It will then be remembered that it was shown that for small arcs the pendulum would keep good time provided you let it have as much swing as it wanted to use up the force which the escapement had applied to it, but not otherwise, so the pendulums only acted really well when the impulse was given about the middle of the swing, and they were free to go on and stop when they pleased, and turn back at the end of it.
This essential condition was fairly approximated to in the dead beat escapement of clocks which left them at the end of their swing with only a very slight friction to impede their free motion.
But when you come to deal with a watch the case is quite different. Here the escapement is of a great size compared with the balance wheel, and the friction even of the most dead beat watch escapement that could be contrived was so big compared with the forces acting on the balance wheel as seriously to derange its motion, and render it far from a perfect time-keeper.
Now about this time—I am speaking of the early part of the eighteenth century—a demand of a very exceptional character arose for a really perfect watch. The demand did not arise from gentlemen who wanted to keep appointments to play at ombre at their clubs, or even from merchants to time their counting house hours. For these the old-fashioned watch did very well. The demand came from mariners. But the seamen did not want to know the time merely to arrange the hours for meals on the ship or to determine when the watch was to be relieved, but for a far more important purpose, namely, to find out by observation of the heavens their place upon the ocean when far out of sight of the land. It will be very interesting to see how this problem arose, and how the patient industry and ingenuity of man has solved it.
The ancient navigators never went very far from the shore, for, once out of sight of land, a ship was out of all means of knowing where she was. On clear days and nights the compass, and the sun and stars would tell the mariner the direction he was sailing in, but it was quite a problem to determine where he was on the surface of the earth.
Fig. 63.
Let us consider the problem. Suppose for convenience that the earth is divided up into “squares,” as nearly, at least, as you can consider a globe to be so marked out. Let us suppose that it has been agreed to draw on it from pole to pole 360 lines of longitude, commencing with one through say Greenwich Observatory as a starting-point, and going right round the earth till you come back to Greenwich again. Also suppose that there have been drawn a series of circles parallel to the equator, but going up at equal distances apart towards the poles. Let us have 179 of these circles, so as to leave 180 spaces, a to b, b to c, etc., from pole to pole. This will divide the earth up like a bird-cage into squares, as if we had robed it in a well-fitting Scotch plaid. The length measured along the equator of the side p q of each square at the equator is taken as exactly sixty nautical miles (apart from a small error of measurement, which makes it in actual practice 59·96). This is equal to sixty-nine and a quarter English statute miles. The side of the square leading towards the poles q s would also be sixty nautical miles were it not that the earth is not truly spherical, which introduces a slight error. We may, however, roughly say that at the equator each square measures sixty nautical miles each way.
Fig. 64.