Fragments of science Part 1

Fragments of science.

by John Tyndall.

PREFACE.

TO AVOID unwieldiness of bulk this edition of the 'Fragments' is published in two volumes, instead of, as heretofore, in one.

The first volume deals almost exclusively with the laws and phenomena of matter. The second trenches upon questions in which the phenomena of matter interlace more or less with those of mind.

New Essays have been added, while old ones have been revised, and in part recast. To be clear, without being superficial, has been my aim throughout.

In neither volume have I aspired to sit in the seat of the scornful, but rather to treat the questions touched upon with a tolerance, if not a reverence, befitting their difficulty and weight.

Holding, as I do, the nebular hypothesis, I am logically bound to deduce the life of the world from forces inherent in the nebula. With this view, which is set forth in the second volume, it seemed but fair to a.s.sociate the reasons which cause me to conclude that every attempt made in our day to generate life independently of antecedent life has utterly broken down.

A discourse on the Electric Light winds up the Second volume. The incongruity of its position is to be referred to the lateness of its delivery.

VOL. I.

INORGANIC NATURE.

I. THE CONSt.i.tUTION OF NATURE.

[Footnote: 'Fortnightly Review,' 1865, vol. iii. p. 129.]

WE cannot think of s.p.a.ce as finite, for wherever in imagination we erect a boundary, we are compelled to think of s.p.a.ce as existing beyond it. Thus by the incessant dissolution of limits we arrive at a more or less adequate idea of the infinity of s.p.a.ce. But, though compelled to think of s.p.a.ce as unbounded, there is no mental necessity compelling us to think of it either as filled or empty; whether it is so or not must be decided by experiment and observation. That it is not entirely void, the starry heavens declare; but the question still remains, Are the stars themselves hung in vacuo? Are the vast regions which surround them, and across which their light is propagated, absolutely empty? A century ago the answer to this question, founded on the Newtonian theory, would have been, 'No, for particles of light are incessantly shot through s.p.a.ce.' The reply of modern science is also negative, but on different grounds. It has the best possible reasons for rejecting the idea of luminiferous particles; but, in support of the conclusion that the celestial s.p.a.ces are occupied by matter, it is able to offer proofs almost as cogent as those which can be adduced of the existence of an atmosphere round the earth. Men's minds, indeed, rose to a conception of the celestial and universal atmosphere through the study of the terrestrial and local one. From the phenomena of sound, as displayed in the air, they ascended to the phenomena of light, as displayed in the _aether_; which is the name given to the interstellar medium.

The notion of this medium must not be considered as a vague or fanciful conception on the part of scientific men. Of its reality most of them are as convinced as they are of the existence of the sun and moon. The luminiferous aether has definite mechanical properties.

It is almost infinitely more attenuated than any known gas, but its properties are those of a solid rather than of a gas. It resembles jelly rather than air. This was not the first conception of the aether, but it is that forced upon us by a more complete knowledge of its phenomena. A body thus const.i.tuted may have its boundaries; but, although the aether may not be co-extensive with s.p.a.ce, it must at all events extend as far as the most distant visible stars. In fact it is the vehicle of their light, and without it they could not be seen.

This all-pervading substance takes up their molecular tremors, and conveys them with inconceivable rapidity to our organs of vision. It is the transported s.h.i.+ver of bodies countless millions of miles distant, which translates itself in human consciousness into the splendour of the firmament at night.

If the aether have a boundary, ma.s.ses of ponderable matter might be conceived to exist beyond it, but they could emit no light. Beyond the aether dark suns might burn; there, under proper conditions, combustion might be carried on; fuel might consume unseen, and metals be fused in invisible fires. A body, moreover, once heated there, would continue for ever heated; a sun or planet once molten, would continue for ever molten. For, the loss of heat being simply the abstraction of molecular motion by the aether, where this medium is absent no cooling could occur. A sentient being on approaching a heated body in this region, would be conscious of no augmentation of temperature. The gradations of warmth dependent on the laws of radiation would not exist, and actual contact would first reveal the heat of an extra ethereal sun.

