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SCIENCE LECTURES FOR THE PEOPLE.
No. 4.—FOURTH SERIES—1872.
ATOMS.
A LECTURE
BY
PROFESSOR CLIFFORD, M.A.,
OF CAMBRIDGE.
Delivered in the Hulme Town Hall, Manchester,
November 20th,
Also before
the
1872;
Sunday Lecture Society, in London,
ON THE 7TH OF JANUARY, 1872.
Air. Davies Benson in the chair.
[REPORTED BY HENRY PITMAN.]
PRICE
OZE" ZE
IE3 IE ZEST ZEST AT _
I
MANCHESTER :
JTO II N HEYWOOD, 141 and 143, DEANSGATE.
LONDON : F. PITMAN, PATERNOSTER ROW.
��ATOMS.
A LECTURE
By
PROFESSOR CLIFFORD, M.A.,
Delivered in the Hulme Town Hall, Manchester, Nov. 20th., 1872 ;
yjfso before the Sunday Lecture Society, in London, on the yth of January, 1872.
If I were to wet my finger and then rub it along the edge of this
glass, I should no doubt persuade the glass to give out a certain
musical note. So also if I were to sing to that glass the same
note loud enough, I should get the glass to answer me back with
a note.
I want you to remember that fact, because it is of capital
importance for the arguments we shall have to consider to-night.
! The very same note which I can get the tumbler to give out by
I agitating it, by rubbing the edge, that same note I can also get
the tumbler to answer back to me when I sing to it. Now,
I .remembering that, please to conceive a rather complicated thing
I that I am now going to try to describe to you. The same
I -property that belongs to the glass belongs also to a bell which is
I made out of metal. If that bell is agitated by being struck, or in
I .any other way, it will give out the same sound that it will answer
| back if you .sing that sound to it; but if you sing a different
I '-Sound to it then it will not answer.
Now suppose that I have several of these metal bells which
| ‘.answer to quite different notes, and that they are all fastened
to a set of elastic stalks which spring out of a certain centre
? to which they are fastened. All these bells, then, are not only
: fastened to these stalks, but they are held there in such a way
that they can spin round upon the points to which they are
»-■fastened.
And then the centre to which these elastic stalks are
fastened or suspended, you may imagine as able to move in all
manner of directions, and that the whole structure made up of
■these bells and stalks and centre is able to spin round any axis
�4
whatever. We must also suppose that there is surrounding thisstructure a certain framework. We willsuppose the framework to bemade of some elastic material, so that it is able to be pressed in toa certain extent. Suppose that framework is made of whalebone,
if you like. Now this structure I am going for'the present to call
an “atom.” I do not mean to say that atoms are made of a
structure like that. I do not mean to say that there is anything
in an atom which is in the shape of a bell; and I do not mean
to say that there is anything analogous to an elastic stalk in it..
But what I mean is this-—that an atom is something that iscapable of vibrating at certain definite rates; also that it is
capable of other motions of its parts besides those vibrations at
certain definite rates; and also that it is capable of spinning
round about any axis. Now by the framework which I suppose
to be put round that structure made out of bells and elastic
stalks, I mean this—that supposing you had two such structures,
then you cannot put them closer together than a certain distance,
but they will begin to resist being put close together after you .
have put them as near as that, and they will push each other
away if you attempt to put them closer. That is all I mean then.
You must only suppose that that structure is described, and that
set of ideas is put together, just for the sake of giving us some
definite notion of a thing which has similar properties to that
structure. But you must not suppose that there is any special,
part of an atom which has got a bell-like form, or any part like an
elastic stalk made out of whalebone.
Now having got the idea of such a complicated structure,
which is capable, as we said, of vibratory motion, and of othersorts of motion, I am going on to explain what is the belief of
those people who have studied the subject about the composition
of the air which fills this room. The air which fills thisroom is what is called a gas; but it is not a simple gas;
it is a mixture of two different gases, oxygen and nitrogen.
Now what is believed about this air is that it consists of
quite distinct portions or little masses of air—that is, of littlemasses each of which is either oxygen or nitrogen; and that
these little masses are perpetually flying about in all directions.
The number of them in this room is so great that it strains the
powers of our numerical system to count them. They are flying?
about in all directions and mostly in straight lines, except where
they get quite near to one another, and then they rebound and fly
off in other directions. Part of these little masses which compose
the air are of one sort—they are called oxygen. All those little
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masses which are called oxygen are alike; they are of the same
weight; they have the same rates of vibration; and they go about
on the average at a certain rate. The other part of these
little masses is called nitrogen, and they have a different weight;
but the weight of all the nitrogen masses is the same, as nearly as
we can make out. They have again the same rates of vibration;
but the rates of vibration that belong to them are different from
the rates of vibration that belong to the oxygen masses; and the
nitrogen masses go about on the average at a certain rate, but this
rate is different from the average rate at which the oxygen masses
go about. So then, taking up that structure which I endeavoured
to describe to you at first, we should represent the state of the air
in this room as being made up of such a lot . of compound atoms
of those structures of bells and stalks, with frameworks round
them, that I described to you, being thrown about in all directions
with great rapidity, and continually impinging against one another,
-each flying off in a different direction, so that they would go mostly
in straight lines (you must suppose them for a moment not to fall
■down towards the earth), excepting where they come near enough
for their two frameworks to be in contact, and then their frame
works throw them off in different directions : that is a conception
of the state of things which actually takes place inside of gas.
Now, the conception which scientific men have of the state of
things which takes place inside of a liquid is different from that.
