_Dynamics._—At the beginning of the nineteenth century mechanics was
the only major branch of physical science which had attained any
considerable degree of development. Two centuries earlier, Galileo’s
experiments on the rate of fall of iron balls dropped from the top of
the Leaning Tower of Pisa, had marked the origin of dynamics. He had
easily disproved the prevalent idea that even under conditions where air
resistance is negligible heavy bodies would fall more rapidly than light
ones, and further experiments had led him to conclude that the increase
in velocity is proportional to the _time_ elapsed, and not to the
_distance_ traversed, as he had at first supposed. Less than a century
later Newton had formulated the laws of motion in the same words in
which they are given to-day. These laws of motion, coupled with his
discovery of the law of universal gravitation, had enabled him to
correlate at once the planetary notions which had proved so puzzling to
his predecessors. His success gave a tremendous stimulus to the
development and extension of the fundamental dynamical principles that
he had brought to light, which culminated in the work of the great
French mathematicians, Lagrange and Laplace, a little over a hundred
years ago.
Newton’s laws of motion, it must be remembered, apply only to a
particle, or to those bodies which can be treated as particles in the
problem under consideration. In his “Mécanique Analytique” Lagrange
extended these principles so as to make it possible to treat the motion
of a connected system by a method almost as simple as that contained in
the second law of motion. Instead of three scalar equations for each of
the innumerably large number of particles involved, he showed how to
reduce the ordinary dynamical equations to a number equal to that of the
degrees of freedom of the system. This is made possible by a combination
of d’Alembert’s principle, which eliminates the forces due to the
connections between the particles, and the principle of virtual work,
which confines the number of equations to the number of possible
independent displacements. The aim of Lagrange was to make dynamics into
a branch of analysis, and his success may be inferred from the fact that
not a single diagram or geometrical figure is to be found in his great
work.
_Celestial Mechanics._—Almost simultaneously with the publication of the
“Mécanique Analytique” appeared Laplace’s “Mécanique Celeste.” Laplace’s
avowed aim was to offer a complete solution of the great dynamical
problem involved in the solar system, taking into account, in addition
to the effect of the sun’s gravitational field, those perturbations in
the motion of each planet caused by the approach and recession of its
neighbors. So successful was his analysis of planetary motions that his
contemporaries believed that they were not far from a complete
explanation of the world on mechanical principles. Laplace himself was
undoubtedly convinced that nothing was needed beyond a knowledge of the
masses, positions, and initial velocities of every material particle in
the universe in order to completely predetermine all subsequent motion.
The greatest triumph of these dynamical methods was to come half a
century later. The planet Uranus, discovered in 1781 by the elder
Herschel, was at that time the farthest known planet from the sun. But
the orbit of Uranus was subject to some puzzling variations. After
sifting all the known causes of these disturbances, Leverrier in France
and Adams in England independently reached the conclusion that another
planet still more remote from the sun must be responsible, and computed
its orbit. Leverrier communicated to Galle of Berlin the results of his
calculations, and during the next few days the German astronomer
discovered Neptune within one degree of its predicted position!
[Illustration: H. A. Newton]
We shall mention but one other achievement of the methods of celestial
mechanics. Those visitors of the skies, the comets, which become so
prominent only to fade away and vanish perhaps forever, had interested
astronomers from the earliest times. Soon after the discovery of the law
of gravitation, Newton had worked out a method by which the elements of
a comet’s orbit can be computed from observations of its position. It
was found that the great majority of these bodies move in nearly
parabolic paths and only a few in ellipses. Of the latter the most
prominent is the brilliant comet first observed by Halley in 1681. It
has reappeared regularly at intervals of seventy-six years; the last
appearance in the spring of 1910 is no doubt well remembered by the
reader. Kant had considered comets to be formed by condensing solar
nebulæ, whereas Laplace had maintained that they originate in matter
which is scattered throughout stellar space and has no connection with
the solar system. A study of the distribution of inclinations of comet
orbits by H. A. Newton (=16=, 165, 1878) of New Haven substantiated
Laplace’s hypothesis, and led to the conclusion that the periodic comets
have been captured by the attraction of those planets near to which they
have passed. Of these comets a number have comparatively short periods,
and are found to have orbits which are in general only slightly inclined
to those of the planets, and are traversed in the same direction.
Moreover, the fact that the orbit of each of these comets comes very
close to that of Jupiter made it seem probable that they have been
attached to the solar system by the attraction of this planet. Further
confirmation of this hypothesis was furnished by H. A. Newton’s (=42=,
183 and 482, 1891) explanation of the small inclination of their orbits
and the scarcity of retrograde motions among them.
In 1833 occurred one of the greatest meteoric showers of history.
Olmstead (=26=, 132, 1834) and Twining (=26=, 320, 1834) of New Haven
noticed that these shooting stars traverse parallel paths, and were the
first to suggest that they must be moving in swarms in a permanent
orbit. From an examination of all accessible records, H. A. Newton
(=37=, 377, 1864; =38=, 53, 1864) was able to show that meteoric showers
are common in November, and of particular intensity at intervals of 33
or 34 years. He confidently predicted a great shower for Nov. 13th,
1866, which not only actually occurred but was followed by another a
year later, showing that the meteoric swarm extended so far as to
require two years to cross the earth’s orbit. H. A. Newton (=36=, 1,
1888) in America and Adams in England took up the study of meteoric
orbits with great interest, and the former concluded that these orbits
are in every sense similar to those of the periodic comets, implying
that a swarm of meteors originates in the disintegration of a comet. In
fact Schiaparelli actually identified the orbit of the Perseids, or
August meteors, with Tuttle’s comet of 1862, and shortly after the orbit
of the Leonids, or November meteors, was found to be the same as that of
Tempel’s comet.
_Electromagnetism._—During the eighteenth century much interest had been
manifested in the study of electrostatics and magnetism. Du Fay,
Cavendish, Michell and Coulomb abroad and Franklin in America had
subjected to experimental investigation many of the phenomena of one or
both of these sciences, and in the early years of the nineteenth century
Poisson developed to a remarkable extent the analytical consequences of
the law of force which experiment had revealed. Both Laplace and he made
much use of the function to which Green gave the name “potential” in
1828, and which is such a powerful aid in solving problems involving
magnetism or electricity at rest.
