In Philip Yampolsky's translation of Hakuin's Orategama I, he writes (bottom of page 41 at the link, click to enlarge - it's the only way I could figure out to excerpt this!):
In effect what Hakuin describes here, and in following pages, is a breath practice to be used in accordance with one's meditation practice (which in Hakuin's case invariably means koan practice). The koan is kept and stoked in the dāntián. This is quite distinct to Hakuin, and I haven't found correlates in the Soto writings, whether it's Dogen or Suzuki or Loori or even that Brad Warner guy. There are other variations of this as well in the books linked here. In Wild Ivy there is a reproduction of a 書道 that Hakuin did that practically screams his endorsement of the efficacy of this method.
The use of this type of practice continues today. Yamada Mumon Zenji has been translated as saying:
In his autobiography, Kodo Sawaki Roshi relates a humorous experience which happened in his youth at his master's temple. One day all the disciples left the temple except the young monk, Kodo. Having nothing to do he entered a small closet and practiced zazen. At that time the elderly maid of the temple came to the closet, opened the door and was so surprised to see him there, meditating, that she began to bow deeply again and again. Kodo thus realized how noble the zazen posture must appear. Zazen posture, having dignity, is Buddha himself.(To practice zazen) we must sit in a cross-legged posture (lotus posture). The Chinese word, kekka fuza, literally means folding the legs showing the soles of the feet. First of all, put the right foot on the left groin (the root of the thigh), then the left foot on the right groin so that both legs are crossed tightly. This is called kekka fuza which is a perfectly immovable posture. This position, however, is rather hard to maintain for the beginner because it may cause cramps. In such cases, hanka fuza is allowed. This is only a half-crossed legged posture. Either leg can be put on the other. The posture in which left foot is placed on the right thigh is called kissho-za and the opposite is called goma-za.After the legs have been fixed, put the right hand on the crossed legs and the left hand on the right palm, making a small round circle with the thumbs barely touching each other. Next, raise the body quietly and move it forward and backward, to left and right several times to fix the central axis of the body. Then sit upright, extending the backbone as much as possible. Our teachers compare this to the bamboo that is so straight that a stone dropped from the top of it reaches the bottom without any interruption.The perfect posture of zazen creates an isosceles triangle with legs and backbone forming a ninety degree angle. We have to be very careful not to bend too far forward nor too far backward. In this way the zazen posture should resemble a stupa by piling up hip bone, backbone and skull, one on top of the other.In India after the Buddha's death, eight stu-pa (or pagoda) were built in eight districts to be worshipped as symbols of the Buddha.... In Burma and Thailand the pagoda is considered to be most holy. In China and Japan there are many outstanding pagodas made of wood, stone and marble of three or five stories. When we investigate the framework of the five-story pagoda, we are surprised to discover its layered structure balances by hanging from a central axis from the top of the pagoda instead of being built up from a stone base. For this reason these pagodas have stood a thousand years in countries of frequent typhoons and earthquakes. Our human life should be like that. If we are free from all disturbance from the outer world and the inner world, we might remain apart from all attachments, progress to the world of Nirvana, and grasp eternal life. This is zazen.Zazen requires a correct and orderly posture, yet it should not be too strained. It is not recommended to throw the head so far back that others feel uncomfortable. Since it is said "Zazen is the dharma teaching of comfort", it should be done in a totally relaxed and comfortable position. However one must make the body erect by straightening the backbone directly upward. Ears and shoulders should be parallel, nose and navel also. But it would be almost impossible to keep nose and navel in one line unless one's abdomen is extended outward as much as possible. "The tongue should touch the upper jaw." The author of the text is very careful even about small parts of the body. It is true that every part of the body should be correctly positioned, otherwise correct zazen cannot be done. Lips and teeth should be closed. Eyes should remain slightly open so that an area only three feet ahead can be seen. People might suppose that with the eyes closed, one could reach calmness more easily ; however, that is mistaken. Closing our eyes, our mind fills with illusions, and we might easily fall asleep. The patriarch, taught us to open our eyes as much as possible in zazen just as the picture of Bodhidharma, the founder of Zen Buddhism, shows us. We have never seen a picture of Bodhidharma with his eyes closed. Even though visual distractions occur, you should always be free from them, letting them go as they arise. If you become accustomed to zazen with your eyes closed, zazen will be ineffective when your eyes are opened, especially in busy places. On the contrary, if you train your samadhi power throug11 open-eyed zazen, wherever you are, you will not lose your power of meditation.The author of the text warns not to think that practicing zazen in a dark place where nothing is seen or heard is relaxing. This dark place is not the area of the awakened at all. It is in the midst of the ignorant. You cannot achieve real kensho (seeing the Buddha nature) unless you break through this dark place. "Deep significance lies here. Only a man of attainment would know it."
