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Help me find out this word.

Clue:

The understanding of a subject of study (9)

C??????r?

Is it chemistry?

Suggested what he had in his hands when he exited (4, 3, 4)

c????????t?
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Wow! We're doing crossword puzzles now? What's next? Sudoku? Emotion: smile

That's a weird clue for 'chemistry'. I'd say no. Seems more like it would be 'knowledge'.

in his hands? No clue what this could be.

CJ
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CalifJimWow! We're doing crossword puzzles now?

Isn't the Games section a better place for stuff like this?
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I've had these scrawled on a piece of paper at my desk for a day, Sooris, but had no luck.

I can't really see the double meaning ('chemistry' = 'understanding'??), but it's possible, I suppose.

For your second, I've been playing with ( ___ ____ LEFT) and ( ____ HIS ___) , but I have had no success.
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Perhaps, but it's pretty close to Vocabulary-- and I would never have found it in Games.
PS: And cryptic crosswords are a word maven's vade mecum, Philip-- I'm hoping that if we can solve this, Sooris will help me take on the unfinished stack of Times Crosswords on my desk.

... now let's see...
Rats! LEFT is no good-- it's the penultimate letter that's a T.... ... _ _ TE? GATE?.... C _ _ _ THE GATE?..... hmmm..