Meantime electric currents had been brought under the hand of the
experimenter by the discoveries of Galvani and Volta. Large numbers of
cells were connected in series, and interest seemed to lie largely in
producing brilliant sparks or fusing metals by means of a heavy current.
Hare (=3=, 105, 1821) of the University of Pennsylvania constructed a
battery consisting of two troughs of forty cells each, so arranged that
the coppers and zincs can be lowered simultaneously into the acid and
large currents obtained before polarization has a chance to interfere.
This “deflagrator” was used to ignite charcoal in the circuit, or melt
fine wires, and was for some time the most powerful arrangement of its
kind. That “galvanism” is something quite different from static
electricity was the opinion of many investigators; Hare considered the
heat developed to be the distinguishing mark of the electric current. He
says: “It is admitted that the action of the galvanic fluid is upon or
between atoms; while mechanical electricity when uncoerced, acts only
upon masses. This difference has not been explained unless by my
hypothesis, in which caloric, of which the influence is only exerted
between atoms, is supposed to be a principal agent in galvanism.”
Questioning minds were beginning to suspect that there must be some
connection between electricity and magnetism. For lightning had been
known to make magnets of steel knives and forks, and Franklin had
magnetized a sewing needle by the discharge from a Leyden jar. Finally
Oersted of Copenhagen undertook systematic investigation of the effect
of electricity on the magnetic needle. His researches were without
result until during the course of a series of lectures on “Electricity,
Galvanism, and Magnetism” delivered during the winter of 1819–20 it
occurred to him to investigate the action of an electric current on a
magnetic needle. At first he placed the wire bearing the current at
right angles to the needle, with, of course, no result; then it occurred
to him to place it parallel. A deflection was observed, for to his
surprise the needle insisted on turning until perpendicular to the wire.
Oersted’s discovery that an electric current exerts a couple on a
magnetic needle was followed a few months later by Ampère’s
demonstration before the French Academy that two currents flowing in the
same direction attract each other, while two in opposite directions
repel. The story goes that a critic attempted to belittle this discovery
by remarking that as it was known that two currents act on one and the
same magnet, it was obvious that they would act upon each other.
Whereupon Arago arose to defend his friend. Drawing two keys out of his
pocket he said, “Each of these keys attracts a magnet; do you believe
that they therefore attract each other?”
A few years later Ampère showed how to express quantitatively the force
between current elements, and indeed developed to a considerable degree
the equivalence between a closed circuit carrying a current and a
magnetic shell. So convincing was his analysis and so thorough his
discussion of the subject, that Maxwell said of this memoir half a
century later, “The whole, theory and experiment, seems as if it had
leaped, full grown and full armed, from the brain of the ‘Newton of
electricity.’ It is perfect in form and unassailable in accuracy; and it
is summed up in a formula from which all the phenomena may be deduced,
and which must always remain the cardinal formula of electrodynamics.”
Shortly afterwards the dependence of a current on the conductivity of
the wire used and the grouping of cells employed, was made clear by the
work of Ohm. Many of his results were obtained independently by Joseph
Henry (=19=, 400, 1831) of the Albany Academy, who described in 1831 a
powerful electromagnet in which a great many coils of wire insulated
with silk were wound around an iron core and connected in parallel with
a single cell. He remarks in this paper that with long wires, as in the
telegraph, many cells arranged in series should be used, whereas for
several short wires connected in parallel a single cell with large
plates is more efficient.
_Current Induction._—Impressed by the fact that electric charges have
the power of inducing other charges on neighboring conductors without
coming into contact with them, Faraday was engaged in investigating the
possibility of an analogous phenomenon in the case of electric currents.
His idea at first seems to have been that a current should induce
another current in any closed conducting circuit which happens to be in
its vicinity. Experiment readily showed the falsity of this conception,
but a brief deflection of the galvanometer in the secondary circuit was
noticed at the instant of making and breaking the current in the
primary. Further experiments showed that thrusting a permanent steel
magnet into a coil connected to a galvanometer caused the needle to
deflect. In fact Faraday’s report to the Royal Society on November 24th,
1831, contains a complete account of all experimental methods available
for inducing a current in a closed circuit.
While Faraday is entitled to credit for the discovery of current
induction by virtue of the priority of his publication, it must not pass
unnoticed that Henry obtained many of the same experimental results
independently and some even earlier. Henry was at this time instructor
in mathematics at the Albany Academy, and seven hours of teaching a day
made it well nigh impossible to carry on original research except during
the vacation month of August. As early as the summer of 1830 he had
wound 30 feet of copper wire around the armature of a horseshoe
electromagnet and connected it to a galvanometer. When the magnet was
excited, a momentary deflection was observed. “I was, however, much
surprised,” he says, “to see the needle suddenly deflected from a state
of rest to about 20° to the east, or in a contrary direction, when the
battery was withdrawn from the acid, and again deflected to the west
when it was re-immersed.” In addition a deflection was obtained by
detaching the armature from the magnet, or by bringing it again into
contact. Had the results of these experiments been published promptly,
America would have been entitled to credit for the most important
discovery of the greatest of England’s many great experimenters. But
Henry desired first to repeat his experiments on a larger scale, and
while new magnets were being constructed, the news of Faraday’s
discovery arrived. This occasioned hasty publication of the work already
done in an appendix to volume =22=, 1832, of the Journal.
At almost the same time Henry made another important discovery and this
time he was anticipated by no other investigator in making public his
results. In the paper already referred to be describes the phenomenon
known to-day as self-induction. “When a small battery is moderately
excited by diluted acid and its poles, which must be terminated by cups
of mercury, are connected by a copper wire not more than a foot in
length, no spark is perceived when the connection is either formed or
broken; but if a wire thirty or forty feet long be used, instead of the
short wire, though no spark will be perceptible when the connection is
made, yet when it is broken by drawing one end of the wire from its cup
of mercury a vivid spark is produced.... The effect appears somewhat
increased by coiling the wire into a helix; it seems to depend in some
measure on the length and thickness of the wire; I can account for these
phenomena only by supposing the long wire to become charged with
electricity which by its reaction on itself projects a spark when the
connection is broken.”
