None
Mean S.T. of Night Obs. Diff. Day — Night. Date. Observer. 1 S.T. of Day Ol.s. Mean S.T. of Night Obs. Diff. Day- Night. 1910. h in h in s 1910. h m li m s 1910. h m h m s Jan. 13 AP 16 44 4 5 + 0'08 Mar. 6 RC I9 46 13 52 — o'o3 May 2 C ° 39 19 25 O'OO 13 i? 5 fl - -08 6 21 27 JJ •oo 5 AP o 39 19 37 — . -12 16 JW 16 24 3 S3 - -07 8 M I9 46 14 9 - -09 6 AW 2 2 19 37 •oo 16 16 32 )J - '°5 8 21 40 11 — '10 8 AW I 50 '9 57 - -03 16 17 5 11 — -10 9 AW I9 46 '4 45 + -02 8 2 2 JJ + -06 '9 AP 17 39 5 6 - '13 16 JW 21 40 15 16 + -02 9 5 1° jj + -04 '9 18 15 11 - '07 16 22 53 u - '07 ii M ° 39 20 16 •oo i9 18 22 J» - -16 20 RC 21 40 15 32 •oo 12 5 I0 jj + '03 21 C 18 15 5 3 - -08 20 21 42 )J - -04 12 C ° 39 20 33 + -03 21 l8 22 I) - -09 22 M 21 39 '5 33 — -02 12 I 10 J> + "OS 25 JJ 18 15 5 5* - -06 22 22 53 J) - '°7 13 RC o 9 20 33 - -03 25 18 50 11 — 'O2 23 M « 53 15 42 — '1 I 13 ° 39 >. + -04 26 EC 18 o 4 55 •oo 28 JJ 21 27 16 27 + '06 18 M o 39 20 JI - '°4 26 18 15 » - -03 28 22 53 n — 'Ol 18 2 2 )) - '07 26 18 22 H - -06 29 JW 21 40 16 39 + '°4 24 RC i 49 2° 4° •oo 27 M 17 31 8 34 - -03 29 2* 53 11 - '°5 24 2 2 Jt + -02 z? 17 39 11 - -09 30 M 21 42 «6 S3 •oo 25 M i 49 20 40 + -02 28 AW '7 39 8 25 - -04 3° 22 I 11 •oo 25 2 2 » + 'OS 28 18 o H + -oi 3° 22 17 It - -03 June 5 M 2 58 20 31 + -07 28 18 15 n - "06 3' AW 22 I 17 17 + -03 12 M 2 58 21 I5 - ^5 28 18 18 11 + 'OS 3i 22 6 11 + -08 '3 AP 2 58 21 27 + -07 28 l8 22 i) - -03 3' 22 50 I) + -05 '3 4 3° j) + -oi 30 M 18 18 9 ° — 'OI 3' 23 o 11 + -09 '4 JW 2 58 21 59 + 'OS 30 18 22 >> - -04 Apr. 5 M 21 40 16 2 — -oi 15 AW 3 54 22 9 + -io jo 18 50 ?» •oo 5 22 I i> + -03 15 4 3' Jt + 'JO Feb. 2 AW 17 3' 9 '9 + -02 6 AW ° 39 16 21 - -05 15 4 45 Jj + -16 2 '7 39 11 — 'OI 7 -2 58 JJ + -02 19 AP 2 58 22 I I + -05 2 18 22 H — 'OI 7 JJ 22 53 1 6 40 + '06 '9 4 3° " + '04 4 JJ 17 31 ii 17 + -06 8 JW 22 53 16 34 — '12 26 RC 2 58 22 4 + -08 4 '7 39 M + -oi 8 23 o » - -09 26 3 54 JJ + -io 4 18 15 H - -04 1 1 JW 22 53 18 14 - '°3 26 4 3i H + -04 4 l8 22 »» — -oi 14 AP 22 53 18 3 + -02 27 M 2 58 22 40 + -06 13 RC 18 15 13 18 + -03 17 AP 22 53 18 31 — 'O2 27 3 42 j j + "f2 13 l8 22 M - -05 17 23 o jj + -oi 3° AP 3 54 23 46 + -03 13 18 50 M + -06 '9 RC 22 53 18 44 - -08 3° 4 3i )j + 'I' '5 AP 19 46 12 52 — 'OI 21 JW 22 53 19 14 - -04 July AW 3 54 23 Si 4- -10 16 M 18 22 12 14 - -05 21 o 39 JJ - -05 4 3i 11 + -°9 16 18 50 )» — -02 25 C o 39 18 56 - '05 4 45 jj + -10 20 AP 19 46 12 30 - -°5 25 i 4 tt — '02 5 3 11 + '06 21 AW 19 42 12 I4 + -oi 26 M ° 39 18 52 — 'O2 5 1° u + '06 21 19 46 It — '01 27 3 42 JJ - -08 10 AP 4 3i 23 51 + '°9 22 JW 19 4 13 2 + -03 27 AW o 9 18 47 + 'OS 10 S 3 jj + '03 22 19 46 H + -08 27 o 39 11 — -O2 10 5 I0 jj + -06 *3 RC 19 42 '3 2 + -06 28 RC o 9 18 59 + 'O2 10 5 20 11 + -03 23 19 46 » - -04 28 o 39 jJ + -oi 13 AW 4 30 o 7 + '04 24 JJ 19 46 14 10 — 'OI 29 JJ o 9 18 59 + -05 13 5 1° 11 + -13 Mar. xvn TABLE VII. — continued. Date. Observer. 1 S.T. of Day Obs. Mean S.T. of Night Obs. Dill'. Day- Night. Date. Observer. 1 S.T. of Day Obs. Mean S.T. of Night Obs. Oiff. Day- Night. Date. Observer. 1 S.T. of Day Obs. Mean S.T. of Night Obs. Dill'. Day- Night. 