Tears are a touchy subject. Crying, especially in public, is often quickly followed by the impulse to excuse oneself.

In one sense of the word, of course, we are tearing up all the time. Basal tears—the thin film coating the eye and lubricating it round-the-clock—are endemic to all mammals. Every blink reboots this watery emulsion. Then there are reflex tears; the ones hardwired to swiftly wash out any wind-borne irritants. Without these stinging tears, chopping onions would no longer be a kitchen sink drama.

The third category, colloquially known as emotional tears, differ both in function and in chemical composition. The tears we cry when we are sad tend to contain higher quantities of hormonal proteins, including leucine-enkephalin—one of the body’s many endogenous opioids. P...