58 
Dr. Brinkley on the 
. exact constant of refraction will be found one of great diffi- 
culty, if we consider the nature of it. Mr. Bessel and I have 
proceeded by different methods, and, in some respects, my 
method appears more likely to lead to an accurate result. 
Mr. Bessel’s object is to obtain a formula that shall em- 
brace all elevations from the zenith to the horizon, and, there- 
fore, he necessarily assumes a law of variation of density in 
the atmosphere. 
In my investigation, I only consider zenith distances not 
greater than about 7 5 0 or 7 6°, where no sensible effect is 
produced from our ignorance of the law of variation of 
density. Let us consider the advantages and disadvantages 
of each method. 
Mr. Bessel* supposes the equation of density to be 
P=(p)e g — i 
p being the density at the height, as & ( p ) that at the surface, 
a being the radius of the earth, and l the height of an uni- 
form atmosphere. He proposes to find g, so that the formula 
of refraction deduced may satisfy the observations. He has 
therefore two unknown quantities, g, and the constant of re- 
fraction, k. 
When we consider the irregularities of refraction at low 
altitudes, and the number of observations required to make 
those irregularities disappear, it may be thought that the, pro- 
blem is unnecessarily involved by requiring the investigation 
of two unknown quantities, and, under the circumstances of 
the case, there is reason to suppose that the observations may 
be satisfied within certain small limits, by assigning values 
* Astronom. Fundament, p. 28. 
