It grieves me much to think that I may have been a cause of disturbance
in your Christmas arrangements[1], for nothing is more satisfactory
to my mind than to perform what I undertake; but such things are not
always left in our own power, and we must submit to circumstances as
they are appointed. I will to-day do my best, and will ask you to
bear with me if I am unable to give more than a few words; and as a
substitute, I will endeavour to make the _illustrations_ of the sense I
try to express as full as possible; and if we find by the end of this
lecture that we may be justified in continuing them, thinking that next
week our power shall be greater,--why, then, with submission to you,
we will take such course as you may think fit,--either to go on, or
discontinue them; and although I now feel much weakened by the pressure
of illness (a mere cold) upon me, both in facility of expression and
clearness of thought, I shall here claim, as I always have done on
these occasions, the right of addressing myself to the younger members
of the audience. And for this purpose, therefore, unfitted as it may
seem for an elderly infirm man to do so, I will return to second
childhood and become, as it were, young again amongst the young.
Let us now consider, for a little while, how wonderfully we stand upon
this world. Here it is we are born, bred, and live, and yet we view
these things with an almost entire absence of wonder to ourselves
respecting the way in which all this happens. So small, indeed, is our
wonder, that we are never taken by surprise; and I do think that, to a
young person of ten, fifteen, or twenty years of age, perhaps the first
sight of a cataract or a mountain would occasion him more surprise than
he had ever felt concerning the means of his own existence,--how he
came here; how he lives; by what means he stands upright; and through
what means he moves about from place to place. Hence, we come into this
world, we live, and depart from it, without our thoughts being called
specifically to consider how all this takes place; and were it not
for the exertions of some few inquiring minds, who have looked _into_
these things and ascertained the very beautiful laws and conditions by
which we _do_ live and stand upon the earth, we should hardly be aware
that there was anything wonderful in it. These inquiries, which have
occupied philosophers from the earliest days, when they first began to
find out the laws by which we grow, and exist, and enjoy ourselves,
up to the present time, have shewn us that all this was effected in
consequence of the existence of certain _forces_, or _abilities_ to
do things, or _powers_, that are so common that nothing can be more
so; for nothing is commoner than the wonderful powers by which we are
enabled to stand upright--they are essential to our existence every
moment.
It is my purpose to-day to make you acquainted with some of these
powers; not the vital ones, but some of the more elementary, and,
what we call, _physical_ powers: and, in the outset, what can I do to
bring to your minds a notion of neither more nor less than that which
I mean by the word _power_, or _force_? Suppose I take this sheet of
paper, and place it upright on one edge, resting against a support
before me (as the roughest possible illustration of something to be
disturbed), and suppose I then pull this piece of string which is
attached to it. I pull the paper over. I have therefore brought into
use a _power_ of doing so--the _power_ of my hand carried on through
this string in a way which is very remarkable when we come to analyse
it; and it is by means of these powers conjointly (for there are
several powers here employed) that I pull the paper over. Again, if I
give it a push upon the other side, I bring into play a _power_, but
a very different exertion of power from the former; or, if I take now
this bit of shell-lac [a stick of shell-lac about 12 inches long and
1½ in diameter] and rub it with flannel, and hold it an inch or so in
front of the upper part of this upright sheet, the paper is immediately
moved towards the shell-lac, and by now drawing the latter away, the
paper falls over without having been touched by anything. You see--in
the first illustration I produced an effect than which nothing could
be commoner--I pull it over now, not by means of that string or the
pull of my hand, but by some action in the shell-lac. The shell-lac,
therefore, has a _power_ wherewith it acts upon the sheet of paper; and
as an illustration of the exercise of another kind of power, I might
use gunpowder with which to throw it over.
