Whitney Smith, founder of the field of vexillology, was born on February 26th 1940. He coined the word "vexillology" and the first time it appeared in print was in his very first article, written for the discontinued journal The Arab World, in 1958.
The above picture is the article in question, where he details the composition and origins of many Arab countries' flags at the time. A couple of things to note:
Algeria's flag is standardised and Algeria is considered an independent country even if the article was written more than 4 years before the independence of Algeria from France.
Likewise, Kuwait was not yet independent in 1958 it would only reach independence 3 years later. The flag present here is likely to be an unofficial standard, to represent the territory.
The flag of the United Arab Republic was made official only shortly before the redaction of this article, as the UAR was created in 1958. This flag would keep being in use until the fall of the Assad régime in Syria in December 2024.
Saudi Arabia's flag has never officially been like the one in the document. This flag was used as the flag of the king of the KSA in the 1950s and 1960s.
