who asked what was the velocity of light, that is, what time it would
take for a light struck at one place to become visible at another, a
certain distance away.[13]
The method which Galileo devised was as simple as it was natural. Two
practised observers, with muffled lanterns, were to take up positions in
a dark night at a considerable distance from each other, one at _A_ and
one at _B_. At a moment previously fixed upon, _A_ was instructed to
unmask his lantern; while as soon as _B_ saw the light of _A_'s lantern
he was to unmask his. Now it is clear that the time which _A_ counted
from the uncovering of his lantern until he caught sight of the light of
_B_'s would be the time which it would take light to travel from _A_ to
_B_ and from _B_ back to _A_.
[Illustration: Fig. 13.]
The experiment was not executed, nor could it, in the nature of the
case, have been a success. As we now know, light travels too rapidly to
be thus noted. The time elapsing between the arrival of the light at _B_
and its perception by the observer, with that between the decision to
uncover and the uncovering of the lantern, is, as we now know,
incomparably greater than the time which it takes light to travel the
greatest earthly distances. The great velocity of light will be made
apparent, if we reflect that a flash of lightning in the night
illuminates instantaneously a very extensive region, whilst the single
reflected claps of thunder arrive at the observer's ear very gradually
and in appreciable succession.
During his life, then, the efforts of Galileo to determine the velocity
of light remained uncrowned with success. But the subsequent history of
the measurement of the velocity of light is intimately associated with
his name, for with the telescope which he constructed he discovered the
four satellites of Jupiter, and these furnished the next occasion for
the determination of the velocity of light.
The terrestrial spaces were too small for Galileo's experiment. The
measurement was first executed when the spaces of the planetary system
were employed. Olaf Römer, (born at Aarhuus in 1644, died at Copenhagen
in 1710) accomplished the feat (1675-1676), while watching with Cassini
at the observatory of Paris the revolutions of Jupiter's moons.
[Illustration: Fig. 14.]
Let _AB_ (Fig. 14) be Jupiter's orbit. Let _S_ stand for the sun, _E_
for the earth, _J_ for Jupiter, and _T_ for Jupiter's first satellite.
When the earth is at _E₁_ we see the satellite enter regularly into
Jupiter's shadow, and by watching the time between two successive
eclipses, can calculate its time of revolution. The time which Römer
noted was forty-two hours, twenty-eight minutes, and thirty-five
seconds. Now, as the earth passes along in its orbit towards E₂, the
revolutions of the satellite grow apparently longer and longer: the
eclipses take place later and later. The greatest retardation of the
eclipse, which occurs when the earth is at _E₂_, amounts to sixteen
minutes and twenty-six seconds. As the earth passes back again to _E₁_,
the revolutions grow apparently shorter, and they occur in exactly the
time that they first did when the earth arrives at _E₁_. It is to be
remarked that Jupiter changes only very slightly its position during one
revolution of the earth. Römer guessed at once that these periodical
changes of the time of revolution of Jupiter's satellite were not
actual, but apparent changes, which were in some way connected with the
velocity of light.
Let us make this matter clear to ourselves by a simile. We receive
regularly by the post, news of the political status at our capital.
However far away we may be from the capital, we hear the news of every
event, later it is true, but of all equally late. The events reach us in
the same succession of time as that in which they took place. But if we
are travelling away from the capital, every successive post will have a
greater distance to pass over, and the events will reach us more slowly
than they took place. The reverse will be the case if we are approaching
the capital.
At rest, we hear a piece of music played in the same _tempo_ at all
distances. But the _tempo_ will be seemingly accelerated if we are
carried rapidly towards the band, or retarded if we are carried rapidly
away from it.[14]
[Illustration: Fig. 15.]
Picture to yourself a cross, say the sails of a wind-mill (Fig. 15), in
uniform rotation about its centre. Clearly, the rotation of the cross
will appear to you more slowly executed if you are carried very rapidly
away from it. For the post which in this case conveys to you the light
and brings to you the news of the successive positions of the cross will
have to travel in each successive instant over a longer path.
