This is the forum for helping you out if you're stuck in Grimrock 2 or if you want to discuss about the mysteries of the Isle of Nex. Warning: forum contains spoilers!
This book is very dicey, think twice before using it!
SpoilerShow
The character that uses Rites of the Moon will be strengthend when the moon is up and weakend when the sun is up. This means at night a Rites of the Moon user has +25 health and +10 poison resist while during daylight he has -25 health and -10 poison resist, all based on his original vitality stat of course!
You shouldn't need the timepiece for that. You get the message "[character name] feels strong." when night falls, and "[character name] feels weak." when the sun comes up again (and you could always just look at your vitality).