( 35? ) 



diculars from the system of points to the line a minimum. The line 

 thus determined will be the principal axis of inertia of the system 

 of points '-'). 



Performing this calculation we find thai the l»esi fitting lower line 

 passes through the point with the coordinates 398, 351, at a slope 

 determined by <9 t = 43 t>'. Kor the upper line these numbers become 

 398, 386, whereas 6, = 45°35'. 



In order to judge of the accuracy obtained in the representation 

 of the observations by these straight lines the following table may 

 serve. The third and fourth column, resp. the sixth and seventh 

 column contain the errors of the abscissae and ordinates of the two 

 point systems to he assumed, if the straight lines are supposed correct. 



It appears from this table that the lines completely represent the 

 observations, if we admit mean uncertainty of 0.0013 A. U. in 

 the observations concerning line 5770 and of 0.0014 A. U. resp. 

 of 0.0011 A. I'. in the determination of the components towards the 

 red resp. towards the violet in the case of line 5791 ; we must 

 admit these as appears from the distribution of deviations. 



10. The position of one point of each line may still be cheeked 

 by the observations of Runge and Paschen. They give for the separa- 

 tion in the ease of line 5770 towards the red resp. towards the 

 violet -f" 414 + 1.7 resp. — 415 +_ 1.7, whereas for the same magnetic 



'-'i Karl Peahson. On Lines and Planes of closest Fit to Systems of Points in 

 space. Phil. Mag. p. 559. Vol. 2. 1901. Here we read: "The b»»st fitting straight 

 line for a system of points in a space of any order goes through the centroid 

 of the system" cf. Keesom. These Proceedings 31 May, 1902. 



