Suppose I have honey of unknown specific gravity. I want to mix a mead must with a target specific gravity g_t and volume V_t. How do I determine how much honey to use?
Determine gravity of honey
Combine a known volume V_w of water with a known volume of honey V_h. measure the gravity of the mixture and denote that quantity g_m. The gravity of the honey g_h is
g_h = (g_m (V_w + V_h) - V_w) / V_h.
For example, if you mix 1 gallon of honey with 2 gallons of water and measure a specific gravity of g_m = 1.14, then the specific gravity of the honey is
g_h = (1.14 (2gal + 1gal) - 2gal) / 1gal = 1.42.
Volume of honey for target starting gravity
Given a target total must volume V_t, and target starting gravity g_s, the volume of honey V_h needed is
V_h = V_t (g_s - 1) / (g_h - 1).
For example, if we want V_t = 5 gallons total must volume with starting gravity g_s = 1.1, then the volume of honey we need is
V_h = 5gal (1.1 - 1) / (1.42 - 1) = 1.2gal.