171 



tiohs on horizontal refractions. The following are the foun- 

 dations of the calculations, of which we have given only the 

 result, in that chapter. Let m (fig-. 2) be the Peak of Te- 

 neriffe, and N the coast, the distance of which from the foot 

 of the Peak is the arc P T Q = 2° 49' 0". As refraction 

 makes objects appear higher than they really are, it will be 

 possible to see from the top of the Peak the point N, al- 

 though it is concealed by the curve of the Earth. This point 

 will be really visible if it be elevated enough to send forth a 

 ray, which, in describing the curve N T M across the strata 

 of the atmosphere, only skims the Earth in T. From the 

 summit of the Peak we should perceive then at once the 

 points T and N, and an observer placed in T would see the 

 points M and N in his horizon N' T M'. If we designate 

 by h = 1904 toises, the height of the Peak, according to the 

 geometrical measurement of Borda ; by R = 3271225 toises, 

 the radius of the Earth ; and finally by c the coefficient of 

 the terrestrial refraction, the mean value of which was found 

 to be 0 08 by Mr. Delambre ; we shall have the distance 

 P T, at which the observer ought to be in order to see the 

 summit M, at M' in the horizon, by the formula, 



1 V^h 



tang. PT = ~- 



b (1— c) R 



which gives PT = 2«7' 26 ", Such is the greatest distance 



at which we can perceive the Peak from the level of the sea. 



If we deduct P T from P T Q = 2° 49' 0", there will remain 



Q T = 4 1 34" } and with this distance we shall easily find 



the height N Q = h', which the coast must have to appear 



at N ' at the horizon. In fact, if in the preceding formula 



we substitute Q T for the arc P T, and h' for the height h, 



we shall have 



tang. QT= L_ ^j^ 7 . 



(1 — c) R ' 



whence we deduce 



R (1 — c) 4 tang. Z QT 



