Important Points of Dragon Shaped Pa Kua Pushing
Hands by Fu Wing Fai.
(from the Pa Kwa Chang Journal, v.2#6, available on CD-ROM from
http://www.plumpub.com/sales/bagua/coll_crandallBG.htm ).
 
One’s hands, eyes, body, and stepping should maintain the
same height and move as one.
One should remain as lively as a frolicking dragon and one’s
palms should be like the shuttle of a loom.
One’s movements should be continuous and executed in a
single breath.
In single and double palm change, it should be like a dragon
flicking out its tongue.
In “Azure Dragon Extends its Claws”, “Straight On Palm”,
and “Palm Pressing Against Chest” the movement should be
like a clap of thunder.
In the “Waist Wrapping Palm” and the “Spinning Body Palm”
the movement should be like a black dragon coiling its body.
One twists and spins, tumbles, and turns.
One’s entire body is rounded, making a big circle.
One’s hands and feet make small circles everywhere.
One advances circularly, one retreats circularly, undulating
like a wave.
One’s lively stepping is circular.
One uses one’s waist as the axis. The waist impelling the
four extremities.
The hands arrive with the feet.
The body moves with the palms.
One can strike from a stationery posture or one palm for each
step, or one can take many steps with a single strike.
The whole body moves with a single breath.
There should be springiness suffusing its suppleness.
After considerable practice, one can increase the flow of ch’i
and blood, strengthening the body, improving the health and
making one live to a long life.

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Principles shared across the internal styles

The movement begins at the feet, is carried through the legs, is steered by the waist, rises up the back, and travels out to the hands.
The 'coarse' and 'muddy' sinks, the 'fine' and 'clear' rises (within the body). If the body is flexible and relaxed, then the heavy can sink down and the light can rise up.
Where the mind directs, the body follows. The mind directs the waist and the waist directs the body.
The top of the head must have an empty feeling and float, as if it is lifted from above by a fine string. The central axis of the body is an imaginary line, rising up to the crown of the head, and down to the perineum. The waist causes the body to turn around this.
The chin should be slightly tucked in, and the pelvis should be tilted slightly upwards. The anus should be slightly tensed.
The body movement should be supple, and not 'wooden.'
The martial techniques and applications are superficial, the main focus should be on following the above requirements in a relaxed manner, and always refining them further.
With dedicated practice, powers of concentration will improve, and further advancement will be possible. This follows the saying: the human body is like a machine, if it is not polished it will rust.

 
Philosophy
 
Internal styles are inspired by Chinese breath control and meditational practices, sometimes referred to as "Taoist yoga". These philosophies describe the formation of the universe in abstract terms. The original state of the universe is 'nothingness', wu chi. From this 'something' forms, which is yin and yang joined together and is called tai chi. NASA scientists have described the same state in a different way with the phrase "diversity is the binary function." Yin and Yang might later seperate, and this is called leung yi. Two things can be divided into four, this is called ssu hsiang. To describe how two becomes four, Grandmaster Su Lu Tan (a friend of Fu Chen Sung) said "Night and day, pushing together, creates the four seasons."
Further subdivisions can be made, one being to divide things up into the five elements.
Another way is to divide things into twelve. The five 'elements' and the twelve 'animals' together make the oldest internal style, h'sing yi ch'uan (form-mind boxing, or mind-intent boxing). The linking form of Fu style of h’sing yi ch’uan joins the five element and twelve animal forms. Each element gives power to one other, and subdues a different element, to create an overall balance and to make victory possible. The twelve animals operate in the same way. These numbers, five or twelve, are not random. Different numbers do not balance so perfectly.
Another way is to divide things up into eight. This is pa kwa, the eight trigrams. Each trigram is a unique combination of three (eg three 'yin' or three 'yang', or anything in between). Each of the eight can then divide into a further eight (giving the sixty-four hexagrams).Pa kwa chang (eight element palm, or eight trigram palm) is based upon the number eight, but each element is a separate thing. One does not control the other. The martial art pa kwa chang was first called 'turning palms' and came from walking the circle. The theory was merely added later because the other internal styles had such philosophies, and to match the I Ching 'Book of Changes.'
Tai chi ch'uan was based upon seeing yin and yang everywhere in nature, and how one compliments the other. It was inspired by a fight between a snake and a crane (a kind of bird). There are four basic stances. Adding central equilibrium (balance) makes five. There are eight basic movements. Every movement in tai chi is a variation of these eight movements. Eight plus five gives the thirteen postures. All movements in nature are variations on these 13 movements.
In between tai chi (two things joined) and pa kwa (the eight trigrams) is leung yi (two things separated). The leung yi ch'uan form is a physical embodiment of this, containing both yin and yang aspects, and performed in a way that is in between how tai chi (relaxed) and how pa kwa (relaxed but with tension and a slight twisting) are expressed. Each compliments the other, and practicing one correctly will help the practitioner understand and achieve more in the other.

