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Claims  |
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We claim:
1. A method of determining particle size distribution with respect to
fraction classes in the direction of flow in a flowing medium containing
particles comprising the steps of:
establishing a plurality of measuring configurations for illuminating
portions of said medium containing a plurality of particles and detecting
light transmitted through said portions of said medium containing said
plurality of particles, each of said plurality of measuring configurations
exhibiting a different resolution for illuminating portions of said medium
and detecting light transmitted therethrough representing differing
cross-sectional portions of said medium, each differing cross-sectional
portion of said medium containing a plurality of particles;
illuminating a portion of said medium containing a plurality of particles
through one of said plurality of measuring configurations and detecting
light transmitted through said portion of said medium containing said
plurality of particles;
converting light detected from said one of said plurality of measuring
configurations into a first measuring signal representative of the
plurality of particles within said cross-sectional portion represented by
said one of said plurality of measuring configurations;
illuminating a portion of said medium containing a plurality of particles
through another of said plurality of measuring configurations and
detecting light transmitted through said portion of said medium containing
said plurality of particles;
converting light detected from said another of said plurality of measuring
configurations into a second measuring signal representative of said
plurality of particles within said cross-sectional portion represented by
said another of said plurality of measuring configurations; and
determining the particle size distribution by employing first and second
measuring signals from said measuring configurations obtained during a run
of said medium and sensitivity coefficients of said measuring signals,
each of said coefficients being dependent upon a measuring configuration
of a fraction class.
2. The method defined in claim 1, further comprising the step of
determining the sensitivity coefficients of the measuring signals for the
selected fractions and the measuring configurations by passing and
measuring a number of said fractions each of which is representative of
one of the fraction classes into which the fraction range is divided
through all measuring configurations.
3. The method defined in claim 1, further comprising the steps of
determining the sensitivity coefficients of the measuring signals for
selected fractions and the measuring configurations by passing and
measuring a number of samples with known fraction composition through all
measuring configurations.
4. The method defined in claim 1, further comprising the step of choosing
an indication of the measuring signals by allotting during a measuring of
a medium with a standardized desired composition the values obtained for
the different fraction classes with predetermined values.
5. The method defined in any of claims 2, 3, 4, or 1, further comprising
the steps of forming and squaring an effective value of an alternating
current voltage portion of the measuring signals received from each of the
measuring configurations.
6. The method defined in claims 2 or 3, further comprising the steps of
forming and squaring at the obtaining of the sensitivity coefficients of
the measuring signals the effective value of an alternating current
voltage portion of the signal received from each of the measuring
configurations, and forming the direct current voltage portion from each
of the measuring configurations obtained at the running of samples
representative for one of the fraction classes, each of these values
obtained comprising the basis for calculating one of the sensitivity
coefficients.
7. The method defined in claim 1, further comprising the step of
linearizing the measuring signals with respect to concentration, whereby
the equations used for deducing the weight proportion of particles in
every class becomes linear.
8. The method defined in claim 7, wherein said linearization step comprises
forming a linearized effective value signal according to the formula
##EQU6##
where V.sup.2 RMS is the square of the effective value of an alternating
current voltage signal from a first light detector, V.sub.DC(0.degree.)
and V'.sub.DC(0.degree.) are the direct current voltage portion of the
signal from the first detector obtained during a measuring of a medium
with suspended substances and during a measuring of a medium without
suspended substances respectively, and c.sub.2 is a constant.
9. The method defined in claim 8, further comprising the step of obtaining
values of the weight proportion of particles in the selected fraction
classes expressed in percent of the total particle concentration in the
medium for each measuring configuration by dividing the alternating
current voltage signal by lnV'.sub.DC(0.degree.) /V.sub.DC(0.degree.).