Soon after, Henry went to Princeton and there continued his experiments
in electromagnetism. No difficulty was experienced in inducing currents
of the third, fourth and fifth orders by using the first secondary as
primary for yet another secondary circuit, and so on (=38=, 209, 1840).
The directions of these currents of higher orders when the primary is
made or broken proved puzzling at first, but were satisfactorily
explained a year later (=41=, 117, 1841). In addition induced currents
were obtained from a Leyden jar discharge. Faraday failed to find any
screening effect of a conducting cylinder placed around the primary and
inside the secondary. Henry examined the matter, and found that the
screening effect exists only when the induced current is due to a make
or break of the primary circuit, and not when it is caused by motion of
the primary.
Henry’s work was mainly descriptive; it remained for Faraday to develop
a theory to account for the phenomena discovered and to prepare the way
for quantitative formulation of the laws of current induction. This he
did in his representation of a magnetic field by means of lines of
force; a conception which he found afterwards to be equally valuable
when applied to electrostatic problems. Every magnet and every current
gives rise to these closed curves; in the case of a magnet they thread
it from south pole to north, while a straight wire bearing a current is
surrounded by concentric rings. The connection between lines of force
and the induction of currents is contained in the rule that a current is
induced in a closed circuit only when a change takes place in the number
of lines of force passing through it. Furthermore the dependence of the
current strength on the conductivity of the wire employed has led to
recognition of the fact that it is the electromotive force and not the
current itself which is conditioned by the change in magnetic flux.
Great interest was attached to the utilization of the newly discovered
forces of electromagnetism. In 1831 Henry (=20=, 340, 1831) described a
reciprocating engine depending on magnetic attraction and repulsion, and
C. G. Page (=33=, 118, 1838; =49=, 131, 1845) devised many others. The
latter’s most important work, however, was the invention of the
Ruhmkorff coil. In 1836 (=31=, 137, 1837) he found the strongest shocks
to be obtained, from a secondary coil of many windings forming a
continuation of a primary of half the number of turns. His perfection of
the self-acting circuit breaker (=35=, 252, 1839) widened the usefulness
of the induction coil, and his substitution of a bundle of iron wires
for a solid iron core (=34=, 163, 1838) greatly increased its
efficiency.
_Conservation of Energy._—Perhaps the most important advance of the
nineteenth century has been the establishment of the principle of
conservation of energy. Despite the fact that the “principe de la
conservation des force vives” had been recognized by the French
mathematicians of the early part of the century, the application of this
principle even to purely mechanical problems was contested by some
scientists. Through the early numbers of the Journal runs a lively
controversy as to whether there is not a loss of power involved in
imparting momentum to the reciprocating parts of a steam engine only to
check the motion later on in the stroke. Finally Isaac Doolittle (=14=,
60, 1828), of the Bennington Iron Works, ends the discussion by the
pertinent remark: “If there be, as is contended by one of your
correspondents, a loss of more than one third of the power, in
transforming an alternating rectilinear movement into a continuous
circular one by means of a crank, I should like to be informed what
would be the effect if the proposition were reversed, as in the case of
the common saw mill, and in many other instances in practical
mechanics.”
A realization of the equivalence of heat and mechanical work did not
come until the middle of the century, in spite of the conclusive
experiments of the American Count Rumford and the English Davy before
the year 1800. So firmly enthroned was the caloric theory, according to
which heat is an indestructible fluid, that evidence against it was
given scant consideration. In fact the success of the analytical method
introduced by Fourier in 1822 for the solution of problems in conduction
of heat only added to the difficulties of the adherents of the kinetic
theory. But recognition of heat as a form of energy was on the way, and
when it came it made its appearance almost simultaneously in half a
dozen different places. Perhaps Robert Mayer of Heilbronn was the first
to state explicitly the new principle. His paper “On the Forces of
Inorganic Nature” was refused publication in Poggendorff’s Annalen, but
fared better at the hands of another editor. During the next few years
Joule determined the mechanical equivalent of heat experimentally by a
number of different methods, some of which had already been devised by
Carnot. Of those he used, the most familiar consists in churning up a
measured mass of water by means of paddles actuated by falling weights
and calculating the heat developed from the rise in temperature.
However, the work of the young Manchester brewer received little
attention from the members of the British Association before whom it was
reported until Kelvin showed them its significance and attracted their
interest to it. Meanwhile Helmholtz had completed a very thorough
disquisition on the conservation of energy not only in dynamics and heat
but in other departments of physics as well. His paper on “Die Erhaltung
der Kraft” was frowned upon by the members of the Physical Society of
Berlin before whom he read it, and received the same treatment as
Mayer’s from the editor of Poggendorff’s Annalen. Helmholtz’s “Kraft,”
like the “vis viva” of other writers, is the quantity which Young had
already christened energy. Not many years elapsed, however, until the
convictions of Mayer, Joule, Kelvin and Helmholtz became the most
clearly recognized of all physical principles. As early as 1850 Jeremiah
Day (=10=, 174, 1850), late president of Yale College, admitted the
improbability of constructing a machine capable of perpetual motion,
even though the “imponderable agents” of electricity, galvanism and
magnetism be utilized.
_Thermodynamics._—The importance of the principle of conservation of
energy lies in the fact that it unites under one rule such diverse
phenomena as gravitation, electromagnetism, heat and chemical action.
Another principle as universal in its scope, although depending upon the
coarseness of human observations for its validity rather than upon the
immutable laws of nature, was foreshadowed even before the first law of
thermodynamics, or principle of conservation of energy, was clearly
recognized. This second law was the consequence of efforts to improve
the efficiency of heat engines. In 1824 Carnot introduced the conception
of cyclic operations into the theory of such engines. Assuming the
impossibility of perpetual motion, he showed that no engine can have an
efficiency greater than that of a reversible engine. Finally Clausius
expressed concisely the principle toward which Carnot’s work had been
leading, when he asserted that “it is impossible for a self-acting
machine, unaided by any external agency, to convey heat from one body to
another at a higher temperature.” Kelvin’s formulation of the same law
states that “it is impossible, by means of inanimate material agency, to
derive mechanical effect from any portion of matter by cooling it below
the temperature of the coldest of the surrounding objects.”
