Finding Longitude: Shadows, Sundials and Chronometers

The hardest question at sea

Latitude was never the problem. Measure how high the Sun or the Pole Star climbs and you know how far north or south you are. Longitude was different, and ships were lost over it for three hundred years. There is nothing to measure: every line of longitude looks exactly like every other. The answer, when it came, was not a better telescope. It was a clock.

Longitude is time

The Earth turns once, 360 degrees, in 24 hours. Divide one by the other and you have the whole topic: 15 degrees of longitude for every hour of time difference. 4 minutes of time for every single degree. So if you know what time it is where you are, and what time it is at Greenwich at that same instant, the gap between them tells you how far around the world you have travelled. That is why it needed a clock. Not to tell you your own time - the Sun does that - but to carry Greenwich time with you, accurately, for months, on a rolling ship.

Minutes per degree

The Earth turns 360 degrees in 24 hours, which is 1440 minutes. How many minutes of time correspond to one degree of longitude?

How many zones?

Time zones are each about 15 degrees of longitude wide. How many such zones fit around the Earth's 360 degrees?

The two times you need

Finding longitude means knowing two times at the same moment. These are the terms the question will use:

East or west?

Your local noon happens LATER than noon GMT. Where are you?

• West of Greenwich, because the Sun reaches you after it reaches Greenwich
• East of Greenwich
• On the Prime Meridian itself
• It cannot be told from the time alone

Find the longitude

At the moment of your local mean noon, the chronometer shows 14:00 GMT. Using 15 degrees of longitude for every hour of difference, how many degrees of longitude are you from Greenwich?

Two ways to carry Greenwich with you

Both methods were real, and the specification names both. Each is a way of knowing GMT while nowhere near Greenwich.

Order the method

Put the shadow-stick method of finding longitude into a workable order.

• Set a vertical stick on level ground and mark the tip of its shadow through the day
• The shortest shadow marks local apparent noon
• Read the chronometer, which is keeping GMT, at that moment
• Apply the Equation of Time to turn apparent time into mean time
• Work out the difference between your local mean time and GMT
• Convert the difference at 15 degrees per hour, east if ahead of GMT and west if behind

What do you actually need?

Select the TWO things without which longitude cannot be found by this method.

• A way of finding your own local time, such as the Sun and a shadow stick
• A way of knowing the time at the Prime Meridian at that same instant
• Your latitude
• A telescope powerful enough to see the coast

On the deck

Three decisions while finding your longitude at sea.

• Your shadow stick shows the shortest shadow of the day. What have you just measured?
• You are about to compare that reading with the chronometer. What must you do first?
• Your chronometer has been running four minutes slow for the whole voyage. What is the effect?

Fifteen degrees an hour

The Earth turns _____ degrees in 24 hours, so every hour of time difference is _____ degrees of longitude and every single degree is _____ minutes of time. To find your longitude you need your own local time and the time at the _____ Meridian at the same instant. And if your local noon happens after noon GMT, you are _____ of Greenwich.

Why longitude was the hard one

A friend asks why finding longitude was so much harder than finding latitude, and why the solution turned out to be a clock. Write them an explanation.

• Say what makes latitude measurable directly, and why longitude is not
• Explain the relationship between time and longitude, giving both the 15 degrees and the 4 minutes
• Describe how a shadow stick and a chronometer are used together, including the Equation of Time
• Say what a clock running slow would do to the answer, and why that made accuracy at sea so hard to achieve