The Trial of the Pyx is a procedure in which the integrity of the coinage of England (now Great Britain) is tested. During the Stuart Dynasty, when the Baroque Cycle is set, the trial was an unfriendly, adversarial procedure with real political and legal stakes, including several ceremonies intended to highlight the integrity of the process. It is also a demonstration of the use of random sampling as a testing procedure.
The core of the procedure is the melting and weighing of coins. Periodically while making coins, the Master of the Mint removes coins from the product and puts them in leather pouches, called Sinthias. Each Sinthia is then deposited into a triply-locked box called the Pyx, which is stored in the White Keep in the Tower of London. When the Trial of the Pyx is called for, the Pyx is ceremonially transported from the Tower to Westminster Abbey, where samples of the coins in the Pyx are selected at random, and tested by goldsmiths by way of measuring them and assaying their contents to determine the purity of the metal used to create them. In theory, if the coins are found to be of substandard quality, the Master of the Mint stood liable for high treason and could be mutilated as punishment for allowing the currency to be questioned.
In The System of the World, a substantial amount of the action involves a Trial of the Pyx which is part of an elaborate political game taking place at the very end of the reign of Queen Anne Stuart and the start of the reign of King George I Hanover.
Spoiler Alert: The Trial of the Pyx in The System of the World represents the culmination of Daniel Waterhouse's maturation as a political, scientific, and economic player. Waterhouse must use all the skills he has spent a lifetime developing, including relying on the discipline of alchemy which he despises, to rig the trial and help his friend Isaac Newton avoid being caught up in the web of political machinations surrounding the coronation of King George in the wake of the malfeasance of Jack Shaftoe. Waterhouse's success or failure will not only make the difference between life and death for his friend, but also determine whether France or England will be the dominant power of Europe for the next hundred years, and set the guides for the political path of the emerging modern world.