Imagine if you created a whole new type of clock, how would it work? Find Flamsteed's brilliant (but doomed) attempt to make a perfect astronomers' clock.
One of only two angle clocks ever made. This clock was designed by John Flamsteed, first Astronomer Royal, to show the time in degrees, minutes and seconds of arc.
In astronomy it is often more convenient to express time in this way. The earth turns through 360°on its axis every 24 sidereal hours. 24 hours = 360° 1 hour = 15° 4 minutes of time = 1° 4 seconds of time = 1' of arc 1 second of time = 15" of arc.
The clock reads as follows: small window right of centre – tens of degrees; 'minute' hand – degrees, with 10-minute of arc subdivisions; 'second' hand – minutes of arc with 10-second of arc subdivisions.
To convert the clock to read normal hours a special pendulum of 39.1 inches can be fitted and the small dial behind the aperture reversed to show I to XII hours. The clock then shows hours - and decimal parts of an hour.
In practice this system was not very useful for astronomers and it is believed that only two 'angle clocks' were ever made: this one, and one by John Arnold, also in the Royal Observatory collection
taken from http://www.rmg.co.uk/see-do/we-recommend/attractions/angle-clock-tompion
hope that helps