_A Lecture delivered in the Sanders Theatre of Harvard
University, March 6, 1878._
No one who is not familiar with the history of physical science can
appreciate how very modern are those grand conceptions which add so much
to the loftiness of scientific studies; and, of the many who, on one of
our starlit nights, look up into the depths of space, and are awed by
the thoughts of that immensity which come crowding upon the mind, there
are few, I imagine, who realize the fact that almost all the knowledge
which gives such great sublimity to that sight is the result of
comparatively recent scientific investigation; and that the most
elementary student can now gain conceptions of the immensity of the
universe of which the fathers of astronomy never dreamed. And how very
grand are the familiar astronomical facts which the sight of the starry
heavens suggests!
Those brilliant points are all suns like the one which forms the center
of our system, and around which our earth revolves; yet so inconceivably
remote, that, although moving through space with an incredible velocity,
they have not materially changed their relative position since recorded
observations began. Compared with their distance, the distance of our
own sun--92,000,000 miles--seems as nothing; yet how inconceivable even
that distance is when we endeavor to mete it out with our terrestrial
standards! For if, when Copernicus--the great father of modern
astronomy--died, in 1543, just at the close of the Protestant
Reformation, a messenger had started for the sun, and traveled ever
since with the velocity of a railroad train--thirty miles an hour--he
would not yet have reached his destination!
Evidently, then, no standards, which, like our ordinary measures, bear a
simple or at least a conceivable relation to the dimensions of our own
bodies, can help us to stretch a line in such a universe. We must seek
for some magnitude which is commensurate with these immensities of
space; and, in the wonderfully rapid motion of light, astronomy
furnishes us with a suitable standard. By the eclipses of Jupiter's
satellites the astronomers have determined that this mysterious
effluence reaches us from the sun in eight minutes and a half, and
therefore must travel through space with the incredible velocity--shall
I dare to name it?--of 186,000 miles in a second of time! Yet,
inconceivably rapid as this motion is, capable of girdling the earth
nearly eight times in a single second, the very nearest of the fixed
stars, [alpha] Centauri, is so remote that the light by which it will
be seen in the southern heavens to-night, near that magnificent
constellation, the Southern Cross, must have started on its journey
three years and a half ago. But this light comes from merely the
threshold of the stellar universe; and the telescope reveals to us stars
so distant that, had they been blotted out of existence when history
began, the tidings of the event could not yet have reached the earth!
Compare now with these grand conceptions the popular belief of only a
few centuries back. Where we look into the infinite depths, our Puritan
forefathers saw only a solid dome hemming in the earth and skies, and
through whose opened doors the rain descended. They regarded the sun and
moon merely as great luminaries set in this firmament to rule the day
and night, and to their understandings the stars served no better
purpose than the spangles which glitter on the azure ceiling of many a
modern church. The great work of Copernicus, "De Orbium Coelestium
Revolutionibus," which was destined, ultimately, to overthrow the crude
cosmography which Christianity had inherited from Judaism, was not
published until just at the close of the author's life in 1543, the date
before mentioned. The telescope, which was required to fully convince
the world of its previous error, was not invented until more than half a
century later, and it was not until 1835 that Struve detected the
parallax of [alpha] Lyrae. The measurement of this parallax, together
with Bessel's determination of the parallax of 61 Cygni, and Henderson's
that of [alpha] Centauri, at about the same time, gave us our first
accurate knowledge of the distances of the fixed stars.
To the thought I have endeavored to express, I must add another, before
I can draw the lesson which I wish to teach. Great scientific truths
become popularized very slowly, and, after they have been thoroughly
worked out by the investigators, it is often many years before they
become a part of the current knowledge of mankind. It was fully a
century after Copernicus died, with his great volume--still wet from the
press of Nuremberg--in his hands, before the Copernican theory was
generally accepted even by the learned; and the intolerant spirit with
which this work was received and the persecution which Galileo
encountered more than half a century later were due solely to the
circumstance that the new theory tended to subvert the popular faith in
the cosmography of the Church. In modern times, with the many popular
expositors of science, the diffusion of new truth is more rapid; but
even now there is always a long interval after any great discovery in
abstract science before the new conception is translated into the
language of common life, so that it can be apprehended by the mass even
of educated men.
I have thus dwelt on what must be familiar facts in the past history of
astronomy, because they illustrate and will help you to realize the
present condition of a much younger branch of physical science; for, in
the transition period I have described, there exists now a conception
which opens a vision into the microcosmos beneath us as extensive and as
grand as that which the Copernican theory revealed into the macrocosmos
above us.
The conception to which I refer will be at once suggested to every
scientific scholar by the word _molecule_. This word is a Latin
diminutive, which means, primarily, a small mass of matter; and,
although heretofore often applied in mechanics to the indefinitely small
particles of a body between which the attractive or repulsive forces
might be supposed to act, it has only recently acquired the exact
significance with which we now use it.
In attempting to discover the original usage of the word molecule, I
was surprised to find that it was apparently first introduced into
science by the great French naturalist, Buffon, who employed the term in
a very peculiar sense. Buffon does not seem to have been troubled with
the problem which so engrosses our modern naturalists--how the vegetable
and animal kingdoms were developed into their present condition--but he
was greatly exercised by an equally difficult problem, which seems to
have been lost sight of in the present controversy, and which is just as
obscure to-day as it was in Buffon's time, at the close of the last
century, and that is, Why species are so persistent in Nature; why the
acorn always grows into the oak, and why every creature always produces
of its kind. And, if you will reflect upon it, I am sure you will
conclude that this last is by far the more fundamental problem of the
two, and one which necessarily includes the first. That, of two eggs, in
which no anatomist can discover any structural difference, the one
should, in a few short years, _develop_ an intelligence like Newton's,
while the other soon ends in a Guinea-pig, is certainly a greater
mystery than that, in the course of unnumbered ages, monkeys, by
insensible gradations, should _grow_ into men.