The consequences of the second law were rapidly developed by Kelvin,
Clausius, Rankine, Barnard (=16=, 218, 1853, _et seq._) and others.
Kelvin introduced the thermodynamic scale of temperature, which he
showed to be independent of such properties of matter as condition the
size of the degree indicated by the mercury thermometer. This scale,
which is equivalent to that of the ideal gas thermometer, was used
subsequently by Rowland in his exhaustive determination of the
mechanical equivalent of heat by an improved form of Joule’s method. He
found different values for different ranges in temperature, showing that
the specific heat of water is by no means constant. Since then
electrical methods of measuring this important quantity have been used
to confirm the results of purely mechanical determinations.
The definition of a new quantity, entropy, was found necessary for a
mathematical formulation of the second law of thermodynamics. This
quantity, which acts as a measure of the unavailability of heat energy,
was given a new significance when Boltzmann showed its connection with
the probability of the thermodynamic state of the substance under
consideration. If two bodies have widely different temperatures, a large
amount of the heat energy of the system is available for conversion into
mechanical work. From the macroscopic point of view this is expressed by
saying that the entropy is small, or if the motions of the individual
molecules are taken into account, the probability of the state is low.
The interpretation of entropy as the logarithm of the thermodynamic
probability has thrown much light on the meaning of this rather abstruse
quantity. Gibbs’s “Elementary Principles in Statistical Mechanics”
treats in detail the fundamental assumptions involved in this point of
view, its limitations and its consequences. In his “Equilibrium of
Heterogeneous Substances”[154] he had already extended the principle of
thermal equilibrium to include substances which are no longer
homogeneous. The value of the chemical potential he introduced
determines whether one phase is to gain at the expense of another or
lose to it. It is unfortunate that the analytical rigor and austerity of
his reasoning combined with lack of mathematical training on the part of
the average chemist, delayed true appreciation of his work and full
utilization of the new field which he opened up.
_Liquefaction of Gases._—Meanwhile the problem of liquefying gases was
attracting much attention on the part of experimental physicists.
Faraday had succeeded in making liquid a number of substances which had
hitherto been known only in the gaseous state. His method consists in
evolving the gas from chemicals placed in one end of a bent tube, the
other end of which is immersed in a freezing mixture. The high pressure
caused by the production of the gas combined with the low temperature is
sufficient to bring about liquefaction in many cases. Failure with other
more permanent gases was unexplained until the researches of Andrews in
1863 showed that no amount of pressure will produce liquefaction unless
the temperature is below a certain critical value. The method of
reducing the temperature in use to-day depends on a fact discovered by
Kelvin and Joule in connection with the free expansion of a gas. These
investigators allowed the gas to escape through a porous plug from a
chamber in which the pressure was relatively high. With the single
exception of hydrogen, the effect of the sudden expansion is to cool the
gas, and even with it cooling is found to take place after the
temperature has been made sufficiently low. By this method all known
gases have been liquefied. Helium, with a boiling point of –269°C, or
only 4°C. above the absolute zero, was the last to be made a liquid,
finally yielding to the efforts of Kammerlingh Onnes in 1907. This
investigator[155] finds that at temperatures near the absolute zero the
electrical conductivity of certain substances undergoes a profound
modification. For example, a coil of lead shows a superconductivity so
great that a current once started in it persists for days after the
electromotive force has ceased to act.
_Electrodynamics._—Faraday’s representation of electric and magnetic
fields by lines of force had been of great value in predicting the
results of experiments in electromagnetism. But a more mathematical
formulation of the laws governing these phenomena was needed in order to
make possible quantitative development of the theory. This was supplied
by Maxwell in his epoch-making treatise on “Electricity and Magnetism.”
Starting with electrostatics and magnetism, he gives a complete account
of the mathematical methods which had been devised for the solution of
problems in these branches of the subject, and then turning to Ampère’s
work he shows how the Lagrangian equations of motion lead to Faraday’s
law if the single assumption is made that the magnetic energy of the
field is kinetic. In the treatment of open circuits Maxwell’s intuition
led to a great advance, the introduction of the displacement current.
Consider a charged condenser, the plates of which are suddenly connected
by a wire. A current will flow through the wire from the positively
charged plate to the negative, but in the gap between the two plates the
conduction current is missing. So convinced was Maxwell that currents
must always flow in _closed_ circuits, that he postulated an electrical
displacement in the medium between the plates of a charged condenser,
which disappears when the condenser is short-circuited. Thus even in the
so-called open circuit the current flows along a closed path.
Maxwell’s theory of the electromagnetic field is based essentially on
Faraday’s representation by lines of force of the strains and stresses
of a universal medium. So it is not surprising that he was led to a
consideration of the propagation of waves through this medium. The
introduction of the displacement current made the form of the
electrodynamic equations such as to yield a typical wave equation for
space free from electrical charges and currents. Moreover, the
disturbance was found to be transverse, and its velocity turned out to
be _identical with that of light_. The conclusion was irresistible. That
light could consist of anything but electromagnetic waves of extremely
short length was inconceivable. In fact so certain was Maxwell of this
deduction from theory that he felt it altogether unnecessary to resort
to the test of experiment. For the electromagnetic theory explained so
many of the details which had been revealed by experiments in light,
that no doubt of its validity could be entertained. Even dispersion
received ready elucidation on the assumption that the dispersing medium
is made up of vibrators having a natural period comparable with that of
the light passing through it.
