F.P. Journe

markkeenan
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Is the frequency of the Centigraph not irrelevant in measuring increments of 1/100th sec?

The criticisms of the ability of the Centigraph in being able to measure time periods down to 1/100^th of a sec seem to be centred around the frequency only being 21,600 rather than 360,000. I do not really understand why this has to be a requirement with a mechanically oscillating device.

If, however the oscillation of the escapement at 21,600 vph (3Hz) was the equivalent of the oscillation in an electronic circuit (i.e a binary switch), then I would understand the logic that the resolution of any time measurement would be restricted to the frequency of oscillation. In a mechanical device I don’t think this is relevant.

Consider the following example:

A pendulum of length X oscillating at frequency Y describing a arc of distance at the base of Z. If these variables were such that the pendulum covered a distance of 10cm every second and we were trying to use it to measure time intervals with it, we could simply place a scale behind the pendulum and take two photographs at a certain time interval (say half a sec) and we would expect the pendulum to have travelled 5cm. If we used a an extremely fast automatic camera and produced 2 photographs in which the pendulum had moved 1cm, we could conclude that the time period between the two photographs was 1/10^th of sec. This resolution in measuring time intervals is far in excess of the frequency of the pendulum, so is this measurement invalid? Now if we illuminated the swinging pendulum with a stroboscope that flashed every half a second, i.e. a none mechanical oscillating device – we would essentially convert a fluid movement into a binary staggered movement. The maximum resolution we could get would now be half a sec only as we simply could not see anything during the dark periods. If we wanted to measure time periods of 1/10^th of a sec, it would have to flash ten times a sec and so on. I think the confusion in how the Centigraph can measure such time intervals is a function of not appreciating the continous nature of the movement.

Therefore if the facility exists to stop or freeze an oscillating mechanical body of know frequency it is possible to measure the time periods irrespective of the frequency of oscillation, and in the case of the Centigraph, all FP Journe has done, I think, is to provide a hand on the dial that covers a certain distance in 1 second that has the ability to be stopped at any interval in between. Although however its motion is constant around the dial, and it does not instantaneously shift in 1/6^th sec increments as an electronically oscillating device would do, I do acknowledge a very marginal error in the speed of the hand not being completely linear around the dial due to the escapement, from which it is driven, only receiving fresh energy pulses every sixth of a second, thus the speed of the hand my be slightly faster after each pulse, but the overall rotation is still at a period of 1 sec and these speed variations are extremely small.

I see the Centigraph as no different to magnifying the dial of a simple mechanical watch beating at 21,600 and reading the scale, except the watch has a convenient dial for this to be done on and no different to the following. If we assume a average watch has a dial diameter of 38mm, that means that the second hand covers a distance of about 100mm in 60 sec (2 pi r), or about 1.7 mm in 1 sec, and hence 0.017mm in 1/100^th of sec. Now if we were to magnify the watch 100 times and film it, say on a cinema screen, put a normal scale over the image – and then take two images of the screen such that that the second hand had moved a distance of 1.7mm, have we not essentially recorded an interval of 1/100^th of a sec?

Therefore to stop rambling now and try and summarise: because the motion of the escapement is continuous between oscillations (and neglecting the marginal changes in acceleration every sixth of a second), if we can stop it at any point and measure the distance travelled, the frequency of oscillation is completely irrelevant. It is only relevant on electronically (binary) oscillating system.