Chapter C: E. Dutton, Critical observations on theories of the earth’s (8)

_A New Point of View._—While the dynamical school was still dominant in England, another point of view was developing on the continent. Kirchhoff denied that it was the province of science to provide mechanical explanations of the ether and electrodynamic phenomena such as Kelvin conceived to be necessary in order to make these phenomena intelligible. Kirchhoff’s contention was that the object of science is purely descriptive,—phenomena must be observed, classified, and mutual connections described by the fewest number of differential equations possible. Mach expressed the same idea somewhat more concisely when he asserted that the aim of science is “economy of thought.” For instance, in the time of Newton, planetary motions could be described quite satisfactorily by means of the three laws of Kepler. The motion of falling bodies on the earth’s surface had been described with a fair degree of accuracy by Galileo. The value of Newton’s law of gravitation, however, lay in the fact that this great generalization made it possible to describe these and many other types of motion by a single simple formula, instead of leaving each to be governed by a number of separate and apparently unrelated laws. The importance of such a generalization is measured by the economy of thought which it introduces.

_Electron Theory._—The electron theory was leading to a reversal of Kelvin’s idea that dynamical principles must underlie electrodynamics. Lorentz had shown that a rigorous solution of the electrodynamic equations did away entirely with Maxwell’s displacement current, but made the electromagnetic field at a point in space depend not upon the distribution of charges and currents at the _same_ instant, but at a time earlier sufficient to allow the effect to travel with the velocity of light from the charges and currents producing the field to the point at which the electric and magnetic intensities are to be found. The position of a charge or current element at this earlier time he denoted its “effective position.” The effective distribution, then, is that actually _seen_ by an observer stationed at the point under consideration at the instant for which the intensity of the electromagnetic field is to be determined. This solution of the electrodynamic equations led in turn to rigorous expressions for the electric and magnetic intensities produced by a very small charged particle, such as an electron. Fig. 1 shows the electrostatic field produced by a charged particle at rest. The lines of force spread out radially and uniformly in all directions. In fig. 2 the electron is supposed to have a velocity _v_ horizontally to the right of an amount smaller than, though comparable with, the velocity of light _c_. It is seen that the lines of electric force still diverge radially from the charge, but are crowded in the equatorial plane and spread apart in the polar regions. The dissymmetry grows as the velocity increases until if the velocity of light should be reached the field would be entirely concentrated in a plane at right angles to the direction of motion. Now it may be shown that fig. 2 is obtainable from fig. 1 by _reducing dimensions in the direction of motion in the ratio of_

√(1 − β^2) : 1, where β ≡ _v_/_c_.

For a uniformly convected electric field differs from an electrostatic field only in that the dimensions in the direction of motion are contracted in this particular ratio. Fig. 3 represents the electric field of a charged particle which has a uniform acceleration to the right. Consider Faraday’s analogy between lines of force and stretched elastic bands. The symmetry of the first two figures shows that in neither of these cases would there be a resultant force on the charged particle. But in the third figure it is obvious that a force to the left is exerted on the charge by its own field. Calculation shows this force to be proportional in magnitude to the acceleration. Let it be postulated that the resultant force on a charged particle is always zero. Then if _F_ is the applied force, the force on the particle due to the reaction of its field will be — _m f_, where _f_ stands for the acceleration and _m_ is a positive constant, and we have the fundamental equation of dynamics

_F_ − _m_ _f_ = 0

Hence, instead of admitting Kelvin’s contention that all physical phenomena must be given a mechanical explanation, it would seem more logical to assert that electrodynamics actually underlies mechanics.

Calculation shows the electromagnetic mass _m_ to vary inversely with the radius of the charged particle. Now Thomson’s experiments made it possible to calculate the mass of an electron. Hence its radius can be computed, and is found to be about 2(10)^{–13} part of a centimeter, or one fifty-thousandth part of the radius of the atom. Since numbers so small convey little meaning, consider the following illustration, due, in part, to Kelvin. Imagine a single drop of water to be magnified until it is as large as the earth. The individual atoms would then have the size of baseballs. Now magnify one of these atoms until it is comparable in size with St. Peter’s cathedral at Rome. The electrons within the atom would appear as a few grains of sand scattered about the nave. This separation between the constituent electrons of the atom,—so great in comparison with their dimensions,—explains how alpha particles can be shot by the billion through thin-walled glass tubing without leaving any holes behind or impairing in the slightest degree the high vacuum within the tube. The much smaller high speed beta particles pass through an average of ten thousand atoms without even coming near enough to one of the component electrons to detach it and form an ion.

_Michelson-Morley Experiment._—In 1881 Michelson (=22=, 120, 1881) conceived an ingenious and bold method of measuring the orbital motion of the earth through the luminiferous ether. As the experiment was one involving considerable expense, Bell, the inventor of the telephone receiver, was appealed to successfully for the funds necessary to carry it through. Michelson’s experimental plan was as follows: A beam of light traveling in the direction of the earth’s motion strikes an unsilvered mirror _m_ at an angle of 45°. Part of the light passes through, the rest being reflected at right angles to its original direction. Each ray is returned by a mirror at a distance _l_ from _m_. On meeting again, the ray whose path has been at right angles to the direction of the earth’s motion passes on through the mirror, while the other ray is reflected so as to bring the two in line and form interference fringes. Now consider the effect of the earth’s motion on the paths of the two rays. In fig. 4 the earth is supposed to be moving to the right. The unsilvered mirror _m_ bifurcates a beam of light coming from a source _a_. By the time the ray reflected from _m_ has traveled to the mirror _b_ and back, _m_ will have moved forward to _m’_; a distance 2β_l_, where the small quantity β is the ratio of the earth’s velocity to the velocity of light. Hence the length of the path traversed by this ray is approximately

2_l_(1 + ½β^2).

