No-one knows for sure why these stones can do these things, but many believe it is due to the vibrations they send out. If the entire Universe has a vibration, a kind of sound wave if you like, then apparently everything else does too, it's own specific frequency. It's thought that gemstones have particular frequencies which are in tune with ailments either in the body or mind and sometimes both. The 'ailments' are often just emotional blockages that occur and the stones can break the blockage, opening people up to feeling the correct way. What the stones ultimately do is balance people out. For instance if there is a kidney problem certain stones can redress this by balancing the body in other ways so correcting the kidney problem. This is seen as healing the ailment, though it is more of a correction in other areas of the body.
Stones which heal kidneys include Carnelian and Jade.
There is more to it than just the stones themselves, you need to know what to do with them. Sometimes just by holding them can help, or holding them and perhaps meditating with or on them. They can be placed near the problem area, or on the corresponding Chakra area of which there seven, so the stone or crystal for a kidney problem would probably be placed on the nearest Chakra to where the kidney is located, perhaps the sacral Chakra.
Placing a certain stone near where you while you work can increase your alertness to help your productivity, or near your bed to help you sleep. Wearing them as a necklace or in another way can help. If you write and have writers block use a Citrine and hold it to your head or lie with it on your forehead for a while to open your mind to knew ideas.
I am no expert in this matter at all and haven't even had much experience in any way with the healing powers of stones but do find them utterly fascinating. There are many in my home and I buy them frequently. I think after this A Z Challenge I may do an occasional feature on a particular stone and talk more at length about that stone. I'm sure anyone more expert that I may find there are many inaccuracies with what I have written though I have tried to be as correct as possible and am learning all the time about them. I don't know if they really can do all these things or if it is all just a belief in them that makes it work, but there are many many people who claim these stones have helped or healed them in some way, so they are worth trying at least. And they are very pretty, too.
