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on the time required for the assumption of the electrotonic state, round a wire carrying a current, that may help the subject on. The time must probably be short as the time of light; but the greatness of the result, if affirmative, makes me not despair. Perhaps I had better have said nothing about it, for I am often long in realising my intentions, and a failing memory is against me.—Ever yours most truly, M. Faraday.
From The Same.
Albemarle Street, 7th November 1857. I have just read and thank you heartily for your papers. I intended to send you copies of two of mine. I think I have sent them, but do not find them ticked off. So I now send copies, not because they are assumed as deserving your attention, but as a mark of my respect, and desire to thank you in the best way that I can.
From Prof. Q. G. Stokes.
School of Mines,
I have just received your papers on a dynamical top, etc., and the account of experiments on the perception of colour. The latter, which I missed seeing at the time when it was published, I have just read with great interest. The results afford most remarkable and important evidence in favour of the theory of three primary colour-perceptions, a theory which you, and you alone, so far as I know, have established on an exact numerical basis.
From Prof. Tyndall.
Royal Institution, 7th November 1857. I am very much obliged to you for your kind thoughtfulness in sending me your papers on the Dynamical Top and on the Perception of Colour, as also for your memoir on Lines of Force, received some time ago. I never doubted the possibility of giving Faraday's notions a mathematical form, and you would probably be one of the last to deny the possibility of a totally different imagery by which the phenomena might be represented.1
To Professor Faraday.
129 Union Street, Aberdeen, 9th November 1857.
Dear Sir—I have to acknowledge receipt of your papers on the Relations of Gold to Light, and on the Conservation of Force. Last spring yon were so kind as to send me a copy of the latter paper, and to ask what I thought of it.
That question silenced me at that time, but L have since heard and read various opinions on the subject, which render it both easy and right for me to say what I think. And first I pass over some who have never understood the known doctrine of conservation of force, and who suppose it to have something to do with the equality of action and reaction.
Now, first, I am sorry that we do not keep our words for distinct things more distinct, and speak of the "Conservation of Work or of Energy" as applied to the relations between the amount of " vis viva" and of "tension" in the world; and of the "Duality of Force" as referring to the equality of action and reaction.
Energy is the power a thing has of doing work arising either from its own motion or from the " tension" subsisting between it and other things.
Force is the tendency of a body to pass from one place to another, and depends upon the amount of change of "tension" which that passage would produce.
Now, as far as I know, you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle to be actually believed in. We have had streams of hooks and eyes flying around magnets, and even pictures of them so beset;
1 For confirmation of this, see Maxwell's (fragmentary) preface to the smaller treatise on electricity, published posthumously in 1881 ; especially these words: "In the larger treatise I sometimes made use of methods which I do not think the best in themselves, but without which the student cannot follow the investigations of the founders of the Mathematical Theory of Electricity. I have since become aware of the superiority of methods akin to those of Faraday, and have therefore adopted them from the first." but nothing is clearer than your descriptions of all sources of force keeping up a state of energy in all that surrounds them, which state by its increase or diminution measures the work done by any change in the system. You seem to see the lines of force curving round obstacles and driving plump at conductors, and swerving towards certain directions in crystals, and carrying with them everywhere the same amount of attractive power, spread wider or denser as the lines widen or contract.
You have also seen that the great mystery is, not how like bodies repel and unlike attract, but how like bodies attract (by gravi[ta]tion). But if you can get over that difficulty, either by making gravity the residual of the two electricities or by simply admitting it, then your lines of force can "weave a web across the sky," and lead the stars in their courses without any necessarily immediate connection with the objects of their attraction.
The lines of Force from the Sun spread out from him, and when they come near a planet curve out from it, so that every planet diverts a number depending on its mass from their course, and substitutes a system of its own so as to become something like a comet, if lines of force were visible.
