One is a modern-day version of a camera obscura, which uses a lens and mirror to project an image of the object to be drawn onto a piece of frosted glass, allowing the artist to trace it.
The two others are the camera lucida and the patent graphic telescope - the latter a replica of an instrument invented by Varley himself. These two devices aim light directly into the artist's eye, so it only appears that the image is on the paper.
All three are challenging, as attested by visitors' artistic attempts that hang on the museum's wall.
"If you think that these optical drawing instruments are going to turn you into Michelangelo, it'll be fun for you to find out that in fact they're really hard to use," said Erin Lehman, a research associate at the Philosophical Society.
Such optical devices became a source of controversy a few years ago, when painter David Hockney and optics researcher Charles Falco contended that they had been used by certain Renaissance painters as drawing aids.
Some critics charged that to entertain such a theory was tantamount to an accusation of cheating. Hockney replied that he had meant nothing of the sort, as it requires tremendous talent to transform a simple tracing into a masterpiece with color, form, light, and shadow.
By the mid-19th century, Varley made no secret of using his patent graphic telescope and other such devices, inscribing many works with the abbreviation "P.G.T."
He is commonly thought of as an artist, but in the exhibit, titled Through the Looking Lens, the Philosophical Society Museum takes pains to portray Varley as equal parts artist, scientist, and inventor.
"Varley really crosses all those boundaries that now exist," said Lisa Karena Weidman, the museum's associate curator of education.
He used a telescopic version of his device to draw clouds, landscapes, and other large-scale natural phenomena, and he designed a "vial microscope" for illustrating algae. He inscribed these with detailed scientific notations and arrows to indicate the direction of fluid flowing through the algae.
His devices used lenses to magnify the image and mirrors to redirect it into the artist's eye.
The museum acquired 16 of Varley's algae watercolors in the 1970s, but until recently they had been largely forgotten. The idea for the exhibit arose when a researcher came across them.
The show is supplemented with 25 other works on loan from collections in Britain.
Varley was not one of those gentleman scholars who supported their craft with family wealth, Weidman said. He had to earn a living by making technical drawings of others' inventions and by teaching classes in art and the use of microscopes.
He also made money by selling his instruments. One of his original patent graphic telescopes is part of the exhibit, on loan from the Franklin Institute. The version that visitors can use is a replica, a modification of a period telescope.
The two other devices that visitors can use - the camera lucida and the camera obscura - are modern versions made by Kristen Frederick-Frost, a former researcher at the museum and now curator of artifacts at the nearby Chemical Heritage Foundation.
Later in life, Varley saw the invention of the first photographic cameras. The exhibit describes how he referred to the daguerreotype as a "splendid discovery."
But as the gleaming brass instrument on display attests, Varley's inventions were pretty splendid in their own right.
If You Go
Through the Looking Lens: Cornelius Varley's Wondrous Images of Art and Science, 1800-1860
Where: American Philosophical Society Museum, 104 S. Fifth St.
When: Fridays, Saturdays and Sundays from 10 a.m. to 4 p.m., through Dec. 29
Cost: $1 donation requested
Information: www.apsmuseum.org and 215-440-3400
Guided tours for groups of 10 or more may be scheduled on Tuesdays and Wednesdays (subject to staff availability)