34G Mr Galbraith on Trigonometrical Surveying, fyc. 



2. In carrying out these views, will the Koenigsberg Astro- 

 nomical Refractions, given by M. Bessel in the Tabulae Re- 

 giomontanaa, be conformable to the climate of Greenwich ? 

 To me there appears to be some doubt, even though they have 

 been adopted by Mr Airy, the Astronomer-Royal there. 



3. If the formula (14) be restricted to primary triangula- 

 tion, by assuming a mean value for 



F - 0.7456, there will be obtained for secondary, 



n " §Bi - h C i +£<*— *oV ' i +*'&■— «*3 • • • • ( I5 ) 



II. Const log = log ^ = 7-451274. 



4. If, instead of using proportional logarithms, the usual 

 tables of sines, tangents, &c. be employed, the following for- 

 mulae must be substituted in place of those at page 341. 



1. tan u — tan p cos /. 



2. sin X = sec p cos u cos z. 



3. I - X + u. 



4. tan m = tan p sin t sec X. 



Here u is minus in the first and fourth quadrants of t, and 

 plus in the second and third. 



In like manner m is west in the first and second quadrants 

 of t, and east in the third and fourth. 



These formulae may all be included in the same operation 

 as in the example in page 343, and they will be found very 

 useful in finding latitudes and azimuths by the pole-star. 



P. S. — Since the preceding paper was drawn up I have ap- 

 plied the small correction to the latitude, on account of the 

 irregularity of the motion of the star between observations, 

 first pointed out by Soldner, and estimated the probable error 

 by the formula of Baron Fourier, and the final latitude of 

 Inchkeith Light is 56° V 59".82 N., with a probable error of 

 + 0."5. The Baron's formula, however, shews merely the 

 deviation from consistency, and not the absolute error, because 

 it takes no account of constant errors in the instrument, &c. 



