E. A. (Edward Albert) Sharpey-Schäfer.

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^ "Die Anwendung des Spektral-apparates zur Photometiie der Absorptionsspektren,"
Tubingen, 1873.

2 1 4 HyEMO GL OB IN.

1. Relation hchoeen the concentration of a solution and the percentage
of light aisorhecl hy it. — Before investigating the theory of the methods
of spectrophotometry, to be subsequently described, it is essential to
examine (1) the relation which exists between the power of light
absorption exerted by a coloured liquid of constant composition and the
thickness of the laj^^er traversed : (2) to study the influence of concen-
tration on the absorption of light by a stratum of a liquid holding a
colouring matter in solution.

It was shown by Lambert that if light of intensity /, by transmission
through one layer of an absorbing medium of thickness 1, has its in-
tensity reduced to /- = - by transmission through cl such layers, the
fnal intensity of the light, which we shall represent by /', will be re-
duced to - , i.e. T = — . Beer showed that Lambert's law holds good,

not only for transparent solid media, but also for liquids, i.e. that the
amount of light absorhecl hy a solution of a given colouriruj matter of con-
stant concentration is dependent upon the thickness of the stratum.'^ This
law is only true, hovjever, in respect to monochromatic light.

We must now examine the influence of the concentration of a liquid
containing a colouring matter in solution upon the percentage of light
which it absorbs and transmits, w^hen the stratum examined remains of a
constant width, 1. It has been experimentally proved that the absorp-
tion exerted by a stratum of a coloured solution of known width is
equal to that exerted by a stratum twice as thick of a solution of half
the concentration ; i.e. the absorption which light undergoes in passing
through a stratum of coloured liquid of unit thickness increases propor-
tionally to the concentration.

2. Definition of the " extinction-coefficient." — In their photo-chemical
researches, studying the comparative absorption of light by different
gases, Bunsen and Eoscoe- introduced the conception of, and defined,
the so-called extinction-coefficient. They ascertained the relative thick-
nesses of the strata of various media required to reduce the intensity
of light passed through them to one-tenth of its initial value, and defined
the extinction-coefficient as the reciprocal of the numher expressing the

' width of the stratum of a given medium, required to reduce the intensity of
light passed through it to one-tenth its initial value.

For any given coloured medium, e.g. a solution of a colouring matter
of a definite strength, there must be a definite thickness of layer which
we shall call d, capable of reducing the intensity of light to one-tenth

its original value. The reciprocal of d is -r, and if by £ we represent

the extinction-coefficient,

As will be shown in the sequel, the method of spectrophotometry
discovered by Vierordt rests upon the determination of this constant g,
for particular, very limited, regions of the spectrum. The practical diffi-
culties of varying the thiclcness of the stratum of a coloured liquid, until

^ When the thicknesses of various strata increase in arithmetical, the intensities of
the light decrease in geometrical, ratio.

- Ann. d. Chem., Leipzig, 1S57, Bd. ci. S. 238.


the intensity of the light remaining unabsorbed is reduced precisely to
one-tenth, would be extremely great. Fortunately, the coefficient of
extinction can be determined in a manner presenting far smaller practical
difficulties and admitting of great accuracy.

If, instead of varying the thickness of the stratum of the coloured
solution until the initial intensity of the light entering it is reduced to
one-tenth its value, we invariably examine in our photometric investi-
gations a stratum of unit width (say 1 cm.), or a stratum of known
width, and possess the means of estimating the proportion of light which
remains unabsorbed, we possess data enabling us to calculate the ex-

It was previously shown that /' = — and that s = ^, and when x = cl,

/' = tV Then log I' = -x log '^ and cl log ?i = 1 . •. 2 = log n = ;

so that, if the thickness of the stratum traversed by the light be known,
and the intensity of the unabsorbed light /' ascertained, the coefficient
s can be calculated. But if x be of the constant value 1 (say 1 cm.),
then £ = — log /'; that is to say, the extinction-coefficient is equal to the
negative logarithm of the unahsorled light. Let us suppose that by pass-
ing through a stratum of coloured solution 1 cm. wide, the intensity of
light has been reduced to two-thirds its original value, then

