My Note - 5) Maxwell, On Physical Lines of Force

Although Dr Yuakawa did not refer to other Maxwell's original writings, the prefaces or introductions of other Maxwell's original writings are also worth reading. Why don't we try whole writings if we have time and interests we can get more from him.

On Physical Lines of Force (published in March, 1861)

No title of introduction but Part I stats with introductory story, which does mean.

Part I - The Theory of Molecular Vortices applied to Magnetic Phenomena

  In all phenomena involving attractions and repulsions, or any forces depending on the relative positions of bodies, we have to determine the magnitude and direction of the force which would act on a given body, if placed in a given position.
  In the case of a body acted on by the gravitation of a sphere, this force is inversely as the square of the distance, and in a straight line to the centre of the sphere. In the case of two attracting spheres, or of a body not spherical, the magnitude and direction of the force vary according to more complicated laws. In electric and magnetic phenomena, the magnitude and direction of the resultant force at any point is the main subject of investigation. Suppose that the direction of the force at any point is known, then, if we draw a line so that in every part of its course it coincide in direction with the force at that point, this line may be called a line of force, since it indicates the direction of the force in every part of its course.
  By drawing a sufficient number of lines of force we may indicates the direction of the force in every part of the space it acts.
  Thus if we strew iron filings on paper near a magnet, each filing will be magnetized by induction, and the consecutive filings will unite by their opposite poles, so as to form fibers, and these fibers will indicate the direction of the lines of force. The beautiful illustration of the presence of magnetic force afforded by this experiment, naturally tends to make us think of the lines of force as something real, and as indicating something more than the mere resultant of the two forces, whose seat of action is at a distance, and which do not exist there at all until a magnet is placed in that part of the field. We are dissatisfied with the explanation founded on the hypothesis of attractive and repellent forces directed towards the magnetic poles, even though we may have satisfied ourselves that the phenomenon is in strict accordance withe hypothesis, we cannot help thinking that in every place where we find these lines of force, some physical state or action must exist in sufficient energy to produce the actual phenomena.

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My Internal Note - 1 (underlined by sptt)

This part verbally but clearly states what Dr Yukawa said in the lecture.

"
Maxwell wrote in the preface (of Treaties on Electricity and Magnetism (published in 1973)) is that he takes a standpoint of  "Near Force" like Faraday. And by this he thoroughly explained the then Electromagnetic theory based on Action-at-distance in terms of  "Near Force", plus he drew a conclusion the light being Electromagnetic phenomenon. This is written in this book. This story is just an opposite direction of the development of mechanics. Thus was what actually happened.

"
===
On Physical Lines of Force - continued

  My object in this paper is to clear the way for speculation in this direction, by investigating the mechanical results of certain states of tension and motion to a medium, and comparing these with the observed phenomena of magnetism and electricity. By pointing out the mechanical consequences of such hypotheses, I hope to be of some use to those who consider the phenomena as due to the action of a medium, but are in doubt as to the relation of this hypothesis to the experimental laws already established, which have generally been expressed in the language of other hypotheses.

===

My Internal Note - 2 (underlined by sptt)

Other hypotheses are supposed to be those of  "action at distance" as Dr Yukawa lectured in Day One - 13.遠隔力と近接力 Action-at-distance and "Near Force".

 ===
On Physical Lines of Force - continued

  I have in a former paper *(* See a paper "On Faraday's Lines of Forces") endeavoured to lay before the mind of the geometer a clear conception of the relation of the lines of force to the space in which they are traced. By making use of the conception of currents in a liquid, I showed how to draw lines of force, which should indicate by their number the amount of force, so that each line may be called a unit-line of force (see Faraday's 'Researches,' 8122); and I have investigated the path of the lines where they pass from one medium to another.
  In the same paper I have found the geometrical significance of the "Electronic State," and have shown how to deduce the mathematical relations between the electronic state, magnetism, electric currents, and the electromotive force, using mechanical illustrations to assist the imagination, but not to account for the phenomena.
  I propose now to examine magnetic phenomena form mechanical point of view, and to determine what tensions in, or motions of, a medium are capable of producing the mechanical phenomena observed. If, by the same hypothesis, we can conduct the phenomena of magnetic attraction with electromagnetic phenomena and with those of induced currents, we shall have found a theory which, if not true, can only be proved to be erroneous by experiments which will greatly enlarge our knowledge of this part of physics.
  The mechanical conditions of a medium under magnetic influence have been variously conceived of, as currents, undulations, or states of displacement or strain, or pressure or stress.
  Currents, issuing from the north pole and entering the south pole of a magnet, or circulating round an electric current, have the advantage of representing correctly the geometrical arrangement of the lines of force, if we could account on mechanical principles for the phenomena of attraction, or for the currents themselves, or explain their continued existence. 

