528 
the displacements of the selected lines show with regard to their 
own mean: 
0,0472 + (21 X 0,00015) + 0,0547 — (29 < 0,00015) = 0,1007 A, 
it appears, that the average departure from that mean was 
0,1007 
50 
Suppose we made a non systematic, absolutely arbitrary choice 
of 26 cases out of our gronp, then the average departure of their 
arithmetic mean from the mean of the group would only be 
0,002 ° 
= = = £0, 0004A 
Vb 
to which corresponds a probable departure: 
r = 0,8453 4 — 0,00034 A. 
Our real selection, however, was not at random; we took 26 
lines with companion on the red side, and found an average depar- 
ture — (0,0017 — 0,00015) = — 0,00155 ie moreover 24 lines with 
companion on the violet side, giving an average departure + 0,0015 
+ 0,00015 = + 0,00165 A. 
In both cases the departures from the mean of the group are 
about 4,6 times as great as the probable departure 7 (in case of 
random choice) would have been. 
Now the probability for a departure to lie between — 4,6 7 and 
+ 4,6 r is given by 
zee e—? dt (in which 9 = hr = 0,477) 
een: 4 rn err 
0 
the value of this integral being 0,998'). So there is only 0,002 left 
for the probability that, by mere chance, the mean departure of 25 
values from the general mean should exceed those limits. 
On the basis of ADAMs’ measurements we find, therefore, a pro- 
bability of 500 to 1 that there really exists a mutual influence of 
Fraunhofer lines. An analogous treatment applied to the limb-centre 
displacements measured by HEvrersnep and Royps’) has yielded a 
similar result, which will be published later. *) 
It is necessary, however, also to consider how far this mutual 
influence may be due to systematic errors in the way we estimate 
the place of a line when there is another line very near. 
— 0,002 A. 
y= 
4,6¢ 
1) CHAUVENET, Spherical and practical astronomy, Vol. II, Table IX A. 
*) Eversuep and Royps, Kodaikanal Bull. 39. 
5) A subsequent perusal and combination of all the data at our disposal has 
brought the probability of non-existence of mutual influence down to 10-68 (Note 
added in Dec. 1920). 
