Formulae represent direct application of the experience a protagonist has gained by using her magic in conflict. They allow the protagonist to create more consistent effects despite the essentially random nature of arcane energy.
In play, a formula can be used to grant the protagonist a momentary advantage, as she sees a way to connect her past experience with her present troubles. This can be done in a relatively minor way, or in a major way.
A player may recall a formula, indicating one of the formulae she has written down and explaining how it connects to her protagonist’s present troubles. If the GM agrees that the formula is applicable, the player makes a check mark next to the formula, indicating that it has been recalled, and may pick any one of her dice pools (gift, curse, or fixation) and reroll the dice in it, replacing the previous roll. At the end of the session, the player may remove any check marks she has made next to her formulae, allowing her to use them again in subsequent sessions.
More seriously, a player may expend a formula for a more potent effect. Again, this requires that she explain how the formula connects to present events. If the GM agrees that the formula is relevant, the player should draw an X beside the formula on her sheet. The X is not automatically removed between sessions. The player must spend a token of knowledge during an extended period of down time for the protagonist. This represents the protagonist researching and contemplating the intricacies of the formula and becoming familiar with it again.
When a player expends a formula, she may immediately use up to three tokens of knowledge without taking them from the knowledge coffer. This is a truly immediate effect; for example, if the protagonist is about to be discovered because her fixation has increased to seven, she could expend a formula to get and spend three knowledge tokens, immediately reducing her fixation to four, and avoiding discovery.
Formulae will provide your players a feeling of ongoing change and evolution, and a little bit of a bump in power, over time. Ultimately, formulae are your vehicle for giving the development of the story an extra rules-based punch.