This was a keen disappointment to him, but seems to have really been the means of determining his career. The sickly, suffering boy could not be idle, though 'a day's short reading caused so violent a headache;' and a month or two after he had left school, he had a book lent to him--Sacrobosco's _De Sphæra_, in Latin--which was the beginning of his mathematical studies. A partial eclipse of the sun in September of the same year seems to have first drawn his attention to astronomical observation, and during the winter his father, who had himself a strong passion for arithmetic, instructed him in that science. It was astonishing how quickly his appetite for his new subjects grew. The _Art of Dialling_, the calculation of tables of the sun's altitudes for all hours of the day, and for different latitudes, and the construction of a quadrant--'of which I was not meanly joyful'--were the occupations of this winter of illness. In 1664 he made the acquaintanceship of two friends, Mr. George Linacre and Mr. William Litchford; the former of whom taught him to recognize many of the fixed stars, whilst the latter was the means of his introduction to a knowledge of the motions of the planets. 'I had now completed eighteen years, when the winter came on, and thrust me again into the chimney; whence the heat and dryness of the preceding summer had happily once before withdrawn me.' The following year, 1665, was memorable to him 'for the appearance of the comet,' and for a journey which he made to Ireland to be 'stroked' for his rheumatic disorder by Valentine Greatrackes, a kind of mesmerist, who had the repute of effecting wonderful cures. The journey, of which he gives a full and vivid account, occupied a month; but though he was a little better, the following winter brought him no permanent benefit. But, ill or well, he pressed on his astronomical studies. A large partial eclipse of the sun was due the following June; he computed the particulars of it for Derby, and observed the eclipse itself to the best of his ability. He argued out for himself 'the equation of time'; the difference, that is, between time as given by the actual sun, or 'apparent time,' and that given by a perfect clock, or 'mean time.' He drew up a catalogue of seventy stars, computing their right ascensions, declinations, longitudes, and latitudes for the year 1701; he attempted to determine the inclination of the ecliptic, the mean length of the tropical year, and the actual distance of the earth from the sun. And these were the recreations of a sickly, suffering young man, not yet twenty-one years of age, and who had only begun the study of arithmetic, such as fractions and the rule of three, four years previously!