272 PROFESSOR L. BECKER ON 
according to formula (7). m)—2Zm ranges between —0°6 and — 2°2 for b=1-08, and 
between +0°4 and +24 for b=1°4. 
Let dm, . . . dm, be the corrections of the degrees m, . . . m, which change the 
degree of blackness m, by dm, therefore, 
(8) Stn) sr 
C My, 
A change 6m, at wave-length X of band 1 can be brought about only by all the 
degrees of blackness being changed at every place of this band. I express dm, by the 
change dw; of the degree of blackness , of the maximum of band 1; », being the 
quantity which was shortly called the intensity of the band, and I do the same for all the 
indices 1 ton. Employing (6) I replace in (8) dm, by du, and eliminate function f by F. 
(9) LEF(m ae log ae = af Ee) Sm 
mM 
To reduce the work of San I Cranes the ae of the maximum of every 
band by an amount dz, determined by 
dE (mM) 3, é 
dm : 
(10) gut eli, 
and obtain from (9) and (7) 
_ dlog F(m)) 
(11) = eee 
(129) = My + mM, « 
I determine x by (11) with dm=2Zm—m, and calculate dm, at each point 
from the mean value of a For b=1°4, u of band \,=4425 was reduced by 1 in 
addition to du, and the intensities of the last four bands were not changed at all. 
(29) =m) + 5m, which appears in Table X. is then the calculated intensity curve if the 
degrees of blackness of the maxima of the bands given in Table VII. be changed by certain 
amounts to be calculated from (10), and the degrees at each point be compounded ac- 
cording to (7). The last three columns give the residuals left in the observed intensity 
curve. 2m differs from the observed intensity curve on an average 0°58 degree, (m,) 
differs 0°57 for b= 1°08, and 0°63 for b=1°4, while (m,) differs on an average 0°26 from 
2m. ‘The observed intensity curve is therefore equally well represented by 2m and by 
(m,), and therefore the hydrogen lines of Table VII. represent the spectrum, no matter 
whether the degrees of intensity of their bands be compounded by mere addition, or 
according to formula (7). Combinations of bands which, if compounded according to 
the additive rule, leave inadmissible residuals in the observed intensity curve, must give 
errors of the same order if formula (7) be employed ; and I conclude that if this formula 
had been used at the outset in analysing the spectrum into bands, the result would have 
been identical with that contained in Table VII. 
A similar calculation for the intensity curve of photo-plate No. 3, assumption A, 
gave an average error, observed m—2m=0°'63, observed m—(m))=0'59 for b=1°08, 
and 0°58 for b=1°4, while (m)) differs on an average 0°25 from 2m for both values of 
b. This agreement proves again that the use of the additive rule cannot have influenced 
the analysing of the spectrum into bands. 
