The standard method of measuring velocity for many years was the LeBoulenge electromechanical chronograph, designed in 1860, improved in the late 19th century by Col Holden, and used for many more years. The bullet clipped a near wire which turned off power to two electromagnets. One released a long iron rod to drop vertically, the other tripped a knife that marked the rod. Then the bullet clipped a far wire which turned off another electormagnet to trip another knife to mark the rod again. The distance between the two marks could be converted into milliseconds and then into velocity.
There were a variety of other designs using tuning forks, clock pendulums, spinning drums, etc. to time the bullet's flight over known distance, but I don't know how much the different ones were actually used.
Remington started using the Chronoscope vacuum tube oscillator counter chronograph in 1940 but the LeBoulenge stayed in use most places until the late 1940s. Hatcher has LeBoulenge data for 1947.
Velocity has been measured by ballistic pendulum. Fire a shot into a free-swinging bullet trap and measure the swing. Calculation yields momentum, taking account of trap and bullet weight allow figuring velocity.
There have been various rotating chronographs. Spin two cardboard discs several feet apart on a common axis at a known rpm. Fire a shot parallel to the axis, measure the angle between the holes in the discs and calculate the