Also, "Te Kagami," page 53-55 of Dennis Palumbo, Secret Nidan Techniques Of Hakkoryu Jujutsu, Paladin Press, 1988.
Also, "Kote Gaeshi," page 68-69 of Shiro Omiya, The Hidden Roots of Aikido: Aiki Jujutsu Daitoryu, Kodansha, 1998.]
Also, "Kote Gaeshi," page 144-145 of Gozo Shioda, Total Aikido: The Master Course, Kodansha, 1996.
Step 14-19 of Empi are the footsweep/handsweep gesture and the "look at your palm" gesture in step 14, the "strike palm with forearm" gesture in step 15, the kake uke blocking gesture in step 16, the renzuki (two punches) of step 17-18, and the gedan barai (downblock) to the west in step 19.
Te kagami (hand mirror) is a variation of the basic te nage (hand throw). Te nage, in turn, is called kanoha gaeshi (turning leaf) and kote gaeshi (wrist turnover). It is very well known in jujutsu and aikido circles, as shown by the fact that te kagami is the third technique presented in Palumbo's beginner book on Hakkoryu jujutsu. It is called the "hand mirror" because you stare into your open palm, as if looking into a hand mirror. Jujutsu and aikido players instantly recognize this gesture in step 14 of Empi.
At the shodan (beginner) level of Hakkoryu jujutsu, te kagami is taught as follows. Picture the left downblock in step 13. Your partner grasps your left wrist in his right hand. Rotate your left forearm in an arc across your belly, up toward your right shoulder, and then to a position in front of your face (step 14). Stare into your open palm as if it were a mirror. This gesture weakens his grip and opens a gap between the heel of his right hand and the back of your wrist.
Te nage and kanoha gaeshi are always preceded by a mitsubishi (blinding or distracting) strike. The kiai attack in step 15 offers a hammerfist strike, seemingly to the head, and a knee to the groin at the same time. Those would certainly do as "blinding" strikes.
Bring your right hand up beneath his left hand. Place the jujutsu "pistol grip" on the back of his right hand.
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WIth the pistol grip established, pull your left hand free of his grip. Using the edge of the left sword-hand (called tegatana in Hakkoryu), push against the knuckles on the back of his captured hand. The pushing motion is very similar to step 16, where we slowly push something away using the edge of our hand. By pushing his hand away to lock the wrist, and rotating it anti-clockwise to lock the forearm, we can easily drop him on his back. (Te kagami is just te nage using a different grip. The wristlock and throw are the same.
In the nidan (intermediate) variant of te kagami, the Hakkoryu student takes the partner to the balance point and then allows the left knife-hand to seize the back of the partner's right hand, simultaneously releasing the pistol grip. Your left hand then executes a motion rather similar to a downblock to the left (step 19 of the kata) to drop the partner on his back. This sets up a particularly painful submission that is not explored in the kata.
This accounts for all of the motions in the cluster except for the footsweep and the renzuki. Karate students assume that a footsweep is supposed to drop the opponent on the ground, but as an atemi strike before a hand throw, a footsweep need only unbalance or distract.
The renzuki punches are a deadly "twist and shout" application. Take the opponent to the balance point using the kake te edge of the hand pressing against the back of his right hand. This twists the opponent around so that the right side of his head is quite close to his captured hand. Ball your left fist and punch him in the temple. Then let your left hand seize his hand, freeing your right. Punch him in the head using your right hand, too. Turn west and downblock to put him on the ground. This technique of changing hands in the middle of the kanoha gaeshi is a nidan-level application in hakkoryu jujutsu. It lets you regrip his twisted wrist to get more torsion on it. It is hideously painful.
