Two spaces after the period is a holdover from typewriters with their evenly spaced characters. Some computer fonts such as Courier also have even spacing.
Modern software has kerning which spaces characters proportionally, thus making a single space after a period more distinct and precluding the need for two spaces.
Free Republic holds a place in U.S. history related to such kerning. Freeper Buckhead exposed CBS' Dan Rather's fraudulent Texas National Guard documents for then-presidential candidate George Bush. Buckhead identified within minutes that the documents were a fraud because the IBM typewriter at the time didn't have kerning yet Dan Rather's documents did.
https://freerepublic.com/focus/f-news/3347939/posts
On a related note, it would be nice if Free Republic switched the default font from Times New Roman to a sans serif font such as Aptos, Arial, Calibri, Tahoma, etc. because it's read on a screen, not paper.
Two spaces after period.
I still use them and think they make reading much easier.
TBY: thanks for reminding us of Buckhead & the Dan Rather scandal. That was heartwarming.