You cannot directly add an adapter as datasource. In datasource you need to mention the table. So try the following,
DataSet ds = new DataSet();
adapter.Fill(ds);
Chart1.DataSource = ds[table_name];
Replace the following portion of the code with the above code:
DataTable table = new DataTable();
adapter.Fill(table);
DataSet ds = new DataSet();
adapter.Fill(ds,"Chart1");
Chart1.DataSource = adapter ;