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The problem with that layout is that the Bristol Box Kite, like the Henri Farman biplane it was essentially ripped off from, is one where the power to weight ratio is pretty critical. You can tell that from the positioning of the engine and payload, which is all very close to the CoG, this being so that there is no need to add any frivolous weight fore or aft to balance things up.
If you attempted to place engines at the rear of a redesigned twin tailboom Box Kite, you'd have a lot of weight well back from the CoG, necessitating some weight forward of the CoG to counteract it, and then with more weight, you'd negate the additional power from another engine, since you would need it simply to attain enough lift to counteract the weight, which would also necessitate a tougher airframe, since the aerodynamic loads would be increased with the increased speed. Look at where the Wright brothers placed the engine and props on the Wright Flyer for example.
You'd get a faster aeroplane, but it would have to land and take off faster too, which is sort of pointless for something of that ilk. The only vague possibility without adding considerably more weight, would be to move the pilot position to the nose to control the CoG.
Another way around the weight issue, would be to keep the engines over the wing and run the propellers to the rear with extended propshafts, sort of in the manner of how the mid-engined Bell P-39 Aerocobra runs power to the prop on its nose. But that kind of thing is complex from an engineering standpoint and only really advantageous if you are trying to solve the problem of mounting weaponry in a central location, as with the P-38. This aside, more problematic is that if not done correctly, such propshaft arrangements lead to massive vibration. In a pair, they would in any case create a lot of torque unless you had the engines turning the props in opposite directions to cancel one another out, necessitating either gearing or two engines of the same type and weight, but with opposite rotations. But if you lost an engine on something with the kind of control authority a Box Kite had when fitted with two engines, you could probably kiss your ass goodbye. In short, you are getting into a lot of engineering problems for very little benefit other than increased speed, but with greatly reduced control.
The last solution would be propshafts and both props geared to one engine via chains (again, see the Wright Flyer), but it seems to me that there would sinply be no advantage in having the props behind the tail surfaces, since you'd lose the advantage gained from having the propwash act on the control surfaces.
Al
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Wiseman: When you removed the book from the cradle, did you speak the words?
Ash: Yeah, basically.
Wiseman: Did you speak the exact words?
Ash: Look, maybe I didn't say every single little tiny syllable, no. But basically I said them, yeah.
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