87< PHILOSOPHICAL TKANSACTIOM9. [aNNO l/fiS. 



trial measure of the distanceof the said parallels is next to be found. This is 

 composed of the sum of the lines np, cd, Dg, and ar, the last-mentioned line 

 being the reduction of ab to a meridian line passing through a; therefore br 

 expresses a parallel of latitude passing through b. Let Bt be an arch of a great 

 circle drawn perpendicular to the meridian line ar produced. The triangle BAt, 

 on account of the smallness of its sides with respect to the radius of the earth, 

 and the smallness of the angle BAt = 3» 43' 30", may be taken for a plane 

 rectilinear triangle, in what follows, without any sensible error, as will appear 

 to any one who makes the trial. — ^Therefore it will be, by proportion, as radius 

 is to the cosine of the angle BAt = 3" 43' 30', so is ab = 43401 1.6 English 

 feet, to At = 433094.6 English feet. But this is to be lessened by the small 

 quantity Rt, or the distance of the parallel circle br from the great circle Bt, which 

 is to a 3d proportional to the diameter of the earth and the line br, as the 

 tangent of the latitude of the point b, to the radius. Whence Rt = 1 5.8 feet; 

 which subtracted from At just found = 



.1!; ;,'. -J 43 3094.6' leaves AK ss 433078.8 feel 



To which add\ Y= Sin 

 as found before r '''' = ^^^^^^ 



The'stim'is! . ! . ; , 1 ... . = 538067 feet 



== an arch of meridian intercepted between the parallels of latitude passing 

 through the points n and A, answering to the celestial arch 1° 28' 45". 



Then say, as 1° 28' 45* : is to 1° : : so is 538o67 feet, to 663763 English feet, 

 which is the length of a degree of latitude in the provinces of Pennsylvania and 

 Maryland. The latitude of the northernmost point n, was determined from the 

 zenith distances of several stars, = 39° 56' 19", and the latitude of the 

 southernmost point a = 38° 27' 34". Therefore the mean latitude expressed 

 in degrees and minutes is = 39° 12'. 



To reduce this measure of a degree to the measure of the Paris toise, it must 

 be premised, that the measure of the French foot was found on a very accurate 

 comparison, made by Mr. Graham, of the toise of the Royal Academy of 

 Sciences at Paris, with the Royal Society's brass standard, to be to the English 

 foot, as 1 14 to 107. See Phil. Trans, vol. xlii, p. 1 85, or p. 606, vol. viii, of these 

 Abridgments. Therefore say as 1 14 : is to 107 " so is 363763 the measure of 

 the degree in English feet, to 341427 the measure of the degree in French feet, 

 which divided by 6, the number of feet in a toise, gives the length of the 

 degree = 569044- Paris toises, in the latitude 39° 12' north. 



Such is the length of a degree in this latitude, supposing the 5 feet brass 

 standard made use of in this measure to have been exactly adjusted to 

 the length of the Royal Society's brass standard. It was really adjusted by 

 Mr. Bird, by his accurate brass scale of equal parts, which he makes such 



