Mars retrograde 1900
No retrograde period falls inside 1900. That is not an omission — the loop lands either side of the year boundary.
Why a year can have none
A retrograde recurs every 779.94 days — the synodic period of Mars. Because that does not divide evenly into 365.25 days, the loops drift through the calendar. For the slower planets a single loop can start in one year and finish in the next, leaving a calendar year with nothing inside it.
Check the previous year and 1901 — the period you are looking for will be in one of them.
Computed from the actual motion
The nearest Mars retrogrades either side of 1900
Gap across 1900
1.9 years between the two — long enough for a whole calendar year to fall inside it with nothing to report.Both dates are computed from the planet’s apparent motion, not taken from a table. A retrograde begins the moment its daily movement against the stars turns negative, and that moment is findable to the hour.