In order to explain the remarkable constancy of species, Buffon advanced
a theory which, when freed from a good deal that was fanciful, may be
expressed thus: The attributes of every species, whether of plants or
of animals, reside in their ultimate particles, or, to use a more
philosophical but less familiar word, _inhere_ in these particles, which
Buffon names _organic molecules_. According to Buffon, the oak owes all
the peculiarities of its organization to the special oak molecules of
which it consists; and so all the differences in the vegetable or animal
kingdom, from the lowest to the highest species, depend on fundamental
peculiarities with which their respective molecules were primarily
endowed. There must, of course, be as many kinds of molecules as there
are different species of living beings; but, while the molecules of the
same species were supposed to be exactly alike, and to have a strong
affinity or attraction for each other, those of different species were
assumed to be inherently distinct and to have no such affinities. Buffon
further assumed that these molecules of organic nature were diffused
more or less widely through the atmosphere and through the soil, and
that the acorn grew to the oak simply because, consisting itself of oak
molecules, it could draw only oak molecules from the surrounding media.
With our present knowledge of the chemical constitution of organic
beings, we can find a great deal that is both fantastic and absurd in
this theory of Buffon; but it must be remembered that the science of
chemistry is almost wholly a growth of the present century, while
Buffon died in 1788; and, if we look at the theory solely from the
standpoint of his knowledge, we shall find in it much that was worthy of
this great man. Indeed, in our time, the essential features of the
theory of Buffon have been transferred from natural history to chemistry
almost unchanged.
According to our modern chemistry, the qualities of every substance
reside or inhere in its molecules. Take this lump of sugar. It has
certain qualities with which every one is familiar. Are those qualities
attributes of the lump or of its parts? Certainly of its parts; for, if
we break up the lump, the smallest particles will still taste sweet and
show all the characteristics of sugar. Could we, then, carry on this
subdivision indefinitely, provided only we had senses or tests delicate
enough to recognize the qualities of sugar in the resulting particles?
To this question, modern chemistry answers decidedly, No! You would
before long reach the smallest mass that can have the qualities of
sugar. You would have no difficulty in breaking up these masses, but you
would then obtain, not smaller particles of sugar, but particles of
those utterly different substances which we call carbon, oxygen, and
hydrogen--in a word, particles of the elementary substances of which
sugar consists. These ultimate particles of sugar we call the molecules
of sugar, and thus we come to the present chemical definition of a
molecule, "_The smallest particles of a substance in which its qualities
inhere_," which, as you see, is a reproduction of Buffon's idea,
although applied to matter and not to organism.
A lump of sugar, then, has its peculiar qualities because it is an
aggregate of molecules which have those qualities, and a lump of salt
differs from a lump of sugar simply because the molecules of salt differ
from those of sugar, and so with every other substance. There are as
many kinds of molecules in Nature as there are different substances, but
all the molecules of the same substance are absolutely alike in every
respect.
Thus far, as you see, we are merely reviving in a different association
the old ideas of Buffon. But just at this point comes in a new
conception, which gives far greater grandeur to our modern theory: for
we conceive that those smallest particles in which the qualities of a
substance inhere are definite bodies or systems of bodies moving in
space, and that _a lump of sugar is a universe of moving worlds_.
If on a clear night you direct a telescope to one of the many
star-clusters of our northern heavens, you will have presented to the
eye as good a diagram as we can at present draw of what we suppose
would, under certain circumstances, be seen in a lump of sugar if we
could look into the molecular universe with the same facility with
which the telescope penetrates the depths of space.
Do you tell me that the absurdities of Buffon were wisdom when compared
with such wild speculations as these? The criticism is simply what I
expected, and I must remind you that, as I intimated at the outset, this
conception of modern science is in the transition period of which I then
spoke, and, although very familiar to scientific scholars, has not yet
been grasped by the popular mind. I can further only add that, wild as
it may appear, the idea is the growth of legitimate scientific
investigation, and express my conviction that it will soon become as
much a part of the popular belief as those grand conceptions of
astronomy to which I have referred.
Do you rejoin that we can see the suns in a stellar cluster, but can not
even begin to see the molecules? I must again remind you that, in fact,
you only see points of light in the field of the telescope, and that
your knowledge that these points are immensely distant suns is an
inference of astronomical science; and, further, that our knowledge--if
I may so call our confident belief--that the lump of sugar is an
aggregate of moving molecules is an equally legitimate inference of
molecular mechanics, a science which, although so much newer, is as
positive a field of study as astronomy. Moreover, sight is not the only
avenue to knowledge; and, although our material limitations forbid us to
expect that the microscope will ever be able to penetrate the molecular
universe, yet we feel assured that we have been able by strictly
experimental methods to weigh molecular masses and measure molecular
magnitudes with as much accuracy as those of the fixed stars.
Of all forms of matter the gas has the simplest molecular structure,
and, as might be anticipated, our knowledge of molecular magnitudes is
as yet chiefly confined to materials of this class. I have given below
some of the results which have been obtained in regard to the molecular
magnitudes of hydrogen gas, one of the best studied of this class of
substances; and, although the vast numbers are as inconceivable as are
those of astronomy, they can not fail to impress you with the reality of
the magnitudes they represent. I take hydrogen gas for my illustration
rather than air, because our atmosphere is a mixture of two gases,
oxygen and nitrogen, and therefore its condition is less simple than
that of a perfectly homogeneous material like hydrogen. The molecular
dimensions of other substances, although varying very greatly in their
relative values, are of the same order of magnitude as these.[A]
[A] As some of the readers of this volume may be interested to
compare these values, we reproduce the "Table of Molecular Data"
from Professor Clerk Maxwell's lecture on "Molecules," delivered
before the British Association at Bradford, and published in
"Nature," September 25, 1873.
