CHAPTER XI.

On the next day the student rose early and went forth alone. He did not,

as was his wont, go amongst the people, but he passed through the

streets towards the open country. On his way he was stopped by an old

woman, bent with age and many infirmities. She had no place amongst the

people, and had so many pains and such a barrenness of existence that

any one who had thought of her would have wondered that she remained

alive.

She stopped him and said, “Master, I have heard that you can take my

pain. Help me.”

But he answered, looking at her, “No, I cannot, but I have a message for

you.”

And she said, “A message for me? I do not know any one who would send me

a message.”

But he answered, “Nevertheless, I have a message to you from my lord,

and he bids me thank you.”

She answered, “It cannot be. You must have made a mistake.”

But he said, “I have made no mistake; he thanks you.”

He could not explain to her how by her bearing pain, according to the

law of the valley, she took it from that which the king bore. Instead of

saying that, he gave her the message, and somehow the old woman believed

it.

The rest of the day he spent in the open country. When he returned it

was getting towards dusk. There was an unusual movement in the streets.

On passing into the public market-place he saw a crowd collected; and

when he had penetrated to their midst, he saw lying on the ground the

child he had kept so long. It had been lying uncared for and exposed for

many hours; and the want of food, the fright, and its gasping breathing

made it the most pitiable object. He at once stepped towards it and took

it up in his arms.

“Is that your child?” said one of the crowd.

“It is not my own,” he answered, “but I take care of it.”

“Then it is you that are bringing pain upon us all,” shouted several

voices from the back of the crowd. And some one shouted out:

“I know you. You pretend to take pain away and you really bring much

more in secret.”

And moved with a feeling of indignation against the one who had caused

such a painful object to exist as the child was, the crowd closed on

him, and barred his way to his own place. But they did not lay hands on

him. As he stood with the child it gradually began to regain its

composure. But with a sudden movement the crowd swept towards the

council chamber. And when they had come there they demanded that this

cruel and wicked act of keeping pain in existence should be punished.

There happened to be several of the chief magistrates on the spot, and

in obedience to the voices of the crowd they proceeded to sit in

judgment at once. It was not known how the child had come into the

streets; but it was admitted by the prisoner to be his doing that it had

been kept alive. The doctors unanimously said that it ought to have been

put out of existence directly it was born. There was practically no

defence. The charge of subverting the laws was established. The people

clamoured for the extreme penalty. The judges passed sentence on the

student.

Before morning he was put to death.

He met his fate without sorrow, even with gladness. The pain in his life

had for long been as much as he could bear. He did not, like the prince

of long ago, look upon nothingness as the desired end of existence. He

felt the presence of the one whom he had discerned through thought, and

this seemed more real to him than life or death.

On the following day, whether in reaction from the excitement of the

previous evening, or from some other cause, an unusual quiet pervaded

the streets of the city. There was not much discussion as to the event

which had happened. The prevailing feeling was one of wonder that there

should have been so much commotion about an unimportant affair. For the

most part before the next evening the whole circumstances were on the

way to be forgotten. And yet every here and there were persons in whose

lives the loss of their friend was deeply felt. The joy and spring of

life seemed gone. The poor child lay pale and motionless, save when

every now and then it gasped convulsively for breath. None felt the

despondency more than the clerk. The interest and value of life seemed

to have gone. He did not care for his new honours.

That day some most unexpected news went through the town. The chief of

the council of sensation had sunk into apathy. He was in the prime of

his life. It was most unexpected. Every one was astonished at the news,

but were still more astonished at how little they felt concerned.

Following on these tidings came others. Many of the inhabitants of the

metropolis whose lives were most strenuous suddenly succumbed. The clerk

had made up his mind to go into the country. But tidings came from there

also that the poorer labourers, and those who were exposed to the

fatigue of long journeys or exposure were in many cases sinking. The

wave of torpor seemed passing over the whole valley and not to be

confined to the metropolis. The rich and unoccupied classes only were

comparatively unaffected. They betook themselves to the store of

enjoyable things at their service, and so replaced the natural spring of

life which seemed tending to fail in every one.

On the confines of the valley, where the ravine struck its vast depth

between this land and that, vast and endless as the sea stretched the

plain whence the king had come. It was struck silvery grey by the light

of the moon, dark shadows marked the nearer strands, and gradually the

rocks which cast them showed their sharp outlines, hardly

distinguishable from the ground out of which they rose.

Over the great gulf floated the sounds of a pipe, the strains were low,

winning the soul with the sweetness of an unearthly melody, throbbing as

with a call to a distant land away and beyond.

And when the eye found the source of the sounds, there stood, once more,

solitary in the untenanted vast, the king’s devoted friend, the same old

man who before had hailed him. Gradually the music sank lower and lower,

till at length silence spread in folds unruffled. Then on the edge of

the valley a form appeared. It came and seemed to gaze across the gulf,

standing motionless and intent. At length a voice came.

“Art thou there?”

“Yea, O king, what wouldst thou? Art weary?”

No answer came.

Then the old man spoke. “Behold the roads where they stretch gleaming

white in the moonlight; behold the fields, the villages; see in the

distance the great walls of the palace. Have not these risen up for

thee, O king?”

Then the king made answer: “I am weary.”

Suddenly the old man raised his pipe with both his hands to his lips.

Wave after wave of triumphant sound pealed forth. Great harmonies such

as marching nations might hear and rejoice, noble notes of unbounded

gladness.

Then, crossing by an unknown way, he came and stood by the king’s side.

After a while the two moved on together, and by a secret path passed

away from the valley—whither I know not.

As soon as the king had departed from the valley the beings in it began

to sink into the same state of apathy as those were whom he had first

found there. Those who sank first were the ones in whose lives the

stress of labour or thought was the most intense, for they first felt

the loss of that bearing of pain by one beyond themselves which gave

them a difference of pleasure. And slowly as the accumulated enjoyment

was exhausted, a chill death in life crept over the land. ’Tis useless

to ask after the fate of any one of those that were there, for each was

involved in the same calamity that overwhelmed all. Every hand forgot

its cunning. The busy hum of life in the streets was hushed. In the

country the slowly moving forms gradually sank to rest. At every spot

was such unbroken quiet as might have been had all the inhabitants gone

to some great festival. But there was no return of life. No watchful

eye, no ready hand was there to stay the slight but constant inroads of

ruin and decay. The roads became choked with grass, the earth encroached

on the buildings, till in the slow consuming course of time all was

buried—houses, fields, and cities vanished, till at length no trace was

left of aught that had been there.

_PART II._

CHAPTER I.

There are certain respects in which our world resembles the valley.

Instead of regarding pleasure, pain, and feeling, let us examine the

world we live in with regard to motion in one direction and another, and

in respect of energy.

If we observe the movements which go on in the world, we find that in

great measure they consist of movements which if put together would

neutralize each other.

A pendulum swings to and fro. If the two movements took place at the

same time the pendulum would be still. Taking a more ample motion—that

of the earth round the sun. The earth moves in the course of its orbit

as much towards the sun as away from it, and as much towards the east as

towards the west. If all the motion were to be gone through at one and

the same time the earth would not move with regard to the sun.

Again, if we notice what goes on on the surface of the earth, we see

that there is a motion of rising up and of sinking down. There is an

approximation of the chemical elements into some compounds, and a

separation of them again. Of all the myriad processes which go on, the

swing of a pendulum is the type. But the downward swing may be very

different to the upward swing. It may be that the downward swing is

represented by the violent action of the chemical affinities in a charge

of gunpowder when exploded, and the upward swing may be represented by

the swift motion imparted to a cannon ball, and the swift motion of the

cannon ball in its turn comes to rest, and as it comes to rest slowly or

quickly other changes take place.

And what we notice in our world is similar to what the inhabitants of

the valley noticed about pleasure and pain—that they do not neutralize

one another as a matter of fact.

The contrary motions on the earth which, if they were put together,

would neutralize one another, do not as a matter of fact neutralize one

another. We call motion in one direction positive—in the opposite

direction negative. But in the world as a matter of fact positive and

negative motion do not together come to nothing.

As in the valley the states of pleasure and of pain did not coalesce

into a state of apathy, but always succeeded one another, in simple or

complicated fashion, so on the earth it is impossible from two opposite

moving bodies to get stillness. If the two come into contact in opposite

directions the movement does not stop, but makes its appearance in an

alteration of the shape of the bodies, in a disturbance of their

particles, or in some such fashion.

Again in the valley, by measuring the pleasure and pain simply as

feeling, and not taking into account whether it was pleasure or pain,

the inhabitants found that the feeling was always the same in amount.

So we on the earth, measuring the amount of movement, and leaving out of

account whether it is positive or negative, come to the conclusion that

the quantity of movement, reckoned in the way in which we call it

energy, is always the same. The principle of the conservation of energy

has become a fundamental one in science.

But besides the discovery that the amount of sensation as such was

always constant, the inhabitants of the valley discovered that a portion

of the sensation was passing away from a form in which they could feel

it.

And there is an analogous discovery in science. We know that a portion

of the energy of our system is passing away. It is not being

annihilated, but is disappearing. With the energy which can be collected

from the falling of a stone, the same stone cannot be raised to its

former level again. Some of the energy has disappeared from the form in

which it can be known as the energy of moving masses. The energy has in

some measure irrecoverably passed off in the form of heat.

Hence, just as the inhabitants of the valley came to the conclusion that

in point of sensation they were “running down,” and that after a time

all sensation would have passed away from the form in which they could

feel it, so we have come to the conclusion that the energy of the system

in which we live is running down, that the energy is passing out of the

form in which it can be manifested as moving masses, that finally all

movement of masses will come to a standstill, and there be nothing left

save motionless matter, with warmth equally diffused through it.

Now in coming to the conclusion about the valley, that the amount of

sensation was gradually passing away, the inhabitants, as we have seen,

had come upon the very secret and cause of all the life in the valley.

But coming upon it from the outside they had not recognized the

significance of what they had found. The cause and prime mover of all

their existence indicated itself to them, coming thus upon it, as a

process whereby all that went on was doomed to a distant but certain

extinction.

