From Thomas Archer Hirst   Nov 4th / 55

Broughton | Nov 4^th / 55

My dear John.

I have been engaged all the week in my spare time in reading Faraday’s 3^rd vol.¹ I find it exceedingly tough work, though exceedingly instructive. In experimental descriptions Faraday is admirably lucid, but in Theoretical matters decidedly obscure. There is an absence of mathematical strictness in his explanations which makes them exceedingly unsatisfactory[.] It is impossible to appreciate these explanations without fathoming, in some manner, his notions of lines of force, and he talks of them so loosely, now giving them a kind of physical reality, and again a merely representative character that it is exceedingly difficult to avoid confusion. In order to understand the very simplest action of a diamagnetic particle in the magnetic field I tried to get a correct interpretation of that often quoted passage on page 33 ‘its tendency is to move from stronger to weaker places of magnetic force’.² The first question is what is meant by ‘the strength of a place of magnetic force’³ and how is it estimated; the second question is, what is the nature of the mutual action between the particle and the magnet which gives to the former this tendency, and what is the state of the particle which causes such mutual action. For this tendency is a mere effect uninteresting in comparison to the state of the particle which causes it. Yet strange to say Faraday often speaks as if this tendency were a final cause⁴ of phenomena. Well now to answer the first question we must examine the definition of lines of force in their representative character merely. The clearest definition I find on pages 328 and 329.⁵

Lines are to be drawn from a magnet in directions indicated by a small magnetic needle moved so as always to be a tangent to its line of motion. These lines are supposed to proceed in a certain direction indicated by the direction in which a marked pole of the needle points. Thus each line represents the direction of the magnetic force at any point. It is also conceived to represent a constant intensity, so that the ‘strength of any place of magnetic force’ is to be estimated by the number of lines which pass through any space of constant area which we may suppose spherical in form. I conceive Faraday’s notion to be something of this kind, though I cannot yet see how we can adapt his notion to mathematical expression.

Consistently with Faradays notion, after having settled arbitrarily how many lines of force are to be drawn from a given magnet into the surrounding space, they must be distributed along the face of the magnet according to the intensity of the part from which they start, that is to say, more lines must be drawn from A and B than from C according as the magnetic intensity at A & B exceeds that at C. Now let a and b be two spheres at different parts of the field having equal radii then the comparative strength of these places is to be considered proportional to the number of lines which intersect the spheres. If instead of an extended magnet a magnetic point be taken this law will be found to coincide with the law of the inverse square of the distance.

According to Faraday’s law of paramagnetic and diamagnetic action the sphere a[,] if paramagnetic and free to move, would change its position so that the greatest number of lines should pass through it and if diamagnetic so that the least possible number should pass through it. Understanding Faraday thus I turn now to the experimental verification of his law. I take his simplest experiment with two pointed poles and an elongated piece of bismuth suspended in the axial line midway between them. I imagine then, roughly, the nature of the lines of force between the poles (a very uncertain way of proceeding I know) which for simplicity I consider to be mere points one possessing N the other S polarity. Between such points the bismuth sets equatorially and the action appears to agree with the law that every particle of bismuth strives to move from stronger to weaker places of force.

For it appears probable that a is a weaker place of force than aʹ and b than bʹ.

But with a single pole the explanation of the action, which is similar, is not so easy. For if aʹ bʹ is the original and ab the final position then although all particles between aʹ and c have moved from places of stronger to places of weaker force those between bʹ and c have moved from places of weaker to places of stronger force.

Faraday never mentions that the tendency of the particles between aʹ and c is stronger than the anti tendency of the particles between bʹ and c.

Indeed I am not sure that he would admit this for on page 344 he says ‘The amount of magnetic is determinate for the same lines of force, whatever the distance of the point or plane, at which their power is exerted is from the magnet.’⁶ On page 349 he says ‘The relative amount of force, or lines of force in a given space is indicated by their number in that space.’⁷ If so then a glance at the last two figures will shew that the amount of force in the space occupied by the bar in its final position is greater than the amount in any other position for more lines of force cross it. The whole bar then has moved in both cases from a place of weaker to a place of stronger magnetic force. Is this not curious? At any rate it shews that although his law may have led Faraday into no error it is an extremely obscure law not at all fitted to define accurately the action of diamagnetic bodies in all circumstances or rather it is a law very easily misunderstood and not very easily understood.

How are you suited with lodgings? How is your health? This week’s close reading has had its usual effect upon my bowels⁸ from which I am only just recovering. Anna joins me in love.

Yours affectionately | T A Hirst

I have written this letter for my own benefit rather than yours in order to force myself to close thoughts on the subject.

RI MS JT/1/H/219