The other ray will reach the mirror _c_ after the latter has moved forward a distance

β_l_/(1 − β^2)

and on returning find _m_ at _m’_. Hence its path has a length of roughly 2_l_(1 + β^2). The difference in path of the two rays is β^2_l_ and consequently they should be a little out of phase on meeting at _d_. By rotating the apparatus clockwise through 90° the directions of the two rays relative to the earth’s motion are interchanged, and the interference fringes would be expected to shift an amount corresponding to a difference in path of 2β^2_l_. This quantity is of course small,—β^2 is about one one hundred millionth,—but so sensitive are the methods of interferometry that Michelson felt confident that he would be able to detect the earth’s motion through the ether. The apparatus consisted of a table which could be rotated about a vertical axis in much the same way as a spectrometer table, and provided with arms a meter long to carry the mirrors _b_ and _c_. With this length of arm the interference fringes from sodium light should shift by an amount corresponding to four hundredths of a wave length when the table is rotated through a right angle. When the experiment was first performed the apparatus was placed on a stone pier in the Physical Institute at Berlin. So sensitive was the instrument to outside vibrations that even after midnight it was found impossible to get consistent readings. Finally a satisfactory foundation was constructed in the cellar of the Astrophysical observatory at Potsdam. But what was the astonishment of the experimenters to find that the expected shift of the interference fringes did not exist!

The extreme delicacy of the experiment made it desirable to confirm the result by repeating it. This was done by Michelson and Morley (=34=, 333, 1887) in 1887. In place of a revolving table a massive slab of stone floating on mercury was used to carry the apparatus. This slab was kept in constant rotation, the observer following it around. Moreover, the precision of the experiment was greatly increased by reflecting each ray back and forth across the slab a number of times between leaving and returning to the mirror _m_. The accuracy attained was such as to justify Michelson in declaring that if the effect sought actually existed it could not be so great as one-twentieth of its calculated value. In 1905 Morley and Miller[166] repeated the experiment for the second time and succeeded in increasing the sensitiveness of the apparatus to a point such that a motion through the ether of one-tenth of the earth’s orbital velocity could have been detected.

The displacement looked for in the Michelson-Morley experiment is known as a second-order effect in that it depends upon the square of the ratio of the velocity of the earth to that of light. Michelson at first considered that the negative result obtained confirmed a theory proposed by Stokes in which it was assumed that the ether inside and near its surface partakes of the motion of the earth, while that at a distance is practically quiescent. But there are many objections to Stokes’ theory, one of which was brought out by an experiment of Michelson’s (=3=, 475, 1897) in which he attempted by an interference method to detect a difference in the velocity of light at different levels above the earth’s surface. The negative result obtained led him to conclude that if Stokes’ theory were true the earth’s influence on the ether would have to extend to a distance above its surface comparable with its diameter. Meanwhile a more satisfactory explanation was forthcoming. It has been pointed out that a uniformly convected electric field is derivable from an electrostatic field by contracting dimensions in the direction of motion in the ratio

√(1 − β^2) : 1.

Fitzgerald and Lorentz showed independently that if moving matter is distorted in this same way the result obtained by Michelson would be just that to be expected. For then the distance of the mirror _c_ from _m_ would be

l√(1 − β^2)

instead of _l_, and the path of the ray moving parallel to the earth’s orbit

2_l_(1 + ½β^2),

which is just that of the other ray. Of course when the apparatus is rotated through 90°, the distance of this mirror from _m_ assumes its normal value again, and the distance of the other mirror becomes shortened. As all measurement consists in comparing the object to be measured with a standard this contraction could never be detected by experimental methods, for the measuring rod would contract in exactly the same ratio as the body to be measured.

In computing its electromagnetic mass Abraham had assumed the electron to be a uniformly charged rigid sphere which keeps its spherical form no matter how great a velocity it may be given. He found that the mass increases with the speed at very high velocities, becoming infinite as the velocity of light is approached, and that its value depends upon the direction of the applied force. After the Fitzgerald-Lorentz contraction was seen to be necessary in order to explain Michelson’s result, Lorentz calculated the electromagnetic mass of a charged sphere which is deformed into an oblate spheroid when set in motion. For this type of electron too, the mass approaches infinity for velocities as great as that of light, and is different for different directions. If a force is applied in the direction of motion the inertia to be overcome is a little greater than when the force is applied at right angles to this direction. Thus we have to distinguish between longitudinal and transverse masses. But the masses of Lorentz’s electron are not the same functions of its velocity as those of Abraham’s. Kaufmann and after him Bucherer tested experimentally the relation between transverse mass and velocity by observing the deflections produced by electric and magnetic fields in the paths of high speed beta particles. The latter’s work was such an ample confirmation of Lorentz’s formula that it may be considered as proven that a moving electron at least suffers contraction in the direction of motion in the ratio

√(1 − β^2) : 1.

