Traditionally, the each of the first ten days after the New Moon has it's own attributes and qualities. Here's the folklore on each of those days:
First Day: A good day for new beginnings. To fall ill on this day means the illness might last a long while. A child born at this time will be happy, prosperous, and live long.
Second Day: A good day for buying and selling and for starting a sea voyage. Also a good time for hoeing and sowing.
Third Day: Crimes committed on this day are certain to be found out.
Fourth Day: A good day for building, construction, and home renovations. Also a good day to be born on if you want to enter politics.
Fifth Day: The weather on this day gives an indication of what to expect for the rest of the month. It's a good day for a woman to conceive.
Sixth Day: The best day for hunting and/or fishing.
Seventh Day: A good day for meeting and falling in love.
Eighth Day: A sickness begun on this day was thought to be likely to cause death.
Ninth Day: If the Moon shines in your face on this day, you may have twisted features or go mad.
Tenth: People born on this day are likely to be travelers or have a restless spirit.
Other Days: A New Moon on a Saturday or Sunday indicates rain, as does seeing the outline of the whole Moon at the same time as a New Moon. Furthermore, should the horns of a New Moon point upwards then the weather will be fair for the next lunar cycle, but if they point down, you can expect rain.
Real Witches' Year
by Kate West