1910. b m li m s 1910. h m b m s 1911. h m h m s July 25 AP 5 1° 1 9 + O'IO Sept. 21 JW 9 23 l 48 O'OO Jan. 25 JJ 18 15 4 34 + O'02 25 5 20 1} + -II 21 10 4 n - -05 25 18 22 JJ + -oi 25 5 29 jj + -05 28 RC 9 23 3 6 + -04 26 21 40 J) — 'OI 25 5 43 »J + -07 28 ii 9 JJ •oo 3° AW 18 15 5 47 + -03 25 5 5° )) + -07 29 M 10 4 3 3 + -04 30 18 22 JJ - -07 26 RC 5 20 I 23 + -II 29 ii 9 jj — '02 30 I9 46 n - -08 26 5 29 II + -07 30 AP 10 4 3 2 + -06 31 RC 18 15 5 9 - "03 26 6 19 J) + -05 Oct. 3 AW 10 4 3 9 + -'4 3i l8 22 1) - -08 3i AW 5 5° 21 2O + '°9 3 ii 9 JJ + '03 Feb. i M 18 22 5 15 •oo 3' 6 19 )» + -04 10 M 10 4 2 38 — '02 i 18 50 JI •oo 3i 6 32 jj + -05 10 n 44 JJ - -05 3 JJ 18 50 6 18 - -07 Aug. i EC 5 43 20 30 + -03 18 C n 44 2 I7 + -02 3 19 46 jj - -06 i 6 55 jj + -03 21 JW 12 5 4 ° — -01 7 AW 22 53 6 27 - -03 i 7 4 II + -05 21 12 II 1] + -02 7 22 59 i> + -07 5 AP 5 43 19 48 -1- '°9 23 JW 12 5 2 58 + -oi 8 M 22 53 5 44 — -02 5 5 5° )l + -ii 23 12 II J) + -06 8 JJ 19 4 5 42 •oo 5 6 19 II + -09 24 AW 12 11 2 55 + -02 9 22 53 }j — 'I I 5 7 21 j» + '°5 26 RC 12 5 3 44 + 'U 9 RC 18 50 5 42 - '04 16 0 6 55 21 54 + -04 26 13 20 i J + -08 9 19 4 JJ - '°3 16 7 5 J) + -oi Nov. 3 JW 12 29 2 35 - '06 9 19 46 )J + -04 16 7 45 JJ + -05 3 13 2O Jt - "°5 16 AP 18 50 6 5, - -03 17 AP 6 55 21 55 + '°3 8 JW 12 30 1 51 + -°7 16 19 46 JJ + -07 i7 7 5 |J + -04 8 13 20 |J + -02 '7 22 53 J) - -03 '9 M 8 4 21 52 •oo 13 JW 13 2O 2 16 - -04 '9 AW 19 42 7 45 - -°4 23 M 12 5 23 6 + -02 '3 14 II >! + -04 '9 19 46 u - -08 23 12 I I H - -°3 H C 13 2O 2 I9 + 'O2 20 AP 19 46 7 6 + -oi Sept. AW 19 42 7 42 - -06 9 AP 8 4 2O 41 + -01 29 14 46 J J + 'I* 19 46 )) - -07 9 8 5, jj + -02 Dec. 9 C 16 24 2 30 + -07 19 51 II — -oi 9 9 23 » + -03 1 1 AP 1411 I 27 + '06 19 55 II - "°3 ii AP 8 51 22 46 + -04 1 1 14 46 JJ + -04 20 7 JJ - -06 1 1 9 23 !> + -06 1 1 16 24 It + -12 20 16 JJ + -02 1 1 10 4 JJ + -06 2 S 19 46 7 35 - -14 12 AW 9 23 22 45 + -03 191 1. Apr. 2 RC 21 42 8 29 •oo 12 10 4 JJ + -II Jan. 17 JJ 18 o 3 5° + '°5 2 22 I JJ + -02 '3 12 58 JJ + -16 17 18 49 JJ •oo 6 C 22 53 7 54 — 'IO '3 13 20 JJ + '09 22 AP J7 3' 5 43 + '09 7 2 58 JJ - "°5 16 C 9 *3 21 28 + -06 22 17 39 JJ + -oi 10 JJ 22 53 7 S2 - -06 16 10 4 J» + -06 23 AW 18 15 5 39 •oo 1 1 2 58 )> + -03 18 C 9 23 23 18 + -oi 23 18 22 1) •oo 1 1 C 22 53 7 58 - -°3 it 10 4 i j + -oi 23 18 50 J> + '04 12 2 58 »J - '°3 19 AP 9 23 22 40 + -oi 24 21 40 )j - -04 24 AW 4 3' 8 17 + -07 '9 10 4 jj — 'O2 25 M 21 40 4 53 — 'IO 28 C o 39 9 57 - -04 C. F. C., 1900. XV111 CAPE FUNDAMENTAL CATALOGUE, 1900. TABLE VII. — continued. Date. Observer. 1 S.T. of Day Obs. Mean S.T. of Night Obs. Diff. Day- Night. Date. Observer. 1 S.T. of Day Obs. Mean S.T. of NiKht Obs. Diff. Day- Night. Date. S c o S.T. of Day Obs. Mean S.T. of Night Obs. Dill'. Day- Night. 1911. h m h m s 1911. Ii m h in s 1911. h m h m 3 May 4 C o 39 12 6 + O'OI June 28 AP 8 4 12 41 O'OO Aug. 30 JJ 12 II 2O 6 O'OO 5 4 31 J) + -05 28 C 5 10 15 12 + '01 30 M 7 21 18 16 + -09 5 JJ o 39 9 i - -09 28 5 20 jj + -08 30 7 4° ,, + -05 8 AW o 9 ii 48 + -07 29 7 40 ,, + -05 30 8 4 „ + '04 8 i 50 „ + -II 29 AW 5 44 H 53 + '01 31 AW 9 23 '9 33 + -07 8 2 2 „ + -'3 29 5 5° M + -05 3' io 4 ,, + -17 9 5 32 u + -05 3° 9 23 J) + '03 Sept. 5 S io 4 18 59 - -03 IO M C I O ii 54 4- -06 July 2 S 5 44 12 54 + '09 6 AW 9 23 1 8 42 •oo 10 5 20 J) + '04 2 5 50 jj -f -io 6 io 4 „ + -06 IO 5 27 „ + -04 3 AW 6 19 15 29 + '02 8 C 8 21 20 25 + '04 II JJ 5 1° io 27 + -03 4 9 23 + -03 8 9 23 ,, •oo 1 1 5 20 J) + -03 4 io 4 ,, + -05 12 AW 9 23 19 16 + '09 1 1 5 27 n — 'O2 7 JJ 9 23 '5 33 + '02 12 io 4 „ + -08 II 5 3' M + -01 7 io 4 J J + -04 '9 RC io 4 20 IO + '10 12 RC 5 20 9 12 •oo 7 c 5 lo '3 29 + -oi 28 C II 10 20 34 •oo 12 5 *7 JJ - -04 7 5 20 JJ + '01 29 JJ io _ 4 '9 57 + -05 16 AW C I O 9 21 + -04 10 C 9 23 13 io + 'io Oct. 2 M io 4 20 47 + -07 16 5 20 JJ + -02 10 io 4 > J + '12 2 I I IO ,, + '04 16 5 44 JJ + '06 17 AP 9 23 '5 57 + '02 2 ii 45 jj + -03 16 5 