from first to last, we can hardly fail to be convinced that
diamagnetic bodies operated on by magnetic forces possess a polarity
"the same in kind as, but the reverse in direction of, that acquired
by magnetic bodies." But if this be the case, how are we to conceive
the _physical mechanism_ of this polarity? According to Coulomb's and
Poisson's theory, the act of magnetisation consists in the
decomposition of a neutral magnetic fluid; the north pole of a magnet,
for example, possesses an attraction for the south fluid of a piece of
soft iron submitted to its influence, draws the said fluid towards it,
and with it the material particles with which the fluid is associated.
To account for diamagnetic phenomena this theory seems to fail
altogether; according to it, indeed, the oft-used phrase, "a north
pole exciting a north pole, and a south pole a south pole," involves a
contradiction. For if the north fluid be supposed to be _attracted_
towards the influencing north pole, it is absurd to suppose that its
presence there could produce _repulsion_. The theory of Ampère is
equally at a loss to explain diamagnetic action; for if we suppose the
particles of bismuth surrounded by molecular currents, then, according
to all that is known of electrodynamic laws, these currents would set
themselves parallel to, and in the same direction as, those of the
magnet, and hence attraction, and not repulsion, would be the result.
The fact, however, of this not being the case, proves that these
molecular currents are not the mechanism by which diamagnetic
induction is effected. The consciousness of this, I doubt not, drove
M. Weber to the assumption that the phenomena of diamagnetism are
produced by molecular currents, not _directed_, but actually _excited_ in
the bismuth by the magnet. Such induced currents would, according to
known laws, have a direction opposed to those of the inducing magnet,
and hence would produce the phenomena of repulsion. To carry out the
assumption here made, M. Weber is obliged to suppose that the
molecules of diamagnetic bodies are surrounded by channels, in which
the induced molecular currents, once excited, continue to flow without
resistance.' [Footnote: In assuming these non-resisting channels M.
Weber, it must be admitted, did not go beyond the assumptions of
Ampère.]--Diamagnetism and Magne-crystallic Action, p. 136-7.
********************
XVI. ON FORCE.
[Footnote: A discourse delivered in the Royal Institution, June 6,
1862.]
A SPHERE of lead was suspended at a height of 16 feet above the
theatre floor of the Royal Institution. It was liberated, and fell by
gravity. That weight required a second to fall to the floor from that
elevation; and the instant before it touched the floor, it had a
velocity of 32 feet a second. That is to say, if at that instant the
earth were annihilated, and its attraction annulled, the weight would
proceed through space at the uniform velocity of 32 feet a second.
If instead of being pulled downward by gravity, the weight be cast
upward in opposition to gravity, then, to reach a height of 16 feet it
must start with a velocity of 32 feet a second. This velocity
imparted to the weight by the human hand, or by any other mechanical
means, would carry it to the precise height from which we saw it fall.
Now the lifting of the weight may be regarded as so much mechanical
work performed. By means of a ladder placed against the wall, the
weight might be carried up to a height of 16 feet; or it might be
drawn up to this height by means of a string and pulley, or it might
be suddenly jerked up to a height of 16 feet. The amount of work done
in all these cases, as far as the raising of the weight is concerned,
would be absolutely the same. The work done at one and the same
place, and neglecting the small change of gravity with the height,
depends solely upon two things; on the quantity of matter lifted, and
on the height to which it is lifted. If we call the quantity or mass
of matter m, and the height through which it is lifted h, then the
product of m into h, or mh, expresses, or is proportional to, the
amount of work done.
Supposing, instead of imparting a velocity of 32 feet a second we
impart at starting twice this velocity. To what height will the
weight rise? You might be disposed to answer, 'To twice the height;'
but this would be quite incorrect. Instead of twice 16, or 32 feet,
it would reach a height of four times 16, or 64 feet. So also, if we
treble the starting velocity, the weight would reach nine times the
height; if we quadruple the speed at starting, we attain sixteen times
the height. Thus, with a four-fold velocity of 128 feet a second at
starting, the weight would attain an elevation of 256 feet. With a
seven-fold velocity at starting, the weight would rise to 49 times the
height, or to an elevation of 784 feet.
