Why are the new law students being welcomed with 允公允能 日新月异 (yǔngōngyǔnnéng rìxīnyuèyì)?
First of all, the welcoming sentence is 允公允能 日新月異instead of 日薪日異.
This sentence is their school motto.

允公 means that one should make himself/ herself capable of (允) thinking about the whole welfare of people (公,) and to avoid being selfish.
允能 means that one should apply (允) what he/she learns to what he/she do (能.) 能 usually means capability.

日新月異 is a Chinese proverb meaning that to learn something more everyday and to keep up with the times. 

In general, the motto is to encourage their students to keep learning, and use what they have learnt to help the society become a better place.