I watched the torrential rains today from my market cafe's table, trying to figure out how d.l.G. can say one thing, Beudant the exact opposite and both be right.
Later on Pinochio I gave it a try and found out, that, while he was long and low, moving both wrists to the right (as Beudant suggests to introduce side stepping to the left) most certainly made him turn to the right, no lateral move what so ever. His shoulders, in other words, would give to the left indirect rein on the neck and turn to the right. The right direct rein, moving away from the neck, would make his haunches if anything step slightly towards the left, bringing the inner hindleg under the center of weight. In other words: a perfect turn.
I did not want to insist just then, but from experience I know it takes the same rein (wrists moving to the right), a few half-halts and maybe a touch of the leg and he steps sideways to the left. How can that be?
I should have been able to figure it our right then and there. But I didn't.
So I kept on turning and moving him from one side to another laterally without much attention to details as long as the head stayed up, he reacted promptly and his hindlegs felt attached right to my seat. The trot was a bit laid back. So I went for forward impulsion accepting a change of his posture towards the horizontal balance, head up.
Back in the walk I began to compose my question into a mail. And while I went through the complications of asking myself, how a horse can step to the left, with the rider's wrists moving to the right I could feel Pinochio come up in a nice counted walk. We went back to the first experiment's location and I gave it another try. Again I moved both wrists to the right and promptly Pinochio went into a side-step to the left.
To make a long story short: The difference is in the half-halt, as I knew from experience. But even more so, it is in the type of balance. While the horse is long and low (in the horizontal balance or the first gear) the reins direct the forehand, as d.l.G. states in 1733. Raised and up (in the - shall we call it, for lack of a better term - vertical balance and preparing for the second gear) the reins impact the hindlegs. And that is what Beudant refers to.
But why this shift in the some 200 years between d.l.G. and Beudant?
On one hand I suspect that d.l.G.'s horses (who he directed with an indirect rein) were lively, brilliant and collected (in the second gear, to stick with my vocabulary). On the other hand, horses that today are directed by an indirect rein acting on the neck often remain in the working position. They overbent in the ribs and often also in the neck. They not exactly lively, brilliant (see the international dressage scene) or in second gear. Beudant, however, using the rein that works directly on the hindlegs is known for brilliant horses, not only in dressage, but in all equestrian disciplines.
More research will provide more evidence and - how do the reins impact the horse in the first place.
A day later tests on Fabian: Surprisingly, in the half-pass to the left he reacts to the displacement of my wrists to the right. In the half-pass to the right he understands no such thing. The only way to direct him is with an indirect rein, i.e. also displacing my wrists to the right. Surprisingly, because quite evidently his right haunch tends to block. I can feel it to be higher and resisting my right ringfinger's impact. On the other hand, it may not be so surprising. Because in the half-pass to the right he must lift and put this hindleg fore and sideways, picking up the weight as it goes. Or is it the slightly instable left hindleg, that does not want to be addressed by a direct left rein?