_Molecular Magnitudes at Standard Temperature and Pressure, 0 deg. C.
and 76 c. m._
-----------------------+-----------+---------+----------+---------
RANK ACCORDING TO | Hydrogen. | Oxygen. | Carbonic | Carbonic
ACCURACY OF KNOWLEDGE. | | | Oxide. | Dioxide.
-----------------------+-----------+---------+----------+---------
RANK I. | | | |
Relative mass | 1 | 16 | 14 | 22
Velocity in metres | | | |
per second | 1,859 | 465 | 497 | 396
| | | |
RANK II. | | | |
Mean path in ten | | | |
billionths (10^{-10})| | | |
of a metre | 965 | 560 | 482 | 379
Collisions each | | | |
second--number of | | | |
millions | 17,750 | 7,646 | 9,489 | 9,720
| | | |
RANK III. | | | |
Diameter in hundred | | | |
billionths (10^{-11})| | | |
of a metre | 58 | 76 | 83 | 93
Mass in ten million | | | |
million million | | | |
millionths (10^{-25})| | | |
of a gramme | 46 | 736 | 644 | 1,012
-----------------------+-----------+---------+----------+---------
Number of molecules in one cubic centimetre of every gas is
nineteen million million million on 19 (10^{18}).
Two million hydrogen molecules side by side measure a little
over one millimetre.
_Dimension of Hydrogen Molecules calculated for Temperature of Melting
Ice, and for the Mean Height of the Barometer of the Sea Level:_
Mean velocity, 6,099 feet a second.
Mean path, 31 ten-millionths of an inch.
Collisions, 17,750 millions each second.
Diameter, 438,000, side by side, measure 1/100 of an inch.
Mass, 14 (millions^3) weigh 1/1000 of a grain.
Gas-volume, 311 (millions^3) fill one cubic inch.
To explain how the values here presented were obtained would be out of
place in a popular lecture,[B] but a few words in regard to two or
three of the data are required to elucidate the subject of this lecture.
[B] _See_ Professor Maxwell's lecture, _loc. cit._; also, Appletons'
"Cyclopaedia," article "Molecules."
First, then, in regard to the mass or weight of the molecules. So far as
their relative values are concerned, chemistry gives us the means of
determining the molecular weights with very great accuracy; but when we
attempt to estimate their weights in fractions of a grain--the smallest
of our common standards--we can not expect precision, simply because the
magnitudes compared are of such a different order; and the same is true
of most of the other absolute dimensions, such as the diameter and
volume of the molecules. We only regard the values given in our table as
a very rough estimate, but still we have good grounds for believing that
they are sufficiently accurate to give us a true idea of the order of
the quantities with which we are dealing; and it will be seen that,
although the numbers required to express the relations to our ordinary
standards are so large, these molecular magnitudes are no more removed
from us on the one side than are those of astronomy on the other.
Passing next to the velocity of the molecular motion, we find in that a
quantity which, although large, is commensurate with the velocity of
sound, the velocity of a rifle-ball, and the velocities of many other
motions with which we are familiar. We are, therefore, not comparing, as
before, quantities of an utterly different order, and we have confidence
that we have been able to determine the value within very narrow limits
of error. But how surprising the result is! Those molecules of hydrogen
are constantly moving to and fro with this great velocity, and not only
are the molecules of all aeriform substances moving at similar, although
differing rates, but the same is equally true of the molecules of every
substance, whatever may be its state of aggregation.
The gas is the simplest molecular condition of matter, because in this
state the molecules are so far separated from each other that their
motions are not influenced by mutual attractions. Hence, in accordance
with the well-known laws of motion, gas molecules must always move in
straight lines and with a constant velocity until they collide with each
other or strike against the walls of the containing vessel, when, in
consequence of their elasticity, they at once rebound and start on a new
path with a new velocity. In these collisions, however, there is no loss
of motion, for, as the molecules have the same weight and are perfectly
elastic, they simply change velocities, and whatever one may lose the
other must gain.
But, if the velocity changes in this way, you may ask, What meaning has
the definite value given in our table? The answer is, that this is the
mean value of the velocity of all the molecules in a mass of hydrogen
gas under the assumed conditions; and, by the principle just stated, the
mean value can not be changed by the collisions of the molecules among
themselves, however great may be the change in the motion of the
individuals.
In both liquids and solids the molecular motions are undoubtedly as
active as in a gas, but they must be greatly influenced by the mutual
attractions which hold the particles together, and hence the conditions
are far more complicated, and present a problem which we have been able
to solve only very imperfectly, and with which, fortunately, we have not
at present to deal.
Limiting, then, our study to the molecular condition of a gas, picture
to yourselves what must be the condition of our atmosphere, with its
molecules flying about in all directions. Conceive what a molecular
storm must be raging about us, and how it must beat against our bodies
and against every exposed surface. The molecules of our atmosphere move,
on an average, nearly four (3.8) times slower than those of hydrogen
under the same conditions; but then they weigh, on an average, fourteen
and a half times more than hydrogen molecules, and therefore strike with
as great energy. And do not think that the effect of these blows is
insignificant because the molecular projectiles are so small; they make
up by their number for what they want in size.
Consider, for example, a cubic yard of air, which, if measured at the
freezing-point, weighs considerably over two pounds. That cubic yard of
material contains over two pounds of molecules, which are moving with an
average velocity of 1,605 feet a second, and this motion is equivalent,
in every respect, to that of a cannon-ball of equal weight rushing along
its path at the same tremendous rate. Of course, this is true of every
cubic yard of air at the same temperature; and, if the motion of the
molecules of the atmosphere around us could by any means be turned into
one and the same direction, the result would be a hurricane sweeping
over the earth with this velocity--that is, at the rate of 1,094 miles
an hour--whose destructive violence not even the Pyramids could
withstand.
