mind of any one competent to form an opinion on the matter, though,
as we shall presently see, some students of science and one or two
mathematicians have raised doubts as to the validity of the reasoning
by which it is shown that a change should occur. That the reasoning is
sound cannot, in reality, be questioned, and after careful examination
of the arguments urged against it by one or two mathematicians, I
can form no other opinion than that these arguments amount really
but to an expression of inability to understand the matter. This
may seem astonishing, but is explained when we remember that some
mathematicians, by devoting their attention too particularly to special
departments, lose, to a surprising degree, the power of dealing with
subjects (even mathematical ones) outside their department. Apart
from the soundness of the reasoning, the facts are unmistakably in
accordance with the conclusion to which the reasoning points. Yet some
few still entertain doubts, a circumstance which may prove a source of
consolation to any who find themselves unable to follow the reasoning
on which the effects of approach and recession on wave-lengths depend.
Let such remember, however, that experiment in the case of the aerial
waves producing sound, accords perfectly with theory, and that the
waves which produce light are perfectly analogous (so far as this
particular point is concerned) with the waves producing sound.
Ordinary white light, and many kinds of coloured light, may be compared
with _noise_—that is, with a multitude of intermixed sounds. But light
of one pure colour may be compared to sound of one determinate note.
As the aerial waves producing the effect of one definite tone are all
of one length, so the ethereal waves producing light of one definite
colour are all of one length. Therefore if we approach or recede from a
source of light emitting such waves, effects will result corresponding
with what has been described above for the case of water-waves and
sound-waves. If we approach the source of light, or if it approaches
us, the waves will be shortened; if we recede from it, or if it
recedes from us, the waves will be lengthened. But the colour of light
depends on its wave-length, precisely as the tone of sound depends on
its wave-length. The waves producing red light are longer than those
producing orange light, these are longer than the waves producing
yellow light; and so the wave-lengths shorten down from yellow to
green, thence to blue, to indigo, and finally to violet. Thus if a body
shining in reality with a pure green colour, approached the observer
with a velocity comparable with that of light, it would seem blue,
indigo, or violet, according to the rate of approach; whereas if it
rapidly receded, it would seem yellow, orange, or red, according to the
rate of recession.
Unfortunately in one sense, though very fortunately in many much more
important respects, the rates of motion among the celestial bodies are
_not_ comparable with the velocity of light, but are always so much
less as to be almost rest by comparison. The velocity of light is about
187,000 miles per second, or, according to the measures of the solar
system at present in vogue (which will shortly have to give place to
somewhat larger measures, the result of observations made upon the
recent transit of Venus), about 185,000 miles per second. The swiftest
celestial motion of which we have ever had direct evidence was that of
the comet of the year 1843, which, at the time of its nearest approach
to the sun, was travelling at the rate of about 350 miles per second.
This, compared with the velocity of light, is as the motion of a person
taking six steps a minute, each less than half a yard long, to the
rush of the swiftest express train. No body within our solar system
can travel faster than this, the motion of a body falling upon the sun
from an infinite distance being only about 370 miles per second when it
reaches his surface. And though swifter motions probably exist among
the bodies travelling around more massive suns than ours, yet of such
motions we can never become cognizant. All the motions taking place
among the stars themselves would appear to be very much less in amount.
The most swiftly moving sun seems to travel but at the rate of about 50
or 60 miles per second.
Now let us consider how far a motion of 100 miles per second might be
expected to modify the colour of pure green light—selecting green as
the middle colour of the spectrum. The waves producing green light
are of such a length, that 47,000 of them scarcely equal in length a
single inch. Draw on paper an inch and divide it carefully into ten
equal parts, or take such parts from a well-divided rule; divide one
of these tenths into ten equal parts, as nearly as the eye will permit
you to judge; then one of these parts, or about half the thickness of
an average pin, would contain 475 of the waves of pure green light.
