On the other hand, he made in 1726 an interesting practical application of his superior knowledge of Jupiter’s satellites by determining, in accordance with Galilei’s method (chapter VI., § 127), but with remarkable accuracy, the longitudes of Lisbon and of New York. 217. Among Bradley’s minor pieces of work may be mentioned his observations of several comets and his calculation of their respective orbits according to Newton’s method; the construction of improved tables of refraction, which remained in use for nearly a century; a share in pendulum experiments carried out in England and Jamaica with the object of verifying the variation of gravity in different latitudes; a careful testing of Mayer’s lunar tables (§ 226), together with improvements of them; and lastly, some work in connection with the reform of the calendar made in 1752 (cf, chapter II., § 22). 218. It remains to give some account of the magnificent series of observations carried out during Bradley’s administration of the Greenwich Observatory. These observations fall into two chief divisions of unequal merit, those after 1749 having been made with some more accurate instruments which a grant from the government enabled him at that time to procure. The main work of the Observatory under Bradley consisted in taking observations of fixed stars, and to a lesser extent of other bodies, as they passed the meridian, the instruments used (the “mural quadrant” and the “transit instrument”) being capable of motion only in the meridian, and being therefore steadier and susceptible of greater accuracy than those with more freedom of movement. The most important observations taken during the years 1750-1762, amounting to about 60,000, were published long after Bradley’s death in two large volumes which appeared in 1798 and 1805. A selection of them had been used earlier as the basis of a small star catalogue, published in the _Nautical Almanac_ for 1773; but it was not till 1818 that the publication of Bessel’s _Fundamenta Astronomiae_ (chapter XIII., § 277), a catalogue of more than 3000 stars based on Bradley’s observations, rendered these observations thoroughly available for astronomical work. One reason for this apparently excessive delay is to be found in Bradley’s way of working. Allusion has already been made to a variety of causes which prevent the apparent place of a star, as seen in the telescope and noted at the time, from being a satisfactory permanent record of its position. There are various instrumental errors, and errors due to refraction; again, if a star’s places at two different times are to be compared, precession must be taken into account; and Bradley himself unravelled in aberration and nutation two fresh sources of error. In order therefore to put into a form satisfactory for permanent reference a number of star observations, it is necessary to make corrections which have the effect of allowing for these various sources of error. This process of =reduction=, as