The balance point would rarely also be on the north-south, east-west intersection. The only time that would happen is if the distance of each person was also equal on either side of your meridian and your latitude.

In reality, the clumpiness of the populations on either side of your dividing lines are going to be different. You could have a dispersed population on the west side of the meridian, but a concentrated population far away on the east side of the meridian.