how does the theme develop in the theme determination?

Nearly every action by Billy and his dogs is an exercise in determination. To start with, Billy demonstrates great determination in simply getting his dogs - he works odd jobs for two years to save up enough money to buy the hounds, then walks through the night to pick up his hounds. The dogs return the favor. Little Ann does not deviate from the trail of a coon, whereas Old Dan never gives up the chase - Billy has to force him away. If Billy ever falters in his will power - as when he has to chop down the big sycamore for the dogs' first coon - his love for his hounds restores his determination. Many characters comment on the persistence of the dogs, notably during the championship hunt in the blizzard. Old Dan is determined until the very end - Billy must pry away his jaws from the mountain lion. Only after Old Dan dies does Little Ann show a loss of will power, but this is because she and Old Dan - and Billy - were a team who fed off the others' strong determination.