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close inquiry, have stood through much investigation, and con-
tinually increase in force. For instance, time is growing up
daily into importance as an element in the exercise offeree. The
earth moves in its orbit in time ; the crust of the earth moves
in time; light moves in time; an electro-magnet requires time
for its charge by an electric current : to inquire, therefore,
whether power, acting either at sensible or insensible distances,
always acts in time, is not to be metaphysical ; if it acts in time
and across space, it must act by physical lines of force ; and
our view of the nature of the force may be affected to the ex-
tremest degree by the conclusions, which experiment and ob-
servation on time may supply ; being, perhaps, finally determi-
nable only by them. To inquire after the possible time in
which gravitating, magnetic, or electric force is exerted, is no
more metaphysical than to mark the times of the hands of a
clock in their progress ; or that of the temple of Serapis in its
ascents and descents ; or the periods of the occupations of
Jupiter's satellites ; or that in which the light from them comes
to the earth. Again, in some of the known cases of action in



1857.] On the Conservation of Force. 445

time, something happens whilst the time is passing which did
not happen before, and does not continue after : it is therefore
not metaphysical to expect an effect in every case, or to endea-
vour to discover its existence and determine its nature. So in
regard to the principle of the conservation of force ; I do not
think that to admit it, and its consequences, whatever they
may be, is to be metaphysical : on the contrary, if that word
have any application to physics, then I think that any hypo-
thesis, whether of heat, or electricity, or gravitation, or any
other form of force, which either willingly or unwillingly dis-
penses with the principle of conservation, is more liable to the
charge, than those which, by including it, become so far more
strict and precise.

Supposing that the truth of the principle of the conservation



EERATUM.
Page 445, line 10, for willingly or unwillingly read wittingly or unwittingly.



sidered under it, that state or result is only partial, and must
not be accepted as exhausting the power or being the full
equivalent, and therefore cannot be considered as representing
its whole nature ; that, indeed, it may express only a very small
part of the whole, only a residual phenomenon, and hence give
us but little indication of the full natural truth. Allowing the
principle its force, we ought, in every hypothesis, either to
account for its consequences by saying what the changes are
when force of a given kind apparently disappears, as when ice
thaws, or else should leave space for the idea of the conversion.
If any hypothesis, more or less trustworthy on other accounts,
is insufficient in expressing it or incompatible with it, the place
of deficiency or opposition should be marked as the most im-
portant for examination ; for there lies the hope of a discovery



444 On the Conservation of Force. [1857.

changeable in its manifestation, it offers an unchanging test of
the matter which we recognize by it.

Agreeing with those who admit the conservation of force to
be a principle in physics as large and sure as that of the inde-
structibility of matter, or the invariability of gravity, I think
that no particular idea of force has a right to unlimited or un-
qualified acceptance, that does not include assent to it ; and
also, to definite amount and definite disposition of the force,
either in one effect or another, for these are necessary conse-
quences : therefore, I urge, that the conservation of force ought
to be admitted as a physical principle in all our hypotheses,
whether partial or general, regarding the actions of matter. I
have had doubts in my own mind whether the considerations I



in time ; light moves in time ; an electro-magnet requires nine
for its charge by an electric current : to inquire, therefore,
whether power, acting either at sensible or insensible distances,
always acts in time, is not to be metaphysical ; if it acts in time
and across space, it must act by physical lines of force ; and
our view of the nature of the force may be affected to the ex-
tremest degree by the conclusions, which experiment and ob-
servation on time may supply ; being, perhaps, finally determi-
nable only by them. To inquire after the possible time in
which gravitating, magnetic, or electric force is exerted, is no
more metaphysical than to mark the times of the hands of a
clock in their progress ; or that of the temple of Serapis in its
ascents and descents ; or the periods of the occupations of
Jupiter's satellites ; or that in which the light from them comes
to the earth. Again, in some of the known cases of action in



