Final answer:
Harlow Shapley determined the Sun's position in the Milky Way using observations of RR Lyrae variable stars in globular clusters, not the 21cm hydrogen line, which was used by Tully and Fisher to study spiral galaxies.
Step-by-step explanation:
The statement that Harlow Shapley used the 21cm hydrogen line to work out the position of the Sun in the Milky Way is false. Shapley, in fact, determined the Sun's location using the observation of RR Lyrae variable stars within globular clusters around 1917. By assessing the intrinsic luminosity and the apparent brightness of these stars, he could ascertain their true distance. Since the luminosity diminishes with the square of the distance, knowing how far one star in a cluster was, gave him the measurement to the entire cluster itself.
The 21cm hydrogen line was later used by Tully and Fisher for a different purpose - to measure the rotation speed of material in spiral galaxies. They discovered that the width of the 21cm line, which comes from cold hydrogen gas, could inform them about the range of orbital velocities of the galaxy's hydrogen gas. Therefore, it wasn't Shapley who used the hydrogen line for galactic measurements, but rather other astronomers who employed it in a different context.
Overall, Shapley's work on variable stars was crucial for mapping the Milky Way and determining our Sun's place in our Galaxy, earning him recognition as a significant figure in modern astronomy.