The electromagnetic theory of light had proved so successful when applied to bodies at rest that Lorentz was anxious to extend this theory to the optics of moving media. His problem was to find a group of homogeneous linear transformations that would leave the form of the electrodynamic equations unchanged. The Michelson-Morley experiment had shown that dimensions in the direction of motion must be contracted in the moving system, those at right angles remaining unaltered. But Lorentz soon found that it was also necessary to use a new unit of time in the moving system, and as this time was found to depend upon the _position_ of the point at which it is to be determined, he called it the _local_ time. Lorentz’s transformation is just that of the principle of relativity, but he did not succeed in expressing the electrodynamic equations in terms of the new coördinates and time in exactly the same form as for a system at rest, for the reason that he failed to endow these new units with sufficient reality to justify him in using them when it came to transforming the velocity term involved in an electric current.

_Principle of Relativity._—In 1905 appeared in the Annalen der Physik[167] a paper destined to alter entirely the point of view from which problems in light and electromagnetic theory are to be approached. The author was Albert Einstein, of Berne, Switzerland, a young man of twenty-six who had already made a number of notable contributions to theoretical physics.

The principle of relativity proposed by Einstein was by no means new to students of dynamics. Newton’s first two laws of motion express very clearly the fact that in mechanics all motion is relative. Force is proportional to acceleration, and the relation between the two is the same whether the motion under consideration is referred to fixed axes or to axes moving with a constant velocity. But in connection with the phenomena of light and electromagnetism the case seemed to be quite different. There everything was referred to a fixed ether, and even though Lorentz had found a set of transformations which left the electrodymanic equations practically unchanged, he continued to think in terms of an ether. So physicists were not a little startled when Einstein postulated that no experiment, practical or ideal, could ever distinguish between two systems in such a manner as to warrant the assertion that one of them is at rest and the other in motion. All motion is relative, and the laws governing physical, chemical and biological phenomena are the same in terms of the units of one system as in terms of those of any other.

Einstein next considers some very fundamental questions. What do we mean when we say that two events, one at A and the other at a point B far from A, occur at the same time? Obviously the expression has no significance unless synchronous clocks are stationed at the two points. But how is it to be determined whether or not these two clocks are synchronous? If instantaneous communication could be established between A and B the matter would be simple enough. Since no infinite velocity of transmission is available, however, let a light wave be sent from A to B and returned to A immediately upon its arrival. If the time indicated by the clock at B when the signal is received is half way between that at which it left A and the time at which it arrives on its return, then the two clocks may be considered synchronous. Now if it desired to measure the length of a bar which is moving parallel to the scale with which the measurement is to be made, it is necessary to note the positions of the two ends of the bar at the _same_ instant. So even the measurement of the length of a moving body depends upon the condition of synchronism at different points in space.

The principle of relativity requires that the velocity of light shall be the same in one system as in another relative to which the first is in motion. Hence the definition of synchronism makes it possible to obtain a set of transformations connecting space and time measurement on one system with those on another. This group of transformations is exactly that which Lorentz had found would transform the electrodynamic equations into themselves. But Einstein’s point of view brought out a remarkable reciprocity which Lorentz had missed. If two parallel rods MN and OP are in motion relative to each other in the direction of their lengths, not only does OP appear shortened to an observer at rest with respect to MN, but MN appears shorter than normal in the same ratio to an observer who is moving along with the rod OP.

Einstein’s theory makes the velocity of light the maximum speed with which a signal can be transmitted. This leads to his celebrated addition theorem. Consider three observers A, B and C. Let B be moving relative to A with a velocity of nine-tenths the velocity of light, and C in the same direction with an equal velocity relative to B. In terms of old-fashioned notions of time and space, the velocity of C relative to A would be computed as one and eight-tenths the velocity of light. But the relativity theory gives it as ninety-nine hundredths the velocity of light. For the velocity of light can never be surpassed by that of any material object. This deduction from theory is most strikingly confirmed by the fact that although beta particles have been observed with velocities as high as ninety-nine hundredths that of light, the velocity of light is never quite equalled. It may be remarked in passing that the principle of relativity requires that the masses of all material bodies shall vary with the velocity in the same manner as Lorentz found to be the case for the electromagnetic mass of the deformable electron. In this connection Bumstead (=26=, 498, 1908) has devised an elegant method of deducing the ratio of longitudinal to transverse mass.

The close connection between electrodynamics and the principle of relativity is obvious from the fact that both lead to the same time and space transformations. Furthermore L. Page (=37=, 169, 1914) has shown that the electrodynamic equations can be derived exactly and in their entirety from nothing more than the kinematics of relativity and the assumption that every element of charge is a center of uniformly diverging lines of force. Hence it may safely be asserted that no purely electromagnetic phenomenon can ever come into contradiction with this principle. The simplicity thus introduced into the solution of a certain class of problems is enormous. As an example consider the question as to whether a moving star is retarded by the reaction of its own radiation. This purely electrodynamical problem is of such complexity that attempts to solve it have led to some controversy among mathematical physicists. The principle of relativity tells us without recourse to analysis that no retardation can exist.

