'''.9; arch 

 between n and a = 1° 28' 44".9; which leaves the lat. of the point a 

 38° 27' 34", and the mean lat. 39° 1 1' 56". 

 The Length of a Degree of Latitude in the Province oj Maryland and 



Pennsylvania, deduced from the foregoing Operations; by the Astronomer 

 • Royal. 



The difference of latitude of the points n and a, or the amplitude of the 

 celestial arch, answering to the distance between the parallels of latitude passing 

 through N and a, has been found by the sector, to be 1° 28' 45'''.0. The terres- 



