“I should like to accompany you to your friend and hear what he has to say.”
“Come, certainly.”
So they went together to the town. On the way the clerk felt a brightness of existence such as he had not enjoyed for a long time. They talked together, and confided in one another. At length they came near the town where the student’s friend lived. They separated, the clerk going into the town, the student to the house of his friend. On his way there the path led through a small wood of very thick growth. Passing along, he found that he had left the path. Pausing to reflect in which direction he ought to go, he thought he heard a sound. It was repeated. Penetrating deep into the obscurest part of the wood, he searched till at length he found—carefully concealed—a child, a mere infant.
The child was nearly perished with exposure. He took it up and warmed it. When the child was a little better the cause of its having been hidden away was apparent. Its breathing was distressed and laboured. It suffered under some affection of the lungs, which made it gasp at every breath. Still in other respects the child was well developed and seemed strongly made. It seemed to have been left too long without care to recover. The pain of exhaustion from the neglect, and added to this the pain of its breathing, was too much for it, it was sinking.
“If I could bear the pain of its breathing,” thought the student, “it might not sink till I could get some nourishment for it.”
He looked up, for it seemed to him as if some one struck him in the chest. There was no one there. The pain continued. He did not drop the child but continued on his way to the house of his friend. When he got there he noticed a stillness unusual in the housesof the inhabitants. He entered, and was met by his friend’s sister. He saw at once that something must have happened. She took him into a dimly lighted room, where he saw his friend lying motionless and his face quite white.
“He has been suffering great pain for long,” she said; “it was hoped that if he could bear up the pain would have run its course and he would not sink. But all we could do was no use.” The room was full of all things accounted pleasurable, and she looked round as she spoke. “It was no good.” Taking the child from his arms she left him with the form of her brother.
Sitting down by his side the student felt the strange oppression on his chest continue. He went out and found that the child had completely revived. It had still the appearance of being agonized in its breathing, but its eyes were bright, and it laughed.
“It will be all right soon,” said his friend’s sister.
“Tell me what was the matter with your brother.”
When he had heard about his malady he returned to the room. After he had sat there for some time he felt more and more the sorrow for the loss of his friend, and the need of his counsel. This aimless, inert form, this lifeless mass, was that which he had come to seek—was the being with whom he had longed to confer.
He bent over him. “Could I but snatch him back into life; could I but have one hour’s intercourse with him. If I had been with him I might have borne some of the pain of his complaint before he was overpowered with it.” He touched the lifeless hands, they were cold and damp. He gazed into the expressionless face. He seemed to feel the pain of the inner struggle his friend had waged against the disease. The quiet of that still chamber was gone for him; in his own person he felt the pangs of the struggle for life. A mist came over hiseyes, and he sank down holding his friend’s hands. Suddenly he heard a voice. He rose and looked about him. The sound came faintly from the lips of his friend.
“I have been very ill,” were the words he caught. “I am so glad you have come; I was thinking of you in my worst moments. You have come just as I am getting better.”
Indeed the features were regaining expression, the hands were warm. It was his living friend again.
After a few hours he was sufficiently recovered to hear about all that had happened. They talked together long and earnestly. His friend was convinced.
“Let us go to your companion,” he said.
They went into the town together. They found that the clerk had gone to the magistrates’ hall where a trial was being held. They did not see the clerk at first, so they listened to the proceedings. A woman was brought in who had been kept in prison for some days, accused of concealing her child. The case was clearly proved. The woman received her sentence with an appearance of apathy.
“She will not come out of prison alive,” said the student’s friend, noting her expression.
But he called out to her from where they stood in the body of the court, “Do not fear, your child is safe.”
The woman’s face brightened, and she went with her jailers buoyantly.
The magistrate had remarked who it was that had spoken, and was about to give orders for the disturber of order to be brought up for punishment. But the clerk, who was sitting near to the magistrate with whom he was acquainted, said:
“This is the one I have told you about; pray do not punish him.”
The magistrate accordingly contented himself with warning the audience in general terms.
But he said to the clerk, “Something about him is very repulsive to me, do not tell me anything more about him.”
The three returned together, and together they deliberated as to how the new idea about the king could be made known. It seemed best to go to the metropolis and talk with the wisest and most learned there.
The student asked about the child. His friend’s sister came and told him that its breathing was not any better, but that the child itself was strong and playful.
“It belongs to the woman who was tried to day,” said the student, “and must be kept safely till she is out of prison.”