We should conceive it in this way: We should suppose that a
number of these structures are put so close together that their
frameworks are always in contact; and yet they are moving about
and rolling among one another, so that no one of them keeps the
same place for two instants together, and any one of them is
travelling all over the whole space. Inside of this glass, where
there is a liquid, all the small particles or molecules are running
about among one another, and yet none of them goes for any
-appreciable portion of its path in a straight line, because there is
310 small distance that it goes without being in contact with others
all around it; .and the effect of this contact of the others all around
it is that they press against it and force it out of a straight path.
'So that the path of a particle in a liquid is a sort of wavy path ;
it goes in and out in all directions, and a particle at one part of
the liquid will, at a certain time, have traversed all the different
parts one after another.
The conception of what happens inside of a solid body, say a
crystal of salt, is different again from this. It is supposed that
the very small particles which constitute that crystal of salt do not
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travel about from one part of the crystal to another, but that each
one of them remains pretty much in the same place. I say
“ pretty much,” but not exactly, and the motion of it is like this:
Suppose one of my structures, with its framework round it, to be
fastened up by elastic strings, so that one string goes to the ceiling,
and another to the floor, and another to each wall, so that it is
fastened by all these strings. Then if these strings are stretched,
and a particle is displaced in any way, it will just oscillate about
its mean position, and will not go far away from it; and if forced
away from that position it will come back again. That is the
sort of motion that belongs to a particle in the inside of a solid
body. A solid body, such as a crystal of salt, is made up, just as
a liquid or a gas is made up, of innumerable small particles, but
they are so attached to one another that each of them can only
oscillate about its mean position. It is very probable that it is
also able to spin about any axis in that position or near it; but it
is not able to leave that position finally, and to go and take up
another position in the crystal: it must stop in or near about the
same position.
These, then, are the views which are held by scientific men at
present about what actually goes on inside of a gaseous body, or
a liquid body, or a solid body. In each case the body is supposed
to be made up of a very large number of very small particles ;
but in one case these particles are very seldom in contact with
one another, that is, very seldom within range of each other’s
action; in this case they are during the greater part of the time
moving separately along straight lines. In the case of a liquid
*they are constantly within the range of each other’s action, but
they do not move along straight lines for any appreciable part of
the time; they are always changing their position relatively to the
other particles, and one of them gets about from one part of theliquid to another. In the case of a solid they are always alsowithin the range of each other’s action, and they are so much
within that range that they are not able to change their relative
positions; and each one of them is obliged to remain in very
nearly the same position.
Now what I want to do this evening is to explain to you, so
far as I can, the reasons which have led scientific men to adopt
these views; and what I wish especially to impress upon you is
this, that what is called the “ atomic theory ”—that is what I have
-just been explaining—is no longer in the position of a theory, but
that such of the facts as I have just explained to you are really
things which are definitely known and which are no. longer
�7
Suppositions; that the arguments by which scientific men have
been led to adopt these views are such as, to anybody who fairly
considers them, justify that person iri believing that the statements
are true.
Now first of all I want to explain what the reasons are
why we believe that the air consists of separate portions, and that
these portions are repetitions of the same structures. That is to
say that in the air we have two structures really, each of them a
great number of times repeated. Take a simple illustration,
which is a rather easier one to consider. Suppose we take a
vessel which is filled with oxygen. I want to show what the
reasons are which lead us to believe that that gas consists of a
certain structure which is a great number of times repeated, and
that between two examples of that structure which exist inside of
the vessel there is a certain empty space which does not contain
any oxygen. That oxygen gas contained in the vessel is made up
of small particles which are not close together, and each of these
particles has a certain structure, which structure also belongs
to the rest of the particles. Now this argument is rather a
difficult one, and I shall ask you therefore to follow it as closely
as possible, because it is an extremely complicated argument to
follow out the first time that it is presented to you.
I want to consider again the case of this finger glass. You
must often have tried that experiment—that a glass will give out
when it is agitated the same note which it will return when it is
sung to. Well, now, suppose that I have got this room filled with
a certain number of such atomic structures as I have endeavoured
to describe—that is to say, of sets of bells, the bells answering to
certain given notes. Each of these little structures is exactly
alike, that is to say, it contains just the bells corresponding to the
same notes. Well, now, suppose that you sing to a glass or to a
bell, there are three things that may happen. First, you may sing
a note which does not belong to the bell at all. In that case the
bell will not answer; it will not be affected or agitated by your
singing that note, but it will remain quite still. Next, if you sing
a note that belongs to the bell, but if you sing it rather low, then
the effect of that note will be to make the bell move a little, but
the bell will not move so much as to give back the note in an
audible form. Thirdly, if you sing the note which belongs to the
bell loud enough, then you will so far agitate the bell that it will
give back the note to you again. Now exactly that same property
belongs to a stretched string, or the string of a piano. You know
that if you sing a certain note in a room where there is a piano,
�8
the string belonging to that note will answer you if you sing loud
enough. The other strings won’t answer at all. If you don’t sing
loud enough the string will be affected, but not enough to answer
you. Now let us imagine a screen of piano strings, all of exactly
the same length, of the same material, and stretched equally, and
that this screen of strings is put across the room; that I am at one
end and that you are at another, and that I proceed to sing notes
straight up the scale. Now while I sing notes which are different
from that note which belongs to the screen of strings, they will
pass through the screen without being altered, because the
agitation of the air which I produce will not affect the strings.
