ÖFVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1899, N:0 2. 91 



From these, by raeans of the method of least Squares, the 

 foUowing normal equations result: 



+ 6.5079 r + 0.9328 s —11.0262 t + 17.5742 = 

 + 0.9328 r + 31.0829 s —11.0923 t + 11.8055 = O 

 — 11.0262 r —11.0923 s + 56.1926 t —100.1522 = O 



Solving these I got 



log r = 9.75138 



log s = 9.47702 



log t = 0.29052 

 and thus 



X = 2.054 ± 0.0042 



i = + 18.12 ± 0.25 



O = + 28.00 ± 0.50. 



As DuNÉR could not from all his observations determine a 

 quantity corresponding to my x witli its probable error, it was 

 impossible for me to compare my p. e. with DuNÉR. I have 

 therefore proceeded in the following manner. From the p. e. of 

 v given by Dunér pag. 73 for each year and latitude I have 

 at first for q) = O calculated the p. e. in one observation in 

 that latitude and so examined what would become the p. e. if 

 the number of observations on the latitude cp = O were equal to 

 the whole number of observations on all latitudes. Then I have 

 made equal proceeding with the p. e. of v for (p = 75° which 

 p. e. I have afterwards multiplied with sec 75^ The p. e. 

 which ought to be comparable to my p. e. of x then must 

 lay between these two probable errors viz. between + 0.0050 

 and + 0.0207. As ray p. e. of x thus is considerably smaller 

 than that of Dltnér, I have concluded that an uniform rotation 

 better accords with the observations then the law found from 

 the sunspots. It was also my intention to determine x, i and 

 Q for each latitude separately, a determination that cannot 

 but be uncertain, but as the probable errors of ^, i and Q are all 

 small, such an examination could not have given essentially 

 difFerent values to these quantitees for the diflferent latitudes; 

 thus I have considered such a calculation unnecessary. 



