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Any number of mechanisms could serve this purpose, though: urination, sweating, blowing your nose. Why should these chemicals leave our eyes? I believe that is what the author is trying to answer.

Many features of human physiology serve more than one function -- our eyebrow ridges protect our eyes from sun, dust, getting punched. I don't mean to reject your idea; but it doesn't seem to go very far towards explaining why tears are the way they are.

Do you have any reason to believe the same chemicals are exclusively in tears (vs feces, urine, sweat, saliva, etc)? Also, it should be easy to do an order-of-magnitude estimate of the effect, even if a chemical is exclusively in tears (concentration * volume). It's highly implausible tears contain anywhere near enough of a particular hormone to affect concentrations across a volume as large as a human body, and deserves some scrutiny/evidence.

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