Edmund Halley was an English scientist who lived over 200years ago. He studied the observations of comets which other scientists had made. The orbit of one particular comet was a very difficult mathematical problem. He could not figure it out. Neither could other scientists who dealt with such problems. However, Halley had a friend named Isaac Newton. Who was a brilliant mathematician. Newton thought he had already which he had done it. He told Halley that the orbit of a comet had the shape of an ellipse. Now Halley set to work. He figured out the orbits of some of the comets that had been observed by scientist. He made a surprising discovery. The comets that had appeared in the years 1531, 1607 and 1682 all had the same orbit. Yet their appearances had been 75 to 76 years apart. This seemed very strange to Halley. Three different comets followed the same orbit. The more Halley thought about it, the more he thought that there had not been three different comets, as people thought. He decided that they had simply seen the same comet three times. The comet had gone away and had come back again. It was an astonishing idea! Halley felt certain enough to make a prediction of what would happen in the future. He decided that this comet would appear in the year 1758. There were 53 years to go before Halley's prediction could be tested. In 1758 the comet appeared in the sky. Halley did not see it, for he had died some years before. Ever since then that comet been called Halley's comet, in his honor. Halley made his discovery   _  .
by doing experiments by means of his own careful observation by using the work of other scientists by chance