Combine all ingredients in a nonreactive saucepan over medium-high heat. Bring to a boil, reduce heat, cover loosely, and simmer for 15 minutes. Remove the pot from the heat, uncover, and let cool to room temperature.
Funnel the mixture into a half-gallon glass jar or a two-quart nonreactive vessel. Cover and refrigerate for two days, giving it a stir or a shake a few times each day.
Strain the mixture through a fine-mesh strainer and discard the solids. Strain again through several layers of cheesecloth, a coffee filter, or muslin into a nonreactive vessel. Cover and refrigerate overnight to allow sediment to sink to the bottom.
The next day, pour or siphon off the mixture into a new nonreactive vessel, taking care not to disturb or pour out any sediment at the bottom (you can strain once more through cheesecloth or a coffee filter after pouring off the mixture to be extra-sure that you've removed any remaining trace of cinchona powder if you like). Choosing to pour off the tonic water will result in a slightly smaller yield than siphoning.
Combine the tonic water with an equal amount of simple syrup and stir or shake gently to combine. Store in the fridge loosely covered for up to one year. To serve, cut the tonic syrup with seltzer water by at least 50%. Consume in moderation.