Chemistry are as explained in the game chains of elemental magics.
To valid chemistry, you must cast and hit your target with the second spell while the foe is still under the effects of the first.
Here are the four chains you must perform to unlock:
Earth => Fire
fire => Thunder
Thunder => Ice
Ice => earth
It is possible to chain the four of them, but you'll have to use an equipment that makes magic less powerful and passive skills to enhance your SP.. and find an ennemy that resist three spells in a row.
As Magic can be very powerful and instant kill, in chapter 3 when in the first garde, you'll find Fire and Ice Elementals: using fire and ice won't harm them but they feel the effect of the spell, making it easier for you to chaines.
Forests in chapter 2 also contain Earth and Thunder affinity foes, so use them for that purpose.