171 



tions 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 woidd 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 j 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 y in the horizon, by the formula, 



which gives P T == 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 

 QT = 4' 34" ; and with this distance we shall easily find 

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

 atN* 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 



1 



~R 



tang. P T — 



(1-c) 



tang. Q T = 



1 



V 2h' 



(1-c) 



whence we deduce 



h' = 



R (1 — c) z tang. 2 Q T 

 2 



= 202 2 toises. 



