Try either doing a search here with the words ' proporta battery' or just go to Proportas web page. I currently have one of these on order from them. It is external and does , of course, have a wire that connects to your power input port since it comes with Nokia adapters. It will probably easily power your n810 for the 10 hours you need.
And I think the price is quite reasonable as well. It is costing me $64 including shipping from the UK to Seattle, WA, USA. It is quite versatile since that price buys you the battery, plus a power charge cable that has a USB end that can be plugged into your computer or a car power adapter, or a universal AC power adapter. ( both of these supplied with the product)
Check out youtube for video on this product.
My experience was that they seem to only sell direct rather than through other dealers.

Hope this helps.
Neil