or the apparent displacement of projectment of an object when seen by
our two eyes separately. If you hold up a finger and look at it, with
each eye separately, you will see that the finger is projected by each
eye on to a different part of the background; the angle which the
lines of sight, from each eye, make when they meet at the object, is
called the angle of parallax, and the further the object is away the
smaller that angle becomes; it is, in fact, the angle subtended, at
the object, by the distance between the two eyes. As the object is
brought nearer the eyes have to be inclined inwards to impinge on that
object; the appreciation of distance then, in our sense of sight, is
dependent upon our perception of the amount of inclination of those
two lines of sight, and is therefore an acquired knowledge. The
distance between the eyes is about 2-1/2 inches, and this is a very
short base line upon which to estimate distance; in fact, without the
help of perspective and known dimensions of surrounding objects, it is
doubtful if anyone could by its means estimate distance beyond a few
hundred yards. The object would, of course, also have to be an unknown
one, as, otherwise, the converse of the above comes into play, and the
distance could be estimated by the angle which the known diameter of
the object subtends at the eye; but this necessitates the size of the
object being known beforehand and the employment of perspective.
We can extend our perception of distances by, ourselves, moving from
one place to another, gaining thereby a longer base line, and noting
the displacement of projection of the object on a distant background;
by that means, distance up to several miles can probably be
appreciated. But, when we try to determine the distance of, say, the
Moon (240,000 miles away), we are helpless, especially as we have no
marked background, except in the case of occultations of the Sun or
Stars. But the Astronomer at once comes to our aid; a distance of
several miles is carefully measured on a level plane, and, by placing
telescopes at the extremities of that known line, we can mark the
inclination of those telescopes to each other when focussed upon a
particular mountain peak on the moon; by this means we know the angle
of parallax (180 deg. less the sum of the two angles of inclination), and,
from this and our known length of base line, we can calculate the
distance. When however we go a step further and attempt to calculate
the distance of the Sun (93,000,000 miles), we find our last base line
again absolutely inadequate. But the astronomer helps us again; we now
separate our two telescopic eyes by the whole diameter of the earth
(7900 miles); this is accomplished by taking from the Equator two
simultaneous observations of the Sun, at its rising and setting; for
when the Sun is setting, at say the Equinox, it is at that moment
rising at exactly the other side of the earth; the inclination of the
two telescopes, directed to a certain point on the Sun, will now give
the distance approximately, though even this base line is too short
for exactitude. When however we attempt to go still further and try to
ascertain the distance of stars, which are a million times further off
than the Sun, such a base line is quite out of the question. How then
can we get a base line for our telescopes longer than the whole width
of the earth? The Astronomer again provides the means. The earth takes
one year to complete its vast orbit round the sun, and the diameter of
that path is 186,000,000 miles. This is made our new base line for
separating our telescopes; an observation of a star is taken, say,
to-day, and after waiting six months, to enable the earth to reach the
other extremity of its vast orbit, another observation is taken, and
yet it is found, as we shall see later on, that the distance of the
nearest fixed star is so _stupendous_ that even this base line, of
186,000,000 miles, shows absolutely no inclination between the two
telescopes except in about a dozen cases, and even in those the angle
of parallax, perceivable, is so minute that no reliable distance can
be calculated; we can only say that the star is at least as far away
as a certain distance, but it may be much farther.
Let us now try by other means to get a clearer insight into the
subject of this View, by tracing Space to the utmost limit of human
conception. I think the best method I can adopt will be to take you,
in imagination, for a journey as far as is possible by means of the
best instruments at our disposal.
