Mystery bottle fragment

Wandering about just off Gaze Road, Settlement I came across this bottle fragment in the undergrowth. At first glance it just looked like a piece of broken glass of no consequence and easily ignored. But on closer inspection I was excited to see a partial stamp. On the first line were the words THE PROPERT (that I presume would have read THE PROPERTY OF) and on the second line starting with AGY.LTD.EDINBUR (also presumed to be the final three letters of a company name LTD EDINBURGH). The oval base of the bottle indicated that it was not a large bottle. As I found it not too far away from the old hospital site I have to wonder if it was not a medicine bottle of some sort. The fact that there is a Scottish connection and that the stamp font appears vintage, makes me think that it is dated perhaps before the 1930s? I regret that I didn’t have a coin or ruler so that I could have included it in the photo to indicate the scale or size.

I would dearly love to be able to identify and date this fragment and be able to find out more about it. Unfortunately up until now, my searches on the internet have not revealed anything, but I will keep persevering. If there are any bottle collectors or others out there who could help identify this piece, that would be greatly appreciated and acknowledged on this page.