It's a bit hard to understand, I THINK that "that account" refers to a previous sentence. It's not a common phrase in modern English so probably not worth learning. I even googled it to make sure it wasn't just me, and got almost no results ;-)
Please note that the sentence you posted looks like very old-fashioned English, I'm guessing it's from a book written over 200 years ago? While old writers like Shakespeare, Austen, Dickens, etc. are WONDERFUL they're not the best guides on useful modern English.