Living as we do in the midst of a molecular tornado capable of such
effects, our safety lies wholly in the circumstance that the storm beats
equally in all directions at the same time, and the force is thus so
exactly balanced that we are wholly unconscious of the tumult. Not even
the aspen-leaf is stirred, nor the most delicate membrane broken; but
let us remove the air from one of the surfaces of such a membrane, and
then the power of the molecular storm becomes evident, as in the
familiar experiments with an air-pump.
As has already been intimated, the values of the velocities both of
hydrogen and of air molecules given above were measured at a definite
temperature, 32 deg. of our Fahrenheit thermometer, the freezing point of
water; and this introduces a very important point bearing on our
subject, namely, that the molecular velocities vary very greatly with
the temperature. Indeed, according to our theory, this very molecular
motion constitutes that state or condition of matter which we call
temperature. A hot body is one whose molecules are moving comparatively
rapidly, and a cold body one in which they are moving comparatively
slowly. Without, however, entering into further details, which would
involve the whole mechanical theory of heat, let me call your attention
to a single consequence of the principle I have stated.
When we heat hydrogen, air, or any mass of gas, we simply increase the
velocity of its moving molecules. When we cool the gas, we simply lessen
the velocity of the same molecules. Take a current of air which enters a
room through a furnace. In passing it comes in contact with heated iron,
and, as we say, is heated. But, as we view the process, the molecules of
the air, while in contact with the hot iron, collide with the very
rapidly oscillating metallic molecules, and fly back as a billiard-ball
would under similar circumstances, with a greatly increased velocity,
and it is this more rapid motion which alone constitutes the higher
temperature.
Consider, next, what must be the effect on the surface. A moment's
reflection will show that the normal pressure exerted by the molecular
storm, always raging in the atmosphere, is due not only to the impact of
the molecules, but also to the reaction caused by their rebound. When
the molecules rebound, they are, as it were, driven away from the
surface in virtue of the inherent elasticity both of the surface and of
the molecules. Now, what takes place when one mass of matter is driven
away from another--when a cannon-ball is driven out of a gun, for
example? Why, the gun _kicks_! And so every surface from which molecules
rebound must _kick_; and, if the velocity is not changed by the
collision, one half of the pressure caused by the molecular bombardment
is due to the recoil. From a heated surface, as we have said, the
molecules rebound with an increased velocity, and hence the recoil must
be proportionally increased, determining a greater pressure against the
surface.
According to this theory, then, we should expect that the air would
press unequally against surfaces at different temperatures, and that,
other things being equal, the pressure exerted would be greater the
higher the temperature of the surface. Such a result, of course, is
wholly contrary to common experience, which tells us that a uniform mass
of air presses equally in all directions and against all surfaces of the
same area, whatever may be their condition. It would seem, then, at
first sight, as if we had here met with a conspicuous case in which our
theory fails. But further study will convince us that the result is just
what we should expect in a dense atmosphere like that in which we dwell;
and, in order that this may become evident, let me next call your
attention to another class of molecular magnitudes.
It must seem strange indeed that we should be able to measure molecular
velocities; but the next point I have to bring to your notice is
stranger yet, for we are confident that we have been able to determine
with approximate accuracy for each kind of gas molecule the average
number of times one of these little bodies runs against its neighbors in
a second, assuming, of course, that the conditions of the gas are given.
Knowing, now, the molecular velocity and the number of collisions a
second, we can readily calculate the mean path of the molecule--that is,
the average distance it moves, under the same conditions, between two
successive collisions. Of course, for any one molecule, this path must
be constantly varying; since, while at one time the molecule may find a
clear coast and make a long run, the very next time it may hardly start
before its course is arrested. Still, taking a mass of gas under
constant conditions, the doctrine of averages shows that the mean path
must have a definite value, and an illustration will give an idea of the
manner in which we have been able to estimate it.
The nauseous, smelling gas we call sulphide of hydrogen has a density
only a little greater than that of air, and its molecules must therefore
move with very nearly as great velocity as the average air
molecule--that is to say, about fourteen hundred and eighty feet a
second; and we might therefore expect that, on opening a jar of the gas,
its molecules would spread instantly through the surrounding atmosphere.
But, so far from this, if the air is quiet, so that the gas is not
transported by currents, a very considerable time will elapse before the
characteristic odor is perceived on the opposite side of an ordinary
room. The reason is obvious: the molecules must elbow their way through
the crowd of air molecules which already occupy the space, and can
therefore advance only slowly; and it is obvious that, the oftener they
come into collision with their neighbors, the slower their progress must
be. Knowing, then, the mean velocity of the molecular motion, and being
able to measure by appropriate means _the rate of diffusion_, as it is
called, we have the data from which we can calculate both the number of
collisions in a second and also the mean path between two successive
collisions. The results, as we must expect, are of the same order as the
other molecular magnitudes. But, inconceivably short as the free[C] path
of a molecule certainly is, it is still, in the case of hydrogen gas,
136 times the diameter of the moving body, which would certainly be
regarded among men as quite ample elbow-room.
[C] There is an obvious distinction between the free and the
disturbed path of a molecule, and we can not overlook in
our calculations the perturbations which the collisions
necessarily entail. Such considerations greatly complicate
the problem, which is far more difficult than would appear
from the superficial view of the subject that can alone be
given in a popular lecture.
Although, in this lecture, I have as yet had no occasion to mention the
radiometer, I have by no means forgotten my main subject, and everything
which has been said has had a direct bearing on the theory of this
remarkable instrument; and still, before you can understand the great
interest with which it is regarded, we must follow out another line of
thought, converging on the same point.