Throughout the nineteenth century the ether has played a fundamental part in all important physical theories of light and electromagnetism. But if it is not possible for experiment to detect even the state of motion of the ether, why postulate the existence of such a medium? If it does not possess the most fundamental characteristic of matter, how can it possess such derived properties as density and elasticity,—properties which any conceivable _mechanical_ medium must have in order to transmit transverse vibrations? The relativist does not deny the existence of an ether. To him the question has no more meaning than if he were asked to express an opinion as to the reality of parallels of latitude on the earth’s surface. As a convenient medium of expression in describing certain phenomena the ether has justified much of the use which has been made of it. But to attribute to it a degree of substantiality for which there is no warrant in experiment, is to change it from an aid into an obstacle to the progress of science. From the relativist point of view the distinction is very sharp between those motions of charged particles which are experimentally observable, and such geometrical conventions as electromagnetic fields, or analytical symbols as electric and magnetic intensities. These modes of representation have been and still are of the greatest use and importance, but their value in scientific description must not lead to lack of appreciation of their purely speculative character.

Finally attention must be drawn to the fact that the discoveries of inductive science, embodied in the great generalization we have just been discussing, have led to a more intimate knowledge of the nature of time and space than twenty centuries of introspection on the part of professional philosophers. Minskowski, whose promise of greater achievement was cut off by an untimely death, has shown that four dimensional geometry makes possible the representation with beautiful simplicity of the time and space relationships of this theory. The one time and three space dimensions merge in such a manner as to form a single whole with not a vestige of differentiation between these fundamental quantities. Wilson and Lewis[168] have made this representation familiar to American readers through their admirable translation of Minskowski’s work into the notation of Gibbs’s vector analysis.

Aberration, the Doppler effect, anomalous dispersion, —indeed all known phenomena,—are found to be in accord with the principle of relativity. It must be borne in mind, however, that this principle applies only to systems moving relative to one another in straight lines with constant velocities. That there is something absolute about rotation has been recognized since Foucault performed his famous pendulum experiment in 1851. This experiment (C. S. Lyman, =12=, 251 and 398, 1851) consisted in setting a pendulum composed of a heavy-brass ball suspended by a long wire into oscillation in such a way as to avoid appreciable ellipticity in its motion. Observation of the rate at which the ground rotates relative to the plane of vibration of the pendulum furnished a method of measuring the rotation of the earth about its axis _without reference to celestial bodies_. The gyroscopic compass in use to-day provides yet another terrestrial method of detecting this rotation.

_The Future of Physics._—At times during the history of physics it has seemed as if the fundamental laws of this science had been so completely formulated that nothing remained to future generations beyond the routine of deducing to the full the consequences of these laws, and increasing the precision of the methods used to measure the constants appearing in them. That Laplace held this view has already been pointed out, and Maxwell, in his introductory lecture at the opening of the Cavendish laboratory in 1871, said, “This characteristic of modern experiments—that they consist principally of measurements—is so prominent, that the opinion seems to have gotten abroad that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals.” That he himself did not entertain this view is made evident by a succeeding paragraph. “But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured. It may possibly be true that, in some of those fields of discovery which lie open to such rough observations as can be made without artificial methods, the great explorers of former times have appropriated most of what is valuable, and that the gleanings which remain are sought after rather for their abstruseness than for their intrinsic worth. But the history of science shows that even during that phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers....”

That Maxwell’s forecast of the prospects of his science was no overestimate will be granted by those who have followed the progress of physics during the last twenty years. Yet the work accomplished in the past appears small compared to that which is left to the future. Many of the unsolved problems are matters of fitting together puzzling details, but there is at least one whose solution appears to demand a radical modification in our fundamental physical conceptions. This is the formulation of the laws which govern the motions of electrons and positively charged particles inside the atom.

_Black Radiation._—The significance of the problem was first brought to light through the study of black radiation. By a black body is meant one whose distinguishing characteristic is that it emits and absorbs radiation of all frequencies, and black radiation is that which will exist in thermal equilibrium with such a body. The interest of this type of radiation lies in the fact, demonstrated by Kirchhoff, that its nature depends only upon the temperature of the black body with which it is in equilibrium, and on none of this body’s physical or chemical characteristics. Thus we may speak of the “temperature” of the radiation itself, meaning by this the temperature of the material body with which it would be in equilibrium.

The problem of black radiation is to find the distribution of energy among the waves of different frequencies at any given temperature. The first step toward a solution was made when Stefan showed experimentally, and Boltzmann as a deduction from thermodynamics and electrodynamics, that the total energy density summed up over all wave lengths varies with the fourth power of the absolute temperature. If the energy density is plotted as ordinate against the wave length as abscissa, the experimental curve for any one temperature rises from the axis of abscissas at the origin, reaches a maximum, and falls to zero again as the wave length becomes infinitely great. Now Wien’s displacement law, the second important step toward the determination of the form of this curve, shows that as the temperature is raised the wave length to which its highest point corresponds becomes shorter,—in fact this particular wave length varies inversely with the absolute temperature. This theoretical conclusion is entirely confirmed by experiment. (J. W. Draper, =4=, 388, 1847.)

