There’s a simpler way to do this:
$(newHtml).appendTo('#myDiv').effects(...);
This turns things around by first creating newHtml with jQuery(html [, ownerDocument ]), and then using appendTo(target) (note the “To” bit) to add that it to the end of #mydiv.
Because you now start with $(newHtml) the end result of appendTo('#myDiv') is that new bit of html, and the .effects(...) call will be on that new bit of html too.