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Scholars of the arcane are always creating new means to use magic.
Associated Bloodline: Arcane.
Bloodline Arcana
Unlike most sorcerers, whose innate magic is powered by force of personality, you use your intellect to understand and master your mystic powers. You use your Intelligence, rather than your Charisma, to determine all class features and effects relating to your sorcerer class, such as bonus spells per day, the maximum spell level you can cast, the save DCs of your spells, and the number of daily uses of your bloodline powers. You gain a +2 bonus on all Knowledge (arcana) and Spellcraft checks.
This ability replaces the Arcane Bloodline Arcana.
Bloodline Powers
Your preferred focus is a bolt of mind-spun magic.
Arcane Bolt (Sp): Starting at 1st level, you can unleash a ray of magic force as a standard action, targeting any foe within 30 feet as a ranged touch attack. This ray deals 1d4 points of damage + 1 for every two sorcerer levels you possess. This damage is treated as a spell of a level equal to half your sorcerer level, and is a force effect. You can use this ability a number of times per day equal to 3 + your (see FAQ/Errata) Charisma modifier.
This bloodline power replaces arcane bond.
FAQ
Does a sorcerer with the sage bloodline use her Int or Cha to determine uses per day of arcane bolt?
Pathfinder Roleplaying Game: Ultimate Magic. © 2011, Paizo Publishing, LLC; Authors: Jason Bulmahn, Tim Hitchcock, Colin McComb, Rob McCreary, Jason Nelson, Stephen Radney-MacFarland, Sean K Reynolds, Owen K.C. Stephens, and Russ Taylor.