Knowing whether a member is currently logged in or not, is not stored in the database. The information is stored in session variables.

You will need to check the SESS_MEMBERSHIP_ID and the SESS_MEMBER_ID variables to cover all bases. I use the following PHP code to send a user to the login page if they are NOT logged in. You would simply add an "else" statement to continue to your external application:

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//start the sessions
session_start();

//specify the script location (root dir)
DEFINE("__VROOT_DIR__","http://yourdomain.com/installpath");

//include the memberspeed global variables so you don't have to recreate them all
require("/absolutepathtoinstallationdirectory/includes/global.php");

 //check if the member is already logged in nor not
 if(!isset($SESS_MEMBER_ID) || $SESS_MEMBERSHIP_ID=="" || !isset($SESS_MEMBERSHIP_ID)){
   //redirect to login if not logged in
   header("Location:".__VROOT_DIR__."/members/login.html");
 }else{
   //go to your external application or enter additional code here
 } 

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Items above in black are comments, items in blue require changing to your own site's details.