That area is the section of the fasciculus of cones
that proceed from each point of the mirror, which, in the case we have
supposed, differs immaterially from the cone reflected from a single
point. Hence, if a man watches the play of the flash from his mirror upon
a very near object, it will appear to him of the shape and size of the
mirror; but as he retreats from the object, the edges of the flash become
rounded, and very soon the flash appears a perfect circle, of precisely
the same apparent diameter as the disc of the sun: it will, in short,
look just like a very faint sun. The signaller has to cause this disc of
light to cover the person whose notice he wishes to attract. I will
proceed to show how he can do so; but in the mean time it will be evident
that a pretty careful aim is requisite, or he will fail in his object.
The steadiness of his aim must be just twice as accurate, neither more
nor less, as would suffice to point a rifle at the sun when it was
sufficiently obscured by a cloud to bear being looked at: for the object
of the aim is of the same apparent size, but a movement of a mirror
causes the ray reflected from it to move through a double angle.
The power of these sun-signals is extraordinarily great. The result of
several experiments that I made in England showed that the smallest
mirror visible under atmospheric conditions such that the signaller's
station was discernible, but dim, subtended an angle of only one-tenth of
a second of a degree.
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