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.

T_{s} = (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)

T_{s} = Time in Seconds.

T_{m} = Time in Minutes.

In PPM, the formula becomes:

T_{s} = (ppm * ml *k) / (W * 1000000 * I)

T_{m} = (ppm * ml *k) / (W * 60000000 * I)

Where:

ml = milliliters

ppm = ppm concentration

OR:

T_{m}= (ppm*ml*V*1.608)/(W*mA)

For Silver, this reduces to T_{m} = (ppm * ml * 0.0150)/mA

Ex, 20ppm 250ml = 9.09 minutes at 8.25 mA

EDITED for clarity by kephra