Including a file over a HTTPS connection

Firstly, let me show you my code:

index.php

<?php
$id = 123456;
include("https://secure.example.com/log.php");
?>

log.php

<?php
echo $id;
?>

This simple code should, in theory, display 123456 on index.php, correct? However, I get nothing. I can only assume it's because I'm trying to include a file over a https connection, but is this actually the case? index.php is NOT on the secure server.

I have the following setting turned on in php.ini:

allow_url_include = 1
allow_url_fopen   = 1

Checking wrappers with the following code:

var_dump(stream_get_wrappers());

Gives me an array showing https:

array(12) {
    [0]=> string(5) "https"
    [1]=> string(4) "ftps"
    [2]=> string(13) "compress.zlib"
    [3]=> string(14) "compress.bzip2"
    [4]=> string(3) "php"
    [5]=> string(4) "file"
    [6]=> string(4) "glob"
    [7]=> string(4) "data"
    [8]=> string(4) "http"
    [9]=> string(3) "ftp"
    [10]=> string(4) "phar"
    [11]=> string(3) "zip"
}