We　discover　a　new　capacity　scaling　law　in　ultra-dense　networks　under　practical　system　assumptions,　such　as　a　general　multi-piece　path　loss　model,　a　non-zero　base　station　to　user　equipment　antenna　height　difference,　and　a　finite　user　equipment　density.　The　intuition　and　implication　of　this　new　capacity　scaling　law　are　completely　different　from　those　found　in　the　year　2011.　That　law　indicated　that　the　increase　of　the　interference　power　caused　by　a　denser　network　would　be　exactly　compensated　by　the　increase　of　the　signal　power　due　to　the　reduced　distance　between　transmitters　and　receivers,　and　thus,　network　capacity　should　grow　linearly　with　network　densification.　However,　we　find　that　both　the　signal　and　interference　powers　become　bounded　in　practical　ultra-dense　networks,　which　leads　to　a　constant　capacity　scaling　law.　Moreover,　our　new　discovery　on　the　constant　capacity　scaling　law　indicates　three　network　optimization　problems　respectively　for　base　station　deployment,　user　equipment　scheduling　and　base　station　coordination.　These　three　optimization　problems　are　justified　and　solved　in　this　paper,　shedding　new　light　on　the　deployment　and　optimization　of　ultra-dense　networks.　©　2002-2012　IEEE.