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Hi, it's me again JK. As usual I have another question ^^

'in another's behalf' what is this supposed to mean? do you need the whole sentence?

if you do, let me know. I'm in a bit of a hurry at the moment, THANX ^^
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Nope, I don't. I think it's usually 'on another's behalf'. In any case, it means in place of, or as a representative of, the other person/entity. 'I accepted the award on the team's behalf' means that I stood up and received the award in my hands, as a representative for the whole team.

Is that enough?
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This is the whole sentence....

'What is the secret mesmerism which friendship possesses, and under the operation of which a person ordinarily sluggish, or cold, or timid, becomes wise, active, and resolute, in another's behalf?'

This is the actual sentence. Will it mean the same thing here?
Sort of. Your sentence, in a rather long-winded way, asks: 'what causes friends to expend so much effort in supporting each other?'. Here 'in another's behalf' means 'in support of another'.

'On' is still the preposition of choice, with 13,800 google hits vs. only 211 google hits for 'in'.