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The point of balance for a weapon is not quite the precise centroid but rather a line which separates the masses of the weapon into two equal portions. Usually this is realized physically as where the balance will balance on an extended finger. When measuring this location on a series of long weapons it can get pretty tiring for the forefinger. Because of lighting effects and camera placement the photos were all shot using the forefinger of the right hand as the fulcrum. However, there was a fair amount of estimating using the forefinger left hand prior to each shot. Most of the students like to practice balancing (separately) with each hand.
As everyone likely knows, there is a great deal of effort in Tai Chi Chuan sets to balance qi across meridians. WujI sitting meditation and WuJi standing meditation both have as one of their goals to train the mind and the body to sense when everything is balanced. This has the practical or tactical consequence of training one to rapidly re-balance and then being able to discharge. One might think of this a a repeated equilibrium-absorb-equilibrium-discharge cycle. One might think of Yi Quan as polishing the balance in multiple poses so that one could move into or out of a number of different configurations.