Drupal and Imagecatch problem (Imagecache seems to work only if thefile system is set to private)

The problem is th epath to the image uploaded does not work correctly.
If you set the File system to Private under Administrator>>Files System, th epath problem is sovled. However this solution will affect other Drupal Modules.
I have tried other ways :

1. set the permission for pth "/var/www/drupal/sites/default" to 777----doe snot work.
2. change the content of .htaccess---doe snot work

The following seems a coorect way to do so:
"Changed case FILE_DOWNLOADS_PUBLIC to be the same as case FILE_DOWNLOADS_PRIVATE and Voila: It worked!. I am now thinking that this must be a path issue of some sort? Assuming that this is the case, I'm changing the status on this to bug report. Correct me if I'm being premature (or just wrong)."

Source:

• http://drupal.org/node/399790#comment-1428428
• http://drupal.org/node/366177