334 Mr Galbraith on Trigonometrical Surveying 



of the arc perpendicular to the meridian at latitude 45°, which 

 may for this and similar purposes be reckoned the mean ra- 

 dius of curvature of the earth very nearly. 



To simplify the calculation of n, the log. of ~ may be used 

 as a constant log. where B = 30 inches and t = 50° Fahren- 

 heit, the standard pressure and temperature of Ivory's refrac- 

 tions. Whence the auxiliary tables accompanying them to 

 correct for pressure and temperature may be employed, which 

 greatly facilitates the application of my formula. 



Log « = log of 0.000283003 . . G.451791 



Log r — log of 20922642 feet log . . 7.320616 



a. clog 2 . • • • 9.698970 



B = 29.9218 a . c . log . . . 8.524012 



I = 26100 feet a . c . log . . . 5.583379 



Log — = I const log • • 7.578768 



The formula will now be applied to the determination of 

 heights from observations which I lately made in the Firth of 

 Forth. 



Having procured, through the favour of Colonel Colby, from 

 the Ordnance Map Office, such lines and angles as I thought 

 desirable for this and other purposes, I made such additional 

 observations as gave the distance between Inchkeith Light- 

 house and my station on Inchcolm, from which, as a base, 

 triangles were extended to several eminences in the vicinity 

 of Edinburgh, such as Carnethy among the Pentlands, the 

 height of which, in conjunction with Professor Henderson, I 

 had determined with great care, in 1828, by the mountain 

 barometer, from numerous observations taken every ten mi- 

 nutes during some hours. The same barometer was employed 

 both at the sea-shore and at Carnethy Cairn, thus rendering 

 the barometer employed at the Calton Hill merely one of 

 comparison, thereby avoiding any error that might arise from 

 the use of different barometers. The results were published 

 in the Edinburgh New Philosophical Journal for October 1831. 

 The height is computed there by two different methods, the 

 mean of which is 1880 feet. I have repeated the calculations 

 with my new tables, which give 1880.7 feet, agreeing almost 

 exactly with the former. This height was verified by Mr 



