336 Mr Galbraith on Trigonometrical Surveying 



the co-efficient of terrestrial refraction computed by formula 

 (14), and D the observed depression or zenith distance, di- 

 minished by 90°. 



In like manner, the height of one point above another will 

 be obtained from the formula 



dh = K sec i u cot {S + (» — 0.5)it} + &c or 

 dh = Acot{S + (« — 0.5) m} . . . . (B) 

 sufficiently near for moderate heights, such as those found in 

 this country, in which K is the chord between the stations, u 

 the angle between their verticals, and n the co-efficient of 

 refraction, or, even using A, the arc between them in feet, 

 and rejecting the other terms as insensible in our observa- 

 tions. 



Constant log for (14) .... 



t r= 64° log x 2 (table xviii.)* 



t — 64° log (table xx.)* .... 



F = 0, 5 - a 4=.0, 6 -»S 



b — 29.75 in. log . 



n= 0.07S05 . 



1.0 



0.7434 log 



7-57877 



9.97502 

 9.99940 



9.87122 



1.47349 



log 8.89790 



0.06C082 



4e = V l0: 



1 + n — 1.07905 log x 2 = . 



from geodetic tables . . 7.020582 



D==0°8'21".2tan*log .... 4.771174 



dh= 72.1 feet log .... 1.857838 



The height of the station above the level of the sea at high 

 water nearly by formulas (14), and (A). 



II. By a mean of several observations, the observed zenith 

 distance of Carnethy Cairn was 88° 34' 16" from the same 

 station, while the barometer stood at 29.725 inches, and the 

 thermometer at 63°.5. 





* These are the numbers of the auxiliary tables accompanying Ivory's 

 tables in my collection of Mathematical and Astronomical Tables. The 

 value of / is taken from the same table, iv., page 64 of the introduction to 

 them, while log. O is taken from my previous paper, in No. LI. of the Edin- 

 burgh New Philosophical Journal. 



