The purpose of federated  Search is to be able to include results from
external search  engines when searching in SharePoint. So for example you
might want to include results from Bing or Google when people issue a search
in SharePoint.



So is the external  web site that you pointed your content  source at a search
engine? or a site that returns RSS? or just a web site? If its just a web
site then you don't need Federated Search. You just need to define a
content source  for the external web site and tell SharePoint to crawl it.
The results will be incorporated right into the regular search results. You
won't need the federated search web part.



If it is a search engine or an RSS feed then you don't need to do a crawl.
The external site is responsible for that when using federated search.



Could you provide a bit more information. It sounds to me like you are
trying to use federated search to search an external site when you don't
need to.

Its working  fine in the search  webpart itself in the search centre Site ...

*what made me is to block to search Federated search in Federated Webpart:*
"I tried to add a Federated Search webpart  in the results page  and i have
given the search option as "new content  Source(external website)" This made
me blocked to search external  website in the Federated webpart..."

In the normal search web part itself we can search the External Websites
Data..

As I pointed out. The Federated search  is used to connect to external
search sources, not to internal content  types. If the results from the
external website  show up in the regular Search web part then they won’t show
up in a Federated Search web part.