But that note will be heard quite well at the other side of the
screen. You must remember that when the air carries a sound it
vibrates at a certain rate belonging to the sound. I make the air
vibrate by singing a particular note, and if that rate of vibration
corresponds to the strings the air will pass on part of its vibration
to the strings, and so make the strings move. But if the rate of
vibration is not the one that corresponds to the strings, then the
air will not pass on any of its vibrations to the strings, and
consequently the sound will be heard equally loud after it has
passed through the strings. Having put the strings of the piano
across the room, if I sing up the scale, when I come to the note
which belongs to each of the strings my voice will suddenly
appear to be deadened, because at the moment that the rate of
vibration which I impress upon the air coincides with that
belonging to the strings, part of it will be taken up in setting the
strings in motion. As I pass the note, then, which belongs to the
strings, that note will be deadened.
Instead of a screen of piano strings let us put in a series ot
sets of bells, three or four belonging to each set, so that each set
of bells answers to three or four notes, and so that all the sets are
exactly alike. Now suppose that these sets of bells are distributed
all over the middle part of the room, and that I sing straight up
the scale from one note to another until I come to the note that
corresponds to one of the bells in these sets, then that note will
appear to be deadened at the other end, because part of the
vibration communicated to the air will be taken up in setting those
bells in motion. When I come to another note which belongs to
them, that note will also be deadened ; so that a person listening
at the other end of the room would observe that certain notes were
deadened, or even had disappeared altogether. If, however, I sing
loud enough, then I should set all these bells vibrating. What
would be heard at the other end of the room ? Why just the
�9
chord compounded out of those sounds that belonged to the bells,
because the bells having been set vibrating would give out the
corresponding notes. So you see there are here three facts.
When I sing a note which does not belong to the bells, my voice
passes to the end of the room without diminution. When I sing
a note that does belong to the bells, then if it is not loud enough
it is deadened by passing through the screen ; but if it is loud
enough it sets the bells vibrating, and is heard afterwards. Now
just notice this consequence. We have supposed a screen made
out of these structures that I have imagined to represent atoms,
and when I sing through the scale at one end of the room certain
notes appear to be deadened. If I take away half of those
structures, what will be the effect ? Exactly the same notes will
be deadened, but they will not be deadened so much ; the notes
which are picked out of the thinner screen to be deadened will be
exactly the same notes, but the amount of the deadening will not
be the same.
So far we have only been talking about the transmission of
sound. You know that sound consists of certain waves which are
passed along in the air ; they are called “ aerial vibrations.” Now
we also know that light consists of certain waves which are passed
along not in the air, but along another medium. I cannot stop at
present to explain to you what the sort of evidence is upon which
that assertion rests, but it is the same sort of evidence as that
which I shall try to show you belongs to the statement about
atoms ; that is to say, the “ undulatory theory,” as it is called, of
light; the theory that light consists of waves transmitted along a
certain medium, has passed out of the stage of being a theory,
and has passed into the stage of being a demonstrated fact. The
difference between a theory and a demonstrated fact is something
like this : If you supposed a man to have walked from Chorlton
Town Hall down here say in ten minutes, the natural conclusion
would be that he had walked along the Stretford Road. Now
that theory would entirely account for all the facts, but at the same
time the facts would not be proved by it. But suppose it happened
to be winter time, with snow on the road, and that you could
trace the man’s footsteps all along the road, then you would know
that he had walked along that way. Now the sort of evidence
we have to show that light does consist of waves transmitted
through a medium is the sort of evidence that footsteps upon the
snow make; it is not a theory merely which simply accounts for
the facts, but it is a theory which can be reasoned back to from
the facts without any other theory being possible. So that you
�io
must just for the present take it for granted that the arguments
in favour of the hypothesis that light consists of waves are such
as to take it out of the region of hypothesis, and make it into
demonstrated fact.
Very well, then, light consists of waves transmitted along this
medium in the same way that sound is transmitted along the air.
The waves are not of the same kind; but still they are waves, and
they are transmitted as such; and the different colours of light
correspond to the different lengths of these waves, or to the
different rates of the vibration of the medium, just as the different
pitches of sound correspond to the different lengths of the air
waves, or to the different rates of the vibration of the air. Now
if we take any gas, such as oxygen, and we pass light through it,
we find that that gas intercepts, or weakens, certain particular
colours. If we take any other gas, such as hydrogen, and pass
light through it, we find that that gas intercepts, or weakens,
certain other particular colours of the light. Now, there are two
ways in which it can do that: it is clear that the undulations, or
waves, are made weaker, because they happen to coincide with the
rate of vibration of the gas they are passing through. But the
gas may vibrate as a whole in the same way that the air does
when you transmit sound. Or the waves may be stopped, because
the gas consists of a number of small structures; just as my
screen, which I imagine to consist of structures; or just as the
screen of piano strings is made up of the same structure many
times repeated. Either of these suppositions would apparently at
first account for the fact that certain waves of light are intercepted
by the gas, while others are let through. But now how is it that
we can show one of these suppositions is wrong and the other is
right ? Instead of taking so small a structure as piano strings, let
us suppose we had got a series of fiddles, the strings of all of
them being stretched exactly in tune. I suppose this case because
it makes a more complicated structure, for there would be two or
three notes corresponding in each fiddle. If you suppose this
screen of fiddles to be hung up and then compressed, what will
be the effect ? The effect of the compression will be, if they are
all in contact, that each fiddle itself will be altered. If the fiddles
are compressed longways, the strings will give lower notes than
before, and consequently the series of notes which will be inter
cepted by that screen will be different from the series of notes
which were intercepted before. But if you have a screen made
out of fiddles which are at a distance from one another, and then
if you compress them into a smaller space by merely bringing
�IT
them nearer together, without making them touch, then it is clear
that exactly the same notes will be intercepted as before; only, as
there will be more fiddles in the same space, the deadening of the
sound will be greater.
