September

A few days early, it's true.  There are many things going on this time of year - back to school, soon the leaves will start to change, and August 23-September 22 birthdays fall within the sign Virgo. 

The birthstone of September is the sapphire, which is a gemstone variety of corundum, which in turn is an aluminum oxide.  It is quite a hard stone, at 9 on the Mohs scale.  Depending on which trace elements are present, the colour can vary quite widely, but the blue sapphire is the best known. 

Modern alternates to sapphire as September's birthstone include lapis lazuli, diamond, and chrysolite (see also olivine, peridot). 

Sapphire is said to clear unwanted thoughts. 
Lapis lazuli is said to promote the physical-metaphysical link.
Diamond is said to amplify strengths and weaknesses. 
Chrysolite is said to dispel negative emotions.

August

I've got birthstones on the brain at the moment.  Depending on where you come from and what sources you look at, there seems to be a little variation in what birthstones go with each month. 

August's birthstone is peridot, a lovely, translucent olive green stone.  Peridot forms in magma beneath the earth.  The green is due to the iron present within the stone.  Peridot is said to encourage assertiveness. 

Modern alternates to peridot as August's birthstone are sardonyx, sapphire, jade and aventurine. 

Sardonyx is said to encourage willpower and integrity. 
Sapphire is said to clear unwanted thoughts.
Jade is said to encourage calm and empathy.
Aventurine is said to strengthen the heart.