 ===

My Internal Note - 3

I will try the introductory part of "On Faraday's Lines of Forces" layer in the next post.The key word is of course " force ". Dr Yukawa mentioned the importance of force in physics repeatedly especially in the lecture - Day One and Day Two. Please see below.

From Wiki <Line of Force>

"
Historian Nancy J. Nersessian in her paper "Faraday's Field Concept" distinguishes between the ideas of Maxwell and Faraday:^[5]

The specific features of Faraday's field concept, in its 'favourite' and most complete form, are that force is a substance, that it is the only substance and that all forces are interconvertible through various motions of the lines of force. These features of Faraday's 'favourite notion' were not carried on. Maxwell, in his approach to the problem of finding a mathematical representation for the continuous transmission of electric and magnetic forces, considered these to be states of stress and strain in a mechanical aether. This was part of the quite different network of beliefs and problems with which Maxwell was working.

"

I want to quote what Dr Yukawa wrote in his book Invisible things (published in 1946).

Chapter 3 Force and Energy

........ there is a close relation between electromagnetic force and photon. Looking at the electric force between electron and nucleus from a different perspective we can say that electron and nucleus always exchange energy by means of photon. In our visible world force and matter are totally different concepts but in invisible micro world this difference between force and matter become quite unclear. In this micro world the exchange of matter like photon and force working are the front side and the back side of the same fact.

===
On Physical Lines of Force - continued

  Undulations issuing from a centre world, according to the calculations of Professor Challis, produce an effect similar to attraction in the direction of the centre; but admitting this to be true, we know that two series of undulations traversing the same space do not combine into one resultant as two attractions do, but produce an effect depending on relations of phase as well as intensity, and if allowed to proceed, they diverge from each other without any mutual action. In fact the mathematical laws of attractions are not analogous in any respect to those undulations, while they have remarkable analogies with those of currents, of the conduction of heat and electricity and of elastic bodies. 

=== 

My Internal Note - 4

This part is difficult to understand without some knowledge of the background in this year and some writing of Professor Challis. "Undulations" seem to be "waves".

https://books.google.com.hk/books?id=zfM8AAAAIAAJ&pg=PA693&lpg=PA693&dq=Challis+undulations&source=bl&ots=kmbmqGi5O8&sig=sGh1xCzlYvFEbHa0ZHVjCUqyiAg&hl=en&sa=X&ei=PTAWVeeDF4K3mwW2z4DwDA&redir_esc=y#v=onepage&q=Challis%20undulations&f=false 

===  

On Physical Lines of Force - continued

  In the Cambridge and Dublin Mathematical Journal for January 1847, Professor William Thomson has given a "Mechanical Representation of Electric, Magnetic and Galvanic Forces," by means of the displacements of the particles of an elastic solid in a state of strain. In this representations we must make the angular displacement at every point of the solid proportional to the magnetic force at the corresponding point of the magnetic field, the direction of the axis of rotation of the displacement corresponding to the direction of the magnetic force. The absolute displacement of any particle will then correspond in magnitude and direction to that which I have identified with the electrotonic state; and the relative displacement of any particle, considered with reference to the particle in its immediate neighbourhood, will correspond in magnitude and direction to the quantity of electric current passing through the corresponding point of the magneto-electric field. The author of  this method of representations does not attempt to explain the origin the observed  forces by the effects due to these strains in the elastic solid, but makes use of the mathematical analogies of the two problems to assist the imagination in the study of both.


My Internal Note - 5 (underlined by sptt)

This part is also difficult to understand without knowing what Professor William Thomson says in "Mechanical Representation of Electric, Magnetic and Galvanic Forces" as well as also the background in this ear. (* 1) Ref Note at the end. 