Farther than this general thermodynamical principles are unable to go. Statistical mechanics, however, asserts that when a large number of like elements are in thermal equilibrium, the average kinetic energy associated with each degree of freedom is equal to a universal constant multiplied by the absolute temperature. This “principle of equi-partition of energy” has been applied in various ways to obtain a radiation law. The most straightforward method is based on the equilibrium which must ensue between radiation field and material oscillators when the latter emit, on the average, as much energy as they absorb. From whatever aspect the problem is treated, however, the radiation law obtained from the application of the equi-partition principle is the same. And while this law agrees well with the experimental curve for long wave lengths, it shows an energy density that becomes indefinitely great for extremely short waves, which is not only at variance with the facts, but actually leads to an _infinite_ value of this quantity when integrated over the entire spectrum.

_The Energy Quantum._—Now the principle of equi-partition of energy rests securely on most general dynamical principles. That these dynamical laws are inexact to any such extent as the divergence between theory and experiment would indicate, is inconceivable; that they are _insufficient_ when applied to motions of electrons in such intense fields as occur within the atom seems no longer open to doubt. In order to obtain a radiation formula in accord with experiment Planck has found it necessary to extend the atomic idea to energy, which he conceives to exist in multiples of a fundamental quantum _h_ν, ν being the frequency and _h_ Planck’s constant. That some such hypothesis of discontinuity is essential in order to obtain any law that will even approximately fit the experimental facts has been proved by Poincaré. But the precise spot at which the quantum is introduced differs for every new derivation of Planck’s law. As deduced most recently by Planck himself, the quantum shows itself in connection with the emission of energy by the material oscillators with which the radiation field is in equilibrium. These oscillators are supposed to act quite normally in every respect except emission; here the radiation demanded by the electrodynamic equations is cast aside, and an oscillator is supposed to emit at once all its energy after it has accumulated an amount equal to some integral multiple of _h_ν. A form of the theory which does not contain this improbable contradiction of the firmly established facts of electrodynamics introduces the quantum into the specification of the energy of vibration which is permitted to each oscillator. Here both emission and absorption follow the classical theory, but the motion of an emitting and absorbing linear oscillator of frequency ν is supposed to be stable only for those amplitudes for which the energy of its oscillations is an integral multiple of _h_ν. In order to maintain the energy at these particular values, the oscillator may draw energy from, or deposit surplus energy with, other degrees of freedom which partake neither in emission nor absorption, but act merely as storehouses.

_Photoelectric Effect._—When investigating the production of electromagnetic waves, Hertz had noticed that a spark passed more readily between the terminals of his oscillator when the negative electrode was illuminated by light from another spark. Further investigation by Hallwachs, Elster and Geitel, and others showed that this effect was due to the emission of electrons by a metal exposed to the influence of ultra-violet light. Lenard discovered that the energy with which a negatively charged particle is ejected is entirely independent of the intensity of the light, and further investigation showed it to depend only on the frequency. Einstein suggested that the electrons appearing in this so-called photo-electric effect start from within the metal with an initial energy _h_ν. In passing through the surface a resistance is encountered, however, so he concluded that the energy with which the fastest moving electrons appear outside the metal should be equal to _h_ν less the work done in overcoming this resistance. Recent experiments not only confirm this relation, but provide a most satisfactory method of determining the value of _h_. Millikan[169] finds it to be 6·57(10)^{–27} ergs sec., which gives the quantum for yellow light a value sixty times as great as the heat energy of a monatomic gas molecule at O°C. That this large amount of energy can be transferred from the incident light to the ejected electron is quite out of the question; it must come from within the atom. In this way some indication is obtained of how vast intra-atomic energies must be.

_Structure of the Atom._—The generally accepted model of the atom is that due chiefly to Rutherford.[170] He considers it to be constituted of electrons revolving about a positive nucleus either singly or grouped in concentric rings, in much the same manner as the planets revolve around the sun. Experiments on the scattering of alpha rays, however, show that the nucleus, while it must have a positive charge sufficient to neutralize the charges of all the electrons moving around it, cannot have a volume of an order of magnitude greater than that of the electron. The number of unit charges residing on it, except in the case of hydrogen, which is supposed to consist of a singly charged nucleus and only one electron, is found to be approximately half the atomic weight. Thus helium, with an atomic weight of about four, has a doubly charged nucleus with two electrons revolving about it, and lithium a triply charged nucleus and three electrons. The number of unit charges on the nucleus is supposed to correspond with the atomic number used by Moseley in interpreting the results of his experiment on the X-ray spectra of the elements.

Now the electron which is revolving around the positive nucleus of a hydrogen atom, must, according to electrodynamic laws, radiate energy. This radiation will act as a resistance to its motion, causing its orbit to become smaller and its frequency to increase. Hence luminous hydrogen would be expected to give off a continuous spectrum. The very fine lines actually found seem inexplicable on the classical dynamical and electrodynamical theories. These lines, and those of many other spectra, may even be grouped into series, and the relations between them expressed in mathematical form. Formulæ have been proposed by Balmer, Rydberg, Ritz and others, all of which contain a universal constant _N_ as well as certain parameters which must be varied by unity in passing from one line of a series to the next.

