A demonstration video posted to his YouTube channel on Sunday has been viewed almost 2 million times.
The paediatrician of 30 years executes The Hold on a number of wailing wee patients, and it works.
His technique involves picking up the child, folding his or her arms across its chest and holding them firmly, then lifting the baby's bottom with the other hand.
Holding the baby at a 45 degree angle, he lifts the infant up and down, rocks it back and forth and "shakes the little booty".
"Everything you do is very gentle, you don't want to do any jerky motions ever," Dr Hamilton advises.
"You hold the child with the fleshy part of your hand [the palm] not the fingertips, and I am supporting his chin, which is why I am holding him at a 45 degree angle."
According to Hamilton, The Hold works best for babies up to three months, beyond that they are generally too heavy.
Viewers of the video responded with dubious, humorous comments:
Black Socrates asked: "Is this like the human version of grabbing a cat by the back of the neck?", while musicisme656 asked: "Will this work on a wife that nags?".