Now the work done--or, as it is sometimes called, the _mechanical
effect_--other things being constant, is, as before explained,
proportional to the height, and as a double velocity gives four times
the height, a treble velocity nine times the height, and so on, it is
perfectly plain that the mechanical effect increases as the square of
the velocity. If the mass of the body be represented by the letter m,
and its velocity by v, the mechanical effect would be proportional to
or represented by m v2. In the case considered, I have supposed the
weight to be cast upward, being opposed in its flight by the
resistance of gravity; but the same holds true if the projectile be
sent into water, mud, earth, timber, or other resisting material. If,
for example, we double the velocity of a cannon-ball, we quadruple its
mechanical effect. Hence the importance of augmenting the velocity of
a projectile, and hence the philosophy of Sir William Armstrong in
using a large charge of powder in his recent striking experiments.
The measure then of mechanical effect is the mass of the body
multiplied by the square of its velocity.
Now in firing a ball against a target the projectile, after collision,
is often found hot. Mr. Fairbairn informs me that in the experiments
at Shoeburyness it is a common thing to see a flash, even in broad
daylight, when the ball strikes the target. And if our lead weight be
examined after it has fallen from a height it is also found heated.
Now here experiment and reasoning lead us to the remarkable law that,
like the mechanical effect, the amount of heat generated is
proportional to the product of the mass into the square of the
velocity. Double your mass, other things being equal, and you double
your amount of heat; double your velocity, other things remaining
equal, and you quadruple your amount of heat. Here then we have
common mechanical motion destroyed and heat produced. When a violin
bow is drawn across a string, the sound produced is due to motion
imparted to the air, and to produce that motion muscular force has
been expended. We may here correctly say, that the mechanical force
of the arm is converted into music. In a similar way we say that the
arrested motion of our descending weight, or of the cannon-ball, is
converted into heat. The mode of motion changes, but motion still
continues; the motion of the mass is converted into a motion of the
atoms of the mass; and these small motions, communicated to the
nerves, produce the sensation we call heat.
We know the amount of heat which a given amount of mechanical force
can develope. Our lead ball, for example, in falling to the earth
generated a quantity of heat sufficient to raise its own temperature
three-fifths of a Fahrenheit degree. It reached the earth with a
velocity of 32 feet a second, and forty times this velocity would be
small for a rifle bullet; multiplying 0.6 by the square of 40, we find
that the amount of heat developed by collision with the target would,
if wholly concentrated in the lead, raise its temperature 960 degrees.
This would be more than sufficient to fuse the lead. In reality,
however, the heat developed is divided between the lead and the body
against which it strikes; nevertheless, it would be worth while to pay
attention to this point, and to ascertain whether rifle bullets do
not, under some circumstances, show signs of fusion. [Footnote: Eight
years subsequently this surmise was proved correct. In the
Franco-German War signs of fusion were observed in the case of bullets
impinging on bones.]
From the motion of sensible masses, by gravity and other means, we now
pass to the motion of atoms towards each other by chemical affinity. A
collodion balloon filled with a mixture of chlorine and hydrogen being
hung in the focus of a parabolic mirror, in the focus of a second
mirror 20 feet distant a strong electric light was suddenly generated;
the instant the concentrated light fell upon the balloon, the gases
within it exploded, hydrochloric acid being the result. Here the atoms
virtually fell together, the amount of heat produced showing the
enormous force of the collision. The burning of charcoal in oxygen is
an old experiment, but it has now a significance beyond what it used
to have; we now regard the act of combination on the part of the atoms
of oxygen and coal as we regard the clashing of a falling weight
against the earth. The heat produced in both cases is referable to a
common cause. A diamond, which burns in oxygen as a star of white
light, glows and burns in consequence of the falling of the atoms of
oxygen against it. And could we measure the velocity of the atoms
when they clash, and could we find their number and weights,
multiplying the weight of each atom by the square of its velocity, and
adding all together, we should get a number representing the exact
amount of heat developed by the union of the oxygen and carbon.
