1830 .] 
Repealing Reflecting Circle. 
ii 
which was then in progress of execution : as this instrument appeared, so far as 
could be judged from the design, to promise to supply precisely what was wanting, 
I requested him to make a second on my account, intending to give it an extensive 
trial 2 . 
When used as a sextant only, this instrument possesses the following advantage 
over sextants of the ordinary construction ; first, it enables the angle to be mea- 
sured alternately on each side of zero, whence the index error is compensated, 
and the liability to those of imperfect division and centering diminished ; secondly, 
by clamping the vernier of the circle successively at primary divisions, about a 
third of the circle apart, in succeeding pairs of observation, the errors of centering 
may be destroyed; and thirdly, the angle which may be measured is not limited 
by the extent of the arc, hut may he carried to the utmost amount in which the 
relative position of the glasses will admit of reflection. 
When used as a circle, the following additional advantages are gained ; the pro- 
cess of observation is shortened at least a half, by dispensing with the reading off 
and writing down the angle at each repetition. The errors which are frequently 
introduced in those operations are avoided ; those of imperfect graduation and 
eccentricity are rendered insensible ; and in night observations, especially, the eye 
is spared the alternate reference to a strong artificial light, necessary for reading 
the arc, hut extremely prejudicial to the most favourable state of the eye for obser- 
vation. > 
An incidental advantage arising from thus shortening the process of observation 
is, that it places the whole operation within the power of an individual to accom- 
plish by himself ; whereas it previously consisted of too many distinct parts, and 
•was consequently too laborious and fatiguing for accuracy. The subjoined obser- 
vations were made (with very few exceptions) without an assistant, the times 
being noted by the beats of a chronometer. The satisfaction is great to an ob- 
server to have all the parts of an observation thus within his own command ; it is 
convenient also, because assistance is not always to he obtained ; and it is con- 
ducive to accuracy, because the attention of an assistant is rarely equal to that of 
the observer. 
In the subjoined tabular abstract, the “ Time by the Chronometer” is a mean of 
the number of observations expressed in column 4, the details of the time corre- 
sponding to eacli observation being omitted. The correction of the chronometer 
No. 423, to the mean time at the several stations is inserted in column 3 ; in 
column 5 is shewn, the whole are passed through by the vernier (A) of the circle 
in the process of repetition ; and in column 6, being the whole arc divided by 
the number of repetitions, is the apparent distance corresponding to the mean 
chronometer time in column 2. Column 7 and 8 exhibit the apparent altitudes 
of the moon and sun, or star, calculated for the known apparent time at the 
station. The corrections for refraction, or the differences between the true 
and apparent altitudes, have been computed for the states of the atmosphere 
shewn in columns 9 and 10, by Dr. Young’s table in the “Nautical Almanac,” 
for 1822 ; much pains was taken to obtain the true temperature of the air, unin- 
fluenced by radiation on the thermometer from the surfaces around; for which 
purpose the thermometer was enclosed in a highly polished metal cylinder, pierced 
with holes in the top and bottom, and placed in the shade. The true distances in 
column 11 have been deduced by Dr. Maskelyne’s method, published in the preface 
to “ Taylor’s Logarithms,” with corrections introduced, —of the horizontal par- 
rallax on account of the ellipticity of the earth,— and of the distance where the 
oblique semi-diameters were sensibly affected by refraction 3 . 
In deducing the time at Greenwich, corresponding to the true distances, from 
those inserted in the “ Nautical Almanac” for every third hour, the second dif- 
ferences of the moon’s motion, in relation to the sun or star, have been duly taken 
into the account. It sometimes happens that the second difference of the distances 
of the moon and stars, inserted in the Nautical Almanac for every third hour, 
amounts to more than one minute of space ; in such instances, the correction due 
to the second difference will exceed six seconds of space during more than half the 
2 A description of the instrument here follows, but as it would be a repetition of 
what has preceded, it is here omitted.- — E d. . „ 
a These tables contain all the details of |350 observations, hut as they won o^et py 
so much room, we have been obliged to omit them, especially as a e ‘ . “ 
teresting to the reader is contained in the text, and in the small ta a 
ceeding page. — E d. 
