Are you assuming that all of your other non-mortgage debt has already been paid off?
Dollar-cost-average into a Vanguard index fund.
Dollar-cost-average into a Vanguard index fund.
There are also benefits to your psyche. If you invest all at once, the asset value could drop by 50% the next day, and you feel horrible. If you had invested that money over time, your asset would not be 50% of your total investment.
Again, this doesn't actually mean you get more returns. It just reduces the volatility of your returns at any one point in time.
If you would like to get a good overview of strategies like this, read this wiki. http://www.bogleheads.org/wiki/Dollar_cost_averaging