Now, is this process of the passing of mechanical energy into the form

of heat to be interpreted by us in a way analogous to that in which the

inhabitants of the valley could have interpreted the process they found?

In this cessation of sensation in the form in which they could

experience it lay the central fact of the life of the valley. Has this

passing away of energy from the form in which we can experience it an

analogous significance to us?

In order to examine into the possibility thus suggested there are four

convergent lines of thought which it will be well to follow up

separately. Each of these lines of thought bears in an independent

manner on the central question—the significance of the passing away of

energy. These lines of thought may be connected with the following

words, which indicate their significance: (1) Permission; (2) Causation;

(3) Conservation of Energy; (4) Level.

CHAPTER II.

When we observe any movement taking place we ask what is the cause of

it? what is the force which produces it? But surely, if we confine our

inquiry to this point, we have made an omission. That we are not

conscious of having made an omission may perhaps come from our living in

the air which yields so easily to any moving body. If we lived in a

rigid medium we should, when we became aware of any moving body, ask two

questions. First, what urges it along? secondly, what prepared the

channel for its motion?

But seriously, without laying any stress on the above illustration, we

see that to every movement two conditions are necessary: a pushing and a

yielding, a force and a permission. If the particles of the air could

not yield, a pendulum could not swing through it. If again the air could

not pass on the motion it has received, it could not yield to the motion

of the pendulum.

Now since every motion requires a permission, we are led to ask the

question, What is the ultimate permission? What again is that which by

yielding allows motion at all to take place?

If we trace any movement scientifically we find an indication of what

the ultimate permission is.

A body swings through the air. Currents in the air are set up. These

currents impinge on the objects with which the air is in contact, and in

them produce heat—producing heat also by friction with other portions of

the same air. Every motion thus passes off finally, at however long an

interval, in the form of heat. Motion may reappear as motion through

myriads of phases, but at each change of form some of it passes off into

the form of heat, and finally all passes off into the form of heat.

Thus, unless matter admitted of being warmed, there would be no ultimate

permission. A motion once started would never come to rest. Or, rather,

no motion could take place at all.

The tendency of the above remarks is to avoid the conception of there

being absolute laws of motion, true of bodies when surrounded by no

medium, modified when a medium is present. Surely such a conception is

an instrument of the mind for exploring nature, not an absolute fact in

nature. The abstract laws of motion are mental aids in creating

knowledge; like scaffolding for the builder, even from their very

usefulness they have probably but little to do with the permanent

edifice.

This passing into the form of heat supplies a place analogous to that of

the “void” in the speculations of the Epicurean philosophers. They

argued that motion was not possible without a void. Given a void,

somewhere into which matter could move, then any amount of motion could

be accounted for. But without a void into which a portion of matter

could move, how was it possible for motion to begin?

Thus repeating their inquiry with our altered conceptions, we ask this

question about motion, or energy (which is a particular way of reckoning

motion).

Unless motion can in some way pass off, how can there be all these

transformations of energy?

Now the ultimate transformation of all energy of motion is into the form

of heat. In this change into the form of heat is to be sought the

ultimate permission which makes all transformations of energy, all

motions, possible. It is this being acted on of the finer particles of

matter which permits the movements of the larger masses.

This passing of energy into the form of heat must not be regarded as a

side circumstance, as less essential to the laws of nature than that law

which we call the conservation of energy. It is at the same time the end

of every motion, and that which makes every motion possible.

The passing of energy into the form of heat takes place in that which we

call friction, and in all those modes in which any movement is brought

to a standstill. But so far from these being simply “hindrances” to

motion, it is through them that we learn that which makes motion

possible. It is with us as with the inhabitants of the valley, the

gradual cessation of feeling from their life and the modes in which it

ceased were the way in which they regarded the action of the king who

was the cause of all. We have thought of motion as a thing in itself

impaired by the multitudinous obstacles it meets in the world. Let us

look on the circumstances more impartially. Let us look on them as

something co-equal with motion. Let us find in that mode whereby all

motion comes to an end the originating cause also whereby all motion

comes to be.

The passing of the motion of masses into the form of heat is the

ultimate permission.

CHAPTER III.

If we reflect cautiously on the history of our opinions, we find that we

often fall into error in respect to our freedom in attributing causes.

If we are unfortunate we are apt to look on our neighbours, or the

world, or, if we are of a self-depreciatory turn of mind, ourselves as

the cause.

Again in past times people really felt sure about certain things being

causes which we now know had a very slight connection with the result.

Incantations have been supposed to have an effect on physical phenomena,

such as eclipses. Numbers and their properties have really been

conceived as the causes of the modes of existence. Ideas have been

supposed to have causative power over the order of the world.

We should be very careful in attributing the notion of causation. If we

see a stone lying on the ground, and proceed to pick it up by the

strength of the arm, we say that the exertion of the arm is the cause of

the stone being lifted. But in this respect even we are too hasty. The

arm may exert itself and yet the stone not be lifted up—if it is too

heavy. All that we can say about it is that if the stone is lifted, a

certain set of muscular actions has gone on in the arm, and a certain

movement of the stone has taken place. If we look closely at the matter,

the movements in the arm are related to the movements in the stone in a

strictly measurable way. There has been so much exertion corresponding

to the weight of the stone. But suppose the arm had done anything else,

there would have been the same relation traceable between the movements

in the arm and the actions which followed its movements. The energy

spent by the arm would be equal to the energy imparted to the object

moved, whether it be a stone sent flying through the air, or one lifted

to a higher position (bearing in mind always the small quantity of

energy passing off in the form of heat).

It does not seem advisable that the notion of cause should be brought in

to denote the relation of the movement of the arm and the movement of

the stone. These are two sets of actions between which the regular

relations which hold good between the consecutive states of moving

systems hold good.

The notion of “cause” should rather be applied to that act of the will

whereby the movements of the arm are connected with the movement of that

particular stone rather than the movement of any other object.

We are the cause of the actions we will. The notion of cause is derived

from our “will” action, and the notion of cause ought to be kept to this

connection.

All that goes on outside us can only be apprehended as consecutive

states following on one another. Between certain sets of consecutive

events we notice that the same relation holds good which we have

observed in other consecutive states. If some water is heated in England

it passes off into steam; if water is heated in another part of the

world it also passes off into steam. There is an exact analogy in the

behaviour of water under the action of heat wherever we observe it. But

all that we have obtained as knowledge is the fact that we may

practically be confident of an analogous behaviour on the part of water

wherever circumstances are similar. We may use the expression that heat

is the cause of water boiling for convenience. But the expression should

not be used as containing any deep meaning. To say one external event is

the cause of another is to put an absolutely unknown and spiritual

relation in place of impartial observation.

To cause a motion is the name for the action of our soul on matter—a

thing shrouded in mystery. To be the antecedent in a chain of movements

is the fact which we can observe about any movement in the external

world. We cannot strictly say what movements of gases, water, &c., cause

this volcano. We can only say what movements of gases, water, &c.,

precede this volcanic eruption analogous to movements which have

preceded other volcanoes.

There are invariable sequences in the external world to which we do not

affix the notion of cause and effect—day and night, summer and winter.

Why we should do so in any case is not clear, except that by familiarity

and mystery the sequences have become to us something like our own will

action. Indeed, is it not the case that when we can trace intermediate

links we say so and so comes from so and so in such a manner. But when

no intermediate links can be traced we say one event causes another.

If, however, we omit the feeling of causation from the external chain of

events, it does not follow that there is no causation to be apprehended

in the external world.

Let us not introduce the notion of causation at haphazard. But if we

find in the external world signs of an action like our own will action,

let us then say, Here is causation.

The inhabitants of the valley would not have been right in saying that

one act of a routine caused another: But they were right in saying that

the amount of sensation was constant, and that some of it passed off in

a form in which they could not feel it.

And so let us not say that one action causes another. Let us not say,

for example, that the downward swing of a pendulum is the cause of its

upward swing. But let us simply say that the one follows the other; that

the amount of energy present is the same except for the small portion

that passes off into the form of heat.

CHAPTER IV.

Suppose certain sets of numbers were being presented to us one after the

other, and amongst these three consecutive sets were the following.

First set: 3, 5, 6. Second set: 8, -2, -1, 1. Third set: 7, 4, 2, -1.

A little consideration will show us that there is a certain uniformity

in these sets.

Take the square of each of the numbers in the first set and add them

together, the result is 70. Thus 3² + 5² + 6² = 9 + 25 + 36 = 70.

The sums of the squares of the numbers in the second set come to the

same. 8² + (-2)² + (-1)² + 1² = 64 + 4 + 1 + 1 = 70. Also in the third,

7² + 4² + 2² + (-1)² = 49 + 16 + 4 + 1 = 70, and so on.

Having noticed this we should regard it as a purely formal law, having

nothing to do with why the numbers were presented to us. But we should

consider it likely that it would characterize all the numbers that were

presented to us. And if this expectation were found to be realized, we

should after a time feel a certain assurance that the next set of

numbers presented would satisfy the same law. If this assurance was

indefinitely satisfied we should get to regard the satisfying this law

as an invariable condition of the numbers presented. But we should never

regard this purely formal law—that is, a law about the particular

characteristics of the numbers—we should never regard this formal law as

the cause of the next set of numbers appearing after the first had gone.

When, however, we talk about the conservation of energy we are apt to

think of it as more than a merely formal law, more than a statement

about numbers which has been found to hold true.

Yet it is no more. The law of the conservation of energy asserts that in

any system in motion the sum of the squares of the velocities of the

particles at any one moment is equal to the sum of the squares of the

velocities of the particles at the next moment.

The conservation of energy is but a mode of reckoning motion, by which

it is found to be constant in all changes of a system. The system must

embrace all the particles concerned in the motion. It may be made as

large as we like.

The principle of the conservation of energy as here stated is confined

to the case of moving bodies. Sometimes the energy is said to disappear

from the form of motion and become potential energy. That case will be

treated under the fourth consideration of level, but it introduces no

alteration in what has been said.