Imagine a paddle-wheel placed in water and caused to rotate. From it, as a centre, waves would issue in all directions, and a wader as he approached the place of disturbance would be met by stronger and stronger waves. This gradual augmentation of the impression made upon the wader is exactly a.n.a.logous to the augmentation of light when we approach a luminous source. In the one case, however, the coa.r.s.e common nerves of the body suffice; for the other we must have the finer optic nerve. But suppose the water withdrawn; the action at a distance would then cease, and, as far as the sense of touch is concerned, the wader would be first rendered conscious of the motion of the wheel by the blow of the paddles. The transference of motion from the paddles to the water is mechanically similar to the transference of molecular motion from the heated body to the aether; and the propagation of waves through the liquid is mechanically similar to the propagation of light and radiant heat.

As far as our knowledge of s.p.a.ce extends, we are to conceive it as the holder of the luminiferous aether, through which are interspersed, at enormous distances apart, the ponderous nuclei of the stars.

a.s.sociated with the star that most concerns us we have a group of dark planetary ma.s.ses revolving at various distances round it, each again rotating on its own axis; and, finally, a.s.sociated with some of these planets we have dark bodies of minor note--the moons. Whether the other fixed stars have similar planetary companions or not is to us a matter of pure conjecture, which may or may not enter into our conception of the universe. But probably every thoughtful person believes, with regard to those distant suns, that there is, in s.p.a.ce, something besides our system on which they s.h.i.+ne.

From this general view of the present condition of s.p.a.ce, and of the bodies contained in it, we pa.s.s to the enquiry whether things were so created at the beginning. Was s.p.a.ce furnished at once, by the fiat of Omnipotence, with these burning orbs? In presence of the revelations of science this view is fading more and more. Behind the orbs, we now discern the nebulae from which they have been condensed. And without going so far back as the nebulae, the man of science can prove that out of common non-luminous matter this whole pomp of stars might have been evolved.

The law of gravitation enunciated by Newton is, that every particle of matter in the universe attracts every other particle with a force which diminishes as the square of the distance increases. Thus the sun and the earth mutually pull each other; thus the earth and the moon are kept in company, the force which holds every respective pair of ma.s.ses together being the integrated force of their component parts. Under the operation of this force a stone falls to the ground and is warmed by the shock; under its operation meteors plunge into our atmosphere mid rise to incandescence. Showers of such meteors doubtless fall incessantly upon the sun. Acted on by this force, the earth, were it stopped in its...o...b..t to-morrow, would rush towards, and finally combine with, the sun. Heat would also be developed by this collision. Mayer first, and Helmholtz and Thomson afterwards, have calculated its amount. It would equal that produced by the combustion of more than 5,000 worlds of solid coal, all this heat being generated at the instant of collision. In the attraction of gravity, therefore, acting upon non-luminous matter, we have a source of heat more powerful than could be derived from any terrestrial combustion. And were the matter of the universe thrown in cold detached fragments into s.p.a.ce, and there abandoned to the mutual gravitation of its own parts, the collision of the fragments would in the end produce the fires of the stars.

The action of gravity upon matter originally cold may, in fact, be the origin of all light and heat, and also the proximate source of such other powers as are generated by light and heat. But we have now to enquire what is the light and what is the heat thus produced? This question has already been answered in a general way. Both light and heat are modes of motion. Two planets clash and come to rest; their motion, considered as that of ma.s.ses, is destroyed, but it is in great part continued as a motion of their ultimate particles. It is this latter motion, taken up by the rather, and propagated through it with a velocity of 186,000 miles a second, that comes to its as the light and heat of suns and stars. The atoms of a hot body swing with inconceivable rapidity--billions of times in a second--but this power of vibration necessarily implies the operation of forces between the atoms themselves. It reveals to us that while they are held together by one force, they are kept asunder by another, their position at any moment depending on the equilibrium of attraction and repulsion. The atoms behave as if connected by elastic springs, which oppose at the same time their approach and their retreat, but which tolerate the vibration called heat. The molecular vibration once set up is instantly shared with the aether, and diffused by it throughout s.p.a.ce.

We on the earth's surface live night and day in the midst of aethereal commotion. The medium is never still. The cloud canopy above us may be thick enough to shut out the light of the stars; but this canopy is itself a warm body, which radiates its thermal motion through the aether. The earth also is warm, and sends its heat-pulses incessantly forth. It is the waste of its molecular motion in s.p.a.ce that chills the earth upon a clear night; it is the return of thermal motion from the clouds which prevents the earth's temperature, on a cloudy night, from falling so low. To the conception of s.p.a.ce being filled, we must therefore add the conception of its being in a state of incessant tremor.

