the same, with the additions:—­that I formally gave the corrections of relative right-ascension of fundamental stars (without alteration of equinox, which I had not the means of obtaining) to be used in the year 1831; and that I reduced completely the observed occultations (with a small error, subsequently corrected).  In 1831 the system of correction of broken transits was improved:  the errors of assumed R.A. of Fundamental Stars were exhibited:  Mean Solar Time was obtained from Sidereal Time by time of Transit of [Symbol:  Aries] (computed by myself):  the method of computing occultations was improved.  In 1832 the small Equatoreal was erected, and was soon employed in observations of the elongation of the 4th Satellite of Jupiter for determining the mass of Jupiter.  The Mural Circle was erected at the end of the year, but not used.  The calculation of R.A. of Fundamental Stars was made homogeneously with the others:  separate results of all were included in ledgers:  a star-catalogue was formed:  all as to the present time (1871).  With the Equatoreal the difference of N.P.D. of Mars and stars was observed.

“With the beginning of 1833 the Mural Circle was established at work, a second assistant (Mr Glaisher) was appointed, and the Observatory might be considered complete.  I made experiments on the graduations of the Circle.  I detected and was annoyed by the R—­D.  I determined the latitude.  I exhibited the separate results for N.P.D. of stars in ledger, and their means in Catalogue.  I investigated from my observations the place of equinox and the obliquity of the ecliptic.  I made another series of observations of Jupiter’s 4th Satellite, for the mass of Jupiter.  I observed the solar eclipse with the Equatoreal, by a method then first introduced, which I have since used several times at Cambridge and Greenwich with excellent effect.  The Moon and the Planets were usually observed till near two in the morning.  Correction for defective illumination applied when necessary.  The volume is very complete, the only deficiency being in the observation of Moon and Planets through the severe morning hours.  In 1834 the only novelties are—­examination of the graduations of the declination circle of the Equatoreal (excessively bad):  observations of a spot on Jupiter for rotation, and of Mars and stars.  In 1835 (including January 1836) there is a more complete examination of the Equatoreal graduations:  parallax and refraction for Equatoreal observations:  a spot on Jupiter:  a series of observations on Jupiter’s 4th Satellite for the mass of Jupiter:  Mars and stars:  Halley’s Comet (the best series of observations which could be made in the season):  and a short series of meteorological observations, on a plan suggested by Sir John Herschel then at the Cape of Good Hope.