The underlined part suggests an idea of 'curl' or 'rotation'. Wiki once stated that <The name "curl" was first suggested by James Clerk Maxwell in 1871> but later changed as follows:


Wiki "Curl (Mathematics)
"
The name "curl" was first suggested by James Clerk Maxwell in 1871^[1] but the concept was apparently first used in the construction of an optical field theory by James MacCullagh in 1839.<sup>[2]

"</sup> 

Mathematical concept of curl is important to understand electromagnetic phenomena. Curl is not a physics law but a mathematician invention or definition, which however explains electromagnetic phenomena well or mathematically in a compact form, at least better than by language if you understand it (to some extent at least). You can find in this writing (On Physical Lines of Force) the direction of rotation is (not a circular but) an axis, which is a definition like 'cross product'. 



===  

On Physical Lines of Force - continued

  We come now to consider the magnetic influence as existing in the form of some kind of pressure or tension, or more generally, of stress in the medium.
  Stress is action or reaction between the consecutive parts of a body, and consists in general of pressure or tension different in different directions at the same point of the medium.
  The necessary relations among these forces have been investigated by mathematicians; and it has been shown that the most general type of a stress consists of a combination of three principal pressures or tensions, in directions at right angles to each other.
  When two of the principal pressures are equal, the third becomes an axis of symmetry, either greatest or least pressure, the pressure at right angle to this axis being all equal.
  When the three principal pressures are equal, the pressure is equal in every direction, and there results a stress having no determinate axis of direction, of which we have an example of in simple hydrostatic pressure.

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My Internal Note - 6

This part also will be easy to understand if you have knowledge of curl to a certain extent.

　　－－－＞
　　　  []
　　ーーー＞
　

　　－－－＞
　　　　 []
　　＜ーーー

　  －－－ーー＞
　　　　 []
　　ーーー＞


Consider and visualize the rotation of []. The axis is <into or from the screen>.


 ===  

On Physical Lines of Force - continued

  The general type of a stress is not suitable as a representation of a magnetic force, because a line of magnetic force has direction and intensity, but has no third quality including any difference between the sides of the line, which would be analogous to that observed in the case of polarized light*.

* See Faraday's 'Researches' : 3252

  We must therefore represent the magnetic force at one point by a stress having a single axis of greatest of least pressure, and all the pressures at right angle to this axis is equal. It may be objected that it is inconsistent to present a line of force, which is essentially dipolar, by an axis of stress, which is necessarily isotropic; but we know that every phenomenon of action and reaction is isotropic in its results, because the effects of the force on the bodies between which it acts are equal and opposite, while the nature and origin of the force may be dipolar, as in the attraction between a north and a south pole.
  Let us next consider the mechanical effect of a state of stress symmetrical about an axis. We may resolve it, in all case, into a simple hydrostatic pressure, combined with a simple pressure or tension along the axis. When the axis is that of greatest pressure, the force along the axis will be a pressure. When the axis is that of least pressure, the force along the axis will be a tension.
  If we observe the lines of force between two magnets, as indicated by iron flings, we shall see that whenever the lines of force pass from one pole to another, there is attraction between those poles; and where the lines of force from the poles avoid each other and are dispersed into space, the poles repel each other, so that in both cases they are drawn in the direction f the resultant of the lines of force.
  It appears therefore that the stress in the axis of a line of magnet force is a tension, like that of a rope.
  If we calculate the lines of force in the neighbourhood of two gravitating bodies, we shall find them the same direction as those near two magnetic of the same name; but we know that the mechanical effect is that of attraction instead of repulsion. The lines of force in this case do not run between the bodies, but avoid each other, and are dispersed over space. In order to produce the effect of attraction, the stress along the lines of gravitating force must be a pressure.
  Let us now suppose that the phenomena of magnetism depend on the existence of a tension in the direction of the lines of force, combined with a hydrostatic pressure; or in other words, a pressure greater in the equatorial than in the axial direction; the next question is what mechanical explanation can we give of this inequality of pressure in a fluid or mobile medium?  The explanation which most readily occurs to the mind is that the excess of pressure in the equatorial direction arises from the centrifugal force of vortices or eddies in the medium having their axes in the directions parallel to the lines of force.
  The explanation of the cause of the inequality of pressure at once suggests the means of representing the dipolar character of the line of force. Every vortex is essentially dipolar, the two extremities of its axis being distinguished by the direction of its revolution as observed from those points.
  We also know that when electricity circulates in a conductor, it produces line of magnetic force passing through the circuit, the direction of the lines depending on the direction of the circulation. Let us suppose that the direction of the revolution of our vortices is that in which vitreous electricity must revolve in order to produce lines of force whose direction within the circuit is the same as ttat of the given lines of force.