As to the practical truth of the law of conservation of energy there can

be no doubt; nor as to the value of the results obtained from tracing

its validity in obscure actions. But there is nothing final about it. It

is a numerical statement of extreme value, and it introduces a mode of

reckoning by which motion can be looked upon as indestructible as matter

is.

There is a possible objection to the law of conservation of energy.

It is no less a law in nature that in every one of a series of changes

some of the energy passes off into the form of heat. Now heat is

reckoned as a mode of energy. And there is in science a method of

calculating how much energy any given quantity of heat is the equivalent

of. And this equivalence is calculated on the supposition that no energy

is lost. When heat is produced and motion passes away, the proportion

between the motion that disappears and the heat that appears is

represented by a number calculated on the assumption that no energy is

lost. Thus whenever any quantity of energy takes the form of heat, the

quantity of heat which is produced is exactly given by the calculation.

But the reverse process is not possible. It is not possible to turn back

all the energy in the form of heat into the form of motion. Consequently

it cannot be proved that the energy in the form of heat would, if all

turned into motion, produce as much motion as that from which it was

produced. There may be an absolute loss of energy—only a very small one.

The law of the conservation of energy may be the expression that this

loss is a minimum.

This objection is not essential to the line of argument pursued above

with regard to the conservation of energy. It forms no necessary part of

the line of thought we are pursuing. It merely tends to show that the

law of the conservation of energy is no axiom which we cannot suppose

not true. The real conclusion to which this part of our line of thought

tends is that the conservation of energy is a purely formal law.

CHAPTER V.

The most apparently simple movements are those which we see taking place

on the surface of the earth, connected with the agency which we call

gravitation. We see the rivers flowing from a higher to a lower level,

rocks when loosened from a mountain side rolling down, rain falling, and

many minor changes of this sort.

But there are many actions besides these. For instance, suppose before

us a spring coiled up. When it unwinds it “exerts force,” it transmits

movement. In its first state it is like a stone at the top of a

mountain. In its second state it is like a stone which has fallen to the

bottom of the mountain. It had a power of movement and of communicating

movement, now it has lost that power.

Again, the powder in a gun when it explodes expands and imparts movement

to the shot. When the gun has been fired off the powder enters a

different state. Before, the chemical affinities of its constituents

were in a state of tension, now that it is fired off, they have formed

fresh combinations. The power of transmitting movement has been lost by

that which was the powder. It is like a portion of water at the top of a

fall of water. If it remains at the top it has at any time the power of

producing a shock, and of effecting, say, the movement of a water-wheel

under it. But if it falls it has exerted and lost that power.

The difference of level associated with gravity is familiar to us. But

we have no right, other than our own familiarity with it, to look on

gravity as less in need of explanation than any other phenomenon of the

external world. Newton did not suppose that there was any force inherent

in matter which attracted other matter inversely as the square of the

distance. He showed that a great many astronomical facts were capable of

being explained and calculated on this hypothesis. He left the

explanation of how it is that matter gravitates unsolved, and it remains

unsolved to the present day.

But gravitation affords us a useful term—“Level.”

Let us agree to call the following on a high level—a stone at the top of

a precipice, a wound-up spring, oxygen and hydrogen mixed in the

proportion to form water. Let us call the following at a low level—the

stone at the foot of the precipice, a spring straightened so far as it

tends to straighten, oxygen and hydrogen united in the form of water.

In passing from their first state to their last all these have

manifested a power of movement and of communicating movement. They have

now relatively to their former state lost that power.

Difference of level in this general sense is the most universal

distinction of matter.

No motion takes place unless matter passes from a higher to a lower

level.

The universal cause of motion is that which produces this difference of

“level” in the general sense.

If there were no difference of level the state of things in nature would

be as if one spring in order to unwind had to wind up an exactly equal

spring of the same amount; as if a stone falling from a height had to

raise an exactly equal stone to the same height from which it fell.

Under such conditions of things no motion would begin. In such a state

of things all nature would be like the inhabitants of the valley when

the king bore no pain, for no course would be preferable to any other

course.

What is the cause of the “Difference of Level?” Whenever matter passes

from a higher to a lower level some of the energy which is given out

passes away in the form of heat. This passing away of some of the energy

into the form of heat is an invariable accompaniment of the transition

from a higher to a lower level. Is it the cause of the difference of

level?

In the valley the king by bearing some pain made action worth while. Is

there any indication in nature of the production of a lower level which

makes the course of things run on?

It is certain that energy in every action passes off into the form of

heat, and unless it is through the power of the finer particles of

matter to absorb the energy, it is difficult to see how any action can

take place.

As with the other lines of thought, this line also terminates with a

possibility. Nothing has been proved, but a place has been provided.

In the first part of this paper a possible mode of action was exhibited

in the imaginary relations of a world subject to certain laws of

pleasure and pain.

In the second part it has been shown that something is wanting in our

conception of the natural processes. There is room for a central idea.

No scientific doctrines properly understood would clash with one

properly located.

Can the mode of action exhibited in terms of sensation in the fictitious

world be applied to the case of the world of force and matter?

Before passing on, however, it is worth while to examine a little more

closely into what is meant by the expression so often used: “Passing off

into the form of heat.”

The modes in which energy passes off into the form of heat are in

general those modes by which movement is brought to a standstill such as

friction. And we are apt to think motion the primary fact, the cessation

of motion a secondary and disagreeable fact. But both are equally

existent phenomena, and the convenience to ourselves is not to mislead

us as to their relative importance.

But what is this passing off of energy into the form of heat? The phrase

is unsatisfactory, for we are told by science almost in the same breath

that heat is the motion, the mechanical motion, of the particles of

matter. So the statement resolves itself into this. Only when some of

the motion passes off into the form of motion of the smaller particles

of matter does motion take place in larger masses.

As a corollary it follows that at some date, however distant, all the

motion of masses will have passed away into the form of motion of

smaller masses.

It may be urged that when the larger masses move, the smaller particles

also move. This is true; but motion in this sense is used to denote

change of position amongst the smaller particles with regard to one

another. The particles in a flying cannon-ball are relatively still with

regard to one another as far as the motion of the cannon-ball as a whole

is concerned.

We thus arrive at the following principle: The condition of the motion

of masses taking place is that some of the motion passes off into the

motion of the smaller particles.

But if the motion of the smaller particles is just the same as that of

the larger portions, we are obviously not at the end. The very same

principle just applied must be applied again.

These motions of the small particles of matter cannot take place unless

some of their movement is transmitted and passed on, and transformed

into the motion of still finer particles of matter.

But here obviously we are brought to the beginning of an infinite

series. An infinite series passing from finer matter to still finer

matter, and so on endlessly.

The assumption by which we are led to this endless series of

transmissions must be clearly apprehended. We take the law—that the

motion of masses only takes place when some of the motion passes off

into the motion of the finer particles of matter, and we assume that it

holds always.

In a lever there is a fixed point, the fulcrum, which supports it, and

the power raises the weight; but the weight may be fixed, and then the

fulcrum can be lifted by the power. So we obtained this law from the

consideration of material relations; and now we suppose this law to be

the fixed point, and shift our notions of material relations.

Thus we are landed on an endless series. Before proceeding, however, to

inquire what the significance of this endless series may be, let us

assume an end to it. Let us assume that we come at last to a final

transmission. Let us assume that the energy is transmitted to the

ultimate particles of matter.

Or, if we have gone beyond matter, let us suppose an ultimate medium

which by its modifications builds up matter, and which is the last and

ultimate substance.

Let us suppose this ultimate medium absolutely to receive some of the

energy. Let it absolutely receive and absorb some of the energy, and

thereby give rise to the difference of level, to give the ultimate

permission which sets all things going.

What are the properties of this medium? We obtain an indication of what

they are when we examine the properties of the finer kinds of matter.

Compared with the motions of masses, motions which affect the smaller

particles of bodies are infinitely quick. Light and electricity are

actions affecting the smaller particles of bodies, and by them distances

are speedily traversed, which relatively to moving masses are very

great.

Now in point of speed of transmission the properties of this ultimate

medium must be infinitely beyond those of luminiferous ether.

To this ultimate medium all movements at any distance from each other

must be almost equally present at every part. At whatever distance from

one another two affections of this ultimate medium be supposed to take

place, the effect of the one will travel to the place of action of the

other instantaneously.

Such a medium is a kind of visible symbol of the universe, being one

system in which all motions should be co-determined.

To make this clear, suppose a transformation of energy was produced in

one part of space of an absorption of energy on the part of this

ultimate medium, this transformation of energy would be produced by a

medium in instantaneous contact with every other part of space, and the

transformation of energy thus originated would harmonize with, and have

reference to, the transformations of energy in every other part of

space.

There are two infinities—the infinite of space extending out each way,

the infinite of the smaller and smaller divisions of matter. The

ultimate medium we have supposed partakes of both infinities. It is

infinite in extent, and infinitely fine in its particles.

Now this medium by absorbing energy sets movements going. And that

movements do not neutralize one another—_i.e._, that movements in

opposite directions do not mutually destroy one another—has this result,

that a given amount of this absorption produces the greatest possible

amount of motion. If motion came to a rest in any other way, more of

this absorption by the ultimate medium would be needed. Hence, by a

given amount of absorption in the ultimate medium the greatest possible

amount of motion is produced. That is, the absorption of motion into the

ultimate medium is a minimum, and the law of the conservation of energy

is the expression of this being a minimum.

But here again a further remark is called for. We start by assuming

energy to be an absolute existence. But why not assume this action on

the part of the ultimate medium to be the real action, and consider the

phenomena of motion and energy as the mode of its action.

What this action of the ultimate medium may be needs examination. All

that we can say at present is that relatively to that which we call

energy, the action of this medium is that of being acted on.

CHAPTER VI.

In the preceding, however, it must be remembered that this conception of

an ultimate medium was merely a supposition to enable us to see and

roughly map out the relations of the things we are investigating. Where

we were really landed was in an infinite series—we were brought

logically to the conception of an infinite series of media, one behind

the other.

What does an infinite series indicate?

Let us turn to a region of thought where infinite series are familiar

objects, and we can learn about them.

