Lecture 10

The Earth spins on a north-south axis that hardly changes its orientation from century to century. This accounts for the relative stability in the north-south orientation of the map of the fixed stars. Using familiar celestial markers as guides (the star Polaris, for example), a navigator out in the open sea can readily determine her geographic latitude (position north or south of the equator). Figuring out her longitude (position in the east-west direction) is a different story. There is nothing comparable to the equator or the poles for the navigator to use as reference points.

It is inconvenient for everyone around the globe to awaken, work and sleep according to a schedule defined by a single global clock. Most people in Hong Kong, Los Angeles and Nairobi prefer to rise with the Sun, mark the noon hour when the Sun crosses the local meridian and sleep after the Sun has set.

The Earth makes one complete turn on its axis nearly every twenty-four hours. As shown in the illustration above, every 15° of longitude (360° ÷ 24) marks a difference of one hour in local time. Longitude measures are intimately connected to time -- in particular, to comparisons of local time in different parts of the globe.

To see how a navigator in the open sea can use time to determine her longitude, imagine that each day, when her trusty chronometer tells her it is precisely noon in London, she determines her own local time by observing the Sun's position on the sky. On the first day, when her chronometer strikes twelve noon, she notes her local time is 11 a.m., a reading that lets her know she is currently located 15° west of London. On the second day, she sees that her local time is only 10 a.m., an indication that she is now 30° west of London. Unfortunately, her chronometer falls and breaks on the third day! With no way of knowing when it is precisely noon in London, she has no signal to tell her when to measure her local time. Unable to compare her local time with time in London, she is left with no easy way to determine her longitude.

Reliable and accurate chronometers are a modern invention. Mariners have ventured across the open sea for centuries. How did the early seafaring adventurers determine their longitude?

1693	born in Yorkshire
1725	investigated effects of temperature change on expansion and contraction of metals used results of experiments to design gridiron pendulum
1726	completed two "regulators" made of wood, accurate to within one second per month

1730	Harrison obtained support from Astronomer Royal Edmond Halley and clockmaker George Graham for his plan to build H1
1735	H1 completed
H1 weight = 75 lbs size = 4' X 4' X 4'

1736	H1 sent on trial run to Lisbon
1737	Commissioners of the Board of Longitude met for the first time examined H1 advanced Harrison £250 toward production costs of H2 promised additional £250 when H2 is completed

1739	H2 completed
1740	Harrison started work on H3
1742	death of Halley; James Bradley (1693-1762) appointed third Astronomer Royal
1749	Harrison awarded the Royal Society's prestigious Copley medal
1757	most of the work on H3 completed
1769	H4 completed
H4 weight = 3 lbs size = 5 in. diameter

1761-2	first voyage to test H4 made to Jamaica on the Deptford by determining their position at sea using H4, the crew of the Deptford was able to correct the ship's course and avoid delays that would have resulted had they relied solely on estimates based on traditional methods
1763	Nevil Maskelyne (1732-1811) published the first Mariner's Guide
1764	second voyage to test H4 made to Barbados on the Tartar (return to England on the New Elizabeth).
1765	Maskelyne appointed fifth Astronomer Royal H4 examined by committee appointed by Board of Longitude Harrison awarded half of longitude prize money!! Board ordered Harrison to turn over-- H4 drawings written explanations of mechanisms
1766	Harrison ordered to turn over H1, H2, and H3 H1 is dropped and damaged in transit
1767	Larcum Kendall requested to make copy of H4 Harrison began work on H5
1770	Kendall completed H4 copy called K1 K1 used by Capt. James Cook on his second voyage (1772-1775) Harrison completes work on H5, improved version of H4
1772	Harrison wrote to King George III
1773	Harrison given £8,750 by special act of parliament
1774	new act of parliament set out terms for winning the prize; all entries must: be submitted in duplicate undergo trials of one year testing at Greenwich be further tested on at least two sea voyages of Board's choosing
1776	death of Harrison

1730	John Hadley (1682-1744) invented a new, more accurate altitude-measuring instrument -- the "octant" or "Hadley's quadrant" accurate to within 3 minutes of a degree (~ 3 mi)
Hadley's quadrant