There is great difficulty in correcting the residual fault, not only because an inconceivably small movement of the weights on the balance-curve is required, but also because it endangers the equilibrium of the balance. The mechanism adopted to remedy the defect is described in a Paper in the Horological Journal of July 1875 by Mr W. Ellis, and has received the approval of some able chronometer-makers.--With respect to the Transit of Venus Expeditions: The parties from Egypt and Rodriguez are returned. I am in continual expectation of the arrival of the other parties. I believe the eye-observations and the ordinary photographs to be quite successful; I doubt the advantage of the Janssen; one of the double-image-micrometers seems to have failed; and the Zenith-telescope gives some trouble. At three stations at Rodriguez, and three at Kerguelen, the observations appear to have been most successful. At the Sandwich Islands, two of the stations appear to have been perfectly successful (except that I fear that the Janssen has failed), and a rich series of lunar observations for longitude is obtained. At New Zealand, I grieve to say, the observations were totally lost, entirely in consequence of bad weather. There has been little annoyance from the dreaded 'black drop.' Greater inconvenience and doubt have been caused by the unexpected luminous ring round Venus.--With regard to the progress of my proposed New Lunar Theory: Three computers are now steadily employed on the work. It will be remembered that the detail and mass of this work are purely numerical; every numerical coefficient being accompanied with a symbolical correction whose value will sometimes depend on the time, but in every case is ultimately to be obtained in a numerical form. Of these coefficients, extracted (for convenience) from Delaunay's results, there are 100 for parallax, 182 for longitude, 142 for latitude; the arguments being preserved in the usual form."--After reviewing the changes that had taken place at the Observatory during the past forty years, the Report to the Board of Visitors concludes thus: "I much desire to see the system of time-signals extended, by clocks or daily signals, to various parts of our great cities and our dockyards, and above all by hourly signals on the Start Point, which I believe would be the greatest of all benefits to nautical chronometry. Should any extension of our scientific work ever be contemplated, I would remark that the Observatory is not the place for new physical investigations. It is well adapted for following out any which, originating with private investigators, have been reduced to laws susceptible of verification by daily observation. The National Observatory will, I trust, always remain on the site where it was first planted, and which early acquired the name of 'Flamsteed Hill.' There are some inconveniences in the position, arising principally from the limited extent of the hill, but they are, in my opinion, very