Sadly, turgidity, tangentiality, and talkativity have always been my locution's Achilles hill. Expressing dissension cannot always be done succinctly, in my case. And for that, I am sorry (or so I am after my comment attracts a passel of booing, contemptuous curmudgeons into the discussion).
Ah I see, I assumed one could weigh the product pre- and post-purification, and stratify the purity based on mass lost retrospectively. A bit laborious, but anyone could do that.
Theoretically, this would work. But if the purification process removes the adulterants along with a not insignificant quantity of the desired substance then the resulting mass of purified material would not give us a precise indication of the starting purity of the material.
For example, suppose we acquire 1kg MDMA. We don't feel too confident in its being twenty-four carat, intemerate ecstacy—it doesn't look kosher or the high seems out of kilter, say. But we are absolutely sure there's at least some amount of molly in that 1kg. So we decide to purify it through whatever process. After the purification is completed, we get 250g pure MDMA, and 750g of junk is extracted and expunged. If and only if every mg MDMA is retained and if and only if every mg non-MDMA material is removed, then we could use arithmetic to easily calculate the ratio of MDMA as 250g/1000g (or 1g molly per 4g rejectamenta). Therefrom, the purity of the original 1kg of material is effortlessly arrived at mathematically and is precisely 25% .
But how might we arrive at such a precise percentage if, say, for every 1g bunk we isolate from the starting 1kg, an indeterminate amount of pure xtc is also extricated along with it? Or how might our math work if with every 1g MDMA we have successfully liberated, there's an accompanying residue of denaturant with unknown mass? Or what if both scenarios occur concomitantly, wherein every quantity MDMA extracted has some proportionable quantity non-MDMA and vice versa?
The result of our attempted purification would be two piles of material—piles A and B, we shall denominate them. But it would be impossible to attain any degree of precision greater than just knowing one pile is more pure and the other pile is less pure than their sum (the unrefined 1kg at the outset).
If either these two confounding factors arise, we must necessarily know the exact proportion of residual dross to refined distilland before we may obtain an on-the-beam estimation of the stuff's starting quality by dint of figuring out its starting mass and post-purification mass and using these data to find the latter's percentage of the former. (E.g., 50kg middling dope minus 20kg superfluous fluff and feculence equals 30kg purum. Since 30kg is 60% of 50kg, the purity of the congeries of kilos is hence 60%.)
But I feel I must reiterate Hong Gildong's objective here. He could not care less about purification; rather he is only concerned with purity because he feels it is vitally important to know a substance's purity level before diluting it, insofar as one wants their formulation to be precise. Gildong probably wants to achieve an exact formulation because it would allow him to retail his drug in singular units each consisting of one exact dose.
For example, let's suppose this hypothetical person, Gildong, has a supply of a drug and it has an unknown purity. Let's suppose further that a single dose (ED50, say) of this drug is ~25mg. Let's suppose even further that Mr. Gildong wants to cut this drug such that 1kg gives him 1.5kg after cutting—i.e., his formula is 2 parts drug per every 1 part cutting agent, which effectively increases his quantity 2/3rds and decreases his quality by 1/3rd.
But since Gildong is an inordinately parsimonious and chintzy businessman, yet more scrupulous than most, he would not want to sell a consumer more than one dose if that's what they're paying for—too much drug wouldn't be prudent and too little drug may be perceived as skimpy and duplicitous, but hbad business at any rate. If a dose is 25mg (of pure drug) and he is unwittingly selling 60mg for the same price as if it were one dose, then this would mean a drastic reduction in his net profit.
For Hong Gildong to maximize his earnings, he must know how much of his cut product equals 25mg uncut product. Only if the starting purity (before he applies his cutting ratio/formula) is known will he know how much substance contains the active ingredient and thus how much substance to include in each minimum unit.
Yes, I'm as effusive and prolix as they come. That doesn't concern me nor should it you, though. I only care if I make sense. So, did I?
I look forward to reading more of the Amazing Adventures of Mr. Hong Gildong
In East Asia (specifically Korea), Hong Gildong is used as a placeholder name, tantamount to John Doe, John Q. Public, and Joe Schmo in English. It's just an amphibological, pronomial metasyntacic variable. It's used ubiquitously in the Korean language when one is speaking in a hypothetical or stereotypical mode.
I've appropriated its use for English because it sounds jocular and it's not as trite and hackneyed as, say, John Doe or (for fuck sake!) "SWIM".