According to The Rodale Book of Composting:
"Wood ash is a valuable source of potash for the compost heap. Hardwood ashes generally contain from 1 to 10 percent potash, in addition to 35 percent calcium and 1.5 percent phosphorus. Wood ashes should never be allowed to stand in the rain, as the potash would leach away. Wood ashes should be used very cautiously - it is not uncommon for home gardeners to create difficult nutrient imbalance problems by applying too much wood ash. It is a strong alkalinizing agent and also increases soil salinity. You should use it in the garden only if a soil test indicates acid soil and a lack of potassium."