Now this must also be the case with the rotation (the revolution) of the
satellite of Jupiter. The greatest retardation of the eclipse (16½
minutes), due to the passage of the earth from _E₁_ to _E₂_, or to its
removal from Jupiter by a distance equal to the diameter of the orbit of
the earth, plainly corresponds to the time which it takes light to
traverse a distance equal to the diameter of the earth's orbit. The
velocity of light, that is, the distance described by light in a second,
as determined by this calculation, is 311,000 kilometres,[15] or 193,000
miles. A subsequent correction of the diameter of the earth's orbit,
gives, by the same method, the velocity of light as approximately
186,000 miles a second.
The method is exactly that of Galileo; only better conditions are
selected. Instead of a short terrestrial distance we have the diameter
of the earth's orbit, three hundred and seven million kilometres; in
place of the uncovered and covered lanterns we have the satellite of
Jupiter, which alternately appears and disappears. Galileo, therefore,
although he could not carry out himself the proposed measurement, found
the lantern by which it was ultimately executed.
Physicists did not long remain satisfied with this beautiful discovery.
They sought after easier methods of measuring the velocity of light,
such as might be performed on the earth. This was possible after the
difficulties of the problem were clearly exposed. A measurement of the
kind referred to was executed in 1849 by Fizeau (born at Paris in 1819).
I shall endeavor to make the principle of Fizeau's apparatus clear to
you. Let _s_ (Fig. 16) be a disk free to rotate about its centre, and
perforated at its rim with a series of holes. Let _l_ be a luminous
point casting its light on an unsilvered glass, _a_, inclined at an
angle of forty-five degrees to the axis of the disk. The ray of light,
reflected at this point, passes through one of the holes of the disk and
falls at right angles upon a mirror _b_, erected at a point about five
miles distant. From the mirror _b_ the light is again reflected, passes
once more through the hole in _s_, and, penetrating the glass plate,
finally strikes the eye, _o_, of the observer. The eye, _o_, thus, sees
the image of the luminous point _l_ through the glass plate and the hole
of the disk in the mirror _b_.
[Illustration: Fig. 16.]
If, now, the disk be set in rotation, the unpierced spaces between the
apertures will alternately take the place of the apertures, and the eye
o will now see the image of the luminous point in _b_ only at
interrupted intervals. On increasing the rapidity of the rotation,
however, the interruptions for the eye become again unnoticeable, and
the eye sees the mirror _b_ uniformly illuminated.
But all this holds true only for relatively small velocities of the
disk, when the light sent through an aperture in _s_ to _b_ on its
return strikes the aperture at almost the same place and passes through
it a second time. Conceive, now, the speed of the disk to be so
increased that the light on its return finds before it an unpierced
space instead of an aperture, it will then no longer be able to reach
the eye. We then see the mirror _b_ only when no light is emitted from
it, but only when light is sent to it; it is covered when light comes
from it. In this case, accordingly, the mirror will always appear dark.
If the velocity of rotation at this point were still further increased,
the light sent through one aperture could not, of course, on its return
pass through the same aperture but might strike the next and reach the
eye by that. Hence, by constantly increasing the velocity of the
rotation, the mirror _b_ may be made to appear alternately bright and
dark. Plainly, now, if we know the number of apertures of the disk, the
number of rotations per second, and the distance _sb_, we can calculate
the velocity of light. The result agrees with that obtained by Römer.
The experiment is not quite as simple as my exposition might lead you to
believe. Care must be taken that the light shall travel back and forth
over the miles of distance _sb_ and _bs_ undispersed. This difficulty
is obviated by means of telescopes.
If we examine Fizeau's apparatus closely, we shall recognise in it an
old acquaintance: the arrangement of Galileo's experiment. The luminous
point _l_ is the lantern _A_, while the rotation of the perforated disk
performs mechanically the uncovering and covering of the lantern.
Instead of the unskilful observer _B_ we have the mirror _b_, which is
unfailingly illuminated the instant the light arrives from _s_. The disk
_s_, by alternately transmitting and intercepting the reflected light,
assists the observer _o_. Galileo's experiment is here executed, so to
speak, countless times in a second, yet the total result admits of
actual observation. If I might be pardoned the use of a phrase of
Darwin's in this field, I should say that Fizeau's apparatus was the
descendant of Galileo's lantern.
