Integrating Uno into existing system

I'm powering the Arduino through its external power supply.

If I connect the positive and negative lines of my power adapter to one battery, I get 12V, and can run the Arduino, but the voltage I read from the pot on the UNO is incorrect.

If I connect the positive and negative lines of my power adapter to different batteries, then I have 24V at the power adapter.

I did not run a ground to the UNO. Should have I?