10. The method defined in claim 8, further comprising the steps of
obtaining values of the weight proportion of particles in the selected
fraction classes expressed in percent of the total particle concentration
in the medium for each measuring configuration by indicating light emitted
from the medium in a definite direction different from the optical axis
using a second light detector, forming a linearized direct voltage signal
according to the formula
##EQU7##
where V.sub.DC(0.degree.) is the direct current voltage portion obtained
during a measuring of a medium with suspended substances at the angle
0.degree., V'.sub.DC(0.degree.) is the direct current voltage portion
during a measuring of a medium without suspended substances of the signal
from the first light detector, V.sub.DC(.theta..degree.) is the direct
current voltage portion at the measuring of a medium with suspended
substances at the angle .theta..degree., V'.sub.DC(.theta..degree.) is the
direct current voltage portion obtained during a measuring of a medium
without suspended substances of the signal from a second light detector,
and c.sub.1 is a constant and forming for each measuring configuration the
quota between the linearized alternating voltage signal and the linearized
direct voltage signal.
11. The method defined in claim 7, further comprising the step of forming
for each measuring configuration a signal according to the formula
##EQU8##
where V.sub.AC is a linearized alternating current voltage signal,
V.sub.DC is a linearized direct current voltage signal, and .alpha. .beta.
.delta. .rho. are constants, the values obtained for said signals
comprising the starting values from which the weight proportion of
particles in every selected class is indicated.
12. The method defined in claim 1, wherein said determining step comprises
using an equation system for calculating the weight proportion of
particles in the given fraction classes of the type K=A.sup.-1 or
K=(A.sup.T A).sup.-1 A.sup.T U, where A is a matrix, in which the elements
of said matrix A are the sensitivity coefficients of an alternating
current voltage and direct current voltage signal for the different
measuring geometries represented as rows of said matrix A and length
fractions represented as columns of said matrix A measured on the
fractions, which are representative of the fraction classes required,
A.sup.-1 is the inverted matrix A, A.sup.T is the transposed matrix A, U
is a column matrix where the elements are linearized alternating current
voltage values from each of the measuring geometries during measurings of
the suspension, the content of which is to be divided into classes, and
where U is a column matrix where the elements are the wanted
concentrations or the wanted percentages for the different length fraction
classes.
13. The method defined in claim 1 further comprising the steps of making
calculated values of weight proportion of particles in the selected
fraction classes in a coordinate system with the fraction along the
abscissa and the particle along the ordinate in such manner that
predetermined fractions of the calculated values for each fraction class
are marked in a predetermined place along the abscissa within each
fraction class, and calculating, using knowledge of the general appearance
of the fraction distribution plot in a coordinate system, a curve for the
medium with the unknown fraction composition.
14. The method defined in claim 11, wherein said determining step comprises
individually calculating the alternating current voltage values or the
alternating current voltage values divided by respective direct current
voltage values, deriving the values of the fractions within the respective
classes by using said values calculated in said previous step, forming the
signal T.sub.F for every measuring configuration by using a suitable
choice of constants .alpha., .beta., .delta., .rho., marking an indication
along an abscissa within the respective classes a predetermined fraction
of the values for the fractions for each class along the ordinate in a
coordinate system with the fraction along the abscissa and the particle
amount along the ordinate, and calculating, by using knowledge of the
general appearance of the fraction distribution plot in a coordinate
system, a curve for the medium with the unknown fraction.
15. Apparatus for indicating particle size distribution with respect to
fraction classes in a flowing medium containing said particles, said
apparatus comprising:
measuring configuration means for illuminating a plurality of portions of
said medium and for detecting light transmitted through each of said
plurality of portions of said medium to provide a plurality of measuring
signals, each of said plurality of portions of said medium illuminated
containing a plurality of particles and being illuminated and having light
detected therefrom by said measuring configuration means to cause light
detected from each of said plurality of portions to exhibit differing
light resolutions corresponding to a different cross-sectional area for
each portion and differing fields of vision and different sensitivity
coefficients relative to one another; and
means responsive to said plurality of measuring signals obtained during a
passage of said medium through said measuring configuration means and said
sensitivity coefficients for determining the particle size distribution of
said medium with an unknown particle composition for each of said fraction
classes, each of said sensitivity coefficients being dependent upon the
manner in which each of said plurality of portions of said medium is
illuminated by said measuring configuration means and the fraction classes
associated therewith.
16. The apparatus defined in claim 15, wherein said measuring configuration
means comprises a measuring unit including a light source element, an
optical element, a diaphram element and a detector element, at least one
of said elements being adjustable or exchangeable to provide said
differing resolutions.