Now, I want you to endeavour to comprehend that when I am speaking of
a _power_ or _force_, I am speaking of that which I used just now to
pull over this piece of paper. I will not embarrass you at present with
the _name_ of that power, but it is clear there was a _something_ in
the shell-lac which acted by attraction, and pulled the paper over;
this, then, is one of those things which we call _power_, or _force_;
and you will now be able to recognise it as such in whatever form I
shew it to you. We are not to suppose that there are so very many
different powers; on the contrary, it is wonderful to think how few are
the powers by which all the phenomena of nature are governed. There
is an illustration of another kind of power in that lamp; _there_ is
a power of heat--a power of doing something, but not the same power
as that which pulled the paper over: and so, by degrees, we find that
there are certain other powers (not many) in the various bodies around
us. And thus, beginning with the simplest experiments of pushing and
pulling, I shall gradually proceed to distinguish these powers one from
the other, and compare the way in which they combine together. This
world upon which we stand (and we have not much need to travel out of
the world for illustrations of our subject; but the mind of man is not
confined like the matter of his body, and thus he may and does travel
outwards; for wherever his sight can pierce, there his observations
can penetrate) is pretty nearly a round globe, having its surface
disposed in a manner of which this terrestrial globe by my side is a
rough model; so much is land and so much is water, and by looking at
it here we see in a sort of map or picture how the world is formed upon
its surface. Then, when we come to examine further, I refer you to
this sectional diagram of the geological strata of the earth, in which
there is a more elaborate view of what is beneath the surface of our
globe. And when we come to dig into or examine it (as man does for his
own instruction and advantage, in a variety of ways), we see that it
is made up of different kinds of matter, subject to a very few powers,
and all disposed in this strange and wonderful way, which gives to man
a history--and such a history--as to what there is in those veins,
in those rocks, the ores, the water springs, the atmosphere around,
and all varieties of material substances, held together by means of
_forces_ in one great mass, 8,000 miles in diameter, that the mind is
overwhelmed in contemplation of the wonderful history related by these
strata (some of which are fine and thin like sheets of paper),--all
formed in succession by the forces of which I have spoken.
I now shall try to help your attention to what I may say by directing,
to-day, our thoughts to one kind of power. You see what I mean by the
term _matter_--any of these things that I can lay hold of with the
hand, or in a bag (for I may take hold of the air by enclosing it in
a bag)--they are all portions of matter with which we have to deal at
present, generally or particularly, as I may require to illustrate
my subject. Here is the sort of matter which we call _water_,--it
is _there_ ice [pointing to a block of ice upon the table], _there_
water [pointing to the water boiling in a flask], _here_ vapour--you
see it issuing out from the top [of the flask]. Do not suppose that
that ice and that water are two entirely different things, or that
the steam rising in bubbles and ascending in vapour _there_ is
absolutely different from the fluid water. It may be different in
some particulars, having reference to the _amounts_ of power which
it contains; but it is the same, nevertheless, as the great ocean
of water around our globe, and I employ it here for the sake of
illustration, because if we look into it we shall find that it supplies
us with examples of all the powers to which I shall have to refer.
For instance, here is water--it is heavy; but let us examine it with
regard to the _amount_ of its heaviness, or its gravity. I have before
me a little glass vessel and scales [nearly equipoised scales, one of
which contained a half-pint glass vessel], and the glass vessel is at
present the lighter of the two; but if I now take some water and pour
it in, you see that that side of the scales immediately goes down; that
shews you (using common language, which I will not suppose for the
present you have hitherto applied very strictly) that it is _heavy_:
and if I put this additional weight into the opposite scale, I should
not wonder if this vessel would hold water enough to weigh _it_ down.
[The Lecturer poured more water into the jar, which again went down.]
Why do I hold the bottle _above_ the vessel to pour the water into it?
You will say, because experience has taught me that it is necessary.
I do it for a better reason--because it is a law of nature that the
water should fall towards the earth, and therefore the very means
which I use to cause the water to enter the vessel are those which
will carry the whole body of water down. That power is what we call
_gravity_, and you see _there_ [pointing to the scales] a good deal of
water gravitating towards the earth. Now _here_ [exhibiting a small
piece of platinum[2]] is another thing which gravitates towards the
earth as much as the whole of that water. See what a little there is
of it--_that_ little thing is heavier than so much water [placing the
metal in opposite scales to the water]. What a wonderful thing it is to
see that it requires so much water as _that_ [a half-pint vessel full]
to fall towards the earth, compared with the little mass of substance
I have _here_! And again, if I take this metal [a bar of aluminium[3]
about eight times the bulk of the platinum], we find the water will
balance that as well as it did the platinum; so that we get, even in
the very outset, an example of what we want to understand by the words
_forces_ or _powers_.
