PHP BASIC (Login class)

<?php
 class Auth
    {
    var $user_id;
    var $username;
    var $password;
    var $ok;
    var $salt = "34asdf34";
    var $domain = ".domain.com";

    function Auth()
    {
    global $db;

    $this->user_id = 0;
    $this->username = "Guest";
    $this->ok = false;

    if(!$this->check_session()) $this->check_cookie();

    return $this->ok;
    }

    function check_session()
    {
    if(!empty($_SESSION['auth_username']) && !empty($_SESSION['auth_password']))
    return $this->check($_SESSION['auth_username'], $_SESSION['auth_password']);
    else
    return false;
    }

    function check_cookie()
    {
    if(!empty($_COOKIE['auth_username']) && !empty($_COOKIE['auth_password']))
    return $this->check($_COOKIE['auth_username'], $_COOKIE['auth_password']);
    else
    return false;
    }

    function login($username, $password)
    {
    global $db;
    $db->query("SELECT user_id FROM users WHERE username = '$username' AND password = '$password'");
    if(mysql_num_rows($db->result) == 1)
    {
    $this->user_id = mysql_result($db->result, 0, 0);
    $this->username = $username;
    $this->ok = true;

    $_SESSION['auth_username'] = $username;
    $_SESSION['auth_password'] = md5($password . $this->salt);
    setcookie("auth_username", $username, time()+60*60*24*30, "/", $this->domain);
    setcookie("auth_password", md5($password . $this->salt), time()+60*60*24*30, "/", $this->domain);

    return true;
    }
    return false;
    }

    function check($username, $password)
    {
    global $db;
    $db->query("SELECT user_id, password FROM users WHERE username = '$username'");
    if(mysql_num_rows($db->result) == 1)
    {
    $db_password = mysql_result($db->result, 0, 1);
    if(md5($db_password . $this->salt) == $password)
    {
    $this->user_id = mysql_result($db->result, 0, 0);
    $this->username = $username;
    $this->ok = true;
    return true;
    }
    }
    return false;
    }

    function logout()
    {
    $this->user_id = 0;
    $this->username = "Guest";
    $this->ok = false;

    $_SESSION['auth_username'] = "";
    $_SESSION['auth_password'] = "";

    setcookie("auth_username", "", time() - 3600, "/", $this->domain);
    setcookie("auth_password", "", time() - 3600, "/", $this->domain);
    }

    }
?>