Maritime Maths

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The aspects touched are:

The tragedy on October 22nd, 1707

Admiral Sir Clowdisley Shovell

Computing your position from bearings

Using bearings from North

Including error allowances

Using relative bearings between multiple points

Generalisation of Thales' Theorem

Thales was about 600BC

Doesn't work over the horizon

What shape is the Earth?

Shadows during Lunar Eclipses show it's a sphere
Eratosthenes of Cyrene measured the circumference of the Earth

Summer Solstice (not necessary)
Reflected in a deep well => Sun overhead - no shadow
7.2 degree shadow in Alexandria, some distance north
Divide by $2\pi$ to get the Radius of the Earth

Eratosthenes also invented Latitude and Longitude

How far is the horizon?

"Mountain" 5 metres high

How far to get to that point?

Uses Pythagoras - about 550BC

Pythagoras of Samos - student of Thales

Wouldn't accept Irrational Numbers

That means from 5m high, distance to the horizon is that
Add answers for total distance

Out of sight of land

Measure Latitude with a Sextant or an Octant

How does that work?

Dead reckoning

Log / Knots

7 fathoms in 30 seconds = 5040ft/hour
47'3" in 28 seconds = 6075ft/hour

How do we measure Longitude?

That is the £6m question

Prize offered in 1714 - 6 million pounds in today's money

Many methods suggested

wounded dogs
Anchored ships with flares and cannons
Measuring the Moon against a fixed star map

Parallax
Distance to the Moon?

Acceleration due to gravity - value of g?

Regular dropping - two ticks per second
Pendulum timing

Clocks

Existing clocks were out by minutes per day

Robert Hooke had a clock in the late 1600s
Required sub-second error

John Harrison, 1693-1776

H1 - still can be seen in the Worshipful company of Clockmakers Guild Museum
H4 - Met the requirement

Never given the prize

K1 carried by James Cook on his second and third voyages

not on his first to Tahiti for the transit of Venus

Galileo Galilei

Acceleration is a time squared thingy
Analysed the pendulum

Or was that Isaac Newton?

CPA / Closest Point Of Approach
Intercept Problem
Isaac Newton (1643-1727)

Royal Mint / Royal Society
Inverse square law of gravity

Acceleration due to gravity

Reflecting telescope

GPS / Global Positioning System

Speed of light

1638 Galileo Galilei

Lanterns

1676 Ole Roemer

Eclipses of moons of Jupiter

Galilean Moons

1728 James Bradley

Stellar Aberration (1/200 degrees)

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