94 THE HAMILTON ASSOCIATION, 
instalments, the maximum reward of £20,000. Harrison was a 
Yorkshire carpenter, who would have had little chance of success in 
a modern competitive examination ; but his ingenious application of 
the different expansion by heat of two different metals to the con- 
struction of chronometers, was an inestimable service to his country 
and to the world. He made four or five chronometers. Of these, 
it is said, one was of such exactness that it did not vary a whole 
minute in ten years. Two of the Harrison chronometers are pre- 
served at Greenwich Observatory. Sharp’s biographer says: ‘‘ A part 
of the escapement was, a few years since, removed from one of these, 
when the train of wheels ran down with velocity, though they had 
not turned for more than a hundred years.” 
In 1724, five years after Flamsteed’s death, an Act of Parlia- 
ment offered £45,000 reward for a set of tables giving lunar distances 
correctly to fifteen seconds of arc. Mayer, of Gottingen, worked 
out such a set, and sent them in 1757 to be. tested, as, by terms of 
the Act, they had to be compared with actual observations for eight- 
een years and a-half. These tables were used in the Nautical 
Almanac first issued in 1767. Mayer died in 1762. His wife 
received the sum of £3,000, and Euler, a Swiss mathematician, 
was awarded a like sum. LEuler’s service was an approximate solu- 
tion of the famous problem known as that of “the three bodies,” 
namely : given their distances, velocities, masses and direction, what 
will be the path of one of three bodies around another, when all 
move in accordance with the law of gravitation? Hansen’s lunar 
tables have since superseded those of Mayer. The British nautical 
almanac devotes six of its pages each month to lunar distances. 
They are now given to one second of arc, and are published three 
years in advance. 
With what accuracy the position of a ship at sea can now be 
determined was exemplified a few years since by picking up the 
broken Atlantic cable from the bottom of mid-ocean. ‘The cable 
was no larger in section than a ten cent piece; the buoys left to 
indicate place of the break were washed away, and nothing but his 
nautical skill was left to guide the navigator in what looked to be so 
hopeless a search. Yet with such extreme precision was the place 
of breakage recorded, and the searching vessel guided in her forlorn 
quest, that in a few hours the lost cable was successfully grappled. 