Now when you compress any gas you find that it intercepts
exactly the same colours of light which it intercepted before it
was compressed. It follows, therefore, that the rates of vibration
which it intercepts depend not upon the mass of the gas whose
properties are altered by the compression, but upon some
individual parts of it which were at a distance from one another
before, and which are only brought nearer together without being
absolutely brought into contact so as to squeeze them. That is the
sort of reasoning by which it is made clear that the interception
of light, or particular waves of light by means of a gas, must
depend on certain individual structures in the gas which are at
a distance from one another, and which by compression are not
themselves compressed, but only brought nearer to one another.
There is an extremely interesting consequence which follows
from this reasoning, and which was deduced from it by Professor
Stokes in the year 1851, and which was afterwards presented in a
more developed form in the magnificent researches of Kirchhoff—
namely the reasoning about the presence of certain matter in the
Stm. If you analyse the solar light by passing it through a prism,
the effect of the prism is to divide it off so as to separate the
light into the different colours which it contains. That line of
variously coloured light which is produced by the prism is, as you
know, called the spectrum. Now when that spectrum is made in
a very accurate way, so that the parts of it are well defined, it is
observed to contain certain dark lines. That is, there is a certain
kind of light which is missing in the sun light; certain kinds of
light, as we travel along the scale of lights, are missing. Why are
they missing? Because there is something that the light has
passed through which intercepts or weakens those kinds of light.
Now that something which the light has passed through, how
shall we find out what it is ? It ought to be the same sort of
substance which if it were heated would give out exactly that
Hud of light. Now there is a certain kind of light which is
intercepted which makes a group of dark lines in the solar
Spectrum. There are two principal lines which together are
called the line D; and it is found that exactly that sort of light is
emitted by sodium when heated hot enough. The conclusion
therefore is that that matter which intercepts that particular part
of the solar light is sodium, or that there is sodium somewhere
�T2
between us and the hot portion of the sun which sends us the
light And other reasons lead us to conclude that this sodium is
not in the atmosphere of the earth, but in the neighbourhood
the sun—that it exists in a gaseous state in the sun’s atmosphere.
And nearly all the lines in the solar spectrum have been explained
in that way, and shown to belong to certain substances which we
are able to heat here, and to show that when they are heated they
give out exactly the same kind of light which they intercepted
when the light was first given out by the sun and they stood in
the.way. So you see that is a phenomenon exactly like the
phenomenon presented by the finger-glass that we began with.
Precisely the same light which any gas will give out when it is
heated, that same kind of light it will stop or much weaken it if
the light is attempted to be passed through it. That means that
this medium which transmits light, and which we call the
“ luminiferous ether,” has a certain rate of vibration for every
particular colour of the spectrum. When that rate of vibration
coincides with one of the rates of vibration of an atom, then it
will be stopped by that atom, because it will set the atom
vibrating itself. If therefore you pass light of any particular
colour through a gas whose atoms are capable of the corresponding
rate of vibration, the light will be cut off by the gas. If on the
other hand you so far heat the gas that the atoms are vibrating
strongly enough to give out light, it will give out a light of a kind
which it previously stopped.
We have reason then for believing that a simple gas consists
of a great number of atoms; that it consists of very small portions,
each of which has a complicated structure, but that structure is
the same for each of them, and that these portions are separate,
or that there is space between them.
In the next place I want to show you what is the evidence
upon which we believe that these portions of the gas are in motion—
that they are constantly moving.
If this were a political instead of a scientific meeting, there
would probably be some people who would be inclined to disagree
with us, instead of all being inclined to agree with one another;
and these people might have taken it into their heads, as has been
done in certain cases, to stop the meeting by putting a bottle of
sulphuretted hydrogen in one corner of the room and taking the
cork out. You know that after a certain time the whole room
would contain sulphuretted hydrogen, which is a very unpleasant
thing to come in contact with. Now how is it that that gas which
was contained in a small bottle could get in a short time over the
�13
whole room unless it was in motion? What we mean by motion
is change of place. Now the gas was in one corner and it is after
wards all over the room. There has therefore been motion some
where, and this motion must have been of considerable rapidity,
because we know that there was the air which filled the room
beforehand to oppose resistance to that motion. We cannot
suppose that the sulphuretted hydrogen gas was the only thing
that was in motion, and that the air was not in motion itself,
because if we had used any other gas we should find that it would
diffuse itself in exactly the same way. Now an argument just like
that applies also to the case of a liquid. Suppose this room were
a large tank entirely filled with water and anybody were to drop a
little iodine into it, after a certain time the whole of the water
would be found to be tinged of a blue colour. Now that drop
may be introduced into any part of the tank you like, either at the
top or bottom, and it will always diffuse itself over the whole
water. There has here again been motion. We cannot suppose
that the drop which was introduced was the only thing that moved
about, because any other substance would equally have moved
about. And the water has moved into the place where the drop
was, because in the place where you put the drop there is not so
much iodine as there was to begin with. Well then it is clear that
in the case of a gas, these particles of which we have shown it to
Consist must be constantly in motion; and we have shown also
that a liquid must consist of parts that are in motion, because it is
able to admit the particles of another body among them.
Now when we have decided that the particles of a gas are
in motion, there are two things that they may do—they may
either hit against one another, or they may not. Now it is esta
blished that they do hit against one another, and that they do
not proceed along straight lines independent of one another.