One of the most remarkable results of modern science is the discovery
that all energy at work on the surface of this planet comes from the
sun. Most of you probably saw, at our Centennial Exhibition, that great
artificial cascade in Machinery Hall, and were impressed with the power
of the steam-pump which could keep flowing such a mass of water. But,
also, when you stood before the falls at Niagara, did you realize the
fact that the enormous floods of water which you saw surging over those
cliffs were in like manner supplied by an all-powerful pump, and that
pump the sun? And not only is this true, but it is equally true that
every drop of water that falls, every wave that beats, every wind that
blows, every creature that moves on the surface of the earth, one and
all, are animated by that mysterious effluence we call the sunbeam. I
say mysterious effluence; for how that power is transmitted over those
92,000,000 miles between the earth and the sun is still one of the
greatest mysteries of Nature.
In the science of optics, as is well known, the phenomena of light are
explained by the assumption that the energy is transmitted in waves
through a medium which fills all space called the luminiferous ether,
and there is no question that this theory of Nature, known in science as
the Undulatory Theory of Light, is, as a working hypothesis, one of the
most comprehensive and searching which the human mind has ever framed.
It has both correlated known facts and pointed the way to remarkable
discoveries. But, the moment we attempt to apply it to the problem
before us, it demands conditions which tax even a philosopher's
credulity.
As sad experience on the ocean only too frequently teaches, energy can
be transmitted by waves as well as in any other way. But every mechanic
will tell you that the transmission of energy, whatever be the means
employed, implies certain well-known conditions. Assume that the energy
is to be used to turn the spindles of a cotton mill. The engineer can
tell you just how many horse-power he must supply for every working-day,
and it is equally true that a definite amount of energy must come from
the sun to do each day's work on the surface of the globe. Further, the
engineer will also tell you that, in order to transmit the power from
his turbine or his steam-engine, he must have shafts and pulleys and
belts of adequate strength, and he knows in every case what is the
lowest limit of safety. In like manner, the medium through which the
energy which runs the world is transmitted must be strong enough to do
the immense work put upon it; and, if the energy is transmitted by
waves, this implies that the medium must have an enormously great
elasticity, an elasticity vastly greater than that of the best-tempered
steel.
But turn now to the astronomers, and learn what they have to tell us in
regard to the assumed luminiferous ether through which all this energy
is supposed to be transmitted. Our planet is rushing in its orbit around
the sun at an average rate of over 1,000 miles a minute, and makes its
annual journey of some 550,000,000 miles in 365 days, 6 hours, 9
seconds, and 6/10 of a second. Mark the tenths; for astronomical
observations are so accurate that, if the length of the year varied
permanently by the tenth of a second, we should know it; and you can
readily understand that, if there were a medium in space which offered
as much resistance to the motion of the earth as would gossamer threads
to a race-horse, the planet could never come up to time, year after
year, to the tenth of a second.
How, then, can we save our theory by which we set so much, and rightly,
because it has helped us so effectively in studying Nature? If we may be
allowed such an extravagant solecism, let us suppose that the engineer
of our previous illustration was the hero of a fairy tale. He has built
a mill, set a steam-engine in the basement, arranged his spindles above,
and is connecting the pulleys by the usual belts, when some stern
necessity requires him to transmit all the energy with cobwebs. Of
course, a good fairy comes to his aid, and what does she do? Simply
makes the cobwebs indefinitely strong. So the physicists, not to be
outdone by any fairies, make their ether indefinitely elastic, and their
theory lands them just here, with a medium filling all space, thousands
of times more elastic than steel, and thousands on thousands of times
less dense than hydrogen gas. There must be a fallacy somewhere, and I
strongly suspect it is to be found in our ordinary materialistic notions
of causation, which involve the old metaphysical dogma, "_nulla actio in
distans_," and which in our day have culminated in the famous apothegm
of the German materialist, "Kein Phosphor kein Gedanke."
But it is not my purpose to discuss the doctrines of causation, and I
have dwelt on the difficulty, which this subject presents in connection
with the undulatory theory, solely because I wished you to appreciate
the great interest with which scientific men have looked for some direct
manifestation of the mechanical action of light. It is true that the
ether waves must have dimensions similar to those of the molecules
discussed above, and we must expect, therefore, that they would act
primarily on the molecules and not on masses of matter. But still the
well-known principles of wave motion have led competent physicists to
maintain that a more or less considerable pressure ought to be exerted
by the ether waves on the surfaces against which they beat, as a partial
resultant of the molecular tremors first imparted. Already, in the last
century, attempts were made to discover some evidence of such action,
and in various experiments the sun's direct rays were concentrated on
films, delicately suspended and carefully protected from all other
extraneous influences, but without any apparent effect; and thus the
question remained until about three years ago, when the scientific world
were startled by the announcement of Mr. Crookes, of London, that, on
suspending a small piece of blackened alder pith in the very perfect
vacuum which can now be obtained with the mercury pump, invented by
Sprengel, he had seen this light body actually repelled by the sun's
rays; and they were still more startled, when, after a few further
experiments, he presented us with the instrument he called a radiometer,
in which the sun's rays do the no inconsiderable work of turning a small
wheel. Let us examine for a moment the construction of this remarkable
instrument.