5o ,, + '06 17 io 4 - '04 4 RC n 45 '9 53 + '09 21 AP 2 58 21 44 + -04 18 JJ 9 23 16 o — '01 6 AW I I IO 21 0 + -04 22 5 io n + -08 18 io 4 + '01 6 12 I I „ + -05 22 5 20 jj + '12 '9 RC 9 23 '5 49 — 'O2 '9 JJ 12 II 21 44 + 02 22 5 43 jj + 'io io 4 JJ — '01 20 M ii 45 21 37 + -02 22 5 50 „ + 'io 27 AP 5 5° 16 29 + -I3 20 12 25 „ + -04 22 C 2 58 21 52 + "05 27 6 19 JJ + -04 24 C 13 21 22 19 — 'O2 23 5 io — '02 27 6 32 J) + -13 25 JJ ii 45 22 12 - '06 23 5 20 II - -oi 3' S io 4 15 42 + '03 31 S ii 45 23 9 - -16 26 M 2 2 21 52 n 9 jj + -03 Nov. 8 RC u 45 2 33 •oo 26 2 58 •oo Aug. INTRODUCTION. xix This has further been regarded as possibly associated with a diurnal periodicity, either due to different habits of the observers in daylight observing as contrasted with night observing, or to a diurnal change in the conditions of the transit circle or a diurnal period in the clock rate. Thus each of the differences Day — Night has been equated to an expression of the form K+A^cosa^ — cos a2) + .B1(sin ctj — sin a.2)+^2(cos 2ai — cos 2a.,) + 5.,(sin zaj — sin 2a.,), where aj denotes the K.A. of the day star and'a2 the mean R.A. of the night stars on which the comparison depends. The quantities alt a2 are given under the headings S.T. (sidereal time) of Day Observations and Mean S.T. of Night Observa- tions in columns 3 and 4 of Table VII. While the quantities A1} Blt A2, Bz have been regarded as constant throughout the series of observations, the quantity K has been considered as possibly variable with the observer or the method of observing. We give in Table VIII. partial normal equations obtained by grouping the observations according to the observer and the year of observation and combining the separate equations with equal weight. TABLE VIII. — Partial Normals for the Determination of Periodic Errors in Right Ascension. Observer C. V. v' '. 1908. S s s 3oA' — 6.4j + 14^ H^o + 3#2 = + 0'55 + 0-19 +63 +26 16 — 8 — 0-18 — 0-18 — O'O2 + 44 18 — 10 = + I 'OO + 0-36 + 0-05 + 22 o = — 0-40 — O'OI O'OO + '9 — 0'54 — 0-4.7 — O'l I 1909. 55/i + t,Al + ioZ?j + •jAv + 155., = + 0-04 — O'I2 — O'O2 104 — 10 24 — 35 " = + 076 + 1-55 + 0'15 87 + 4 - 3 + 174 + 0-39 + 0'04 40 + ii = — O'24 — O'lO — 0'O2 4" — 0'49 — 0-69 — OMI 1910. ^ 2oK — i6A1 + 5.5, + 5-do + 4#2 = + 0-25 + 0-05 + O'OI 33 -2 + 6 + 6 — 0-51 — O'll — 0-02 33 + 3 + 12 = + 0'49 — O'OI O'OO 21 + 9 = — OM2 + 0-09 + 0'02 IO = + O'Og + o'O3 + O'OI 1911. 3iK + 5^j + 235, SA2 — 35, = + 0-40 + 0'O2 O'OO 43 - 2 4 — 3 — 0-29 + 0-07 + O'OI 57 26 — 19 + 1-28 + 0-16 -f* O'O2 + 24 + 2 = — 0-61 — O'OI — O'OO 3' — 0-86 — 0-61 — O'l I XX CAPE FUNDAMENTAL CATALOGUE, 1900. TABLE VIII. — continued. Observer AP. •". V.' 1908. 3 s s 30-ST — $A! + •>,6Bl gA.2 - 8/;2 = — o 13 - 0-48 — 0-09 44 + '4 1 1 - H + 0-44 + °'47 + 0-07 67 16 - 19 = + 0-82 + 0-16 + 0'02 9 + 8 — 0-18 — 0-03 — O'OI '7 - 0-42 — 0-27 — 0*07 1909. 49-K" + 2O^j — 4/f, + ioA2 + 5#2 = - 1-38 — 0-56 — 0-08 92 - 15 4 — 22 = - z-23 — i'o6 — O'l I 88 5 + I = + 1-89 + o'37 + 0-04 16 + 3 - 0-15 .+ 0-15 + 0-04 19 = + 0-19 + 0-06 + O'OI 1910. 47 K - 34^ + 17^ 27^2 + 9^-2 = + i '40 + i '04 + 0-15 59 -i* 7 - 4 - 1-82 - ''55 — 0'2O 79 29 + 22 = + 2-13 + 072 + 0-08 7' - '4 — rg6 — 1'iz - 0-13 25 + 0'70 + 0-27 + 0-05 1911. ^itK + 1^1 + 87^ nA, + 3-82 = + I'42 O'OO O'OO 17 + 5 3 — i = - 0'14 - 0-15 — o'O4 58 25 + 7 - 0-17 — O'O2 22 — 12 = — ''37 — 0*24 — 0-05 21 = + 0-24 - 0-15 — 0-03 Observer RC. 1908. i8K — 3^] + 22.B, — 6A.2 — 5-^2 = + 0-29 — O'22 — O'OJ + 26 +2 — 10 — 2 = — °'39 — 0-28 — o 06 38 - 6 — '3 + 0-14 — 0-56 — 0-09 '3 + 2 = + O'OI + 0-17 + 0-05 IO = O'O? + 0-26 + 0-08 1909. 