[Illustration: James Clerk Maxwell]
Maxwell’s book was published in 1873. Fifteen years later, Hertz,[156]
at the instigation of Helmholtz, succeeded in detecting experimentally
the electromagnetic waves predicted by Maxwell’s theory. His oscillator
consisted of two sheets of metal in the same plane, to each of which was
attached a short wire terminating in a knob. The knobs were placed
within a short distance of each other, and connected to the terminals of
an induction coil. By reflection standing waves were formed, and the
positions of nodes and loops determined by a detector composed of a
movable loop of wire containing an air gap. Thus the wave length was
measured. Hertz calculated the frequency of his radiator from its
dimensions, and then computed the velocity of the disturbance. In spite
of an error in his calculations, later pointed out by Poincaré, he
obtained very nearly the velocity of light for waves traveling through
air, but a velocity considerably smaller for those propagated along
wires. Subsequent work by Lecher, Sarasin and de la Rive, and Trowbridge
and Duane (=49=, 297, 1895; =50=, 104, 1895) cleared up this
discrepancy, and showed the velocity to be in both cases identical with
that of light. The last-named investigators increased the size of the
oscillator until it was possible to measure the frequency by
photographing the spark in the secondary with a rotating mirror. The
positions of nodes and loops were obtained by means of a bolometer after
the secondary had been tuned to resonance with the vibrator. The
velocity thus found for electromagnetic waves along wires is within
one-tenth of one percent of the accepted value of the velocity of light.
Hertz’s later experiments showed that waves in air suffer refraction and
diffraction, and he succeeded in polarizing the radiation by passing it
through a grating constructed of parallel metallic wires.
In order to satisfy the law of action and reaction, it is found
necessary to attribute a quasi-momentum to electromagnetic waves. When a
train of such waves is absorbed, their momentum is transferred to the
absorbing body, while if they are reflected an impulse twice as great is
imparted. This consequence of theory, foreseen by Maxwell and developed
in detail by Poynting, Abraham and Larmor, has been verified by the
experiments of Lebedew, and Nichols and Hull.[157] The latter used a
delicate torsion balance from which was suspended a couple of silvered
glass vanes. In order to eliminate the effect of impulses imparted by
the molecules of the residual gas, such as Crookes had observed in his
radiometer, readings were made at many different pressures and the
ballistic rather than the static deflection recorded. After the pressure
produced by light from a carbon arc had been measured, the intensity of
the radiation was determined with a bolometer. Preliminary experiments
indicated the existence of a pressure of the order expected, and later
more careful measurements showed good quantitative agreement with
theory. This pressure had already found an important application in
Lebedew’s explanation of the solar repulsion of comet’s tails. These
tails are made up of enormous swarms of very minute particles, and as
the comet swings around the sun they suffer a repulsion due to the
pressure of the intense solar radiation which counteracts the sun’s
gravitational attraction. Hence the tail, instead of following after the
comet in its orbit, points in a direction away from the sun.
Some uncertainty existed as to whether a convection current produces a
magnetic field. A compass needle is deflected by a current from a
Daniell cell; is the same effect obtained when a conductor is charged
electrostatically and then whirled around the needle by means of an
insulating handle? The experimental difficulties involved in settling
this question are realized when the enormous difference between the
electrostatic and electromagnetic units of current is taken into
consideration. For a sphere one centimeter in radius, charged to a
potential of 20,000 volts, and revolving in a circle sixty times a
second, constitutes a current of little over a millionth of an ampere.
This problem was undertaken by Rowland (=15=, 30, 1878) in Helmholtz’s
laboratory at Berlin in 1876. A hard rubber disk coated on both sides
with gold was charged and rotated about a vertical axis at a rate of
sixty revolutions a second. On reversing the sign of the electrification
on the disk, the astatic needle hung above its center showed a
deflection of over five millimeters. The current was calculated in
electrostatic units from the charge on the disk and its rate of motion,
and in electromagnetic units from the magnetic deflection. The ratio of
these two quantities gave fair agreement with its theoretical value, the
velocity of light.
Although the result of this experiment was confirmed by Rowland and
Hutchinson in 1889, Crémieu was convinced by an investigation carried
out at Paris in 1900 that the Rowland effect did not exist. Consequently
further repetition of the experiment was desirable. So the following
year Adams (=12=, 155, 1901) arranged two rings of eight spheres each so
that they could be rotated about their common axis from fifty to sixty
times a second. One set of spheres was connected by brushes to the
positive pole of a battery of 20,000 volts, the other to the negative
pole. The deflection of a nearby magnetometer needle was observed when
the electrification of the two rings was reversed, and from the reading
so obtained the ratio of the electromagnetic to the electrostatic unit
of current computed. This quantity was found to differ from the velocity
of light by only a few percent. This experiment and the even more
exhaustive investigations carried out by Pender, both independently and
in collaboration with Crémieu, finally convinced the scientific world
that a convection current produces the same magnetic field as a
conduction current of the same magnitude.
In discussing the ponderomotive force experienced in a magnetic field by
a conductor through which a current is passing, Maxwell had said, “It
must be carefully remembered, that the mechanical force which urges a
conductor carrying a current across the lines of magnetic force, acts,
not on the electric current, but on the conductor which carries it.”
Hall (=19=, 200, 1880), one of Rowland’s students, questioned this
statement, and determined to put it to the test of experiment. Efforts
to find an increase in the resistance of a wire placed at right angles
to the lines of magnetic force were unsuccessful. So the current was
passed through a moderately broad strip of gold leaf and the effect of
the magnetic field on the equipotential lines investigated. The results
obtained confirmed Hall’s belief that the force exerted by the field
acts on the current itself, and is transmitted through it to the
conductor. Further investigation (=20=, 161, 1880) revealed the same
deflection of equipotential lines in thin strips of other metals,
although the effect was found to be reversed in iron.
During the closing years of the nineteenth century occurred three events
of far reaching importance. The electron was isolated, and its charge
and mass measured by J. J. Thomson in England; X-rays were discovered by
Röntgen in Germany; and the first indications of radioactivity were
found by Becquerel in France. The first two are certainly to be
attributed largely to the great advances which had been made in
obtaining high vacua, and the last two might not have occurred so soon
had it not been for the photographic plate.
