The Wallace Stone is an eighteenth century memorial in the Strathbrock & Kirkhill Woodlands on Drumshoreland Muir, just off the road to the northern car park for Almondell & Calderwood Country Park. It appears to be of reddish sandstone and has approximate dimensions of 1.38m x 0.74m x 0.18m.

The Wallace Stone, Drumshoreland Muir
According to Primrose,[1] this stone originally stood a few hundred yards to the west of its current location, which would presumably put it within what is now a horse paddock. Click here for a location map provided by StreetMap.
Local lore claims that prior to the Battle of Falkirk (1298) Wallace was on Drumshoreland Muir observing Edward I's encampment to the north near Kirkliston (the nearby placename of Lookaboutye may be related to this story). An alternative puts Wallace's reconnaissance on the summit of Cockleroy Hill near Linlithgow, known as "Wallace's Bed" or "Wallace's Cradle".
One way or another, this was a crucial moment for Edward, when he was faced with suppressing a violent mutiny by his Welsh archers, narrowly averting their defection to the Scottish cause. Some sources claim that Wallace was aware of this skirmish and considered exploiting it — perhaps these were the thoughts passing through his mind while at Drumshoreland. Fatefully, though, he failed to act on this information. Edward successfully suppressed the mutiny and bought off the Welsh. According to many interpretations, he ultimately prevailed at Falkirk due to the devastating impact of their archers on the Scottish ranks.
The inscription is in conventionally-abbreviated Latin script, which is transcribed by Primrose as:
M.S.
GUL. VALLAS
OCTOB: XV.
MDCCLXXXIV.
However, Primrose's transcribed punctuation differs slightly from that in his illustration:[2]

"The Wallace Stone" (Primrose, 1898)
Due to weathering, even less punctuation is visible today, but it does seem likely that Primrose's illustration was more accurate than his transcription:

Wallace Stone — The Inscription
On close examination, some markings can be found where Primrose indicates punctuation, but weathering has made these uncertain and similar natural markings can be found elsewhere on the stone, rendering our current best transcription as follows:
M S
GUL · VALLAS
OCTOB XV
MDCCLXXXIV
Equally, when we consider this inscription in combination with that on its companion stone (see below), it seems clear that instead of a full stop to divide "GUL" from "VALLAS", we in fact have an ano teleia (middle dot).
The date of the dedication is October 15th, 1784, while the first two lines can be expanded conventionally to:
Memoria Sacrum
Gulielmus Vallas
Translating this and following a further conventional expansion, we have, in full:
[in] Sacred Memory
[of] William Wallace
Primrose hypothesised that the stone was erected by David Stewart Erskine, 6th Lord Cardross, 11th Earl of Buchan (1742-1829) of Kirkhill House in Broxburn and primary founder of the Society of Antiquaries of Scotland in 1780. Certainly, the circumstantial evidence is compelling: Almondell House (now the park's visitor centre) was also a family property, and a second stone in similar style, material and size can be found to its west (NT 089 689), erected by Erskine's wife on the very same day as the Wallace Stone and dedicating the entire forest to the memory of her ancestor who fought with the Bruce:

The Fraser Stone, Almondell
Here, the inscription is still very clear and provides good contextual clues for interpreting the actual form of punctuation used on the Wallace Stone itself:
MARGARET·COUNTESS:OF:BUCHAN
DEDICATED THIS FOREST
TO:HER·ANCESTOR:SIR·SIMON:FRASER
OCTOBER XV
MDCCLXXXIV
Moreover, Erskine himself also later commissioned the more famous 1814 statue of Wallace on his acquired estate of Dryburgh (NT 591 326). This monument is often credited with being the first modern Wallace monument, but Erskine's previous and more modest memorial at Almondell must clearly take that credit.

Wallace Statue, Bemersyde
According to a later account, not all went to plan, and the Dryburgh statue never quite met the high standards of Erskine's more famous neighbour (who seems to have had a generally low opinion of him!):
It was installed with great ceremony. A huge curtain was drawn before the statue, which dropped at the discharge of a cannon, and then the Knight of Ellerslie was discovered with a large German tobacco-pipe in his mouth, which some wicked wag had placed there—to the unspeakable consternation of the peer, and amusement of the company. Sir Walter Scott used to say that when a revolution should take place, his first act would be to procure a cannon, and batter down this monstrosity.[3]
Ironically, given Erskine's obsession with the Wallace, his titular (but not familial) predecessor, John Comyn had infamously sided with the English against the Bruce. Perhaps an embarrassment over the origins of his peerage was the impetus for Erskine's Wallace memorials!
thanks are due to Rachel Alden for re-inspiring an interest in the local Wallace connection
footnotes
[1] James Primrose, Strathbrock or the History and Antiquities of the Parish of Uphall (Edinburgh: Andrew Elliot, 1989), p.103.
[2] ibid.
[3] James Taylor, The Great Historic Families of Scotland (London: J.S. Virtue, 1887).