Rating a Watch by means of a Seconds-Clock

The problem consists in determining, within a fraction of a second, the time indicated by the watch at the two instants denoted by two beats of the clock with a known interval between them. It will be noticed that the seconds-finger of the clock remains stationary during the greater part of each second, and then rather suddenly moves on to the next point of its dial. Our object is to determine to a fraction of a second the time at which it just completes one of its journeys.

To do this we must employ both the eye and ear, as it is impossible to read both the clock and watch at the same instant of time. As the watch beats more rapidly than the clock, the plan to be adopted is to watch the latter, and listening to the beating of the former, count along with it until it can be read. Thus, listening to the ticking of the watch and looking only at the clock, note the exact instant at which the clock seconds-finger makes a particular beat, say at the completion of one minute, and count along with the watch-ticks from that instant, beginning 0, 1, 2, 3, 4,.... and so on, until you have time to look down and identify the position of the second-hand of the watch, say at the instant when you are counting 21. Then we know that this time is 21 ticks of the watch after the event (the clock-beat) whose time we wished to register; hence if the watch ticks 4 times a second, that event occurred at ²¹/₄ seconds before we took the time on the watch.

We can thus compare to within ¹/₄ sec. the time as indicated by the clock and the watch, and if this process be repeated after the lapse of half an hour, the time indicated by the watch can be again compared, and the amount gained or lost during the half-hour determined. It will require a little practice to be able to count along with the watch.

During the interval we may find the number of ticks per second of the watch. To do this we must count the number of beats during a minute as indicated on the clock. There being 4 or 5 ticks per second, this will be a difficult operation if we simply count along the whole way; it is therefore better to count along in groups of either two or four, which can generally be recognised, and mark down a stroke on a sheet of paper for every group completed; then at the end of the minute count up the number of strokes; we can thus by multiplying, by 2 or 4 as the case may be, obtain the number of watch-ticks in the minute, and hence arrive at the number per second.

Experiment - Determine the number of beats per second made by the watch, and the rate at which it is losing or gaining.

Enter results thus: -

No. of watch-ticks per minute: 100 groups of 3 each
      No. of ticks per second: 5
                                                     hr. m.  s.
                                     Clock-reading:  11  38   3
Estimated watch-reading, 11 hr. 34 m. and 10 ticks:  11  34   2
                                        Difference:       4   1

                                     Clock-reading:  12   8   3
   Estimated watch-reading, 12 hr. 4m. and 6 ticks:  12   4   1.2
                                        Difference:       4   1.8

Losing rate of watch, 1.6 sec. per hour.