1857.] On the Conservation of Force. 445

time, something happens whilst the time is passing which did
not happen before, and does not continue after : it is therefore
not metaphysical to expect an effect in every case, or to endea-
vour to discover its existence and determine its nature. So in
regard to the principle of the conservation of force ; I do not
think that to admit it, and its consequences, whatever they
may be, is to be metaphysical : on the contrary, if that word
have any application to physics, then I think that any hypo-
thesis, whether of heat, or electricity, or gravitation, or any
other form of force, which either willingly or unwillingly dis-
penses with the principle of conservation, is more liable to the
charge, than those which, by including it, become so far more
strict and precise.

Supposing that the truth of the principle of the conservation
of force is assented to, I come to its uses. No hypothesis
should be admitted, nor any assertion of a fact credited, that
denies the principle. No view should be inconsistent or in-
compatible with it. Many of our hypotheses in the present
state of science may not comprehend it, and may be unable to
suggest its consequences ; but none should oppose or contra-
dict it.

If the principle be admitted, we perceive at once, that a
theory or definition, though it may not contradict the principle,
cannot be accepted as sufficient or complete unless the former
be contained in it ; that however well or perfectly the definition
may include and represent the state of things commonly con-
sidered under it, that state or result is only partial, and must
not be accepted as exhausting the power or being the full
equivalent, and therefore cannot be considered as representing
its whole nature-, that, indeed, it may express only a very small
part of the whole, only a residual phenomenon, and hence give
us but little indication of the full natural truth. Allowing the
principle its force, we ought, in every hypothesis, either to
account for its consequences by saying what the changes are
when force of a given kind apparently disappears, as when ice
thaws, or else should leave space for the idea of the conversion.
If any hypothesis, more or less trustworthy on other accounts,
is insufficient in expressing it or incompatible with it, the place
of deficiency or opposition should be marked as the most im-
portant for examination; for there lies the hope of a discovery



446 On the Conservation of Force. [1857.

of new laws or a new condition of force. The deficiency should
never be accepted as satisfactory, but be remembered and used
as a stimulant to further inquiry ; for conversions of force may
here be hoped for. Suppositions may be accepted for the time,
provided they are not in contradiction with the principle. Even
an increased or diminished capacity is better than nothing at
all ; because such a supposition, if made, must be consistent
with the nature of the original hypothesis, and may therefore,
by the application of experiment, be converted into a further
test of probable truth. The case of a force simply removed or
suspended, without a transferred exertion in some other direc-
tion, appears to me to be absolutely impossible.

If the principle be accepted as true, we have a right to pursue
it to its consequences, no matter what they may be. It is,
indeed, a duty to do so. A theory may be perfection as far
as it goes, but a consideration going beyond it, is not for that
reason to be shut out. We might as well accept our limited
horizon as the limits of the world. No magnitude, either of
the phenomena or of the results to be dealt with, should stop
our exertions to ascertain, by the use of the principle, that
something remains to be discovered, and to trace in what di-
rection that discovery may lie.

I will endeavour to illustrate some of the points which have
been urged, by reference, in the first instance, to a case of
power which has long had great attractions for me, because
of its extreme simplicity, its promising nature, its universal
presence, and its invariability under like circumstances ; on
which, though I have experimented* and as yet failed, I think
experiment would be well bestowed : I mean the force of gra-
vitation. I believe I represent the received idea of the gravi-
tating force aright, in saying, that it is a simple attractive force
exerted between any two or all the particles or masses of matter,
at every sensible distance, but with a strength varying inversely
as the square of the distance. The usual idea of the force
implies direct action at a distance ; and such a view appears
to present little difficulty except to Newton, and a few, inclu-
ding myself, who in that respect may be of like mind with himf.

This idea of gravity appears to me to ignore entirely the
principle of the conservation of force ; and by the terms of its
* Philosophical Transactions, 1851, p. 1. * See note, p. 451.