We will start outwards from the Sun, and glance on our way at the
worlds involved in the Solar System. Let us first understand what are
the dimensions of our central Luminary. The distance of the Moon from
the Earth is 240,000 miles, but the dimensions of the Sun are so great
that, were the centre of the Sun placed where the centre of the Earth
is, the surface of the Sun would not only extend as far as the Moon,
but as far again on the other side, and that would give the radius
only of the enormous circumference of the Sun; another way to
understand its size is, to remember that, light travelling 186,000
miles per second, would actually take five seconds to go across its
disc. Let us now start outward from this vast mass. The first world we
meet is the little planet Mercury, only 3000 miles in diameter,
revolving round the Sun at a distance of 36 million miles. We next
come upon Venus, at a distance of 67 million miles. She is only 400
miles smaller in diameter than our Earth, and, with the dense
atmosphere with which she is surrounded, animal and vegetable life
similar to that on our Earth would be possible. Continuing our course,
we arrive at our Earth, situated 93 million miles away from the Sun.
Still speeding on, a further 50 million miles brings us to Mars, with
a diameter of nearly 5000 miles, and accompanied by two miniature
moons. The sight of this planet in a good instrument is most
interesting. Ocean beds and continents are visible, and the telescope
shows large tracts of snow, though not necessarily formed from water
(perhaps carbonic dioxide), surrounding its polar regions, which
increase considerably during the winter, and decrease during the
summer seasons on that planet; but there are no canals! The fact that
our largest and best telescopes failed to show these imaginary canals,
was an insurmountable barrier to the advocates of these markings, but
the "Canalites" made their contention ridiculous when they actually
suggested that the reason for this failure to perceive them was that
our telescopes were too large to see such small markings! How such a
statement could have been made is incomprehensible on any supposition,
as everybody knows that the whole use of size, or what is called
aperture, in a telescope, is to help us to see more clearly small and
faint markings.
The distances we now have to travel become so great that I shall not
attempt to give them; you can, however, form an idea of the tremendous
spaces we are traversing when you consider that each successive planet
is nearly double as far from the Sun as the preceding one.
In the place where, by Bode's law, we should expect to have found the
next world, we find a group of small planets, ranging in size from
about 200 miles in diameter down to only a few hundred yards. They
pass through nearly the same point once in each of their periods of
revolution round the Sun, and it has been suggested that they are
fragments of a great globe rent asunder by some mighty catastrophe;
over 400 of these little worlds have been discovered and have received
names, or are known under certain numbers.
We now continue our voyage over the next huge space and arrive at
Jupiter, the largest and grandest of the planets. This world is more
than 1000 times larger than our Earth, its circumference being
actually greater than the distance from the Earth to the Moon. It has
seven moons, and its year is about twelve times as long as ours.
Pursuing our journey, we next come to Saturn. It is nearly as large as
Jupiter, and has a huge ring of planetary matter revolving round it in
addition to seven moons. Further and further we go, and the planets
behind us are disappearing, and even the Sun is dwindling down to a
mere speck; still we hurry on, and at last alight on another planet,
Uranus, about sixty times larger than our Earth; we see moons in
attendance, but they have scarcely any light to reflect; the Sun is
only a star now; but we must hasten on deeper and deeper into space.
We shall again, as formerly, have to go nearly as far beyond the last
planet as that planet is from the Sun. The mind cannot grasp these
huge distances. Still we travel on to the last planet, Neptune,
revolving on its lonely orbit; sunk so deep into space that, though it
rushes round the Sun at the rate of 22,000 miles per hour, it takes
164 of our years to complete one revolution. Now let us look back from
this remote point. What do we see? One planet only, Uranus, is visible
to the unaided eye; the giant planets, Jupiter and Saturn, have
disappeared, and the Sun itself is now only a star; practically no
heat, no light, all is darkness in this solitary world; the Sun is
1000 times smaller than we see it from the earth, and gives,
therefore, only one-thousandth part of its heat and light. Thus far
have we gone, and, standing there at the enormous distance of
3,000,000,000 miles from our starting-point, we can begin to
comprehend the vast limits of the solar system; we can begin to
understand the ways of this mighty family of planets and satellites.
But let us not set up too small a standard whereby to measure the
Infinity of Space. We shall find, as we go on, that this stupendous
system is but an infinitesimal part of the whole universe.
