452 Astronomical Society. 
paper is to diminish as much as possible the inaccuracies oc- 
casioned, even inthe most perfect instrument, by rapid and 
partial changes of temperature. In the Greenwich system of 
observations, assistance from the spirit-level or plumb-line, or 
indeed from any previous verification, is rejected altogether. 
Two circles are employed simultaneously, each of which is 
furnished with six microscopes, which it is desirable should be 
placed at nearly equal distances on the limb; and previously 
to observation each circle is placed nearly in the plane of the 
meridian, and early perpendicular to the horizon. Each cir- 
cle is provided with an artificial horizon of mercury, so as to 
command the greatest possible portion of the reflected meridian. 
The first part of the process- consists in observing a num- 
ber of stars simultaneously with each instrument, either by 
direct, or by reflected vision ; the object of this is to determine 
the exact quantity that one instrument marks more or less 
than the other, when both are directed to the same object. 
This is determined not by a single observation, but by a great 
variety; thus obtaining the quantity denominated the mean 
difference for every 24 hours. 
In the second part of the process, a series of stars is ob- 
served reciprocally, that is, the direct image of a star by one 
instrument, at the same time that its reflected image is ob- 
served by the other. This, combined with the results of the 
previous process, in which the mean difference serves the same 
purpose as the index-error in Hadley’s sextant, enables the 
observer to ascertain the altitude; with which is likewise ob- 
tained the knowledge of the position of the horizontal diame- 
ter of each instrument. The observer, however, does not rest 
contented with a single determination of one diameter; but 
must in a similar manner, from altitudes, observed on various 
points of the arc, and by taking sometimes the direct, and 
sometimes the reflected observation with the same instrument, 
endeavour by every possible variety to obtain the maximum 
of precision of which the method is capable. 
The position of the horizontal diameter of each instrument 
being thus deduced from a mean of all the preceding experi- 
ments, sufficient data are obtained for computing the places 
of those stars that have been observed in the first part of the 
process, and employed in computing the mean difference ; be- 
cause without the knowledge of the position of their horizontal 
diameters, the instruments, with respect to the stars in question, 
give nothing but differences of declination ; but such position 
being known, their altitudes can be accurately determined. 
The Astronomer Royal terminates his paper, by pointing 
out the principal advantages of the method described. 
There 