_The Electron._—The atomic theory of electricity dates from the time of
Faraday. His experiments on electrolysis showed that each monovalent
atom or radical, whatever its nature, carries the same charge, each
bivalent ion a charge twice as great. Only a lack of knowledge of the
number of atoms in a gram of the dissociated salt prevented him from
calculating the value of the elementary charge. As the discharge of
electricity through gases at low pressures became a subject for
experimental investigation, another line of approach to the study of the
atom of electricity was opened up. As early as the seventies Hittorf and
Goldstein had observed that a shadow is cast by a screen placed in front
of the cathode of a Crookes tube. Varley suggested that the cathode rays
producing the shadow consist of “attenuated particles of matter,
projected from the negative pole by electricity.” The discovery that
these rays are deflected by a magnetic field led English physicists to
the conclusion that they must be composed of charged particles, and the
direction of the deflection was such as to require the charge to be
negative. Hertz contested this view on the ground that his experiments
showed the rays to be unaffected by an electrostatic field, and
suggested that they consist of etherial disturbances. Finally Perrin
succeeded in passing the rays into a metal cylinder which received from
them a negative charge, and Lenard showed how excessively minute these
negatively charged particles must be by actually passing them through a
thin sheet of aluminium in the wall of a vacuum tube, and detecting
their presence in the air outside. Conclusive information as to the
nature of the electron, as it was named by Johnstone Stoney, was
supplied by the classic experiments of J. J. Thomson.[158] First he
showed that Hertz’s failure to find a deflection when a stream of
electrons passes between the plates of a charged condenser was due to
the screening effect of the gaseous ions produced by the discharge. With
a much more highly evacuated tube he found no difficulty in obtaining a
deflection in an electrostatic field. By using crossed electric and
magnetic fields the deflection produced by one was just balanced by that
caused by the other, and from the field strengths employed both the
velocity of the particles and the ratio (_e_)/(_m_) of charge to mass
was calculated. The former was found to be about one-tenth the velocity
of light, but the most startling result of the experiment was that the
same value of (_e_)/(_m_) was obtained no matter what residual gas was
contained in the tube or of what metal the cathode was made.
To calculate _e_ and then _m_ other methods are necessary. C. T. R.
Wilson has shown that in supersaturated air, water drops form easily on
charged molecules, and that negative ions are more effective in causing
condensation than positive ones. By making use of the results of this
research Thomson has been able to measure the elementary charge. For
suppose a stream of negative ions to pass through supersaturated air. A
little drop forms on each charged particle, and the cloud of condensed
vapor settles to the bottom of the vessel. The charge carried and the
mass of water deposited can be measured directly. Stokes’ law for the
rate of fall of a minute particle through a gaseous medium enables the
average size of the drops to be computed from the observed rate of
descent of the cloud. Hence the number of drops formed and the charge
carried by each follows at once. H. A. Wilson improved the method by
noting the effect of an electric field upon the rate of fall of the
charged drops, and subsequent experiments undertaken by Millikan[159]
have been of such a character as to enable him to follow the motion of a
single drop. Instead of water, the latter uses oil drops less than one
ten-thousandth of a centimeter in diameter. A drop, after one or more
electrons have attached themselves to it, is actually _weighed_ in terms
of the charge on its surface by applying an upward electric force just
sufficient to balance the force of gravity. Then its weight is
independently obtained from the density of the oil and the radius of the
drop as determined by the rate of fall when the electric field is
absent. Comparison of these two expressions gives 4·774(10)^{–10}
electrostatic units for the elementary charge. Combining this result
with the value of (_e_)/(_m_) found by Thomson, the mass of the electron
comes out to be about one eighteen-hundredth that of an atom of the
lightest known element, hydrogen.
That the electron is a fundamental constituent of all matter is attested
by the fact that charge and mass are the same regardless of the source
or manner of production. Whether emitted by a heated metal, under the
action of ultra-violet light, from a radioactive substance, by a body
exposed to X-rays, as a result of friction, it is the same negatively
charged particle that constitutes the cathode ray of the discharge tube.
Moreover, it makes its effect felt indirectly in many other phenomena,
and from an investigation of some of these the ratio of charge to mass
can be determined independently. Of such perhaps the most interesting is
the Zeeman effect.
_Spectroscopy._—Early in the nineteenth century Fraunhofer had observed
that the solar spectrum is crossed by a large number of dark lines.
Their presence was unexplained until in 1859 Kirchhoff and Bunsen showed
“that a colored flame, the spectrum of which contains bright sharp
lines, so weakens rays of the color of these lines when they pass
through it, that dark lines appear in place of bright lines as soon as
there is placed behind the flame a light of sufficient intensity, in
which the lines are otherwise absent.” For intra-atomic oscillators must
have the natural frequency of the radiation which they emit, and
consequently resonance will take place when they are exposed to rays of
this frequency coming from an outside source, and selective absorption
ensue. By comparing the bright lines in the spectra of metallic vapors
made luminous by a gas flame with the dark lines in the sun’s spectrum
these investigators showed that many of the common terrestrial elements
exist in the sun. The interest in spectroscopy grew rapidly. The
excellent diffraction gratings made by Rutherfurd were succeeded by the
superior concave gratings of Rowland. In 1877 Draper (=14=, 89, 1877)
announced the discovery of the bright lines of oxygen in the solar
spectrum, but his interpretation of his photographs has not been
corroborated by the work of later investigators. Langley (=11=, 401,
1901), by the aid of his newly invented bolometer, succeeded in
detecting the emission of energy from the sun in the infra-red in
amounts far exceeding that contained in the visible spectrum. In 1842
Doppler drew attention to the fact that motion of the source should
cause a displacement of the spectral lines, the shift being to the blue
if the light is approaching and to the red if it is receding, and a few
years later Fizeau suggested the application of Doppler’s principle to
the measurement of the velocity of a star moving in the line of sight.
Thus the spectroscope has been able to supply one of the deficiencies of
the telescope, and the two together are sufficient to reveal all
components of stellar motion. When spectra formed by light from the
sun’s limb and from its center are compared, the same effect reveals the
rotation of the sun about its axis. (C. S. Hastings, =5=, 369, 1873; C.
