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Skill System - The skill levels in EVE, whatever which skill it is, stack. Concretely, it means the following: using the skill mining as an example, which gives a 5% FFXI Gil bonus to the yield of your mining laser per level, if you trained Mining to level 4, it means you get:
5%*4=20% bonus from the skill Mining at level 4
The effect of the different skills you trained though has to be multiplied together. Say you have Astrogeology at level 4 (which also gives a 5% bonus per level to your yield) and Mining at level 4, then your net yield would be:
Base laser yield * 1.20 * 1.20 = XXX
Using T2 Miners, which has a 60 m3/cycle base yield, you would get:
60 * 1.20 * 1.20 = 86.4 m3/cycle (note that the yield is neither truncated nor rounded)
Simple enough? Let's keep going!
Cycles - Cycles determine how many seconds your laser need to complete a full, well, "mining cycle". The ore you mined will appear in your cargo at the end of that cycle.
Named, T1 and T2 mining lasers have a cycle of 60 seconds (1 minute) and strip mining lasers (T1 and T2) as well as the Modulated Deep Core Mining Lasers II (MDCM2) have a cycle of 180 seconds (3 minutes).
Ice harvesters will be covered in another section, as the whole ice mining system is quite different from the asteroid mining system.