616 



SCIENCE. 



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



flj and dj denotiBg — and --, a, and d^ the 



mean motion of the perturbing body (Sun 

 or Moon) in ]& and D, n the diurnal 

 motion of the Earth. 



C' = S— 2 7, E' = R — 2t, t being the 

 mean between the sidereal times of both 

 observations, S= A + 2D. R = A — 2D. 



A = JR, D = Decl. of the perturbing bodj-, 

 calculated for the time t. 



x = vsin2L', i/ = voos2L', L' ^L-{-r^ 



whence tg2L' -- 



\L-- 



The observations give J a and J o, differ- 

 ences between the residuals na and n& ob- 

 tained bj^ each observation ; whence we de- 

 duce by means of the known formute of 

 transformation Ad and J/. 



(9) The following table gives all the ele- 

 ments of the calculation, extracted from the 

 '■'■ Annalesi de Vobservatoire de Kiev (5 min. W. 

 from Pulkova), Vol. I., Observations de la 

 Polaris sime par Fabritius." All the cal- 

 culations were kindlj^ made by M. Niesten, 

 astronomer at the Royal Observatory of 

 Belgium. 



June 17 

 " 20 

 " 21 

 " 22 

 " 25 

 Jul. 1 

 " 4 

 7 

 9 

 17 

 18 



Aug. 



17 25 



17 45 



18 33.5 



19 49 



17 22.5 



19 41 



18 4 



20 31 

 20 8.5 



20 20 



21 17 



a; 



h m 

 4 53.5 

 4 9 



2 31 



53 

 4 52 



1 40.5 



3 45 

 1.13 



4 51 



5 28 

 7 26 



Aa Arf hy A9 ly i^X S^ 



0.4975 n 



9.8754ra 



9.9921 



9.6383 



9.5111 



9.5488 



0.1130 



0.2992 



9.8052 



0.3256 



0.1224 



0.4737 

 0.0340 

 0.0590 ?i 

 9.6798 re 

 9.5828 re 

 9.8870 re 

 0.1801 re 

 0.3666 re 

 9.8693 

 0.3920 m 

 0.1884 



132 39 



135 55.5 



136 50 

 138 5 

 141 4 

 146 42 

 149 16 

 151 35 

 170 52 

 173 34 

 173 50.5 121 43 



39° 3 



42 7 



43 2 



44 19.5 

 67 3 

 54 18 

 57 45.5 

 61 47 



107 38.5 

 120 5 



111 31 



150 47 

 158 59 

 164 19.5 

 169 3 

 199 44.5 

 255 9 

 325 46 

 82 5 



167 31 



168 51 



11 35.6 



53 58.5 



74 



95 44 



153 19.5 



303 15.5 



339 28.5 



348 41 



358 36 



124 9.5 



149 48.5 



Whence the following equations, where the numbers are expressed in logarithms: 



V 



( 1.3529 y 

 \ 0.5659 y 

 j 1.2713 y 

 1—1.1354 2/ 

 f 1.0142 y 

 I 0.6425 y 

 r 0.4661 y 

 \ 0.6055 y 

 r 0.6698 y 

 '1—0.3485 3/ 

 f 0.3477 2/ 

 \ 1.2464 2/ 

 f 1.1805 2/ 

 I— 1.1661 J/ 

 / —9.9292 y 

 1—0.7693?/ 

 f —1.9162 2/ 

 1—0.3163 2/ 

 j 1.0950 y 

 I 0.8918 y 

 f 0.9663 3/ 

 I 1.2182 y 



—0.1658 a; 

 +1.7530 X 

 +0.7353 .r 

 +1.6713 X 

 —0.2424 a; 

 +1.4143 X 

 —0.2054 X 

 +0.8662 X 

 +9.9484 X 

 +1.0699 X 

 —0.8464 X 

 +0.7478 X 

 +0.7660 X 

 +1.5806 X 

 +0.3691 X 

 —0.3293 X 

 —1.1526 X 

 +1.5527 X 

 —0.4917 X 

 +1.4951 X 

 —0.8181 X 

 +1.3664 X 



=0.4975 re \ 

 =0.4737 i 

 =9.8754 re \ 

 =0.0340 / 

 =9.9921 1 

 =0.0590 n / 

 =9.6383 1 

 =9.6798 re/ 

 =9.5111 \ 

 =9.. 5828 re / 

 =9.5488 \ 

 =9.8870 re J 

 =0.1130 \ 

 =0.1801 re j 

 =0.2992 \ 

 =0.3666 re ( 

 =9.8052 \ 

 =9.8693 j 

 =0.3256 1 

 =0.3920 n J 

 =0.1224 \ 

 =0.1884 J 



Mean, 0.091 



0.122 

 0.044 

 0.104 

 0.102 

 0.076 

 0.063 

 0.119 

 0.095 

 0.050 

 0.114 

 0.128 



2U 

 1.35°7 

 127.18 

 132.20 

 151.24 

 127.32 

 154.18 

 201.00 

 166.16 

 142.56 

 167.25 

 180.30 



1,1 

 h m 

 4 30 



4 14.5 



4 24.5 



5 3 



4 15 



5 8.5 



6 42 



5 32.5 



4 45.5 



5 45 



6 1 



L 

 h m 



11 5 



10 29.5 



9 51 



9 14 

 10 52.5 



9 27.5 



12 38 



9 1.5 



8 37 



9 25 

 8 44 



ff 58.6 



The agreement between these various de- 

 terminations is truly most satisfactory, so 

 much the more so as many of them (the 

 4th, 6th and 8th), are from observations 

 whose interval does not reach two hours. 



It is sufficient to establish, not the val- 

 ues of the constants (the number of obser- 

 vations is too small), but the existence of 

 diurnal nutations. 



(10) In conclusion, I believe asti'onomers 



