170 



values. For this examination, as was said, a mean of a very con- 

 siderable number of observations will be required, for each of the 

 zenith distances that shall be considered necessary to be examined 

 for the verification of the Table. 



The Table I have adopted for computing the mean values of log. 



t ' '"" I fvid. my Table I.) is the French Table of mean refrac- 



a sin. I ^ ■' ^ 



tions. It appears to me, that for zenith distance very near the 

 horizon, more weight is to be given to that than to any other we 

 possess. The well known accuracy, skill, and judgment of 

 M. Delambre, seem justly entitled to this confidence. He tells us he 

 constructed it by help of many hundred observations made by a 

 repeating circle from 70° to 90° 20'. 



But it must be confessed, that reference can no where be had to a 

 sufficient number of observations to verify the numbers in my 

 Table I. corresponding to any one zenith distance between 88° and 

 90°. Mr. Groombridge, to whom we are much indebted for his 

 immerous observations of Stars at low altitudes, was unable, from 

 local circumstances, to obserVe much below 88° ; above 88°, several 

 references may be had to observations sufficiently numerous, (among 

 others those of Dr. Bradley, computed by Mr. Bessel,_) by which 

 it will appear that Table I. is very exact, and consequently the 

 French Table of mean refractions from which it was deduced. 



When however it is required to compute the refraction for other 

 states of the Barometer and Thermometer, the results by my tables 

 and the French differ for low altitudes. This is occasioned from it 

 being supposed in the French Tables that the refraction is propor- 

 tional to the density, which is by no means sufficiently exact in very 

 low altitudes. ^ /,, .»;. . 



The mvestigations of M. Laplace, on which the French tables 



