614 



SCIENCE. 



[N. S. Vol. II. No. 45. 



a = —0.18 sin S2 +0.39 sin 2 © +0.89 sin 2 (T 



+0.18 sin (2C— i2). 

 6 = —1.155 —0.134 cos H +0.36 cos 2 Q 



+0.82 cos 2 C +0.14 cos (2(i:— 0). 

 writing, with Peters, 



d= II = correction for the position (E or W) 

 of the cii'cle ; lo = correction of the mean ^ 

 of Polai-is, and remembering that the cor- 

 rection of the terms in 2 © has been elimin- 

 ated hy taking the difference between two 

 pairs of observations, we have only the 

 equation of condition 



aa; + byzhi) + w + m=:o; 



the vinity of the residual, w, is the second of 

 time. 



(4) By taking the diiferences between the 

 equations formed for such a pair of upper 

 and lower culminations, two by two, it is 

 clear that we shall obtain the simpler equa- 

 tion 



{a^ — ai).r, + (Jj — ^i)2' + "2 — "u ^= o> 

 which we write 



ax + Jj + « = 0. 



The following table gives the values of 

 p weights of the two equations used; a, b, 

 n, n', multiplied by 100; the point after 

 a number signifies 0.5. n' is the new resid- 

 ual obtained after the substitution, in each 

 equation, of the values found for x and y. 



1822. Nov. 5 and 12 



1823. May 6 and 16 



" 16 and 19 



" 19 and 21 



" 21 and 30 



May 30 & June 2 



Sept. 8 and 11 



Oct. 9 and 11 



" 11 and 13 



" 13 and 28 



" 28 & Nov. 8 



Nov. 8 and 14 



" 14 and 26 



" 26 & Dec. 8 



1824. Apr. 6 and 11 



" 11 and 23 

 "23 and May 1 



P- 



(1.4)- 

 (1.2)- 



(1.2) - 



(2.3) - 

 (3 )- 



(3.4) - 



(1.2) ■ 

 (1.2) 

 (2.3) 

 (3 )- 

 (2.3)- 



(1 ) 

 (1.2)- 

 (1.2)- 

 (1 )- 

 (1.3) 



(2.3) - 



-182 — 10 

 -138 + 77 

 -110 — 82 

 -26+56 



145 



47 



120 



- 12 



- 52 



- 39 



- 29 



- 84 



- 53 

 58 

 63 



- 28 



- 17 80 

 63 50 



-132 — 96 



-88—38 



-102 —175 



81 149 



- 76 + 58 



—87 —88 



6—5 



33 45 



—36—45 



14 8 

 —10 4 



2—17 



15 18 

 —34 —25 

 —37 —32 



37 24 

 —59 —66 



23 37 

 —15— 8 

 —90 —63 

 +79 +56 

 —30 —40 



May 1 and 3 



' ' 21 and 22 



" 22 and 28 



" 28 & June 2 



June 2 and 7 



" 7 and 9 



" 9 and 12 



" 12 and 17 



" 17 and 22 



Sept. 22 and 25 



" 29 & Oct. 3 



Oct. 18 and 22 



Nov. 20 & Dec. 5 



Dec. 5 and 19 



1825. Mar. 15 and 17 



" 17 and 20 



"20&Aprill 



April 1 and 8 



May 1 and 7 



" 7 and 10 



" 10 and 18 



June 1 and 3 



Oct. 2 and 5 



" 3 and 4 



" 22 & Nov. 7 



55- 



- 72- 



- 6- 



- 96- 



- 33- 

 -119 



144 



- 5- 

 -121 

 -100 

 -156- 

 -142 



53 

 62 



- 54- 

 -102 



45 



12- 



147 



3 



-125 



- 59- 



- 30- 

 35- 



- 62- 



- 10 



- 15- 

 -199- 

 -146- 



- 37 

 114 



25- 

 -136 

 62- 

 70- 



- 16- 

 65 

 29- 

 17- 



- 61- 

 57 



- 38 

 -116 



44- 



- 52- 

 84 



- 40 

 -110- 



72 74 

 -25 —24 

 -23— 1 

 -15 10 

 43 48 

 64 44 



- 7— 9 

 15 37 



-19 —30 



- 7—20 

 -27 —22 



26 14 



-61 

 -41 

 -33 

 2 . 



51 



70 

 -82 

 -18- 

 2—13 



27+33 

 -49 —32 



11 +13 



34+33 



(5) From this system we have deduced 

 the normal equations 



3882.5 a; + U2.6 y — 27.6 = 

 142.6 + 3801.7 + 613.9 = 0, 



which gives 



X — OJ.013 ± 0.0044 

 J/ — 0.162 zt 0.0049, 



Where we deduce fi'om 



x~ — vig<5 sin (2Z, + a) 

 y = — '' /17 t5 cos (2 Z + o) 



v=0."070 ±0.''0019. 



2 i + o =357° 20' ±46'. 



2 L =342° 52' ±46'. 



L =11" 25™. 7 E. from Dorpat 



=111 iim E. from Pulkova. 



The agreement between the constants de- 

 duced from Gj'lden's observations of Po- 

 laris in Declination v = 0."0665, L =12'" 0°" 

 E. from Pulkova, and from Struve's obser- 

 vations in Ji, together with aU the deter- 

 minations I have made of these constants 

 since 1888,* and with the smallncss of the 



* Annuaire de rObservatoire Eoyal de Belgique, 



1888-1894. 



