Final answer:
The church in Lantern Yard determined Silas Marner's guilt through a drawing of lots, an impartial method believed to reveal divine will.
Step-by-step explanation:
The church in Lantern Yard determined Silas Marner's guilt through a drawing of lots, which was a common practice at the time for making decisions or determining the truth in a seemingly impartial way.
Silas Marner, a fictional character in George Eliot's novel of the same name, is a weaver who is falsely accused of stealing the congregational funds.
His innocence or guilt is decided by the drawing of lots in the church, which unfortunately indicates his guilt, leading to his social and spiritual downfall, and ultimately his decision to leave Lantern Yard.