I have spoken of water, and first of all of its property of falling
downwards. You know very well how the oceans surround the globe--how
they fall round the surface, giving roundness to it, clothing it like
a garment; but, besides that, there are other properties of water.
_Here_, for instance, is some quick-lime, and if I add some water to
it, you will find another power or property in the water.[4] It is
now very hot, it is steaming up, and I could perhaps light phosphorus
or a lucifer match with it. Now, that could not happen without a
_force_ in the water to produce the result; but that force is entirely
distinct from its power of falling to the earth. Again, here is another
substance [some anhydrous sulphate of copper[5]] which will illustrate
another kind of power. [The Lecturer here poured some water over the
white sulphate of copper, which immediately became blue, evolving
considerable heat at the same time.] Here is the same water, with a
substance which heats nearly as much as the lime does; but see how
differently. So great indeed is this heat in the case of lime, that it
is sufficient sometimes (as you see here) to set wood on fire; and this
explains what we have sometimes heard, of barges laden with quick-lime
taking fire in the middle of the river, in consequence of this power
of heat brought into play by a leakage of the water into the barge.
You see how strangely different subjects for our consideration arise,
when we come to think over these various matters,--the power of heat
evolved by acting upon lime with water, and the power which water has
of turning this salt of copper from white to blue.
I want you now to understand the nature of the most simple exertion
of this power of matter called _weight_, or _gravity_. Bodies are
heavy--you saw that in the case of water when I placed it in the
balance. Here I have what we call a _weight_ [an iron half cwt.]--a
thing called a weight, because in it the exercise of that power of
pressing downwards is especially used for the purposes of weighing;
and I have also one of these little inflated india-rubber bladders,
which are very beautiful although very common (most beautiful things
are common), and I am going to put the weight upon it, to give you
a sort of illustration of the downward pressure of the iron, and of
the power which the air possesses of resisting that pressure. It may
burst, but we must try to avoid that [During the last few observations
the Lecturer had succeeded in placing the half cwt. in a state of
quiescence upon the inflated india-rubber ball, which consequently
assumed a shape very much resembling a flat cheese with round edges.]
There you see a bubble of air bearing half a hundred weight, and you
must conceive for yourselves what a wonderful _power_ there must be to
pull this weight downwards, to sink it thus in the ball of air.
[Illustration: Fig. 1.]
Let me now give you another illustration of this power. You know what
a pendulum is. I have one here (fig. 1), and if I set it swinging, it
will continue to swing to and fro. Now, I wonder whether you can tell
me why that body oscillates to and fro--that pendulum bob as it is
sometimes called. Observe, if I hold the straight stick horizontally,
as high as the position of the balls at the two ends of its journey
you see that the ball is in a higher position at the two extremities
than it is when in the middle. Starting from one end of the stick, the
ball falls towards the centre; and then rising again to the opposite
end, it constantly tries to fall to the lowest point, swinging and
vibrating most beautifully, and with wonderful properties in other
respects--the time of its vibration, and so on--but concerning which we
will not now trouble ourselves.
If a gold leaf, or piece of thread, or any other substance, were hung
where this ball is, it would swing to and fro in the same manner, and
in the same time too. Do not be startled at this statement: I repeat,
in the same manner and in the same time; and you will see by and by
how this is. Now, that power which caused the water to descend in the
balance--which made the iron weight press upon and flatten the bubble
of air--which caused the swinging to and fro of the pendulum,--that
power is entirely due to the attraction which there is between the
falling body and the earth. Let us be slow and careful to comprehend
this. It is not that the earth has any _particular_ attraction towards
bodies which fall to it, but, that _all_ these bodies possess an
attraction, every one towards the other. It is not that the earth has
any special power which these balls themselves have not; for just as
much power as the earth has to attract these two balls [dropping two
ivory balls], just so much power have they in proportion to their bulks
to draw themselves one to the other; and the only reason why they fall
so quickly to the earth is owing to its greater size. Now, if I were to
place these two balls near together, I should not be able, by the most
delicate arrangement of apparatus, to make you, or myself, sensible
that these balls did attract one another: and yet we know that such is
the case, because, if instead of taking a small ivory ball, we take
a mountain, and put a ball like this near it, we find that, owing to
the vast size of the mountain, as compared with the billiard ball, the
latter is drawn slightly towards it; shewing clearly that an attraction
_does_ exist, just as it did between the shell-lac which I rubbed and
the piece of paper which was overturned by it.