Thus far we have regarded the heat developed by the clashing of
sensible masses and of atoms. Work is expended in giving motion to
these atoms or masses, and heat is developed. But we reverse this
process daily, and by the expenditure of heat execute work. We can
raise a weight by heat; and in this agent we possess an enormous store
of mechanical power. A pound of coal produces by its combination with
oxygen an amount of heat which, if mechanically applied, would suffice
to raise a weight of 100 lbs. to a height of 20 miles above the
earth's surface. Conversely, 100 lbs. falling from a height of 20
miles, and striking against 'the earth, would generate an amount of
heat equal to that developed by the combustion of a pound of coal.
Wherever work is done by heat, heat disappears. A gun which fires a
ball is less heated than one which fires blank cartridge. The
quantity of heat communicated to the boiler of a working steam-engine
is greater than that which could be obtained from the re-condensation
of the steam, after it had done its work; and the amount of work
performed is the exact equivalent of the amount of heat lost. Mr.
Smyth informed us in his interesting discourse, that we dig annually
84 millions of tons of coal from our pits. The amount of mechanical
force represented by this quantity of coal seems perfectly fabulous.
The combustion of a single pound of coal, supposing it to take place
in a minute, would be equivalent to the work of 300 horses; and if we
suppose 108 millions of horses working day and night with unimpaired
strength, for a year, their united energies would enable them to
perform an amount of work just equivalent to that which the annual
produce of our coal-fields would be able to accomplish.
Comparing with ordinary gravity the force with which oxygen and carbon
unite together, chemical affinity seems almost infinite. But let us
give gravity fair play by permitting it to act throughout its entire
range. Place a body at such a distance from the earth that the
attraction of our planet is barely sensible, and let it fall to the
earth from this distance. It would reach the earth with a final
velocity of 36,747 feet a second; and on collision with the earth the
body would generate about twice the amount of heat generated by the
combustion of an equal weight of coal. We have stated that by falling
through a space of 16 feet our lead bullet would be heated
three-fifths of a degree; but a body falling from an infinite distance
has already used up 1,299,999 parts out of 1,300,000 of the earth's
pulling power, when it has arrived within 16 feet of the surface; on
this space only 1/1,300,000 of the whole force is exerted.
Let us now turn our thoughts for a moment from the earth to the sun.
The researches of Sir John Herschel and M. Pouillet have informed us
of the annual expenditure of the sun as regards heat; and by an easy
calculation we ascertain the precise amount of the expenditure which
falls to the share of our planet. Out of 2300 million parts of light
and heat the earth receives one. The whole heat emitted by the sun in
a minute would be competent to boil 12,000 millions of cubic miles of
ice-cold water. How is this enormous loss made good--whence is the
sun's heat derived, and by what means is it maintained? No
combustion--no chemical affinity with which we are acquainted, would
be competent to produce the temperature of the sun's surface.
Besides, were the sun a burning body merely, its light and heat would
speedily come to an end. Supposing it to be a solid globe of coal,
its combustion would only cover 4600 years of expenditure. In this
short time it would burn itself out. What agency then can produce the
temperature and maintain the outlay? We have already regarded the
case of a body falling from a great distance towards the earth, and
found that the heat generated by its collision would be twice that
produced by the combustion of an equal weight of coal. How much
greater must be the heat developed by a body falling against the sun!
The maximum velocity with which a body can strike the earth is about 7
miles in a second; the maximum velocity with which it can strike the
sun is 390 miles in a second. And as the heat developed by the
collision is proportional to the square of the velocity destroyed, an
asteroid falling into the sun with the above velocity would generate
about 10,000 times the quantity of heat produced by the combustion of
an asteroid of coal of the same weight.
