Looking at the individual lists the changes from 1900 to 1950 are interesting, China and India rejoin the top 10 after absences:Tertius Chandler's compilation of the population of cities throughout history, Four Thousand Years of Urban Growth: An Historical Census is an amazing work providing the population of cities throughout time. Chandler utilized a plethora of historical sources to locate approximate populations for the world's largest cities since 3100 BCE.
As there were few censuses prior to the end of the eighteenth century, Chandler used a variety of methods to determine the size of the world's largest cities: he used traveler's estimates, data on the number of households within cities, the number of wagons of food that arrived at the cities, the size of the military (commonly 1/6 of the size of a city during peace and 1/5 of the size of the city during times of crises), the area of the city walls along with typical densities, church records, the amount of food distributed to citizens, city comparisons (i.e. London is larger than Paris but smaller than Moscow), and even the loss of life in a disaster!
Therefore, in many cases, Chandler's numbers can only be considered rough approximations of the urban population. His figures include the city and surrounding suburban or urbanized area....the list, back to 3100 BCE
|Top 10 Cities of the Year 1900|
|1||London, United Kingdom||6,480,000|
|2||New York, United States||4,242,000|
|5||Chicago, United States||1,717,000|
|8||St. Petersburg, Russia||1,439,000|
|9||Manchester, United Kingdom||1,435,000|
|10||Philadelphia, United States||1,418,000|
|Top 10 Cities of the Year 1950|
|1||New York, United States||12,463,000|
|2||London, United Kingdom||8,860,000|
|7||Buenos Aires, Argentina||5,000,000|
|8||Chicago, United States||4,906,000|
A quick look at Wikipedia (what, I'm supposed to use the greatest encyclopedia ever? The 11th edition of the Britannica was published in 1910) shows that among cities proper there are no North American cities and only one European (Moscow) in the current rankings.
HT: Infectious Greed
A vaguely related exercise was George Cram's “Diagram of the Principal High Buildings of the World.” from his 1884 volume, modestly titled "Cram’s Unrivaled Family Atlas of the World":
(click to enlarge, then click again to ginormousize or follow link)