Part of an occasional series on predicting Boston’s future.

Globe reporter Thomas F. Anderson’s assignment for his Christmas Day 1900 story was sweeping: Consult the best experts and sketch out a vision of what the city would look like in a hundred years.

After a preamble introducing his themes, he kicked off his article, “Boston at the End of the 20th Century — “A Glimpse Into the Distant Future, and What It Reveals to the Local Prophets.’’

He relied on what he thought were solid numbers to estimate the future population of the city.

Things quickly went sideways. He estimated that the city’s population would be 5.2 million in 2000. That’s a massive statistical fail; it’s seven-plus times more than today’s actual population of more than 685,000.

But historians say it was understandable, given the times.

Here’s what he wrote:

One of the most fascinating questions is that relating to the city’s probable increase in population and in this matter we have something more than the mere human imagination to aid us.

It so happens that the city of Boston itself has a department of municipal statistics, wherein, if you give them any tangible basis whatsoever to work upon, they can furnish you any statistical information bearing upon the future that you may desire.

To Dr. Edward M. Hartwell, secretary of this department, The Globe is indebted for a computation from which it appears that the population of Boston is likely to have increased to more than 5,000,000, by the year 2000.

This population is estimated on the rate of increase of the last 20 years, and on the same basis (the population according to the census of 1900 being 560,892), the figures for consecutive 10-year periods will probably be as follows. . .

Anderson then cited a series of population figures that appeared to reflect an approximately 25 percent increase per decade for 100 years. The numbers culminated in the number 5,251,330.

Anderson continued:

If the population of Boston itself stands at this astounding figure 100 years from now, it is safe to assume that what will then be greater Boston in fact as well as in name will have combined population of not less than 8,000,000, making it almost as large as two Londons.

It’s not clear what Anderson thought of as greater Boston. But the population of the entire state is only estimated to be about 6.9 million now.

Anderson and Hartwell had just seen the population of the city explode by 54 percent from 1880 to 1900, according to the US Census. So it’s little wonder they saw strong growth ahead. But history would take a different path than they expected.

“The new century brought with it generous projections from urban boosters, not only in Boston, but in numerous other cities, particularly in the Northeast and Midwest,’’ said David Goldfield, a professor at the University of North Carolina Charlotte who is an expert on the history of American cities. “Boosters at the turn of the 20th century fastened on population growth as a symbol of progress — not only for the pride involved, but also for drawing investment.’’

The cities were “in the midst of two unprecedented events in American history. The first was the arrival of millions of immigrants from Europe and Asia — 14 million in all between 1890 and 1914. This influx ratcheted up the population of the nation and, especially, of the cities in these regions,’’ Goldfield said in an e-mail.

The second event, he said, was the Industrial Revolution, which required huge workforces, many of whom were immigrants.

Marilynn Johnson, a Boston College professor who is an expert on urban history and on the history of immigration to Boston, said Globe reporter Anderson appeared to be “an incorrigible optimist.’’

“Presumably, this rapid influx [foreseen by Anderson] was a continuation of what was already happening, as the 1890s-1913 were the peak years of US immigration,’’ she said.

Obviously, Anderson did not support curbs on immigration — even at a time when groups like Boston’s Immigration Restriction League were busy lobbying for that, Johnson said in an e-mail.

“He seems to assume that immigrants will be needed to propel the rapidly expanding economy and commerce of the city,’’ she said. “The textile and shoe industries were flourishing, absorbing new workers as fast as they came in.’’

Anderson and the experts he consulted would have been hard-pressed to predict that the textile boom would decline go in the 1920s, Johnson said, and that the Depression was just around the corner.

Martin Finucane can be reached at Martin.Finucane@Globe.com