Problem with classes in PHP

So, I've been learning PHP for the past few days from a book, and I seem to understand everything, but whenever I try to create my own classes, something goes awry.

Here's the full code of my document:


<!DOCTYPE html 

     PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"

     "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">

<head>

<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />

<meta name="description" content="Php testing. " />

<meta name="keywords" content="phptesting" /> 

<meta name="author" content="Noah Lowenthal" />


<title>Age of Sorcery</title>        

</head>


<body>

<?php // AoS.php

echo "Welcome to The Age of Scorcery.<br />";

global $dummyhealth;

$dummyhealth = 500;

class Bow

{

    public $arrows;

    public $drawn;

    public $shot;

    public $dummyhealth;

    function __construct()

    {

        $this->arrows = "50";

        $this->drawn = "false";

    }

    function draw()

    {

        echo "The bow has been drawn.<\br>";

        $this->drawn = "true";

    }

}

class Wooden_Bow extends Bow

{

    public $attack;

    

    function __construct()

    {

        parent::__construct();

        $this->$attack = 40;

    }

    function shoot()

    {

        echo "The wooden bow has been shot.<\br>";

        $this->drawn = "false";

        $this->shot = "true";

        $dummyhealth -= $attack;

    }


}

class Silver_Bow extends Bow

{   

    public $attack;

    

    function __construct()

    {

        parent::__construct();

        $this->$attack = 60;

    }

    function shoot()

    {

        echo "The gold bow has been shot.<\br>";

        $this->drawn = "false";

        $this->shot = "true";

        $dummyhealth -= $attack;

    }

}

class Gold_Bow extends Bow

{   

    public $attack;

    

    function __construct()

    {

        parent::__construct();

        $this->$attack = 80;

    }

    function shoot()

    {

        echo "The gold bow has been shot.<\br>";

        $this->drawn = "false";

        $this->shot = "true";

        $dummyhealth -= $attack;

    }

}

echo $dummyhealth;

$mygoldbow = new Gold_Bow;

echo "Ready! <\br>";

$mygoldbow->draw();

$mygoldbow->shoot();

echo $dummyhealth;        

?>           


</body>

</html>

I keep getting a "Notice: Undefined variable: attack in C:\web\AoS.php on line 76

Fatal error: Cannot access empty property in C:\web\AoS.php on line 76" error whenever I run it.

I'm sorry if this is a really trivial error, but I can't seem to find what I did wrong.

I'd really appreciate help.

Thanks,
Noah