The same length would equal the length of 440 waves of pure yellow
light, and of 511 waves of pure blue light. (The green, yellow, and
blue, here spoken of, are understood to be of the precise colour of
the middle of the green, yellow, and blue parts of the spectrum.) Thus
the green waves must be increased in the proportion of 475 to 440 to
give yellow light, or reduced in the proportion of 511 to 475 to give
blue light. For the first purpose, the velocity of recession must bear
to the velocity of light the proportion which 30 bears to 475, or
must be equal to rather more than one-sixteenth part of the velocity
of light—say 11,600 miles per second. For the second purpose, the
velocity of approach must bear to the velocity of light the proportion
which 36 bears to 475, or must be nearly equal to one-thirteenth part
of the velocity of light—say 14,300 miles per second. But the motions
of the stars and other celestial bodies, and also the motions of matter
in the sun, and so forth, are very much less than these. Except in the
case of one or two comets (and always dismissing from consideration
the amazing apparent velocities with which comets’ tails _seem_ to
be formed), we may take 100 miles per second as the extreme limit of
velocity with which we have to deal, in considering the application
of our theory to the motions of recession and approach of celestial
bodies. Thus in the case of recession the greatest possible change
of colour in pure green light would be equivalent to the difference
between the medium green of the spectrum, and the colour 1-116th part
of the way from medium green to medium yellow; and in the case of
approach, the change would correspond to the difference between the
medium green and the colour 1-143rd part of the way from medium green
to medium blue. Let any one look at a spectrum of fair length, or even
at a correctly tinted painting of the solar spectrum, and note how
utterly unrecognizable to ordinary vision is the difference of tint for
even the twentieth part of the distance between medium green and medium
yellow on one side or medium blue on the other, and he will recognize
how utterly hopeless it would be to attempt to appreciate the change
of colour due to the approach or recession of a luminous body shining
with pure green light and moving at the tremendous rate of 100 miles
per second. It would be hopeless, even though we had the medium green
colour and the changed colour, either towards yellow or towards blue,
placed side by side for comparison—how much more when the changed
colour would have to be compared with the observer’s recollection of
the medium colour, as seen on some other occasion!
But this is the least important of the difficulties affecting the
application of this method by noting change of colour, as Doppler
originally proposed. Another difficulty, which seems somehow to have
wholly escaped Doppler’s attention, renders the colour test altogether
unavailable. We do not get _pure_ light from any of the celestial
bodies except certain gaseous clouds or nebulæ. From every sun we get,
as from our own sun, all the colours of the rainbow. There may be an
excess of some colours and a deficiency of others in any star, so as
to give the star a tint, or even a very decided colour. But even a
blood-red star, or a deep-blue or violet star, does not shine with
pure light, for the spectroscope shows that the star has other colours
than those producing the prevailing tint, and it is only the great
_excess_ of red rays (all kinds of red, too) or of blue rays (of all
kinds), and so on, which makes the star appear red, or blue, and so on,
to the eye. By far the greater number of stars or suns show all the
colours of the rainbow nearly equally distributed, as in the case of
our own sun. Now imagine for a moment a white sun, which had been at
rest, to begin suddenly to approach us so rapidly (travelling more than
10,000 miles per second) that the red rays became orange, the orange
became yellow, the yellow green, the green blue, the blue indigo, the
indigo violet, while the violet waves became too short to affect the
sense of sight. Then, _if that were all_, that sun, being deprived of
the red part of its light, would shine with a slightly bluish tinge,
owing to the relative superabundance of rays from the violet end of
the spectrum. We should be able to recognize such a change, yet not
nearly so distinctly as if that sun had been shining with a pure green
light, and suddenly beginning to approach us at the enormous rate just
mentioned, changed in colour to full blue. _Though_, if that sun were
all the time approaching us at the enormous rate imagined, we should be
quite unable to tell whether its slightly bluish tinge were due to such
motion of approach or to some inherent blueness in the light emitted by
the star. Similarly, if a white sun suddenly began to recede so rapidly
that its violet rays were turned to indigo, the indigo to blue, and
so on, the orange rays turning to red, and the red rays disappearing
altogether, then, _if that were all_, its light would become slightly
reddish, owing to the relative superabundance of light from the red
end of the spectrum; and we might distinguish the change, yet not so
readily as if a sun shining with pure green light began to recede at
the same enormous rate, and so shone with pure yellow light. _Though_,
if that sun were all the time receding at that enormous rate, we should
be quite unable to tell whether its slightly reddish hue were due to
such motion of recession or to some inherent redness in its own lustre.
_But in neither case would that be all._ In the former, the red rays
would indeed become orange; but the rays beyond the red, which produce
no effect upon vision, would be converted into red rays, and fill up
the part of the spectrum deserted by the rays originally red. In the
latter, the violet rays would indeed become indigo; but the rays beyond
the violet, ordinarily producing no visible effect, would be converted
into violet rays, and fill up the part of the spectrum deserted by the
rays originally violet. Thus, despite the enormous velocity of approach
in one case and of recession in the other, there would be no change
whatever in the colour of the sun in either case. All the colours of
the rainbow would still be present in the sun’s light, and it would
therefore still be a white sun.
Doppler’s method would thus fail utterly, even though the stars were
travelling hither and thither with motions a hundred times greater than
the greatest known stellar motions.