Have we any reason to believe that such bodies exist in space, and
that they may be raining down upon the sun? The meteorites flashing
through the air are small planetary bodies, drawn by the earth's
attraction. They enter our atmosphere with planetary velocity, and by
friction against the air they are raised to incandescence and caused
to emit light and heat. At certain seasons of the year they shower
down upon us in great numbers. In Boston 240,000 of them were
observed in nine hours. There is no reason to suppose that the
planetary system is limited to 'vast masses of enormous weight;' there
is, on the contrary, reason to believe that space is stocked with
smaller masses, which obey the same laws as the larger ones. That
lenticular envelope which surrounds the sun, and which is known to
astronomers as the Zodiacal light, is probably a crowd of meteors; and
moving as they do in a resisting medium, they must continually
approach the sun. Falling into it, they would produce enormous heat,
and this would constitute a source from which the annual loss of heat
might be made good. The sun, according to this hypothesis, would
continually grow larger; but how much larger? Were our moon to fall
into the sun, it would develope an amount of heat sufficient to cover
one or two years' loss; and were our earth to fall into the sun a
century's loss would be made good. Still, our moon and our earth, if
distributed over the surface of the sun, would utterly vanish from
perception. Indeed, the quantity of matter competent to produce the
required effect would, during the range of history, cause no
appreciable augmentation in the sun's magnitude. The augmentation of
the sun's attractive force would be more sensible. However this
hypothesis may fare as a representant of what is going on in nature,
it certainly shows how a sun _might_ be formed and maintained on known
thermo-dynamic principles.
Our earth moves in its orbit with a velocity of 68,040 miles an hour.
Were this motion stopped, an amount of heat would be developed
sufficient to raise the temperature of a globe of lead of the same
size as the earth 384,000 degrees of the centigrade thermometer. It
has been prophesied that 'the elements shall melt with fervent heat.'
The earth's own motion embraces the conditions of fulfilment; stop
that motion, and the greater part, if not the whole, of our planet
would be reduced to vapour. If the earth fell into the sun, the
amount of heat developed by the shock would be equal to that developed
by the combustion of a mass of solid coal 6435 times the earth in
size.
There is one other consideration connected with the permanence of our
present terrestrial conditions, which is well worthy of our attention.
Standing upon one of, the London bridges, we observe the current of
the Thames reversed, and the water poured upward twice a-day. The
water thus moved rubs against the river's bed, and heat is the
consequence of this friction. The heat thus generated is in part
radiated into space and lost, as far as the earth is concerned. What
supplies this incessant loss? The earth's rotation. Let us look a
little more closely at the matter. Imagine the moon fixed, and the
earth turning like a wheel from west to east in its diurnal rotation.
Suppose a high mountain on the earth's surface approaching the earth's
meridian; that mountain is, as it were, laid hold of by the moon; it
forms a kind of handle by which the earth is pulled more quickly
round. But when the meridian is passed the pull of the moon on the
mountain would be in the opposite direction, it would tend to diminish
the velocity of rotation as much as it previously augmented it; thus
the action of all fixed bodies on the earth's surface is neutralised.
But suppose the mountain to lie always to the east of the moon's
meridian, the pull then would be always exerted against the earth's
rotation, the velocity of which would be diminished in a degree
corresponding to the strength of the pull. _The tidal wave occupies
this position_--it lies always to the east of the moon's meridian. The
waters of the ocean are in part dragged as a brake along the surface
of the earth; and as a brake they must diminish the velocity of the
earth's rotation. [Footnote: Kant surmised an action of this kind.]
Supposing then that we turn a mill by the action of the tide, and
produce heat by the friction of the millstones; that heat has an
origin totally different from the heat produced by another mill which
is turned by a mountain stream. The former is produced at the expense
of the earth's rotation, the latter at the expense of the sun's
radiation.