2oK - 6A, + ioA + 6A,, + 4*2 = + 0-09 — O'2O — 0-04 31 - 8 4 — 13 • = O'OO + 0-38 + 0-07 60 +10 + I = + ro6 + Q'l 5 + O'O2 27 + 7 — 0'O2 —I— O *O C + O'OI 23 + 0'27 + 0-19 + O'O4 1910. jSK + jXj + 5/?j — 7.<42 — SB2 = + 074 + °'45 + 0'07 39 +1 - 8 — 16 = — I '2 I - °'99 — 0-16 45 +9 + 3' + 0'28 — 0-34 — 0-05 62 + 22 = — 078 - 0-31 — 0-04 55 = + 0'37 + O'OI O'OO 1911. ^^K — SA-, — loB + iSA., _ 6B.2 = — OM.8 O'OO O'OO 23 — 2 — 21 + 7 — 0-09 — 0-06 — O'OI 40 - 2 + 6 = + 0-51 — 0-08 — O'OI — 7 — 0-07 + 0-04 + O'OI '5 + 0*17 + o'o8 + 0-02 INTRODUCTION. xxi TABLE VIII. — continued. Observer AW. V. V.' 1908. s s s 4i A' + 5/4, + 5o// - 24^ — 5#> = + I -08 — 0^69 — O'lO 63 + 19 - 32 - 7 = + 0-27 + O'lO + o-oi 79 - 3° - '9 = + 1-42 — 0-89 — O'lO 41 + 7 = — 0-69 + 0-38 + o'o6 20 = — O'I2 + 0-26 + 0-06 1909 34AT + 14.4, — 34/J, + 2 4 2' + 3#j = — O'03 — 0-07 — O'OI 67 - 14 + '5 + 3 = — 0'42 — 0-23 — 0-03 56 - 4 - 5 = + °'33 + O'OZ O'OO 12 + i = — 0-27 O'OO O'OO '9 + °'53 + 0'57 + 0-13 I9IO 54/iT — ig-dj + 21.8, — 20i42 — iBz = + 2-48 + 072 + O'lO 73 - 25 + 18 - 18 i - 2-23 - 0-66 — 0-08 76 — 10 + 43 + 2-24 + 0-36 + 0-04 91 - 8 = - i'63 + O'OI O'OO 55 = + 0-86 — O'OZ O'OO 191 1 49AT + 4^4j + oB L + i642 — i3_B2 = + 0-83 O'OO O'OO 55 - z6 - 25 + 11 = - 0-86 — 0-36 — 0-05 99 + 9 - 19 + 1-98 + 0'39 + 0-04 49 — 22 = + 0-37 + O'ZI + °'°3 39 = + O'lO + °'49 + 0-08 Observer M. 1908. 35^T + S^lj + 4z#j — i8A% — 16.82 = + 0-05 + 0-09 + O'OZ 45 + I* — 25 — 3 = + 0 44 + 0-56 + 0-09 75 — 23 — 32 = + O'ZI — O'IO — O'OI 33 + 8 = — 0'59 — 0-52 — 0-09 23 = — 0-09 + o'07 + O'OZ 1909. 1 6 A' — 5.4 j — iSfij — 3^2 + 4^2 = — 0 56 - O'OI O'OO 14 - 2 + 5 + i = 0 oo + 0-09 — 0'02 36 + 8 + 4 = + 0 90 + 0-03 + O'OI 18 + 3 = + 0' 5° + °'54 + 0-13 '3 = — 0 04 + O'O2 + O'OI 1910. 39# + 5^! + 7&l + 3^2 — iB2 = — o1 9' — 0'07 — O'OI 54 - 4 + 2 — 10 = — O' 5° + o'i6 + O'OZ 5° + 2O + 16 = + O' 75 + 0-33 + 0-05 37 — 1 1 = + O' 09 + 0-26 + O'O4 77 = + 0 94 + 0-43 + o'o5 1911. 24A" — ^Al + 2oB1 — 2^2 + 3^2 + 0' 72 — O'OZ O'OO 25 - zi — 9 — 8 = — O' 40 + o'i6 + 0-03 52 — 12 + 6 = + r 44 + 0-09 + O'OI 26 — 6 = _ 0' 32 + 0-08 + O'OZ '9 = — 0 '3 — 0-40 — 0*09 XX11 CAPE FUNDAMENTAL CATALOGUE, 1900. TABLE VIII. — continued. Observer JJ. V. V. 1908 a s a 27^ - 12.4, + 285, - 7^2 + oJ {2 = + 0'89 — O'OI O'OO 49 ~ z - '3 - 8 = — 0-19 + 0-27 + 0-04 53 - 7 - 8 = + °'93 — 0-28 — 0-04 H + i = — 0-40 — 0-19 — O'OJ 7 = — 0-08 — O'O2 — O'OI 1909 54^ + 9.4, + 2o5, 4^2 — 3^ ?2 = + 076 - 0'15 — O'O2 67 +12 — 12 - 17 : - 0-25 — 0'08 — O'OI 1 06 0 - 4 = + ''44 - 0'27 — 0-03 33 + 21 = + 0-04 + 0-32 + 0-06 45 = - 0-15 'OO O'OO 1910 I9A' + 6Al - 1 85, — 3^2 ?2 ' + °'>5 + O'2I + 0-05 18 +8 — I - 6 = + 0'2I + 0-16 + 0-04 4° + '4 - 4 + 0'24 + 0-08 + O'OI 3' - 6 = + 0'27 + 0-41 + 0-08 1 1 - - 0'05 — 0-09 - 0-03 191 1 37.fi: — iAl — 125, + 7^2 — 2l ?2 = + 0'25 + O'OI O'OO 40 - 1 8 - 9 — I • - °'37 + 0-16 + 0-03 72 - 9 — 21 = — o'07 — I'2I — 0-14 32 - '3 = - 0-27 + 0'04 + O'OI 45 = O'OO + 0'17 + 0-03 Observer J VV. 1908. iqK — 104, + 85, — 3^2 — i5s = O'OO — O'OJ — O'OI 35 + J3 2 — i = + 0'49 + 0-48 + 0-08 4° O - 3 = + 0-36 — 0-04 — O'OI 2 — i = — 0-03 — 0-06 — 0-04 6 = — O'O2 — O'OI O'OO 1909. 23^ + 24^, — 45, 5^2 — 65 2 =: — °'4' + 0-03 + O'OI 37 - 5 1 + i = — °'37 + 0-24 + 0-04 45 IO + i = + I '01 + 0-16 + O'O2 9 + 7 = + O'll + 0-29 + 0-09 9 = + O'll + O'l I + 0-04 1910. ^K - 12^, - 155, + nA2 — 2I.fi 2 = - 0-66 — O*O7 — O'OI 64 +3° + 2 - 3 + 0-04 ~~\~ O'OA + O'OI 36 + 9 + 7 = + O'22 — O'll — O'O2 37 - 4 = - 0'52 — 0-14 — O'O2 33 = + 0'50 + O'lO + 0'O2 INTRODUCTION. XX11I TABLE VIII. — continued. Observer S. V. V. 191 1. 