A still more refined and delicate method for the measurement of the
velocity of light was employed by Foucault, but a description of it here
would lead us too far from our subject.
The measurement of the velocity of sound is easily executed by the
method of Galileo. It was unnecessary, therefore, for physicists to rack
their brains further about the matter; but the idea which with light
grew out of necessity was applied also in this field. Koenig of Paris
constructs an apparatus for the measurement of the velocity of sound
which is closely allied to the method of Fizeau.
The apparatus is very simple. It consists of two electrical clock-works
which strike simultaneously, with perfect precision, tenths of seconds.
If we place the two clock-works directly side by side, we hear their
strokes simultaneously, wherever we stand. But if we take our stand by
the side of one of the works and place the other at some distance from
us, in general a coincidence of the strokes will now not be heard. The
companion strokes of the remote clock-work arrive, as sound, later. The
first stroke of the remote work is heard, for example, immediately after
the first of the adjacent work, and so on. But by increasing the
distance we may produce again a coincidence of the strokes. For example,
the first stroke of the remote work coincides with the second of the
near work, the second of the remote work with the third of the near
work, and so on. If, now, the works strike tenths of seconds and the
distance between them is increased until the first coincidence is noted,
plainly that distance is travelled over by the sound in a tenth of a
second.
We meet frequently the phenomenon here presented, that a thought which
centuries of slow and painful endeavor are necessary to produce, when
once developed, fairly thrives. It spreads and runs everywhere, even
entering minds in which it could never have arisen. It simply cannot be
eradicated.
The determination of the velocity of light is not the only case in which
the direct perception of the senses is too slow and clumsy for use. The
usual method of studying events too fleet for direct observation
consists in putting into reciprocal action with them other events
already known, the velocities of all of which are capable of comparison.
The result is usually unmistakable, and susceptible of direct inference
respecting the character of the event which is unknown. The velocity of
electricity cannot be determined by direct observation. But it was
ascertained by Wheatstone, simply by the expedient of watching an
electric spark in a mirror rotating with tremendous known velocity.
[Illustration: Fig. 17.]
[Illustration: Fig. 18.]
If we wave a staff irregularly hither and thither, simple observation
cannot determine how quickly it moves at each point of its course. But
let us look at the staff through holes in the rim of a rapidly rotating
disk (Fig. 17). We shall then see the moving staff only in certain
positions, namely, when a hole passes in front of the eye. The single
pictures of the staff remain for a time impressed upon the eye; we think
we see several staffs, having some such disposition as that represented
in Fig. 18. If, now, the holes of the disk are equally far apart, and
the disk is rotated with uniform velocity, we see clearly that the staff
has moved slowly from _a_ to _b_, more quickly from _b_ to _c_, still
more quickly from _c_ to _d_, and with its greatest velocity from _d_ to
_e_.
A jet of water flowing from an orifice in the bottom of a vessel has the
appearance of perfect quiet and uniformity, but if we illuminate it for
a second, in a dark room, by means of an electric flash we shall see
that the jet is composed of separate drops. By their quick descent the
images of the drops are obliterated and the jet appears uniform. Let us
look at the jet through the rotating disk. The disk is supposed to be
rotated so rapidly that while the second aperture passes into the place
of the first, drop 1 falls into the place of 2, 2 into the place of 3,
and so on. We see drops then always in the same places. The jet appears
to be at rest. If we turn the disk a trifle more slowly, then while the
second aperture passes into the place of the first, drop 1 will have
fallen somewhat lower than 2, 2 somewhat lower than 3, etc. Through
every successive aperture we shall see drops in successively lower
positions. The jet will appear to be flowing slowly downwards.
[Illustration: Fig. 19.]
Now let us turn the disk more rapidly. Then while the second aperture is
passing into the place of the first, drop 1 will not quite have reached
the place of 2, but will be found slightly above 2, 2 slightly above 3,
etc. Through the successive apertures we shall see the drops at
successively higher places. It will now look as if the jet were flowing
upwards, as if the drops were rising from the lower vessel into the
higher.