In 1913 Bohr[171] proposed anatomic theory which brings to light a remarkable numerical relationship between this quantity _N_ and Planck’s constant _h_. He postulated that the electron in the hydrogen atom, for instance, cannot revolve in a circle of any arbitrary radius, but is confined to those orbits for which its kinetic energy is an integral multiple of ½_hn_, _n_ being its orbital frequency. Now at times this electron is supposed to jump from an outer to an inner orbit, when the excess energy of the first orbit over the second is radiated away. But the energy emitted is also taken to be equal to _h_ν, where ν is the frequency of the radiation. Hence ν can be determined, and the expression obtained for it is exactly that given long before by Balmer as an empirical law. The most remarkable thing about it, however, is that Bohr’s result contains a constant involving _h_ and the electronic charge and mass which has precisely the value of the universal constant _N_ of Balmer’s and Rydberg’s formulæ. In all, the theory accounts for three series of hydrogen, and yields satisfactory results for helium atoms which have lost an electron, or lithium atoms which have a double positive charge. But for atoms which retain more than a single electron it seems no longer to hold.

The three mentioned are only the most clearly defined of a growing group of phenomena in which the quantum manifests itself. Its significance and the alteration in our fundamental conceptions to which it seems to be leading is for the future to make clear. That it presents the most important and interesting problem as yet unsolved few physicists would deny.

_American Physicists._—In attempting to cover the progress of physics during the last hundred years in the space of a few pages, many important developments of the subject have of necessity remained untouched, and the treatment of many others has been entirely inadequate. Among those appearing in the Journal of which no mention has been made are LeConte’s (=25=, 62, 1858) discovery of the sensitive flame and Rood’s (=46=, 173, 1893) invention of the flicker photometer. However, enough has been recounted to indicate the preeminent position in the history of physics in America occupied by four men: Joseph Henry, of the Albany Academy, Princeton, and the Smithsonian Institution; Henry Augustus Rowland, of Johns Hopkins University; Josiah Willard Gibbs, of Yale; and Albert Abraham Michelson, of the United States Naval Academy, Case School of Applied Science, Clark University, and the University of Chicago. Of these, the last named has the distinction of being the only American physicist to have received the Nobel prize, though there is little doubt that the other three would have been similarly honored had not their important work been published prior to the institution of this award. All four occupy high places in the ranks of the world’s great men of science, and the investigations carried out by them and their fellow workers in America have given to their country a position in the annals of physics which is by no means insignificant.

_The Journal’s Part in Meteorology._

The meteorological investigations published in the early numbers of the Journal have played an important role in establishing a correct theory of storms. Before the origin of the United States Signal Service in 1871 no systematic weather reports were issued by any governmental agency in this country, and consequently the work of collecting as well as interpreting meteorological data rested entirely in the hands of interested individuals and institutions. The earliest important studies of storms to appear in the Journal were contributed by Redfield of New York, whose first paper (=20=, 17, 1831) treated in considerable detail a violent storm which passed over Long Island, Connecticut and Massachusetts in 1821. He concluded that “the direction of the wind at a particular place, forms no part of the essential character of a storm, but is only incidental to that particular portion ... of the track of the storm which may chance to become the point of observation, ... the direction of the wind being, in all cases, compounded of both the rotative and progressive velocities of the storm.” A few years later, analyses of twelve “gales and hurricanes of the Western Atlantic” (=31=, 115, 1837) led to the statement that the phenomena involved “are to be ascribed mainly to the mechanical gravitation of the atmosphere, as connected with the rotative and orbital movements of the earth’s surface.” In this paper is emphasized the fact that the wind may blow in diametrically opposite directions at points near the storm center. “While one vessel has been lying-to in a heavy gale of wind, another, not more than thirty leagues distant, has at the very same time been in another gale equally heavy, and lying-to with the wind in quite an opposite direction.” From an accompanying sketch showing wind directions, the reader would infer that, at this time, Redfield believed the motion of the air to be very nearly in circles about the storm center. The same idea is conveyed by a later paper (=42=, 112, 1842). Espy (=39=, 120, 1840) of Philadelphia, however, claimed that observation showed rather that the wind blew inwards toward a central point, if the storm were round in shape, or toward a central line, if it were oblong. This view Redfield (=42=, 112, 1842) contested, and brought forth much evidence to prove its falsity. A later statement (=1=, 1, 1846) of his own theory is as follows: “I have never been able to conceive, that the wind in violent storms moves only in _circles_. On the contrary, a vortical movement ... appears to be an essential element of their violent and long-continued action, of their increased energy towards the center or axis, and of the accompanying rain.... The _degree_ of vorticular inclination in violent storms must be subject, locally, to great variations; but it is not probable that, on an average of the different sides, it ever comes near to forty-five degrees from the tangent of a circle,—and that such average inclination ever exceeds two points of the compass, may well be doubted.” A qualitative explanation of the effect of the earth’s rotation on the direction of the wind near the storm center had already been given by Tracy (=45=, 65, 1843), and this was followed some years later by Ferrel’s (=31=, 27, 1861) very thorough quantitative investigation of the dynamics of the atmosphere.

