glad that you've posted again on this matter - gives a chance to put right some possible errors which your comments have thrown up

firstly, are you sure it's the 9th of May on your lozenge - might there be the chance that you're looking at the parcel No., rather than the date.............there doesn't appear to be a registration from Sowerby on the 9th of May 1877, but there were three on the 31st, all of which were parcel 9?
Very unfortunately, it didn't occur to any of us to quote the Rd. No. for Roy's creamer, which might have helped avoid what I believe to be an error in Slack's book.
Roy quoted 31st May (and I believe yours will be the same date), and having now looked at the Kew images for that date, and cross referenced to some extent with Thompson/Slack/Cottle and Sheilagh Murray, it seems that Sowerby made three Registrations on that date.
These are:
No. 310595 - (Cottle's 'angular vase' - Slack's 'rare butter dish')...........appears to be identical to this most recently posted item (factory pattern 1224)
310596 - similar design to 595 but smaller lidded item (possibly a lidded sugar) with pedestal and foot - another of Cottle's 'angular' items (factory pattern 1231).
310597 - A spill vase (in Vitro-Porcelain possibly) with parrot and tree in moulded relief (factory pattern 1217)
This last item is entirely unrelated, and so will be ignored for the remainder of this note.
(The above factory pattern Nos. are taken from Cottle, who states that all three are shown on page 3 of Sowerby Pattern Book No. IX (June 1882). Whilst it's true that page 3 of the Pattern Book does show these three factory Nos., the shape of both 1224 and 1231 appear unrelated to the Kew images for Rd. Nos. 595 and 595.
Of course, this might be an example of Sowerby Registering the design only, and not the shape. Looking at Pattern Book IX, you can see why Cottle keeps saying 'angular' - did this author look at the Kew Board of Trade images - or did he look only at Sowerby archive material? Had he looked at the Kew images, then we might have assumed his comments to have been otherwise.
Roy's creamer (for which I've yet to find a Kew image) plus 595 and 595 above, are all related by design - with this short reeded effect around the edges and the stippled/frosted ground - it's always possibly that Sowerby didn't Register an image of the creamer, although from what I've seen other factories appear to have included whole suits of shapes where the pattern was identical. I may have missed seeing the creamer, so will look again.
So...........we appear to have a suit of table items.........a creamer, a possible butter and a (possible) lidded sugar - and there are other Sowerby items around that period that have a similar reeded edge with frosted ground that could be design related.
Coming back to the probable error in Slack, it does seem that the date he quotes is questionable, especially as he shows nothing corresponding to this in his list of Rd. Nos. at the back of his book. I'm also unable to see a Sowerby Registration for 31st of August in any of the other books.
It's a shame also that the matter is made more difficult to unravel by the fact that Cottle's references are to images of pieces (from the Pattern Book) that don't match with the corresponding images from the Kew Rd. Nos.
I'll post pix of the Kew images for Rd. Nos. 310595/6/7 shortly - from which it can be seen that this butter appears as No. 310595.
sorry this is long winded - it's a pain correcting these matters - so many references to check etc., and so many more manholes for the unwary to fall down