3 8 S 7K - iA, + 4#1 I^jj - 4^2 = — 0'08 4- O'OI O'OO 8 3 4 0 = + 0-44 + 0-49 + 0-17 1 1 i - 5 = + °'45 + °'35 + OMO ii — i = - 0-32 - 0-25 — O-07 5 = - 0-17 — O-2I — 0-09 For the further combination of these equations the observations in the different years were first treated independently. By means of the normal in K, the quantity K was first eliminated, and reduced partial normals in Aly B^ A.2, Bz were derived. The reduced parti.il normals for the separate observers were then combined by addition and the resulting complete normals solved. The results for the separate years are as follows : — TABLE IX.— Coefficients of Periodic Errors in the Clock-Star System. A,. »,. A,. S,. 8 i S S S 1908 — 0-O057 + O-OI22 -0-0155 — 0-0046 1909 + 'OO2O + -0177 — '0005 + -0047 1910 - -0149 + -0165 — -0103 + 'OOIO 1911 — -0090 + 'OI22 — -0148 — -0069 The observations made by each observer during the years 1908-10 were next regarded as furnishing homogeneous groups, which were combined among themselves in like manner, those of 1911 however being excluded, as a different method of observing was used in this year. The results from the separate groups are as follows : — TABLE IXA. — Coefficients of Periodic Errors in Clock-Star System (1908-10) grouped according to Observers. Observer. A,. B,. A* B,. s 3 s 8 C — 0-0073 + 0-0181 — 0-0154 — 0-0237 AP — '0231 + -0176 - '0*34 - -0079 KG — '0172 + -0080 - 'CH37 + 'DOSS AW - -0095 + -0118 — -0082 + '0092 M •oooo + -0164 — -0052 -f- 'OO66 JJ - -0037 + -oin — -0003 — -0024 JW — -0026 + -0127 — -0086 + -0053 XXIV CAPE FUNDAMENTAL CATALOGUE, 1900. According to either method of grouping, the values of the quantities A}, Blt A*,, JBz appear to be persistent, indicating real periodic errors in the Cape Ledger system. The definitive values have been derived by combining by addition all the reduced partial normals Al} JBlt A,, B2, which result after the elimination of K from each homogeneous group. The final complete normals are as follows :— with the solution 1275 Ai - l8 Bl -'94 — 18 A) +1498 Bl — 92 • 194 Al — 92 Bl +781 - 168 Al - 27/^+12 A.2 — \68B.2 = — 9-08 A2 - 27 B.2 -- +23-29 A.2 + 12 B.2 = - 778 A2 +686 B.2 = + 1-33 A, = *i = s — 0-0085 ) +0-0148 , weight l 183, ., '486, B\ = — 0-0103 > + 0-0006 , 74', „ 663. If we substitute these values in the respective partial normals in K, we derive the following values for K, which represent the personal discordances in time determina- tions by day as compared with those of the mean observer by night. TABLE X. — Discordances between Day and Night Determinations of Clock Error (in sense Day — Night), grouped according to Observers. Year of Observation. 1908. 1909. 1910. 1908-10. 1911. 3 S 3 S s c + 0-005 O'OOO + 0-OO4 + 0-OO2 O'OOO AP — -026 — 'O2I + -012 — -oio + -050 EC — -007 — -OO2 + -017 + -005 + -004 AW + -004 + -oi 8 + -033 + -O2O + -02 1 M — -019 — 'O23 — -024 — -O22 + -014 JJ + 'OI2 + -009 + -023 + -012 + '013 JW - -008 — '009 — 'OI2 — -oio S ... ... - -024 Mean — '0056 — -0040 + '0076 — -0004 + -oiio 1 The quantities here derived, except in so far as they are due to purely accidental causes, may be attributed in part to personal and partly to instrumental causes. If we give equal weight to the determinations in each of the four years involved, the mean result derived from all the observations amounts only to +0'S0023 for the mean observer. It follows that there can be little or no danger of the determinations of the