17. The apparatus defined in claim 15, wherein said measuring configuration
means comprises individual measuring units located in a side by side
relationship, each of said plurality of measuring configuration means
including a light source, a detector and optics located between said
source and said detector.
18. The apparatus defined in any one of claims 16, 17, or 15, further
comprising a cylindric bulb for conveying said medium, said bulb having an
axis of symmetry and walls transparent to light emitted by said measuring
configuration means, said measuring configuration means including a light
source and means to focus the light from at least said light source on the
axis of symmetry of the bulb.
19. The apparatus defined in any one of claims 16, 17, or 15, further
comprising a bulb for conveying said medium, said bulb having plane
sidewalls perpendicular to the direction of light emitted by said
measuring configuration means, said light means including optical means
for illuminating the bulb with collimated radiation.
20. The apparatus defined in claim 15, wherein said for determining means
comprises a calculation and linearization circuit responsive to detected
light transmitted through said medium.
21. The apparatus defined in claim 15, wherein said means for determining
comprises first memory means for storing sensitivity coefficients of the
measuring signals, second memory means for temporarily storing values
representative of the measuring signals obtained during a passing of a
medium having unknown fraction composition through all said measuring
configuration means, and calculation unit means responsive to contents in
said first and second memory means for calculating a required indication
of the fraction composition.
22. The apparatus defined in claim 21, wherein said first memory means
comprises a fixed memory.
23. The apparatus defined in any one of claims 16 or 17, further comprising
means for filtering out a direct current voltage portion of a signal
resulting from detecting the light transmitted through said medium.
24. The apparatus defined in claim 20, wherein said measuring configuration
means comprises a detector means for detecting light transmitted through
said medium, said detector means and said calculation and linearization
circuit having a DC filter coupled therebetween, the calculation and
linearization circuit carrying out a calculation according to the formula
##EQU9##
where V.sub.RMS is the true effective value of the alternating current
portion of the output signal from the detector means, V.sub.DC(0.degree.)
.gamma. and V'.sub.DC(0.degree.) .gamma. are the direct voltage portion of
the signal from the detector means during the measuring of a medium with
suspended substances and at the measuring of a medium without suspended
substances respectively, and c.sub.2 is a constant, said calculation and
linearization circuit including a memory means for storing values of
.gamma. and V'.sub.DC(0.degree.).
25. The apparatus defined in claim 24, wherein the linearization and
calculation circuit additionally acts to carry out a division by 1n
V'.sub.DC(0.degree.) /V.sub.DC(0.degree.).
26. The apparatus defined in claim 24, further comprising an additional
detector for indicating light scattered from the medium in a direction
apart from an axis along which the transmission of light through the
medium occurs, and circuit means for filtering a direct voltage portion of
the signal from said additional detector, which portion is fed to said
calculation and linearization circuit, said calculation and linearization
circuit carrying out the calculation
##EQU10##
where V.sub.DC(0.degree.) and V'.sub.DC(0.degree.) are the direct voltage
portions of the signal from the detector means during the measuring of a
medium with suspended substances and a medium without suspended
substances, respectively, V.sub.DC(0.degree.) and V'.sub.DC(0.degree.) are
the direct voltage portion of the signal from the additional detector
during the measuring of a medium with suspended substances and a medium
without suspended substances, respectively, and c.sub.1 is a constant, and
said calculation and linearization circuit including a memory for the
storage of values for V.sub.DC(0.degree.) and V'.sub.DC(0.degree.).
27. The apparatus defined in claim 26, wherein the calculation and
linearization circuit additionally acts to carry out a division between
the first and second formulas recited.
28. The apparatus defined in claim 24, wherein the linearization and
calculation circuit carries out the calculation
##EQU11##
where V.sub.AC is the linearized alternating voltage portion of said
signal, V.sub.DC is the linearized direct voltage portion of said signal,
and .alpha., .beta., .gamma., .sigma. are constants.