Now, it is not very easy to make these things quite clear at the
outset, and I must take care not to leave anything unexplained as I
proceed; and, therefore, I must make you clearly understand that all
bodies are attracted to the earth, or, to use a more learned term,
_gravitate_. You will not mind my using this word; for when I say
that this penny-piece _gravitates_, I mean nothing more nor less than
that it falls towards the earth, and if not intercepted, it would go
on falling, falling, until it arrived at what we call the _centre of
gravity_ of the earth, which I will explain to you by and by.
[Illustration: Fig. 2.]
I want you to understand that this property of gravitation is never
lost, that every substance possesses it, that there is never any change
in the quantity of it; and, first of all, I will take as illustration
a piece of marble. Now this marble has weight--as you will see if I
put it in these scales; it weighs the balance down, and if I take
it off, the balance goes back again and resumes its equilibrium. I
can decompose this marble and change it, in the same manner as I can
change ice into water and water into steam. I can convert a part of
it into _its own_ steam easily, and shew you that this steam from
the marble has the property of remaining in the same place at common
temperatures, which _water_-steam has not. If I add a little liquid
to the marble, and decompose it[6], I get that which you see--[the
Lecturer here put several lumps of marble into a glass jar, and poured
water and then acid over them; the carbonic acid immediately commenced
to escape with considerable effervescence]--the appearance of boiling,
which is only the separation of one part of the marble from another.
Now this [marble] steam, and that [water] steam, and all other steams
_gravitate_, just like any other substance does--they all are attracted
the one towards the other, and all fall towards the earth; and what
I want you to see is, that _this_ steam gravitates. I have here (fig.
2) a large vessel placed upon a balance, and the moment I pour this
steam into it, you see that the steam gravitates. Just watch the index,
and see whether it tilts over or not. [The Lecturer here poured the
carbonic acid out of the glass in which it was being generated into the
vessel suspended on the balance, when the gravitation of the carbonic
acid was at once apparent.] Look how it is going down. How pretty
that is! I poured nothing in but the invisible steam, or vapour, or
gas which came from the marble, but you see that part of the marble,
although it has taken the shape of air, still gravitates as it did
before. Now, will it weigh down that bit of paper? [Placing a piece of
paper in the opposite scale.] Yes, more than that; it nearly weighs
down this bit of paper. [Placing another piece of paper in.] And
thus you see that _other_ forms of matter besides solids and liquids
tend to fall to the earth; and, therefore, you will accept from me
the fact--that _all_ things gravitate, whatever may be their form or
condition. Now _here_ is another chemical test which is very readily
applied. [Some of the carbonic acid was poured from one vessel into
another, and its presence in the latter shewn by introducing into it a
lighted taper, which was immediately extinguished.] You see from this
result also that it gravitates. All these experiments shew you that,
tried by the balance, tried by pouring like water from one vessel to
another, this steam, or vapour, or gas, is, like all other things,
attracted to the earth.
[Illustration: Fig. 3. and Fig. 4.]
There is another point I want in the next place to draw your attention
to. I have here a quantity of shot; each of these falls separately,
and each has its own gravitating power, as you perceive when I let
them fall loosely on a sheet of paper. If I put them into a bottle, I
collect them together as one mass; and philosophers have discovered
that there is a certain point in the middle of the whole collection
of shots that may be considered as the _one point_ in which all their
gravitating power is centred, and that point they call the _centre of
gravity_: it is not at all a bad name, and rather a short one--the
centre of gravity. Now suppose I take a sheet of pasteboard, or any
other thing easily dealt with, and run a bradawl through it at one
corner A (fig. 3), and Mr. Anderson hold that up in his hand before
us, and I then take a piece of thread and an ivory ball, and hang that
upon the awl--then the centre of gravity of both the pasteboard and the
ball and string are as near as they can get to the centre of the earth;
that is to say, the whole of the attracting power of the earth is, as
it were, centred in a single point of the cardboard--and this point is
exactly below the point of suspension. All I have to do, therefore, is
to draw a line, A B, corresponding with the string, and we shall find
that the centre of gravity is somewhere in that line. But where? To
find that out, all we have to do is to take another place for the awl
(fig. 4), hang the plumb-line, and make the same experiment, and there
[at the point C] is the centre of gravity--there where the two lines
which I have traced cross each other; and if I take that pasteboard,
and make a hole with the bradawl through it at that point, you will see
that it will be supported in any position in which it may be placed.
