330 Mr Galbraith on Trigonometrical Surveying 



under given circumstances by formulae (A) and (B), page GO 

 of the same work. 



From various experiments on the refringent power of the 

 air, and by numerous astronomical observations, the co-effi- 

 cient of the astronomical refractions at the freezing point and 

 30 inches of the English barometer, is 



« = 0.000294144 = PD nearly ... (8) 



This value of * becomes at 30 inches of the English barometer 

 and 50° of Fahrenheit's thermometer 



« = 0.000283003 (x) 



This is the standard pressure and temperature of Ivory's table 

 of refractions, which, on account of then- extreme accuracy, I 

 o-enerally prefer, and to whose standard, for the purpose of 

 employing the auxiliary tables accompanying it, the following 

 formula will be adapted. The co-efficient of astronomical re- 

 fraction here assumed at 45°, or « = 0.000283003, equal to the 

 length of the circular arc to radius unity, or equal to 53". 38, 

 agrees closely with 58". 36, that adopted by Ivory for his table. 

 But this co-efficient varies directly as the pressure, and in- 

 versely as the temperature, of the atmosphere, consequently 



^4-rb <9) 



in which b is the given pressure, B the standard, and t the 

 given temperature. 



In like manner, the barometer must be corrected for the 

 expansion of mercury by heat. Let this expansion for 1° of 

 the centigrade thermometer be denoted by /3', while r is the 

 temperature of the mercury indicated by the attached ther- 

 mometer, and equal to 0.00018, then 

 b l l 



C. = CL — 



(10) 



B 1 + /3 t 1 + /3' t 



Combining the results in (8), (9), and (10), in formula (7), and 

 it becomes 



By observation it has been found necessary to modify this ex- 

 pression by considerations depending upon the difference of 

 altitude, and the expansion of moist air. From barometric 



