"The order in which the aids are applied plays a role in collecting work as well. The calves come first, asking the hind legs to step under. The weight is second, bending the hind legs and directing the horseís body towards the hand. Finally come the limiting and flexing aids of the hand.
"The final result must be an elastic horse, an unweighted hand, and a rider who joins the movement in the horseís center of gravity with an elastic seat and an active leg that maintains impulsion and hence collection. The horse has to step underneath the riderís seat by himself on account of the impulsion from the back, and he must absorb the riderís weight with his hind legs. Triggering himself the flexion of the haunches as well as the impulse to swing, the horse must absorb the riderís weight with his hind legs. "
- G.v.Dreyhausen (1951, 65, translation: TR).
The circle of aids is one of the most central concepts the student has to learn. There are different ways of going about explaining it. The reason why this circle of aids is so important is because it refers to the connectivity or coherence of the rider's aids. You could compare it to the syntax in language that dictates the word order in a sentence and thereby connects and lends meaning to otherwise isolated words. It is what makes the orchestra of the rider's aids larger and more meaningful than the sum of its individual instruments.
To me, the circle of aids always has to begin with a driving calf aid, however small, because it is the calf's job to bring the horse's hind legs closer to the center of gravity, and to watch that they stay there. For the purpose of the present discussion, you could also say that the calf brings the hind leg into the sphere of influence of the rider's seat. If the hind legs are dragging out behind, and the horse's back is consequently dropped, the hind legs are literally out of reach for the seat. Trying to apply any seat aid on a strung out horse will only cause the horse's back to drop and hurt more, and the hind legs will then actually be prevented from stepping under by the weight aid. The calf can do its job only if it is slightly in touch with the horse's side - and this is where 90% of all riders go off course, before they have even started to try and apply an aid. Here is the reason why: A calf that is dangling in the air, "like a corpse's leg" as Egon von Neindorff would say, cannot feel anything, because it is too far away from the horse. Any aid of the dangling leg will come too late, because it takes too long to close the gap between the leg and the horse's side.
Since it comes out of nowhere, it will surprise and most likely startle the horse, especially if the horse is by nature hot and nervous. On the other hand, a leg that is gripping the horse's side cannot feel anything, either, because tense muscles cannot perceive the smaller and bigger changes in the horse's muscles tone. Most riders at any level ride either with their calves completely off the horse, or with a death grip as if they wanted to squeeze the air out of their poor horse's lungs. Since their horses are consequently off the legs, strung out and hollow backed, they cannot be on the seat, and a horse who is not "on the leg" and not "on the seat" will never be on the bit, either.
When the hind legs have entered the sphere of influence of the seat, i.e. when the rider can feel each hind leg clearly underneath his seat bones, the seat administrates the energy impulses that the hind legs send forward along the spine. The seat then dictates the rhythm, tempo, stride length, and direction of the horse's movement. That is why the seat is sometimes referred to as the conductor in the orchestra of the aids. The seat can also enhance the thrust or the carrying activity of each hind leg. Obviously, this can only work if the rider's pelvis is placed in the deepest point of the saddle, vertical and straight in its "neutral" position, so that it can tilt or rotate evenly in any direction that may be necessary for the application of an aid. The muscles that contribute the most to the control of the seat and its aids are located all the way around the rider's waist. The seat is anchored by the draped, stretched rider's legs. It is not so much the pressure of the rider's thighs and knees, but the downward-backward stretch itself that allows the rider's torso to grow out of the horse's back like a tree, while the rider's legs form the roots that secure the connection with the ground.
The rider's seat not only directs and administrates the energy flow coming from the hind legs, it also connects the horse's front and hind ends through his back. An interesting observation you can make is that when the rider's seat is balanced and connected in his or her own waist, the horse's back will be connected, i.e. it will rise and swing. When the rider's waist becomes limp and disconnected, the horse's back disconnects and drops as well, and the horse sucks back and inverts. In other words, the rider's midsection blends with the horse's back and passes the energy impulses from the hind legs on through the withers, the top line of the neck, the poll, to the horse's mouth, where the rider's hands can feel these impulses - if the hands are connected to the rider's midsection via the elbows. If the elbows are too far away from the hips, the rider's hands are disconnected, i.e. the rein aids are limited to the horse's mouth only instead of reaching the hind legs, and the circle of aids cannot be completed. If the rider's upper arms and elbows are lightly connected to the waist, the energy that flows
from the hind legs through the rider's midsection, along the spine into the mouth, can return via the reins, hands, elbows and seat bones to the hind legs, where it is then recycled. When horse and rider are thus connected, the rider's hands communicate not so much with the horse's mouth, but with his hind legs. The rider can then feel each hind leg in his hand on the same side. Rein aids can then serve a variety of purposes. One of them is to "borrow weight" from the horse's head and neck and add it to the rider's own body weight in order to bend the hind legs more. The seat translates the rein aid into a weight aid in this case. Through the elbow/upper arm connection the rider's hands can become extensions of his seat bones. In this capacity, the hands can form a back up system for the seat aids. If the horse should ignore the seat and try to run through the seat aids, he will encounter the rider's hand, which refers him straight back to the seat. By the same token, if the horse should start to lag behind with his hind legs, the rider's legs refer him forward to the seat. Ultimately, the reins and legs take on the function of guards more and more. As long as the hind legs stay underneath the rider's seat and he does not try to run out from underneath the rider, the reins and legs can remain attentive but relatively passive. But since they are paying close attention to everything the horse is doing, they are ready to take an active role immediately, as soon as the horse is no longer on the seat.
This is a rough description of the basic concept of the circle of aids. It is a simplification. Reality is more complex than this, but it is a starting point for developing an understanding of how the aids interact to communicate with the horse. As a rule of thumb, it is good to try and use the leg first to ensure a sufficient energy flow. The seat comes immediately afterwards, and the hands are last. As in an electric circuit, all the elements of the circle of aids are necessary. If any one of them is absent or malfunctioning, the circle of aids cannot be completed, the horse remains disconnected, and the communication between horse and rider essentially breaks down. Even the often maligned, misunderstood, and misused rein aids are an integral part of the circle of aids, which could not be established without them.
There is another circle of aids, which the rider can discover with the help of a good teacher after he has developed a feel and an understanding of the circle of aids described above. This other circle is formed by sequences of aids that address and connect the inside front leg, outside front leg, outside hind leg, and inside hind leg one after another. This circle of aids can then be expanded into a "network of aids" by connecting the horse laterally and diagonally through combinations of aids, i.e. by connecting the outside hind leg to the outside front leg, the inside hind leg to the inside front leg, the inside hind leg to the outside front leg, and the outside hind leg to the inside front leg.