In algebra infinite series are common. Thus take series 1 - _x_²/2 +

_x_⁴/4 and so on for ever. This is the attempt in algebra to represent a

trigonometrical idea. In trigonometry it is expressed as cos. _x_. But

in algebra it needs this infinite series.

In algebra infinite series occur when the object which it is wanted to

represent in algebraical terms cannot be grasped by algebra. When there

is no single term or set of them in algebra which will serve, the object

is represented by means of an infinite series. Thus we may say that in

any calculus, when the object to be treated of cannot be expressed in

the terms of the calculus, it is represented by means of an infinite

series.

Now, dealing with material considerations, going on in the calculus of

matter, we have come to an infinite series. This indicates that we have

gone as far as the material calculus will carry us. We have now to bring

in an idea from a different quarter if we will simplify our expression.

It may well be that within our experience there is nothing which will

serve. But let us suppose that that which in material terms we represent

as an infinite series is a will—a will in contact with all existence, as

shown by the properties it had when we conceived it as an ultimate

medium. For, regarding it as an ultimate substance, we found that it

would be affected by pulsations infinitely quicker than light and

electricity; considered as a substance, it was such that distance to it

tended to be annihilated. Hence as a will we must say of it that to it

all that is is present—a will which by a fiat that to our notions is

being acted on rather than acting, accepting pain rather than taking

pleasure, sets the course of the world in motion, which holds all in one

system, which creates all activities. For although we apprehend this

will relatively to the appearances which we suppose we know, mechanical

energy and feeling, still we see that both are caused by it, and that

the sum of both is nothing, save for that which this will is in them.

Is there any other way of apprehending this will than through the

external world?

We have two apprehensions of nature—one of external things, the other of

our own wills.

Does this will not exist in those who are true personalities, and not

mere pleasure-led creatures?—have they not some of this power, the power

of accepting, suffering, of determining absolutely what shall be?—a

creative power which, given to each who possesses it, makes him a true

personality, distinct, and not to be merged in any other—a power which

determines the chain of mechanical actions, of material sequences—which

creates it in the very same way in which it seems to be coming to an

end—by that which, represented in material terms, is the absorption of

energy into an ultimate medium; which, represented in terms of

sensation, is suffering; but which in itself is absolute being, though

only to be known by us as a negation of negations.

CHAPTER VII.

In conclusion let us remark that we have supposed two different

worlds—one of sensation in the first part, one of motion in the second

part. And these have been treated as distinct from one another. And

especially in the first part, by this avoidance of questions of

movement, an appearance of artificiality was produced, and occasionally

inconsistencies, for sometimes sensations were treated as independent of

actions, sometimes as connected with them. But it remains to be decided

if these inconsistencies are in themselves permanent, or whether, when

we remove the artificial separation, and let the world of sensation and

the world of motion coalesce, the inconsistencies will not disappear,

thereby showing that their origin was merely in the treatment, not in

the fact; that they came from the particular plan adopted of writing

about the subject and are not inherent in the arguments themselves.

The king in the first part was supposed to have all the material

problems of existence solved. There was a complete mechanism of nature.

He took up the problem of the sentient life. But this problem can only

artificially be separated from that of the material world. The gap

between our sensations and matter can never be bridged, because they are

really identical.

Let us then allow this separation to fall aside. Let us suppose the king

to have all the reins of power in his own hands. Let us moreover suppose

that he imparts his rays to the inhabitants so that they have each a

portion of his power. And let us suppose that the inhabitants have

arrived at a state of knowledge about their external world corresponding

to that which we have about the world which we know.

Let us listen to a conversation between two of them.

_A._ The energy of the whole state of things is running down.

_B._ How do you prove that?

_A._ Whenever any motion of masses takes place a certain portion of the

energy passes irrecoverably into the form of heat, and it is not

possible to make so large a movement with those same masses as before,

do all that is possible to obtain the energy back again from the heat

into which it has passed.

_B._ Well, what about the heat? Energy in the form of the motions of the

masses passes off into the energy of heat. But what is heat?

_A._ It is the motion of the finer particles of matter.

_B._ Well, I would put forward this proposal. We have by observation got

hold of a certain principle that where any movement takes place some of

the energy goes in working on the finer particles of matter. Let us now

take this principle as a universal one of motion, and apply it to the

motions of the finer particles of matter themselves, which are simply

movements of the same kind as the movements of the larger ones. This

principle would show that these movements are only possible inasmuch as

they hand over a portion of their energy to work on still finer matter.

_A._ Then you would have to go on to still finer matter.

_B._ Yes, and so on and on; but to fix our thoughts, suppose there is an

ultimate fine matter which is the last worked on. Now I say that we may

either suppose that this is being gradually worked on and all the energy

is dissipating, or else we may put it in this way. When we regard so

much energy we are apt to think that it is the cause of the next

manifestation in which it shows itself. But this is really an

assumption. Energy is a purely formal conception, and all that we do is

to trace in the actions that go on a certain formal correspondence,

which we express by saying that the energy is constant.

_A._ But I feel my own energy.

_B._ Allow me to put your feeling to one side. If we take then the

conservation of energy to be merely a formal principle, may we not look

for the cause of the movements in the invariable accompaniment of them,

namely, in the fact that a certain portion of the energy is expended

irrevocably on the finer portions of matter. If now we take this

ultimate medium which suffers the expenditure of energy on it, may we

not look on it as the cause, and the setter in action of all the

movements that there are. By its submitting to be acted on in the way in

which it does submit, it determines all the actions that go on. For what

is all else than a great vibration, a swinging to and fro. When we count

it as energy, we by reckoning it in a particular manner make it seem to

be indestructible, but that the energy should be indestructible would be

a consequence from the supposition which we could very well make, that

to produce a given series of effects the submitting to be worked on of

this ultimate medium must be a minimum. If it were a minimum no

movements could neutralize one another when once set going, for if they

did there would be a waste of the submission of this ultimate medium.

_A._ But what do you suppose this ultimate medium would be?

_B._ That I cannot tell, but we seem to have indications. For the more

fine the matter which we investigate, the more its actions seem to

annihilate distance: light and electricity produce their effects with

far greater rapidity than do the movements of masses. We might suppose

that to this ultimate matter all parts were present in their effects, so

that anything emanating from the ultimate matter would have the

appearance of a system comprehending everything.

_A._ But you have not got any evidence of an ultimate matter.

_B._ No, all that we can think of is an endless series of finer and

finer matter. But is that not an indication rather, not that the

direction of our thoughts is false, but that there are other

characteristics of this ultimate, so that when looked at under the form

of matter it can only be expressed as an infinite series.

Let us omit the considerations brought forward in the preceding

conversation and examine more closely the philosophy of the inhabitants

of the valley in so far as it corresponds with ours.

They laid great stress on a notion of _vis viva_, or what we should term

energy, but said it was gradually passing away from the form of

movements of large bodies to that of movements of small bodies. So that

in the course of time the whole valley would consist of nothing but an

evenly extended mass of matter moving only in its small particles—and

this motion of the small particles they called heat. Now they had very

clearly arrived at the conviction that with every mechanical motion

there was a certain transference of _vis viva_ to the smaller particles

of matter, so that it did not appear again as mechanical motion. But

they did not accept this as a principle to work by. They did not

consider that the motions of the smaller particles of matter were just

the same as those of the larger masses. They did not see that if a

condition held universally for the movements of the visible world, it

must also hold for the smaller motions which they experienced as heat.

So the conclusion which they should logically have come to that there

was a transference of _vis viva_ on and on was not held. But the step

was a very little one for them to take from regarding an invariable

condition as always there to regarding it as a cause. For the causes

they assigned were all purely formal relations, and only got to assume

an appearance of effective causes by familiarity with them, and a

throwing over them of that feeling of effectiveness which they derived

from the contact which they had with the king.

They might have reasoned. This universal condition of anything happening

must be the cause. Energy goes from a higher to a lower level. That

which causes the difference of level is the cause, and the cause of the

difference of level must be that which invariably accompanies such a

transference of energy from a higher to a lower level. Now this

invariable condition is the passing of a portion of the energy into the

form of motions of the finer parts of matter. Hence there is an

apparently endless series. But to realize the matter, suppose an

ultimate medium, suppose there is a kind of matter of infinite fineness

distributed everywhere which let itself be worked on, and so determines

differences and wakens the sleeping world. What are the qualities of

this fine matter? We see them in the properties of the finer kind of

matter which we know, such as light, electricity. The property of the

finer kind of matter is in general that it tends to bring distant places

together, so that a change in one part is rapidly communicated to every

other part. If they followed this indication they would have supposed

that the ultimate fine matter was of such a nature as to make all parts

of the valley as one, so that there was no distance, and any

determination of a difference of level on the part of this ultimate

matter would have reference to all the conditions everywhere. It would

be in immediate contact with every part, so that anything springing

therefrom would present the appearance of a system having regard to the

whole. Now if they had imagined such an ultimate medium doing that which

to them would seem bearing rather than exerting force, suffering rather

than acting, they would not have been far from a true conception of the

king who directed them all. For he himself by reason of his very

omnipresence could not be seen by them. There was nothing for them to

distinguish him by. But they could have discovered somewhat of the means

by which he acted on them, which can only be described from the

appearances they present to the creatures whom the king calls into life.

But of truth they would have had another and perhaps a truer

apprehension of the king in a different way. For when he acted on them

so that they took one course rather than another, it was his action in

themselves that they felt. If they were mere pleasure-led creatures then

they were shaped outwardly, but if in their inner souls he acted and

through them suffered, then they were true personalities conscious of

being true selves, the oneness of all of them lying in the king, but

each spontaneous in himself and absolute will, not to be merged in any

other.

Thus they had two modes of access to the king, one through their own

selves where he had made them exist, one through the outer world. And in

the outer world it was but a direction in which they could look. They

could never behold the personality of the king, but only an infinite

series of different kinds of matter, one supporting the other as it were

and underlying it, but doing more also than this, for in proportion as

they considered the kinds of matter that lay deeper they found that

distant became near, absent, present, that time gave no longer such

distinctions, but from the phenomenal side they seemed by a gradual

diminution of the limitations of experience to arrive at an external

presentation of that absolute which exists in the fulness of things,

which they knew more immediately in themselves when they truly were.

