I have been reading some books about Great Debate that whether the Milky Way Galaxy was the entire universe and Edwin Hubble settled the debate by identifying some Cepheid variable star (V1) in Andromeda that had 31 days period.
According to the period-luminosity relationship by Leavitt V1 should be much brighter than Hubble observed. So it must be too far way to be in the Milky Way Galaxy. But how did astronomers at Edwin Hubble time measure/decide the size of the Milky Way Galaxy and supported Edwin Hubble claim ? Did they agree on the size of Milky Way back then?
--- update ---
With answers I got so far I learned that Shapley and Curtis disagreed on the size of the Milky Way, which actually made me even more interested in this question because if they disagreed with the size of Milky Way how did Hubble's finding settle the debate ?
https://en.wikipedia.org/wiki/Harlow_Shapley said "Shapley used Cepheid variable stars to estimate the size of the Milky Way Galaxy" without many details. But Mr. Rennie's answer said Shapley used globular clusters to measure the size.
I also read articles like "Where is the edge of the Milky Way? Star discovery could redraw boundaries", which also makes me puzzled that if we just found the new boundary of Milky Way in 2014, how can astronomers in Hubble times agree on the size of Milky Way (with acceptable margin of error)?