WII - Tales of Symphonia: Dawn of the New World Hints

Emil's Centurion boost

Influence COULD be the right word to use, but to answer your question, here's what happens.

When you get a Centurion's core, you also obtain a skill of the same name. That skill, when equipped, takes a certain arte and gives it the elemental attribute of the Centurion.

Other than getting type advantages/disadvantages, the only other useful part I've found of this, is being able to fill up that meter in the bottom left with on element so you can capture a monster.

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