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Please refer to the following youtube video (pause it as soon as it starts)...

"USS William D Porter, the Unluckiest Ship in the Navy" by The History Guy https://youtu.be/f9Gb4PakFTU?t=162

There is a running clock super-imposed over the film which gives a HH:MM:SS:FF (where FF is the number of frames elapsed this second, 0-29).

How did 1940's technology achieve this?

I suppose I must concede that this counter may have been added years or even decades later, but the clocks on display here (there are several clips within this video that feature different styles of clocks) seem to "blend in" with the old footage which leads me to believe that they were added (perhaps in post-processing) during the war period.

Given the astonishing ingenuity of wartime engineers I think this would be a relatively trivial task for them, but I would like to know how it was done.

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If you right click on the YouTube video and set the playback speed to the minimum, if is obvious that the video has been converted from 24 FPS cine film to 30 FPS video for TV broadcasting. Every fourth frame in the original is repeated.

The sequence numbers correspond to the video frames (0-29 in each second) not to the original cine frames, and therefore must have been added when the cine film was converted. There is no indication when or why that was done, but first commercially successful video recorder with helical scanning heads (the Ampex 1000) was developed in 1953-54. It is unlikely that any video conversions made before that date would be in a format that was still playable, and they would probably have been of lower quality than the YouTube video.

To summarize, the time stamps could have been added at any time in the last 60 years or so, but were not part of the original film footage.

At a superficial look, the video seems to simply repeat every 4th frame, rather than using the so-called 3:2 pulldown interpolation that was used for telecine broadcasting. That fact might limit the time when the conversion might have been done, but of course "obsolete" equipment sometimes continues to be used long after there are "better" alternatives available.

If the conversion was done for historical archiving, the lack of interpolation may be a deliberate choice to preserve the original content of each film frame as accurately as possible, in case someone wants to examine it frame by frame for research purposes.

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0-29 or 0-23? If it was film, it would have been 24 frames per second.

I don't know how 1940's technology did achieve this, but it could be done either in post-processing, with a counter that runs at any speed, or the same stop-motion mechanism that advanced the film could advance a 24-position wheel with the numbers 0-23 on it, and flashed a light. That wheel could have been geared to the seconds, minutes, & hours wheels.

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