178 
THE RECENT REMARKABLE SUNSETS. 
lias passed after sunset until the appearance of the pheno¬ 
menon, and from the position of the place of observation 
upon the earth as regards latitude, or distance from the 
equator towards the pole. At the equator the sun in setting 
descends vertically in passing below the horizon, and as the 
whole circle of its course, 300°, is traversed in twenty-four 
hours, the extent of motion in one hour is 15°, which is the 
amount of depression of the sun below the horizon at one 
hour after sunset at the equator. 
In our latitude of 52°, however, the course of the sun in 
setting is oblique to the horizon, and the deviation from a 
vertical direction is the same in amount as the latitude, or 
52°; the consequence of which is that at one hour after sun¬ 
set the sun instead of having descended 15° below the horizon 
is only about two-thirds of that amount, or 10° below. The 
extreme case of this difference is of course at the pole, where 
the latitude being 90°, the deviation of the sun’s path from a 
vertical direction is 90°, or a right angle, and the sun travels 
round the horizon in a level course without rising or falling, 
being altogether above the horizon through the summer and 
altogether below through the winter. 
The time of appearance of the special sunset and sunrise 
phenomena was about an hour after sunset or before sunrise, 
and the position of the sun at that time was, therefore, about 
10° below the horizon in our latitude, consequently the angle 
was half that amount, or 5°, between the reflecting surface 
and the reflected ray. Then, as in any triangle all the parts 
can be calculated when any three of them are known, pro¬ 
vided that one of the known parts is a side so as to give a 
measure of length ; in the triangle that is formed by the 
horizontal reflected ray, the vertical line from the place of 
observation to the centre of the earth, and the oblique line 
from the reflecting surface to the same centre, one side is. 
known to be 4000 miles length (being the half diameter of 
the earth), and two angles, 5° and 90°, are known (the latter 
being a right angle between the horizontal line to the horizon 
and the vertical line to the centre of the earth); the long 
side of the triangle can then be calculated, and amounts to 
4015 miles, or 15 miles more than the distance from the 
surface to the centre of the earth, and this gives 15 miles as 
the elevation of the reflecting surface above the surface of 
the earth. 
This calculation gives the height for a reflection at the 
horizon, but the special phenomenon was seen at an eleva¬ 
tion of about 20° above the horizon, and a further calculation 
has therefore to be made for ascertaining the actual height of 
