Hi Marvel!
Do you have a photo for us?
The serial number should be on a little brass plate right in front of the pillar. If the tension is on the faceplate of the machine, it is a model 15, if the tension faces you as you sit at the machine, then it's a different model. It sounds as tho it's a 15...
I'm curious, what makes you think that the head is older than the cabinet?