38 B, E. Moore 
As soon, however, as one omits the quadruplets, there remain but ~ 
few lines which suggest this difficulty.. With respect to the quad- 
ruplets one can very frequently change the interval and at the 
same time change the factors so that the line is practically just 
as well represented. Also, with two values, i. e. four components, 
distinction is difficult, whereas with six and more components the 
intervals can be determined with considerable sharpness. 
Lines with many components have frequently a larger interval 
which occurs as a common difference in passing from component 
to component instead of measuring from the position of the un- 
disturbed component. In Neon one finds the s-components of the 
line 6217.5 represented by + (14, 9, 5) a/6, or a common differ- 
ence of 5a/6 repeated four times. The p-components of the same 
line are represented by -+ (5.0) a/6, or 54/6 repeated twice more. 
In zircon, 3459.1, the s-components are + (23, 15, 7)a/11, or the 
distance 8a/11 occurs four times. [or the p-components of this 
line one finds 12a/11 two times repeated. In yttrium, 4235.80, 
the perpendicular components are represented by +(7, 5, 3) a/6 
and the parallel components by (4, a)a/6, or the distance a/3 is 
measured eight times in this line. Numerous other cases can be 
found in the table. 
From the examples given one sees that the distance between 
the adjacent p- and s-components is much smaller than the dis- 
tance becween the single f- or single s-components. This smaller 
distance is naturally more accurately determinable as the number 
of components increases. Then it is evident that the greater sep- 
arations are always whole multiples of small distances, and also 
that the distances from the position of the undisturbed component 
are whole multiples of such a small distance of “interval.” 
In the quadruplets the small interval is more difficult to deter- 
mine, and they therefore have less weight in determining this fun- 
damental question, of the rationality or irrationality of the “inter- 
val” space. In these quadruplets, however, one sees that the com- 
ponents stand in a simple numerical relation to each other. 
The multiples and their intervals remind one of the law of mul- 
tiple proportions in chemistry. 
38 
