To send distant Reiki you must have had a Level 2 attunement. There are some Level 2 reiki symbols (in Level 1 there are no symbols, you are just taught hands positions) that can be used to send reiki and make it more powerful even at a distance, rather than just using them in a direct hands-on healing.
You can actually send reiki to a list (I actually have 4 ongoing lists) or use a proxy (like a teddybear, for example). I use the list sistem to send reiki to a lot of people at the same time, while I use the teddy for specific healings, that is, if I have to send energy for a backache, or stomach pains... I do reiki on the teddy so that the person actually feels the energy being directed to part or organ that needs it most.
