Explanation:
The method based on the distribution law among two immiscible liquids is the Parkes process. Let's discuss each option to understand why the Parkes process is the correct answer.

a) Parkes Process:
- The Parkes process is a method used for the extraction of silver from lead.
- It is based on the distribution law, which states that when two immiscible liquids are shaken together, a solute present in one liquid distributes itself between the two liquids based on their relative solubilities.
- In the Parkes process, lead is melted and zinc is added to it. Zinc dissolves the silver present in the lead, forming a solid solution.
- The lead-zinc-silver alloy is then cooled, and the solidified zinc is removed by simple mechanical processes, leaving behind a solid residue containing silver.
- This residue is then further processed to obtain pure silver.

b) Poling Process:
- The Poling process is used for refining impure copper.
- It involves the removal of impurities like sulfur and oxygen by adding a small amount of molten copper to the impure copper and stirring the mixture.
- The impurities react with the added copper, forming copper sulfide or copper oxide, which can be easily removed.
- This process is not based on the distribution law, but rather on chemical reactions.

c) Monds Process:
- The Monds process is used for refining nickel.
- It involves the reaction of impure nickel with carbon monoxide gas at high temperatures to form volatile nickel carbonyl.
- The volatile nickel carbonyl is then decomposed at a lower temperature to obtain pure nickel.
- This process is also not based on the distribution law, but rather on chemical reactions.

d) Cupellation Process:
- The Cupellation process is used for refining precious metals like gold and silver.
- It involves the heating of the impure metal in a cupel (a shallow, porous dish) in the presence of a strong air blast.
- The impurities in the metal oxidize and form a slag, which is absorbed by the cupel, leaving behind pure metal.
- This process is also not based on the distribution law, but rather on oxidation and absorption.

Therefore, out of the given options, only the Parkes process is based on the distribution law.