You see, physics grows gradually more and more terrible. The physicist
will soon have it in his power to play the part of the famous lobster
chained to the bottom of the Lake of Mohrin, whose direful mission, if
ever liberated, the poet Kopisch humorously describes as that of a
reversal of all the events of the world; the rafters of houses become
trees again, cows calves, honey flowers, chickens eggs, and the poet's
own poem flows back into his inkstand.
* * * * *
You will now allow me the privilege of a few general remarks. You have
seen that the same principle often lies at the basis of large classes of
apparatus designed for different purposes. Frequently it is some very
unobtrusive idea which is productive of so much fruit and of such
extensive transformations in physical technics. It is not otherwise here
than in practical life.
The wheel of a waggon appears to us a very simple and insignificant
creation. But its inventor was certainly a man of genius. The round
trunk of a tree perhaps first accidentally led to the observation of the
ease with which a load can be moved on a roller. Now, the step from a
simple supporting roller to a fixed roller, or wheel, appears a very
easy one. At least it appears very easy to us who are accustomed from
childhood up to the action of the wheel. But if we put ourselves vividly
into the position of a man who never saw a wheel, but had to invent one,
we shall begin to have some idea of its difficulties. Indeed, it is
even doubtful whether a single man could have accomplished this feat,
whether perhaps centuries were not necessary to form the first wheel
from the primitive roller.[16]
History does not name the progressive minds who constructed the first
wheel; their time lies far back of the historic period. No scientific
academy crowned their efforts, no society of engineers elected them
honorary members. They still live only in the stupendous results which
they called forth. Take from us the wheel, and little will remain of the
arts and industries of modern life. All disappears. From the
spinning-wheel to the spinning-mill, from the turning-lathe to the
rolling-mill, from the wheelbarrow to the railway train, all vanishes.
In science the wheel is equally important. Whirling machines, as the
simplest means of obtaining quick motions with inconsiderable changes of
place, play a part in all branches of physics. You know Wheatstone's
rotating mirror, Fizeau's wheel, Plateau's perforated rotating disks,
etc. Almost the same principle lies at the basis of all these apparatus.
They differ from one another no more than the pen-knife differs, in the
purposes it serves, from the knife of the anatomist or the knife of the
vine-dresser. Almost the same might be said of the screw.
It will now perhaps be clear to you that new thoughts do not spring up
suddenly. Thoughts need their time to ripen, grow, and develop in, like
every natural product; for man, with his thoughts, is also a part of
nature.
Slowly, gradually, and laboriously one thought is transformed into a
different thought, as in all likelihood one animal species is gradually
transformed into new species. Many ideas arise simultaneously. They
fight the battle for existence not otherwise than do the Ichthyosaurus,
the Brahman, and the horse.
A few remain to spread rapidly over all fields of knowledge, to be
redeveloped, to be again split up, to begin again the struggle from the
start. As many animal species long since conquered, the relicts of ages
past, still live in remote regions where their enemies cannot reach
them, so also we find conquered ideas still living on in the minds of
many men. Whoever will look carefully into his own soul will acknowledge
that thoughts battle as obstinately for existence as animals. Who will
gainsay that many vanquished modes of thought still haunt obscure
crannies of his brain, too faint-hearted to step out into the clear
light of reason? What inquirer does not know that the hardest battle, in
the transformation of his ideas, is fought with himself.
Similar phenomena meet the natural inquirer in all paths and in the most
trifling matters. The true inquirer seeks the truth everywhere, in his
country-walks and on the streets of the great city. If he is not too
learned, he will observe that certain things, like ladies' hats, are
constantly subject to change. I have not pursued special studies on this
subject, but as long as I can remember, one form has always gradually
changed into another. First, they wore hats with long projecting rims,
within which, scarcely accessible with a telescope, lay concealed the
face of the beautiful wearer. The rim grew smaller and smaller; the
bonnet shrank to the irony of a hat. Now a tremendous superstructure is
beginning to grow up in its place, and the gods only know what its
limits will be. It is not otherwise with ladies' hats than with
butterflies, whose multiplicity of form often simply comes from a slight
excrescence on the wing of one species developing in a cognate species
to a tremendous fold. Nature, too, has its fashions, but they last
thousands of years. I could elucidate this idea by many additional
examples; for instance, by the history of the evolution of the coat, if
I were not fearful that my gossip might prove irksome to you.
