Estimates of the turnout for Glenn Beck's "Restoring Honor" rally at the Lincoln Memorial last weekend have varied widely, from a low of 87,000 to a high of one million.

As a result, the already-controversial rally has sparked a secondary controversy over a report by CBS News that the organization it hired to make a scientific count from aerial photos had come up with a figure of only 87,000, plus or minus 9,000 -- a number greatly at odds with Beck's own estimate of 300,000 to 500,000.

Conservative bloggers like Anthony G. Martin have been quick to deride the CBS figure as "laughable" and suggest -- clearly inaccurately -- that "CBS apparently failed to notice that beyond the large fountain [sic] on the mall, around which there were probably 87,000 people, there was an entire area on the other side of the trees where at least another 500,000 or more were gathered."

Ironically, one of the analysts who provided the CBS figure -- crowd estimate expert Stephen Doig of Arizona State University -- was hailed by conservative bloggers in January 2009, when he came up with a size for the crowd at the Obama inauguration that was half of what most media sources were suggesting.

Doig himself notes in a blog post that when he estimated the Obama inauguration crowd as 800,000, "my reality-based estimate was ignored by many left-wing commentators and embraced by those on the right."

As one example of that reaction, Doig links to a conservative blog post from January 2009, titled "MSM Applies Moonbat Math to Inauguration Crowd," which uses his numbers to bash "Obama's toadies in the mainstream media" for uncritically accepting the Washington Post estimate of 1.8 million.

"The frothing underscores the problem with hyped predictions of crowd size," Doig remarks. "Organizers and supporters are forced to insist loudly that the actual crowd met or exceeded their expectations, for fear that the realistic estimate will be painted as a disappointment. The time-honored way to dismiss scientific estimates that don’t reflect the pre-event hype is to claim political bias on the part of those doing the estimate. I am amused to see that those who embraced my Obama inauguration estimate as soberly realistic are now attacking the Beck rally estimate, produced using exactly the same methods, as deliberately biased."

On Tuesday, CBS responded to criticism of its figures with a more detailed exploration of the methodology employed by Doig and by AirPhotosLive, which provided the aerial images of the rally.

Curt Westergard, president of AirPhotosLive, explained that the photo which Beck used to demonstrate that the area in front of the Lincoln Memorial was tightly packed with people was misleading because "you really have to have a position overhead to count it well, and if you use a very oblique angle from the top of the Washington Monument, the sparse areas -- and there were many because of people with blankets and chairs -- tend to look more dense because you're looking at it from the edge."

According to one Fox News affiliate, "Organizers of the rally had permits for a crowd of up to 300,000 and expected 100,000." In the course of the rally, however, Beck estimated that there were 300,000 to 500,000 people present, and that estimate of has been widely accepted by the mainstream media, with NBC News and the New York Times both going with 300,000 and the Drudge Report and MSNBC's Joe Scarborough reporting 500,000.

The highest guess of all came from Rep. Michele Bachmann (R-MN), who told the Washington Post, "We're not going to let anyone get away with saying there were less than a million here today, because we were witnesses."

The National Parks Service no longer provides figures for these kind of events, since the numbers have proven to be controversial, leaving everyone free to offer their own guesses. Bachmann's figure is certainly too high. The CBS calculation may or may not be too low. The only thing certain is that the controversy is not likely to die down soon.

This video with aerial shots of the Glenn Beck rally used for its analysis was posted by CBS News on August 31, 2010.