For many decades the 1040 due date was the anniversary of Julius Caesar's assassination (March 15), and the quarterlies were due March 15, June 15, September 15 and December 15.  Then people complained about having to estimate their income only a few weeks before the end of the year, when they would have the actual amount, so they changed the date of the final payment to January 15 because, you know, before computers it was common to have the W-2s issued by then anyway.  Then others complained that March 15 was too early to do all those complicated calculations, so they changed the 1040 filing date to April 15, and that became the first quarterly payment date also because it was easier to estimate based on previous year, once that return had been done.