It was towards the end of the sixteenth century that it was finally being fully recognised that the calculation of longitude truly had its roots in mathematics.

Depending on an accurate timekeeper to provide a simple way to calculate longitude was first considered in 1530 by the astronomer Gemma Frisius. However, it was not until the late 1650s that any real progress was made by Huygens in Holland and Hooke in Britain. Both worked independently of each other. Hooke developed a spring that coiled and recoiled over a particular interval defined by the torsion of the spring and the size of the balance weights. It was obeying a principle now called Hooke’s Law. Huygens chose to use a pendulum. Both Hooke’s and Huygen’s clocks operated well on land although they proved far too temperature sensitive as a result of the contraction and expansion of the metal in the spring or the pendulum. Only Huygen’s clock was tested at sea and it did not prove reliable. However, observations of the movement of the pendulum did help confirm Newton’s law of universal gravitation so there was some gain (Berthon and Robinson, 1991:121).

The problem of accurately determining longitude remained and hindered, although did not stop European exploration and commercial expansion.