His friend after some deliberation gave it in charge to a faithful servant to take to the metropolis. A suffering child there would be much more likely to be overlooked, “and you,” he said, “will be able to look after it.”
As the student and the clerk were about to set out on their way to the metropolis his friend took him apart.
“My sister tells me that I had sunk into apathy when you came.”
“Yes.”
“And that you called me back?”
“Yes.”
“How can I thank you! had it not been for you I should never have enjoyed life again. I am grateful to you.”
“Do not say grateful to me, but rather to that power which does for you all your life that which I do for you momentarily now. And even now it is not to me that you should be grateful, but to him, for it is only because he has enabled me to do so that I have taken of your pain.”
With this he took farewell of his friend, and with the clerk proceeded on their way.
They had not got very far when a train of servants came up behind them. They stood by on one side, but from the midst of his attendants a youth stepped forward.
“I have learned what you have done, and I have overtaken you with great haste.”
“What is your wish?”
“I want to come with you. I know that you have restored your friend from apathy to life. No power is so great as that. I have riches in abundance. All that I have is at your service; teach me your power.”
Now in the valley riches meant abundance of pleasant things. At the time the student was bearing the constant pain which he took of the child’s breathing, and the pain also of his friend’s illness. He felt that before beginning to take pleasure—which was the meaning of having pleasant things—it would be necessary to give up the power which he was exercising, so he said to the youth somewhat harshly:
“You cannot compare riches and that which I do, nor can you exchange the one for the other. First give up all your riches, then you can begin to learn what I do.”
The youth turned back, but once again spoke, saying:
“I will give up a great part of my riches if you will teach me.”
“If you want to keep any, however small a portion, you cannot do what I do.”
Then the youth with all his attendants passed away.
When they came to the metropolis the clerk brought many of his acquaintances to see the student. From his position in the council chamber, he was able to address and induce many of the ablest of the councillors to come and inquire. But as soon as they came into the presence of the student a sort of constraint sprang up between them. They did not take his words as having any real meaning. They were occupied all the time on speculating what motive it was that made him say these things, and as to what kind of difference it was which they felt existing between him and them.
In fact, as time passed on, no one of any position or power would be brought into any sort of approximation to him. On the other hand he used to speak continually with the poorer people. Those that were sick especially delighted in his presence. There seemed to be in him a power of stimulating those that were sinking into apathy back again into life. Those who were worst off in the city seemed to feel when he spoke to them a promise of an alleviation of their sufferings.
One day the clerk asked him
“How is the child?”
“It is well.”
“But it still seems to breathe with as much difficulty.”
“Yes, but see how happily it runs about.”
“How do you manage to preserve it? Any child which I have seen would be pining miserably with such an affliction. What is the power which the being you tell of has given you?”
“It is no power in the sense you mean.”
“Surely it must be. Have I not followed you faithfullyand done all I could to get the wisest in the city to listen to you? Surely the time has now come when you will tell me what this power is, and, if you can, let me share it.”
“You do not know what you ask.”
“Tell me, I pray.”
“It is simply this, when I became aware through thought of the being that is over us I had no message or command from him. But I found that I could when I stood by any suffering being take some of the suffering and bear it myself. So as he of whom I tell does with us each moment of our lives I do occasionally and in a little manner.”
“But what pleasure do you get that makes all this worth your while?”
“There is no pleasure. I am glad to see the being freed from suffering, and living instead of sinking.”
“Do you mean to say that there is nothing to hope for?”
“I hope the time will come when I shall have a fuller knowledge of the being I know.”
The clerk was silent. He went out. While he was still thinking over what he had heard in answer to his inquiries, a messenger came to him from the chief of the councillors of pleasure and pain, asking him to an interview.
When the clerk had been ushered into the presence of the chief councillor, and was alone with him, the latter said:
“I should like a little quiet conversation with you about your companion.”
“I shall be glad.”
“When you gave up your office and retired you had no expectation of being concerned in affairs of state again so soon.”
“I did not expect, certainly, and I do not know what your meaning may be about my being concerned in affairs of state.”
“What I mean is very simple. The continued deliberations, generation after generation, of the wise men who assemble in the council chamber have been the cause of the continued progress of the inhabitants. Nothing is done by them hurriedly or violently, but gradually improvement after improvement is worked out. But besides this, there have always been at every age certain disturbances in the state; certain doctrines are brought forward, and sometimes these tend to good, and should be encouraged; sometimes they are of unknown import, and must be studied; sometimes they are against the happiness of the state, and then the grave responsibility rests upon us of checking them. Now from your position you have more opportunity of knowing than any one else in what direction your companion’s doctrines tend. I have sent for you to ask you to share with me this grave responsibility.”