* * * * *
We have now wandered through an odd corner of the history of science.
What have we learned? The solution of a small, I might almost say
insignificant, problem--the measurement of the velocity of light. And
more than two centuries have worked at its solution! Three of the most
eminent natural philosophers, Galileo, an Italian, Römer, a Dane, and
Fizeau, a Frenchman, have fairly shared its labors. And so it is with
countless other questions. When we contemplate thus the many blossoms of
thought that must wither and fall before one shall bloom, then shall we
first truly appreciate Christ's weighty but little consolatory words:
"Many be called but few are chosen."
Such is the testimony of every page of history. But is history right?
Are really only those chosen whom she names? Have those lived and
battled in vain, who have won no prize?
I doubt it. And so will every one who has felt the pangs of sleepless
nights spent in thought, at first fruitless, but in the end successful.
No thought in such struggles was thought in vain; each one, even the
most insignificant, nay, even the erroneous thought, that which
apparently was the least productive, served to prepare the way for those
that afterwards bore fruit. And as in the thought of the individual
naught is in vain, so, also, it is in that of humanity.
Galileo wished to measure the velocity of light. He had to close his
eyes before his wish was realised. But he at least found the lantern by
which his successor could accomplish the task.
And so I may maintain that we all, so far as inclination goes, are
working at the civilisation of the future. If only we all strive for the
right, then are we _all_ called and _all_ chosen!
FOOTNOTES:
[Footnote 11: According to Mr. Jules Andrieu, the idea that nature
must be tortured to reveal her secrets is preserved in the name
_crucible_--from the Latin _crux_, a cross. But, more probably,
_crucible_ is derived from some Old French or Teutonic form, as
_cruche_, _kroes_, _krus_, etc., a pot or jug (cf. Modern English
_crock_, _cruse_, and German _Krug_).--_Trans._]
[Footnote 12: Xenophon, Memorabilia iv, 7, puts into the mouth of
Socrates these words: [Greek: oute gar heureta anthrôpois auta
enomizen einai, oute chaoizesthai theois an hêgeito ton zêtounta ha
ekeinoi saphênisai ouk eboulêthêsan].]
[Footnote 13: Galilei, _Discorsi e dimostrazione matematiche_.
Leyden, 1638. _Dialogo Primo._]
[Footnote 14: In the same way, the pitch of a locomotive-whistle is
higher as the locomotive rapidly approaches an observer, and lower
when rapidly leaving him than if the locomotive were at
rest.--_Trans._]
[Footnote 15: A kilometre is 0.621 or nearly five-eighths of a
statute mile.]
[Footnote 16: Observe, also, the respect in which the wheel is held
in India, Japan and other Buddhistic countries, as the emblem of
power, order, and law, and of the superiority of mind over matter.
The consciousness of the importance of this invention seems to have
lingered long in the minds of these nations.--_Tr._]
WHY HAS MAN TWO EYES?
Why has man two eyes? That the pretty symmetry of his face may not be
disturbed, the artist answers. That his second eye may furnish a
substitute for his first if that be lost, says the far-sighted
economist. That we may weep with two eyes at the sins of the world,
replies the religious enthusiast.
Odd opinions! Yet if you should approach a modern scientist with this
question you might consider yourself fortunate if you escaped with less
than a rebuff. "Pardon me, madam, or my dear sir," he would say, with
stern expression, "man fulfils no purpose in the possession of his eyes;
nature is not a person, and consequently not so vulgar as to pursue
purposes of any kind."
Still an unsatisfactory answer! I once knew a professor who would shut
with horror the mouths of his pupils if they put to him such an
unscientific question.
But ask a more tolerant person, ask me. I, I candidly confess, do not
know exactly why man has two eyes, but the reason partly is, I think,
that I may see you here before me to-night and talk with you upon this
delightful subject.