The moving part of the radiometer is a small horizontal wheel, to the
ends of whose arms are fastened vertical vanes, usually of mica, and
blackened on one side. A glass cap forms the hub, and by the
glass-blower's art the wheel is inclosed in a glass bulb, so that the
cap rests on the point of a cambric needle; and the wheel is so
delicately balanced on this pivot that it turns with the greatest
freedom. From the interior of the bulb the air is now exhausted by means
of the Sprengel pump, until less than 1/1000 of the original quantity is
left, and the only opening is then hermetically sealed. If, now, the
sun's light or even the light from a candle shines on the vanes, the
blackened surfaces--which are coated with lampblack--are repelled, and,
these being symmetrically placed around the wheel, the several forces
conspire to produce the rapid motion which results. The effect has all
the appearance of a direct mechanical action exerted by the light, and
for some time was so regarded by Mr. Crookes and other eminent
physicists, although in his published papers it should be added that Mr.
Crookes carefully abstained from speculating on the subject--aiming, as
he has since said, to keep himself unbiased by any theory, while he
accumulated the facts upon which a satisfactory explanation might be
based.
Singularly, however, the first aspects of the new phenomena proved to be
wholly deceptive, and the motion, so far from being an effect of the
direct mechanical action of the waves of light, is now believed to be a
new and very striking manifestation of molecular motion. To this opinion
Mr. Crookes himself has come, and, in a recent article, he writes:
"Twelve months' research, however, has thrown much light on these
actions, and the explanation afforded by the dynamical theory of gases
makes what was a year ago obscure and contradictory now reasonable and
intelligible."
As is frequently the case in Nature, the chief effect is here obscured
by various subordinate phenomena, and it is not surprising that a great
difference of opinion should have arisen in regard to the cause of the
motion. This would not be an appropriate place to describe the numerous
investigations occasioned by the controversy, many of which show in a
most striking manner how easily experimental evidence may be honestly
misinterpreted in support of a preconceived opinion. I will, however,
venture to trespass further on your patience, so far as to describe the
few experiments by which, very early in the controversy, I satisfied my
own mind on the subject.
When, two years ago, I had for the first time an opportunity of
experimenting with a radiometer, the opinion was still prevalent that
the motion of the wheel was a direct mechanical effect of the waves of
light, and, therefore, that the impulses came from the outside of the
instrument, the waves passing freely through the glass envelope. At the
outset, this opinion did not seem to me to be reasonable, or in harmony
with well-known facts; for, knowing how great must be the molecular
disturbance caused by the sun's rays, as shown by their heating power, I
could not believe that a residual action, such as has been referred to,
would first appear in these delicate phenomena observed by Mr. Crookes,
and should only be manifested in the vacuum of a mercury pump.
On examining the instrument, my attention was at once arrested by the
lampblack coating on the alternate surfaces of the vanes; and, from the
remarkable power of lampblack to absorb radiant heat, it was evident at
once that, whatever other effects the rays from the sun or from a flame
might cause, they must necessarily determine a constant difference of
temperature between the two surfaces of the vanes, and the thought at
once occurred that, after all, the motion might be a direct result of
this difference of temperature--in other words, that the radiometer
might be a small heat engine, whose motions, like those of every other
heat engine, depend on the difference of temperature between its parts.
But, if this were true, the effect ought to be proportional solely to
the heating power of the rays, and a very easy means of roughly testing
this question was at hand. It is well known that an aqueous solution of
alum, although transmitting light as freely as the purest water,
powerfully absorbs those rays, of any source, which have the chief
heating power. Accordingly, I interposed what we call an alum cell in
the path of the rays shining on the radiometer, when, although the light
on the vanes was as bright as before, the motion was almost completely
arrested.
This experiment, however, was not conclusive, as it might still be said
that the _heat_-giving rays acted _mechanically_, and it must be
admitted that the chief part of the energy in the rays, even from the
most brilliant luminous sources, always takes the form of heat. But, if
the action is mechanical, the reaction must be against the medium
through which the rays are transmitted, while, if the radiometer is
simply a heat engine, the action and reaction must be, ultimately at
least, between the heater and the cooler, which in this case are
respectively the blackened surfaces of the vanes and the glass walls of
the inclosing bulb; and here, again, a very easy method of testing the
actual condition at once suggested itself.
If the motion of the radiometer wheel is an effect of mechanical
impulses transmitted in the direction of the beam of light, it was
certainly to be expected that the beam would act on the lustrous as well
as on the blackened mica surfaces, however large might be the difference
in the resultants producing mechanical motion, in consequence of the
great absorbing power of the lampblack. Moreover, since the instrument
is so constructed that, of two vanes on opposite sides of the wheel, one
always presents a blackened and the other a lustrous surface to an
incident beam, we should further expect to find in the motion of the
wheel a differential phenomenon, due to the unequal action of the light
on these surfaces. On the other hand, if the radiometer is a heat
engine, and the reaction takes place between the heated blackened
surfaces of the vanes and the colder glass, it is evident that the total
effect will be simply the sum of the effects at the several surfaces.
In order to investigate the question thus presented, I placed the
radiometer before a common kerosene lamp, and observed, with a
stop-watch, the number of seconds that elapsed during ten revolutions of
the little wheel. Finding that this number was absolutely constant, I
next screened one half of the bulb, so that only the blackened faces
were exposed to the light as the wheel turned them into the beam. Again,
I several times observed the number of seconds during ten turns, which,
although equally constant, was greater than before. Lastly, I screened
the blackened surfaces so that, as the wheel turned, only the lustrous
surfaces of mica were exposed to the light, when, to my surprise, the
wheel continued to turn in the same direction as before, although much
more slowly. It appeared as if the lustrous surfaces were attracted by
the light. Again I observed the time of ten revolutions, and here I have
collected my results, reducing them, in the last column, so as to show
the corresponding number of revolutions in the same time:
----------------------+--------------------------+--------------------
CONDITIONS. | Time of ten revolutions. | No. of revolutions
| | in same time.
