In 1714 British Longitude Act established the Longitude Prize and Board of Longi
ID: 1316583 • Letter: I
Question
In 1714 British Longitude Act established the Longitude Prize and Board of Longitude to administer it. 20 000 pounds were offered to the person who will create a method (or device) allowing for establsihing the longitude with precission of 30degrees or better.
At that point the most promissing method was that offered by precise chronometer-- after synchronizing the clock with the noon at Greenwich observatory (0 meridian) a voyager could establish his longitude by recoroding the time of the local noon ( highest postion of the Sun) and calculating the time difference (15deg corresponing to 1hr difference).
Ultimate test was to demonstrate better than 30minutes of the precision in position established at the end of a roundtrip in transatlantic voyage.( take it to be 10000km lasting 30 days).
In the second part of XVIII century John Harrison created a very succesful line of "marine chronometers which ultimately fulfilled the conditions set in the Longitude Act.
Question:
During one-month-long oceanic voyages the tested watch H4 allowed to determine the position of the ship with the precision of 41 nautical miles with respect to the port.
By how many seconds was this chronometer off ?
Explanation / Answer
The latitude is easily measured by "shooting" the sun.
To measure longitude you could measure the displacement from, say from noon to noon,
and you need a clock to determine noon.
Using 6.37 * 10E6 m for the radius of the earth and 1852 m / nautical mile
the speed of a point on the surface of the earth is
2 * pi * 6.37 * 10E6 m / (24 * 3600) sec = 463 m/sec
41 nautical miles = 41 * 1852 = 75,900 m
t = 75900 / 463 = 164 sec = 2.7 min
That is, for the sun to have the same overhead position in the sky as when
the ship left port the chronometer would need an adjustment of 164 sec
in order to agree with the actual longitude.