Mr Galbraith on the English Arc of the Meridian. 265 



that the trigonometrical operations haA^e, in general, been con- 

 ducted with so much precision, that he was justified in the 

 process which he pursued. The diflFerence between my new 

 calculations and those of the late General Mudge amount to a 

 few feet only, when both are given in the imperial standard. 

 Having come to this conclusion, it might be supposed that I 

 need not have extended my remarks farther ; but as some cir- 

 cumstances are alluded to that have not hitherto been observ- 

 ed, it may not, perhaps, be unnecessary or uninteresting to 

 notice them. It is very probable that new computations have 

 been made in the Ordnance Map Office nearly analogous to 

 ours ; but as they have not, to my knowledge, been yet made 

 public, I may thus be excused for communicating mine. 



I. Of the Bases. 

 From the remarks made by General Roy himself in the 

 Trigonometrioftl Survey, vol. i. page 15, &c., there can be little 

 doubt that, of the first base measured on Hounslow Heath with 

 glass-rods, the results were in Roy'^s own scale. Again, from 

 the observations made by Mudge in p. 218, it is clear, I think, 

 that the second base was measured in terms of Ramsden's 

 scale. Now, the ratio of the first to the imperial standard is, 

 from the best information we possess, 1.0000244 to 1, and that 

 of the second as 1.0000691 to 1. The same applies to the 

 bases measured on Salisbury Plain and Misterston Carr. From 

 these data, the whole arc is readily converted into the impe- 

 rial standard. 



1. Roy's base, measured on Hounslow Heath, In terms of his own 

 scale, at 62° Fahrenheit, and 100 above the mean level of the sea, 



was 27404.0137 feet. 



Reduction of Roy's scale to the imperial standard 



= 27404X0.0000244= . . . + 0.6699* 



Length of base in imperial feet, .... 27404.6836 



Log. of 27404.6836 feet, 4.4378248 



Reduction for 100 feet of height to sea, . . — 21 



Reduction to chord, — 



Log. at level of the sea (1784), . . . 4.4378227 



* The ingenious writer of the article Trigonometrical Surveying in the Ency- 

 clopedia Britannica has applied this correction with a wrong sign. 



