Passing database resource to object (OO)

Wan I insatiate an object I want to pass a database resource that can be used throughout the object. The below code should indicate what I want but I get the error "mysql_query(): supplied argument is not a valid MySQL-Link resource". I guess this is because "$this->$db = $db" is wrong. Ben class Contacts{

        var $SESSION = array();
        var $db;

        function Contacts( $SESSION, $db ) {

                $SESSION = array();

                $this->$db = $db;

                echo $this->db;

        }

****************************************************************

* Ben Edwards           Tel +44 (0)1179 553 551  ICQ 42000477  *

* Homepage - nothing of interest here http://gurtlush.org.uk *

* Webhosting for the masses         http://www.serverone.co.uk *
* Critical Site Builder    http://www.criticaldistribution.com *

* online collaborative web authoring content management system * * Get alt news/views films online http://www.cultureshop.org *

* i-Contact Progressive Video      http://www.videonetwork.org *
* Fun corporate graphics             http://www.subvertise.org *
* Bristol Indymedia               http://bristol.indymedia.org *
* Bristol's radical news             http://www.bristle.org.uk *

****************************************************************