action against the change of its density, that is, of the number of tubes per unit area. When the surrounding medium is a vacuum or an ideal insulator, that is, a dielectric with a constant specific inductive capacity, then the numerical value of this reaction can be calculated. According to Maxwell's hypothesis, the electrical reaction in this case per unit length and unit cross-section of the tube is equal to the density of the tubes in the direction in which the reaction is considered, divided by the specific inductive capacity. The hypothetical reaction had a most significant corollary; it located the energy of the field in the volume elements of the tubes of force and assigned to each element, per unit of volume, an amount proportional to the square of the density of the tubes of force at that volume element. Dynamically, therefore, there is a perfect resemblance between the field of electrical reactions in ideal insulators and the field of elastic reactions in the interior of an elastically strained body which obeys the so-called Hooke's law. According to this view, the charges transmit their action through the volume elements of the tubes against the reaction of the tubes. When the field of electrical force is in equilibrium then the external actions coming from the electrical charges and the internal electrical reactions of the tubes are equal and opposite to each other at every point of space.

This form of statement is suggested by Newtonian dynamics and furnishes a law which conforms to Newton's third axiom. It is different from Coulomb's law in form and meaning, and it holds good no matter how the impressed electrical forces are generated or what the physical character of the material insulators is upon which these forces are impressed. It is obtained from the hypothesis that the tubes of force are physical entities which react against a change of their density. There is nothing in Coulomb's law which suggests this hypothesis and there can not be, because this law suggests nothing concerning the velocity or the mechanism of transmission of force between eleetrical charges, whereas a reacting tube of force was suggested to Faraday and to Maxwell by the intuition that electrical actions are transmitted through the tubes of force with a finite and definite velocity which depends upon the dynamical properties, that is, upon the reactions, of the tubes. The tubes of force attached to electrical charges or otherwise generated are, according to this hypothesis, the transmitting mechanism reacting in every one of its elements by reactions which in the case of the vacuum and of ideal dielectrics are identical in form with the elastic reactions of an ideal elastic body. This view of the field of electrical force is one of the foundation pillars of the Faraday-Maxwell electromagnetic theory. I shall next describe briefly the second foundation pillar of this theory.

What has been said above about our knowledge of electrical phenomena is also true of our knowledge of magnetic phenomena. It started its career as a science when Coulomb's measurements succeeded in formulating a law of force between magnetic charges. Since this law is identical in form with that for electrical charges, and since the presence of material bodies affects similarly a magnetic field as the presence of material insulators affects an electrical field it is obvious that the Faraday-Maxwell intuitive philosophy leads here to the same results as in the case of electrical fields of force. Coulomb's law can, therefore, be replaced by a law which is identical in form with the law formulated above for electrical fields. It is as follows: When the field of magnetic force is in equilibrium then the external magnetic actions and the internal reactions of the magnetic tubes of force are equal and opposite to each other at every point of space. Description and hypothesis serve here the same object as in the case of the electric fields, namely, to point out that the magnetic tubes of force are the transmitting mechanism of the magnetic force and that the quantitative relation between the forces impressed upon the tubes and their reactions is one of the determining factors of the mode of propagation.

It is obvious that so far I have been endeavoring to show that Faraday's and Maxwell's views paved the way to the formulation of new concepts, the concepts of electrical and magnetic actions and reactions, which like ordinary material actions and reactions obey Newton's third law. These endeavors will be continued in what follows.

The law of equality between electrical and magnetic actions and the respective reactions in fields which are in static equilibrium can, obviously, tell nothing definite about the velocity of propagation. Reactions brought into play when this equilibrium is disturbed must be considered. Do they exist, and if so, do they show that the velocity of propagation of electrical force is the same as or different from that of the magnetic force? The electrical science prior to Oersted's and Faraday's discoveries could not have answered this question. These discoveries supplied the necessary knowledge. Broadly stated, they revealed the following new truth: Oersted discovered that electrical charges moving through conductors produce magnetic tubes of force which are interlinked with the conductors; Faraday discovered that magnetic charges and their tubes of force produce by their motion or variation electrical forces in conducting circuits which are interlinked with these tubes. This description of the discoveries intentionally emphasizes the two facts, namely, that Oersted made his discovery while experimenting with conduction currents, and that Faraday explored the electrical field in conducting wires, only,

