218 
MR. W. H. BARLOW ON DIFFERENT MODES 
As regards the vertical divergences, if the maximum be sufficient for the situation 
of the lighthouse, the minimum will in most cases be enough to admit of a vessel ap- 
proaching so near that some diminution in the power of the light will not be felt ; 
and for this reason it is unnecessary to enter very minutely into this part of the 
question ; we shall proceed therefore at once to notice the action of reflectors and 
lenses in reference to their horizontal divergences. 
If we examine the effect of a reflector as it revolves on its frame, when seen from 
a distance of several miles (that is to say at such a distance that lines drawn from 
either side of the reflector to the eye may be considered as parallel) it will be found that 
it first begins to give its assistance when the eye is in the line A C, which is the ex- 
treme of the angle of maximum divergence, or when the angle formed between the 
line of the axis C E and a line drawn from the eye to the reflector is equal to half 
the angle subtended by the light in its focus at the minimum focal distance C F, and 
the reflected light will first appear at C. 
A 
As the reflector continues its revolution the eye is brought into the line GH; G H E 
being the angle formed between a line drawn from the eye to the reflector and the 
line of its axis, and F H will be the distance at which the light would subtend that 
angle : now here the reflected light will have extended itself from C along the surface 
of the reflector to that part where its distance from the focal point is equal to H F. 
With H F describe the arc I H I, then I C I is the part of the reflector acting at that 
time, and the area of the circle of which 1 1 is the diameter multiplied into the 
intensity of the light will be the illuminating power at that time. 
In the same manner the illuminating power will continue to increase until the angle 
formed between the axis of the reflector and a line drawn from it to the eye is equal 
to half the angle subtended by the light in the focus, at the maximum focal distance 
F M, when it will have attained its full power, at which it will continue until, by the 
revolution of the reflector, the same angle is formed on the other side of the axis, 
that is to say, the light will have its full power only during the range of the angle of 
minimum divergence, when it will begin to diminish; the reflected light receding from 
the edges of the reflector, and ceasing at the apex C. 
