Once you prove that the gravity arm is restored every thirty seconds, then pursue adding the pilot dial into the series circuit. I would therefore guess that your serial number (its at the bottom of the NRA plate) would lie between 9 (approx), and the clock date to 1922 to 1924 or thereabouts. This clock is interesting because it doesn't have a gravity arm buffer - added in approx 1924 at or about serial number 1300. I have added a picture below to show the basic basic circuit to show how simple the circuit can be. That case style - known as a 'flat top' was used from about 1922 to 1946, 'factory' clocks ranging in serial number from 980 to 3220 approx. You may find connections inside the right hand side of the case near the top, two fahnstock or other terminals to connect the battery. Three or four "D" size flashlight cells in series is usually ample. Generally with only the pilot dial and no slaves, only three or four volts is suitable provided there is minimal DC resistance in the battery or wires. The battery voltage is not important because the time transmitter and all connected slaves (the pilot dial is a slave) are in a series "loop circuit" with the battery. The design of the master which is often simply called a "time transmitter" provides for a brief electrical circuit closure every thirty seconds using a battery to provide 300 milliamperes current (one third of an ampere) when the circuit closes. The Hope-Jones Synchronome is exceedingly simple in principle as well as electrically.
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