7^2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



therefore (-^— - 54° X 272.8) X ^~ = 3.1069 feet; which Feet. 



also add + 3.1069 



Again, from the comparison of the 50-feet chain with the standard 

 b, it appeared that the excess above 50 feet, in the temperature of 

 54°, was O.O9075 parts of an inch; therefore /fej X 8 = 0.0005 



part of a foot: this also add -f- 0.0005 



The sum of all the degrees shown by the thermometers placed by 



1372 



the sides of the 50-feet chain, was 1372; therefore (—7 54° X 



5 



4) X : — ■" = 0.0365 parts of a foot: and this add -f 0.0365 



The sum is 27682.3944 

 And for the reduction of the base to the temperature of 62 , viz. 



01237 x 272 8x8° 



for 8° on the brass scale, we have - — — \ =2.2497 feet; 



which subtract — 2.2497 



Therefore, the length of the base is , 2768O.1447 



which, neglecting decimals, may be taken at 27 680 feet. As to the probable error 

 of the above conclusion, Col. M. knows not how to form a just opinion. On 

 ground sufficiently hard, and otherwise favourable, he thinks a base of 5 miles 

 might be measured so accurately, as to afford a result not differing from the truth 

 more than 3 inches: but, on this occasion, he should not suppose the error can be 

 less than 6, nor more than 9 inches. 



Next follows a calculation of the sides of certain principal triangles in Cornwall 

 and Devonshire, not necessary to be here detailed ; and afterwards the sides of all 

 the other angles in succession, from the west towards the eastern counties. After 

 these particulars are stated the circumstances relating to the latitudes and longitudes 

 of the chief stations, and the direction of the meridian at the same. After which 

 occurs the following note : 



It may probably be expected, says Col. Mudge, that I should determine the directions of the meri- 

 dians at Black Down, Butterton Hill, and St. Agnes Beacon, by calculation, and afterwards compare 

 them with the observed ones 5 I have desisted from the measure in the body of the work, and reserved 

 the little I have to say for this note. If the earth were a perfect sphere, or an ellipsoid of known dia- 

 meters, the direction of the meridian, at any station not very remotely situated from the parallel of an- 

 other, might be determined, provided the direction of the meridian at that station were observed, and 

 the value of the arc subtended by the space between them pretty accurately ascertained, and also the 

 latitude of the station, at which the angle is given, nearly obtained. Thus, if it be required to find the 

 angle at Dunnose, between Beachy Head and the meridian, from the observed angle at the latter station, 

 and the arc between them, we shall have 39° 15'36".3, the co-latitude of Beachy Head, and 55' 28". 7 

 for the oblique arc. These data, two sides and an included angle, give 1° 26 v 48".4, for the difference 

 of longitude between Beachy Head and Dunnose, and 81° 56' 52''. .6, for the angle which the meridian 

 at the latter makes with the former station. The difference of longitude found in a rather more correct 

 way, has been heretofore shown to be 1° Q6' 47 ".93, and the angle at Dunnose was also shown to be 



