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In a well known Maxwell paper he uses the units of wavelength which he calls the Fraunhofer Measure. He states it for the Fraunhofer D and F bands as

$$\lambda_D = 2175 \text{ crazy units} = 589nm$$

$$\lambda_F = 1794 \text{ crazy units} = 486nm$$

So the conversion is:

$$1nm \approx 3.69\text{ crazy units}$$ $$1 \text{ crazy unit} \approx 0.270nm$$

But what is the motivation for this?

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I think the original conversion factor in the question was wrong; I've made an edit fixing it. –  Jason Davies Nov 24 '12 at 21:26
The "crazy unit" is probably a characteristic lattice length scale (between neighboring atoms in a lattice) for a common material, which was easy to compare diffraction experiments with. So all materials were measured relative to this "standard candle" material. –  Qmechanic Nov 24 '12 at 21:59
@Qmechanic I think the reference in my answer below clears it up; the Paris inch was probably more common in those days! –  Jason Davies Nov 24 '12 at 22:06
@JasonDavies oops wrong way round :) –  Lucas Nov 24 '12 at 23:22
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up vote 2 down vote accepted

I'm guessing this is related to the archaic Paris inch, which is $27.069$mm, i.e. $10^8 \times$ the conversion factor.

Reference: Scientific Papers Vol 2 1881-1887, John William Strutt.

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It's from exactly the same area of literature, so it makes sense. Oh, and it says K is Mrs Maxwell (J is Mr) –  Lucas Nov 24 '12 at 23:20
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