Q. I'm looking for National Geographic Magazine articles from 1922 - 1925.

Our collection only goes back to 1938. We have 1938-1959 under "National Geographic Magazine" and then 1959-2001 (or so) as "National Geographic". From there on, our collection is entirely digital.
 
I did a Worldcat search, and it says that the Huntsville Madison County Public Library has it back to the dates you need, but then I did a search on their catalog and got nothing. It might be worth it to call them (256)532-5940. I think they also have digital reference on their website: http://hmcpl.org.
 
Other hits that do seem to have it that are not terribly far away include Jackson State University:
 
http://library.jsu.edu/cgi-bin/Pwebrecon.cgi?DB=local&BOOL1=as+a+phrase&FLD1=ISSN+%28ISSN%29&CNT=50&SAB1=1044-6613

and Samford University
 
http://library3.samford.edu/search/o?search=1643684
 
The latter, at least, seems to have it via a CD-ROM and, again, you might want to check first about availability.
 
If you want to do a Worldcat search yourself, you can get to it from http://worldcat.org
 
 
Depending on what you want/need, I also found that NG themselves sell a huge collection that has every issue through 2010 across 6 DVDs.
 
http://shop.nationalgeographic.com/ngs/browse/productDetail.jsp?productId=2000745&code=NG80460

 
Finally, the person at the following link has free issues through 1922 linked (seems like through Google Books): http://subjectguides.fortlewis.edu/content.php?pid=67772&sid=619590
 
After 1923, they would no longer be in public domain, so that would explain that cut off.