Six Lectures on Light | Page 8

a distant object,
striking very obliquely on the surface of the heated stratum, are
sometimes totally reflected upwards, thus producing images similar to

those produced by water. I have seen the image of a rock called Mont
Tombeline distinctly reflected from the heated air of the strand of
Normandy near Avranches; and by such delusive appearances the
thirsty soldiers of the French army in Egypt were greatly tantalised.
The angle which marks the limit beyond which total reflection takes
place is called the limiting angle (it is marked in fig. 6 by the strong
line E _n_''). It must evidently diminish as the refractive index
increases. For water it is 48½°, for flint glass 38°41', and for diamond
23°42'. Thus all the light incident from two complete quadrants, or
180°, in the case of diamond, is condensed into an angular space of
47°22' (twice 23°42') by refraction. Coupled with its great refraction,
are the great dispersive and great reflective powers of diamond; hence
the extraordinary radiance of the gem, both as regards white light and
prismatic light.
§ 5. _Velocity of Light. Aberration. Principle of least Action._
In 1676 a great impulse was given to optics by astronomy. In that year
Olav Roemer, a learned Dane, was engaged at the Observatory of Paris
in observing the eclipses of Jupiter's moons. The planet, whose distance
from the sun is 475,693,000 miles, has four satellites. We are now only
concerned with the one nearest to the planet. Roemer watched this
moon, saw it move round the planet, plunge into Jupiter's shadow,
behaving like a lamp suddenly extinguished: then at the other edge of
the shadow he saw it reappear, like a lamp suddenly lighted. The moon
thus acted the part of a signal light to the astronomer, and enabled him
to tell exactly its time of revolution. The period between two successive
lightings up of the lunar lamp he found to be 42 hours, 28 minutes, and
35 seconds.
This measurement of time was so accurate, that having determined the
moment when the moon emerged from the shadow, the moment of its
hundredth appearance could also be determined. In fact, it would be
100 times 42 hours, 28 minutes, 35 seconds, after the first observation.
Roemer's first observation was made when the earth was in the part of
its orbit nearest Jupiter. About six months afterwards, the earth being
then at the opposite side of its orbit, when the little moon ought to have
made its hundredth appearance, it was found unpunctual, being fully 15
minutes behind its calculated time. Its appearance, moreover, had been
growing gradually later, as the earth retreated towards the part of its

orbit most distant from Jupiter. Roemer reasoned thus: 'Had I been able
to remain at the other side of the earth's orbit, the moon might have
appeared always at the proper instant; an observer placed there would
probably have seen the moon 15 minutes ago, the retardation in my
case being due to the fact that the light requires 15 minutes to travel
from the place where my first observation was made to my present
position.'
This flash of genius was immediately succeeded by another. 'If this
surmise be correct,' Roemer reasoned, 'then as I approach Jupiter along
the other side of the earth's orbit, the retardation ought to become
gradually less, and when I reach the place of my first observation, there
ought to be no retardation at all.' He found this to be the case, and thus
not only proved that light required time to pass through space, but also
determined its rate of propagation.
The velocity of light, as determined by Roemer, is 192,500 miles in a
second.
For a time, however, the observations and reasonings of Roemer failed
to produce conviction. They were doubted by Cassini, Fontenelle, and
Hooke. Subsequently came the unexpected corroboration of Roemer by
the English astronomer, Bradley, who noticed that the fixed stars did
not really appear to be fixed, but that they describe little orbits in the
heavens every year. The result perplexed him, but Bradley had a mind
open to suggestion, and capable of seeing, in the smallest fact, a picture
of the largest. He was one day upon the Thames in a boat, and noticed
that as long as his course remained unchanged, the vane upon his
masthead showed the wind to be blowing constantly in the same
direction, but that the wind appeared to vary with every change in the
direction of his boat. 'Here,' as Whewell says, 'was the image of his
case. The boat was the earth, moving in its orbit, and the wind was the
light of a star.'
We may ask, in passing, what, without the faculty which formed the
'image,' would Bradley's wind and vane have been to him? A