The first time teams wore an NL patch was in 1925, the league's 50th season.
This patch has all sort of writing on it, much different than the one they wore in '51. The patch was also very big. I couldn't find any baseball cards with the patch (there weren't too many out there in 1925), so I created my own. These mimic the W590 cards that were issued between 1925 and 1931
Look how big that thing is on their sleeve. It seems pretty low on the sleeve, too; almost right at the elbow.
Fifty one years later, the National League was celebrating its 100th birthday and all of the team (except for the Expos) wore an NL Centennial Patch.
The best view of the patch I could find on a Cubs card was on these two. You don't get a full look at it, but you can tell that's what is on the right sleeve.
At the same time the NL was turning 100, the Cubs were, too. They are the only original NL team that is still playing in its original city. The Cubs wore a 100th anniversary team patch on the left sleeve.
The next time the NL should have worn a commemorative patch was in 2001, the league's 125th anniversary. Sadly, by that time, the independent National League disappeared, as all the teams were under the auspices of MLB. No anniversary patch was used.
But, one team still honors the National League, and has done so since they first started wearing an alternate uniform top...