Final answer:
The reading for the API gravity test is correctly taken at the point where the principal surface intersects the hydrometer scale when the instrument is floating freely and at equilibrium in the liquid.
Step-by-step explanation:
The correct place to take the reading for the American Petroleum Institute (API) gravity test is at the point where the principal surface of the liquid cuts the hydrometer scale. This occurs when the hydrometer is floating freely in the liquid and is at equilibrium, meaning it's neither sinking further nor floating up. To obtain an accurate reading, ensure that your line of sight is level with the principal surface of the liquid when observing the scale on the hydrometer. This technique ensures that the reading reflects the true specific gravity of the liquid according to the API standards.