James Clerk Maxwell

TO H. R. DROOP, Esq. (of the Equity Bar).

                                                            8 Palace Gardens Terrace, W.,
                                                           24th January 1862.

     . . . When I wrote to you about closed currents, it was partly to arrange my own thoughts by imagining myself    speaking to you. Ampère's formula containing n and k is the most general expression for an attractive or repulsive   force in the line joining the elements; and I now find that if you take the most general expression consistent with   symmetry for an action transverse to that line, the resulting expression for the action of a closed current on an  element gives a force not perpendicular to that element. Now, experiment 3d (Ampère) shows that the force on a movable element is perp. to the directions of the current, so that I see Ampère is right.

     But the best way of stating the effects is with reference to "lines of magnetic force." Calculate the magnetic force in   any plane, arising from every element of the circuit, and from every other magnetising agent, then the force on an   element is in the line perp. to the plane of the element and of the lines of force.

     But I shall look up Cellerier and Plann, and the long article in Karsten's Cyclopædia. I want to see if there is any   evidence from the mathematical expressions as to whether element acts on element, or whether a current first    produces a certain effect in the surrounding field, which afterwards acts on any other current.

Perhaps there may be no mathematical reasons in favour of one hypothesis rather than the another.

     As a fact, the effect on a current at a given place depends solely on the direction and magnitude of the magnetic   force at that point, whether the magnetic force arises from currents or from magnets. So that the theory of the    effect taking place through the intervention of a medium is consistent with fact, and (to me) appears the simplest in   expression; but I must prove either that the direct action theory is completely identical in its results, or that in some   conceivable case they may be different. My theory of the rotation  of the plane of polarised light by   magnetism is coming out in the Phil. Mag. I shall send you a copy.

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                                                       8 Palace Gardens Terrace,
                                         Kensington, London, W., 

Some time ago, when investigating Bernoulli's theory of gases, I was surprised to find that the internal friction of a    gas (if it depends on the collision of particles) should be independent of the density.

Stokes has been examining Graham's experiments on the rate of flow of gases through fine tubes, and he finds that    the friction, if independent of density, accounts for Graham's results, but, if taken proportional to density, differs    from those results very much. This seems rather a curious result, and an additional phenomenon, explained by the    "collision of particles" theory of gases. Still one phenomenon goes against that theory—the relation between  specific heat at constant pressure and at constant volume, which is in air = 1·408, while it ought to be 1·333.

My brother-in-law, who is still with us, is getting better, and had his first walk on crutches to-day across the room.