Mr Scoresby m msasuriiig the heights of Cliffs^ ^c. ^9 
which case the presence of the sun is not necessary), or by find^ 
ing the true altitude of the sun, or other heavenly body, by 
means of an artificial horizon, and deducting this altitude from 
the angular distance, corrected for terrestrial refraction, between 
the sun and the visible horizon. The common tables of depression 
seldom going beyond 100 feet of elevation, a table for the mensura^ 
tion of heights should be constructed, extending to 20,000 or even 
30,000 feet. The semi-diameter of the earth, (or 21,000,000 feet), 
at th6 surface of the sea, being to the same increased by the height 
of the eye, as radius is to the secant of the depression of the ho- 
rizon, this depression, at the altitude of 100 feet, would ap- 
pear to be about 10' 38^/; at 1000 feet, 33' 36" ; at 2000 feet, 
47' 23"; at 3000 feet, 58' 0' ; at 4000 feet, 1° 6' 30" ; at 5000 
feet, r 14' 20"; at 10,000 feet, T 46' 10"; at 20,000 feet, 
2° 30'; at 30,000 feet, 3°3'40''^; at 40,000 feet, 3° 32' 5"; 
land at 50,000 feet, about 3° 57'. 
Hence, if we suppose, for example, on the top qf a cliff, the 
height of which was required, that the sun’s true altitude, by an 
artificial horizon, should be found to be 48®, and the altitude 
at the same instant (or the mean of two altitudes, at equal in- 
tervals before and after the same instant,) by the horizon, cor-f 
rected for terrestrial refraction, should be 49® 6' 30", the differ 
rence, 1 ® 6' 30", would be the depression of the horizon, corr 
responding, as appears above, with an elevation of 4000 feet. 
An error of a minute in the depression, at this elevation, would 
be productive qf an error only of 40 yards in the altitude ; and 
at the height of 20,000 feet, the same mistake in the depression 
would produce an error not exceeding 86 yards. 
This mode of determining heights, is applicable in all situac 
tions where the sea can be seen on the horizon, however distant, 
and is simplified in every case where the sun appears in azimuth 
above the sea, or, if over the land, with an altitude of 60° or 
upwards ; so that, with a common s^tant, it can be brought tq 
the horizon on the qpposite side of the zenith. 
The only circumstance, perhaps, that will render the practice 
of this method in any way uncertain, is the variable nature of the 
terrestrial refraction. Whether an allowance in minutes of one- 
twelfth of the distance of the horizon in miles, (the mean effect 
at equal altitudes), combined with the refraction produced by 