Let us now look forward along the path we are to take. We are standing
on the outermost part of our Solar System, and there is no other
planet towards which we can wing our flight; but all around are
multitudes of stars, some shining with a brightness almost equal to
what our Sun appears to give forth at that great distance, others
hardly visible, but the smallest telescope increases their number
enormously, and presents to our mind the appalling phantom of
_immensity_ in all its terror, standing there to withstand our next
great step. How are we to continue on our journey when our very senses
seem paralysed by this obstruction, and even imagination is powerless
from utter loneliness? One guide only is there to help us, the
messenger which flits from star to star, universe to universe; Light
it is which will help us to appreciate even these bottomless depths.
Now, Light travels 186,000 miles per second, or 12 million miles every
minute of time. It therefore takes only about four hours to traverse
the huge distance between our Sun and Neptune, where we are now
supposed to be standing; but to leap across the space separating us
from the nearest star, it would require many years for Light,
travelling at 186,000 miles every second of that time, to span the
distance. There are, in fact, only fifteen stars in the whole heaven
that could be reached, on the wings of Light, in sixteen years!
Let us use this to continue our voyage. On a clear night the human eye
can perceive thousands of stars, in all directions, scattered without
any apparent order or design; but in one locality, forming a huge ring
round the heavens, there is a misty zone called the Milky Way. Let us
turn a telescope with a low aperture on this, and what a sight
presents itself! Instead of mist, myriads of stars are now seen
surrounded by nebulous haze. We put a higher aperture on, and thus
pierce further and further into space; the haze is resolved into
myriads more stars, and more haze comes up from the deep beyond,
showing that the visual ray was not yet strong enough to fathom the
mighty distance; but let the full aperture be applied and mark the
result. Mist and haze have disappeared; the telescope has pierced
right through the stupendous distance, and only the vast abyss of
space, boundless and unfathomable, is seen beyond.
Let us pause here for a moment to think what we have done. Light,
travelling with its enormous velocity, requires on an average
considerably over ten years to traverse the distance between our Solar
System and Stars of the first magnitude, but the dimensions of the
Milky Way are built up on such a huge scale that to traverse the whole
stratum would require us to pass about 500 stars, separated from each
other by this same tremendous interval; 10,000 years may therefore be
computed as the shortest time which light, travelling with its
enormous velocity, would take to sweep across the whole cluster, it
being borne in mind that the Solar System is supposed to be located
not far from the centre of this great star cluster, and that the
cluster comprises all stars visible arrayed in a flat zone, the edges
of which, where the stratum is deepest, being the locality of the
Milky Way.
Let us once more continue our journey. We have traversed a distance
which even on the wings of light we could only accomplish in many
thousands of years, and now stand on the outskirts of our great star
cluster, in the same way, and I hope with the same aspirations, as
when we paused the last time on the confines of our Solar System.
Behind us are myriads of shining orbs, in such countless numbers that
human thought cannot even suggest a limit, and yet each of these is a
mighty globe like our Sun, the centre of a planetary system,
dispensing light and heat under conditions similar to what we are
accustomed to here. Let us, however, turn our face away from these
clusterings of mighty suns, and look steadfastly forward into the
unbroken darkness, and once more brace our nerves to face that
terrible phantom--_Immensity_.
We require now the most powerful instruments that science can put into
our hands, and by their aid we will again essay to make another stride
towards the appreciation of our subject. In what, to the unaided eye,
was unbroken darkness, the telescope now enables us to discern a
number of luminous points of haze, and towards one of these we
continue our journey. The myriads of suns in our great star cluster
are soon being left far behind; they shrink together, resolve
themselves into haze, until the once glorious universe of countless
millions of suns has dwindled down to a mere point of light, almost
invisible to the naked eye. But look forward: the luminous cloud to
which we are urging our flight has expanded, until what, at one time,
was a mere patch of brightness, has now swelled into a mighty star
cluster; myriads of suns burst into sight--we have traversed a
distance which even on the wings of light would take hundreds of
thousands of years, and have reached the confines of another Milky Way
as glorious and mighty as the one we have left; whose limits light
would require 10,000 years to traverse; and yet, in whatever direction
the telescope is placed, star clusters are to be seen strewn over the
surface of the heavens.
