DR L. BECKER ON THE SOLAR SPECTRUM. 125 



wave-lengths of 2395 different lines obtained on one side of the normal with those found 

 on the other side, we find the average difference 



[Vl*J = o-065 lU. 



n 



The probable error of one wave-length, which is the mean of all low sun observations, 

 then becomes for p = q 



r = ± 001 9 A.U. 



One series, however, contains on an average twice as many observations, hence p = 2q 

 and 



r = ± 0018 A.U. 



which nearly holds for the mean of six observations of the same line in low sun. 



The same comparisons give on an average a systematic difference of 0*007 A.U. 



We next compared the wave-lengths which result from all the low sun observations 

 with those derived from high sun. They were divided into two classes, one of which 

 comprised the faint lines of intensity 1 to 3, and the other the darker lines. 1710 faint 

 lines show an average difference of 0*074 A.U. and + 0*007 systematic difference, whereas 

 1215 well-defined lines give respectively 0*048 A.U. and + 0*001 A.U. Supposing 

 the low sun observations to be twice as numerous as those made at medium altitudes, 

 we find the probable error of one definite wave-length 



r = ± 0*021 A.U. for intensity <4 

 r = ± 0*014 A.U. for intensity ^4. 



There is an increase of 1 in the last decimal, if the mean of the observations in low 

 and high sun are considered equally accurate. The greater probable error of the fainter 

 lines is sufficiently explained by the smaller number of observations on which each 

 wave-length rests, and the greater difficulty in perceiving them. 



From the preceding examination we gather that there is no systematic difference 

 either between the observations on opposite sides of the normal or between those made 

 at medium altitudes and near the horizon. The probable error of one definite wave-length 

 may be considered to amount on an average to ± 0*02 A.U., if the line has been observed 

 about six times. There will be lines, of course, which may turn out to deviate considerably 

 more than this from the true value, in spite of having been frequently observed. But 

 this will not surprise anybody who has ever compared the difference of two independent 

 series of results with the probable errors as given by their authors. 



The probable error is not so small as to render it worth while to correct the morning 

 and evening observations for the displacement of the lines due to the rotation of the earth. 

 For the latitude of Dun Echt the maximum effect is about 0*005 A.U. The displacement 

 produced by the eccentricity of the earth's orbit can also be neglected, although it 

 amounts to about 0*01 A.U. at the time of the equinoxes. 



