What's the simplest way to maintain the vertical page position in existing browser window when opening a new browser window?

Example: I have a long "results" page and at various points down the page I have links that open new browser windows. The problem is, that when one clicks on one of these links to open the other browser window, the "results" page in the first window automatically jumps back up to the top of the page. This gets annoying when one has to keep paging back down to where they last were on the "results" page after closing the new browser window.