ME rilODS OF SPECTR OPHO TOMETR V. 219 
We shall suppose this result to have been attained, and next direct our atten- 
tion to the relative illumination of the two spectral areas under examination. 
It will be at once seen that the interposition of the absorption cell has brought 
about a greal difference in this respect. The upper spectrum is seen to be 
much less bright than the lower, the difference depending upon the amount 
of colouring matter in solution. Unless the concentration he excessive, we can 
restore the equality of illumination of the two superposed spectral areas by 
narrowing the lower slit. This is clone with great care until we are convinced 
that the luminous intensity is the same in both, or that we have secured the 
greatest attainable equality (see, below, the discussion of the objections to 
Vierordt's method). We have then merely to read the division on the 
divided circle of the micrometer screw of the lower half of the slit. Supposing 
we find that the width of the lower slit is represented by division 20, whilst 
the width of the upper slit remains at 100, then the former number represents 
the percentage of unabsorbed light. We have seen that the extinction- 
coefficient e can be determined by the formula — 
e= — log /', where I' 
represents the unabsorbed light. By a table of logarithms, or more quickly by 
special tables, we find that in our case — 
e = - lot? -A9_ = loo- 100 - loe 20 
u >3 100 O O w " 
e = 0-69897 
As has been shown, having determined e, we may, if we know the precise 
proportion of colouring matter contained in the coloured solution, calculate the 
value of A ; or supposing that the substance is one of which the value of A 
has been determined, and that we are unacquainted with its concentration, we 
can ascertain the latter by the formula c — Az. 
Although Vierordt's method of determining the extinction-coefficient 
possesses historical interest, and its study is the natural introduction to that 
of the more perfect methods which have been suggested by it, it is open to 
serious objections, to the principal of which reference may here be made. 
However wide one slit may be, and however much the other may be 
narrowed, it is, in the case of solutions of high colorific intensity, most difficult, 
or impossible, to obtain by these means alone equality in the illumination 
of the spectra ; and accordingly Vierordt frequently had recourse to the use of 
smoke-tinted glass plates (Mauchgldser) of previously determined absorptive 
power, these being interposed in the path of the light which had not traversed 
the coloured solution. There are unquestionably theoretical and practical 
objections to this mode of proceeding. The principal objection to Vierordt's 
method is, however, a fundamental one, namely, that no absolute comparison 
is possible between spectra obtained with slits varying considerably in width. 
The more the slit of a spectroscope is widened, not only does the amount of 
light admitted increase and the spectrum become brighter, but the more and 
more impure does it become, i.e. the greater the admixture of light of different 
wave lengths in any region of the spectrum. But the accurate determination 
of the coefficient e is only possible with monochromatic light. It has been 
sought to diminish the error due to the cause just referred to by substituting 
for the original double slit of Vierordt one of which both edges move symmet- 
rically, so that the centre of the slit remains in a constant position. Although, 
doubtless, the error is reduced in this way, it is not entirely corrected. 
Although Vierordt's method of determining the value of the co-efficient e 
will probably fall in future into disuse, his great merit of having been the 
first to work out a method of spectrophotometry admitting of considerable 
accuracy, and of having discovered and established its applicability to the 
quantitative analysis of colouring matters, will always endure. 
Hiifner's method. — This method, which has been made more and more 