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My Internal Note - 6

This part is difficult to follow without some knowledge of fluid dynamics, equations and drawings.
Refer to "right- hand rule", which is, as the name shows, a rule, not a law of nature.

  We shall suppose at present that all the cortices in any one part of the field are revolving  in the same direction about axes nearly parallel, but that in passing from one part of the field to another, the direction of the axes, the velocity of rotation, and the density of the substance of the vortices are subject to change. We shall investigate the resultant mechanical effect upon an element of the medium, and from the mathematical expression of this resultant e shall deduce the physical character of its different component parts.

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My Internal Note -7

Please remind that the title of Part I is "The theory of Molecular Vortices applied to Magnetic Phenomena".  Maxwell tries to explain the source of magnetic forces by using the model of Molecular Vortices which are revolving.
 


Note at the end

(*1)  Evolution of Electromagnetics in the 19th Century
I. V. Lindell
Helsinki Univ. Tech., Otakaari 5A, Espoo 02015HUT, Finland

3.2 Thomson’s analogies

William Thomson (Kelvin) (1824–1907) had read Fourier’s
book when entering the University of Cambridge in 1840.
He wrote a paper showing that Fourier’s stationary flow of
heat was mathematically analogous to Coulomb’s force law
even if the former applied contiguous transfer of heat and the
latter action over a distance. The lines of heat flow appeared
to follow exactly Faraday’s electric lines of force. This gave
Thomson the idea to represent the electric field in terms of
a flux of electricity starting from the charge point. Another
set of analogies was found between electrostatic polarization
in insulating media and displacements in elastic solids due to
stress. In 1856 he made an attempt to explain the Faraday rotation
in terms of molecular vortices caused by the magnetic
field.
 
The underlined part (made by sptt) may closely related this Maxwell paper, especially Part I "The Theory of Molecular Vortices applied to Magnetic Phenomena. (1861)"

------

"Evolution of Electromagnetics in the 19th Century" is an outline and treat "the Continental Theories" and "British Theories' equally or rather neutrally.

 
sptt

My Note - 4) Maxwell, PREFACE of A TREATISE ON ELECTRICITY AND MAGNETISM

Dr Yukawa talked in his lecture Day One of his three day lecture about the debates on <Action-at-distance and Contract Force ("Near Force" )> and made a brief history of these two theories and as a conclusion he referred to what Maxwell did. Please see Day One - 13.遠隔力と近接力 Action-at-distance and Contact Force and 14.マクスウェルによる解決 Solution by Maxwell.


14.マクスウェルによる解決 Solution by Maxwell

Dr Yukawa said as quoted as below at the end of this chapter and which is also the last chapter of the lecture of Day One.

"
Then after the story had become more and more complicated Maxwell came in. His famous book on Electromagnetism, Treaties on Electricity and Magnetism, 1873 is a very thick book. I have not read much and those who have read are few, I suppose. A very interesting thing is written in the preface of this book. Generally a book having a poor preface is not a good book. There is no exception, I think. At least one thing very striking a cord should be written in the preface, otherwise the book is not a good book. What Maxwell wrote in the preface is that he takes a standpoint of  "Near Force" like Faraday. And by this he thoroughly explained the then Electromagnetic theory based on Action-at-distance in terms of  "Near Force", plus he drew a conclusion the light being Electromagnetic phenomenon. This is written in this book. This story is just an opposite direction of the development of mechanics. Thus was what actually happened.

"
So it is not a bad thing to see what Maxwell wrote in the preface of Treaties on Electricity and Magnetism (published in 1973).

