"This is where we start seeing what we call empathy or compassion in elephants," said Hamilton. "And that's a very human quality that very few other animals possess."
The outpouring of emotion is all part of what researchers can see. But the group from Save the Elephants is also interested in what they cannot see.
"We have it down to a fine art by now, where I think we can get a collar on an elephant in about four minutes, from darting to the antidote being given and the animal then gets up," Hamilton said.
The team carefully collars and tracks elephants, using satellite technology. The collars show the team where the elephants go and how they migrate. They also tell the team when the elephants come in contact with humans.
"It's extraordinary to think that an animal that is so big and powerful as an elephant is actually under threat, but elephants are facing an uncertain future," said Hamilton. One of the most ominous threats is this enormous growing human population, which is constantly encroaching into elephant habitat and coming into conflict with elephants. Elephants need huge amounts of space to survive. The other thing that is beginning to raise its head again now is ivory poaching."
One of the largest elephants in the herd, Mungu --which means "god" in Swahili-- was killed by poachers. They wanted his giant tusks, which could sell in Japan and China for $250 a pound. And the demand seems to be growing.
Hamilton and her team can't save every elephant from hunters, but occasionally they can make an immediate difference.
The team decided to help one young elephant with a broken leg. First they had to sedate the mother, which would never have let the team get close. It was a harrowing moment.
After being hit with the sedative, the mother looked as if she might fall on her own chest -- possibly crushing her lungs under her own weight. The researchers moved fast and frantically to roll her over.
Then they gave the young elephant antibiotics. The calf's leg would be saved. But the real moment of success was the reunion between mother and daughter, both in good health.
"I just feel very connected to the earth when I'm with them," said Hamilton. "I feel very small and insignificant and human. And it makes me realize what we are on this planet.
"I think the delight of little elephants is that they are filled with so much sort of joie de vivre and joy, and they have just so much energy and they're just exploring the world. So you have this, I don't know you, you just feel so ... I think you start seeing the world through their eyes, really."