which are interlinked with the magnetic tubes of force. The laws resulting from these experiments, namely, Ampère's law and Faraday's law, were necessarily limited to the conditions of the experiments which led to their formulation. Neither one nor the other were sufficiently general to give direct information concerning the unknown reactions associated with the variable electric and magnetic tubes of force at any point of a dielectric. Oersted's and Faraday's experiments did not detect them, nor was it obvious how to detect them experimentally. New hypotheses were needed and Maxwell was the first to formulate them; they were as follows: First, a variation of the flux, that is, of the total number of electrical tubes of force through any area, is equivalent to the motion of electrical charges through that area; in other words, the so-called displacement current produces according to Maxwell the same magnetic effect as the conduction or convection current. Secondly, the variation of the flux of the tubes of magnetic force through any area produces an electromotive force around the boundary curve of this area which is independent of the material through which this boundary curve passes. These two hypotheses extended the meaning of the Ampère and of the Faraday law and gave them that symmetry which is expressed in the following statements:

The rate of variation of the electric flux through any area is equal to the magnetomotive force in the circuit which forms the boundary curve of that area.

The rate of variation of the magnetic flux through any area is equal to the electromotive force in the circuit which forms the boundary curve of that area. The first statement represents Maxwell's generalization of Ampère's law, and the second that of Faraday's law. Mathematical physicists call them Maxwell's field equations. This name does not convey clearly their physical meaning, nor does it express fully their historical significance. Prior to the time of Oersted and Faraday there were only a few, rather feeble, processes of generating and impressing upon material bodies electric and magnetic forces; frictional machines, galvanic cells, action of permanent magnets, etc. . . . Ampère's and Faraday's generalized laws describe new processes of generating and impressing magnetic and electric forces upon any part of space. They might be called Maxwell's laws of electrodynamic generation, or briefly Maxwell's laws, the rest of the proposed title being understood. These laws give the total sum of the electric and magnetic forces impressed by those processes upon any circuit; the energy principle tells us that this sum is equal to the sum of the electric and of the magnetic reactions in the circuit. The parcelling out of the total impressed forces thus generated among the volume elements of the circuit and the character of the

reactions of each volume element must be determined by the character of each problem and by the physical properties of each volume element of the circuit. Circuits in ideal isotropic dielectrics present the simplest illustration of the general procedure, and this was the subject which Maxwell considered first. In this case the reaction per unit cross-section and unit length of the circuit is, as already pointed out, equal to the ratio of the flux density to the specific inductive capacity, or permeability, respectively, and this reaction must be equal to the force generated by the variable fluxes and impressed per unit length of the circuit. This leads to a reciprocal relation between the electric and magnetic reactions in variable fields which in an isotropic dielectric exhibits a process of propagation identical in form with that obtained by Newtonian dynamics for the actions and reactions in an isotropic, incompressible, elastic medium. Maxwell's greatest achievement is, in my opinion, his introduction into the electrical science of new concepts, electric and magnetic actions and reactions, which obey the same laws as the corresponding concepts in Newtonian dynamics. But it should be observed here that Maxwell's success was due to Faraday's suggestive description of the electric and magnetic fields in terms of tubes of force and to the intuition which created the epoch-making hypotheses endowing these tubes with dynamical attributes formerly belonging to material substances only. These hypotheses demanded experimental verification; Hertz seized the opportunity and furnished the epoch-making demonstration of the correctness of Maxwell's hypotheses.

The propagation of force through an ideal elastic solid makes the velocity of propagation depend upon two constants only, the density and the elastic constant. The first determines the inertia reaction and the second the elastic reaction per unit volume of the solid. Similarly in the propagation of the electric force through the electric and magnetic tubes of force in an ideal dielectric the velocity of propagation depends upon two constants only; the specific inductive capacity of the tubes and their magnetic permeability. One determines the reaction of the electrical tubes of force, and the other the reaction of the magnetic tubes. These reaction constants determine the velocity of propagation through the electric and magnetic tubes in the same manner as density and elastic constant determine the velocity of propagation through ideal elastic bodies. The question arises, which of the two reaction constants of Faraday's tubes corresponds to the density and which to the elastic constant of material bodies? In other words, which of the two constants is characteristic of the inertia reaction of the tubes?