periodic errors in JR. A. being vitiated by periodic errors due to diurnal changes in the instrument or the clock. INTRODUCTION. xxv The quantities contained in the two final columns of Table X. have been adopted as definitive, and, together with the finally derived values of AI, Slt Az, B2, have been substituted in the original equations of condition. From the sum of the squares of the residuals thus formed the probable accidental error corresponding to weight unity has been derived as db08'031 ; whence, with the weights derived, the probable accidental errors of A,, B,, At, Bt, amount to ±0S'0009, ±0«-0008, ±08'0011, ±0S'0012. The agreement between the derived values of these same quantities from the groups of observations, either arranged according to time or according to the observers, does not confirm this high estimate of the precision, doubtless on account of cumulative systematic errors. To obtain a more reliable estimate of the probable errors, both accidental and systematic, of the results, the derived values have been substituted in the partial normals (Table VIII.) ; the residuals are given in the last column but one of this Table. Now it is evident that if any one of these partial normals be written in the symbolical form )x + (ab)y+(a<;)z+ .... =(an), where each of the quantities n is of weight unity, the square of the mean error of the absolute term will be (aa)e2, e denoting the mean error corresponding to unit weight. Hence we may reduce the equations to equal weight unity by multiplying by the factor \l J(aa). The final column in Table VIII. gives the residuals from the equations thus reduced. Now if the quantities thus obtained represented true errors, instead of residual phenomena, since each has the same weight unity, the mean of their squares would give a determination of the square of the mean error for unit weight, but in that the derived phenomena depend on the equations themselves, we may anticipate that the average residual will be less than the average error. On the other hand, the sum of the squares of the residuals will exceed that which would be derived from a least square combination of the partial normal equations re- garded as equations of condition. But, according to the usual conventions of least squares, if 2i>2 denote the sum of the squares of the residuals, m the number of equations, and n the number of unknown quantities, Hence if v' denote residuals from a solution other than a least square solution, Applying this formula to the present case, a superior limit to the probable error corresponding to unit weight is found to be ±0S'043 and the corresponding probable errors of Alt B± do not exceed ±08'0013, those of A^ Bz, ±08'0018. C. F. 0., 1900. 4 xxvi CAPE FUNDAMENTAL CATALOGUE, 1900. On the basis of this determination the probable error, inclusive of residual systematic error, as well as purely accidental error of the quantity Al cos a+5j sin a-\-A» cos 2a-\-B2 sin 2a, amounts at a maximum in any right ascension to db08'0022. As regards the actual values derived for the coefficients Alt £lt A2, Bz, confirmation has been sought from comparison with approximately simultaneous series of observations made in other observatories, with results that support the values here derived (see Monthly Notices, January 1913). For the purposes of the present Catalogue it has, however, been thought desirable, in order to maintain its fundamental character, to avoid the introduction of extraneous evidence. Thus the definitive corrections which have been applied to the Ledger right