£ = — log ^ =r log 3 — log 2

= 0-176091

3. Definition of the term " ahsorption relation." — It has already been
stated (see previous page) that the more concentrated a coloured liquid,
the greater its absorbing power, the smaller, therefore, is the width of
the stratum required to reduce the intensity of the light passed through
it to one-tenth of its initial value. As the extinction-coefficient is, by
definition, the reciprocal of the thickness of the stratum required to
bring about this result, it follows that the greater the concentration of
the solution, the greater will be the extinction-coefficient ; in other words,
the extinction-coefficient g and the concentration c are proportional.
Let c and c' represent the concentration of two coloured solutions, of
which the extinction-coefficients are s and s' respectively, then

c : z = c' : z
and - = _ = ^

i.e. the relation of the concentration of a coloured solution to its extinction-
coefficient is a constant, represented hy A, and termed the "Absorption-
relation " {Absorptionsverhdltniss, Vierordt). Upon the determination of
this constant rests Vierordt's method of quantitative spectrophotometric
analysis. If we have, in the case of a solution of a particular body,
determined by analysis its concentration c, and then with the spectro-
photometer determined its extinction-coefficient for a particular spectral
region, and thus obtained the value of A, we can find out how much
of the same substance is contained in a solution of unknown strength
(c') by merely determining g', according to the equation :

d = Ai



It is usual to determine the value of the constant A of any coloured
body under examination for, at least, two spectral regions. The reasons
for this practice will appear in the sequel.

(b) The actual methods of spectrophotometry. — The elementary theo-
retical discussion of the theory of spectrophotometry which has preceded has
shown that, as developed by Vierordt, it resolves itself into the determination
of the extinction-coefficient and of the absorption relation of coloured bodies,
and that the optical investigation is concerned with, and confined to, the
determination of the value of e. We have now to consider the two principal
methods by which this determination can be effected.

Vierordfs method. — For the determination of the extinction-coefficient
according to the original method of Vierordt, any good spectroscope of the
type introduced by Eunsen for laboratory purposes may be employed, provided
certain modifications and additions are made. The most essential of these
modifications consists in replacing the usual single slit of the collimator by a
double slit, i.e. by a slit composed of two independent halves — an upper one
and a lower one — each of which is controlled by a micrometer screw provided
with a divided circle or drum, so that the width of each half of the slit may
be ascertained by direct reading (see Fig. 26). In so-called symmetrical slits,

Fig. 26. — Double slit employed in Vierordt's method of spectrophoto-
metry, as adjusted to their spectrophotometers hy the Brothers
Kriiss of Hamburg.

both edges of the slit move symmetrically. When the two halves of such a
slit are of the same width, if the illumination be uniform, the observer, on
looking through the telescope of the spectroscope, observes two superposed
spectra of equal brightness. If one slit be narrower than the other, the
illumination of the corresponding spectrum will be diminished in proportion.

The second modification which has to be made in the ordinary spectro-
scope consists in substituting for the usual eyepiece, one which is provided
with a slit for isolating any desired region of the spectrum, the remainder of the
spectrum being concealed from view. In Vierordt's original instrument this slit
was formed by two lateral shutters, moving in the focal plane of the eyepiece,
which could be approximated to any desired extent. This simple contrivance
has been perfected by Hiifner, and adapted to his beautiful spectrophotometer.
A very ingeniously contrived and readily adjusted slit has been devised by the
Brothers Kriiss of Hamburg, and adapted to the spectrophotometers made by



their firm. Whatever the precise form of the slit in the eyepiece, it must
permit of the isolation of a perfectly defined spectral region, and of the precise
determination of the limits of that region, these being expressed in Avave
lengths.! For all coloured solutions there are regions in which the absorption
of light is peculiarly distinctive, and which are specially favourable to the
determination of the coefficient of extinction. In the case of oxyhajmoglobin,
Hiifner has in his most recent researches selected a part of the region
between the two absorption-bands (A. 550-A, 540) and a part of the region
lying within the second band (X .542-5-A. 531-5).

There remains to be described an absolutely essential accessory to the
spectroscope, without which it would be impossible to determine the spectro-
photometric constants. This is a specially contrived glass trough, for holding
the solutions to be investigated, the anterior and posterior walls of which
are formed by two perfectly parallel glass plates. Two forms of this trough
are shown in Fig. 27, whilst Fig. 28 exhibits a trough mounted on its

Fig. 27. — Glass troughs for containing the liquids
to be examined by the methods of spectro-
photometry. — After Kriiss.

Fig. 28. — Trough mounted on stand,
as used in spectrophotometry. —
After Kriiss.

stand, the stand permitting of the trough being
lowered or raised, and of its being accurately levelled.
The inner surfaces of the parallel glass plates of the
little trough are exactly 11 mm. apart. A glass
cube (called after the person who suggested its use,
der Schuh'sche Glaslwrper) exactly 10 mm. broad,
and half the height of the interior of the trough,
rests on the floor of the latter, so that the anterior
and posterior surface of the cube shall be parallel
with the glass plates of the trough (Fig. 29). When
the coefficient of extinction of a coloured liquid is
to be determined, such a trough is filled with it.
When light passes through the lower half of the
trough, it must traverse a stratum of coloured liquid
1 mm. in thickness, whilst light passing through
the upper half traverses a stratum 11 mm. thick

easily and gradually




Fig. 29. — Section of glass
trough with the Schulz-
'sclie Glaskorper, a, in situ
(schematic). — After Kriiss.