The generalized laws of Ampère and of Faraday, which I call the Maxwell laws, suggest a permissible

answer to this question. They indicate a scheme which demands one fundamental flux, the electric flux, called here the primary flux. A variation or velocity of motion of the electric flux generates, according to the first Maxwell law, magnetic forces and corresponding magnetic fluxes which in an isotropic dielectric are proportional to the impressed magnetic forces, the factor of proportionality being the magnetic permeability of the tubes of the magnetic field. If, therefore, we consider the magnetic flux of the field, thus generated, as the momentum of the varying or moving electric flux, since it is proportional to its rate of variation or velocity of motion, then the electrical field generated, according to the second Maxwell law, by the variation of the magnetic flux will be due to the change of this momentum. According to this scheme the permeability constant in the electromagnetic theory would correspond to density in the theory of propagation through elastic solids.

Electron physics supports this scheme. It traces the origin of all magnetic forces of magnets to the orbital motions of electrons. This reminds us of the old Ampèrean conception. Magnetic tubes of force associated with so-called permanent magnets are, according to electron physics, the result of the motion of electric tubes of force attached to electrons. Maxwell always associated with magnetic tubes of force the momentum of some electric motions. What Faraday called the electrotonic state he called the electrokinetic momentum of a circuit, that is, the magnetic flux interlinked with the circuit. The reactions of varying magnetic tubes of force are, therefore, inertia reactions and their reaction constant, the permeability, should, as already pointed out, be considered as corresponding to the density of elastic solids, whereas the reciprocal of their specific inductive capacity corresponds to the elastic constant. Faraday's tubes of force in free space have, in electromagnetic units, a permeability equal to unity and, measured in the same system of units, an exceedingly small specific inductive capacity. They behave, therefore, like incompressible elastic bodies of moderate density but of very high elastic constant for shearing strains. It is equal to 9 x 1020. Hence the great velocity of propagation of electromagnetic disturbances through tubes of force in free space, as experimentally verified by Hertz.

Electrical propagation through ideal dielectrics, including the vacuum, demands, according to the above picture, nothing more than Faraday tubes of electric force capable of two distinct reactions, one an electrical reaction and the other a magnetic, that is an inertia, reaction. The tubes react like a material medium of reasonable density but of most extraordinary stiffBut neither this similarity to material bodies nor anything else in our present knowledge of electrical phenomena justifies the hypothesis that they

ness.

consist of a substance which has qualities of ordinary matter in bulk. One can not resist the temptation of asking the question: What are these tubes made of? I venture, therefore, to offer the following pardonable suggestion.

Our ideas of these tubes are associated with our concepts of electrical charges which are the terminals of the tubes when they have a terminal. In this we follow in the footsteps of Faraday. It is not an unreasonable hypothesis to assume that they are made of the same fundamental substance of which the electrical charges are made. The name "electricity" may, therefore, be reserved for that substance, whatever it may be, so that we may say: The medium which transmits electrical disturbances is "electricity," meaning thereby the substance out of which electrical tubes of force are made. Light is an electrical disturbance and it is, according to this view, transmitted by electricity. The concept suggested by the word "electricity" is much more definite than that suggested by the words "lumeniferous ether," because we associate with electricity two perfectly well-known and experimentally determinable reaction constants, that is, the reaction constants of the primary flux of force at rest and in motion. These are the only attributes that we can dynamically predicate of a material substance, hence the concept "electricity" is dynamically just as definite as the concept "material substance"; the concept "ether" is not.

Perhaps I have dwelt too much upon that part of the electromagnetic theory which is a little outside of the daily problems of the electrical engineer. Some people think that it is entirely outside of the theory which underlies electrical engineering problems. Permit me to show you, as briefly as I can, that this is not so, and that the same form of laws and the same dynamical methods apply to electrical engineering problems as to the problems discussed above. Electrical engineering problems deal with actions and reactions in electrical and magnetic circuits and so does the general electromagnetic theory. I have pointed out how starting with Coulomb's law a more general law was formulated for the field of force due to electrical or to magnetic charges at rest, the law of equality of actions and reaction in every volume element of the field in static equilibrium. The validity of this law was maintained for the dynamical equilibrium of variable fields when Ampère's and Faraday's laws were formulated by Maxwell in their most general form. The principle of conservation of energy demands that this law be always true irrespective of the physical character of the circuit or of the process of generating the impressed forces. This furnishes then the most fundamental basis in theoretical electrical engineering. It may be stated as follows:

In every circuit or part of a circuit the algebraic

sum of electrical reactions is equal to the algebraic sum of the impressed electric actions.

