328 Mr Galbraith on Trigonometrical Surveying 



from which it is usual to deduce it by experiment. Indeed 

 the latter method cannot be generally followed without great 

 expense both in money and time. If, for example, an ob- 

 server on the summit of Benlomond should proceed to take 

 the elevation or depression of a hundred mountains round bis 

 range of the horizon, then to make reciprocal and simultaneous 

 observations on Benlomond from all these hundred mountains, 

 it would require one hundred surveying parties placed on 

 their summits provided with all necessary instruments and ac- 

 commodations, thus entailing an expense upon the country far 

 surpassing its finances, great as they may be, or otherwise 

 causing a corresponding loss of time to enable two parties to 

 accomplish the same end. It is clear, therefore, that, though 

 in some peculiar situations this mode may be occasionally fol- 

 lowed to serve particular purposes, such as determining the 

 amount of terrestrial refraction now and then, which may be 

 sufficient for ordinary practice, yet it cannot be generally fol- 

 lowed. 



From these considerations it has been an object with me for 

 a considerable number of years past, during which I have, in 

 conjunction with others, made numerous observations, baro- 

 metric and thermometric, on many of the mountains of Scot- 

 land, to deduce, among other results, from these, combined 

 with known laws regulating the refringent power of the atmo- 

 sphere, such as pressure, temperature, elastic force of vapour, 

 &c. a formula depending upon the employment of the usual 

 meteorological instruments, that would give the co-efficient of 

 terrestrial refraction independent of reciprocal and simulta- 

 neous observations, which, from what has been just said, are 

 frequently, and at least generally, impracticable in an exten- 

 sive survey. 



In order to determine the co-efficient of terrestrial refrac- 

 tion for pressure and temperature at the place of observation, 

 we have from the known laws of hydrostatics 



« = RD 4 ^ (l) 



in which n is the co-efficient of refraction, R the refringent 

 power of dry air, D its density, r the mean radius of the earth, 

 and I the height of the homogeneous atmosphere. 