THE END.

_INTRODUCTION._

In the next two or three of these papers certain questions connected

with the subject of a space higher than our own will be treated. It is

well, therefore, first to recede and to form definite conceptions about

a world of plane space, about a world in which the beings can only move

in two independent directions. Then, proceeding thence to our own world,

we may gain the means of passing on to a higher world. And I should have

wished to be able to refer the reader altogether to that ingenious work,

“Flatland.” But on turning over its pages again, I find that the author

has used his rare talent for a purpose foreign to the intent of our

work. For evidently the physical conditions of life on the plane have

not been his main object. He has used them as a setting wherein to place

his satire and his lessons. But we wish, in the first place, to know the

physical facts.

With this aim it is necessary to form a clear idea of what matter would

be in a world of two dimensions, and the following illustration is a

convenient one.

Place on the smooth surface of a table a half-crown piece, and suppose

it to slide on the table perfectly freely. Imagine it to exercise an

attractive force along the surface of the table in all directions round

itself. By it and near it place a sixpence, and let the sixpence also

slide freely on the table. It will, however, not be so free to move

equally in all directions as the half-crown was, for it will be

attracted by the half-crown. It will slip over the surface of the table

under the influence of this supposed force, and will come into contact

with the half-crown. Now if we suppose that both the half-crown and the

sixpence are very thin, that they are both of them only the thickness of

the ultimate particles of matter, then we shall have a representation of

what material bodies will be in a plane world.

We must suppose that the particles cannot lift themselves or be lifted

up from the plane so as to lie upon each other. Under no circumstances

can they quit the surface of the plane.

Moreover, at no point must the particles adhere to the plane, nor must

there be any friction impeding their movements over it. The only purpose

which the support serves is to keep them on the same level surface and

to convey influences from one particle to another. The gravity which we

know, and which acts at right angles to the table on which the coins

rest, will not have any effect on the particles in their motions on the

plane, but will simply keep them to the plane. Any force of attraction

which concerns their motions proceeds from one particle to another.

Thus, conceive the half-crown to be a very large disk of matter, and the

sixpence to be a sentient being. This being would feel a force of

attraction towards the centre of the half-crown, and this force of

attraction would keep him to the rim of the half-crown. If he weighed

anything it would be by balancing it with his weight against the force

which tended to pull it to the centre of the half-crown. He would not

feel the gravity which keeps him against the surface of the table; he

would not know that there was a hard, smooth surface on which he rested.

He would always have been in contact with it, and so he could not tell

what it would be like to be free from it. He would have no contrast

whereby to apprehend its effect on him. Moreover, he would only know of

movements in directions along the plane. He would not conceive that such

a thing was possible as movement in another direction than to and fro,

hither and thither on the plane. It is difficult to suppose that a being

would be supported on one side by a plane, and not be in contact with

anything on the other side, even atmosphere. Yet if we suppose a being

of real matter free to move on the plane, this is what must be

conceived. If the sixpence is conceived as such a being, it must receive

its impressions through its rim. The rim represents its skin.

And if it be supposed to be surrounded by air for its respiration, this

air must not be able, any more than the particles of solid matter, to

rise away from the plane. The plane being must be conceived to have a

different air to that which we know. The particles of its air, however

free to move amongst themselves, must not have the power of moving away

from the surface of the plane, as if so they would be able to pass to

the interior of the body without passing through the skin. Any passage

leading to the interior of the body would have to terminate in an

opening in the rim, otherwise it would be completely shut up from the

exterior.

Now it is obvious that if the table is struck so that it quivers, this

movement will be communicated to the coins lying on it. Either the coins

as a whole will move, or their particles will be disturbed.

Again, if we suppose there to be some particles loosely cohering

together, lying on a smooth sheet of iron, it is evident that the

quivering and jostling of the iron, if it is struck, would have an

effect on the particles, and may cause the breaking up of the thin

masses in which the particles cohere. Thus, if the material of which the

sheet is composed be very dense and rigid, compared to the substances

lying on it, they may undergo many alterations, being broken up and

coming together again while the supporting matter which bears them all

up simply moves and vibrates.

[Illustration: Diagram I.]

It is evident that just as the particles are affected by the vibration

and shaking of the sheet of metal on which we suppose them, so they

might in turn possibly affect the sheet of metal and cause vibrations

and shakings in it. These shakings and vibrations would go forth from a

particle which excited them in every direction along the sheet. They

would not pass out into the air, except secondarily and in a very minute

degree. The shake would be transmitted in the sheet. And the effect on

neighbouring particles would be great, on more distant particles it

would be less, and on those at a great distance barely perceptible.

The following is a good plan for obtaining in a definite way the feeling

of what existence in a plane would be like; it enables us to realize the

conditions in such a way as to lay the basis for subsequent thought.

Let the reader take a sheet of note-paper and hold it before himself

edgewise, so that he sees it with one eye as a single line. And let him

hold it so that this line runs downwards from his eyebrows to his mouth,

as shown in Diagram I. Now on this sheet of paper, on one side of it,

let a straight line be drawn running across it, away from the observer.

Suppose all below this line to be a thin layer of particles which,

keeping compactly together, form a solid sheet of particles, every one

of which touches the paper. This would be the solid earth to a being in

the plane world.

Let the surface of the paper above this be covered by a layer of

particles which move freely amongst each other, but which do not rise

from the surface of the paper. These particles form the air of such a

world.

On the surface of the earth draw a line standing upright. Let this line

represent a man. Another line will represent a wall which the man could

not pass except by getting over it.

It will be found that the objects on the paper are felt to be subject to

the action of gravity. The question will occur, Why will not this thin

layer of particles slip off the paper?

Now, the sense of gravity must not be got rid of, but it must be

connected with the matter in the sheet of paper.

Suppose, then, that the sheet were to grow bigger and bigger till it

filled out reaching through the whole world and cutting the globe in

two. Then let all the earth be removed except a thin layer on one side

of this enlarged sheet of paper. This thin layer will be the only

portion of matter left. And such a thin layer will represent a plane

world. The force of gravity must be conceived as remaining, but as

coming from a large and thin disk.

Now to keep this thin layer on the paper it would be necessary to have

some force acting sideways, so as to keep the particles to the paper.

And the paper itself may be conceived to exercise such a force: it is

many particles thick, while the thin layer of matter is only one

particle thick, and thus it will keep the layer of matter, which covers

one side of it, in its place by virtue of its own attraction.

We suppose that the paper exerts an attractive force which keeps the

thin layer of matter to it. This attractive force is not felt by the

sentient beings on the paper, nor does it influence the movements of the

particles of matter amongst themselves. We also suppose another

attractive force proceeding from particle to particle of the matter on

the plane. This would be felt by the beings and produce movements of

matter.

Thus the conception of a plane world necessarily involves that of

something on which it is.

A Plane World.

Where the sun’s rays grazing the earth in January pass off and merge

into darkness lies a strange world.

’Tis a vast bubble blown in a substance something like glass, but harder

far and untransparent.

And just as a bubble blown by us consists of a distended film, so this

bubble, vast beyond comparison, consists of a film distended and

coherent.

On its surface in the course of ages has fallen a thin layer of space

dust, and so smooth is this surface that the dust slips over it to and

fro and forms densities and clusters as its own attractions and

movements determine.

The dust is kept on the polished surface by the attraction of the vast

film; but, except for that, it moves on it freely in every direction.

And here and there are condensations wherein have fallen together

numbers of these floating masses, and where the dust condensing for ages

has formed vast disks.

And these disks are glowing hot—yet no light comes from them into our

universe.

For this world lies beyond the æther—far beyond. And however hot or

glowing the masses are, if there is no medium to transmit the vibrations

of heat the influence cannot travel.

Thus the only directions in which the heat can travel are on the film.

From each of these glowing disks the luminous influence streams forth

carried by the vibrations of the film which supports everything. For the

heat and intense agitation of these glowing disks shakes and disturbs

the bubble, and just as a thin soap bubble quivers and shakes, so this

film quivers and shakes. And so elastic is it, and so rigid, that it

carries the light and heat to all surrounding regions. Yet so vast is

the bubble, so tremendous in its dimensions, that the agitation from

these glowing disks travels almost in straight lines, till, spreading

out on every side, it merges into darkness—like the ripples in the

centre of a vast calm lake gradually become indistinguishable.

And round these central orbs of fire—for orbs of fire they are, though

they only transmit their fire along the film of the bubble—round these

orbs pass in due order and succession other disks, which, cold or warm,

have not that energy of light and heat which the central orbs possess.

These disks, though large, are so immeasurably small compared with the

vast surface of the all-supporting bubble, that their movements seem to

lie on a plane flat surface; the curving of the film on which they rest

is so slight compared to their magnitude, that they sail round and round

their central fires as on a perfect level surface.

And one of these orbs is fitted by nature to be the habitation and home

of living beings. For it is neither so hot as it was for long ages after

it had condensed from the film of dust wherefrom all orbs are made, nor

has it so cooled down as to render life unsupportable.

And, moreover, it is full of vast crevices and channels, for in many

places the interior in cooling after the rim had set from its molten

condition has left long caverns and passages, not only in one layer, but

in many.

And on the rim and in these passages and caverns live the inhabitants of

whom I speak.

They do not rise from the surface of the film, but as all matter lies on

the smooth surface but one particle deep, so their bodies formed out of

matter lie, as we should say, on this smooth surface.

Yet of this they know nothing. They say that they stand and walk.

For this orb has an attractive force.

[Illustration: Diagram II.—“Two beings walking round.”]

By that very same impulse of coming together whereby it gathered its

particles out of the dust on the bubble, by that very same force it

draws towards its centre all that is near it or on it. Thus “up” is to

these inhabitants a movement from the centre of the disk on the rim of

which they live and away from it. “Down” is a movement from the rim

towards the centre. The thin layer which forms the mass of the disk is

their solid matter. They are not able even in thought to rise away from

the surface of the bubble, and look from space upon their mode of

existence. They ever pass to and fro upon a line, upon a rim; and no two

can walk except after one another. If you look at the rude picture you

will see that the two beings represented by two triangles cannot pass

one another if they are unable to lift themselves up from lying on the

surface of the paper. The surface of the paper represents the surface of

the bubble, and sliding freely on it, but unable to lift up from it, are

tenuous shapes that are the inhabitants, and that thin layer of

particles that is to them solid matter.