----------------------|--------------------------|--------------------
Both faces exposed | 8 seconds. | 319
Blackened faces only | 11 " | 232
Mica faces only | 29 " | 88
----------------------+--------------------------+--------------------
It will be noticed that 88 + 232 equals very nearly 319. Evidently the
effect, so far from being differential, is concurrent. Hence, the action
which causes the motion must take place between the parts of the
instrument, and can not be a direct effect of impulses imparted by
ether waves; or else we are driven to the most improbable alternative,
that lampblack and mica should have such a remarkable selective power
that the impulses imparted by the light should exert a repulsive force
at one surface and an attractive force at the other. Were there,
however, such an improbable effect, it must be independent of the
thickness of the mica vanes; while, on the other hand, if, as seemed to
us now most probable, the whole effect depended on the difference of
temperature between the lampblack and the mica, and if the light
produced an effect on the mica surface only because, the mica plate
being diathermous to a very considerable extent, the lampblack became
heated through the plate more than the plate itself, then it would
follow that, if we used a thicker mica plate, which would absorb more of
the heat, we ought to obtain a marked difference of effect. Accordingly,
we repeated the experiment with an equally sensitive radiometer, which
we made for the purpose, with comparatively thick vanes, and with this
the effect of a beam of light on the mica surface was absolutely null,
the wheel revolving in the same time, whether these faces were protected
or not.
But one thing was now wanting to make the demonstration complete. A heat
engine is reversible, and if the motion of the radiometer depended on
the circumstance that the temperature of the blackened faces of the
vanes was higher than that of the glass, then by reversing the
conditions we ought to reverse the motion. Accordingly, I carefully
heated the glass bulb over a lamp, until it was as hot as the hand would
bear, and then placed the instrument in a cold room, trusting to the
great radiating power of lampblack to maintain the temperature of the
blackened surfaces of the vanes below that of the glass. Immediately the
wheel began to turn in the opposite direction, and continued to turn
until the temperature of the glass came into equilibrium with the
surrounding objects.
These early experiments have since been confirmed to the fullest extent,
and no physicist at the present day can reasonably doubt that the
radiometer is a very beautiful example of a heat engine, and it is the
first that has been made to work continuously by the heat of the
sunbeam. But it is one thing to show that the instrument is a heat
engine, and quite another thing to explain in detail the manner in which
it acts. In regard to the last point, there is still room for much
difference of opinion, although physicists are generally agreed in
referring the action to the residual gas that is left in the bulb. As
for myself, I became strongly persuaded--after experimenting with more
than one hundred of these instruments, made under my own eye, with every
variation of condition I could suggest--_that the effect was due to the
same cause which determines gas pressure_, and, according to the
dynamical theory of gases, this amounts to saying that the effect is due
to molecular motion. I have not time, however, to describe either my own
experiments on which this opinion was first based, or the far more
thorough investigations since made by others, which have served to
strengthen the first impression.[D] But, after our previous discussions,
a few words will suffice to show how the molecular theory explains the
new phenomena.
[D] See notice of these investigations by the author of this
article, in "American Journal of Science and Arts,"
September, 1877 (3), xiv, 231.
Although the air in the bulb has been so nearly exhausted that less than
the one-thousandth part remains, yet it must be borne in mind that the
number of molecules left behind is by no means inconsiderable. As will
be seen by referring to our table, there must still be no less than
311,000 million million in every cubic inch. Moreover, the absolute
pressure which this residual gas exerts is a very appreciable quantity.
It is simply the one-thousandth of the normal pressure of the
atmosphere, that is, of 14-7/10 pounds on a square inch, which is
equivalent to a little over one hundred grains on the same area. Now,
the area of the blackened surfaces of the vanes of an ordinary
radiometer measures just about a square inch, and the wheel is mounted
so delicately that a constant pressure of one-tenth of a grain would be
sufficient to produce rapid motion. So that a difference of pressure on
the opposite faces of the vanes, equal to one one-thousandth of the
whole amount, is all that we need account for; and, as can easily be
calculated, a difference of temperature of less than half a degree
Fahrenheit would cause all this difference in the pressure of the
rarefied air.
But you may ask, How can such a difference of pressure exist on
different surfaces exposed to one and the same medium? and your question
is a perfectly legitimate one; for it is just here that the new
phenomena seem to belie all our previous experience. If, however, you
followed me in my very partial exposition of the mechanical theory of
gases, you will easily see that on this theory it is a more difficult
question to explain why such a difference of pressure does not manifest
itself in every gas medium and under all conditions between any two
surfaces having different temperatures.
We saw that gas pressure is a double effect, caused both by the impact
of molecules and by the recoil of the surface attending their rebound.
We also saw that when molecules strike a heated surface they rebound
with increased velocity, and hence produce an increased pressure against
the surface, the greater the higher the temperature. According to this
theory, then, we should expect to find the same atmosphere pressing
unequally on equal surfaces if at different temperatures; and the
difference in the pressure on the lampblack and mica surfaces of the
vanes, which the motion of the radiometer wheel necessarily implies, is
therefore simply the normal effect of the mechanical condition of every
gas medium. The real difficulty is, to explain why we must exhaust the
air so perfectly before the effect manifests itself.
