Below, you may view the gear chart for the Moulton MK3 bicycle, calculated using the gear calculator on Sheldon's Web site. Hybrid gearing (using a multi-speed hub as well as derailleur gears) had been known for many years already, though this is a unique, home-built version of it.
The bicycle has many near-duplicate gears and some exact duplicates. The objective of the gearing setup was not to use all 40 gears but to achieve a high-enough top gear despite the small rear wheel. Sheldon disliked coasting down hills, and so he generally equipped his bicycles with a higher top gear than most people would consider necessary.
Smaller sprockets would have allowed smaller chainwheels, but in the 1970s, the choices for the outside sprocket of a 4-speed cluster were limited. The cluster Sheldon installed is probably a Regina or Atom 5-speed freewheel with the outermost cog removed and the ratchet assembly glued or brazed together: the Sturmey-archer hub will not shift properly unless it freewheels.
The very low bottom gear of 19.6 inches is easy enough to achieve with a small, 16-inch driving wheel, but the 108-inch top gear would not be possible without the 72-tooth chainring, even with the 1.5/1 increase ratio of the 5-speed hub's top gear. Some of today's internally-geared hubs offer a higher top gear -- none which are designed for a multi-sprocket cluster offer this.
With Sheldon's gear calculator, you may also calculate meters of development and gain ratio (which accounts for crank length). But note that some of the ratios given for the 5-speed hub are imprecise, leading to further small errors. In case you would care to perform more-accurate calculations, the 5-speed hub's ratios are 2/3, 15/19, 1/1, 19/15 and 3/2, or in decimals to three places, .667, .789, 1.000, 1.267 and 1.500. Sheldon was not such a stickler for accuracy in such calculations as I am!
I have drawn arrows to indicate a couple of sensible gearing progressions. The 5-speed hub offered indexed shifting, a feature that succeeded with derailleur gearing only some 15 years after Sheldon built up this bicycle. When shifting only the 5-speed hub (blue arrows) the bicycle offers an excellent, quick-shifting sequence suitable for stop-and-go urban riding.
The 1/1 middle gear of the 5-speed hub is highly efficient, as the mechanism inside the hub is only idling. A preferred full-range gear sequence (red arrows) uses the hub's middle gear as much as possible to maintain high efficiency except at the extremes of the gear range. The sequence, however, is not simple!
But wait a minute, this is a suspended bicycle, and the torque applied to the rear axle by the hub (except in the middle gear) tends to work the rear suspension. Chain tension and weight transfer due to acceleration both tend to make the rear end of the bicycle dive. The hub reinforces the dive in the higher gears and counteracts it in the lower gears, suggesting that it may be preferable to stay in the low gears of the hub longer. At this point, the analysis, which depends on suspension characteristics, chainwheel and sprocket size and hub efficiency, becomes too complicated for me to attempt.