29. The apparatus defined in claim 21, wherein said calculation unit means
uses the calculated values of the fraction content in different fraction
classes and the general appearance of a distribution function stored in
the calculation unit to calculate the fraction distribution curve for a
medium with unknown fraction composition.
30. Apparatus for determining the particle size distribution with respect
to fractional classes in a flowing medium containing said particles, said
apparatus comprising means for illuminating portions of said medium
containing a plurality of said particles, means for converting into a
measuring signal light transmitted through said medium, said converting
means including first and second light detectors disposed at different
angles with respect to said means for illuminating portions of said medium
containing a plurality of said particles and said medium, and means for
imparting a plurality of resolutions to light transmitted through said
medium and detected by at least one of said first and second light
detectors, each of said plurality of resolutions corresponding to a
different cross-sectional area for portions of said medium illuminated and
each different cross-sectional area containing a portion of said medium
containing a plurality of said particles.
31. The apparatus defined in claim 30, wherein said means for illuminating
comprises a light source and said means for imparting takes the form of a
rotating disc having a plurality of different size holes, whereby said
plurality of resolutions are achieved.
32. The apparatus defined in claim 30, wherein said means for illuminating
comprises a plurality of light sources and said means for imparting takes
the form of diaphram means for each of said plurality of light sources,
each of diaphram means having different beam widths, whereby said
different resolutions are achieved. |
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Claims |
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Description |
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This invention relates to methods for determining particle size
distribution, and to apparatus for carrying out such methods.
The invention can be utilized for indicating the distribution of the
extension of particles in the flow direction in flowing media, which
contain particles, for example fibres, when it is desired for some reason
to know the distribution of the particles in different size fractions. A
special application field for the method is the measuring of fibre
suspensions, which are used as starting material for the manufacture of
paper. The method, therefore, is described in the following with reference
particularly to the measuring of paper pulp.
It applies to paper pulps of all types, for example mechanic pulps or
chemical pulps, where the fractional composition of the pulp is of
decisive importance for the properties of the paper to be manufactured. A
higher proportion of long fibres, for example, results in an increase in
strength. This rule, however, cannot be applied generally. For mechanical
pulps, for example, not only is the content of long fibres of importance,
but also the size distribution of the fibres in general. In order to
obtain a pulp with paper-technical prerequisites, all fractions of the
pulp must have good properties. In the case of mechanical pulps a varying
proportion of fibre material in the so-called medium fraction of the pulp
often has proved to give rise to varying properties of the resulting
paper. It was, therefore, found desirable to develop a method, by which
the content of at least three different fraction classes in the pulp, for
example fine, medium and long fibre fraction, can be determined.
The same applies in a corresponding way to many chemical pulps, for example
sulphite and sulphate pulp. Pulps of this kind should contain a high
proportion of flexible long fibres and a fine material with binding
tendency. This is obtained automatically, for example, for fully bleached
unbeaten sulphate cellulose, as a consequence of the native properties of
the wood, but the fraction composition of the fibrous suspension can be
less favourable for chemical pulps of higher yield or for beaten low-yield
pulps. Such pulps, therefore, require an increased control of the fraction
composition, to render it possible to promptly detect deviations of the
composition from the desired values so that the necessary corrective steps
may rapidly be taken.
Heretofore, the proportions of different desired fractions were determined
by taking a sample of the suspension.
The sample was then screened for the purposes of separating the different
fractions from one another and thereafter the fractions dried and weighed.
It is apparent that such a procedure is both expensive and especially
slow; however, the same yields relatively accurate results. For some time
now it has been desired to find a method for determining the proportions
of desired fractions, which is safe and can be carried out quickly and
preferably on a continuous basis. This desire now has been realized with
the present invention. The method can be used both for providing a warning
signal when the fractional proportions measured are not within
predetermined limit values, and for effecting automatic adjustment of some
element in the pulp manufacture, as for example adjustment of the beating
discs during the manufacture of refined pulp.
