Question : Geometry - Findng and marking a line through center of sphere

Beleive it or not i can not find anywhere on the internet how to do the following.  
I have a pool ball that is 2 1/4" in diameter. (This is an actual ball, not a picture or drawing), with this ball i would like to mark exactly a north and south pole, then scribe a line around the ball connecting the two points. Then would like to do this for the east and west poles. So when i am finished i have a ball with a cross if looking at from any angle. I thought i was really close when using a compass, in which i think this would be the correct route to take.

Please any suggestions would be great.

Answer : Geometry - Findng and marking a line through center of sphere

Okay.... I've been mucking about with a ball and compass. Here goes!

Diameter of ball = 2.25" therefore,



METHOD

Open your compass to a distance of 1.59099" (or as close to as the human eye can see....) (the Rule-Of-Thumb method may apply here).

1) Find any point on the surface of the sphere, called 'O1', draw a circle, C1' whose diameter is 2.25".

2) From any point on 'C1', called 'O2', draw a circle which intersects 'C1' and 'O3' and 'O4' and whose diameter is 2.25".

3) From either point 'O3' OR 'point 'O4', draw a circle which intersects ''C2' at 'O1' and 'O5' and whose diameter is 2.25".


    Point 'O1' = North
    Point 'O2' = West
    Point 'O3' = East
    Point 'O5' = South