This objection to Doppler’s theory, as originally proposed, was
considered by me in an article on “Coloured Suns” in _Fraser’s
Magazine_ for January, 1868. His theory, indeed, was originally
promulgated not as affording a means of measuring stellar motions, but
as a way of accounting for the colours of double stars. It was thus
presented by Professor Nichol, in a chapter of his “Architecture of the
Heavens,” on this special subject:—“The rapid motion of light reaches
indeed one of those numbers which reason owns, while imagination ceases
to comprehend them; but it is also true that the swiftness with which
certain individuals of the double stars sweep past their perihelias,
or rather their periasters, is amazing; and in this matter of colours,
it must be recollected that the question solely regards the difference
between the velocities of the waves constituent of colours, at those
different stellar positions. Still it is a bold—even a magnificent
idea; and if it can be reconciled with the permanent colours of the
multitude of stars surrounding us—stars which too are moving in great
orbits with immense velocities—it may be hailed almost as a positive
discovery. It must obtain confirmation, or otherwise, so soon as we
can compare with certainty the observed colorific changes of separate
systems with the known fluctuations of their orbital motions.”
That was written a quarter of a century ago, when spectroscopic
analysis, as we now know it, had no existence. Accordingly, while the
fatal objection to Doppler’s original theory is overlooked on the
one hand, the means of applying the principle underlying the theory,
in a much more exact manner than Doppler could have hoped for, is
overlooked on the other. Both points are noted in the article above
referred to, in the same paragraph. “We may dismiss,” I there stated,
“the theory started some years ago by the French astronomer, M.
Doppler.” But, I presently added, “It is quite clear that the effects
of a motion rapid enough to produce such a change” (_i.e._ a change
of tint in a pure colour) “would shift the position of the whole
spectrum—and this change would be readily detected by a reference
to the spectral lines.” This is true, even to the word “readily.”
Velocities which would produce an appreciable change of tint would
produce “readily” detectible changes in the position of the spectral
lines; the velocities actually existing among the star-motions would
produce changes in the position of these lines detectible only with
extreme difficulty, or perhaps in the majority of instances not
detectible at all.
It has been in this way that the spectroscopic method has actually been
applied.
It is easy to perceive the essential difference between this way of
applying the method and that depending on the attempted recognition
of changes of colour. A dark line in the spectrum marks in reality
the place of a missing tint. The tints next to it on either side are
present, but the tint between them is wanting. They are changed in
colour—very slightly, in fact quite inappreciably—by motions of
recession or approach, or, in other words, they are shifted in position
along the spectrum, towards the red end for recession, towards the
violet end for approach; and of course the dark space between is
shifted along with them. One may say that the missing tint is changed.
For in reality that is precisely what would happen. If the light of
a star at rest gave every tint of the spectrum, for instance, except
mid-green alone, and that star approached or receded so swiftly that
its motion would change pure green light to pure yellow in one case,
or pure blue in the other, then the effect on the spectrum of such a
star would be to throw the dark line from the middle of the green part
of the spectrum to the middle of the yellow part in one case, or to
the middle of the blue part in the other. The dark line would be quite
notably shifted in either case. With the actual stellar motions, though
all the lines are more or less shifted, the displacement is always
exceedingly minute, and it becomes a task of extreme difficulty to
recognize, and still more to measure, such displacement.
When I first indicated publicly (January, 1868) the way in which
Doppler’s principle could alone be applied, two physicists, Huggins
in England and Secchi in Italy, were actually endeavouring, with the
excellent spectroscopes in their possession, to apply this method. In
March, 1868, Secchi gave up the effort as useless, publicly announcing
the plan on which he had proceeded and his failure to obtain any
results except negative ones. A month later Huggins also publicly
announced the plan on which he had been working, but was also able
to state that in one case, that of the bright star Sirius, he had
succeeded in measuring a motion in the line of sight, having discovered
that Sirius was receding from the earth at the rate of 41·4 miles per
second. I say was receding, because a part of the recession at the time
of observation was due to the earth’s orbital motion around the sun. I
had, at his request, supplied Huggins with the formula for calculating
the correction due to this cause, and, applying it, he found that
Sirius is receding from the sun at the rate of about 29½ miles per
second, or some 930 millions of miles per annum.
I am not here specially concerned to consider the actual results of the
application of this method since the time of Huggins’s first success;
but the next chapter of the history of the method is one so interesting
to myself personally that I feel tempted briefly to refer to details.