A TREATISE ON ELECTRICITY AND MAGNETISM
BY
JAMES CLERK MAXWELL

PREFACE

THE fact that certain bodies, after being rubbed, appear to attract other bodies, was known to the ancients. In modern times, a great variety of other phenomena have been observed, and have been found to be related to these phenomena of attraction. They have been classed under the name of Electric phenomena, amber, ?i\eKTpov (Greek), having been the substance in which they were first described.
Other bodies, particularly the loadstone, and pieces of iron and steel which have been subjected to certain processes, have also been long known to exhibit phenomena of action at a distance. These phenomena, with others related to them, were found to differ from the electric phenomena, and have been classed under the name of Magnetic phenomena, the loadstone, /zayi^? (Greek), being found in the Thessalian Magnesia.
These two classes of phenomena have since been found to be related to each other, and the relations between the various phenomena of both classes, so far as they are known, constitute the science of Electromagnetism.
In the following Treatise I propose to describe the most important of these phenomena, to shew how they may be subjected to measurement, and to trace the mathematical connexions of the quantities measured. Having thus obtained the data for a mathematical theory of electromagnetism, and having shewn how this theory may be applied to the calculation of phenomena, I shall endeavour to place in as clear a light as I can the relations between the mathematical form of this theory and that of the fundamental science of Dynamics, in order that we may be in some degree prepared to determine the kind of dynamical phenomena among which we are to look for illustrations or explanations of the electromagnetic phenomena.
In describing the phenomena, I shall select those which most clearly illustrate the fundamental ideas of the theory, omitting others, or reserving them till the reader is more advanced.
The most important aspect of any phenomenon from a mathematical point of view is that of a measurable quantity. I shall therefore consider electrical phenomena chiefly with a view to their measurement, describing the methods of measurement, and defining the standards on which they depend.
In the application of mathematics to the calculation of electrical quantities, I shall endeavour in the first place to deduce the most general conclusions from the data at our disposal, and in the next place to apply the results to the simplest cases that can be chosen. I shall avoid, as much as I can, those questions which, though they have elicited the skill of mathematicians, have not enlarged our knowledge of science.
The internal relations of the different branches of the science which we have to study are more numerous and complex than those of any other science hitherto developed. Its external relations, on the one hand to dynamics, and on the other to heat, light, chemical action, and the constitution of bodies, seem to indicate
the special importance of electrical science as an aid to the interpretation of nature.
It appears to me, therefore, that the study of electromagnetism in all its extent has now become of the first importance as a means of promoting the progress of science.
The mathematical laws of the different classes of phenomena have been to a great extent satisfactorily made out.
The connexions between the different classes of phenomena have also been investigated, and the probability of the rigorous exactness of the experimental laws has been greatly strengthened by a more extended knowledge of their relations to each other.
Finally, some progress has been made in the reduction of electromagnetism to a dynamical science, by shewing that no electromagnetic phenomenon is contradictory to the supposition that it depends on purely dynamical action.
What has been hitherto done, however, has by no means exhausted the field of electrical research. It has rather opened up that field, by pointing out subjects of enquiry, and furnishing us with means of investigation.
It is hardly necessary to enlarge upon the beneficial results of magnetic research on navigation, and the importance of a knowledge of the true direction of the compass, and of the effect of the iron in a ship. But the labours of those who have endeavoured to render navigation more secure by means of magnetic
observations have at the same time greatly advanced the progress of pure science.
Gauss, as a member of the German Magnetic Union, brought his powerful intellect to bear on the theory of magnetism, and on the methods of observing it, and he not only added greatly to our knowledge of the theory of attractions, but reconstructed the whole of magnetic science as regards the instruments used, the methods of observation, and the calculation of the results, so that his memoirs on Terrestrial Magnetism may be taken as models of physical research by all those who are engaged in the measurement of any of the forces in nature.
The important applications of electromagnetism to telegraphy have also reacted on pure science by giving a commercial value to accurate electrical measurements, and by affording to electricians the use of apparatus on a scale which greatly transcends that of any ordinary laboratory. The consequences of this demand for electrical knowledge, and of these experimental opportunities for acquiring it, have been already very great, both in stimulating the energies of advanced electricians, and in diffusing among practical men a degree of accurate knowledge which is likely to conduce to the general scientific progress of the whole engineering profession.
There are several treatises in which electrical and magnetic phenomena are described in a popular way. These, however, are not what is wanted by those who have been brought face to face with quantities to be measured, and whose minds do not rest satisfied with lecture-room experiments.
There is also a considerable mass of mathematical memoirs which are of great importance in electrical science, but they lie concealed in the bulky Trans actions of learned societies ; they do not form a connected system ; they are of very unequal merit, and they are for the most part beyond the comprehension of any but professed mathematicians.
I have therefore thought that a treatise would be useful which should have for its principal object to take up the whole subject in a methodical manner, and which should also indicate how each part of the subject is brought within the reach of methods of verification by actual measurement.
The general complexion of the treatise differs considerably from that of several excellent electrical works, published, most of them, in Germany, and it may appear that scant justice is done to the speculations of several eminent electricians and mathematicians. One reason of this is that before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday s Experimental Researches on Electricity. I was aware that there was supposed to be a difference between Faraday s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other's language. I had also the conviction that this discrepancy did not arise from either party being wrong. I was first convinced of this by Sir William Thomson *, to whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject.