“I do not think I can help you. I am sure he does not wish to do any harm. What harm can there be in his doctrines?”
“It is not so much about his doctrines which I want to speak to you as about another subject. Many of those who have talked with him have agreed with one another in ascribing a singular oppressiveness to his presence. The expression was even used by a very worthy friend of mine, ‘He made me feel like a puppet.’ Now what right had he to inflict such a sensation on a very worthy individual? I want to ask you yourself if you have ever felt this?”
The clerk hesitated.
“At least, tell me, have you ever found it easy to influence him?”
“No; I do not feel as if I could influence him in the least. He seems to lack the ordinary springs of motive.”
“Now, should you say that it would be a gain to the community if many should become like him? Would not they be difficult to govern?”
“Certainly they would be difficult to govern.”
“Would it be a gain in pleasure to the rest of the inhabitants or to themselves?”
“It would not be a gain to themselves,” said the clerk, recalling the pain which his companion bore, “but it might be good for the rest of the inhabitants.”
“Yes,” said the chief councillor, “that is where his strength lies; he is a very skilful physician or an impostor, and he has the people on his side from the cures he has effected. Can you tell me anything about his life?”
“I have heard from him that he was a student, and was exiled; and that in his place of exile he found out the new doctrines, and he left the place he was sentenced to. On his way I joined him.”
“So much we know, and it is within our power, according to the regulations, to compel him to go back, and to punish him for having left the region he was banished to.”
“If you have that power, why do you not send him back if you think it would be best for the state for him to disappear?”
“Ah, my good friend, you have heard a great deal of our public deliberations from your place in the council; but now that we are consulting together, I must tell you that there are deeper secrets in the art of government, which you will readily apprehend. Suppose we arrested this individual and sent him away, the people would not see the justice of it. They want him now, and they would say that the forms of law were being used to get rid of him. Of course if his partizans became violentsomething of this kind would have to be done. But it is only a decree that seems just in the eyes of the people that we can prudently carry out in such a case without attracting even more attention to him than there is at present.”
The clerk said nothing. The chief councillor went on:
“I am sorry that our conference has come to so little. I was hoping that I might have found in you a successor to the vacant seat in the chamber. I know you have the ability to fill it well. But before the advancements are made some proof of the wisdom of the successor is required. Hitherto you have not had the chance, but I thought that in this difficult case, where you have so much better opportunities of observation than any one else has, you might have shown your mental power and confirmed my opinion of you. Still, no doubt, on some future occasion you will have another opportunity when this affair, difficult as it is, is forgotten.”
The chief councillor made a sign that the interview was at an end, but the clerk remained.
“All that we want,” the chief councillor resumed, “is to form an opinion from inside knowledge of whether this innovator is likely to cause more pain or more pleasure if he gains a hearing. Can you advise us? any particle of knowledge of his inner life, apart from his public professions, is valuable.”
“There is a singular fact which I should like to tell you of, as it has been somewhat of a burden to me.”
The chief councillor made a sign of assent, and the clerk told him about the child, and how it had been preserved.
“And with this child,” he said, “he and I sit when the day’s work is done.”
“It is indeed a strange story,” said the chief councillor;“you are quite right in telling me. I was sure you were one on whose discretion confidence might be placed. You have given me the highest proof I could have expected. The bearings of this matter must be thought over.”
That evening, as the clerk entered the room where they lived, the student was leaning over the child with a wearied expression. He went up to him and laid his hand on his shoulder. The child looked up at them and laughed. It was quite happy despite the apparent struggles of its breathing. The student looked at his companion’s face. His weariness vanished at once, and a strong warm light came into his eyes.
“You seem oppressed, my friend. I know you regret the way in which all the wise and important people you have brought here look on me, and you must feel some sorrow for the partial loss of esteem they have showed you in consequence. Can I help you to bear it?”
At that moment the door opened, and a messenger came in and gave the clerk a sealed packet. He opened it and saw that it was his appointment to the vacant seat in the council chamber. But his face did not brighten. He answered his companion moodily, and thus the day ended.
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 painsand 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 whichhad 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 themoon, 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 thebeings 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.
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 whichgo 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 ofmovement, 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 tothem, 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.
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 aboveillustration, 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 wasthe 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.
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 thatif 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 isan 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 ofan 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.
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 thatwere 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 anumerical 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.