A number of individuals kept systematic records of meteorological observations, among whom was Loomis, whose storm analyses did much to settle the merits of the rival theories of Redfield and Espy. In studying the storm of 1836 (=40=, 34, 1841) he had drawn on the map lines through those points in the track of the storm where the barometer, at any given hour, is lowest. While this method revealed the general direction in which the storm was progressing, it failed to give much indication of its size or shape. In discussing the two tornadoes of February, 1842, one of which had already been described in the Journal (=43=, 278, 1842), he adopted a new and more illuminating graphical method. Instead of connecting points of lowest pressure, he drew a curve through all points where the barometer stood at its normal level, then one through those points at which the pressure was ²⁄₁₀ of an inch below normal, and so on. Temperature he treated in much the same way, and the strength and direction of the wind were indicated by arrows. This innovation gave to his storm analyses a significance which had been entirely lacking in those of his predecessors, and led to the familiar systems of isobars and isotherms in use on the daily charts issued by the Weather Bureau at the present time. Loomis advocated careful observations for one year at stations 50 miles apart all over the United States, so that sufficient data might be obtained to settle once for all the law of storms. His efforts, seconded by those of Henry, Bache, Pierce, Abbe, and Lapham, led eventually to the establishment of the Signal Service, and the publication of daily weather maps according to the plan advocated thirty years before. These maps afforded a basis for further analyses of storms, which he published in numerous “Contributions to Meteorology” (=8=, 1, 1874, _et seq._) between 1874 and his death in 1890.

In addition to his work on storms, Loomis made a careful study of the earth’s magnetism (=34=, 290, 1838 _et seq._), and of the aurora borealis (=28=, 385, 1859 _et seq._). That a connection existed between sunspots, aurora, and terrestrial magnetism was already recognized. Loomis (=50=, 153, 1870 _et seq._), however, showed that the periodicity of the aurora borealis, as well as of excessive disturbances in the earth’s magnetic field, corresponds very closely with that of sunspots.

_Notes._

Footnote 154:

J. W. Gibbs, Trans. Conn. Acad. Arts and Sci., =3=, 108 and 343.
Abstract by the author, the Journal, =16=, 441, 1878.

Footnote 155:

H. K. Onnes, Nature, =93=, 481, 1914.

Footnote 156:

H. Hertz, Wied. Ann., =34=, 551, 1888 _et seq._

Footnote 157:

E. F. Nichols and G. F. Hull, Phys. Rev., =13=, 307, 1901 _et seq._

Footnote 158:

J. J. Thomson, Phil. Mag., =44=, 293, 1897.

Footnote 159:

R. A. Millikan, Phys. Rev., =2=, 109, 1913.

Footnote 160:

P. Zeeman, Phil. Mag., =43=, 226, 1897.

Footnote 161:

H. A. Lorentz, Phil. Mag., =43=, 232, 1897.

Footnote 162:

S. J. Barnett, Phys. Rev., =6=, 239, 1915, and =10=, 7, 1917.

Footnote 163:

W. C. Röntgen, Wied. Ann., =64=, 1, 1898 _et seq._

Footnote 164:

W. Friedrich, P. Knipping, and M. Laue, Ann. d. Phys., =41=, 971,
1913.

Footnote 165:

H. G. J. Moseley, Phil. Mag., =26=, 1024, 1913, and =27=, 703, 1914.

Footnote 166:

E. W. Morley and D. C. Miller, Phil. Mag., =9=, 680, 1905.

Footnote 167:

=17=, 891, 1905.

Footnote 168:

E. B. Wilson and G. N. Lewis, Proc. Am. Acad., of Arts and Sci., =48=,
389, 1912.

Footnote 169:

R. A. Millikan, Phys. Rev., =7=, 355, 1916.

Footnote 170:

E. Rutherford, Phil. Mag., =21=, 669, 1911.

Footnote 171:

N. Bohr, Phil. Mag., 26, =1=, 1913 _et seq._

XII
A CENTURY OF ZOOLOGY IN AMERICA

By WESLEY K. COE

This article is intended as a brief survey of the development of zoology in America, and no attempt is made to give a general history of the science. There are numerous accounts in several languages of zoological history in general, among them being W. A. Locy’s “Biology and its Makers.” Brief outlines of the history of zoology may be found in many zoological and biological text-books.

For the history of American zoology the reader is referred to Packard’s report on “A Century’s Progress in American Zoology,” published in the American Naturalist, (10, 591, 1876), to Packard’s “History of Zoology,” published in volume 1 of the Standard Natural History (pp. lxii to lxxii, 1885); to G. B. Goode’s “Beginnings of Natural History in America,”[172] and “Beginnings of American Science,”[173] and to H. S. Pratt’s Manual of the Common Invertebrate Animals (pp. 1–9), 1916. In Binney’s “Terrestrial Air-breathing Mollusks of the United States” (1851) is a chapter on the rise of scientific zoology in the United States which well describes the zoological conditions in the early part of the century, while numerous monographs and papers give the history of the investigations on the various groups of animals or on special fields of study.

Brief biographical sketches of the most distinguished of our older Naturalists—Wilson, Audubon, Agassiz, Wyman, Gray, Dana, Baird, Marsh, Cope, Goode and Brooks are given in “Leading American Men of Science,” edited by David Starr Jordan, 1910. More extensive biographies have been published separately, and the activities of a number of the more prominent American zoologists have been recorded in the Biographical Memoirs of the National Academy of Sciences.

The developmental history of zoology in America falls naturally into four fairly well marked periods, namely:—1, _Period of descriptive natural history_, previous to 1847, embracing the early studies on the classification and habits of animals, characteristic of the zoological work previous to the arrival of Louis Agassiz in America. 2, _Period of morphology and embryology_, 1847–1870, during which the influence of Agassiz directed the zoological studies toward problems concerning the relationships of animals as indicated by their structure and developmental history. 3, _Period of evolution_, 1870–1890, when the principle of natural selection received general recognition and the zoological studies were largely devoted to the applications of the theory to all groups of animals. 4, _Period of experimental biology_, since 1890, during which time have occurred the remarkable advances in our knowledge of the nature of organisms through the application of experimental methods in the various branches of the modern science of biology.