A. Young, =12=, 321, 1876.)
_Further Evidence of the Electron._—In 1845 Faraday discovered a
rotation of the plane of polarization when light passes in the direction
of the lines of force through a piece of glass placed between the poles
of an electromagnet. Examination of the spectrum from a glowing vapor
situated between the poles of a magnet, however, failed to reveal any
effect of the field. The latter problem was attacked anew by Zeeman[160]
in 1896, and with the aid of the improved appliances of modern science
he succeeded in detecting a broadening of the lines. Later experiments
with more powerful apparatus resolved these broadening lines into
several components.
Lorentz[161] showed at once how the electron theory furnishes an
explanation of the Zeeman effect. He found that when the source is
viewed at right angles to the lines of magnetic force, a spectral line
should be split into three components. Of these he predicted that the
middle, or undisplaced component, would be found to be polarized at
right angles to the direction of the field, and the other components
parallel to the field. When the light proceeds from the source in a
direction parallel to the magnetic lines of force, two components only
should be formed, and these should be circularly polarized in opposite
senses. Moreover, from the separation of the components can be
calculated the ratio of charge to mass of the electronic vibrator which
is responsible for the emission of radiant energy. Zeeman’s experiments
confirmed Lorentz’s theory in every detail, and yielded a value of
(_e_)/(_m_) in substantial agreement with that obtained for cathode
rays. Subsequent research, however, has shown that in many cases more
components are found than the elementary theory calls for. Hale has
detected the Zeeman effect in light from sun spots, proving that these
blemishes on the sun’s face are vortices caused by whirling swarms of
electrified particles. Recently Stark and Lo Surdo have found a similar
splitting up of lines in the spectrum formed by light from canal rays
(rays of positively charged particles) passing through an intense
electric field. This phenomenon has as yet received no adequate
explanation.
On discovering that an electric current is capable of producing a
magnetic field, Ampère had suggested that the magnetic properties of
such substances as iron might be explained on the assumption of
molecular currents. The electron theory considers these currents to be
due to the revolution, inside the atom, of negatively charged particles
about an attracting nucleus. It occurred to Richardson that this motion
should give the atom the properties of a gyrostat. Hence if an iron bar
be rotated about its axis, the atoms should orient themselves so as to
make their axes more nearly parallel to the axis of rotation. Thus its
rotation should cause the bar to become a magnet. Barnett[162] has
tested this hypothesis, and has found the effect Richardson had
predicted. From the strength of the magnetization produced, the value of
(_e_)/(_m_) can be computed. Barnett finds a value somewhat smaller than
that for cathode rays, but of the right order of magnitude and sign.
Einstein and De Haas have detected the inverse of this effect, i. e.,
the rotation of an iron rod when it is suddenly magnetized.
_X-Rays._—In 1895, on developing a plate which had been lying near a
vacuum tube, Röntgen[163] was surprised to find distinct markings on it.
As the plate had never been exposed to light, it was necessary to
suppose the effect to be due to some new and unknown type of radiation.
Further investigation showed that this radiation originates at the
points where cathode rays impinge on the glass walls of the tube.
Besides being able to pass with ease through all but the most dense
material objects X-rays were found to have the power of ionizing gases
through which they pass and ejecting electrons from metal surfaces
against which they strike. The points at which these electrons are
produced are in turn the sources of secondary X-rays whose properties
are characteristic of the metal from which they come.
Röntgen’s discovery excited intense interest among laymen as well as in
scientific circles. Of the many X-ray photographs taken, those of Wright
(=1=, 235, 1896) of Yale were the first to be produced in this country.
His experiments were made immediately on receipt of the news of
Röntgen’s research, and resulted in the publication of a number of
photographs showing the translucency for these rays of paper, wood, and
even aluminium.
As X-rays are undeviated by electric or magnetic fields, Schuster, and
later Wiechert and Stokes, suggested that they might be electromagnetic
waves of the same nature as light, but much shorter and less regular.
The great objection to this hypothesis was the failure either to refract
or diffract these rays. In fact Bragg contended that they were not
etherial disturbances at all, but consisted of neutral particles moving
with very high velocities. Finally Laue[164] demonstrated their
undulatory nature by showing that diffraction took place under proper
conditions. Just as the distance between adjacent lines of a grating
must be comparable to the wave length of light for a spectrum to be
formed, a periodic structure with a grating space of their very much
shorter wave length is necessary to diffract X-rays. Such a structure is
altogether too fine to be made by human tools. Nature, however, has
already prepared it for man’s use. The distance between the atoms of a
crystal is just right to make it an excellent X-ray grating, and Laue
had no difficulty in obtaining diffraction patterns when Röntgen rays
were passed through a block of zincblende. The distance between adjacent
atoms of this cubic crystal can be computed at once from its density and
molecular weight, and then the wave length of the radiation calculated
from the deviation suffered. In this way X-rays are found to have a
length less than one thousandth as great as visible light. Further study
of this phenomenon, particularly by the two Braggs, father and son, has
revealed many of the structural details of more complicated crystals.
The most significant investigation in the field opened up by Laue’s
discovery is that undertaken by Moseley[165] only a couple of years
before he lost his life in the trenches at Gallipoli. Using many
different metals as anticathodes in a vacuum tube, he measured the
frequencies of the characteristic rays emitted. He found that if the
elements are arranged in order of increasing atomic weight, the square
roots of the characteristic frequencies form an arithmetical
progression. If to each element is assigned an integer, beginning with
one for hydrogen, two for helium, and so on, the square root of the
frequency of the characteristic radiation is found to be proportional to
this atomic number. Even though Uhler has shown recently that over wide
ranges Moseley’s law does not hold within the limits of experimental
error, there is undoubtedly much significance to be attached to this
simple relation.
_Radioactivity._—The year following the discovery of X-rays, Becquerel
found that a photographic plate is similarly affected by radiations from
uranium salts. Two years later the Curies separated from pitchblende the
very active elements polonium and radium. Passage of the rays from these
substances through electric and magnetic fields revealed the existence
of three types. The alpha rays have been shown by Rutherford and his
co-workers to be positively charged helium atoms; the beta rays are very
rapidly moving electrons; and the gamma rays are electromagnetic pulses
of the same nature as X-rays but somewhat shorter. In 1902 Rutherford
and Soddy advanced the theory of atomic disintegration, according to
which the emission of a ray is an indication of the breaking down of the
atom to a simpler form. Thus in the radioactive substances there is
going on before our eyes a continual transformation of one element into
another, a change, by the way, which appears to be in no slightest
degree either hastened or delayed by changes in temperature (H. L.