The sources of this vibration are the ponderable ma.s.ses of the universe. Let us take a sample of these and examine it in detail.

When we look to our planet, we find it to be an aggregate of solids, liquids, and gases. Subjected to a sufficiently low temperature, the two last, would also a.s.sume the solid form. When we look at any one of these, we generally find it composed of still more elementary parts. We learn, for example, that the water of our rivers is formed by the union, in definite proportions, of two gases, oxygen and hydrogen. We know how to bring these const.i.tuents together, so as to form water: we also know how to a.n.a.lyse the water, and recover from it its two const.i.tuents. So, likewise, as regards the solid portions of the earth. Our chalk hills, for example, are formed by a combination of carbon, oxygen, and calcium. These are the so-called elements the union of which, in definite proportions, has resulted in the formation of chalk. The flints within the chalk we know to be a compound of oxygen and silicium, called silica; and our ordinary clay is, for the most part, formed by the union of silicium, oxygen, and the well-known light metal, aluminium. By far the greater portion of the earth's crust is compounded of the elementary substances mentioned in these few lines.

The principle of gravitation has been already described as an attraction which every particle of matter, however small, exerts on every other particle. With gravity there is no selection; no particular atoms choose, by preference, other particular atoms as objects of attraction; the attraction of gravitation is proportional simply to the quant.i.ty of the attracting matter, regardless of its quality. But in the molecular world which we have now entered matters are otherwise arranged. Here we have atoms between which a strong attraction is exercised, and also atoms between which a weak attraction is exercised. One atom can jostle another out of its place in virtue of a superior force of attraction. But, though the amount of force exerted varies thus from atom to atom, it is still an attraction of the same mechanical quality, if I may use the term, as that of gravity itself. Its intensity might be measured in the same way, namely by the amount of motion which it can generate in a certain time. Thus the attraction of gravity at the earth's surface is expressed by the number 32; because, when acting freely on a body for a second of time, gravity imparts to the body a velocity of thirty-two feet a second. In like manner the mutual attraction of oxygen and hydrogen might be measured by the velocity imparted to the atoms in their rus.h.i.+ng together. Of course such a unit of time as a second is not here to be thought of, the whole interval required by the atoms to cross the minute s.p.a.ces which separate them amounting only to an inconceivably small fraction of a second.

It has been stated that when a body falls to the earth it is warmed by the shock. Here, to use the terminology of Mayer, we have a _mechanical_ combination of the earth and the body. Let us suffer the falling body and the earth to dwindle in imagination to the size of atoms, and for the attraction of gravity let us subst.i.tute that of chemical affinity; we have then what is called a chemical combination.

The effect of the union in this case also is the development of heat, and from the amount of heat generated we can infer the intensity of the atomic pull. Measured by ordinary mechanical standards, this is enormous. Mix eight pounds of oxygen with one of hydrogen, and pa.s.s a spark through the mixture; the gases instantly combine, their atoms rus.h.i.+ng over the little distances which separate them. Take a weight of 47,000 pounds to an elevation of 1,000 feet above the earth's surface, and let it fall; the energy with which it will strike the earth will not exceed that of the eight pounds of oxygen atoms, as they dash against one pound of hydrogen atoms to form water.

It is sometimes stated that gravity is distinguished from all other forces by the fact of its resisting conversion into other forms of force. Chemical affinity, it is said, can be converted into heat and light, and these again into magnetism and electricity: but gravity refuses to be so converted; being a force maintaining itself under all circ.u.mstances, and not capable of disappearing to give place to another. The statement arises from vagueness of thought. If by it be meant that a particle of matter can never be deprived of its weight, the a.s.sertion is correct; but the law which affirms the convertibility of natural forces was never intended, in the minds of those who understood it, to affirm that such a conversion as that here implied occurs in any case whatever. As regards convertibility into heat, gravity and chemical affinity stand on precisely the same footing.