Let us take now the utmost limit of telescopic power in all
directions. Where are we after all but in the centre of a sphere whose
circumference is 100,000 times as far from us as one of the nearest
fixed stars, a distance that light would take over a million years to
traverse, and beyond whose circuit, infinity, boundless infinity,
still stretches unfathomed as ever? We have made a step, indeed, but
perhaps only towards acquaintance with a new order of infinitesimals.
Once the distances of our Solar System seemed almost infinite
quantities; compare them with the intervals between the fixed stars,
and they become no quantities at all. And now when the spaces between
the stars are contrasted with the gulfs of dark spaces separating
firmaments, they absolutely vanish away. Can the whole firmamental
creation in its turn be nothing but a corner of some mightier scheme?
But let us not go on to bewilderment: we have passed from planet to
planet, star to star, universe to universe, and still infinite space
extends for ever beyond our grasp. We have gone as far towards the
infinite as our sight, aided by the most powerful telescope, can hope
to go. Is there no way then by which we can continue our journey
further towards the appreciation of this infinity? A few years ago we
should probably have denied that it was possible for man to go
further; but quite lately a new method of observation has been
developed, and we will try and use this to continue our flight.
The reason why, to our sight, an object becomes apparently smaller and
smaller as it is withdrawn from the eye, until it at last disappears
entirely, is that the eye is a very imperfect instrument for viewing
objects at a great distance; it can only form an image of an object
when that object is near enough to subtend a certain angle, or, in
popular language, to show itself a certain size--the rays of light
must converge--in fact, the eye cannot single out and appreciate
parallel rays: could it do this, objects would not appear to grow
smaller as they are removed. A pencil might be removed to the Moon,
240,000 miles away, and would still appear to the eye the same size as
it does here close to you; with perfect vision there would be no such
thing as perspective, but, with our present conditions of sight, the
result would be inconvenient. We should never be able to see, at one
and the same time, anything larger than the pupil of our eye. The
beauties of the landscape would be gone, and our dearest friends would
pass us unheeded and unseen; everyday life would resolve itself into a
task similar to that of attempting to read our newspaper every morning
by means of a powerful microscope; we should commence by getting on to
a big black blotch, and, after wandering about for half an hour, we
might perhaps then begin to find out that we were looking at the
little letter "e," but anything like reading would be quite out of the
question. We may, therefore, with our limited aperture of sight, be
thankful that our eyes have the imperfection of not appreciating
parallel rays. But we will now consider how this imperfection may be
remedied by science.
There are two different ways of doing this--viz., first, by increasing
the amount of light received, by means of telescopes of great
aperture; and secondly, by employing an artificial retina a thousand
times more sensitive than the human. Now, the human retina receives
the impression of what it looks at in a very minute fraction of a
second, provided of course that the eye is properly focussed, and no
further impression will be made by keeping the eye fixed on that
object; but in celestial photography, when the telescope is turned
into a camera, the sensitive plate, having received the impression in
the first second, may be exposed not only for many seconds, or
minutes, or hours, but for an aggregate of even days by re-exposure,
every second of which time details on that plate new objects, sunk so
deep in the vast depths of space as to be immeasurably beyond the
power of the human eye, even through telescopes hundreds of times more
powerful than the largest instruments that science has enabled us to
construct; and yet here is laid before us a faithful chart, by means
of which we may once more continue our journey through space. A short
exposure will show us firmaments and nebulae just outside the range of
our greatest telescopes, and every additional second extends our
vision by such vast increases of distances that the brain reels at the
thought; and yet, as we have seen, exposures of these sensitive plates
may be, and have been, made not only for seconds, but for thousands
and even hundreds of thousands of seconds! And still there is no end,
no end where the weary mind can rest and contemplate; the finite mind
of man can only cry out that there is no limit. In spite of all its
strivings and groping by aid of speculative philosophy, the finite
cannot attain to the Infinite, nor get any nearer to where the mighty
sea of time breaks in noiseless waves on the dim shore of eternity.