(* I take this opportunity of acknowledging my obligations to Sir W. Thomson and to Professor Tait for many valuable suggestions made during the printing of this work.)

As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians.
For instance, Faraday, in his mind s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance : Faraday saw a medium where they saw nothing but distance : Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.
When I had translated what I considered to be Faraday s ideas into a mathematical form, I found that in general the results of the two methods coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday s methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.
I also found that several of the most fertile methods of research discovered by the mathematicians could be expressed much better in terms of ideas derived from Faraday than in their original form.
The whole theory, for instance, of the potential, considered as a quantity which satisfies a certain partial differential equation, belongs essentially to the method which I have called that of Faraday. According to the other method, the potential, if it is to be considered at all, must be regarded as the result of a summation of the electrified particles divided each by its distance from a given point. Hence many of the mathematical discoveries of Laplace, Poisson, Green and Gauss find their proper place in this treatise, and their appropriate expression in terms of conceptions mainly derived from Faraday.
Great progress has been made in electrical science, chiefly in Germany, by cultivators of the theory of action at a distance. The valuable electrical measurements of W. Weber are interpreted by him according to this theory, and the electromagnetic speculation which was originated by Gauss, and carried on by Weber, Riemann, J. and C. Neumann, Lorenz, &c. is founded on the theory of action at a distance, but depending either directly on the relative velocity of the particles, or on the gradual propagation of something, whether potential or force, from the one particle to the other. The great success which these eminent men have attained in the application of mathematics to electrical phenomena gives, as is natural, additional weight to their theoretical speculations, so that those who, as students of electricity, turn to them as the greatest authorities in mathematical electricity, would probably imbibe, along with their mathematical methods, their physical hypotheses.
These physical hypotheses, however, are entirely alien from the way of looking at things which I adopt, and one object which I have in view is that some of those who wish to study electricity may, by reading this treatise, come to see that there is another way of treating the subject, which is no less fitted to explain the phenomena, and which, though in some parts it may appear less definite, corresponds, as I think, more faithfully with our actual knowledge, both in what it affirms and in what it leaves undecided.
In a philosophical point of view, moreover, it is exceedingly important that two methods should be compared, both of which have succeeded in explaining the principal electromagnetic phenomena, and both of which have attempted to explain the propagation of light as an electromagnetic phenomenon, and have actually calculated its velocity, while at the same time the fundamental conceptions of what actually takes place, as well as most of the secondary conceptions of the quantities concerned, are radically different.
I have therefore taken the part of an advocate rather than that of a judge, and have rather exemplified one method than attempted to give an impartial description of both. I have no doubt that the method which I have called the German one will also find its supporters, and will be expounded with a skill worthy of its ingenuity.
I have not attempted an exhaustive account of electrical phenomena, experiments, and apparatus. The student who desires to read all that is known on these subjects will find great assistance from the Traite d'Electricite of Professor A. de la Rive, and from several German treatises, such as Wiedemann's Galvanismus, Riess Reibiingselektricitat, Beer s Einleitung in die Elektrostatik, &c.
I have confined myself almost entirely to the mathematical treatment of the subject, but I would recommend the student, after he has learned, experimentally if possible, what are the phenomena to be observed, to read carefully Faraday s Experimental Researches in Electricity. He will there find a strictly contemporary historical account of some of the greatest electrical discoveries and investigations, carried on in an order and succession which could hardly have been improved if the results had been known from the first, and expressed in the language of a man who devoted much of his attention to the methods of accurately describing scientific operations and their results *.
(* Life and Letters of Faraday, vol. i. p. 395.)
It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state, and in the case of Faraday's Researches this is comparatively easy, as they are published in a separate form, and may be read consecutively. If by anything I have here written I may assist any student in understanding Faraday's modes of thought and expression, I shall regard it as the accomplishment of one of my principal aims to communicate to others the same delight which I have  found myself in reading Faraday s Researches.
The description of the phenomena, and the elementary parts of the theory of each subject, will be found in the earlier chapters of each of the four Parts into which this treatise is divided. The student will find in these chapters enough to give him an elementary acquaintance with the whole science.
The remaining chapters of each Part are occupied with the higher parts of the theory, the processes of numerical calculation, and the instruments and methods of experimental research.
The relations between electromagnetic phenomena and those of radiation, the theory of molecular electric currents, and the results of speculation on the nature of action at a distance, are treated of in the last four chapters of the second volume.

