Make, model #, serial # maybe? Did machines made in 1948 have attachments?
http://www.sewalot.com/dating_singer...ial_number.htm
http://wiki.answers.com/Q/What_is_th...sewing_machine
http://www.youtube.com/watch?v=FPuRvNd8tos
http://singeroriginalvintageproducts...chine1948.aspx
I found a lot of information I think you will enjoy. I did learn the 1948's did have attachments. That's a beginning.
Good luck, let us know how it progresses.