I was reading some literature published in the mid-19th century about artillery, and it notes the muzzle velocity of various cannons, mortars, and the like. Were these calculated using a stopwatch and human reaction time? Or did they just calculate the physics of it on paper, and assume that was correct?
Muzzle velocity was first reliably measured in 1742 by Benjamin Robins, described in his New Principles of Gunnery. He had invented a ballistic pendulum to measure the velocity. It worked by using a pendulum bob that caught the projectile. He measured the weight of the bob before and after the firing, and calculated the energy of the projectile from the distance the pendulum swung after impact. From that he could calculate the momentum imparted by the impact and thus the velocity of the projectile. (Momentum being the mass of an object times the velocity).
This principle is still used in freshmen Physics labs (or at least it was when I was in school) using BB guns and styrofoam block pendulums.
Later advancements were to fire a projectile at a pair of spinning disks attached to a shaft rotating at a known speed. Measuring the angular distance between the holes would provide the velocity. Your tables may have been done using a ballistic chronograph, described by Francis Bashworth in 1866, that used electrical signals from the projectile breaking a series of metallic screens to determine the velocity.