34.6 Dr. Brinkley’s observations for investigating 
2. That observations should be continued through a whole 
period of the lunar nodes, in order to ascertain, with ex- 
actness, the annual variation of zenith distances for each 
star. 
The latter condition can only be fulfilled hereafter for my 
instrument. In the mean time, no material uncertainty can 
arise from the want thereof. The accurate reductions of 
Dr. Bradley’s observations by Mr. Bessel, have given us, 
with much exactness, the mean N. polar distances in 1755 of 
the stars I have used. Three periods nearly of the lunar 
nodes intervened between 1755 and my former observations. 
Hence, assuming the change from precession, as deduced by 
Mr. Bessel, the proper motion of each star was obtained ; 
this proper motion was then applied to the precession of each 
star for the years 1815 and 1816, which was also deduced by 
help of Mr. Bessel’s precessions. The annual variation of 
each star, thus obtained, for the middle of the interval 
between my two sets of observations, was used in con- 
necting those sets to determine the exact effect of lunar 
nutation. 
As the lunar nutation in N. P. D. used was, 
— 8", 28 Sin ( jR — S3 ) — 1", 22 Sin ( jR + a ) 
and therefore the greatest term of the nutation of ob- 
liquity of ecliptic = 9", 50 cos a ; I supposed the true co- 
efficient of this latter = 9", 50 (i-f-y) and then found as 
follow : 