Omit the words "electrical" from this statement and you have the most fundamental law in Newton's dynamics, showing that "electricity" obeys the same fundamental law which ponderable matter obeys.

Take for an illustration an electrical circuit in which we have a constant electromotive force, generated by a voltaic cell and a constant current flowing through a conducting wire. Consider any two points on the wire. Heat is generated in the wire between these two points and, therefore, there must be an electrical reaction in the wire between these two points. Heat is the result of the work done against this reaction by the impressed electrical force transmitted by the battery. This reaction may be called a resistance reaction, whereas the impressed action is the difference of potential between these two points. The law of equality of action and reaction says: The resistance reaction is equal to the difference of potential. This relation is independent of the so-called "Ohm's Law." When, however, the wire is maintained at constant temperature then its resistance reaction is found by experiment to be proportional to the current; this empirically established characteristic of most metal wires is called Ohm's law. It really is not a law any more than Joule's rule for the rate of heat generation by a current flowing through a metal wire. Both are accurate empirical descriptions of a physical characteristic of most metal wires. It is occasionally stated, with some show of disappointment, that the flow of current through a gas does not obey Ohm's law, which really means that the resistance reaction is not proportional to the current, and that it can not be described as simply as the resistance reaction of a metal wire. That a conducting gas should react differently than a conducting metal wire should not surprise anybody; but it seems that it does.

Consider, as another simple illustration, a toroidal magnetic circuit consisting of several different radial sections of different kinds of steel separated from each other by small air gaps and magnetized by a current flowing through turns of wire wound around the toroid. The total magnetomotive force generated by the current is given by Ampère's law. Each part of the magnetic circuit receives its definite share of the total magnetomotive force; this share is the magnetizing force impressed upon that part of the circuit. In each part of the magnetic circuit the impressed magnetizing force is equal to the magnetic reaction of that part, so that according to the fundamental law the sum of the magnetic reactions is equal to the total impressed magnetic actions, which is the magnetomotive force. This is the fundamental law, whereas the usual method of calculating, roughly, the magnetic flux from impressed magnetizing forces and reluctances by making use of a new kind of Ohm's law

for the magnetic circuit is, in my opinion, a misleading use of the word law. This spurious Ohm's law is abandoned, of course, as soon as we attempt to devise an experimental method for measuring hysteresis losses during a complete cycle of magnetization, but we do not abandon the dynamical law that in every part of the magnetic circuit the magnetizing force is equal to the magnetic reaction. On the contrary, we could not interpret without it the hysteresis losses during cyclic magnetizations.

When in a network of linear conductors alternating current generators are located at various points of the network, the current distribution in the network can be calculated by setting up equations for each circuit, which state the fundamental dynamical law that in each circuit the algebraic sum of electrical reactions is equal to the algebraic sum of impressed electromotive forces, generated by the alternators. To call these equations mathematical expressions of a Kirchhoff law, as some do, is unpardonable abuse of language. Kirchhoff gave the rule that for any circuit in a network of metallic wire conductors in which there are sources of constant electromotive force the algebraic sum of the electromotive forces is equal to the algebraic sum of the products of current and Ohmic resistance; but he never suspected that this is a special case of the fundamental dynamical law given above.

It is true that in 1858 Kirchhoff, in his analysis of electrical propagation along an overhead telegraph wire, stated correctly the relation between the electrical reactions at any element of the wire, and in this statement he was guided by Thomson's discussion of electrical propagation over a submarine cable. But neither Thomson nor Kirchhoff were aware of the general law, stated above. Maxwell's electromagnetic theory had not yet been published, and prior to that publication the general law implicitly contained in this theory, and which is to-day the foundation of electrical engineering, could not be formulated.

The several simple examples cited above suffice to illustrate clearly that electrical engineering problems, on their purely scientific side, are formulated in the same way as the problems in the general electromagnetic theory. Their solutions are obtained by the application of the same form of the fundamental laws employing the same methods of reasoning and the same terminology which Newton had formulated when he created the science of dynamics. The possibility of describing electrical phenomena in terms of Newton's concepts and language is one of the greatest achievements of Faraday and Maxwell. Law, description and hypothesis were never employed with greater effect than by the genius of these great prophets of the electrical science.

