He then weighed the cup with and without the water, and so found the amount of water that had flowed into the cup. By comparing the amounts of water obtained in different experiments he was able to compare the times. His first object was to find in what way the speed of the body varied with the distance over which it travelled, or the time during which it was travelling. He first of all thought that the speed was proportional to the distance travelled. He soon found, however, that when the distance is doubled the speed at the end of the fall is not doubled. It is less than double what it was before. This can be proved by letting a ball roll along a very smooth surface after it has reached the bottom of the groove. Galileo found at the end of a long set of experiments that the speed attained by a body is exactly proportional to the time during which it is exposed to a force capable of moving it. This discovery was the origin of the whole science of motion. Galileo called the speed which a body acquires in the unit of time the “acceleration” of that body. Galileo was the first to establish the idea of what is known in science as Momentum. He found that the amount of motion in a body must be judged not only by its speed, but also by the weight of the body. It was evident to him that a heavy body moving at a certain speed is equivalent to a number of lighter bodies moving with the same speed, their combined weight being the same as the weight of the heavy body. In order, therefore, to determine the amount of motion in a moving body, it was necessary to take into account both the weight of the body and the speed. Galileo used the word “momentum” to signify the result obtained by multiplying together the two numbers expressing the speed and the weight of a body. He also started the idea of centrifugal force, or the force with which a body stretches a string when it is swung round by the string. But the most important work of Galileo was that which he did with the pendulum. When still quite a young man, it happened that he was at the cathedral at Pisa during a service. He noticed that a great lamp suspended from the ceiling far overhead had been left swinging after it had been lighted. He watched the lamp swinging to and fro for a long time, and noticed that the swinging gradually diminished. But while the amount of swinging diminished, the time of swinging appeared to remain the same. In order to test this he counted the number of times his own pulse would beat between one swing and the next. He had no clock or watch in his possession, and was unable, in the circumstances, to use such a thing as a water-clock, considering that he was supposed to be engaged at his prayers. By counting his pulse he found that the time of swinging remained exactly the same until the swing had quite died away.