[Illustration: Diagram III.—A section of the film of the bubble

showing a disk BD lying on it, and a creature AB on the rim of the

disk. CE is a section of the film, BD is a section of the disk, AB is

a section of the creature. The thickness is enormously magnified and

also the height AB of the creature compared with the diameter BD of

the disk. The attraction which AB feels keeps him to BD; both AB and

BD, the being and the disk, slide freely on the film CE without

knowing of its existence.]

Now were it not for the fact that the orb is reft into these chasms and

passages, the only movement that these beings would have would be of

passing round and round on the rim of their world.

Many words that we have, to them could bear no meaning. Thus “right and

left” is to them unknown. For consider their faces bent in one direction

along the rim. In following this direction, they go forward, in

retracting from it they go backward. If they go away from the centre

they go up, towards the centre is down. And by no means can they turn,

raising themselves from the surface whereon they are. They do not even

know that they have two sides; their movements, thoughts, and

imaginations are all confined to that surface on which they are. This

they call their space, their universe; nor does aught that lies beyond

it, towards the interior of the bubble or away from it, directed

outwards, come into their thoughts, even as an imaginary possibility of

existence.

Life is extremely limited on such a world. To take a single instance, in

order for two beings to pass each other, a complicated arrangement is

necessary, shown in Diagram IV.

At intervals along the rim recesses and chambers are constructed. Near

the openings of these chambers lay movable plates or rods. When two

beings wish to pass, one of them descends into the recess; the other one

pushes the rod so as to form a bridge over the opening, walks across it,

and then removes the plate so that the one who has descended can get up

and go on his way.

[Illustration: Diagram IV.—Two beings passing.]

If by any chance, while a being is in the recess, the plate or rod which

acts as a bridge gets fixed, he is in a dangerous predicament. For

suppose a being confined as shown. If he, suffering from want of air,

cuts through the roof at AB, the whole part to the right of AB comes

tumbling down. For its only support is severed when AB is cut through.

It is impossible to make a hole which is not the whole width of matter

as it lies on the surface. And with regard to this all constructions

have to be made. There cannot be two openings in a wall of a house,

unless when the one is open the other is so fashioned as closing to act

as a rigid support to the wall, which now depends for its upholding

entirely on it.

[Illustration: Diagram V.—A house.]

Thus, in the diagram, the house is held up entirely by the side opposite

to the doorway EF, which is now open. The roof is supported by the side

CD. If an opening AB be made in the wall CD before the doorway EF is

closed, the roof will fall in. So, in order to pass through the house,

EF must be firmly shut up before AB is opened. The houses are always

built in the interior passages so as to leave the rim of the disk free

for locomotion.

And there are many things to be said of the inhabitants on this disk

with respect to their social and political life. It is hardly necessary

for me to put down much about it here, for any one by using the method

of the historian Buckle, and deducing the character of a people from

their geographical influences and physical surroundings, could declare

what the main features of their life and history must be.

But one or two remarks may be made here. First of all they are

characterized by what I may venture to call a crude kind of polarity.

In dwellers in our world this polarity, which shows itself amongst other

ways in the distinction of sexes, is tempered and modified.

In every man there is something of a woman, and in every woman there are

some of the best qualities of a man.

But in the world of which we speak there is no physical possibility for

such interfusion. In a linear existence there would be no consciousness

of polarity. It makes its appearance first in the plane, and in a hard

and unmitigated form.

It is impossible to do otherwise than caricature these beings when we

write of them thus in brief. So let us accept the matter frankly, and,

without scruple, look at them in the broadest possible manner.

If the reader will cut out the triangles in the corners of the two next

pages he will obtain four plane beings, two of which are men, two of

which are women. The lines down which the cutting is to be made are

marked with a black line. Now having cut out two men, whom we will call

Homo and Vir, draw a line on a piece of paper to represent the rim of

the world on which they stand, and, remembering that they cannot slide

over each other, move them about. It must be remembered that the figures

cannot leave the plane on which they are put. They must not be turned

over. The only way in which they can pass each other is by one climbing

over the other’s head. They can go forwards or backwards. Much can be

noticed from an inspection of these figures. Of course it is only

symbolical in the rudest way, but in their whole life the facts which

can be noticed in these simple figures are built up and organized into

complicated arrangements.

[Illustration: Diagram VI.]

[Illustration: Diagram VII.]

It is evident that the sharp point of one man is always running into

another man’s sensitive or soft edge. Each man is in continual

apprehension of every other man: not only does each fear each, but their

sensitive edges—those on which they are receptive of all except the

roughest impressions—are turned away from each other.

On the sensitive edge is the face and all the means of expression of

feeling. The other edge is covered with a horny thickening of the skin,

which at the sharp point becomes very dense and as hard as iron. It will

be evident, on moving the figures about that no two men could naturally

come face to face with each other.

In this land no such thing as friendship or familiar intercourse between

man and man is possible. The very name of it is ridiculous to them. For

the only way in which one man can turn his sensitive edge to another man

is if one of them will consent to stand on his head. Fathers hold their

male children in this way when little, but the first symptom of manhood

is connected with a resentment against this treatment.

If now two women, Mulier and Femina, be looked at, the same relation

will be seen to hold good between them. By their nature they are

predisposed, by accident, to injure one another, and their

impressionable sides are, by the very conditions of their being, turned

away from each other.

If now, however, Homo and Mulier be placed together, a very different

relationship manifests itself. They cannot injure one another, and each

is framed for the most delightful converse with the other. Nothing can

be more secure from the outside world than a pair of approximately the

same height; each protects the sensitive edge of each, and their

armoured edges and means of offence are turned against all comers,

either in one direction or the other. But, if the pair, through a mutual

misunderstanding, happen to be disadjusted, and, their feet on the rim,

turn their sharpnesses against one another, they are absolutely exposed

to the harms and arrows of the world.

Still, even in this case they cannot wound one another—a happy immunity.

In the annals of this race which I have by me I find a curious history,

which, unintelligible for ages to them, admits by us of a simple

explanation.

It is said that two beings, the most ideally perfect Vir and Mulier,

were once living in a state of most perfect happiness, when, owing to

certain abstruse studies of the Mulier, she was suddenly, in all outward

respects, turned irremediably into a man. Vir recognized her as the same

true Mulier. But she occupied the same position with regard to him which

any other man would. It was only by standing on his head that he could,

with his sensitive edge, approach her sensitive edge. She refused to

explain how it was, or impart her secret to any one, but she had, she

said, undergone a great peril. She manifested a strange knowledge of the

internal anatomy of the race, and most of their medical knowledge dates

from her. But no persuasion would induce her to reveal her secret; all

the privacy of existence would be gone, she said, if she revealed it.

She was supposed to have acquired some magical knowledge.

This possession, however, did not make either of them happy, and one

day, with fear, she said that she would either die or be restored to the

outward semblance of her sex.

She disappeared—absolutely; although she was surrounded by her friends,

she absolutely vanished. And had it not been that some days afterwards,

cutting through the solid rock for the purposes of some excavations,

they accidentally came on a chasm, they would never have found her alive

again. For she was found in a cavity in the living rock, warm and

beautiful—her old self again.

Her secret died with her.

From our point of view it is easy to see what had happened. If the

figure Mulier be taken up and turned over it will be easy to see that,

though still a woman, her configuration has become that of a man. To all

intents and purposes she is a man. She is rendered incapable of that

attitude which is the natural one between the men and women in this

land, and the happy relationship between her and Vir is necessarily and

entirely broken off. Move about as you will, keeping her figure turned

thus on the plane, you will not be able to make her a fitting helpmate

for her unfortunate Vir. She must have discovered the secret of raising

herself off the surface, and by some accident been turned over. Perhaps

she had used this new position to study anatomy—for to an observer thus

situated the interior of every body would lie perfectly open—and in

prosecuting her studies had overbalanced herself.

I have only mentioned this anecdote, however, for the sake of a curious

observation which was made at the time. It was found that when she was

in this transformed condition she was absolutely without atmosphere. To

explain: ordinarily, apart from anything she said or did, there was a

kind of influence proceeding from her which made her presence agreeable

to Vir. When she was turned over she lost this. Now the explanation of

this is obvious. To these people light is the agitation of the surface

of the bubble; transparent objects are those which do not hinder this

agitation in its course. But most bodies and the physical frame of the

inhabitants amongst them were not transparent, but stopped and reflected

these agitations of the film, thus sending off from their outer edge

those vibrations which excited sight in their fellows. But besides these

vibrations of light there were finer ones still which were not damped or

deflected by the outer edge of the body, but came through the greater

part of their frame as if it was transparent. In the interior, however,

of their organizations there were certain regions which did arrest these

subtler vibrations, and which had (as the eye of light) the power of

appreciating them. In connection with these regions there were certain

structures, extremely minute, which had the converse power of agitating

the film, and so sending forth through the periphery of the body these

same minute vibrations. These organs were not of any use, but they

formed a sort of means of sympathetic communication between the

inhabitants, acting in no very defined way, but certainly producing a

sensation of a vague kind. Now when Mulier was turned in the way

described, the relation of her frame to the film of the bubble was

disarranged, and it was no wonder that this “atmosphere” disappeared.

In many respects the inhabitants of this world are far more advanced

than we are, having a simpler problem—how to deal with matter in one

plane—they have advanced more nearly to a complete knowledge of its

properties. Yet great as their knowledge is, their performance is small.

If you but reflect on one single fact, you will see how limited all

their efforts must be. _They cannot fix the centre of a wheel, so that

it rotates round an axis._ For consider a wheel—a small disk lying on

their plane. The centre on every part of it touches the surface of the

bubble on which all things slide freely. To fix this point they would

have to drive down into the film—a thing which they cannot do, and which

they are far from even imagining.

