From Joomla! Documentation
Jquery in Joomla 1.5 & 2.5
Given the fact that most users still use Joomla 1.5. and 2.5; and given the popularity of Jquery framework the information about Jquery is very laconic. What about use of Jquery in older versions of Joomla? At the moment I'm trying to add Jquery to my site which runs on Joomla 1.5.26 and it is not that easy to add Jquery scripts to it, I had to install some extension Jquery Easy but this does not fix a problem.
Perhaps someone knowledgeable could add some information about Jquery and older versions of Joomla?
JHtml in Joomla 3.x
JHTML has been renamed to JHtml. Autoloader is still able to recognise the old capitalized name.