But 1 cannot at present explain to you the whole of the reasoning
upon which that conclusion is grounded. It is grounded upon
some rather hard mathematics. It was shown by Professor
Clerk Maxwell that a gas cannot be a medium consisting of small
particles moved about in all directions in straight lines, which do
not interfere with one another, but which bound off from the
surfaces which contain this medium. Supposing we had a box
containing a gas of this sort. Well, these particles do not inter
fere with one another, but only rebound when they come against
the sides of the box; then that portion of the gas will behave not
like a gas but like a solid body. The peculiarity of liquids and
gases is that they do not mind being bent and having their shape
�altered. It has been shown by Clerk Maxwell that a medium
whose particles do not interfere with one another would behave
like a solid body and object to be bent. It was a most extra
ordinary conclusion to come to, but it is entirely borne out by the
mathematical formulae. It is certain that if there were a medium
composed of small particles flying about in all directions and not
interfering with one another, then that medium would be to a
certain extent solid, that is, would resist any bending or change
of shape. By that means then it is known that these particles do
run against one another. Now they come apart again. There
were two things of course they might do, they might either go on
in contact, or they might come apart. Now we know that they
come apart for this reason—we have already considered how two
gases in contact will diffuse into one another. If you were to put
a bucket containing carbonic acid (which is very heavy) upon the
floor of this room it would after a certain time diffuse itself over all
the room; you would find carbonic acid gas in every part of the
room. Now Graham found that if you were to cover over the top
of that bucket with a very thin cover made out of graphite, or
blacklead, then the gas would diffuse itself over the room pretty
nearly as fast as before. The graphite acts like a porous body, as
a sponge does to water, and lets the gas get through. The
remarkable thing is that if the graphite is thin the gas will get
through nearly as fast as it will if nothing is put between to stop
it. Graham found out another fact. Suppose that bucket to
contain two very different gases, say a mixture of hydrogen and
carbonic acid gas. Then the hydrogen would come out through
the blacklead very much faster than the carbonic acid gas. Now
it is found by mathematical calculation that if you have two gases,
which are supposed to consist of small particles which are all
banging about, the gas whose particles are lightest will come out
quickest; that a gas which is four times as light will come out
twice as fast; and a gas nine times as light will come out three
times as fast, and so on. Consequently, when you mix two gases
together and then pass them through a thin piece of blacklead,
the lightest gas comes out quickest, and is as it were sifted from
the other. Now suppose we put pure hydrogen into a bucket and
put blacklead on the top, and then see how fast the hydrogen
comes out. If the particles of the hydrogen are different from one
another, if some are heavier, the lighter ones will come out first.
Now let us suppose we have got a vessel which is divided into
two parts by a thin wall of blacklead. We will put hydrogen into
one of these parts and allow it to come through this blacklead
�15
into the other part; then if the hydrogen contains any molecules
or atoms which are lighter than the others, those will come
through first. If we test the hydrogen that has come through, we
shall find that the atoms, as a rule, on one side of this wall are
lighter than the atoms on the other side. How should we find
that out ? Why we should take these two portions of gas, and
we should try whether one of them would pass through another
piece of blacklead quicker than the other; because if it did, it
would consist of lighter particles. Graham found that it did not
pass any quicker. Supposing you put hydrogen into one half of
guch a vessel, and then allow the gas to diffuse itself through the
blacklead, the gas on the two sides would be found to be of
precisely the same qualities. Consequently, there has not been
in this case any sifting of the lighter particles from the heavier
ones; and consequently there could not have been any lighter
particles to sift, because we know that if there were any they
would have come through quicker than the others. Therefore
we are led to the conclusion that in any simple gas, such as
hydrogen or oxygen, all the atoms are, as nearly as possible, of
the same weight. We have no right to conclude that they are
exactly of the same weight, because there is no experiment in the
world that enables us to come to an exact conclusion of that sort.
But we are enabled to conclude that, within the limits of experi
ment, all the atoms af a simple gas are of the same weight. What
Mows from that ? It follows that when they bang against one
another, they must come apart again; for if two of them were to
go on as one, that one would be twice as heavy as the others,
and would consequently be sifted back. It follows therefore that
two particles of a gas which bang against one another must
come apart again, because if they were to cling together they
would form a particle twice as heavy, and so this clinging
would show itself when the gas was passed through the screen
of blacklead.
Now there are certain particles or small masses of matter
which we know to bang against one another according to certain
laws ; such, for example, as billiard balls. Now the way in which
different bodies, after hitting together, come apart again depends
on the constitution of those bodies. The earlier hypothesis about
the constitution of a gas supposed that the particles of them came
apart according to the same law that billiard balls do; but that
hypothesis, although it was found to explain a great number of
phenomena, did not explain them all. And it was Professor
Clerk Maxwell again who found the hypothesis which does explain
�i6
all the rest of the phenomena. He found that particles when they
come together separate as if they repelled one another, or pushed
one another away; and as if they did that much more strongly
when close together than when further apart. You know that
what is called the great law of gravitation asserts that all bodies
pull one another together according to a certain law, and that they
pull one another more when close than when further apart. Now
that law differs from the law which Clerk Maxwell found out as
affecting the repulsion of gaseous particles. The law of attraction
of gravitation is this; that when you halve the distance, you have
to multiply the attraction four times—twice two make four. If
you divide the distance into three, you must multiply the attraction
nine times—three times three are 9. Now in the case of atomic
repulsion you have got to multiply not twice two, or three times
three, but five twos together—which multiplied make 32. If you
halve the distance between two particles you increase the repulsion
32 times. So also five threes multiplied together make 243 ; and
if you divide the distance between two particles by three, then you
increase the repulsion by 243. So you see the repulsion increases
with enormous rapidity as the distance diminishes. That law is
expressed by saying that the repulsion of two gases is inversely as
the fifth power of the distance. But now I must warn you against
supposing that that law is established in the same sense that these
other statements that we have been making are established. That
law is true provided that there is a repulsion between two gaseous
particles, and that it varies as a power of the distance; it is
proved that if there is any law of repulsion, and if the law is that
it varies as some power of the distance, then that power cannot
be any other than the fifth. It has not been shown that the action
between the two particles is not something perhaps more compli
cated than this, but which on the average produces the same
results. But still the statement that the action of gaseous molecules
upon one another can be entirely explained by the assumption of
a law like that, is the newest statement in physics since the law of
gravitation was discovered. You know that there are other actions
of matter which apparently take place through intervening spaces
and which always follow the same law as gravitation, such as the
attraction or repulsion of magnetical or electrical particles : those
follow the same law as gravitation. But here is a law of repulsion
which follows a different law to that of gravitation, and in that lies
the extreme interest of Professor Clerk Maxwell’s investigation.