ascensions in order to eliminate the errors in the system of right ascension originally adopted for their formation are Aa=+o'-oo85 cos a— 0B'OI48 sina+oB-oio3 cos 2a — o"-ooo6 sin 2<z. For reasons which will be discussed later no constant correction has been applied. Thus the equinox of reference corresponds with that of Newcomb's Catalogue. II. — REVISION OF DECLINATION SYSTEM. The declinations in the Ledgers have been derived from the nadir readings, with the Pulkowa refractions and with an assumed value for the mean latitude of the transit circle, viz. :— -33° 56' 2"'5- Except for the year 1911, they have received corrections on account of the motion of the Earth's axis from data supplied by Albrecht from the latitude determinations at the International Geodetic Stations. The same applies to the time stars of 1911, but not to the circumpolar stars, the observations of which are contained in a separate ledger, and which have formed the subject of a special discussion (Cape Annals, vol. xi., part iii.). No corrections for instrumental flexure have been applied prior to the formation of the Ledgers. Before considering the corrections on account of latitude and flexure, a comparison was first made between the results derived in the four conditions of the instrument I. E., I. W., II. E., II. W. A summary of this comparison, based on observations during the years 1905-10, is given in the following tables. INTRODUCTION. xxvn TABLE XL — Comparison of Declinations with opposite positions of the Clamp. Position I. A^ (E - W). Mean Dec. ot>-4t>. 4h-gl>. 8l>-,2h. i2h-,6>>. l6h-20l1. 20h-0h. Mean. o + 27 + o-i7j4 + 0-4727 + 0->5,8 - °"02,9 + 0-1 13, + 0-2425 + o:i96,54 + '5 + 0-26,6 + °'392, + °"3°Z2 + o"11,; + o-i6zo + o-38,4 + o-267llo + 5 + °'3727 + °-48,7 + 0-3225 -o-oi,, + 0'29,8 + 0-36,8 + 0-325, ,6 - 5 4:0-43,6 + o'5o,9 + 0-24,3 -o-oi,7 +0-06^ + 0'4324 + 0'300101 - '5 + 0-38,0 + °'43,5 + O-SZ,, + °-i622 + o-26I3 + o-3420 + 0-303 9, - 25 + 0-35,5 + °-55,9 + 0'53 9 + 0-l7,j + °-2724 + 0-46,9 + 0-378,02 - 35 + o-27I3 + 0-37,6 + 0-33,0 + 0'22,4 +0-28l6 + 0-30,4 + 0-295 83 - 45 + o'3426 + o-5724 + o'5'27 + 0'2 + 3, ; + 0-3I2g + 0-48,8 + °"396,54 - 55 + 0-25,3 + 0-52,6 + 0-37,9 + 0-39,4 + o'49,z + o'3o,4 + 0-388 88 - 65 + 0-46,; + 0-65 7 + o'36,2 + 0-36 7 + o-5710 + °-5', 2 + 0-479 6, - 75 + °-4°,, + 0-60 9 + °'45 8 + 0-16 g - 0-02 6 + °"47 7 + 0-364 49 - 85 + 0-30 4 + 0-49 5 + 0-53 3. + °'43 4 + °-°7 4 + 0-34 4 , + 0-359 24 - 95 + o-io 4 + o-49 3 + 0'35 4 +0-07 4 - 0-07 5 0-00 i +0-145 22 -105 + 0-62 + 0-69 2 + i -oo 2 + 0-40 5 + 0-37 , + 0-53 4 + 0-578 ,9 Position II. &S (E - W + 27 + o-4834 + 0-4527 + "•'9,8 + 0-12,9 + o''73, + 0'212. + 0291,54 + '5 + 0-65,6 + °"532, + 0-3322 + 0-27,7 + o-2420 + o-24,4 + o-378IIO + 5 + °"5227 + 0-27,7 + 0-4325 + 0-30,, + 0-40,8 +0-51, Q + 0-424,, 7 - 5 + 0-63,6 + o-3920 + 0-44,1 + 0'2O,7 + 0-39,2 + °'3724 + 0-398,02 - "5 + 0-44,4 +0'39il + °'3322 + 0-47,3 + o-4620 + o'42 ' 9o - 25 + 0-62*6 + 0-38,9 + °'4'1 Q + o~4524 + 0-62,8 + 0-477,0, - 35 + 0-43,3 + o-49,6 + o-34,o + 0-33,4 + o-37,6 + 0-47,5 + °-410 84 - 45 + o*4O26 + O 5224 + O'222? + °'3 I i! + 0'3328 i +°-3I,7 + 0-346,. - 55 + o'52i3 + °'34,6 + 0-2319 + 0''9,4 + 0-306 88 - 65 + 0-33,3 '+ O'2 I „ + 0-3I,2 + 0-26 + o-!710 ! +o-33l2 + 0-278 6| - 75 + 0-39,1 + 0-32 9 — O-O6 g + OM9 8 + 0-23 6 + 0-16 ?. + 0-219 49 - 85 + °"44 4 + O"28 + °'19 3 + o;35 4 -0-14 3 + °;j7 4 + 0-234 23 - 95 + 0-64 4 + 0-05 + 0-20 \ + °'19 3 + 0-247 20 -105 + 0-48 5 + 0-852 + O'24 2 + 0-355 + 0-39 , + O'O2 3 + 0-377 ,8 Comparison of Declinations