“At the door from the Front Court to the staircase of the Octagon Room (the original entrance to the Observatory as erected by Sir Christopher Wren), a small porch-shelter has been often desired.  I proposed to fix there a fan-roof of quadrantal form, covering the upper flat stone of the external steps.—­On a critical examination of the micrometer-screws of the Transit Circle it was found that the corrections, which range from -1 deg.38” to +0 deg.76”, indicate considerable wear in the screws; and it was found that as much as one-hundreth part of an inch had been worn away from some of the threads.  The old screws were consequently discarded, and new ones were made by Mr Simms.—­The adjustment of the Spectroscope has occupied a great deal of attention.  There was astigmatism of the prisms; and false light reflected from the base of the prisms, causing loss both of light and of definition.  The latter defect was corrected by altering the angles, and then astigmatism was corrected by a cylindrical lens near the slit.  The definition in both planes was then found to be perfect.—­The number of small planets has now become so great, and the interest of establishing the elements of all their orbits so small,—­while at the same time the light of all those lately discovered is very faint, and the difficulty and doubt of observation greatly increased,—­that I have begun to think seriously of limiting future observations to a small number of these objects.—­All observations with the Spectroscope have been completely reduced; the measures of lines in the spectra of elements being converted into corresponding wave-lengths, and the observations of displacement of lines in the spectra of stars being reduced so as to exhibit the concluded motion in miles per second, after applying a correction for the earth’s motion.  Sixteen measures of the F line in the spectrum of the Moon as compared with hydrogen give a displacement corresponding to a motion of less than two miles a second, which seems to shew that the method of comparison now adopted is free from systematic error; and this is supported by the manner in which motions of approach and recession are distributed among the stars examined on each night of observation.  The results recently obtained appear to be on the whole as consistent as can be expected in such delicate observations, and they support in a remarkable manner the conclusions of Dr Huggins, with regard to the motions of those stars which he examined.—­Photographs of the sun have been taken with the photoheliograph on 182 days.  On one of the photographs, which was accidentally exposed while the drop slit was being drawn up, there appears to be a faint image of a cloud-like prominence close to the sun’s limb, though the exposure probably only amounted to a fraction of a second.  A prominence of unusual brilliancy was seen with the Spectroscope about the same time and in the same position with reference to the Sun’s limb.  All groups of Sun-spots and faculae have been numbered, and the