Yes, the first Featherweight machines were made in 1933 and shown at the World's Fair for the first time. They were improved in 1936, from what I read. So having one made in 1938, I'd say that you have one of the oldest ones. Mine was made in 1939, and has been gently used. They were made until 1963or 1964, according to what I've read.
Did you know that Isac Singer made his first sewing machine to win a bet? He was helping repair sewing machines and said that he could make a better one. He did and won the bet in 11 days!
The things one can find on the net to read.... :) :)
I'll bet that the sewing machine made in 1926 mentioned above is a Singer 99. Does it have a hole in front of the case where a knee bar goes in to run the machine? I also think that it has a bentwood case to it, rounded at the top like an upside down u. If it is a Singer 99, it will just go forward, not in reverse like the Featherweight. The Singer 99 is a larger version of the Singer 66, and is 3/4 size. Without the case, it weighs about 22 pounds, and the Featherweight weighs only 12. It is a great machine too! You can look up the serial number on it to see what it is and when it was made. I hope this helps.
Ya, I've got a Singer 99-13 too, with the knee bar. It was made in 1928 and is in perfect condition. I don't think it was used very much. The Singer 99 was the first 'portable' Singer sewing machine made.