Now, knowing that, what do I do when I try to stand upon one leg? Do
you not see that I push myself over to the left side, and quietly take
up the right leg, and thus bring some central point in my body over
this left leg. What is that point which I throw over? You will know at
once that it is the _centre of gravity_--that point in me where the
whole gravitating force of my body is centred, and which I thus bring
in a line over my foot.
[Illustration: Fig. 5. and Fig. 6.]
Here is a toy I happened to see the other day, which will, I think,
serve to illustrate our subject very well. That toy _ought_ to lie
something in this manner (fig. 5); and would do so if it were uniform
in substance. But you see it does not; it will get up again. And now
philosophy comes to our aid; and I am perfectly sure, without looking
inside the figure, that there is some arrangement by which the centre
of gravity is at the lowest point when the image is standing upright;
and we may be certain, when I am tilting it over (see fig. 6), that
I am lifting up the centre of gravity (_a_), and raising it from the
earth. All this is effected by putting a piece of lead inside the lower
part of the image, and making the base of large curvature; and there
you have the whole secret. But what will happen if I try to make the
figure stand upon a sharp point? You observe, I must get that point
_exactly_ under the centre of gravity, or it will fall over thus
[endeavouring unsuccessfully to balance it]; and this you see is a
difficult matter--I cannot make it stand steadily. But if I embarrass
this poor old lady with a world of trouble, and hang this wire with
bullets at each end about her neck, it is very evident that, owing
to there being those balls of lead hanging down on either side, in
addition to the lead inside, I have lowered the centre of gravity, and
now she will stand upon this point (fig. 7); and what is more, she
proves the truth of our philosophy by standing sideways.
[Illustration: Fig. 7.]
[Illustration: Fig. 8.]
I remember an experiment which puzzled me very much when a boy. I read
it in a conjuring book, and this was how the problem was put to us:
“How,” as the book said, “how to hang a pail of water, by means of a
stick, upon the side of a table” (fig. 8). Now, I have here a table, a
piece of stick, and a pail, and the proposition is, how can that pail
be hung to the edge of this table? It is to be done; and can you at all
anticipate what arrangement I shall make to enable me to succeed? Why,
this. I take a stick, and put it in the pail between the bottom and the
horizontal piece of wood, and thus give it a stiff handle--and there it
is; and what is more, the more water I put into the pail the better
it will hang. It is very true that before I quite succeeded I had the
misfortune to push the bottoms of several pails out; but here it is
hanging firmly (fig. 9), and you now see how you can hang up the pail
in the way which the conjuring books require.
[Illustration: Fig. 9.]
Again, if you are really so inclined (and I do hope all of you are),
you will find a great deal of philosophy in this [holding up a cork
and a pointed thin stick about a foot long]. Do not refer to your
toy-books, and say you have seen that before. Answer me rather, if I
ask you have you _understood_ it before? It is an experiment which
appeared very wonderful to me when I was a boy; I used to take a piece
of cork (and I remember, I thought at first that it was very important
that it should be cut out in the shape of a man; but by degrees I got
rid of that idea), and the problem was to balance it on the point of a
stick. Now, you will see I have only to place two sharp-pointed sticks
one on each side, and give it wings, thus, and you will find this
beautiful condition fulfilled.
[Illustration: Fig. 10.]