COLUMBIA UNIVERSITY

M. I. PUPIN

SAMUEL TAYLOR DARLING

1872-1925

SAMUEL TAYLOR DARLING, who met with a fatal automobile accident while traveling as a member of the League of Nations Malaria Commission near Beirut, Syria, on May 20, 1925, was for twenty years one of the foremost American students of tropical medicine, especially in the field of medical zoology.

Dr. Darling was of English parentage and came from a long line of clergymen. Early in life he exhibited that independence of thought and action which contributed so largely to his later success. After trying out several fields he decided upon medicine as a career and attended the College of Physicians and Surgeons at Baltimore, where he received his degree in 1903 with the honor medal for highest rank in a class of over seventy. The following two years he spent as resident pathologist in the Baltimore City Hospital. Dr. Darling considered himself primarily a pathologist, although he designated his field as tropical medicine in "American Men of Science." However, he will be known to the scientists of the future as a medical zoologist since almost all his published work is on this subject. The stimulus for these investigations in medical zoology was received at Panama. Already in 1903 he showed promise of being an investigator by publishing a paper on typhoid orchitis. He was appointed intern and physician in the Ancon Hospital in the Panama Canal Zone in 1903. Here he exhibited the qualities that led to his being made chief of the laboratories of the Isthmian Canal Commission in 1906; a position he held until 1915.

During the ten years Dr. Darling was in Panama, he became interested in various parasitic organisms that cause disease in man and animals. He observed three cases of histoplasmosis (1906) the causative organism of which he thought to be a protozoon, but which was later found to be a fungus. He then became interested in sarcosporidia and described various species, one of which, from the opossum, was named by Brumpt in his honor, Sarcocystis darlingi in 1913. Two of the very few authentic cases of sarcosporidia in man were reported by Darling (1909 and 1919) and the "blind alley" theory which he proposed to account for their presence is now generally accepted. It will be impossible in the space available to comment critically on all of the important work done by Darling in Panama. Soon after reaching the Canal Zone he began studying malaria and published a number of papers dealing with both the malarial organism and its mosquito vectors. Among the other subjects dealt with in his publications of this period are relapsing fever (1909), trypanosomiasis in horses.

(1910, 1911, 1912), leishmaniasis (1910, 1911), intestinal helminths (1911), Haemoproteus and haemogregarines (1912), Linguatula serrata (1912), anaphylactic serum disease (1912), Endamoebae (1912, 1913), anthrax (1912), piroplasmosis (1913), beriberi and scurvy (1914), Endotrypanum (1914) and arteritis syphilitica obliterans (1915).

In 1913-1914 Dr. Darling was selected to accompany General Gorgas on a sanitary mission to the Rand Mines and Rhodesia, South Africa, where his expert opinion was desired in connection with the high mortality of workers in the diamond mines. In 1915 Darling joined the staff of the International Health Board of the Rockefeller Foundation and continued with this organization until his death. His first project while a member of this board was to head a medical commission which from 1915 to 1917 studied the causes of anemia among the people of Malaya, Java and Fiji. Part of the results of the work of this commission are contained in a book of 191 pages published in 1920 in collaboration with M. A. Barber and H. P. Hacker on "Hookworm and Malaria Research in Malaya, Java and the Fiji Islands." Several other investigations on hookworm disease were carried on by Darling especially on mass treatment (1920, 1922) and on the geographical and ethnological distribution of hookworms (1920). On his return from the Far East, Darling was sent to Sao Paulo, Brazil, where he served as professor of hygiene and director of the Laboratories of Hygiene in the Medical School. Here he established an excellently equipped laboratory for teaching and investigation and carried on work principally with hookworm disease and malaria. He was forced by illness in 1920 to return to the United States, where he became fellow by courtesy in the department of medical zoology of the School of Hygiene and Public Health of the Johns Hopkins University.

In 1922 Darling established for the International Health Board a field laboratory for the investigation of malaria at Leesburg, Georgia. Here for the following three years he did some of the best work of his life both as an investigator and as a teacher, since many young men were sent to his laboratory to obtain training in field work before proceeding to various parts of the world as field directors of malaria control campaigns.

Dr. Darling was an honorary fellow of the Royal Society of Tropical Medicine and Hygiene, London; the only other American so honored was General Gorgas. He was to have delivered the annual address to this society in June. He took an active part in various societies. He was president of the Canal Zone Medical Association in 1908, fellow of the Amer