Note 68 — PART II. MOTION OF COMETS THROUGH THE SYSTEM.
Reading edition
To ascertain the correction for parallax, according to the method pointed out by Gauss, we must first compute the longitudes and latitudes of the zenith point. This is effected by the same formulæ which give the geocentric longitude and latitude, δ being in this case the latitude of Paramatta, and a the sidereal time there:
° ′ ″ ° ′
log tan δ = -33 48 45 = 9·825918 - cos (ξ - e) = -59 58 = 9·699407
log sin a = 64 50 = 9·956684 log tan a = 64 50 = 10·328037
tan ξ = -36 30 = 9·869234 - 10·027444
-e = -23 28 log cos ξ = -36 30 = 9·905179
tan (ξ - e) = -59 58 = 10·237977 - tan l = 52 58 = 10·122265
log sin l = 52 58 = 9·902158
tan b = -54 5 = 10·140135 -
We have now, therefore, the following data by which the parallax may be found, = 83° 15′ 42″, = -32° 8′ 33″, L = 341° 40′ 2″, l = 52° 58′, b = -54° 5′, R = 1·0077198, B = -0″·46, = 8″·6; B being the sun’s latitude, and π the solar parallax. The following are the formulæ:
log R = 10·00334 log π = 10·93450 log (RB + π sin b) = 10·87081-
log B = 9·66275 - log sin b = 9·90832 - log cotan β = 10·20181-
log RB = 9·66609 - 10·84282 - log μ = 11·07262+
log π = 10·93450 C. log 206255 = 4·68557
log cos b = 9·76852 log cos (λ - L)) = 9·30316-
C. log 206255 = 4·68557 + ·0000115 = 5·06135-
log cos (l - L) = 9·50598 + ·0000078
·0000078 = 4·89457 R′ = R + ·0000193 = 1·0077391
log π cos b = 10·70302 log μ = 11·07262
log sin (l - L)) = 9·97645 log sin (λ - L)) = 9·99104
compl. log R′ = 9·99665 compl. log R′ = 9·99665
4″·7 = 10·67612 -11″·5 = 11·06031+
+ 4 ·7
Correction for the sun’s longitude, - 6 ·8 = L′-L