Feb. 1, 1873.

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Generally what Maxwell wrote corresponds what Dr Yukaawa told in his lecture.

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Additions

Although Dr Yuakawa did not mentioned the prefaces or introductions of some other Maxwell's original writings will be certainly also worth reading.

On Physical Lines of Force (published in March, 1861)

Part I - The Theory of Molecular Vortices applied to Magnetic Phenomena

  In all phenomena involving attractions and repulsions, or any forces depending on the relative positions of bodies, we have to determine the magnitude and direction of the force which would act on a given body, if placed in a given position.
  In the case of a body acted on by the gravitation of a sphere, this force is inversely as the square of the distance, and in a straight line to the centre of the sphere. In the case of two attracting spheres, or of a body not spherical, the magnitude and direction of the force vary according to more complicated laws. In electric and magnetic phenomena, the magnitude and direction of the resultant force at any point is the main subject of investigation. Suppose that the direction of the force at any point is known, then, if we draw a line so that in every part of its course it coincide in direction with the force at that point, this line may be called a line of force, since it indicates the direction of the force in every part of its course.
  By drawing a sufficient number of lines of force we may indicates the direction of the force in every part of the space it acts.
  Thus if we strew iron filings on paper near a magnet, each filing will be magnetized by induction, and the consecutive filings will unite by their opposite poles, so as to form fibers, and these fibers will indicate the direction of the lines of force. The beautiful illustration of the presence of magnetic force afforded by this experiment, naturally tends to make us think of the lines of force as something real, and as indicating something more than the mere resultant of the two forces, whose seat of action is at a distance, and which do not exist there at all until a magnet is placed in that part of the field.





sptt

My Note - 3) Quaternion

Dr Yukawa told a brief history of vector in his lecture Day Two and commented on Quaternion as follows:

4.ベクトルの歴史 History of Vector

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One remarkable exception is vector. We think that vectors had come out as they should have and they have been used already since a very long time ago. But it was not so. As I have already mentioned several times in the books of Maxwell we can find ordinary components - ie Maxwell's equations which expressed by Cartesian components, each multiplied by a derivative and no or a very few (if any) vectors involved. This was a story in late 19th century when the symbol of vector was not found.
What existed before vector was quaternion. It is really strange. We know Hamilton. Those who study Quantum Mechanics study Hamilton and Lagrange. Hamilton lived in 19th century. His canonical formalism is studied even now. Both Hamilton and Lagrange were great physicians. Hamilton, also mathematician, created quaternion. What is Quaternion? This is the forth dimension number. Quaternions are not real numbers while the ordinary vectors are real. I do not know why a strange thing like quaternion was used but quaternion was popular back in the 19th century.  Although I had no particular interest in it I investigated it and found that an English (Scottish) physician Tait wrote a large volume of book titled "Quaternion". Tait worked with Lord Kevin.