1857.] On the gravitating Force. 447

definition, if taken in an absolute sense, " varying inversely as
the square of the distance," to be in direct opposition to it ;
and it becomes my duty, now, to point out where this contra-
diction occurs, and to use it in illustration of the principle of
conservation. Assume two particles of matter, A and B, in free
space, and a force in each or in both by which they gravitate
towards each other, the force being unalterable for an un-
changing distance, but varying inversely as the square of the
distance when the latter varies. Then, at the distance of 10,
the force may be estimated as 1 ; whilst at the distance of 1,
i. e. one-tenth of the former, the force will be 100: and if we
suppose an elastic spring to be introduced between the two as
a measure of the attractive force, the power compressing it will
be a hundred times as much in the latter case as in the former.
But from whence can this enormous increase of the power come?
If we say that it is the character of this force, and content
ourselves with that as a sufficient answer, then it appears to me
we admit a creation of power, and that to an enormous amount ;
yet by a change of condition so small and simple, as to fail in
leading the least instructed mind to think that it can be a suffi-
cient cause : we should admit a result which would equal the
highest acts our minds can appreciate of the working of infinite
power upon matter ; we should let loose the highest law in
physical science which our faculties permit us to perceive,
namely, the conservation of force. Suppose the two particles
A and B removed back to the greater distance of 10, then the
force of attraction would be only a hundredth part of that they
previously possessed ; this, according to the statement that the
force varies inversely as the square of the distance, would double
the strangeness of the above results ; it would be an annihilation
of force ; an effect equal in its infinity and its consequences
with creation, and only within the power of Him who has cre-
ated.

We have a right to view gravitation under every form that
either its definition or its effects can suggest to the mind ; it is
our privilege to do so with every force in nature ; and it is only
by so doing, that we have succeeded, to a large extent, in re-
lating the various forms of power, so as to derive one from
another, and thereby obtain confirmatory evidence of the great
principle of the conservation of force. Then let us consider



448 On the gravitating Force. [1857.

the two particles A and B as attracting each other by the force
of gravitation, under another view. According to the defini-
tion, the force depends upon both particles, and if the particle
A or B were by itself, it could not gravitate, i. e. it could have
no attraction, no force of gravity. Supposing A to exist in
that isolated state and without gravitating force, and then B
placed in relation to it, gravitation comes on, as is supposed,
on the part of both. Now, without trying to imagine how B,
which had no gravitating force, can raise up gravitating force
in A, and how A, equally without force beforehand, can raise
up force in B, still, to imagine it as a fact done, is to admit a
creation of force in both particles, and so to bring ourselves
within the impossible consequences which have already been
referred to.

It may be said we cannot have an idea of one particle by
itself, and so the reasoning fails. For my part I can compre-
hend a particle by itself just as easily as many particles; and
though i cannot conceive the relation of a lone particle to
gravitation, according to the limited view which is at present
taken of that force, I can conceive its relation to something
which causes gravitation, and with which, whether the particle
is alone, or one of a universe of other particles, it is always re-
lated. But the reasoning upon a lone particle does not fail ;
for as the particles can be separated, we can easily conceive of
the particle B being removed to an infinite distance from A
and then the power in A will be infinitely diminished. Such
removal of B will be as if it were annihilated in regard to A,
and the force in A will be annihilated at the same time : so
that the case of a lone particle, and that where different di-
stances only are considered, become one, being identical with
each other in their consequences. And as removal of B to an
infinite distance is as regards A annihilation of B, so removal
to the smallest degree is, in principle, the same thing with dis-
placement through infinite space : the smallest increase in
distance involves annihilation of power ; the annihilation of the
second particle, so as to have A alone, involves no other con-
sequence in relation to gravity ; there is difference in degree,
but no difference in the character of the result.