Bronson, =20=, 60, 1905) or external electrical condition of the
radioactive element. Uranium is the progenitor of a long line of
descendants, of which radium was supposed for some time to be the first
member. Boltwood (=25=, 365, 1908) of Yale, however, showed that the
slow growth of radium in uranium solutions is incompatible with this
assumption, and soon isolated an intermediate product which he named
ionium. Radium itself disintegrates into a gas known as radium
emanation, which in turn gives rise to a succession of other products.
Analyses by Boltwood (=23=, 77, 1907) of radioactive minerals from the
same locality show such a constant ratio between the amounts of uranium
and lead present that it is natural to conclude that lead is the end
product of the series. This hypothesis is confirmed by the fact that the
oldest rocks show relatively the greatest amounts of this element.
In addition to the Ionium-Radium series two others have been discovered.
Of these Boltwood’s (=25=, 269, 1908) investigations seem to indicate
that the one which starts with actinium is a collateral branch of the
radium series and comes from the same parent uranium. The other begins
with thorium and comprises ten members. As yet the end products of the
actinium and thorium series have not been identified, although there is
some reason for believing that an isotope of lead may be the final
member of the latter.
As the amount of a radioactive element which disintegrates in a given
time is proportional to the total mass present, an infinite time would
be required for the substance to be completely transformed. Hence the
life of such an element is measured by the half value period, or time
taken for half the initial mass to disintegrate. This time varies widely
for different radioactive substances, ranging from a small fraction of a
second for actinium A to five billion years for uranium. Boltwood’s
(=25=, 493, 1908) original determination of the life of radium from the
rate of its growth in a solution containing ionium gave 2000 years as
its result, although recent measurements by Miss Gleditsch (=41=, 112,
1916) agree more closely with the value 1760 years obtained by
Rutherford and Geiger from the number of alpha particles emitted.
Under the action of X-rays or the radiations from radioactive
substances, gases acquire a conductivity which has been attributed by
Thomson and Rutherford to the formation of ions. Zeleny has found that
ions of opposite sign have somewhat different mobilities in an electric
field, and experiments of Wellisch (=39=, 583, 1915) show that at low
pressures some of the negative ions are electrons. T. S. Taylor (=26=,
169, 1908 _et seq._) and Duane (=26=, 464, 1908) have investigated the
ionization produced by alpha particles, and Bumstead (=32=, 403, 1911
_et seq._) has studied the emission of electrons from metals which are
bombarded by these rays. The investigations of Franck and Hertz, and
McLennan and Henderson, show a significant relation between the ionizing
potential (energy which must be possessed by an electron in order to
produce an ion on colliding with an atom) and a quantity, to be
considered later in more detail, which has been introduced by Planck
into the theory of radiation.
_Methods of Science._—Scientific progress seems to follow a more or less
clearly defined path. Experimentation brings to light the hidden
processes of nature, and hypotheses are advanced to correlate the facts
discovered. As more and more phenomena are found to fit into the same
scheme, the hypotheses at first proposed tentatively, although often
only after extensive alterations, become firmly established as theories.
Finally there may appear a fundamental clash between two theories, each
of which in its respective domain seems to represent the only possible
manner in which a large group of phenomena can be correlated. The maze
becomes more perplexing at every step. At last a genius appears on the
scene, approaches the problem from a new and unsuspected point of view,
and the paradox vanishes. Such changes in point of view are the
milestones which mark the progress of science. That science is stagnant
whose only function is to collect, classify and correlate vast stores of
experimental data. The sign of vitality is the existence of clearly
defined and fundamental problems any possible solution of which seems
irreconcilable with the most basic truths of the science in question.
The greater the paradox grows, the more certain the advent of a new
point of view which will bring one step nearer the comprehensive picture
of nature which is the goal of natural philosophy.
_The Ether._—From the earliest times philosophers have been attracted by
the possibility of explaining physical phenomena in terms of an
all-pervading medium. So strong had this tendency become by the middle
of the nineteenth century that the English school of physicists were
attributing rigidity, density and nearly all the properties of material
media to the ether. In fact most physicists seemed to have forgotten
that no experiment had ever given _direct_ evidence of the existence of
such a medium. Not until the first decade of the twentieth century was
it realized that the experimental evidence actually pointed in quite the
opposite direction, and that a new point of view was needed in dealing
with those phenomena of light and electromagnetism which had been
previously described in terms of a universal medium. Some account of the
development of the ether theory and of the origin and growth of the
point of view which has its principal exemplification in the principle
of relativity is essential for an understanding of present tendencies in
formulating a philosophic basis for scientific thought.
In the time of Newton and for a century after there was much controversy
between the adherents of two irreconcilable theories of light. Hooke had
suggested that light is a wave motion traveling through a homogeneous
medium which fills all space, and Huygens had shown that the law of
refraction can be deduced at once from this hypothesis if it is assumed
that the velocity of light in a transparent body is less than that in
free ether. However, Newton, impressed by the fact that a ray obtained
by double refraction in Iceland spar differs from a ray of ordinary
light just as a rod of rectangular cross section differs from one of
circular cross section, and seeing no way of explaining this dissymmetry
in terms of a wave motion analogous to longitudinal sound waves, adhered
to the view that light consists of infinitesimal particles shot out from
the luminous body with enormous velocities. So great was his reputation
on account of his discoveries in other fields that this theory of light
held sway among his contemporaries and successors until the labors of
Young and Fresnel at the beginning of the nineteenth century definitely
established the undulatory theory. However, in spite of the fact that a
corpuscular theory of light made the assumption of an ether unnecessary
in so far as the simpler of the observed phenomena are concerned, even
Newton postulated the existence of such a medium, partly in order to
explain the more complicated results of experiments in light, and partly
in order to provide a vehicle for the propagation of gravitational
forces.