Julia, at the base on the pillar of your machine, you should find something like this.
This is going to be the serial number of your machine.
This is a machine from 1857. A very early Singer 12. This machine is about half the height of the later Singers - which is why the later machines were called "High Arm" when they first came out. Most of my collection is of the "high arm" machine era, I only have a few that are not.
This is a later (1880's) verison of the Model 12