It seems hardly necessary to observe, that the same line of
thought grows up in the mind if we consider the mutual gra-



1857.] The gravitating Force. 449

vitating action of one particle and many. The particle A will
attract the particle B at the distance of a mile with a certain
degree of force ; it will attract a particle C at the same distance
of a mile with a power equal to that by which it attracts B ; if
myriads of like particles be placed at the given distance of a
mile, A will attract each with equal force ; and if other par-
ticles be accumulated round it, within and without the sphere
of two miles diameter, it will attract them all with a force vary-
ing inversely with the square of the distance. How are we to
conceive of this force growing up in A to a million- fold or more ?
and if the surrounding particles be then removed, of its dimi-
nution in an equal degree ? Or, how are we to look upon the
power raised up in all these outer particles by the action of A
on them, or by their action one on another, without admitting,
according to the limited definition of gravitation, the facile ge-
neration and annihilation of force ?

The assumption which we make for the time with regard to
the nature of a power (as gravity, heat, &c.), and the form of
words in which we express it, i. e. its definition, should be
consistent with the fundamental principles of force generally.
The conservation of force is a fundamental principle ; hence
the assumption with regard to a particular form of force, ought
to imply what becomes of the force when its action is increased
or diminished, or its direction changed ; or else the assumption
should admit that it is deficient on that point, being only half
competent to represent the force ; and, in any case, should not
be opposed to the principle of conservation. The usual defi-
nition of gravity as an attractive force between the particles of
matter VARYING inversely as the square of the distance, whilst
it stands as a full definition of the power, is inconsistent with
the principle of the conservation of force. If we accept the
principle, such a definition must be an imperfect account of
the whole of the force, and is probably only a description of
one exercise of that power, whatever the nature of the force
itself may be. If the definition be accepted as tacitly in-
cluding the conservation of force, then it ought to admit that
consequences must occur during the suspended or diminished
degree of its power as gravitation, equal in importance to the
power suspended or hidden ; being in fact equivalent to that
diminution. It ought also to admit, that it is incompetent to



450 On the Conservation of Force. [1857.

suggest or deal with any of the consequences of the changed
part or condition of the force, and cannot tell whether they
depend on, or are related to, conditions external or internal to
the gravitating particle ; and, as it appears to me, can say
neither yes nor no to any of the arguments or probabilities
belonging to the subject.

If the definition denies the occurrence of such contingent re-
sults, it seems to me to be unphilosophical ; if it simply ignores
them, I think it is imperfect and insufficient ; if it admits these
things, or any part of them, then it prepares the natural phi-
losopher to look for effects and conditions as yet unknown, and
is open to any degree of development of the consequences and
relations of power : by denying, it opposes a dogmatic barrier
to improvement ; by ignoring, it becomes in many respects an
inert thing, often much in the way ; by admitting, it rises to the
dignity of a stimulus to investigation, a pilot to human science.
The principle of the conservation of force would lead us to
assume, that when A and B attract each other less because of
increasing distance, then some other exertion of power, either
within or without them, is proportionately growing up ; and
again, that when their distance is diminished, as from 10 to
1, the power of attraction, now increased a hundred-fold,
has been produced out of some other form of power which has
been equivalently reduced. This enlarged assumption of the
nature of gravity is not more metaphysical than the half as-
sumption ; and is, I believe, more philosophical, and more in
accordance with all physical considerations. The half assump-
tion is, in my view of the matter, more dogmatic and irrational
than the whole, because it leaves it to be understood that
power can be created and destroyed almost at pleasure.

When the equivalents of the various forms of force, as far
as they are known, are considered, their differences appear
very great ; thus, a grain of water is known to have electric
relations equivalent to a very powerful flash of lightning. It
may therefore be supposed that a very large apparent amount
of the force causing the phenomena of gravitation, may be the
equivalent of a very small change in some unknown condition
of the bodies, whose attraction is varying by change of distance.
For my own part, many considerations urge my mind towards
the idea of a cause of gravity, which is not resident in the par-



1857.] . , The gravitating Force. 451

tides of matter merely, but conjointly in them, and all space.
I have already put forth considerations regarding gravity which
partake of this idea*, and it seems to have been unhesitatingly
accepted by Newtonf .

