You have a telescope, mounted on an equatorial axis, with a clockwork to track the stars. It has crosshairs and a scale going through the middle of your image.
You suspect that the positions of stars near the horizon are shifted by refraction of light through the atmosphere. (Air refracts light much less than water or glass--but light from a star near the horizon must pass through a very thick layer.) How can you check this out, and measure the effect if it exists?

Question

You have a telescope, mounted on an equatorial axis, with a clockwork to track the stars. It has crosshairs and a scale going through the middle of your image. 
You suspect that the positions of stars near the horizon are shifted by refraction of light through the atmosphere. (Air refracts light much less than water or glass--but light from a star near the horizon must pass through a very thick layer.) How can you check this out, and measure the effect if it exists?