What items would Jem finch put in a time capsule and how do they represent him?

There are a variety of items that Jem would put into a time capsule to represent himself. The first item is the boy soap doll that Boo Radley leaves for Jem in the tree. This doll is one of the first acts of kindness that Boo shows Jem and his sister, Scout. It also signifies the beginning of the relationship between Boo and the two Finch children.

The second item is the arm cast that Jem wears at the end of the novel. When Bob Ewell attempts to kill Jem and Scout, Jem's left arm breaks during the fight. The cast not only represents his brush with death, but also the debt he owes to Boo Radley for saving his and Scout's life. Also, the cast represents why Jem's left arm will always be a little shorter than his right arm. 

The final item Jem might put inside a time capsule is the small piece of the Radley house he touches to show Scout and Dill that he is brave. Being a brave older brother is very important to Jem, and this item represents a time when he was able to impress his younger sister.