_American Zoology in 1818._

At the beginning of the century which this volume commemorates, the accumulated biological knowledge of the world consisted mainly of what is to-day called descriptive natural history. The zoological treatises of the time were devoted to the names, distinguishing characters and habits of the species of animals and plants known to the naturalists of Europe either as native species or as the results of explorations in other parts of the world. This required little more than a superficial knowledge of their general anatomical structures.

The naturalists of those days had no conception of the life within the cell which we now know to form the basis of all the activities of animals and plants, nor had they even the necessary means of studying such life. The compound microscope, so necessary for the study of even the largest of the cells of the body, was not adapted to such use until 1835, although the instrument was invented in the seventeenth century. With the perfection of the microscope came a period of enthusiastic study of microscopic organisms and microscopic structures of higher animals and plants. It was not until twenty years after the founding of the Journal that the cell theory of structure and function in all organisms was established by the discoveries of Schleiden and Schwann.

The beginning of the nineteenth century saw great zoological activity in Europe, and particularly in France. Buffon’s great work on the Natural History of Animals had recently been completed, Cuvier had only one year before published his classic work in comparative anatomy, “Le Regne Animal,” and Lamarck’s “Philosophie Zoologique” had then aroused a new interest in classification and comparative anatomy from an evolutionary standpoint. E. Geoffroy St.-Hilaire was at the same time supporting an evolutionary theory based on embryonic influences resulting in sudden modifications of adult structure. These epoch-making discoveries and theories gained a considerable following in France, Germany and England, but seem to have had little influence on the zoological work of the following half century in America.

The science of zoology as understood to-day is commonly said to have been founded by Linnæus by the publication of the modern system of classification in the tenth edition of his “Systema Naturæ” in 1758. The influence of Linnæus aroused an interest in biological studies throughout Europe and stimulated new investigations in all groups of organisms. Such studies as related to animals naturally followed first the classification and relationship of species, that is, systematic zoology, and then led gradually into the development of the different branches of the subject, as morphology, comparative anatomy, physiology, and embryology, which eventually were recognized as almost independent sciences.

Of these sciences systematic zoology, which has come to mean the classification, structure, relationship, distribution and habits, or natural history, is the pioneer in any region. Thus we find in our new country at the time of the founding of the Journal in 1818, only sixty years after the publication of Linnæus’ great work, the beginning of American zoology taking the form of the collection and description of our native animals.

It is true that many of our more conspicuous and easily collected animals were described long before the opening of the nineteenth century, but this is to be credited mainly to the work of European naturalists who had made expeditions to this country for the purpose of studying and collecting. These collections were then taken to Europe and the results published there. We thus find in the 12th edition of Linnæus descriptions of over 500 American species, about half of which were birds. As an illustration of the extent to which some of these works covered the field even in those early days may be mentioned a monograph in two quarto volumes with many beautifully colored plates on the “Natural History of the rarer Lepidopterous Insects of Georgia.” This was published in London in 1797 by J. E. Smith from the notes and drawings of John Abbot, one of the keenest naturalists of any period.

During the early years of the nineteenth century, however, economic conditions in our country became such as to give opportunity for scientific thought. Educated men then formed themselves into societies for the discussion of scientific matters. This naturally led to the establishment of publications whereby the papers presented to the societies could be published and made available to the advancement of science generally. The most influential of these was the Journal of the Philadelphia Academy of Natural Science, which was established in 1817, and was devoted largely to zoological papers. The Annals of the New York Lyceum of Natural History date from 1823, and the Journal of the Boston Society of Natural History from 1834. The Transactions of the American Philosophical Society in Philadelphia and the Memoirs of the American Academy of Arts and Sciences in Boston also published many zoological articles.

In these publications and in the Journal, which was founded in 1818, appear the descriptions of newly discovered animal species, with observations on their habits.

The number of investigators in this field in the first quarter of the nineteenth century was but few, and most of these were compelled to take for the work such time as they could spare from their various occupations.

Gradually the workers became more numerous until about the middle of the century zoology was taught in all the larger colleges. The science thereby developed into a profession.

For some years the studies remained largely of a systematic nature, and embraced all groups of animals, but long before the close of the century the attention of the majority of the ever increasing group of zoologists was directed into more promising channels for research and there came the development of the sciences of comparative anatomy, physiology, embryology, experimental zoology, cytology, genetics, and the like, while the systematists became specialists in the various animal groups.

But the work in systematic zoology remains incomplete and many native species are still undescribed or imperfectly classified. It is perhaps fortunate that a few faithful systematists remain at their tasks and tend to keep the experimentalists from the disaster which might otherwise result from the confusion of the species under investigation.

_Period of Descriptive Natural History.—Previous to 1847._

Of the few American naturalists whose writings were published toward the end of the eighteenth century and at the beginning of the nineteenth the names of William Bartram (1739–1823), Benjamin Barton (1766–1815), Samuel Mitchill (1764–1831), William Peck (1763–1822), and Thomas Jefferson (1743–1826), require special mention. Bartram’s entertaining volume describing his travels through the Carolinas, Georgia and Florida, published in 1793, contains a most interesting account of the birds and other animals which he found.