In this journey through space we have apparently exhausted our power
of conception of the _extension_ of this View. Although we have
travelled in one direction only, our flight was applicable to every
possible known direction _outwards_ into the vast abyss of Infinite
space. But there is another path, by which we can also travel with
profit to our understanding of this subject, running in the opposite
direction--namely, _inwards_. Just as the outward journey seemed to
take us towards the appreciation of what our finite senses call the
infinitely great, so does this other path appear to intend to
infinity, in the opposite direction, leading us to appreciate what is
called the infinitely small. We have already considered this direction
in View One, under the heading of "Relativity," and by combining these
two experiences, we may see still more clearly that our very
conception of Space is one of the modes only under which motion or
physical phenomena are presented to our consciousness.
VIEW SEVEN
TIME
In the last View I referred to the mysteries of Time and Space as
twin-sisters; they have, as we saw, many aspects in common, and are
the two modes or conditions under which all our senses act and by
which our thoughts are limited. We arbitrarily divide each of these
two mysteries into two parts, which parts are separated from each
other, in either case, by a point which has, apparently, as its
centre, our very consciousness of living. In the case of Space we call
this point the HERE, and on one side of it, as we saw in our last
View, we have extension towards the infinitely great, and, on the
other, intension towards the infinitely small. In the case of Time we
call the middle point the NOW, and on one side of this we place the
duration of Time towards the future, and, on the other, we place what
we call the duration of Time towards the past. In the case of Space we
have the here and the _overthere_, equivalent in Time to the present
and the _future_, but, though Time and Space are, as it were,
twin-sisters, upon whose combined action depends our very
consciousness of living, we do not treat them both equally.
It is a remarkable fact that the human race on this particular world
has, in some inexplicable way, come to look upon the future as
non-existent until we arrive at, and are able to perceive, with our
senses, what is happening there; this is all the more inexplicable
when we realise that in traversing Space we certainly have to _move_
to get anywhere, but in traversing Time we have nothing equivalent to
movement. This curious way of looking upon the future as non-existent,
may be another sign that our race is still in its infancy, but is more
probably caused by human beings having always hitherto looked upon
Time not only as a reality but as actually moving or extending along a
line from past to future eternity; whereas, under our present outlook,
we have no consciousness of the existence of Time except by intervals
between successive thoughts; our consciousness of the very existence
of Time is based upon our Physical Ego repeating the _present_, by
saying to itself the words, Now--Now--Now; but there is nothing that
can be called movement in this, any more than if you are standing
still and saying, Here--Here--Here--relating to Space. Time is, as it
were, "marking time," and as the present in time is common to all
space, Time is "marking time" everywhere, and the Now therefore
includes the whole of the past and the whole of future eternity
everywhere. We shall get a clearer understanding of this later on;
meanwhile, we are face to face with the fact that we look upon the
future as non-existent.
This curious state of things is probably only accidental to the
present stage of development of the human mind, and may, at any time,
be rectified by perhaps either a slight rearrangement of that slender
network of nerves upon which depends our faculty of thinking, or the
joining together of a few microscopical filaments attached to the
cells in the grey cortical layer, or even a single bridge thrown
across from one convolution to another of the brain; a very slight
alteration would open up to our consciousness the present existence of
the future. The prime perceivable difference between our brains and
those of the Apes and lower animals is the larger number of
enfoldments, or convolutions, that are developed by the Human. Each
new line of thought, or sequence of thoughts, requires, and is
provided with, a new wrinkle or small convolution, and it probably
only requires the attention of the human race to be fixed, for a time,
on the consideration of this subject, to evolve the slight alteration,
or bridge, necessary to enable us to see that the future, as also the
past, does actually exist and is included in the Now. It may make this
a little clearer to consider that if you maintain that, in traversing
the duration of time, the future does not exist until you arrive
there, you should also in fairness insist that, in travelling through
the extension of Space, your destination, say Rome, does not exist
until you get there and can see it with your senses.