There is one wonderful condition of matter, perhaps its only
true indication, namely inertia ; but in relation to the ordinary
definition of gravity, it only adds to the difficulty. For if we
consider two particles of matter at a certain distance apart,
attracting each other under the power of gravity and free to
approach, they will approach ; and when at only half the di-
stance, each will have had stored up in it, because of its inertia,
a certain amount of mechanical force. This must be due to
the force exerted, and, if the conservation principle be true,
must have consumed an equivalent proportion of the cause of
attraction ; and yet, according to the definition of gravity, the
attractive force is not diminished thereby, but increased four-
fold, the force growing up within itself the more rapidly, the
more it is occupied in producing other force. On the other
hand, if mechanical force from without be used to separate the
particles to twice their distance, this force is not stored up in
momentum or by inertia, but disappears ; and three-fourths of
the attractive force at the first distance disappears with it:
how can this be ?

We know not the physical condition or action from which
inertia results ; but inertia is always a pure case of the conser-
vation of force. It has a strict relation to gravity, as appears
by the proportionate amount of force which gravity can com-
municate to the inert body ; but it appears to have the same
strict relation to other forces acting at a distance, as those of
magnetism or electricity, when they are so applied by the tan-

* Proceedings of the Royal Institution, 1855, vol. ii. p. 10, &c.

f "That gravity should be innate, inherent, and essential to matter, so
that one body may act upon another at a distance, through a vacuum, without
the mediation of anything else, by and through which their action and force
may be conveyed from one to another, is to me so great an absurdity, that I
believe no man who has in philosophical matters a competent faculty of think-
ing, can ever fall into it. Gravity must be caused by an agent, acting constantly
according to certain laws ; but whether this agent be material or immaterial, I
have left to the consideration of my readers." See Newton's ' Third Letter
to Bentley.'



452 On the Conservation of Force. [1857.

gential balance as to act independent of the gravitating force.
It has the like strict relation to force communicated by im-
pact, pull, or in any other way. It enables a body to take up
and conserve a given amount of force until that force is trans-
ferred to other bodies, or changed into an equivalent of some
other form ; that is all that we perceive in it : and we cannot
find a more striking instance amongst natural or possible phe-
nomena of the necessity of the conservation of force as a law
of nature ; or one more in contrast with the assumed variable
condition of the gravitating force supposed to reside in the
particles of matter.

Even gravity itself furnishes the strictest proof of the con-
servation of force in this, that its power is unchangeable for
the same distance ; and is by that in striking contrast with the
variation which we assume in regard to the cause of gravity,
to account for the results at different distances.

It will not be imagined for a moment that I am opposed to
what may be called the law of gravitating action, that is, the
law by which all the known effects of gravity are governed ;
what I am considering, is the definition of the force of gravi-
tation. That the result of one exercise of a power may be
inversely as the square of the distance, I believe and admit ;
and I know that it is so in the case of gravity, and has been
verified to an extent that could hardly have been within the
conception even of Newton himself when he gave utterance to
the law : but that the totality of an inherent force can be em-
ployed according to that law I do not believe, either in rela-
tion to gravitation, or electricity, or magnetism, or any other
supposed form of power.

I might have drawn reasons for urging a continual recollec-
tion of, and reference to, the principle of the conservation of
force from other forms of power than that of gravitation ; but
I think that when founded on gravitating phenomena, they
appear in their greatest simplicity ; and precisely for this rea-
son, that gravitation has not yet been connected by any degree
of convertibility with the other forms of force. If I refer for a
few minutes to these other forms, it is only to point in their



Online LibraryMichael FaradayExperimental researches in chemistry and physics → online text (page 44 of 49)