As other nations - Spain, the Netherlands and France - sought to rule the waves, each offered its own rewards; Philip II of Spain had put up a sum 150 years earlier. But it was in Britain that the solution was found, following the passing of the Longitude Act in 1714, which offered a prize for determining a ship's longitude.
Harrison wanted to use a highly accurate chronometer - as one moves across lines of longitude, the local time moves one hour ahead for every 15 eastward. Accurate pendulum clocks existed then, but his challenge was to maintain accuracy in a moving ship that was subject to significant changes in humidity and temperature.
Astronomers, meanwhile, sought the answer in the heavens, notably the Moon's motion relative to the stars. Their most famous legacy, the Royal Observatory in Greenwich, was founded by Charles II in 1675 to carry out observations to discover the much desired longitude of places.
But it was Harrison who succeeded, with his marine chronometer. After tireless campaigning to have his achievement recognised, along with the intervention of George III, he finally managed to wring money out of a reluctant Parliament in 1765, at the age of 72.
Historians of science will carp that the details of the original £20,000 challenge - worth more than £1 million today - were more complicated than the heroic story of Harrison, the lone genius, suggests. There will also be debate about how much a prize is able to spur efforts that depend on a rump of existing talent, ideas and innovations. But no one can doubt the power of the Longitude story to make the mind race, the chest swell and the heart beat faster.
While lines of latitude parallel to the equator are easy to measure accurately using the Sun, the lines of longitude running pole to pole presented a formidable challenge. Photo / Thinkstock
Three centuries on, the resurrected Longitude panel has identified six key challenges of the 21st century, from helping to defer the post-antibiotic era, when a scratch could prove lethal once again, to finding more efficient ways to plumb the planet with safe drinking water. From May 22, the public will be asked to vote for the one they deem most pressing; once the theme is selected in June, experts will have the tricky job of devising a specification that is tough enough to spur creative thinking around defined technical challenges, but not so hard that it seems out of reach. Then it is over to anyone, within specific rules, to come up with a solution.
One key aspect of how we crack problems has changed profoundly since the days of Harrison, thanks to the global reach afforded by the world wide web. When it came to finding the Higgs particle, some 10,000 scientists and engineers joined forces in the Large Hadron Collider, in Geneva, distributing data for analysis worldwide.
The effort to crack the genetic recipe of a human being depended on highly specialist skills splintered among many minds within a wide array of institutions. Even mathematics, once the domain of the gifted loner, is more collaborative now, thanks in part to the Polymath Project to coordinate efforts online, launched by Sir Tim Gowers, a Fields medallist (the mathematical answer to a Nobel).
But this new prize is surely an experiment worth trying, according to Lord Rees, the Astronomer Royal, who chairs the Longitude 2014 committee. He believes it answers a pressing need to channel more brainpower into innovation, to jump-start new technologies, and to enthuse young people. I do, too.
The winning idea, which will probably be announced by 2020, is likely to be the product of many minds, in many countries, using many technologies. But the spur remains the same as in Harrison's day. It is not the money, though £10 million is certainly newsworthy. Nor is it the glory of being the first, or best, or most innovative. It will be the satisfaction of changing the world for the better, not just for the benefit of this generation but for the next.
FLIGHT
How can we fly without damaging the environment?
The UK has agreed to try to reduce its greenhouse gas emissions by at least 80 per cent (from the 1990 baseline) by 2050, and the rapid rise of emissions caused by air travel needs to be tackled. The majority of flights from UK airports are short haul.
If Flight wins the vote, the challenge will be to design and build a zero- (or close to zero-) carbon aeroplane capable of flying from London to Edinburgh, at comparable speeds to today's aircraft. This innovation could significantly change transport.
FOOD
How can we ensure that everyone in the world has a sustainable supply of nutritious food?
As the world's population heads towards nine billion in 2050, and becomes richer, tastes will turn to more resource-hungry foods, such as meat and milk. In the face of limited resources and climate change, we must learn how to feed more people with better food, and for less.
If Food wins the vote, the challenge will be to come up with the next big food innovation, helping to ensure a future where there is enough nutritious, affordable and environmentally sustainable food for all.
PARALYSIS
Photo / Thinkstock
How can we restore movement to those with paralysis?
Because of the success of modern medical technologies, doctors have steadily got better at saving patients with catastrophic injuries and serious conditions, such as stroke, although this has led to a rise in the numbers of paralysed people.
If Paralysis wins the vote, the challenge will be set to a wide range of disciplines, from robotics to stem-cell research, to invent a solution that gives people with paralysis something approaching the same freedom of movement that most of us enjoy.
WATER
How can we ensure that everyone has access to safe and clean water?
Although we live in a water-filled world, 98 per cent of it is too salty for drinking or agriculture, and one in 10 of the world's population don't have access to safe drinking water. As demand grows and our water reserves shrink, many are turning to desalination, though current technologies are too expensive, energy-hungry and damage the environment.
If Water wins the vote, the challenge will be set to create cheap, environmentally sustainable desalination technology for those who need it most.
DEMENTIA
Photo / Thinkstock
How can we help people with dementia to live independently for longer?
As the world's population lives longer, more people are developing dementia, at great personal cost and with a huge impact on society. According to Alzheimer's Research UK, 820,000 people in the UK suffer from dementia and 25 million have a close friend or family member who is affected.
If Dementia wins the vote, the challenge will be to develop intelligent, yet affordable technologies that revolutionise care for people with dementia, enabling them to live more independent lives.
ANTIBIOTICS
How can we prevent the rise of resistance to antibiotics?
The evolution of superbugs is threatening to make antibiotics ineffective, with potentially catastrophic consequences. Yet we are still unable to distinguish bacterial from viral infections, or the type of bacteria, which has caused the overuse of antibiotics and the evolution of multidrug-resistant superbugs.
If Antibiotics wins the vote, the challenge will be to create a cheap, accurate, rapid and easy-to-use test that will allow doctors and nurses to better target their treatments, administering the right antibiotics at the right time.