The new theory is equal to the emergency. As has been already pointed
out, in the ordinary state of the air the amplitude of the molecular
motion is exceedingly small, not over a few ten-millionths of an inch--a
very small fraction, therefore, of the height of the inequalities on the
lampblack surfaces of the vanes of a radiometer. Under such
circumstances, evidently the molecules would not leave the heated
surface, but simply bound back and forth between the vanes and the
surrounding mass of dense air, which, being almost absolutely a
non-conductor of heat, must act essentially like an elastic solid wall
confining the vanes on either side. For the time being, and until
replaced by convection currents, the oscillating molecules are as much a
part of the vanes as our atmosphere is a part of the earth; and on this
system, as a whole, the homogeneous dense air which surrounds it must
press equally from all directions. In proportion, however, as the air is
exhausted, the molecules find more room and the amplitude of the
molecular motion is increased, and, when a very high degree of
exhaustion is reached, the air particles no longer bound back and forth
on the vanes without change of condition, but they either bound off
entirely like a ball from a cannon, or else, having transferred a
portion of their momentum, return with diminished velocity, and in
either case the force of the reaction is felt.[E]
[E] The reader will, of course, distinguish between the differential
action on the opposite faces of the vanes of the radiometer and
the reaction between the vanes and the glass which are the heater
and the cooler of the little engine. Nor will it be necessary to
remind any student that a popular view of such a complex subject
must be necessarily partial. In the present case we not only meet
with the usual difficulties in this respect, but, moreover, the
principles of molecular mechanics have not been so fully developed
as to preclude important differences of opinion between equally
competent authorities in regard to the details of the theory. To
avoid misapprehension, we may here add that, in orderto obtain in
the radiometer a reaction between the heater and the cooler, it
is not necessary that the space between them should actually be
crossed by the moving molecules. It is only necessary that the
momentum should be transferred across the space, and tide may
take place along lines consisting of many molecules each. The
theory, however, shows that such a transfer can only take place
in a highly rarefied medium. In an atmosphere of ordinary density,
the accession of heat which the vanes of a radiometer might
receive from a radiant source would be diffused through the mass
of the inclosed air. This amounts to saying that the momentum
would be so diffused, and hence, under such circumstances, the
molecular motion would not determine any reaction between the
vanes and the glass envelope. Indeed, a dense mass of gas presents
to the conduction of heat, which represents momentum, a wall far
more impenetrable than the surrounding glass, and the diffusion
of heat is almost wholly brought about by convection currents
which rise from the heated surfaces. It will thus be seen that
the great non-conducting power of air comes into play to prevent
not only the transfer of momentum from the vanes to the glass,
but also, almost entirely, any direct transfer to the surrounding
mass of gas. Hence, as stated above, the heated molecules bound
back and forth on the vanes without change of condition, and the
mass of the air retains its uniform tension in all parts of the
bulb, except in so far as this is slowly altered by the convection
currents just referred to. As the atmosphere, however, becomes
less dense, the diffusion of heat by convection diminishes, and
that by molecular motion (conduction) increases until the last
greatly predominates. When, now, the exhaustion reaches so great
a degree that the heat, or momentum, is rapidly transferred from
the heater to the cooler by an exaggeration, or, possibly, a
modification, of the mode of action we call conduction, then we
have the reaction on which the motion of the radiometer wheel
depends.
Thus it appears that we have been able to show by very definite
experimental evidence that the radiometer is a heat engine. We have also
been able to show that such a difference of temperature as the radiation
must produce in the air in _direct_ contact with the opposite faces of
the vanes of the radiometer would determine a difference of tension,
which is sufficient to account for the motion of the wheel. Finally, we
have shown, as fully as is possible in a popular lecture, that,
according to the mechanical theory of gases, such a difference of
tension would have its normal effect only in a highly rarefied
atmosphere, and thus we have brought the new phenomena into harmony with
the general principles of molecular mechanics previously established.
More than this can not be said of the steam-engine, although, of course,
in the older engine the measurements on which the theory is based are
vastly more accurate and complete. But the moment we attempt to go
beyond the general principles of heat engines, of which the steam-engine
is such a conspicuous illustration, and explain how the heat is
transformed into motion, we have to resort to the molecular theory just
as in the case of the radiometer; and the motion of the steam-engine
seems to us less wonderful than that of the radiometer only because it
is more familiar and more completely harmonized with the rest of our
knowledge. Moreover, the very molecular theory which we call upon to
explain the steam-engine involves consequences which, as we have seen,
have been first realized in the radiometer; and thus it is that this new
instrument, although disappointing the first expectations of its
discoverer, has furnished a very striking confirmation of this wonderful
theory. Indeed, the confirmation is so remote and yet so close, so
unexpected and yet so strong, that the new phenomena almost seem to be a
direct manifestation of the molecular motion which our theory assumes;
and when a new discovery thus confirms the accuracy of a previous
generalization, and gives us additional reason to believe that the
glimpses we have gained into the order of Nature are trustworthy, it
excites, with reason, among scientific scholars the warmest interest.
And when we consider the vast scope of the molecular theory, the order
on order of existences which it opens to the imagination, how can we
fail to be impressed with the position in which it places man midway
between the molecular cosmos on the one side and the stellar cosmos on
the other--a position in which he is able, in some measure at least, to
study and interpret both?
Since the time to which we referred at the beginning of this lecture,
when man's dwelling-place was looked at as the center of a creation
which was solely subservient to his wants, there has been a reaction to
the opposite extreme, and we have heard much of the utter insignificance
of the earth in a universe among whose immensities all human belongings
are but as a drop in the ocean. When now, however, we learn from Sir
William Thomson that the drop of water in our comparison is itself a
universe, consisting of units so small that, were the drop magnified to
the size of the earth, these units would not exceed in magnitude a
cricket-ball,[F] and when, on studying chemistry, we still further learn
that these units are not single masses but systems of atoms, we may
leave the illusions of the imagination from the one side to correct
those from the other, and all will teach us the great lesson that man's
place in Nature is not to be estimated by relations of magnitude, but
by the intelligence which makes the whole creation his own.
[F] "Nature," No. 22, March 31, 1870.
But, if it is man's privilege to follow both the atoms and the stars in
their courses, he finds that, while thus exercising the highest
attributes of his nature, he is ever in the presence of an immeasurably
superior intelligence, before which he must bow and adore, and thus come
to him both the assurance and the pledge of a kinship in which his only
real glory can be found.