Would you believe a test for authenticity or usefulness is called an "acid test" because if it fails it must be a lemon? No, not really. In today's lexicon, an acid test is a decisive examination that proves its value.

This noun for a severe or crucial test dates back to as early as 1912. It comes from American English and the frontier days when gold was distinguished from similar metals by the application of nitric acid. Sometimes gold was used as currency in the days before coinage and the beginnings of this expression are quite literal. Over a hundred years ago peddlers would travel through the rural areas of the United States selling all kinds of manufactured goods that otherwise people had no access to. Not only did he sell these important goods, the itinerant merchant also purchased old items made of gold. For this purpose he needed an easy way to estimate the gold content of –say-an old spoon. He did it by scoring it lightly and pouring nitric acid on the nick. The color the liquid turned would then determine the percentage of gold present. In other words the acid test was as good as gold, to coin a phrase.

Up until the early 1900's the phrase was pretty much exclusive as a scientific term, but many times technical terminology of a specialized subject often makes it into general usage. Even though the idiomatic use for acid test as a way to determine worth or quality had been around for a decade as a figure of speech, it gained wide spread notoriety in 1918 when President Woodrow Wilson brought it to the forefront in the sense of ‘an extremely through examination’ when he presented his legendary “Fourteen Points Address,” to the US Congress on January 8th. His proposals were designed to establish the basis for a righteous and lasting peace following the triumph of the Allies in World War I. This is how he defined his idea of an acid test in point six:

    VI. The evacuation of all Russian territory and such a settlement of all questions affecting Russia as will secure the best and freest cooperation of the other nations of the world in obtaining for her an unhampered and unembarrassed opportunity for the independent determination of her own political development and national policy and assure her of a sincere welcome into the society of free nations under institutions of her own choosing; and, more than a welcome, assistance also of every kind that she may need and may herself desire. The treatment accorded Russia by her sister nations in the months to come will be the acid test of their good will, of their comprehension of her needs as distinguished from their own interests, and of their intelligent and unselfish sympathy.
Today’s usage has extended the expression even further metaphorically. Bernice Rubens finds a sharp and biting description with words about words when she says,” The acid test of a good piece of writing, even if it is of violence and cruelty, is that it must make one's ears water.”(Sunday Times), 1988.

Sources:

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Garrison, Webb, Why You Say It, Rutledge Hill Press, 1992.