The attraction in the one case is as indestructible as in the other.

n.o.body affirms that when a stone rests upon the surface of the earth, the mutual attraction of the earth and stone is abolished; n.o.body means to affirm that the mutual attraction of oxygen for hydrogen ceases, after the atoms have combined to form water. What is meant, in the case of chemical affinity, is, that the pull of that affinity, acting through a certain s.p.a.ce, imparts a motion of translation of the one atom towards the other. This motion is not heat, nor is the force that produces it heat. But when the atoms strike and recoil, the motion of translation is converted into a motion of vibration, which is heat. The vibration, however, so far from causing the extinction of the original attraction, is in part carried on by that attraction.

The atoms recoil, in virtue of the elastic force which opposes actual contact, and in the recoil they are driven too far back. The original attraction then triumphs over the force of recoil, and urges the atoms once more together. Thus, like a pendulum, they oscillate, until their motion is imparted to the surrounding aether; or, in other words, until their heat becomes radiant heat.

In this sense, and in this sense only, is chemical affinity converted into heat. There is, first of all, the attraction between the atoms; there is, secondly, s.p.a.ce between them. Across this s.p.a.ce the attraction urges them. They collide, they recoil, they oscillate.

There is here a change in the form of the motion, but there is no real loss. It is so with the attraction of gravity. To produce motion by gravity s.p.a.ce must also intervene between the attracting bodies. When they strike together motion is apparently destroyed, but in reality there is no destruction. Their atoms are suddenly urged together by the shock; by their own perfect elasticity these atoms recoil; and thus is set up the molecular oscillation which, when communicated to the proper nerves, announces itself as heat.

It was formerly universally supposed that by the collision of unelastic bodies force was destroyed. Men saw, for example, that when two spheres of clay, painter's putty, or lead for example, were urged together, the motion possessed by the ma.s.ses, prior to impact, was more or less annihilated. They believed in an absolute destruction of the force of impact. Until recent times, indeed, no difficulty was experienced in believing this, whereas, at present, the ideas of force and its destruction refuse to be united in most philosophic minds. In the collision of elastic bodies, on the contrary, it was observed that the motion with which they clashed together was in great part restored by the resiliency of the ma.s.ses, the more perfect the elasticity the more complete being the rest.i.tution. This led to the idea of perfectly elastic bodies--bodies competent to restore by their recoil the whole of the motion which they possessed before impact--and this again to the idea of the _conservation_ of force, as opposed to that destruction of force which was supposed to occur when unelastic bodies met in collision.

We now know that the principle of conservation holds equally good with elastic and unelastic bodies. Perfectly elastic bodies would develop no heat on collision. They would retain their motion afterwards, though its direction might be changed; and it is only when sensible motion is wholly or partly destroyed, that heat is generated. This always occurs in unelastic collision, the heat developed being the exact equivalent of the sensible motion extinguished. This heat virtually declares that the property of elasticity, denied to the ma.s.ses, exists among their atoms; by the recoil and oscillation of which the principle of conservation is vindicated.

But ambiguity in the use of the term 'force' makes itself more and more felt as we proceed. We have called the attraction of gravity a force, without any reference to motion. A body resting on a shelf is as much pulled by gravity as when, after having been pushed off the shelf, it falls towards the earth. We applied the term force also to that molecular attraction which we called chemical affinity. When, however, we spoke of the conservation of force, in the case of elastic collision, we meant neither a pull nor a push, which, as just indicated, might be exerted upon inert matter, but we meant force invested in motion--the _vis viva_, as it is called, of the colliding ma.s.ses.

Force in this form has a definite mechanical measure, in the amount of work that it can perform. The simplest form of work is the raising of a weight. A man walking up-hill, or up-stairs, with a pound weight in his hand, to an elevation say of sixteen feet, performs a certain amount of work, over and above the lifting of his own body. If he carries the pound to a height of thirty-two feet, he does twice the work; if to a height of forty-eight feet, he does three times the work; if to sixty-four feet, he does four times the work, and so on.

If, moreover, he carries up two pounds instead of one, other things being equal, he does twice the work; if three, four, or five pounds, he does three, four, or five times the work. In fact, it is plain that the work performed depends on two factors, the weight raised and the height to which it is raised. It is expressed by the product of these two factors.

