James W. Christy and Robert Harrington (right) in 1978, U.S. Navy Image
The discovery was made by carefully examining an enlargement of a photographic plate of Pluto and noticing it had a very slight bulge on one side. This plate and others had been marked "poor" because the elongated image of Pluto was thought to be a defect resulting from improper alignment. However, Christy alertly noticed that only Pluto was elongated - not the background stars.
Christy's earlier work at the Naval Observatory had included photographing double stars, so it occurred to him that this bulge might be a companion of Pluto. After examining images from observatory archives dating back to 1965, he concluded that the bulge was indeed a moon. 
The photographic evidence was considered convincing but not conclusive (it remained possible that the bulge was a giant mountain on Pluto). However, based on Charon's calculated orbit, a series of mutual eclipses of Pluto and Charon was predicted and observed, confirming the discovery.
Ironically, the 1965 plates included a note "Pluto image elongated", but observatory astronomers, including Christy, assumed that the plates were defective until 1978.
In more modern telescopes, such as the Hubble Space Telescope or ground-based telescopes using adaptive optics, separate images of Pluto and Charon can very easily be resolved.
1. ^ Planets Beyond: Discovering the Outer Solar System, by Mark Littmann, 1990, pgs. 173-177, including the essay "A Moment of Perception" by James W. Christy.
2. ^ Pluto and Charon: Ice Worlds on the Ragged Edge of the Solar System, by Alan Stern and Jacqueline Mitton, 1999, pg. 58
3. ^ Littmann, pg. 176
* Pluto's Companion from the website "Pluto: The Discovery of Planet X," by Brad Mager
* 25th Anniversary of the Discovery of Pluto's moon CHARON from U.S. Naval Observatory website
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