It comes from Faraday's law of electroplating.
Each electron carried through the cell from cathode to anode releases one atom of silver by chemically combining it with a hydroxide ion.
So, knowing the weight of silver and the number of electrons passing through for a given time, the weight of the silver in the solution can be calculated.
Ts = (k * M * V)/(W * I)
Where :
M= Mass in grams to be liberated ((ppm * ml)/1000000)
V = Valence (number of missing electrons from silver ions = 1)
k = Faraday's constant = 96485
W = Atomic Weight of Anode material (Silver = 107)
I = Current in Amperes (mA / 1000)
Ts = Time in Seconds.
Tm = Time in Minutes.
In PPM, the formula becomes:
Ts = (ppm * ml *k) / (W * 1000000 * I)
Tm = (ppm * ml *k) / (W * 60000000 * I)
Where:
ml = milliliters
ppm = ppm concentration
OR:
Tm= (ppm*ml*V*1.608)/(W*mA)
For Silver, this reduces to Tm = (ppm * ml * 0.0150)/mA
Ex, 20ppm 250ml = 9.09 minutes at 8.25 mA
EDITED for clarity by kephra