REPRESENTING MEASURED ARCS OF THE MERIDIAN. 391 



These latitudes differ from those given in the Phil. Trans, for 

 1S03. They result from a new combination of the reductions 

 made by General Mudge of his own observations. More par- 

 ticulars on this point, and the reasons Avhich have obliged me to 

 introduce alterations in General Mudge's own data, will be con- 

 tained in a separate memoir. The distances of the different 

 parallels from Dunnose, were originally given in the Phil. Trans. 

 1803, pp. 441 and 487, as follows: 



Greenwich 52282*67 fathoms. 



Blenheim 74416-33 „ 



Arbury Hill 97720*00 „ 



^ Clifton 172722-83 „ 



From Kater's examination of the scale employed in the mea- 

 surement, these distances require to be multiplied by 0-00007, 

 and will be thereby respectively augmented 



3-66; 5-21 ; 6-84; 12-09. 

 The distances given above in toises correspond to the distances 

 in fathoms thus augmented. 



6. Hanoverian Arc. 



Taken from Gauss's Breitenunterscheid, ^c, p. 71- 

 7. Danish Arc. 



These results have been communicated to me by Schumacher: 

 They might be combined with those of the preceding measure- 

 ment, if it were not that the latitudes of the two arcs rest on 

 different stars, which would render the combination dependent 

 on the determinations of the declinations of these stars. I think 

 it right to avoid the danger of introducing error into undertak- 

 ings of such distinguished exactness, by bringing in a foreign 

 element, the more so as Lauenburg, which is 9S60'^-46 south of 

 Altona, is 2103l'^-51 to the east of the same, forming an angle of 

 nearly 65° with the meridian. The distance of its parallel from 

 tliat of Altona could not therefore be found with the exactness 

 which is attainable when the inclination to the meridian is less. 



