I am the owner of "Project Harrach" better known as Glasscollector.net, and I apologize for my site email being down at the moment. Unfortunately, aside from the avalanche of spam, the majority of inquiries I receive are from people wanting me to ID their glass and tell them how much it's worth. With a very busy work schedule, it's taken a back seat for a bit as other priorities take precedence. Later this year I will be revamping it, adding new content, new Harrach research (I have a ton), and bringing my site email back online once I get a more robust spam solution. You are more then welcome to email me from this site.
A couple of points to make about some of the comments in this thread:
The Truitt Bohemian glass books are more accurate then most people will ever know. Most of the content, particularly in the first volume, is sourced from exceedingly knowledgeable Czech (as in Czech citizens) Bohemian glass experts who have been researching Bohemian glass most of their adult life. They have hoards of original documents, sales catalogs, factory design books, etc., on which they base their attributions. It's not free from errors, but I would say it is without a doubt one of the more error free books when it comes to glass research.
I would like to clear the following comment: The vase in Gulliver's Victorian Decorative Glass page 103 British Designs 1850-1914 (copyright 2002), that looks to be similar to at least two pieces on the link page you just gave. It also has a P number written on the bottom and a stamped registered design number with the number ascribed to John Walsh Walsh in the Registered Designs book of Representations, although it records that a certificate was not issued for this number. Personally I am of the opinion or guess that the vase has a very Bohemian look to me but that is just instinct/guesswork - and also that the RD issue is an anomaly somehow.
Having known this type of glass was Harrach for quite some time, when I saw this attribution in Gulliver's book, I was shocked that he attributed it to JWW (especially considering it looks nothing remotely similar to anything documented by Eric Reynolds as JWW). There are clearly several other Bohemian pieces in the book attributed to various British makers, but to some extent this is expected as tons of Bohemian glass was made for the British market, much of which was contracted by importers, and even prominent British glass houses. Of course it's well documented that Harrach made not only glass blanks, but also completely finished products (enameled, or cut/engraved, etc.) which were sold by other glass houses as their own products.
The main problem trying to attribute the vase in question based on the mark shown in Gulliver's book, is that the RD# shown is not complete, as the stamp didn't make it's full impression on the base of the vase.
The full stamp reads: Rd No. 107802
MADE IN BOHEMIA
The vase in Gulliver's book was in fact made by Harrach, produced under contract by Krausse and Auerbach, which is the firm that registered the design (a very German sounding importer at that). Deborah Truitt did a research trip to England a few years ago, and as she was planning to visit the British Archives, I asked her to track down this particular RD#. How Gulliver could attribute it to anyone, let alone JWW, based on an incomplete RD#, is anyones guess.
Also this vase is 100% Harrach:http://www.jwartglass.com/sys-catalog_single_details.asp?catid=16517&categoryID=4992&category=Y&seq=2&PageID=128532&SiteID=34884
It's wishful thinking on the part of the seller on the Loetz attribution. I find it ironic that dealers, and auction houses tend to error on the side of the more expensive price tag, then simply saying they don't know.
Now on to the topic of discussion.
I had a hard time seeing the mark on your vase. I was initially thinking it was just a letter, followed by three numbers, but I see now it's more like P.588 or P.688 with a 5/2 underneath it (thanks Alisa for the clarification, I really was having a difficult time seeing anything on there).
Harrach definitely made Carneol glass (as well as a gamete of other "stone" glass), and this would be a typical Harrach mark of design and decoration numbers. I've seen very few pieces of Loetz that had any type of numbers at all on the base, but the few examples I've seen tended to be Roman numerals on Victorian era Loetz glass.
I'm visiting the Harrach factory in May, and plan to spend further time in the Harrach museum depository where there are around 5,000 pieces of Harrach antique glass. I'll examine the examples of Harrach Carneol in their collection to see if they may hold additional clues.