110 Mr Galbraith's Formula for 



risk we run of being visited sooner or later by some ''^powerful 

 Conqueror from the Interior,'''' That such a personage may 

 spring up is rendered more credible than we have hitherto 

 considered it, by the recent acquaintance formed with Dingaan 

 and Massalakitze. Our apprehensions are not strong of any 

 very formidable attack from these chiefs, or from any resembling 

 them in the interior. But it is well to know the character and 

 resources of all who may hereafter become our allies or our 

 eoemies *. 



FORMULAE FOR TRIGONOMETRICAL SURVEYING. By Mr WIL- 

 LI AM Galbraith, a. M. Communicated by the Author, 



Some time ago, it was proposed to me to undertake a series 

 of levels, at properly selected parallels, across the country, and 

 to delineate the sections of these, to serve as a basis for a Geo- 

 logical Survey and Map of Scotland. In consequence of this 

 proposition, my attention was directed to investigate and record 

 formula? and rules, for the purpose of fixing the positions of 

 different points, with regard to latitude, longitude, and eleva- 

 tion, above the mean level of the sea. The instruments chiefly 

 employed for this purpose, are generally the theodolite, the sex- 

 tant or reflecting circle, the spirit-level, and mountain barome- 

 ter. On many of the mountains and islands of Scotland, it oc- 

 curred to me that the dip-sector, when both horizons are visible, 

 might also be advantageously employed ; and some exertions 

 were made to provide as many of these different instruments as 

 might be required to perform the necessary operations in an ac- 

 curate manner, so that the final results might be worthy of con- 

 fidence. 



Problem I. 

 To determine the elevation of a given point, by the depression of 

 the horizon of the sea. 



In my Mathematical Tables, Example xix. Plane Trigonometry, 

 I have shown that the logarithm of the depression d^ in seconds to 

 the height in feet A, is expressed by the following formula : 



• We trust that ere this Dr Smith's expedition has started from the Cape. 

 From the zeal of the conductor we expect much, more especially as, from the 

 well known liberality of Sir James Macgrigor, he travels unfettered. 