Concerning the breath, there are four ways of meditation explained in the Tendai texts. They are fu, zen, ki, soku. Fu implies snorting breath. This is not good. Zen means purring breath which is also not good. Ki means disordered breath, sometimes too fast, sometimes too slow. Lastly, soku means the most perfect breath which is continuous and quiet as if it were faint breath. We have to shape our breathing into such long deep breaths. The ancients made a strenuous effort to practice such breathing. Some of them even placed feathers on their noses while meditating. For correct breathing : exhaling, pull in your abdomen; when you've exhaled all your air completely, you will naturally inhale; air will flow in and your abdomen will expand. While exhaling, include the counting of your breaths. Continue this ring of consciousness, repeating the counting without any pause at all. If a pause occurs at this time, illusions and mirages will come into your zazen at once. If even one illusion is raised, cut it immediately with your concentrated breathing.With the physical posture and breath controlled, start zazen in a relaxed way by naturally concentrating your strength in your abdomen. We must now control the mind or, as the text states it, "Think not of good and evil." It is, however, unimaginably difficult to control the mind. The Buddha said, "The mind is like a venomous serpent, a wild animal, or a sworn enemy." You might think that while sitting in such quiet circumstances nothing arises to disturb the mind, but it is not so. The quieter the circumstances become, the more disordered the mind may grow. Many things may appear, one after the other. Even the great Hakuin Zenji confessed that while he was doing zazen, he remembered such a small event as the lending of a few bowls of rice and beans many years before to the next door neighbor. It is strange that we remember the things we do not usually even consider. In the meditation hall only the sound of the bell and wooden clappers enter through our senses, but many things arise in the mind to be considered. We come to realize how much man thinks about the unnecessary ; how corrupted man's mind is. Our mind is polluted like a muddy ditch from which marsh gas constantly springs. We cannot imagine what will appear or spring up. Buddhism calls this dirt encrusted mind alaya, which means an accumulation of subconscious images. To cut away this mass of delusion with the sword of prajna-wisdom, so that we may discover the bright mind of the real self, is called the controlling of mind.As the text says, we should not think good or evil, advantage or disadvantage, love or hate. This no mind state where nothing exists is the correct posture of the mind. Dogen Zenji says, "Don't think anything." He recommends controlling the mind, pointing to the real self which is the mind of nonthinking. Since illusion and delusion, like mist, have no substance, they will disappear if we do not focus on them. In Zen Buddhism we also throw away all illusions by concentrating our mind on the problem the koan suggests. Therefore, the text says, "Be aware of illusions, then they will disappear." Cut all illusions. Concentrate your whole mind on the koan, day and night, without any dualistic consciousness. Then, naturally, the inward and outer worlds, self and universe, subject and object, become one. In due time, the event we have sought is realized, yet it cannot be explained. At that moment we experience the inexpressible comfort of spiritual freedom, and the unique flavor of zazen springs up from the deep.This experience is not yet satori-awakening ; it is not yet "seeing one's true nature" or "becoming Buddha." In the Mumonkan an old Zen text called the "Gateless Gate," it is said,Once breaking through [the mass of great doubt] as if with the sword of General Kwan, one gains the great freedom at the juncture of life and death to kill the Buddha when he meets him, to kill the Patriarch when he meets the Patriarch and so receives the freedom of enjoying the situation wherever he may stand.> We must have such a breakthrough experience where we realize real subjectivity and real freedom. There man becomes the master of the world and there evolves his life of negating and creating freely.
Clearly there is a lot going on here, not the least of which has to do with careful regulation of the breath; if breathing is done this way the ki ( 気) will naturally be kept as Hakuin mentioned. There's a lot more going on here than was mentioned, as I said, in the Soto literature I've read.
I'd love to hear some feedback from Soto folks on this; in my experience, this method really does focus the mind and energy and (along with understanding of how and where thoughts arise and descend) puts the mind-body into samadhi like nothing else I've practiced.