But a body may be caused to reach a certain elevation in opposition to the force of gravity, without being actually carried up. If a hodman, for example, wished to land a brick at an elevation of sixteen feet above the place where he stood, he would probably pitch it up to the bricklayer. He would thus impart, by a sudden effort, a velocity to the brick sufficient to raise it to the required height; the work accomplished by that effort being precisely the same as if he had slowly carried up the brick. The initial velocity to be imparted, in this case, is well known. To reach a height of sixteen feet, the brick must quit the man's hand with a velocity of thirty-two feet a second. It is needless to say, that a body starting with any velocity, would, if wholly unopposed or unaided, continue to move for ever with the same velocity. But when, as in the case before us, the body is thrown upwards, it moves in opposition to gravity, which incessantly r.e.t.a.r.ds its motion, and finally brings it to rest at an elevation of sixteen feet. If not here caught by the bricklayer, it would return to the hodman with an accelerated motion, and reach his hand with the precise velocity it possessed on quitting it.

An important relation between velocity and work is here to be pointed out. Supposing the hodman competent to impart to the brick, at starting, a velocity of sixty-four feet a second, or twice its former velocity, would the amount of work performed be twice what it was in the first instance? No; it would be four times that quant.i.ty; for a body starting with twice the velocity of another, will rise to four times the height. In like manner, a three-fold velocity will give a nine-fold elevation, a four-fold velocity will give a sixteen-fold elevation, and so on. The height attained, then, is not proportional to the initial velocity, but to the square of the velocity. As before, the work is also proportional to the weight elevated. Hence the work which any moving ma.s.s whatever is competent to perform, in virtue of the motion which it at any moment possesses, is jointly proportional to its weight and the square of its velocity. Here, then, we have a second measure of work-, in which we simply translate the idea of height into its equivalent idea of motion.

In mechanics, the product of the ma.s.s of a moving body into the square of its velocity, expresses what is called the _vis viva_, or living force. It is also sometimes called the 'mechanical effect.' If, for example, a cannon pointed to the zenith urge a ball upwards with twice the velocity imparted to a second ball, the former will rise to four times the height attained by the latter. If directed against a target, it will also do four times the execution. Hence the importance of imparting a high velocity to projectiles in war. Having thus cleared our way to a perfectly definite conception of the _vis viva_ of moving ma.s.ses, we are prepared for the announcement that the heat generated by the shock of a falling body against the earth is proportional to the _vis viva_ annihilated. The heat is proportional to the square of the velocity. In the case, therefore, of two cannon-b.a.l.l.s of equal weight, if one strike a target with twice the velocity of the other, it will generate four times the heat, if with three times the velocity, it will generate nine times the heat, and so on.

Mr. Joule has shown that a pound weight falling from a height of 772 feet, or 772 pounds falling through one foot, will generate by its collision with the earth an amount of heat sufficient to raise a pound of water one degree Fahrenheit in temperature. 772 "foot-pounds"

const.i.tute the mechanical equivalent of heat. Now, a body falling from a height of 772 feet, has, upon striking the earth, a velocity of 223 feet a second; and if this velocity were imparted to the body, by any other means, the quant.i.ty of heat generated by the stoppage of its motion would be that stated above. Six times that velocity, or 1,338 feet, would not be an inordinate one for a cannon-ball as it quits the gun. Hence, a cannon-ball moving with a velocity of 1,338 feet a second, would, by collision, generate an amount of heat competent to raise its own weight of water 36 degrees Fahrenheit in temperature. If composed of iron, and if all the heat generated were concentrated in the ball itself, its temperature would be raised about 360 degrees Fahrenheit; because one degree in the case of water is equivalent to about ten degrees in the case of iron. In artillery practice, the heat generated is usually concentrated upon the front of the bolt, and on the portion of the target first struck. By this concentration the heat developed becomes sufficiently intense to raise the dust of the metal to incandescence, a flash of light often accompanying collision with the target.

Let us now fix our attention for a moment on the gunpowder which urges the cannon-ball. This is composed of combustible matter, which if burnt in the open air would yield a certain amount of heat. It will not yield this amount if it perform the work of urging a ball. The heat then generated by the gunpowder will fall short of that produced in the open air, by an amount equivalent to the _vis viva_ of the ball; and this exact amount is restored by the ball on its collision with the target. In this perfect way are heat and mechanical motion connected.

Broadly enunciated, the principle of the conservation of force a.s.serts, that the quant.i.ty of force in the universe is as unalterable as the quant.i.ty of matter; that it is alike impossible to create force and to annihilate it. But in what sense are we to understand this a.s.sertion? It would be manifestly inapplicable to the force of gravity as defined by Newton; for this is a force varying inversely as the square of the distance; and to affirm the constancy of a varying force would be self-contradictory. Yet, when the question is properly understood, gravity forms no exception to the law of conservation.

