Mike Sigman asked me to describe how O Sensei bounced people who were pushing on his chest. I'll give it a try. Mike please correct my inaccuracies or pick me up if I'm being vague.
First off, let's assume he's standing with one foot in front of the other as this is a more stable stance (doing this with feet side by side is a different issue whilst being also the same if you see what I mean). His partner is pushing squarely on the middle of his chest. Hard.
If he were standing feet together it would be more difficult to redirect the force and maintain balance. Not impossible but more difficult. I say this because I find it easier myself with one foot in front of the other if someone is pushing on my chest, if there's another way and the two shouldn't be any different whatsoever then in all likelihood I've missed something. If you assume he can redirect the force to the ground by first absorbing it into his centre then he'll be pretty much rock solid and no amount of pushing will move him. What's happening here is that his partner is loading force onto the spine which is supported by the hips and centre and the legs, the legs are obviously supported by the floor, the thing that stops him sliding backwards in response to a direct horizontal push (note not up at an angle as that's a slightly different test) is friction on the soles of the feet. I know this because someone in our dojo once mistook a can of furniture polish for whatever it usually was they used to clean the mats and instead polished a large number of PVC mats. Bare feet tended to slide along them until you could adjust the force and use the deformation of the foam under the PVC to check the sliding of you feet. It was a rather fun morning and fwd rolls tended to end up with uke trying to stand up at the end and resembling a snowboarder in the attempt.
Back to the chest bounce.
The harder uke pushes against the chest the easier it is (assuming you can absorb the force and remain in an upright position in the first place). As I said, force is loaded onto the spine. The spine, while being strong is also pliable. So releasing the energy stored in the spine and along ukes arm will move uke backwards (and to an extent the legs although the legs mostly support the back i think, not too sure about that one, I'll have to have a play, but I don't think the legs are anything to do with it because you should be able to do this standing on one leg). The extent to which uke moves backwards depends on their posture and skill in pushing and grounding themselves. An uke who has a coordinated mind and body will propbably be able to absorb the power in the same way the power was absorbed from the initial push uke made. If uke has little to no coordination then they will move, how far depends on them as an individual.
Releasing the power is, I think, a wave that begins at the base of the spine in the one-point or centre. Best way I can explain it is to imagine putting an object like a vase or a plate on the end of a rug. Then lift the other end and whip it downwards to send the wave to the other end of the rug. The plate or vase wil move, possibly break. If you put a heavier item such as an armchair on the end of the rug it would not move when you did this and that is where the analogy breaks down. It breaks down because the rug isn't having force loaded onto it. If it were instead a diving board and you put the armchair on the end furthest from the tower (if we again think of O Sensei and uke pushing his chest his hips and legs are the tower and spine is the diving board) what would happen is someone stamped hard on the end nearest the tower? The force loaded onto the diving board by the weight of the chair would be released and the chair would move. Probably up in the air and then into the pool.
If you watch the end of the 1935 Asahi news film there are a few moments when he kiais into his ukes face and uke jumps backwards. Watch his movement, it starts from his centre and rips up through his back and out of his mouth.
This clip of Akuzawa:
The guy is holding his wrists. Watch the force start from his hips and travel up his arms. It's something similar to the bounce demo but not the same. In this case his partner isn't loading the force onto his spine he's doing something similar but sligthly different, it is however the only video I could think of off the top of my head where the movement is clearly shown and fairly easy to see. I suspect Akuzawa starts this movement by creating and releasing tension in his hips and rolling this coordinated movement upwards and out his arms. But that's just a suspicion based only on video evidence.
Is that ok for you Mr Sigman? If not please correct me.