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Poem of leung yi ch’uan (yin-yang boxing) by Fu Wing Fai. English translation by Douglas Lee.
(from http://www.donet.com/~rwithman/LIANG%20YI%20CHUAN.htm )

Mind fast, movement fast.
Mind slow, movement slow.
Mind leads the movement.
Light to fast forever changing.
Tangible to intangible.
Swinging open, swinging close.
Expanding and contracting the spine.
Twisting left and right.
Turning and spinning.
Upper and lower following.
Wrapping around the waist.
Continuous movement: one after the other.
Balanced movement on both sides.
Use the waist as the central axis.
Axle is centred from shoulders to pelvis.
All movement generated from the waist.
Hand techniques more elaborate than tai chi.
Powerful and fast movement.
Light and fast movement.
Slow and soft movement.
Hard and soft movement.
Light and firm movement.
Lively and agile.
Elegant and harmonious.
Smooth and complementary.
 

 
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Extracts from Chang Naizhou' 18th century writings (translated in Scholar Boxer: Chang Naizhou's Theory of Internal Martial Arts and the Evolution of Taijiquan by Marnix Wells).

When form is co-ordinated, then energy is not tugged or dragged. If form is uncoordinated, then energy is necessarily clogged and obstructed. In every place physically test, without overlooking the slightest detail, to contrive marvels.
The head is round in the image of heaven....If this place is coordinated, then one body's energy entirely enters....Its energy concentration's dropping point has one fixed place.
There is, of the two legs, one vacuous, one substantial.
No matter lateral or level, in straight bursts, little finger ...  leads energy. When you understand this, the rest may be deduced.
All affairs, if concentrated at one, are governed, because they have a ruler.
Generally, man's body energy is shot from "fate's gate" (kidneys), energy's source, and manifests at the four extremities.
Down and up congeal together, completely concentrated in the Central Palace.
To duck and dodge out of contact, without sticking and linking...this is the tenth fault.
Refining form does not exceed motion and stillness.
Generally, when his energy comes, before his energy ceases, I ride and destroy it. It may be east or west, no matter left or right, I meet its source. Its moment is just at one movement. If he moves, I instantly move. He has no leisure to contrive force...In this there is no room for a hair's breadth. Students must pay attention.
How could they know that this research is the Internal Elixir's root foundation? It is heaven and earth's precious secret. To the wrong man, do not transmit; at the wrong time, do not transmit; at the wrong place, do not transmit.
Do not let corrupt scholarists know. If they once know they will quote scripture and ancient precedents and speak a lot of misleading and irrelevant maxims that annoy people. Be careful to avoid this. You may keep it secret.
Bone joints are empty cracks. They are the human body's streams and valleys....These places, with Essential Spirit filled, are then like iron or steel.
Energy must, at the body's center, directly ascend, directly descend. You may only with idea know it, and spirit apprehend it. If you must grasp and seek for what is its appearance, what is its form or traces, then you gouge! You speculate! Not only will you get no achievement, you will get a sickness that is not slight. 
So to study this way, first draw a big circle, gradually draw smaller and smaller, until at completion there are circles, yet no visible circles. They are purely as ideas known, leaving no trace.