So soon as I had heard of Huggins’s success with Sirius, and that an
instrument was being prepared for him wherewith he might hope to extend
the method to other stars, I ventured to make a prediction as to the
result which he would obtain whensoever he should apply it to five
stars of the seven forming the so-called Plough. I had found reason
to feel assured that these five form a system drifting all together
amid stellar space. Satisfied for my own part as to the validity of
the evidence, I submitted it to Sir J. Herschel, who was struck by
its force. The apparent drift of those stars was, of course, a thwart
drift; but if they really were drifting in space, then their motions in
the line of sight must of necessity be alike. My prediction, then, was
that whensoever Huggins applied to those stars the new method he would
find them either all receding at the same rate, or all approaching at
the same rate, or else that all _alike_ failed to give any evidence at
all either of recession or approach. I had indicated the five in the
first edition of my “Other Worlds”—to wit, the stars of the Plough,
omitting the nearest “pointer” to the pole and the star marking the
third horse (or the tip of the Great Bear’s tail). So soon as Huggins’s
new telescope and its spectroscopic adjuncts were in working order, he
re-examined Sirius, determined the motions of other stars; and at last
on one suitable evening he tested the stars of the Plough. He began
with the nearest pointer, and found that star swiftly approaching the
earth. He turned to the other pointer, and found it rapidly receding
from the earth. Being under the impression that my five included both
pointers, he concluded that my prediction had utterly failed, and so
went on with his observations, altogether unprejudiced in its favour,
to say the least. The next star of the seven he found to be receding
at the same rate as the second pointer; the next at the same rate,
the next, and the next receding still at the same rate, and lastly
the seventh receding at a different rate. Here, then, were five stars
all receding at a common rate, and of the other two one receding at
a different rate, the other swiftly approaching. Turning next to the
work containing my prediction, Huggins found that the five stars thus
receding at a common rate were the five whose community of motion I
had indicated two years before. Thus the first prediction ever made
respecting the motions of the so-called fixed stars was not wanting in
success. I would venture to add that the theory of star-drift, on the
strength of which the prediction was made, was in effect demonstrated
by the result.
The next application of the new method was one of singular interest. I
believe it was Mr. Lockyer who first thought of applying the method to
measure the rate of solar hurricanes as well as the velocities of the
uprush and downrush of vaporous matter in the atmosphere of the sun.
Another spectroscopic method had enabled astronomers to watch the rush
of glowing matter from the edge of the sun, by observing the coloured
flames and their motions; but by the new method it was possible to
determine whether the flames at the edge were swept by solar cyclones
carrying them from or towards the eye of the terrestrial observer,
and also to determine whether glowing vapours over the middle of the
visible disc were subject to motion of uprush, which of course would
carry them towards the eye, or of downrush, which would carry them
from the eye. The result of observations directed to this end was to
show that at least during the time when the sun is most spotted, solar
hurricanes of tremendous violence take place, while the uprushing and
downrushing motions of solar matter sometimes attain a velocity of more
than 100 miles per second.
It was this success on the part of an English spectroscopist which
caused that attack on the new method against which it has but recently
been successfully defended, at least in the eyes of those who are
satisfied only by experimental tests of the validity of a process.
The Padre Secchi had failed, as we have seen, to recognize motions of
recession and approach among the stars by the new method. But he had
taken solar observation by spectroscopic methods under his special
charge, and therefore when the new results reached his ears he felt
bound to confirm or invalidate them. He believed that the apparent
displacement of dark lines in the solar spectrum might be due to the
heat of the sun causing changes in the delicate adjustments of the
instrument—a cause of error against which precautions are certainly
very necessary. He satisfied himself that when sufficient precautions
are taken no displacements take place such as Lockyer, Young, and
others claimed to have seen. But he submitted the matter to a further
test. As the sun is spinning swiftly on his axis, his mighty equator,
more than two and a half millions of miles in girth, circling once
round in about twenty-four days, it is clear that on one side the sun’s
surface is swiftly moving _towards_, and on the other side as swiftly
moving _from_, the observer. By some amazing miscalculation, Secchi
made the rate of this motion 20 miles per second, so that the sum of
the two motions in opposite directions would equal 40 miles per second.
He considered that he ought to be able by the new method, if the new
method is trustworthy at all, to recognize this marked difference
between the state of the sun’s eastern and western edges; he found on
trial that he could not do so; and accordingly he expressed his opinion
that the new method is not trustworthy, and that the arguments urged in
its favour are invalid.
The weak point in his reasoning resided in the circumstance that the
solar equator is only moving at the rate of about 1¼ miles per second,
so that instead of a difference of 40 miles per second between the
two edges, which should be appreciable, the actual difference (that
is, the sum of the two equal motions in opposite directions) amounts
only to 2½ miles per second, which certainly Secchi could not hope to
recognize with the spectroscopic power at his disposal. Nevertheless,
when the error in his reasoning was pointed out, though he admitted
that error, he maintained the justice of his conclusion; just as
Cassini, having mistakenly reasoned that the degrees of latitude should
diminish towards the pole instead of increasing, and having next
mistakenly found, as he supposed, that they do diminish, acknowledged
the error of his reasoning, but insisted on the validity of his
observations,—maintaining thenceforth, as all the world knows, that
the earth is extended instead of flattened at the poles.