NOVEMBEK 8, 1895.] 



SCIENCE. 



613 



a progressive betterment of human char- 

 acter, the final, the most precious result of 

 evolution on this earth. 



George Bruce Halsted. 



Austin, Texas. 



DETERMINATION OF THE CONSTANTS OF 

 THE DIURNAL NUTATION. 



(1) In the Annuaire de I' Observatoire 

 Royal de Belgique for 1894, I gave the fol- 

 lowing results deduced from Gylden's 

 observations of the latitude of Pulkova : 



Let K = constant of annual aberration, 



k' =r reduced constant of systematical aberration, 



i. e., projected on the equator, which I derived 

 from my terms of the second order which 

 arise from the combination of annual and 

 systematical aberrations.* 



d = parallax of Polaris ; 



I =Peters's constant of nutation 9". 2235; 



n = the correction of this constant; 



v' --= Peters's constant of the term cos 2 © : 0".555 ; 



n' = its correction ; 



V = the constant of the diurnal nutation ; 

 L = the longitude of the first meridian, 



i. e., the meridian which passes through the 

 axis of the moment of inertia A of the solid 

 crust of the globe. 



Applj'ing my formula, M. Byl, astron- 

 omer adjunct at the Eoyal Observatory of 

 Belgium, has found 



fi=20".408. k' = 39". U-- 0^^0546. 

 M = 0'' .003. «' — — 0".0444. 



V — 0'^0665. L = 12'" 0"° E. from Pulkova. 



Illness has prevented M. Byl from coor- 

 dinating his calculations, and I was com- 

 pelled to make a new determination of both 

 the last constants for the next volume of 

 the Annates de I' Observatoire Royal de Belgique. 



(2) My purpose was to make use of the 

 excellent series of observations of the Po- 

 laris in IR made at Dorpat by F. W. Struve, 



*Cat^ohisme correct d'astronomie sph&ique (Me- 

 morie della Pontificia Accademia dei nuovi Lincei, 

 Roma. Vol. IX.), and Annuaire de I 'Observatoire 

 Eoyal de Belgique pour 1894, p. 346. 



a series which had led me to conclude that 

 the Eulerian period of 305 days was too 

 short.* 



In order to eliminate the variations of 

 latitude, I have onlj' used half of the sum 

 of Si observed at consecutive upper and 

 lower transits. The laborious calculation 

 of the whole series has given me unex- 

 pected results: v = 0".17, twice or three- 

 fold too great; L = 12'' 10" E. from Pul- 

 kova, good result; n' = -f 0^.045, which is 

 in complete discordance with the value 

 w' ^ — 0".0444 deduced from Nyren's obser- 

 vations, and moreover, theoretically inad- 

 missible. In seeking the cause of these un- 

 looked-for results, I found that an error of 

 sign I had noted down some years ago 

 and considered as a simple typographical 

 error has been used by Peters in all his 

 reductions of Struve's observations. In 

 his formulse (p. 13 of Nuinerus Constans nu- 

 tationes) he wrote with -f , instead of — , the 

 terms of nutation in 2 ©, and calculated 

 his reductions with this erroneous sign. 



All my work had to be done over again, 

 as will be the case for Peters's determina- 

 tion of the constant of nutation. 



In order to eliminate this serious error I 

 used Struve's residuals, corrected by in- 

 creasing by 0."2 the Delambre's constant he 

 had used for his reductions, and to avoid the 

 other errors of reduction I have formed the 

 differences between successive pairs of ob- 

 servations chosen so that the coefBcients 1\ 

 and 1\ were sufficiently different in both 

 pairs. 



(3) The diurnal nutation in Al is in the 

 meridian 



where v ^ v sin ( 2 L -|- a ) , ?i = v cos (2 L -\- a); we 

 may write 



A a = X '^2 'i' !l ^1 ^ ^^ '^ ^y- 



The principal terms I have used for the cal- 

 culation of a (I'j) and b (Zj) are 



* Annuaire de I'Observatoire Eoyal de Belgique 

 pour 1891. 



