Hi to all,

I’m quite ignorant in mathematics (I apologize for erroneous technical vocabulary), and I have a mathematical problem to solve.

A series of archaeological artifacts was founded, over years, in a given rural territory. No archaeological research was done on the territory, and all findings were accidental.

The question I would like to answer: is the frequency of archaeological findings due to the "modern" demographic values (more habitants=more works in terrain=more findings) or they are representative to the real ancient occupation?

I have this data:
-Modern boundaries define the territory-units to compare. I call their area “a” Let’s suppose that characteristics of territories are very similar and the land use is the same, so inhabitants of each territory have the same probability to find an artifact. This is not exactly true, but it’s another problem.

-I have a mean of demographic population of each territory over a given span of time (more or less, the period in which findings were made; I call it “b”) and, since I know the areas of those territory-units, I can have a sort of historical mean of population/square Km. I call it "c".

-I have the number of artifacts founded in each modern boundary. I call it "d".

Within my limited mathematical conception, I “feel” that something like 100:x=c:d allow me to homologate data and to compare them (and I could mistake, even on this simple point), but it suffices? If yes, how can I interpret them? I would say that higher values=higher occupation, but I “feel” also that this is not the answer to the question, if it has one, and it only tends to quantify the second part of the question, meaning x just some type of “representativeness of ancient occupation”. Probably I need some other type of data to solve the problem, some reference as like the “exact number of artifact existing” in a territory, for comparing it to the “founded artifacts”, but it is impossible to know it…

As you can see, mine is not only a mathematical problem but, by the point of view of my “humanistic” formation and experience, a conceptual one too.
Anyway, even if this seems to you a very trivial question, every help and/or correction would be appreciated. Thanks in advance.

Best regards,
Alessandro