By Philip Elmer-DeWitt
October 21, 2010

Apple’s video calling app, now on the Mac, is poised for exponential growth, says an analyst

“We believe Apple is acutely aware of the power of networks (Metcalf’s Law), and is applying this concept to accelerate adoption of its platform.”

So writes Deutsche Bank’s Chris Whitmore in a note issued Thursday, the day after Apple’s (AAPL) Back to the Mac event.

Whitmore is talking about FaceTime, the video calling feature that first appeared on the iPhone 4 in June, was picked up by the iPod touch in September, and on Wednesday was made available to Macs running Snow Leopard, the latest version of OS X.

That law he cites — Metcalf’s — says that the value of a telecommunications network is proportional to the square of the number of connected users of the system.

Whitmore estimates that the number of FaceTime equipped devices will have grown from 19 million on Tuesday to nearly 300 million by the end of 2012. Applying Metcalf’s formula, that would bring the number of possible unique connections to more than 40 trillion. See chart.

“Facetime not only adds to the many features that makes Apple’s current product offering the strongest in its history,” Whitmore concludes. “But it also has the potential to increase the stickiness of the platform exponentially.”

The next logical step, according to Kaufman Bros. Shaw Wu is to bring out a free FaceTime app for Microsoft (MSFT) Windows. “We believe,” writes Wu, “that would make it a much more serious challenger to Skype and other video conferencing software.”

“We believe the integrated approach that links software and apps to hardware is Apple’s ‘Secret Sauce’ that competitors simply cannot match,” writes Barclays’ Ben Reitzes, speaking broadly about the way Mac OS is becoming more like iOS. “The truth is that there are far more active users of Apple’s iOS devices (iPhone, iPads and iPod Touches) now than Macs, so the new strategy is pretty simple: Make Macs more like the devices that everyone is trained on and enjoys. As a result, new software and the Mac App store could help accelerate the halo effect, driving Mac adoption.”

NOTE: has stumbled on some security holes in the FaceTime beta released Wednesday that could compromise your Apple ID and allow others to change your password. Apparently caveat emptor applies, even if the product is free.

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[Follow Philip Elmer-DeWitt on Twitter @philiped]

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