The Magnetic Separation of Lines 37 
In determining the intervals of the substances, I have used the 
components only of the line in question, and recorded the largest 
aliquot part of these components as the interval. This process 
yielded intervals which in themselves are multiples of a small 
value, e. g. there are intervals @/11, 2a/11, 3a/11, 4a@/11, 5@/II, 
6a/11, 2a/12, 3a/12, 4a/12, 6a/12, 3a/16, 6a/16, 9a/16, 124/16, 
and possibly others. These intervals may be expressed in a/T11, 
a/12, a/16, and the multiple factors correspondingly increased. 
Professor Runge prefers this method. So far as the comparison 
of lines is concerned, it is entirely immaterial. 
The actual number of intervals is many less than recorded in 
the tables. A bracket indicates that the intervals .53, .54, .55, and 
.57 may all in reality be the interval a/2 (=.554). The greatest 
deviation, .og, is in a four-fold of .53. It is advantageous, how- 
ever, to preserve the factor .53 in the tables just as it is. For, if 
a six-fold or greater factor of .53 should be found in any sub- 
stance, the interval would probably not belong in a@/2. -When 
the multiple factors are small, wider ranges in the intervals can 
‘be regarded as coming under one interval. The inverse is true 
for large multiple proportions. ‘Therefore one could more readily 
classify .33 (with largest factor equal to 4) under .32 (with 
largest factor g) than in the inverse manner. However, ee 
an aliquot (3@/10) of a. Taking 3a/10 as an interval, the .34 
(with factor 4) interval is reasonably near it, but the .32 interval 
is near the limit of allowable error. The interval .29 is midway 
between a4(=.28) and 3a/11 (=.30). Without material error, 
it could be classified a/4 or 3a/11. Its factors are not present in 
either a14 or 3a/11, and for the present may remain unclassed. 
The same difficulty arose with .21 until further classifving showed 
the presence of 2, 3, and 4 times .21, and that these could be rep- 
resented by 3a/16, 6a/16, 9a@/16, and 12a/16. 
It may be contended that the magnitude of the intervals indi- 
cates an irrational part of the normal “a” rather than aliquot parts 
of such a normal value, or in other words that the ‘‘normal” is 
fictitious. Such a conclusion is possible, and if an examination 
of other substances gives other apparent irrational intervals with 
numerous and large factors, it will be the more logical conclusion. 
oF 
