268 Mr Galbraith on the English Arc of the Meridmn. 



In all, the reduction of the distance between the perpendi- 

 culars to that between the parallels has been applied, a quan- 

 tity entirely overlooked in the survey. 



From a combination of the whole we have from 



Roy's base on Hounslow Heath, . 103GGG1.0G ft, £, = — 27-73 



Mudge's base on Hounslow Heath, . 103G418.83 ... i„ = + 30.04 



Mudge's base on Salisbury Plain, . 1036408.78... £3= + 19.99 



Mudge's base on Misterton Carr, . 103G3G6.48 ... i^= — 22.31 



Mean of the whole, . . . 1036888.79 



Now, dividing this mean by the length of the celestial arc 

 2° 50' 23" .497, and we have 1036388.79 -^ 2°.83986027 = 

 364943.58 feet, the length of one degree of the meridian at 

 the middle latitude 52" 2' 19" between Dunnose and Clifton. 



The value employed by M. Bessel agrees very nearly with 

 our third result from Mudge's base on Salisbm-y Plain, and is 

 consequently greater than our mean by about 20 feet, — a small 

 difference in a distance of somewhat less than 200 miles ; and 

 the consistency of the whole is a proof of the great care and 

 general accuracy of all the operations even at that early period. 

 Whence the accuracy of Bessel's conclusions cannot in any 

 appreciable degree be vitiated by the small discrepancy be- 

 tween the length of this arc, assumed by him, and that obtained 

 by me from direct calculation. In short, he, by taking from the 

 survey 1036337 feet, and multiplying this by 1.00007, Katers 

 number for reducing measures taken in Ramsden's scale to 

 those in the imperial standard, obtained 1036409.54 feet, 

 agreeing within less than a foot* of our third result, which, 

 converted into French toises, was used in his subsequent inves- 

 tigations. Having thus proved that the results, in whatever 

 w^ay they be derived, are as accurate as could in general be 

 expected, and that no error of consequence has been made so 

 as to affect any conclusions deduced from the commonly re- 

 ceived length of the arc of the meridian, I shall now pro- 

 ceed to make a very few concluding remarks. 



* Occasioned by the omission, in the Survey, of the reduction of the dis- 

 tance between the perpendiculars to that between the parallels. 