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He did not mention that Maxwell used quaternion (Maxwell used for some time) and why. Quaternion is convenient to describe Curl or "Rotation" like Imaginary number (i² = −1, i = √−1) being convenient to describe the simple rotation (90-degree,180-degree, etc rotation) and frequency. I found this in "On the Notation of Maxwell's Field Equations" by André Waser and others.


"On the Notation of Maxwell's Field Equations" (latest version) issued by André Waser on 28-06.2000,
http://www.itpa.lt/~acus/Knygos/Clifford_articles/Clifford_Authors/05_DeLeo_Quaternions/quaternions5/Orig_maxwell_equations.pdf

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A general quaternion has a scalar (real) and a vector (imaginary) part. In the example below
‚a‘ is the scalar part and ‘ib + jc + kd’ is the vector part.
Q = a + ib + jc + kd
Here a, b, c and d are real numbers and i, j, k are the so-called HAMILTON‘ian unit vectors
with the magnitude of √−1. They fulfill the equations

i² = j² = k² = ijk = −1
 
ij = k,  jk = i,  ki = j

ij = - ji,  jk = - kj,  ki = - ik

A nice presentation about the rotation capabilities of the HAMILTON’ian unit vectors in a
three-dimensional ARGAND diagram was published by GOUGH.
  
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Some parts are modified (the meaning unchanged) and the underlined by sptt.

Please read 

"On the Notation of Maxwell's Field Equations". A concise and nice article to know somewhat original version of Maxwell's Field Equations.

A more kind explanation is found http://hforsten.com/quaternion-roots-of-modern-vector-calculus.html

A full copy

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Quaternion roots of modern vector calculus

2013-02-03 In Mathematics.

Before the vector calculus was invented mathematicians used to do vector calculus like operations using quaternions. Quaternions are four dimensional extension of complex numbers. They have two additional imaginary units j and k. Quaternion multiplication is non-commutative and is defined by the formula:

i2=j2=k2=ijk=−1

One easy way to remember the multiplication rules is with the following diagram:
Multiplying two different imaginary units gives the positive next one in the diagram, if the arrow goes in the right way between them and negative otherwise. For example ij=+k, because arrow between i and j goes the right way. Same way ji=−k, ki=j and so on.
Quaternions with real part zero (q=0+ai+bj+ck) are called pure imaginary quaternions and they have some properties that make them behave like three dimensional vectors.
Multiplication of two pure imaginary quaternions p and q is:
p×q=(p1i+p2j+p3k)×(q1i+q2j+q3k)
=−p1q1−p2q2−p3q3+p1q2k−p1q3j−p2q1k+p2q3i+p3q1j−p3q2i
=−(p1q1+p2q2+p3q3)+(p2q3−p3q2)i+(p3q1−p1q3)j+(p1q2−p2q1)k
If we now think that quaternions p and q were three dimensional vectors p⃗  and q⃗ , this product can be written shorter with vector calculus operators.
p⃗ q⃗ =−p⃗ ⋅q⃗ +p⃗ ×q⃗ 
Where p⃗ ⋅q⃗  is the dot product and p⃗ ×q⃗  is the cross product.
If we change the quaternion multiplication rules to i2=j2=k2=0, quaternion multiplication gives only the cross product. This rule and the diagram above also might help in remembering how to calculate cross product and curl without using the determinant rule.
Maxwell originally wrote his famous equations in quaternion form and they were only later rewritten in the modern vector notation. Quaternion vector calculus can do pretty much everything that the modern vector calculus can do, except the notation is little more cumbersome. For example Maxwell wrote the curl of vector v, ∇×v⃗ , as V∇v. Where V meant the vector part, v is a pure imaginary quaternion and ∇ is the pure imaginary quaternion similar to vector calculus ∇:

∇=ddxi+ddyj+ddzk

Note that ∇2=−(d2d2x+d2d2y+d2d2z), negative of the usual ∇2 in the modern vector calculus.
Even today the i,j and k from quaternions are sometimes used in the vector calculus as basis vectors and sometimes they can be thought to be quaternion basis units.
If you are interested in the old stuff, Maxwell's original paper "A treatise on electricity and magnetism(1873)" with quaternion notation is available at archive.org.

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As Dr Yukawa repeated in his lecture we must read the original writings of the great thinkers to find how the original thoughts and ideas were painfully born.

Other opinions on Quaternion

sptt