A rather dubious comparison. The Bureau of the Census projections are constantly being revised. Using your example of the projecting the population of the US 105 years later usng the period 1870 to 1900 is specious. The Bureau of the Census projection for 2030 is relatively a short timeframe. It is only 23 years from now.
Secondly, the population of the US is not only affected by birth rates, but also by immigration policy and the lack of control over our borders. We are taking in 1 million LEGAL immigrants a year and 500,000 to 1 million illegal aliens. If the senate comprehensive immigration bill passes, then we could be adding an additional 60 million persons by over the next twenty years. Certain public policy changes can affect future population projections.
Finally, more Americans are living longer, which could affect the numbers. Agreed that these are just projections or educated guesses, but there is no dispute that we have added about 100 million to our population since 1970 and about 20 million since 2000 with immigration accounting for about 3/4 of the population increase. There are about 6 million future immigrants waiting in line overseas due to the caps on various categories under the chain migration policies.
Do you believe population projections are useful or worthwhile? We also use projections to forecast when Social Security will start paying out more than it is taking in [2017]. Do you believe these projections?
Any projection for the future based on the past has an excellent chance of being proved inaccurate, since the change brought about by current trends leads to unforeseen consequences in the future.