Now the next thing that I want to give you reasoning for is again
rather a hard thing in respect of the reasoning, but the fact is an
�■exremely simple and beautiful one. It is this. Suppose I have two
vessels, say cylinders, with stoppers which do not fit upon the top of
the vessel, but slide up and down inside and yet fit exactly. These
two vessels are of exactly the same size; one of them contains
hydrogen and the other contains oxygen. They are to be of the
same temperature and pressure, that is to say they will bear
exactly the same weight on the top. Very well, these two vessels
having equal volumes of gas of the same pressure and temperature
will contain just the same number of atoms in each, only the
.atoms of oxygen will be heavier than the atoms of hydrogen.
Now how is it that we arrive at that result? I shall endeavour to
explain the process of reasoning. Boyle discovered a law about
tire dependence of the pressure of a gas upon its volume, which
¡showed that if you squeezed a gas into a smaller space it will press
so much the more as the space has been diminished. If the
space has been diminished one-half, then the pressure is doubled ;
if the space is diminished to one-third, then the pressure is
increased to three times what it was before. This holds for a
Varying volume of the same gas. That same law would tell us
that if we put twice the quantity of gas into the same space, we
should get twice the amount of pressure. Now Dalton made a
new statement of that law, which expresses it in this form, that
when you put more gas into a vessel which already contains gas,
the pressure that you get is the sum of the two pressures which
would be got from the two gases separately. You will see
•directly that that is equivalent to the other law. But the
importance of Dalton’s statement of the law is this, that it enabled
the law to be extended from the case of the same gas to the case
of two different gases. If instead of putting a pint of oxygen into
a vessel already containing a pint, I were to put in a pint of
nitrogen, I should equally get a double pressure. The oxygen
and nitrogen when mixed together would exert the sum of the
pressures upon the vessel that the oxygen and nitrogen would
exert separately. Now the explanation of that pressure is this.
The pressure of the gas upon the sides of the vessel is due to the
impact of these small particles which are constantly flying about
And impinging upon the sides of the vessel. It is first of all
■shown mathematically that the effect of that impinging would be
the same as the pressure of the gas. But the amount of thpressure could be found if we knew how many particles there
were in a given space, and what was the effect of each one
when it impinged on the sides of the vessel. You see directly
why it is that putting twice as many particles, which are
�i8
going at the same rate, into the same vessel, we should get twice
the effect. Although there are just twice as many particles to hit
the sides of the vessel, they are apparently stopped by each
other when they bound off. But the effect of there being more
particles is to make them come back quicker; so that altogether
the number of impacts upon the sides of the vessel is just
doubled when you double the number of particles. Now sup
posing we have got a cubic inch of space, then the amount of
pressure upon the side of that cubic inch depends upon the
number of particles inside the cube, and upon the energy with
which each one of them strikes against the sides of the vessel.
Well now again there is a law which connects together the
pressure of a gas and its temperature. It is found that there is a
certain absolute zero of temperature, and that if you reckon your
temperature from that then the pressure of the gas is directly
proportional to the temperature, that twice the temperature will
give twice the pressure of the same gas, and three times the
temperature will give three times the pressure of the same gas.
Well now we have just got to remember these two rules—the
law of Boyle, as expressed by Dalton, connecting together the
pressure of a gas and its volume, and this law which connects
together the pressure with the absolute temperature. You must
remember that it has been calculated by mathematics that the
pressure upon one side of a vessel of a cubic inch has been got
by multiplying together the number of particles into the energy
with which each of them strikes against the side of the vessel.
Now if we keep that same gas in a vessel and alter its temperature,
then we find that the pressure is proportional to the temperature ;
but since the number of molecules remains the same when we
double the pressure, we must alter that other factor in the
pressure, we must double the energy with which each of the
particles attacks the side of the vessel. That is to say, when we
double the temperature of the gas we double the energy of each
particle; consequently the temperature of the gas is proportional
always to the energy of its particles. That is the case with a
single gas. If we mix two gases, what happens ? They come to
exactly the same temperature. It is calculated also by mathe
matics that the particles of one gas have the same effect as those
of the other; that is, the light particles go faster to make up for
their want of weight. If you mix oxygen and hydrogen, you find
that the particles of hydrogen go four times as fast as the particle^
of oxygen. Now we have here a mathematical statement—that
when two gases are mixed together, the energy of the two particles
�19
is the same; ancl with any one gas considered by itself that
energy is proportional to the temperature. Also when two gasesare mixed together the two temperatures become equal. If you
think over that a little you will see that it proves that whether we
take the same gas or different gases, the energy of the single
particles is always proportional to the temperature of the gas.
