1'30 Astronomical and Nautical Collections. 



Eighthly, this operation evidently supposes the standard re- 

 fraction of the tables to agree with the observations ; but, as a 

 test of this agreement, it will be proper to divide the sum of 

 the whole amount of the corrections, additive and subtractive, 

 by the sum of the several differences from the standard tempe- 

 rature respectively : and it appears that in order to bring these 

 quotients to equality, it will be necessary to alter the supposed 

 standard of the tables to 46°, instead of 48°. Ninthly, we 

 may ultimately adopt, as the best empirical correction to be 

 derived from that set of observations, the mean of the two cor- 

 rections thus obtained. Tenthly, the last column of the table 

 contains the quotient of the refraction at the standard tempera- 

 ture, divided by this mean correction : it will be justifiable, in 

 the present case, to reject two extravagant numbers, derived 

 from 7 and 9 observations respectively ; and, in order to satisfy 

 the most scrupulous, we may venture to reject the least of all 

 the numbers : hence, for the mean of the whole 20, we have 

 438.3; for the mean of the lower 10, 434.3, and of the upper 

 10, 442.3 ; half the difference 4, applied to the means, gives for 

 the lower extreme 430.3, and for the upper 442.3, the difference 

 of altitude being 7° 2' : and we may safely adopt, as the general 

 empirical correction for each degree of temperature, as far as 



R 

 these observations go, the formula -. The first star 



430 + 2 ALT. 



observed ought also to have been rejected in this computation, as 

 affording an irregular result, or too great a refraction : but it re- 

 mains to be ascertained whether the error is in the observation or 

 in the table: and, in fact, the empirical formula, here investigated, 

 will not afford a series of mean refractions agreeing very accu- 

 rately with any existing table ; although we may safely infer from 

 it, that the French astronomers were too precipitate in neglecting 

 the true correction for temperature which their own theory 

 would have afforded them, in opposition to the actual observa- 