If they make an opening in the disk they can arrive at the centre of it.

But then the rod of matter which they put in will prevent the disk from

revolving.

[Illustration: Diagram VIII.—The nearest approach to a wheel.]

The nearest approach to a wheel with a fixed centre which they can

attain is shown in Diagram VIII., a portion of a circular disk which

oscillates about the smooth end of a rod built into the substance of the

cut-away disk.

[Illustration: Diagram IX.—A cart.]

Their carts are shown in the accompanying figure. They are simply rods

placed on rollers: as the rod is pulled along, the rollers turn, and the

rod slides along—just as a boat does on the rollers whereby sailors help

themselves in hauling it up the beach. As soon as these rollers roll

from under the rod, as it goes on in its forward motion, they have to be

secured, and then lifted over the cart and put down in front. Thus there

are to each cart a set of little disks or rollers, and, as the cart goes

on, these rollers have to be lifted over the cart from the back to the

front.

There is no means by which this can be made a continuous action. Each

roller has to be waited for, lifted separately, and carried over

separately. And to put it down in front, the rope by which the cart is

dragged along has to be unfastened and fastened up again.

Looking at the Diagram IX. it will be seen that there is a hollow in the

body of the cart. On the part A B the driver sits. In the hollow from B

to C is put the load. The load cannot then slip out over the ends of the

cart. There is nothing in the cart to prevent it from falling out

sideways.

But the contents, as the whole body of the cart, are kept to the smooth

surface of the bubble, and are thus supported by it on the side remote

from the reader’s eye, and also are kept from rising away from this

surface by the force of attraction exerted by the film.

Thus the surface of the bubble and its attractive force supply the other

two sides of the cart.

But of these two sides, the beings are ignorant, and it seems to them

perfectly natural that loads of any kind, even of fluids, should be kept

securely in a cart with two ends.

[Illustration: Diagram X.—How a rope is fixed to a cart.]

The method by which the rope is fastened to the cart is this: C is the

body of the cart; R is the rope ending in a wooden step B; A is an

oblong piece of wood. When the rope has to be taken out, A is lifted out

by its handle, B is slipped back and taken out of the recess in C, and

then the rope is free from the cart. And in a similar way it is secured

again.

One very ordinary way of driving machinery with us is by shafting. A

long rod is driven round and carries wheels at different places along

its length. Now with these inhabitants it was impossible to do this,

because the twisting motion round a rod could not be imparted without

going out of the thin layer in which they were. Their methods of

transmitting motion were by long rods, by a succession of short rods, by

pendulums attached to one another, or finally by wheels which drove one

another, but which were held by smooth sockets fitting round the rim far

enough to steady them, but not so far as to hinder them from touching

each other.

As to their science, the best plan is to give a short account of its

rise.

They discovered that they were on a disk rotating round an inner centre,

and also proceeding in a path round the source of light and heat.

They found that they were held in their path by a force of attraction.

But this attractive force was not with them as it is with us. With us,

since the effect which any particle has on the surrounding particles

spreads out in our space if the distance is doubled from a centre of

attraction, the force it exercises becomes one-quarter of what it was

when at the less distance.

With them, however, when the distance doubled, the force of attraction

became only one-half of what it was at the less distance. For the light,

or attraction, or force of any kind emanating from a particle, only

spreads along the film, and does not pass out into the space above or

beneath. If they had been on a thick globe instead of a bubble, the laws

of attraction would have been the same as with us. But the bubble on

which they were was thin compared with the paths along which the radiant

forces spread forth. And thus every force being kept to one plane

diminished as the distance from the centre of its action.[2]

Now it was a great problem with them how the light came from the central

orb. Their atmosphere, they knew, extended but a small distance above

the surface of their disk. And it was quite incapable, moreover, of

conveying vibrations such as those of light and heat.

By studying the nature of light they became convinced that to transmit

it there must be a medium of extreme rigidity between them and the great

source of light.

It is easy enough to see that what they thought was a medium between

them and their sun was in reality the rigid surface on which they

rested. This elastic film vibrated in a direction transverse to the

layer they called matter, and carried the particles of matter with it.

But they, having no idea but that the surface on which they were was the

whole of space, thought that space must be filled with a rigid medium.

They found that the vibrations of the medium were at right angles to the

direction in which a ray was propagated. But they did not conceive of a

motion at right angles to their plane; they thought it must be in their

plane.

It was a puzzle to them how their disk glided with so little friction

through this medium. They concluded it was infinitely rare. They were

still more puzzled when they had reason to believe it was an opaque

substance; and yet that it could be anything else than a medium which

filled their space was inconceivable to them. They could never get rid

of it from a vacuum, however perfect. Indeed we see that in producing a

vacuum they merely cleaned the surface on which they were.

In one respect it might have been advantageous if they had known, for,

their law of attraction being what it was, their movement round their

sun was not destined to go on for ever; but they were gradually falling

nearer and nearer. Now, if only they had made the attempt, they might by

some means have got a hold on the surface on which they were, and, by

means of a keel which tended to furrow it, have guided their world and

themselves in their path round their sun. Indeed, it is possible to

imagine them navigating themselves whither they would through their

universe—that is, on the surface of their bubble.

It was also unfortunate in another respect that they did not realize the

fact of the supporting surface, for the feeling which they came to have

of being suspended in space, absolutely isolated, was a very unsettling

one, and tended to cause in them a certain lack of the feeling of

solidarity with the rest of the universe.

We have seen that their laws of mechanics were very different from ours.

But they had after all an experience of our mechanical principles,

though in a curious way. In all motions of any magnitude moving bodies

were confined to the surface of the plane. But where the small particles

were concerned there was more liberty of motion. The small particles

were free in their movement; although they could not go more than a very

small distance away from the film on which they rested, still they were

capable of motion perpendicular to it. Thus a long line of particles

connected together could rotate as a whole, keeping straight like a

twisting wire, and by means of many strings of particles thus connected,

movements could be transmitted in a way which was totally unlike the

mechanical movements to be seen in the case of large masses.

This motion of rotation round an axis lying in the plane was to them

what electricity is to us. It was quite a mysterious force. But it was

extremely useful in its applications. Having no idea of a rotation which

in taking place went out of their surface, they could not conceive a

reason for the results of such movements.

It can easily be seen how many kinds of forces they could have. There

was the spinning motion of the small particles on the surface. This they

were aware of—it produced many appearances, but it was not fitted for

transmission across great distances, as each particle was apt to be

hindered in its rotation by its neighbour. Sometimes, however, when

conditions were favourable, many of these rotations were harmonious, and

waves were produced in their matter resembling the waves in our ocean.

There were only two other kinds of motion. One was an up and down

vibration of the film carrying matter with it; the other was the

twisting of strings of particles which were rigidly connected together.

The up and down motion of the film was to them light. Those kinds of

matter which did not hinder this motion were said to be transparent;

those kinds which, lying on the film, hindered the motion or threw it

back were said to be opaque.

The twisting motion round an axis was to them what electricity is to us.

And when this twisting motion in one direction or another was conveyed

to the particles of small masses which were free to move, many curious

effects were produced analogous to the movements of electrified bodies.

There are obviously no other rotations or vibrations possible; hence in

that world there is nothing corresponding to magnetism. Their light was

simple, and could not be split into two kinds as our light can be—into

two kinds of polarized light.

Was there no sign, then, by which the inhabitants of this world could

gain a knowledge of their own limitation? There was. There was both a

sign and the interpretation of it lying before them. They knew that they

could have two triangles precisely similar, and yet such as could not be

turned the one into the other by any movement in the plane. How two

things could be so alike, and yet differ in some mysterious way, was to

them a puzzle. As an instance of such triangles may be taken those used

in Diagram VI. to represent the man and the woman. They may be exactly

equal, yet the beings in a plane world cannot turn them so that one

would coincide with the other.

Yet had they but considered the case of a being lower in the scale of

space existence than themselves, they would have seen the answer to

their riddle. For consider a being confined altogether to a line

_____________________

C′ B′ A′ M A B C.

Let M be the being, and let him observe the three points A B C, and let

him form an idea of them and their positions with regard to each other,

which he measures by the distance he has to travel to reach one after

passing the other.

Let him also become aware of the three points A′ B′ C′, forming a

precisely similar set on the other side of him.

It may be objected that the being in the line could not conceive any

point lying beyond A, but that his experience would be limited to the

points A and A′. If A and A′ are material particles this would be the

case, but we may suppose them to be places in the line marked out by

cold and heat, or some such means. Then a being could conceive a series

of positions in his space such as A, B and C, A′, B′, C′.

If now he remembers each set, and thinks about them, he finds that they

are alike in every respect. But he cannot make them coincide with each

other. For if he pushes the set A B C along the line, when A B and A′ B′

are together C is just where it ought not to be. It is not on C′. And if

he gets C on C′, then A B has gone far away.

He would neither be able to make them coincide nor to conceive their

coincidence.

There would be no movement within the realm of his experience which

would make them coincide.

Yet the dweller in a plane world could easily make these sets of points

coincide, for he would bend the whole line round in his plane so that A

coming on A′, B should come on B′, and C on C′. There would be no

difficulty to him in doing this. And he does it in virtue of there being

to him a movement possible which is not possible to the being in the

line. He has a liberty of motion unknown to the linear being.

And now why should he not reason thus, “Something which to the linear

being is inconceivable, to me is conceivable. Then may not things

inconceivable to me be yet possible? May it not be possible that two

triangles which are like one another, but yet which cannot be thought by

me as coinciding—may not these triangles be able to be made coincident”?

In this simple fact of his perpetual observation was really the proof of

the whole matter if he had but looked at it, the sign manual of his

limitation, the promise of his liberation from it in thought, the key to

the explanation of the mysterious minute actions by which he was

surrounded, and perchance a help to the comprehension of a higher life.

_APPENDIX._

In our world a particle of matter which sends forth influence on the

surrounding matter does not send its radiant energy off along a plane,

but from the particle all the influence spreads out into space. And the

most convenient instance in our world to consider is that of a luminous

point from which rays spread out in every direction. Let M in Diagram

XI. be such a point—a particle of matter sending forth luminous rays in

our three-dimensional space.

