1 : a unit of avoirdupois weight equal to 1/16 ounce
2 : a unit of apothecaries' weight equal to 1/8 ounce
3 : a unit of liquid capacity equal to 1/8 fluid ounce
4 : a: a small portion of something to drink; b : a small amount
Whoa. Good morning, four definitions. Let's start with the obvious: avoirdupois—the system of weights in British and U.S. use for goods other than gems, precious metals, and drugs. Okay. So this contradicts the second definition which deals with apothecaries, hence drugs, though the amount increases twofold. Then there's liquid in general, and then there's an Alice in Wonderland portion of something to drink, and then simply "a small amount." Everything must get vaguer as we move along.
So. DRAM is intended to emphasize the smallness of an amount so obsolete it's barely relevant. This relationship hasn't a DRAM of potential. Your mother lacks even a DRAM of tact. I have less than a DRAM of dignity left. The figurative examples could go on forever.
When I think of DRAM amounts, in the literal sense, I think: poison. So, exactly how many DRAMS of poison will do the trick? After google-searching "toxic poison levels," the most interesting thing I happen upon is an article about Pennyroyal Toxicity. Pennyroyal is a plant in the mint genus, historically used as a cooking herb, a (yes) tea, a pesticide, and an abortifacient. Pennyroyal essential oil is highly toxic, even in low levels. According to an (other) article published in The Aroma Thymes [sic] in 1995, 25 ml of pennyroyal oil is lethal. If my math is correct, this figures to about 6 DRAMS. 2-3 DRAMS will likely destroy your unborn children, and far less than a DRAM occasionally appears in European mint confectionary for added flavor.