In the latter case, the light is subjected to the absorbing action of a layer of

^ Tlie reader who wishes to understand the details which are necessary for practical
work in spectrophotometry is advised to read in the first instance a useful, indeed almost



coloured liquid 1 cm. broader than that which is contained in the lower half
of the trough, and this is for spectrophotometric purposes exactly equivalent
to interposing a stratum 1 cm. broad in the path of the light impinging on one
(the upper) half of the slit, and no coloured liquid in the path of the light
reaching the other half.

Spectrophotometric measurements are invariably made by the aid of artificial
light. Hitherto, oil or petroleum lamps have been used for this purpose, but
lately Hiifner has adopted a gas lamp fitted with an Auer incandescent burner.

We are now in a position to complete our explanation of Vierordt's
method. We shall assume that a spectrophotometer, such as has been
described, is at the disposal of the observer. The lamp is lighted and the
height of the flame adjusted, so as to equally illuminate the two halves of the
double slit ; this is seen to be the case when with equal widths of the slits
two superposed spectra of exactly equal brightness are seen. The two
halves of the slit are then opened to the extent which is thought advisable ;
we shall, for convenience of description, suppose that they have been opened
to the extent represented by the index on the two divided circles of the
micrometer screws, pointing to the division 100. The observer then arranges
the slit in the eyepiece, so as to isolate and measure precisely the region of
the spectrum for which he desires to determine the coefficient of extinction.
In the case of haemoglobin, of oxyhsemoglobin, and of CO-hsemogiobin, he will
select for his observations one of the two regions which have been shown by
Hiifner to be specially favourable to the determinatiou, and in which he has
determined the constants which he distinguishes as Aq and A'o respectively.

Fig. 30. — A spectrophotometer with absorption trough and lamp as
arranged for spectrophotometric determinations by Vierordt's

This operation having been effected, he will again observe whether the two
limited spectral areas appear to be of precisely equal brightness. If this is
the case, the trough containing the coloured liquid is brought in front of the
double slit, and the height of the former is carefully adjusted, so that the
upper border of the glass cube appears as a line exactly coinciding with the
separation between the upper and the lower spectral strips.

indispensable, book by Dr. Gerliard Kriiss and Dr. Hngo Kriiss, entitled " Kolorimetric
und quantitative Spektralannl\-se, etc.," Hamburg u. Leipzig, 1891. Though specially
written for those who intend to work with Hiifner's instrument, an accurate though very
succinct account of spectroj)hotometry is contained in a pamjihlet entitled " Anleitung
zum Gebrauche des Hlifuer'scheu Spectrophotometers, etc.," von Eugen Albrecht, Uuiver-
sitixts-Mechaniker in Tiibiugeri : Tubingen, 1892. Subsequently, all Hiifner's papers on
spectrophotometry should be studied.


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 great 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 be excessive, we can
restore the equality of illumination of the two superposed spectral areas by
narrowing the lower slit. This is done 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 /'

represents the unabsorbed light. By a table of logarithms, or more quickly by
special tables, we find that in our case —

e= _ log Jy>^ =log 100 -log 20
c = 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 J. ; 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 = A(..

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 {RaucligW ser) 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 A^ierordt'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
ciuantitative analysis of colouring matters, will always endure.

Hilfner^s method. — This method, which has been made more and more


efficient by the long-continued labours of its author, differs from Vierordt's in
the mode by which the equalisation of the intensity of two beams of light is
brought about, the difference in mode requiring a spectrophotometer which
differs in important respects from the instrument already described.

In Hiifner's spectropliotometer there is a smgle slit, the width of whicJi.
after it has been once adjusted, is never varied.

