The purpose of the expedition Buck takes with Thornton and his partners is to?

The quest Thornton, his partners, and the dogs set out on is an expedition to find a fabled lost mine.

When Buck earned sixteen hundred dollars in five minutes for John Thornton, he made it possible for his master to pay off certain debts and to journey with his partners into the East after a fabled lost mine, the history of which was as old as the history of the country. Many men had sought it; few had found it; and more than a few there were who had never returned from the quest. This lost mine was steeped in tragedy and shrouded in mystery. No one knew of the first man. The oldest tradition stopped before it got back to him. From the beginning there had been an ancient and ramshackle cabin. Dying men had sworn to it, and to the mine the site of which it marked, clinching their testimony with nuggets that were unlike any known grade of gold in the Northland.

But no living man had looted this treasure house, and the dead were dead; wherefore John Thornton and Pete and Hans, with Buck and half a dozen other dogs, faced into the East on an unknown trail to achieve where men and dogs as good as themselves had failed. They sledded seventy miles up the Yukon, swung to the left into the Stewart River, passed the Mayo and the McQuestion, and held on until the Stewart itself became a streamlet, threading the upstanding peaks which marked the backbone of the continent.