OF ILLUMINATING LIGHT HOUSES. 
217 
On Divergences. 
The actual quantity of divergence necessary in any case is a question of consider- 
able importance. As regards that in the horizontal direction, we have only to consider 
the practical question of the proportion of light to darkness in a revolution of the light 
frame. Thus, for example, three faces, each illuminating 16° of the horizon, and re- 
volving in 8 minutes, would produce the same effect as six faces, each illuminating 8°, 
and revolving in 16 minutes. The decision will then be made by reference to the 
divergence in the vertical direction, the value of which will depend upon the situation 
of the lighthouse ; for if the vertical divergence be too small, a ship might under pe- 
culiar circumstances be so near the lighthouse as not to catch the light at all, being, 
in fact, under the lowest rays ; whereas should the situation of the lighthouse be such 
that a vessel never can approach within two or three miles of it, it is useless to throw 
away light upon a part where it can never be wanted ; bearing in mind however that 
the refraction which now and then takes place might, in the event of the divergence 
being too small, prevent a vessel on the horizon from seeing the light, even were she 
at a proper distance to be able to discern it in the natural state of the atmosphere : 
some little excess therefore of the practical above the computed angle is requisite. 
The following Table shows the vertical divergence required in lighthouses from 100 
to 500 feet above the level of the sea, the distance at which the light is first required 
to be seen being from half to four miles from the lighthouse. 
Height of 
Lighthouse 
in feet. 
Distance at which the light is first required to be 
seen. 
i Mile. 
I Mile. 
2 Miles. 
3 Miles. 
4 Miles. 
100 
o • 
4 20 
o / 
2 1.2 
0 / 
1 7 
o / 
0 46 
0 36 
200 
8 40 
4 22 
2 12 
1 30 
1 10 
300 
12 58 
6 32 
3 18 
2 14 
1 42 
400 
17 14 
8 42 
4 22 
2 56 
2 14 
500 
20 28 
10 50 
5 28 
3 40 
2 46 
The axis of the instrument being supposed to be horizontal, the vertical divergence 
given in the table is twice the angle formed between the horizontal line and a line 
drawn from the light to the sea at the distance stated at the head of each column. 
Thus supposing a lighthouse 300 feet above the level of the sea, and that a vessel 
could not approach within four miles of it, we should only require 1° 42' vertical di- 
vergence ; but should a light of that height be so situated that a vessel might pass 
within one mile of it, we should require 6° 32'. Under which latter circumstances 
it is clear that the French lens having only 3° could not be made use of. 
Hitherto, however, we have only spoken of the maximum divergences, without con- 
sidering the minimum ; but this is far too important a part of the subject to be over- 
looked, as it is only within the range or angle of minimum divergence that we can 
see the whole light of the reflector. 
