Shortly before noon on Friday, Dr. Francis Collins, the former director of the National Institutes of Health, stood on the steps below the Lincoln Memorial tuning his acoustic guitar — a “very sweet” Huss & Dalton, he said, with a double-helix of DNA winding down the neck in pearl inlay. The nation’s anxious scientists could use a song.

Dr. Collins, a biomedical researcher renowned for leading the Human Genome Project in the 1990s, had steered the N.I.H. through three presidencies, into 2021, and continued working at the agency until his abrupt retirement a week ago. Now he was a headline speaker for Stand Up for Science, a rally to protest the Trump administration’s drastic cuts to the federal work force and to federally funded science.

The organizers weren’t sure how many people would show up — they later estimated that the crowd had peaked at 5,000 — nor quite what to expect. In 2017, tens of thousands gathered on the Washington Mall for the March for Science. The collective mood then was as much perplexity as defiance at Mr. Trump’s suggestions that America could be made greater by greatly reducing the Environmental Protection Agency and perhaps never mentioning climate change ever again.

This year’s crowd was met by Lincoln, over-large and stone-faced in his chair. The organizers had chosen the site for its postcard view of Capitol Hill, perhaps less aware that the 16th president was a champion of science. He established the National Academy of Sciences in 1863 and, an avid astronomer, often visited the Naval Observatory. Early in his career, Lincoln often carried a volume of Euclid under his arm; he studied the mathematician’s argumentative logic to hone his own as a lawyer.Friday’s protesters made their feelings known with a diversity of placards, some pointed (“Fund Science, Defund DOGE”); some catchy (“Make America Think Again,” “No Brains, No Gains”); some clever (“In Evidence We Trust”); some resigned (“I Can’t Believe I’m Marching for Facts”), some too explicit to repeat here. Several read, “Girls Just Wanna Have Fun-ding for Science.”

Meghan Bullard, a fourth-year doctoral student in neuroimmunology at Georgetown University, sat on the steps below the speakers’ area, sharing Lincoln’s gaze down the length of the pool to the distant Capitol Building. Her sign read, “Literally Just Trying to Cure Multiple Sclerosis.” Her dissertation involved a novel cure for M.S., she said: “We’re currently funded on an N.I.H. research grant. They’re telling us that we need to prepare in case it’s not funded next year.”

Dr. Collins, now at the microphone in the sunshine, enjoined the crowd “to celebrate the achievements of science over decades in bettering the human condition, and to advocate for strong public support at a time when serious threats of harm are occurring.” He invoked the Gettysburg Address — “of the people, by the people, for the people” — and noted that it applied to taxpayer-funded science, too.

“We need to sing about this,” he said finally, and offered a reworked folk song, which involved everyone singing the chorus: “We're joined together by this noble dream.”

Several dozen Stand Up for Science rallies were held on Friday in cities around the country and the world. A thousand people attended in Berkeley, Calif. In Chicago, protesters in winter coats, some holding umbrellas against the sideways-falling snow, gathered at Federal Plaza to hear Senator Richard J. Durbin, Democrat of Illinois, and other speakers. Signs not shielded in clear plastic were soon reduced to soggy cardboard and blurs of marker ink.At Montana State University, one of five rallies happening across the state, organizers struggled to confirm speakers. “There are no speakers except me at the moment,” said Roland Hatzenpichler, a biologist at Montana State University, on Thursday evening. Several invitees declined for fear of repercussion from the state or federal government or their tenure committees, Dr. Hatzenpichler said. Many international students, he added, were afraid to attend after recent social media posts by Mr. Trump about cutting funding for universities allowing “illegal protests.”

In Washington, many protesters declined to share their names publicly, for similar reasons. One woman, who wore a surgical mask and a long, white lab coat with the words “Mad Scientist” on the back in red lettering, described herself only as a federally funded researcher “who’s trying to keep things moving forward in these challenging times.” Her field was planetary science, hence her sign: “Good luck getting to Mars without science.”

Elsewhere, three young women, all students, stood together with a sign that read “Science is Apolitical.” One said, “I didn’t tell my parents I’m here,” and they all laughed. She added, “I should be at home doing my research. But I can’t, because we might get defunded. It shouldn’t be political, but because they’re making it that way, we don’t have a choice.”

The speechifying continued through the afternoon. Bill Nye, the Science Guy. Fred Upton, a former Republican representative from Michigan. Representative Bill Foster, Democrat of Illinois and the only Ph.D. physicist in Congress. (“It’s not just science that’s under attack, it’s facts,” he said offstage.) Dr. Allison Agwu, infectious-disease specialist at Johns Hopkins University. Denali Kincaid, a doctoral student in geochemistry and a TikTok communicator. They reminded the audience (unnecessarily, they conceded) of the value of scientific expertise: to make vaccines, accurate weather forecasts, agricultural breakthroughs; to monitor the 150-plus active volcanic systems in the United States alone.

From the sidelines, Mary Doyle, a retired public-health researcher, lamented the depth and seemingly indiscriminate nature of the job and funding cuts. Entire university departments “are going to be gone, because they’re so heavily dependent on federal funding,” she said. Her husband, Scott Nainis, an engineer, said: “We saw a sign that said, ‘Science is best done with scalpels and microscopes, not chainsaws.’”

Both had attended the 2017 march; this one felt different. “It’s a darker mood,” Ms. Doyle said.“This is a lot sadder,” their friend Jackie Agnew said. “The other rally felt like a rally, you know? It actually felt like you could have impact. There's sort of a defeated feeling here.”

Late in the afternoon, Colette Delawalla, a graduate student in psychology at Emory University and one of the organizers, was feeling elated, if tired. “My expectations were pretty low,” she said. “I’d have been pretty excited if 500 people came out.”

One thing her team had learned from the March for Science “was that one protest isn’t enough,” she said. The previous day they had been on Capitol Hill to meet with congressmen, lay out some legislative goals and “ring the bell.”

“I did this because, at the end of the day, I just want to do my research,” Ms. Delawalla said. “I never thought of myself as an activist — that’s never been part of my identity. And I’m reckoning with that.”

The crowd had dwindled to hundreds when the last speaker, Representative Jamie Raskin, Democrat of Maryland, took the microphone around 4:15 p.m. He too invoked Lincoln, as a “champion of liberty and union,” and gave a fiery short course on the Constitution and on science as a First Amendment endeavor. (“‘Diversity’ is not an illegal word.”) He noted that it was the president’s sole task to “take care that the laws are faithfully executed: Do your job, Donald Trump!”

Briefly, the crowd chanted, “Do your job!”

The 16th president did not speak, or maybe he did. In 1860, while passing through Norwich, Conn., Lincoln was a approached by the Reverend J.P. Gulliver, who was writing for The New York Independent. The two men bonded over their mutual admiration for Euclid. “Euclid, well studied, would free the world of half its calamities, by banishing half the nonsense which now deludes and curses it,” Gulliver said.

Lincoln laughed and replied, “I vote for Euclid.”