591 
of Edinburgh, Session 1881 - 82 . 
the ship must have been 7J miles beyond the horizon or altogether 
14 miles away. Taking the proportions shown in the figure, the 
top-mast of the upper image must have 
appeared at the height of 210 feet above 
the water edge, giving an angular eleva- 
tion of about ten minutes of a degree 
(9' 46"). 
The ray of light in rising from the ship, 
encountered air of less and less refractive 
power, and so was bent downwards to 
become horizontal, after which the same 
curvature was repeated inversely ; hence 
it follows that the index of refraction of 
the air at the top of the curve must have 
been less than that of the air below, in 
the ratio of cosine 10' to radius. Assum- 
ing for the season of the year, the tem- 
perature at the ground to have been 15° 
or 59° Fahr. ; its index of refraction comes out 1*0000283 ; where- 
fore the upper air must have had the index 1*0000232, and its 
density must have been what is due to a fall of 5*1 inches with 
the same temperature or to a rise of 86 degrees Fahrenheit with 
the same pressure. 
If we suppose the air to have been of its usual density almost 
up to the limit of height and then to have become suddenly rare, 
the path of the light would have consisted of two straight lines 
united by a short and quick curve, and the height would have 
been the half of 210 feet. But, if the change of density be 
assumed as gradual, the ultimate height must have been less than 
the half ; for a parabolic curve it would have been the fourth part. 
But all analogy tells us that the curvature becomes less as we 
ascend ; wherefore the vertex must have been at not more than 50 
feet above the sea-level. 
Thus, in order to produce any phenomenon like that described 
by Yince, either the barometric pressure must have decreased at 
the average rate of one tenth of an inch for each foot of rise, or 
the temperature must have increased at the rate of 1°*7 Fahr., or 
nearly one degree centigrade for each foot, ultimately to reach 
the extraordinary heat of 145° Fahr. And this condition of the 