[Illustration: Diagram XI.—Particles in space and in a plane exerting

force.]

Instead of studying how these rays spread out in every way all around M,

let us only consider those which, passing out from M, fall on the square

A B C D. A B C D casts a shadow, and this shadow extends, and is found

to be bigger the further off from M it is measured. Suppose, at the

distance from M, M E, we put a square in the path of the shadow so as

just to receive the shadow on it exactly. Let E F G H be this square. As

is shown by the dotted lines, this square will be four times as large as

the square A B C D. So when the distance is doubled, the shadow becomes

four times as big.

Now those rays of light which fall on A B C D would, if they were not

interrupted by it, spread out so as to exactly cover E F G H. Thus the

same amount of light which falls on the small square A B C D would, if

it were taken away, fall on the large square E F G H.

Now since the large square is four times the size of the small square,

and the same amount of rays fall on it—for it only receives those which

would fall on the small square—there must be at any part of it an

illumination one-quarter as strong as there would be at any point on the

small square.

Thus the small square, if placed in its position, would seem four times

as bright as the large square.

Thus, when the distance from the origin of light is doubled, the amount

of light received by a surface of given area becomes one-fourth of what

it was at the less distance.

This is what is meant by varying inversely as the square of the

distance. When the distance is doubled the intensity of the light is not

simply less, but is halved and halved, and becomes one-quarter of its

previous intensity.

But in the case of a particle resting on a thin sheet of metal, and

shaking the metal—as, for instance, a metal plate can be made to shake

by a violin bow—then this law would not hold.

Take the second figure. Let P be the particle, and let the influence

proceeding from it fall on the rod A B lying on the plane, and let us

suppose the rod to stop the vibrations from going beyond it, to receive

them and to turn them back just as a body does the light. Then the

“shadow” of A B would spread out away from P; and if another rod E F

were put in at the distance P E, which is double of P A, then, to

exactly fit the shadow, it would have to be double the length of A B;

and the vibrations which fell on A B would exactly fall on E F. Now

since E F is twice as long as A B, the vibrations which fall on any part

of it will be one-half as intense as the vibrations which fall on a

portion of matter of the same size lying where A B lies.

Thus in a plane the influence or force sent out by any particle would

diminish as the distance. It would not “vary inversely as the square of

the distance,” but would “vary inversely as the distance.”

A Picture of Our Universe.

CHAPTER I.

It seems to me that the subject of higher space is becoming felt as

serious, and fraught with much that is of the deepest interest, not only

as a scientific problem, but in other ways also.

It seems also that when we commence to feel the seriousness of any

subject we partly lose our faculty of dealing with it. The intellect

seems to be overweighted somehow, and clogged. Perhaps the suppositions

we make seem to us of too great importance, and we are not willing

enough to let them go, fearing to lose the thing itself if we lose our

hold of the means by which we have first apprehended it.

But whatever may be the cause, it does seem undoubtedly the fact that

the mind works more clearly and more freely on subjects which are of

slight importance.

And I propose, that without ignoring the real importance of the subject

about which we are treating, we should cast aside any tension from our

minds, and look at it in a light and easy manner.

With this object in view let us contemplate a certain story which bears

on our problem.

It is said that once in a certain region of Ireland there took place a

curious contest. For in Kilkenny there were two cats so alike in size,

vigour, determination, and prowess, that, fighting, they so clawed,

scratched, bit, and finally devoured each other, that nothing was left

of either of them save the tail.

Now, on reflecting on this story, it becomes obvious that it originated

when looking-glasses were first imported into Ireland from Italy. For

when an Irishman sees for the first time anything new, he always

describes it in an unexpected and yet genial and interesting manner.

Moreover, we all know what contentious fellows they are, and how all

their thoughts run on fighting. And I think if we put this problem to

ourselves, how by bringing in fighting to describe a looking-glass, we

shall see that the story of the Kilkenny cats is the only possible

solution. For consider evidently how it arose. Depositing his favourite

shillaly in a corner, the massively-built Irishman, to whom the

possession was a novelty, saw reflected in his looking-glass the image

of his favourite cat. With a scrutinizing eye he compared the two. Point

for point they were like. “Begorra if I know which of the two would

win!” he ejaculates. The combat becomes real to him, and the story of

the Kilkenny cats is made.

Now, to our more sober mind, it is obvious that two cats—two real

material things—could not mutually annihilate each other to such an

extent. But it is perfectly possible to make a model of the Kilkenny

cats—to see them fight, and to mark the issue.

And I propose to symbolize or represent the Kilkenny cat by a twist.

Take a pencil, and round it twist a strip of paper—a flat spill will do.

Now, having fastened the ends on to the pencil by two pins, so that it

will not untwist, hold the paper thus twisted on the pencil at right

angles to the surface of a looking-glass: and in the looking-glass you

will see its image. In Diagram I., M represents the mirror, and on the

left hand is shown the twist, on the right hand the image twist. Now

take another pencil and another piece of paper, and make a model of what

you see in the glass. You will be able to twist this second piece of

paper in a spiral round this second pencil so that it is an exact copy

of what you see in the glass. Now put the two pencils together end to

end, as they would be if the first pencil were to approach the glass

until it touched it, meeting its image: you have the real copy of the

image instead of the image itself. Now pin together the two ends of the

pieces of paper, which are near together, and you have your two Kilkenny

cats ready for the fray. To make them fight (remember that the

twists—not the paper itself, but the paper twisted—represent the cat),

hold firmly and pull the other ends (the tail ends, so to speak), so as

to let each twist exercise its nature on the other.

You will see that the two twists mutually annihilate each other. Without

your unwrapping the paper the twists both go, and nothing is left of

them.

[Illustration: Diagram I.]

Now the image of the twist as a real thing was made by us. It did not

exist in nature other than as a mere appearance.

But I want you to imagine this process of producing a real image as

somehow existing. I want you to lay aside for the present the question

of how it could be done, and to conceive twists and image twists.

This is the mechanical conception I wish you to adopt—there are such

things as twists. Suppose by some means to every twist there is produced

its image twist. These two, the twist and its image, may exist

separately; but suppose that whenever a twist is produced its image

twist is also produced, and that these two when put together annihilate

each other.

With this conception let us explore the domain of those actions which

are called electrical.

When a glass rod is rubbed with silk it becomes excited, its state is

different. It manifests many properties, such as that of attracting

light bodies, giving off a glow of light, &c. The silk also with which

it was rubbed manifests similar properties. It also attracts light

bodies, appears to glow in the dark, &c.

And yet there is a difference between the state of excitement of the

glass and of the silk. The electricity which is in them is of different

kinds. And if the electricity of the silk and of the glass be brought

together, all electrical effect disappears; they become glass and silk

in an ordinary condition.

It may seem strange that, if this is so, they should become electrified

when rubbed together. Yet this is the case, and must be taken as a fact.

It seems to depend partly on the circumstance that glass and silk are

not what is called conductors. In a conductor, if one part receives

electricity, this electricity at once runs over the whole of the

conductor, whether it be an inch long or many feet. And if any part of

the conductor be touched by another conductor which is in contact with

the earth, every trace of electricity leaves the conductor, flowing, as

it were, freely out of it.

Now both glass and silk do not let the electricity run from them so

easily. To discharge a glass rod it has practically to be touched in

every part. Thus, when by the rubbing with silk electricity is produced

on it, it is conceivable that this electricity should be kept to a

certain extent, and not combined immediately with the electricity on the

silk.

Besides, the same cause—the friction which produced the electricity on

the glass, and the other kind of electricity on the silk—would probably

prevent their combination as long as it was applied.

Now let us suppose that the electrical charge which the glass has

consists in this.

Let us suppose that the particles of the glass on the surface of it are

twisted, strained out of their natural position, and twisted.

Let us also suppose that the particles of the silk are twisted too, but

let them have the image twist.

Now these two twists, the glass twist and the silk twist, its image,

when brought together, will run down. In unwinding each other they will

give off a certain amount of energy, which will manifest itself as a

spark, make a crackling sound, and so on. But when they unwind each

other there is no more tension of the particles.

This does not explain in the least why the glass particles should

receive a twist in one direction, the silk particles a twist of the

image kind.

But instead of inquiring into this, it is best to see if this

supposition is in accordance with other known facts of electrical

action; because, if it is not, we may dismiss it more easily than we

could if we had to test it with regard to the very inaccessible question

of why some bodies, when rubbed, get electrified in one way, others in

another.

When the glass and silk are near together the twist on the glass and

that on the silk are related to each other as twist and image twist, and

there is no action on surrounding bodies from either of them, as they,

so to speak, satisfy each other.

But when the glass rod and the silk are moved apart, and brought near

other objects, then each of them calls up on those objects near which it

is brought a twist of the kind which is the image of its own twist.

If the glass rod is brought near a mass of metal, which we will call a

conductor, the following effect is observed:—The part of the conductor

near the glass rod becomes charged with electricity of the silk kind;

the part of the conductor away from the rod becomes charged with

electricity of the glass kind.

Now let us bring into play the supposition which we made before.

Let us suppose that there is some process in nature which, when there is

a twist, makes a real image of that twist come into being. If we assume

this process, we see that, opposite to the silk, on whatever objects are

near it, will be a twist of the glass kind, and opposite the rod will be

a twist of the silk kind. That is to say, that on the conductor there

will be a twist of the silk kind when the glass rod is brought near it.

But there is nothing to make the particles of the conductor twist as a

whole. The glass rod is not supposed to touch the conductor—it is simply

brought near it, and no actual communication takes place between them.

No force is actually applied to it, nor electricity communicated to it.

Hence, on the whole, the particles of the conductor will not be twisted.

That is to say, since there is a twist of the glass kind on one end,

there will be at the other end a twist of the image kind—that is, of the

silk kind. And these two twists are like the two twists on the pencil—if

allowed to run together they will run each other out. So if the

conductor were removed from the neighbourhood of the glass rod it would

be found to be no different from what it was at first. It would not be

“charged.”