Glenlair, the last week of March

Glenlair, the last week of March, 1865. The fire is low and I am redoing the arithmetic I first did in London, because a single figure has been sitting in my notebook like a splinter.

Weber and Kohlrausch, in 1856, measured the ratio between the electrostatic and electromagnetic units of charge. Their number, reduced to velocity, comes to very nearly 310,740,000 metres per second. Fizeau, with his toothed wheel between Suresnes and Montmartre, found light travelling at about 314,000,000. Two instruments, two phenomena, no conceivable connection between them - and the numbers differ by scarcely one part in a hundred. The question that keeps me at this desk is whether that difference is a real discordance or only the accumulated error of two difficult measurements, each honest to within a decimal place or two.

Here is what the agreement buys me, personally. If the electromagnetic ratio and the velocity of light are the same quantity, then light is not a separate mystery but a ripple in the same medium that carries induction - and my equations, which I wrote to bind electricity and magnetism, already contain optics inside them without asking. The whole architecture of the paper I am drafting rests on whether that one digit of agreement is meaningful. Knock out the correspondence and I have an elegant formalism about currents and charges; keep it, and I have the constitution of light itself. A single decimal place is the difference between a curiosity and a unification.

Map the propagation: the dielectric term in my equations gives the wave its speed; the speed is set by two measured constants; those constants were determined by men who never thought of light at all. The wave was in the equations before anyone looked for it, travelling at whatever speed the medium allowed, waiting for the arithmetic to be done.

Tomorrow I shall write to Stokes and tell him plainly: the agreement between Weber’s ratio and Fizeau’s velocity is too close to be accidental, and I intend to say so in print, caveats about experimental error notwithstanding. If a later measurement widens the gap past a decimal place or two, the theory must answer for it - and it will, since the theory now predicts the number rather than borrowing it.