that's a special joint called a "Constant Velocity" or CV joint. there should be CV joints at both the front and back of the driveshaft.
more relevant to your problem, i think the early 70s big cars have a two piece drive shaft. the pieces are joined by rubber. if the rubber has deteriorated ( and it probably has ), it's not going to be possible to balance the drive shaft until you either get that reconditioned or if you replace it with a one piece shaft.
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Vladimir Lenin
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H.H. Goddard, Human Efficiency (1920)
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