Well now what follows ? If I have two vessels containing gas
at the same pressure and the same temperature (suppose that
hydrogen is in one and oxygen in the other) then I know that the
temperature of the hydrogen is the same as the temperature of the
oxygen, and that the pressure of the hydrogen is the same as the
pressure of the oxygen. I also know (because the temperatures
are equal) that the average energy of a particle of the hydrogen is the
same as that of a particle of the oxygen. Now the pressure is
made up by multiplying the energy by the number of particles in
both gases; and as the pressure in both cases is the same, there
fore the number of particles is the same. That is the reasoning;.
I am afraid it will seem rather complicated at first hearing, but it
is this sort of reasoning which establishes the fact that in two
equal volumes of different gases at the same temperature and
pressure, the number of particles is the same.
Now there is an exceedingly interesting conclusion which wasarrived at very early in the theory of gases, and calculated by
Mr. Joule. It is found that the pressure of a gas upon the sides
of a vessel may be represented quite fairly in this way. Let us
divide the particles of gas into three companies or bands. Suppose
I have a cubical vessel in which one of these companies is to go
forward and backward, another right and left, and the other to go
up and down. If we make those three companies of particles to ■
go in their several directions, then the effect upon the sides of the
vessel will not be altered; there will be the same impact and
pressure. It was also, found out that the effect of this pressurewould not be altered if we combined together all the particles
forming one company into one mass, and made them impinge
with the same velocity upon the sides of the vessel. The effect
of the pressure would be just the same. Now we know what the
weight of a gas is, and we know what the pressure is that it
produces, and we want to find the velocity it is moving at on
the average. We can find out at what velocity a certain weight has
got to move in order to produce a certain definite impact. There
fore we have merely got to take the weight of the gas, divide it by
three, and to find how fast that has got to move in order to
produce the pressure, and that will give us the average rate at
�20
which the gas is moving. By that means Mr. Joule calculated
that in air of ordinary temperature and pressure the velocity is
.about 500 metres per second, nearly five miles in sixteen seconds,
or nearly twenty miles a minute—about sixty times the rate of an
ordinary train.
The average velocity of the particles of gas is about i| times
..as great as the velocity of sound. Now you can easily remember
the velocity of sound in air at freezing point—it is 333 metres per
second ; so that about i| times, really 1'432 of that would be the
average velocity of a particle of air. At the ordinary temperature—
•60 degrees Fahrenheit—the velocity would, of course, be greater.
Now then just let us consider how much we have established
so far about these small particles of which we find that the gas
•consists. We have so far been treating mainly of gases. We find
that a gas, such as the air in this room, consists of small particles,
which are separate with spaces between them. They are as a
matter of fact of two different types, oxygen and nitrogen. All
the particles of oxygen contain the same structure, and the rates
•of internal vibration are the same for all these particles. It is
also compounded of particles of nitrogen which have different
■rates of internal vibration. We have shown that these particles
.are moving about constantly. We have shown that they impinge
against and interfere with one another’s motion; and we have
shown that they come apart again. We have shown that in vessels
of the same size containing two different gases of the same pressure
and temperature there is the same number of those two different
sorts of particles. We have shown also that the average velocity
of these particles in the air of this room is about twenty miles
.a minute.
Now there is one other point of very great interest to which I
want to call your attention. The word “ atom,” as you know,
has a Greek origin; it means—that which is not divided. Various
.people have given it the meaning of that which cannot be divided;
but if there is anything which cannot be divided we do not know
it, because we know nothing about possibilities or impossibilities,
■only about what has or has not taken place. Let us then
take the word in the sense in which it can be applied to a
scientific investigation. An atom means something which is not
divided in certain cases that we are considering. Now these atoms
I have been talking about may be called physical atoms, because
they are not divided under those circumstances that are con
sidered in physics. These atoms are not divided under the
ordinary alteration of temperature and pressure of gas, and
�21
variation of heat; they are not in general divided by the
application of electricity to the gas, unless the stream is very
strong. But there is a science which deals with operations by
which these atoms which we have been considering can be
divided into two parts, and in which therefore they are no longer
atoms. That science is chemistry. The chemist therefore will
not consent to call these little particles that we are speaking of
by the name of atoms, because he knows that there are certain
processes to which he can subject them which will divide them
into parts, and then they cease to be things which have
not been divided. Now I will give you an instance of that.
The atoms of oxygen which exist in enormous numbers in
this room consist of two portions, which are of exactly the
same structure. Every molecule, as the chemist would call
it, travelling in this room, is made up of two portions which
are exactly alike in their structure. It is a complicated
structure; but that structure is double. It is like the human
body—one side is like the other side. How do we know
that? We know it in this way. Suppose that I take a vessel
•which is divided into two parts by a division which I can take
Sway. One of these parts is twice as large as the other part, and
will contain twice as much gas. Into that part which is twice as
big as the other I put hydrogen; into the other I put oxygen.
Suppose that one contains a quart and the other a pint; then I
have a quart of hydrogen and a pint of oxygen in this vessel.
Now I will take away the division so that they can permeate one
another, and then if the vessel is strong enough I pass an electric
spark through them. The result will be an explosion inside the
vessel; it won’t break if it is strong enough; but the quart of
hydrogen and the pint of oxygen will be converted into steam;
they will combine together to form steam. If I choose to cool
down that steam until it is just as hot as the two gases were before
I passed the electric spark through them, then I shall find that at
the same pressure there will only be a quart of steam. Now let
us remember what it was that we established about two equal
volumes of different gases at the same temperature and pressure.
First of all, we had a quart of hydrogen with a pint of oxygen.
