code: protected void checkPath(Path path) {
      URI uri = path.toUri();
      if (uri.getScheme() == null)                // fs is relative 
        return;
      String thisScheme = this.getUri().getScheme();
      String thatScheme = uri.getScheme();
      String thisAuthority = this.getUri().getAuthority();
      String thatAuthority = uri.getAuthority();
      //authority and scheme are not case sensitive
      if (thisScheme.equalsIgnoreCase(thatScheme)) {// schemes match
        if (thisAuthority == thatAuthority ||       // & authorities match
            (thisAuthority != null && 
             thisAuthority.equalsIgnoreCase(thatAuthority)))
          return;
  
        if (thatAuthority == null &&                // path's authority is null
            thisAuthority != null) {                // fs has an authority
          URI defaultUri = getDefaultUri(getConf()); // & is the conf default 
          if (thisScheme.equalsIgnoreCase(defaultUri.getScheme()) &&
              thisAuthority.equalsIgnoreCase(defaultUri.getAuthority()))
            return;
          try {                                     // or the default fs's uri
            defaultUri = get(getConf()).getUri();
          } catch (IOException e) {
            throw new RuntimeException(e);
          }
          if (thisScheme.equalsIgnoreCase(defaultUri.getScheme()) &&
              thisAuthority.equalsIgnoreCase(defaultUri.getAuthority()))
            return;
        }
      }
      throw new IllegalArgumentException("Wrong FS: "+path+
                                         ", expected: "+this.getUri());
    }
docs: Check that a Path belongs to this FileSystem.