Help Identifying Rectigraph Lens and f-stop equivalence

Wondering if anyone has any info on this lens. It is inscribed in script, " Lancaster & Sons 1/4 pt Patent, Birmingham -> Rectigraph". It has what appears to be two aperture scales labeled as "Time". The main scale reads, "32, 16, 8, 4, 2, 1". The second scale above it reads, "40, 30, 20, 10, 1". In terms of focal length, at infinity, the distance from ground glass to rear element is about 5 1/2 inches. From ground glass to front element is about 7 inches. The lens came on a 1/4 plate camera marked "The Special Instantograph" by J. Lancaster & Son, Birmingham c 1891.

I'm trying to see how I might be able to put this lens to use but am uncertain what the actual focal length is and what the f-stop equivalencies would be, or at least the actual f-stop wide open.

If anyone can help provide info, please let me know. Thanks.

f/7 Rapid Rectilinear. What you took for "1" on the aperture scale is "7". The marked apertures are f/7, f/10, f/20, f/30, f/40.

The other scale is for relative exposure times. 1 unit @f/7, 2 @ f/10, 4 @ f/14, 8 @ f/20 or so, 16 @ f/30 and 32 @ f/40.

Focal length? 5" for quarter plate.

Dan Fromm said:

f/7 Rapid Rectilinear. What you took for "1" on the aperture scale is "7". The marked apertures are f/7, f/10, f/20, f/30, f/40.

The other scale is for relative exposure times. 1 unit @f/7, 2 @ f/10, 4 @ f/14, 8 @ f/20 or so, 16 @ f/30 and 32 @ f/40.

Focal length? 5" for quarter plate.

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Huge thanks Dan! Didn’t even occur to me that I was misreading the 7. Thanks very much for this info.