NOVEMBEB 8, 1895.] 



SCIENCE. 



615 



probable errors, is an irrefutable proof of the 

 diurnal nutation. 



The observations of Peters on the lati- 

 tude of Pulkova had given me* v =0."17, 

 L — 11" 58™ E. from Pulkova. But these 

 observations are not nearly so precise as 

 Gylden's and have given a constant much 

 too great. 



(6) In order to corroborate my own con- 

 viction, I tested the determination of these 

 constants by means of a short series of 

 observations, treated like the preceding of 

 Struve. This series is from Preuss' obser- 

 vations (1838, May IS-June 29). 



In this case again the equation will be 



ax -\- by ± V -\- to -i- n :^ 0. 



The following table gives the values of p, 

 a, b, n. For such a short series we could 

 not introduce the correction of the term 

 sin 2©, and we can expect a much too great 

 value for v. Our criterion will also be the 

 longitude l. 



All these values are very great, which 

 arises from the size of the residuals. It is 

 to be noticed, however, that the signs of v, 

 u, w are the same as those deduced by Peters 

 from all the observations of Preuss. 



From X and y we deduce tg (2 L -\- a), 

 whence L = 12'' 8" E. from Dorpat, which 

 agrees very well with all the preceding de- 

 terminations. 



(8) I will now give still another remark- 

 able example of deductions, and one which 

 shows the diurnal character of this nuta- 

 tion. For this case I have given the for- 

 mulae referred to the equator, which dis- 

 pense with the calculation of the functions 

 2'2 and ^'if- From these formulae I have 

 deduced the following expressions for the 

 diurnal nutation in obliquity, JO, and in 

 7.14 longitude J?.: 



A e =z J ^ (2 J sin c'l — Ti sin iJ'i ) + 2.18 ( 2o sin f'j — Cj sin Je'2 ) I 



+ x I (2i cosf'i — Ti cos JJ'i) + 2.18 (Sj cosf'j — r^ siniJ'j) | 



SiuSAAnza; j (Sj sin f'j — "i siniJ'j ) + 2.18 (2, sin f'2 — r, sin iJ', ) | 



— 3' I (^lOOSf'i — Ti cos TJ'i) +2.18 (S^ cosf'2 — ^2 siniJ'j) j 



in which the index 1 is referred to the Sun, 2 to the Moon. The notations are the fol- 

 lowing : 



S = (l + 6,)sin(l — Jfj).!*, r=Cl + ^2)sin(l — JeJAf, 



J t being the interval between the two observations. 



3 —0.0167 —2.64 



&. = %> 



C—A 



S^ 



-^=^1^^=0.00328. 

 A A 



-2d, 



T2=a2 + 2d, ; r^=a2 

 *Ibid., 1894. 

 t Theory of the diurnal, annual and secular motions of the axis of the earth. Brussels. 1884. 



