E. A. (Edward Albert) Sharpey-SchÃ¤fer. # Text-book of physiology; (Volume v.1) online

. **(page 31 of 147)**

Online Library → E. A. (Edward Albert) Sharpey-SchÃ¤fer → Text-book of physiology; (Volume v.1) → online text (page 31 of 147)

Font size

Th. 1, S. 50.

^ "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. â€” 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 = â€” . 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." â€” 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 Â£ we represent

the extinction-coefficient,

1

'-d

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 OR Y 6- ME THODS OF SEE CTR OF HO TOME TRY. 215

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-

tinction-coefficient.

It was previously shown that /' = â€” and that s = ^, and when x = cl,

/' = tV Then log I' = -x log '^ and cl log ?i = 1 . â€¢. 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 Â£ = â€” 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

2

Â£ = â€” log ^ =r log 3 â€” log 2

= 0-176091

3. Definition of the term " ahsorption relation." â€” 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

2l6

H^AWGLOBIN.

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. â€” 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. â€” 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 â€” an upper one

and a lower one â€” 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. â€” 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

METHODS OF SPECTRO PHOTO METR Y.

217

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. â€” Glass troughs for containing the liquids

to be examined by the methods of spectro-

photometry. â€” After Kriiss.

Fig. 28. â€” Trough mounted on stand,

as used in spectrophotometry. â€”

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

a

\

J

Fig. 29. â€” Section of glass

trough with the Schulz-

'sclie Glaskorper, a, in situ

(schematic). â€” 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

2l8

HEMOGLOBIN.

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. â€” A spectrophotometer with absorption trough and lamp as

arranged for spectrophotometric determinations by Vierordt's

method.

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.

ME THODS OF SPE CTR OF HO TOME TRY. 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 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 formulaâ€”

e= -log /', where /'

represents the unabsorbed light. By a table of logarithms, or more quickly by

special tables, we find that in our case â€”

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. â€” This method, which has been made more and more

220 HEMOGLOBIN.

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 = â€” 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 : â€”

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) <^ =61Â°*87

Converting the decimal

fractions of a degree into

seconds (^ =61Â°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

HUFNERS SPECTROPHOTOMETER. 221

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.- â€” 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. â€” 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, â€” so that its centre remains constant.

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

222 HAEMOGLOBIN.

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. â€” Schematic representation of the path followed by the rays of

light before entering the slit of the collimator of Hiifner's spectro-

photometer. â€” 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

^ "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. â€” 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 = â€” . 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." â€” 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 Â£ we represent

the extinction-coefficient,

1

'-d

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 OR Y 6- ME THODS OF SEE CTR OF HO TOME TRY. 215

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-

tinction-coefficient.

It was previously shown that /' = â€” and that s = ^, and when x = cl,

/' = tV Then log I' = -x log '^ and cl log ?i = 1 . â€¢. 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 Â£ = â€” 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

2

Â£ = â€” log ^ =r log 3 â€” log 2

= 0-176091

3. Definition of the term " ahsorption relation." â€” 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

2l6

H^AWGLOBIN.

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. â€” 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. â€” 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 â€” an upper one

and a lower one â€” 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. â€” 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

METHODS OF SPECTRO PHOTO METR Y.

217

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. â€” Glass troughs for containing the liquids

to be examined by the methods of spectro-

photometry. â€” After Kriiss.

Fig. 28. â€” Trough mounted on stand,

as used in spectrophotometry. â€”

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

a

\

J

Fig. 29. â€” Section of glass

trough with the Schulz-

'sclie Glaskorper, a, in situ

(schematic). â€” 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

2l8

HEMOGLOBIN.

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. â€” A spectrophotometer with absorption trough and lamp as

arranged for spectrophotometric determinations by Vierordt's

method.

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.

ME THODS OF SPE CTR OF HO TOME TRY. 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 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 formulaâ€”

e= -log /', where /'

represents the unabsorbed light. By a table of logarithms, or more quickly by

special tables, we find that in our case â€”

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. â€” This method, which has been made more and more

220 HEMOGLOBIN.

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 = â€” 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 : â€”

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) <^ =61Â°*87

Converting the decimal

fractions of a degree into

seconds (^ =61Â°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

HUFNERS SPECTROPHOTOMETER. 221

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.- â€” 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. â€” 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, â€” so that its centre remains constant.

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

222 HAEMOGLOBIN.

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. â€” Schematic representation of the path followed by the rays of

light before entering the slit of the collimator of Hiifner's spectro-

photometer. â€” 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

Online Library → E. A. (Edward Albert) Sharpey-SchÃ¤fer → Text-book of physiology; (Volume v.1) → online text (page 31 of 147)