lU 



has exhibited a striking specimen of his great mathematical 

 skill (vid. Mec. eel. torn. 4. p. 246— 253 ) 



His series is sufficiently convenient for computing the hori- 

 zontal refraction, but in deducing from it tiie refraction at 

 87°43'l0" zenith distance, a good deal of calculation is ne- 

 cessary. I deduce the value of a=,0G02882 for the heights 

 of the barometer and therm, abovementioned, and then the 

 six first terms of the series (Mec. eel. torn. 4. p. 251)= 

 817" + I7r',4 + 50",2 + 17",4 + 6",4 + 2",7 + &c. 



The sum of this series must be nearly == 106?". 



Therefore we have at zen. dist. 87"42'10", barom. 29,50 

 and therm. 35°. 



Refraction, density decreasing uniformly = 16.'5r'',0 

 by observation - = 17- 26, 5 



uniform temperature - =17.47,0 



Hence as far as this zenith distance the refraction differs 

 only a few seconds from the mean resulting from the two 

 hypotheses. The difference is far less than what may arise 

 from the irregularity of refraction. 



At the same zenith distance, and same heights of the barom. 

 and therm. 



By the French tables ref. = 17'.21",0 



.By Bradley's formula = I7 48, 2 



By what 1 considered an 

 improvement of Brad- 

 ley's formula vid. art. 14 == 1? 25, 3 , 



