You're right – the manual dose not indicate anything odd here!
I've not been able to photograph it I'm afraid, and I've put it all back together; but visualise it this way…
The slide runs on dovetails with a central channel in which live the screw and nut, and allowing for the channel being still the as-cast finish, the screw looks unexpectedly off-centre to it.
At the apron end of the screw is a plain shank, and measuring from that to the edges of the dovetails, using a vernier caliper, gives an unsymmetrical result.
However, this is not an easy thing to measure; and it's possible the dovetail on one side is wider than the other, to accommodate the tapered gib.
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So let's look at the nut.
In original form this was a rectangular bronze block with a cylindrical spigot on top, locating in a hole drilled in the underside of the slide. A countersunk screw through a smaller-diameter continuation of the hole holds the nut to the slide.
One would expect the spigot to be above the thread's axis, but it is not; by eye and by measuring; although measuring to the thread was chancy because it was so badly worn I think the combination worked from memory. It had about 1/8" backlash – a complete turn of the screw!
Testing this by rotating the nut end-for-end, the side of the nut struck the edge of the entrance to the channel.
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So it would seem the screw is off-centre relatively to the sliding surfaces, and the nut thread is off-centred from its locating spigot, to match the screw.
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When I bored out the nut, by bar between centres, I centred it for height, cross-ways and in axial alignment in a vice on the Myford cross-slide, by centering the screw onto which I had threaded it, and aligning the vice to the nut. This kept the curious off-set intact.
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The mystery remains……