Carnelian aids in understanding the inner self and strengthens concentration. It helps one to overcome the ear of public speaking, increases the self worth, and is a fast acting stone to succeed in one's career.
Carnelian is said to assist in stimulating creativity. It seems to have a clearing effect, dispelling negative energies as it replaces them with positive ones. This can make it easier to find direction, and its grounding effects can make it easier for you to feel in control of your life. This makes carnelian a good stone for people who feel like they are going nowhere.
Carnelian balances creative and organisational abilities, opens doors and creates a need to follow through on plans. Wear this stone to prevent other people from reading your thoughts or from dark forces attempting to influence your mind.
There are quite many ancient beliefs associated with Carnelian, which centered around protection during travels after death and against evil.

Carnelian applied physically, can promote balanced digestion. For lower abdominal pain, especially in women and in pregnancy, this stone placed on the pubic bone each day for twenty minutes will reduce the pain.
Carnelian encourages the formation of new blood cells, and bleeding will respond favorably to treatment with this stone. Physically, carnelian has been used to encourage healing of open sores, rheumatism, kidney stones and other kidney problems.

Magical Properties:
Energy: Projective 
Element: Fire 
Powers: Protection, peace, eloquence, healing and courage.

Carnelian was worn on the hand in ancient Egypt to still anger, as well as jealousy, envy and hatred. It is still used to promote peace and harmony and to dispel depression as well.
It is used to counteract doubt and negative thoughts, and can also be used in spells relating to these problems. It may confer patience.
Carnelian has been worn to guard against others who try to read your thoughts. In Renaissance magic, the carnelian was usually engraved with a sword or images of warriors. Then this as a magical amulet was placed in the home to guard it from lightning and storms or carried as protection against enchantment.

Amethyst is purple Quartz, and is a meditative and calming stone. It works in the emotional, spiritual, and physical planes to provide calm, balance, patience, and peace. Amethyst is also beneficial when dealing with legal problems and money issues, which can lead to prosperity and abundance.
Emotionally, amethyst can help heal personal losses and grief. Amethyst has a gently sedative energy that promotes peacefulness, happiness, and contentment. It also brings emotional stability and inner strength, and can enhance flexibility and cooperation. Amethyst can help get rid of addictions (alcohol, drugs, smoking, etc.) and compulsive behaviors of all kinds.
In the psychic and spiritual realms, amethyst is an excellent all-purpose stone that can increase spirituality and enhance intuition and psychic powers of all kinds. It does this by making a clear connection between the earth plane and other planes and worlds. Amethyst is also excellent for meditation and lucid dreaming. It is known to open one's channels to telepathy, past life regression, clairaudience, clairvoyance, and communication with angels. Amethyst also protects against psychic attacks, especially during spiritual work, and protects one from thieves, and protects travelers.
Physically amethyst is said by spiritual healers and mystical lore to heal the withdrawal symptoms of any sort of addiction, help with headaches, insomnia, arthritis, diabetes, pain relief, circulatory system issues, endocrine system problems, chronic fatigue, fibromyalgia, immune system deficiencies,asthma, phobias, pregnancy and preventing miscarriage, menopause, PMS, and general healing.
Amethyst is associated with the third eye and crown chakras primarily, but can also open the heart chakra.