The sun, by the act of vaporisation, lifts mechanically all the
moisture of our air, which when it condenses falls in the form of
rain, and when it freezes falls as snow. In this solid form it is
piled upon the Alpine heights, and furnishes materials for glaciers.
But the sun again interposes, liberates the solidified liquid, and
permits it to roll by gravity to the sea. The mechanical force of
every river in the world as it rolls towards the ocean, is drawn from
the heat of the sun. No streamlet glides to a lower level without
having been first lifted to the elevation from which it springs by the
power of the sun. The energy of winds is also due entirely to the
same power.
But there is still another work which the sun performs, and its
connection with which is not so obvious. Trees and vegetables grow
upon the earth, and when burned they give rise to heat, and hence to
mechanical energy. Whence is this power derived? You see this oxide
of iron, produced by the falling together of the atoms of iron and
oxygen; you cannot see this transparent carbonic acid gas, formed by
the falling together of carbon and oxygen. The atoms thus in close
union resemble our lead weight while resting on the earth; but we can
wind up the weight and prepare it for another fall, and so these atoms
can be wound up and thus enabled to repeat the process of combination.
In the building of plants carbonic acid is the material from which the
carbon of the plant is derived; and the solar beam is the agent which
tears the atoms asunder, setting the oxygen free, and allowing the
carbon to aggregate in woody fibre. Let the solar rays fall upon a
surface of sand; the sand is heated, and finally radiates away as much
heat as it receives; let the same beams fall upon a forest, the
quantity of heat given back is less than the forest receives; for the
energy of a portion of the sunbeams is invested in building the trees.
Without the sun the reduction of the carbonic acid cannot be effected,
and an amount of sunlight is consumed exactly equivalent to the
molecular work done. Thus trees are formed; thus the cotton on which
Mr. Bazley discoursed last Friday is produced. I ignite this cotton,
and it flames; the oxygen again unites with the carbon; but an amount
of heat equal to that produced by its combustion was sacrificed by the
sun to form that bit of cotton.
We cannot, however, stop at vegetable life, for it is the source,
mediate or immediate, of all animal life. The sun severs the carbon
from its oxygen and builds the vegetable; the animal consumes the
vegetable thus formed, a reunion of the severed elements takes place,
producing animal heat. The process of building a vegetable is one of
winding up; the process of building an animal is one of running down.
The warmth of our bodies, and every mechanical energy which we exert,
trace their lineage directly to the sun.
The fight of a pair of pugilists, the motion of an army, or the
lifting of his own body by an Alpine climber up a mountain slope, are
all cases of mechanical energy drawn from the sun. A man weighing 150
pounds has 64 pounds of muscle; but these, when dried, reduce
themselves to 15 pounds. Doing an ordinary day's work, for eighty
days, this mass of muscle would be wholly oxidised. Special organs
which do more work would be more quickly consumed: the heart, for
example, if entirely unsustained, would be oxidised in about a week.
Take the amount of heat due to the direct oxidation of a given weight
of food; less heat is developed by the oxidation of the same amount of
food in the working animal frame, and the missing quantity is the
equivalent of the mechanical work accomplished by the muscles.
I might extend these considerations; the work, indeed, is done to my
hand--but I am warned that you have been already kept too long. To
whom then are we indebted for the most striking generalisations of
this evening's discourse? They are the work of a man of whom you have
scarcely ever heard--the published labours of a German doctor, named
Mayer. Without external stimulus, and pursuing his profession as town
physician in Heilbronn, this man was the first to raise the conception
of the interaction of heat and other natural forces to clearness in
his own mind. And yet he is scarcely ever heard of, and even to
scientific men his merits are but partially known. Led by his own
beautiful researches, and quite independent of Mayer, Mr. Joule
published in 1843 his first paper on the 'Mechanical Value of Heat;'
but in 1842 Mayer had actually calculated the mechanical equivalent of
heat from data which only a man of the rarest penetration could turn
to account.