with reversed positions of Object Glass and Eye- End. A(5 (Position I. — Position II. ; mean of E and W.) + 27 i - o-H27 - 0-31,8 — . Q" 2 Q -o-373, _0-2225 -0-235,54 + 15 -0-18*6 — O-242, — O'2322 — O *2 0 -0-3120 — 0-24,5 -0-250,,, + 5 -o-io27 + O"02,, - o-o825 o'00,, -o-o6,8 — o-'SiS - 0-070, ,6 - 5 — o 03,6 + o-o52o -0-0', 3 — o-o8,7 + o-oiI2 — o'°723 - 0-024,0, - '5 — O'16^ + o-o6I4 + 0-01,1 — 0'0122 — o'072o - 0-027 90 - 25 + O"I2,6 + o-'3,9 + 0-06 9 + 0-10 + o-o824 — °'OI,9 + o-o8o,02 - 35 + o-o6,3 + °'IO,6 + 0-02,0 + 0-26,; + o-'9,6 o-ooI4 + 0-H3 83 - 45 + o-io26 + °"'424 + 0'IO27 + °-IO3I + °'2l28 + o-oi,9 + 0-112,55 - 55 + °"ZIi3 + 0-22,6 + 0-I3,9 + 0-24,4 + °''5l2 + o-'7,3 + 0-185 87 - 65 + °-20,3 + 0-27 7 + o-i8I2 + 0-27 7 + 0-32,0 + o-|O,2 + 0-212 6, - 75 + 0-26,, + 0-20 + 0-14 8 — 0-06 g + 0-17 6 + 0-20 + 0-158 49 - 85 JJ4 + 0-46 5 + 0-29 3 + 0-40 4 + 0-23 3 + 0-18 5 + 0-320 24 - 95 + O-I4 4 + o-io + 0-46 3 + 0-37 4 + °'2I 3 + O'2O 2 + 0-250 ,9 -105 + o-75 5 + 0-28 2 + °'22 2 + 0-27 5 + o-oi , + 0'32 3 + o-394 ,8 The suffixes indicate the number of stars in the group. XXV111 CAPE FUNDAMKNTAL CATALOGUE, 1900. Fairly pronounced discordances of a systematic character depending on the zenith distance are clearly indicated. These may be in part accounted for by residual division-errors and by the variations in flexure under the different conditions. The separate determinations of the flexure coefficient by means of the horizontal collimators are given in the Introduction to the Meridian Observations. A summary of these is here given : — TABLE XII. — Determinations of Mean Flexure Coefficient. Ypar I. II. E. W. E. w. 1905 + 0-288 + 0-363 1906 + 0-253 + 0-310 1907 + 0-459 + o-335 1908 + 0-213 + 0-137 1909 + 0-27' + 0-323 ... 1910 + 0-305 + 0-384. + 0-061 + 0-068 191 1 -4- 0-298 + 0-384 Mean + 0-317 + 0-347 + 0-187 + 0-189 Within the limits of accidental errors of determination these figures indicate no appreciable change due to reversal between the two clamps, but a strongly marked difference between determinations in Positions I. and II. Accordingly the differences E — W, as given above in Table XL, after being smoothed by graphical interpolation, have been adopted as definitive. To the difference II-I a correction on account of variation in the flexure co- efficient, amounting to — 0"'14 sin £, where £ denotes the zenith distance, has been applied, and the results then smoothed in like manner. Denoting the semi-differences ^(II-I) by A, and the semi-difference |(E-W) by BI or Bn, the following table gives the smoothed values for these quantities which have been used :— Table of Systematic Discordances. Dec. A. B, /A, Dec. A, A B«. Dec. A. * B* + 35° if + 0-07 — o':o8 — o'lz - '5° — 0-04 — 0-16 — 0-21 - 65 — 0-05 — 0'2I -o"i3 30 -1- -06 — '10 - -14 20 - -04 - -16 — '22 70 - -05 — -20 — M2 25 + -05 — '12 - -16 25 — -05 - -'7 — -23 75 - -05 — '19 — 'I I 20 + -04 _ -13 - -18 30 - '°5 — "22 80 - -06 - -18 — 'I I '5 + -03 - -'4 - -19 35 - -'7 — -21 85 - -06 - -18 — 'I I 10 + -oi - ''5 — -20 40 — -05 — -17 - -'9 90 - -07 ~ "'7 — '12 + 5 •oo — -20 45 - -05 - -18 - -18 S.P.85 + -08 + -17 + "!3 0 — -02 — -16 — -2O 50 - -'9 - -16 „ 80 + -08 + -17 + ''4 - 5 - -03 — ''5 — -2O 55 - -05 — -20 — -15 „ 75 + -09 + -18 + -16 10 - -03 - -'5 — -20 60 - -05 — '20 - ''4 INTRODUCTION. xxix i These corrections have to be applied to the observed declinations with the follow- ing signs in order to reduce the whole series to a uniform system :— Position. Clamp. A5. I. E. A +13,. I. W. A-B,. II. E. -A+BU. II. W. -A-Bn. 