Classic/Antique Car Repair: 1965 Mustang Handling, rear axle assembly, center bolt

Question
When I accelerate car pulls to the right, like it wants to change lanes, when I let off it wants to move  back to the left. Car is also feels like it is floating in the rear when I hit a dip in the road. What's up with that? I have checked the rear end and all is tight, checked up front and all seems well. Can not seem to find why. Car is stock with 289 auto. What am I missing?

Answer
John, sounds like you might have broken a center bolt on one of the rear springs. This would allow the rear axle assembly to shift slightly on acceleration or deceleration. The center bolts go through the spring leaves and one end fits into a hole in the rear axle housing. A strange as it may seam this 5/16ths or 3/8ths bolt is all that transmits the power from the engine to the rear wheels. The axle or spring U bolts squeezes the springs together and to the axle but it takes the center bolt to stop movement fore and aft and to keep the rear axle in alignment with the chassis. While you are at it check the shocks and check for a broken main spring leaf. Good luck.
Brad