Following the method pursued by Helmholtz, I will here attempt an elementary exposition of this law. Though destined in its applications to produce momentous changes in human thought, it is not difficult of comprehension.

For the sake of simplicity we will consider a particle of matter, which we may call F, to be perfectly fixed, and a second movable particle, D, placed at a distance from F. We will a.s.sume that these two particles attract each other according to the Newtonian law. At a certain distance, the attraction is of a certain definite amount, which might be determined by means of a spring balance. At half this distance the attraction would be augmented four times; at a third of the distance, nine times; at one-fourth of the distance, sixteen times, and so on. In every case, the attraction might be measured by determining, with the spring balance, the amount of tension just sufficient to prevent D from moving towards F. Thus far we have nothing whatever to do with motion; we deal with statics, not with dynamics. We simply take into account the _distance_ of D from F, and the _pull_ exerted by gravity at that distance.

It is customary in mechanics to represent the magnitude of a force by a line of a certain length, a force of double magnitude being represented by a line of double length, and so on. Placing then the particle D at a distance from F, we can, in imagination, draw a straight line from D to F, and at D erect a perpendicular to this line, which shall represent the amount of the attraction exerted on D.

If D be at a very great distance from F, the attraction will be very small, and the perpendicular consequently very short. If the distance be practically infinite, the attraction is practically _nil_. Let us now suppose at every point in the line joining F and D a perpendicular to be erected, proportional in length to the attraction exerted at that point; we thus obtain an infinite number of perpendiculars, of gradually increasing length, as D approaches F. Uniting the ends of all these perpendiculars, we obtain a curve, and between this curve and the straight line joining F and D we have an area containing all the perpendiculars placed side by side. Each one of this infinite series of perpendiculars representing an attraction, or tension, as it is sometimes called, the area just referred to represents the sum of the tensions exerted upon the particle D, during its pa.s.sage from its first position to F.

Up to the present point we have been dealing with tensions, not with motion. Thus far _vis viva_ has been entirely foreign to our contemplation of D and F. Let us now suppose D placed at a practically infinite distance from F; here, as stated, the pull of gravity would be infinitely small, and the perpendicular representing it would dwindle almost to a point. In this position the sum of the tensions capable of being exerted on D would be a maximum. Let D now begin to move in obedience to the infinitesimal attraction exerted upon it. Motion being once set up, the idea of _vis viva_ arises. In moving towards F the particle D consumes, as it were, the tensions.

Let us fix our attention on D, at any point of the path over which it is moving. Between that point and F there is a quant.i.ty of unused tensions; beyond that point the tensions have been all consumed, but we have in their place an equivalent quant.i.ty of _vis viva_. After D has pa.s.sed any point, the tension previously in store at that point disappears, but not without having added, during the infinitely small duration of its action, a due amount of motion to that previously possessed by D. The nearer D approaches to F, the smaller is the sum of the tensions remaining, but the greater is the _vis viva_; the farther D is from F, the greater is the sum of the unconsumed tensions, and the less is the living force. Now the principle of conservation affirms _not_ the constancy of the value of the tensions of gravity, nor yet the constancy of the _vis viva_, taken separately, but the absolute constancy of the value of both taken together. At the beginning the _vis viva_ was zero, and the tension area was a maximum; close to F the _vis viva_ is a maximum, while the tension area is zero.

At every other point, the work-producing power of the particle D consists in part of _vis viva_, and in part of tensions.

If gravity, instead of being attraction, were repulsion, then, with the particles in contact, the sum of the tensions between D and F would be a maximum, and the _vis viva_ zero. If, in obedience to the repulsion, D moved away from F, _vis viva_ would be generated; and the farther D retreated from F the greater would be its _vis viva_, and the less the amount of tension still available for producing motion.

Taking repulsion as well as attraction into account, the principle of the conservation of force affirms that the mechanical value of the _tensions_ and _vires vivae_ of the material universe, so far as we know it, is a constant quant.i.ty. The universe, in short, possesses two kinds of property which are mutually convertible. The diminution of either carries with it the enhancement of the other, the total value of the property remaining unchanged.