We know that that quart of hydrogen contains twice as many
hydrogen molecules as the pint of oxygen contains of oxygen
molecules. Let us take particular numbers. Suppose instead
of a quart or a pint we take a smaller quantity, and say
that there are ioo hydrogen and 50 oxygen molecules. Well
after the cooling has taken place, I should find a volume of
�22
•steam which was equal to the volume of hydrogen, that is
I should find ioo steam molecules. Now these steam mole■cules are made up of hydrogen and oxygen molecules.
I
have got therefore ioo things which are all exactly alike, made up
of ioo things and 50 things—100 hydrogen and 50 oxygen,
making 100 steam molecules. Now since the 100 steam molecules
are exactly alike, we have those 50 oxygen molecules distributed
•over the whole of these steam molecules. Therefore unless the
oxygen contains something which is common to the hydrogen algo,
it is clear that each of those 50 molecules of oxygen must have
been divided into two ; because you cannot put 50 horses into 100
stables, so that there shall be exactly the same amount of horse in
each stable; but you can divide 50 pairs of horses among 100
stables. There we have the supposition that there is nothing
common to the oxygen and hydrogen, that there is no structure
that belongs to each of them. Now that supposition is made by
.a great majority of chemists. Sir Benjamin Brodie, however, has
made a supposition that there is a structure in hydrogen which is
also common to certain other elements. He has himself, for
particular reasons, restricted that supposition to the belief that
hydrogen is contained as a whole in many of the other elements.
Let us make that further supposition and it will not alter our case
at all. We have then one hundred hydrogen and fifty oxygen
molecules, but there is something common to the two. Well this
something we will call X. Of this we have to make one hundred
equal portions. Now that cannot be the case unless that structure
occurred twice as often in each molecule of oxygen as in each
molecule of hydrogen. Consequently, whether the oxygen mole
cule contains something common to hydrogen or not, it is equally
true that the oxygen molecule must contain the same thing repeated
twice over; it must be divisible into two parts which are exactly
.alike.
Similar reasoning applies to a great number of other elements ;
to all those which are said to have an even number of atomicities.
But -with regard to those which are said to have an odd number,
although many of these also are supposed to be double, yet the
•evidence in favour of that supposition is of a different kind; and.
we must regard the supposition as still a theory and not yet a
■demonstrated fact.
Now I have spoken so far only of gases. I must for one or
two moments refer to some calculations of Sir Wm. Thompson,
which are of exceeding interest as showing us what is the proximity
of the molecules in liquids and in solids. By four different modes
�23
of argument derived from different parts of science, and pointing
mainly to the same conclusion, he has shown that the distance
between two molecules in a drop of water is such that there are
between five hundred millions and five thousand millions of them
in an inch. He expresses that result in this way—that if you
were to magnify a drop of water to the size of the earth, then the
coarseness of the graining of it would be something between that
of cricket balls and small shot. Or we may express it in this
rather striking way. You know that the best microscopes can
be made to magnify from 6,000 to 8,000 times. A microscope
which would magnify that result as much again would show the
molecular structure of water.
There is another scientific theory analogous to this one which
leads us to hope that some time we shall know more about these
molecules. You know that since the time that we have known
all about the motions of the solar system, people have speculated
about the origin of it; and a theory started by Laplace and worked
out by other people has, like the theory of luminiferous ether,
been taken out of the rank of hypothesis into that of fact. We
know the rough outlines of the history of the solar system, and
there are hopes that when we know the structure and properties
of a molecule, what its internal motions are and what are the parts
and shape of it, somebody may be able to form a theory as to
how that was built up and what it was built out of. It is obvious
that until we know the shape and structure of it, nobody will be
able to form such a theory. But we can look forward to the time
when the structure and motions in the inside of a molecule will be
so well known that some future Kant or Laplace will be able to
form a hypothesis about the history and formation of matter.
In acknowledging a vote of thanks, Professor Clifford took the
opportunity of recommending his auditors to read Professor Clerk
Maxwell’s book on the Theory of Heat, at the end of which would
be found a short exposition of the molecular theory of matter.
Note.—The mathematical development of this subject is due to
Clausius and Maxwell. References to the chiefpapers will be found
at the beginning of Maxwell's memoir “ On the Dynamical Theory
of Gascsf Phil. Trans.1867.
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A collection of digitised nineteenth-century pamphlets from Conway Hall Library & Archives. This includes the Conway Tracts, Moncure Conway's personal pamphlet library; the Morris Tracts, donated to the library by Miss Morris in 1904; the National Secular Society's pamphlet library and others. The Conway Tracts were bound with additional ephemera, such as lecture programmes and handwritten notes.<br /><br />Please note that these digitised pamphlets have been edited to maximise the accuracy of the OCR, ensuring they are text searchable. If you would like to view un-edited, full-colour versions of any of our pamphlets, please email librarian@conwayhall.org.uk.<br /><br /><span><img src="http://www.heritagefund.org.uk/sites/default/files/media/attachments/TNLHLF_Colour_Logo_English_RGB_0_0.jpg" width="238" height="91" alt="TNLHLF_Colour_Logo_English_RGB_0_0.jpg" /></span>
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Atoms: a lecture by Professor Clifford ... delivered in the Hulme Town Hall, Manchester, November 20th, 1872; and before the Sunday Lecture Society, in London, on the 7th January 1872
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Clifford, William Kingdon [1845-1879]
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Place of publication: Manchester; London
Collation: [54]-74 p. ; 18 cm.
Series title: Science lectures for the people; fourth series
Series number: No. 4
Notes: Reported by Henry Pitman; Mr Davies Benson in the chair. Publisher's series list on unnumbered back page. From the library of Dr Moncure Conway and part of the NSS pamphlet collection.
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John Heywood; F. Pitman
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[1872]
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N089
G5363
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Physics
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Atoms
Conway Tracts
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