The light which reaches one-half of this slit has been polarised by a small
Xichol's prism (the polariser), whilst that which reaches the other half (Avhich
in the determination of the value of e passes through the thicker stratum of
coloured liquid) is unpolarised. When these two beams of light fall upon the
refracting prism of the spectroscope, they are refracted and furnish two super-
posed spectra, of which that corresponding to the polarised beam is naturally
much less intense than the other. Before making any observations of e, the
two sjDectra must be equalised, this being done by interposing a wedge of
smoke-tinted glass in the path of the unpolarised beam. Equality of both
spectra having been obtained, if a coloured medium be placed in the path of
the unpolarised beam, its spectrum will be correspondingly reduced. Equality
is, however, restored by rotating a second Xichol s prism (the analyser) which
is in the path of the beams issuing from the refracting prism, and the rotation
of which diminishes the intensity of the polarised beam alone. When equahty
in the illumination of both spectra has been restored, the angle (<^), through
which the analysing Xichol has been rotated, is measured in two opposed
quadrants of a divided circle provided with a vernier, and from the value of
that of /' is calculated.

If the original intensity of the light =1, and the intensity of the un-
absorbed light which has traversed the coloured medium be represented by
/', then

/' = cos^c^ ;

If the layer of coloured liquid investigated be always = 1 {e.g. 1 cm.), then

as e = — log /',

e= - log COS^e^

The following example will illustrate the mode of procedure and the steps
of the calculation in an actual experiment for the determination of the ex-
tinction-coefficient of blood, carried out with Hiifner's spectrophotometer : —

1 c.c. of defibrinated blood of the ox was diluted to 160 c.c. with a 0"1
per cent, aqueous solution of ]S[a(OII). The absorption-trough was filled with
some of the perfectly clear red liquid thus obtained. The spectral region (?'),
for which e was determined, was one of the two in which Hiifner has, in his
most recent experiments, determined the constant A of oxyhsemoglobin {i.e.
a portion of the region between the bands a and /3 of oxyhsemoglobin).

r = A557-o-A568-7
(Mean of ten measurements) <^ =61°*87
Converting the decimal

fractions of a degree into

seconds (^ =61°52'

It has been stated that with Hiifner's spectrophotometer

/' = cos^e^
and e = - log cos-<^

In the above experiment

c= - log COS-6F52'
"= -2 logcos6r52'
"= -2 (0-67350-1)
"= -1-34700-1-2
" = 0-653


Hiifner's spectrophotometer is an instrument of so much importance to the
physiologist who intends to work at spectrophotometry, that a short descrip-
tion of the arrangements of its several parts appears desiraljle.

The instrument as a whole, as well as the stand carrying the absorption-
trough and the lamp, are shown in Fig. 31.

Fig. 31.- — Hiifner's spectrophotometer, as made by Albreclit.

The spectrophotometer, the stand for the trough, and the lamp, rest upon
the optical bench Avhich forms the base for the whole. The position of the
siDectrophotometer is constant ; the trough-stand and the lamp move along a
slide, and can be placed at any required distance. During the actual experi-
ment, the anterior edge of the trough is in close contact Avith the anterior part
of the collimator. The lamp (which in the models recently and at present
constructed is a gas lamp provided with an Auer incandescent burner) is
for actual work placed at a distance of 24 to 25 cms. from the distal end of the
collimator. The lamp is fitted with a positive lens the focus of which is
made to correspond with the brightest part of the flame, so that perfectly
parallel rays fall upon the absorption-trough. The latter is in all respects
similar to the one used in Vierordt's method.

Turning our attention to the spectrophotometer, see Fig. 31, it is seen to be
composed of a three-footed stand, furnished with levelling screws, the stand
supporting the platform on which is fixed the dispersing prism, Avhich is
enclosed in a metallic case. To the right is seen the collimator and to the left
the telescope.

1. The collimator. — This is furnished with a single slit formed by the
edges of two slides moving transversely, each of which possesses its own
micrometer screw, furnished with an accurately divided drum. This arrange-
ment enables a slit of a precisely known width to be obtained, and the slit can
be widened or narrowed symmetrically, — so that its centre remains constant.

Unlike ordinary spectroscopes, Hiifner's spectrophotometer has, fixed to the


front of the slit, a metallic box enclosing the following optical parts. (In order
to facilitate our description, these are shown in the following diagram, Fig. 32,

Fig. 32. — Schematic representation of the path followed by the rays of
light before entering the slit of the collimator of Hiifner's spectro-
photometer. — After Krilss.

which indicates also the path of the rays passing through the glass trough
containing the coloured solution.)

Placed centrally, in the position shown in the diagram, is an oblique parallel-
opiped of flint glass, with two of its diagonally-opposed angles in a line with
the optic axis of the collimator. This admirable optical contrivance (which
is known in Germany after the optician who devised it as " der Albrecht'sche
Glaswiirfel oder Glaskorper") refracts light falling on its two anterior faces

Online LibraryE. A. (Edward Albert) Sharpey-SchäferText-book of physiology; (Volume v.1) → online text (page 31 of 147)