The lines of the planet are separated from those of the Sun by the dotted line. Now conceive every one of these lines (which never interfere but proceed from sun and planet to infinity) to have a pushing force instead of a pulling one, and then sun and planet will be pushed together with a force which comes out as it ought, proportional to the product of the masses and the inverse square of the distance.
The difference between this case and that of the dipolar forces is, that instead of each body catching the lines of force from the rest, all the lines keep as clear of other bodies as they can, and go off to the infinite sphere against which I have supposed them to push.
Here then we have conservation of energy (actual and potential), as every student of dynamics learns, and besides this we have conservation of " lines of force" as to their number and total strength, for every body always sends out a number proportioned to its own mass, and the pushing effect of each is the same.
All that is altered when bodies approach is the direction in which these lines push. When the bodies are distant the distribution of lines near each is little disturbed. When they approach, the lines march round from between them, and come to push behind each, so that their resultant action is to bring the bodies together with a resultant force increasing as they approach.
Now the mode of looking at Nature, which belongs to those who can see the lines of force, deals very little with "resultant forces," but with a network of lines of action of which these are the final results, so that I, for my part, can not realise your dissatisfaction with the law of gravitation, provided you conceive it according to your own principles. It may seem very different when stated by the believers in " forces at a distance," but there can be only differences in form and conception, not in quantity or mechanical effect, between them and those who trace force by its lines.
But when we face the great questions about gravitation— Does it require time? Is it polar to the "outside of the universe" or to anything 1 Has it any reference to electricity? or does it stand on the very foundation of matter, mass, or inertia? —then we feel the need of tests, whether they be comets or nebulae, or laboratory experiments, or bold questions as to the truth of received opinions.
I have now merely tried to show you why I do not think gravitation a dangerous subject to apply your methods to, and that it may be possible to throw light on it also by the embodiment of the same ideas, which are expressed mathematically in the functions of Laplace and of Sir W. R. Hamilton in Planetary Theory.
But there are questions relating to the connection between magneto-electricity and certain mechanical effects which seems to me opening up quite a new road to the establishment of principles in electricity, and a possible conformation of the physical nature of magnetic lines of force. Professor W. Thomson seems to have some new lights on this subject.—Yours sincerely,
James Clerk Maxwell.
To Prof. Maxwell From Prof. Faraday.1
Albemarle Street, London, 13th November 1857.
If on a former occasion I seemed to ask you what you thought of my paper, it was very wrong; for I do not think any one should be called upon for the expression of their thoughts before they are prepared, and wish to give them. I have often enough to decline giving an opinion because my mind is not ready to come to a conclusion, or does not wish to be committed to a view that may by further consideration be changed. But having received your last letter, I am exceedingly grateful to you for it, and rejoice that my forgetfulness of having sent the former paper on conservation has brought about such a result. Your letter is to me the first intercommunication on the subject with one of your mode and habit of thinking. It will do me much good, and I shall read and meditate it again and again.
I daresay I have myself greatly to blame for the vague use of expressive words. I perceive that I do not use the word "force" as you define it, "the tendency of a body to pass from one place to another." What I mean by the word is the source or sources of all possible actions of the particles or materials of the universe ; these being often called the powers of nature when spoken of in respect of the different manners in which their effects are shown. In a paper which I have received at the moment from the Phil. Mag., by Dr. Woods, they were called the "forces, such as electricity, heat, etc." In this way I have used the word "force" in the description of gravity which I have given as that expressing the received idea of its nature and source; and such of my remarks as express an opinion or are critical apply only to that sense of it. You may remember I speak to labourers like myself, experimentalists on force generally, who receive that description of gravity as a physical truth, and believe that it expresses all, and no more than all, that concerns the nature and locality of the power. To these it limits the formation of their ideas, and the direction of their exertions, and to these I have endeavoured to speak; showing how such a thought, if accepted, pledged them to a very limited and probably erroneous view of the cause of the force, and to
1 This letter has already been published in the Life of Faraday.