We come now to another point:--All bodies, whether heavy or light, fall
to the earth by this force which we call gravity. By observation,
moreover, we see that bodies do not occupy the same time in falling. I
think you will be able to see that this piece of paper and that ivory
ball fall with different velocities to the table [dropping them]; and
if, again, I take a feather and an ivory ball, and let them fall, you
see they reach the table or earth at different times--that is to say,
the ball falls faster than the feather. Now, that should not be so,
for all bodies do fall equally fast to the earth. There are one or
two beautiful points included in that statement. First of all, it is
manifest that an ounce, or a pound, or a ton, or a thousand tons, all
fall equally fast, no one faster than another: here are two balls of
lead, a very light one and a very heavy one, and you perceive they both
fall to the earth in the same time. Now, if I were to put into a little
bag a number of these balls sufficient to make up a bulk equal to the
large one, they would also fall in the same time; for if an avalanche
fall from the mountains, the rocks, snow and ice, together falling
towards the earth, fall with the same velocity, whatever be their size.
I cannot take a better illustration of this than that of gold leaf,
because it brings before us the reason of this apparent difference in
the time of the fall. Here is a piece of gold-leaf. Now, if I take a
lump of gold and this gold-leaf, and let them fall through the air
together, you see that the lump of gold--the sovereign, or coin--will
fall much faster than the gold leaf. But why? They are both gold,
whether sovereign or gold-leaf. Why should they not fall to the earth
with the same quickness? _They would do so_, but that the air around
our globe interferes very much where we have the piece of gold so
extended and enlarged as to offer much obstruction on falling through
it. I will, however, shew you that gold-leaf _does_ fall as fast
when the resistance of the air is excluded--for if I take a piece of
gold-leaf and hang it in the centre of a bottle, so that the gold,
and the bottle, and the air within shall all have an equal chance of
falling, then the gold-leaf will fall as fast as anything else. And
if I suspend the bottle containing the gold-leaf to a string, and set
it oscillating like a pendulum, I may make it vibrate as hard as I
please, and the gold-leaf will not be disturbed, but will swing as
steadily as a piece of iron would do; and I might even swing it round
my head with any degree of force, and it would remain undisturbed. Or
I can try another kind of experiment:--if I raise the gold-leaf in
this way [pulling the bottle up to the ceiling of the theatre by means
of a cord and pulley, and then suddenly letting it fall to within a
few inches of the lecture-table], and allow it then to fall from the
ceiling downwards (I will put something beneath to catch it, supposing
I should be _maladroit_), you will perceive that the gold-leaf is not
in the least disturbed. The resistance of the air having been avoided,
the glass bottle and gold-leaf all fall exactly in the same time.
Here is another illustration,--I have hung a piece of gold-leaf in the
upper part of this long glass vessel, and I have the means, by a little
arrangement at the top, of letting the gold-leaf loose. Before we let
it loose we will remove the air by means of an air pump, and while that
is being done, let me shew you another experiment of the same kind.
Take a penny-piece, or a half-crown, and a round piece of paper a
trifle smaller in diameter than the coin, and try them, side by side,
to see whether they fall at the same time [dropping them]. You see they
do not--the penny-piece goes down first. But, now place this paper flat
on the top of the coin, so that it shall not meet with any resistance
from the air, and upon _then_ dropping them you see they _do_ both fall
in the same time [exhibiting the effect]. I dare say, if I were to put
this piece of gold-leaf, instead of the paper, on the coin, it would
do as well. It is very difficult to lay the gold-leaf so flat that the
air shall not get under it and lift it up in falling, and I am rather
doubtful as to the success of this, because the gold-leaf is puckery;
but will risk the experiment. There they go together! [letting them
fall] and you see at once that they both reach the table at the same
moment.
We have now pumped the air out of the vessel, and you will perceive
that the gold-leaf will fall as quickly in this vacuum as the coin does
in the air. I am now going to let it loose, and you must watch to see
how rapidly it falls. There! [letting the gold loose] there it is,
falling as gold should fall.
I am sorry to see our time for parting is drawing so near. As we
proceed, I intend to write upon the board behind me certain words, so
as to recall to your minds what we have already examined--and I put the
word FORCES as a heading; and I will then add, beneath, the names of
the special forces according to the order in which we consider them:
and although I fear that I have not sufficiently pointed out to you the
more important circumstances connected with this force of GRAVITATION,
especially the law which governs its attraction (for which, I think, I
must take up a little time at our next meeting), still I will put that
word on the board, and hope you will now remember that we have in some
degree considered the _force of gravitation_--that force which causes
all bodies to attract each other when they are at sensible distances
apart, and tends to draw them together.