Hi Anne,
From your markings' description it should have been registered 29 August 1877. The III in Roman numerals at the top means Glass category. The number below is the date (i.e. 29th), the one on the left is a parcel number, the one at the bottom is the letter code for the month: Aug=R; and the one on the right is the year code: 1877=P (there's no year using R in this layout which applies to 1868-1883).
However, the list of registered designs for 1877 on Great Glass gives us two Sowerby patterns registered on 29 of a month in 1877 - neither in August. One was in March (letter code=W) and the other was in October (letter code=B), so I suspect your bottom letter should be B not P or R. The parcel number for the March registration was 4, whereas the October one was 6, which matches yours.
Checking the Great Glass website for that date gives as follows:
315664-74 Sowerby & Co 29-Oct-77 (parcel) 6
so there were actually 10 designs registered by Sowerby on that date!
Jenny Thompson's book
The Identification of English Pressed Glass gives the following details for the numbers:
315664 = Bowl, 315665-70 = Vases, 315671 = Sugar basin, 315672 = Handled vase, 315673 = Basket, 315674 - no description.
So that narrows it down some more. The 1877 date explains why you didn't find it on Glen's CD (neither did I!) as the earliest catalogue Glen includes there is 1882.
Hope this helps a little.