Adds a capability to an existing role.

add-capability.php

<?php
function add_capability() {
    // gets the author role
    $role = get_role( 'author' );

    // This only works, because it accesses the class instance.
    $role->add_cap( 'edit_others_posts' ); 
}
add_action( 'admin_init', 'add_capability');