The invention is based upon the basic signals utilized in the concentration
determination method described in Swedish Pat. No. 7706320-4 corresponding
to U.S. Pat. No. 4,110,044, where a method of obtaining a measure of the
concentration of particles suspended in a liquid is disclosed. In this
patent a method is described, according to which fraction distribution in
a suspension is measured independent of concentration of fibre and also
independent of light absorption in the liquid, in which the fibres are
suspended. According to this patent the measuring result will only give
information of the distribution of the amount (in MG/L) of long fibres in
relation to the amount of short fibres in a suspension. This means that
the method described in this patent is not intended to give a measure of
the amount of fibres for a predetermined fraction. The measure is
independent of the particle size distribution in the suspension and a
signal is produced which varies linearly with the concentration. According
to the teachings of this patent application, a signal is linearized which
contains the square of the true effective value of the alternating voltage
portion of a signal from a detector, which detects light having been
projected through a suspension. Further a direct voltage signal is
linearized which is obtained by a combination of the direct voltage
portion of signals from a detector preferably located in 0.degree. , or
from two detectors located in different angular positions relative to the
path of the light in the suspension. The linearization takes place with
respect to the concentration. Variations in the sensitivity of the two
signals, which hereinafter are called alternating voltage signal and,
respectively, direct voltage signal are counterdirected with respect to
the mean fibre length. In order to obtain a measure of the concentration
independent of the fractional composition, in the Swedish Pat. No.
7706320-4, as mentioned, the alternating voltage signal and the direct
voltage signal are linearized individually and given such inclinations,
that the linearized signals when being added together have an equal
sensitivity coefficient, i.e. the concentration measure is independent of
the particle size distribution in the suspension.
As investigations of the two signals continued it was found, that the
outgoing signals from the measuring unit comprising the detectors varied
with the measuring geometry. The term measuring geometry here is
understood to refer both to the location of the components and to their
size and design, i.e. for example the surface of the detectors, the focal
length of the lens system present in the measuring unit, the area of
diaphragm utilized, the cross-section of the light beam and the physical
dimensions in general. It was thereby found, that it is particularly the
shape of the alternating voltage signal which is influenced by the
measuring geometry, while the direct voltage signal substantially is
influenced only by the geometry through a multiplicative constant, which
is independent of the mean fibre length of the fibre material.
These physical conditions are utilized according to the present invention,
which is described in greater detail in the following, with reference to
the accompanying drawings, in which:
FIG. 1 is a diagram of different alternating voltage signals,
FIG. 2 is a diagram of different direct voltage signals,
FIG. 3 shows a first embodiment of apparatus for carrying out the method
according to the invention, and
FIGS. 4a-4c show a second embodiment of apparatus for carrying out the
method according to the invention wherein FIG. 4a illustrates such second
embodiment per se and FIGS. 4b and 4c show the cross-sections of exemplary
measuring bulbs used therein.
In FIG. 1 the sensitivity of the alternating voltage signal is shown as a
function of the mean fibre length of the fibre fraction for three
different measuring geometries, where of course the concentration of the
suspension was maintained constant.
In FIG. 2 the sensitivity of the direct voltage signal is shown as a
function of the mean fibre length of the fibre fraction for three
different measuring geometries, also at constant concentration. The curves
designated by 1 are recorded with high resolution, i.e. small diaphragm
dimension, small detector surface or the like, and the curves designated
by 2 are recorded with low resolution. When the flow through the measuring
bulb is accelerated, the fraction-selective procedure is more distinct at
curve 1 in FIG. 1, due to the fact that the long fibres are aligned in the
flow direction. It is, therefore, suitable to use a bulb with a
cross-sectional area, which is smaller than that of the passageway used
for flow through by the suspension, in order to obtain an accelerated flow
through the bulb. The circumstance that it is just the alternating voltage
signal, which changes in the way shown in FIG. 1, will be understood when
it is realized, that at a finer resolution the detector senses a portion
with a smaller cross-section of lighted material in the liquid.
Conclusively, for covering the entire detection area in the longitudinal
direction fibres with a shorter length are required than at a lower
resolution, i.e. when the detector detects a greater cross-section of
lighted material in the liquid. Therefore, the curve for high resolution
proceeds faster to a constant value with increasing fibre length than the
the curve for low resolution. The alternating voltage portion of the
signal from the detector does not provide extra information on fibres
exceeding a certain length. The alternating voltage signal, thus, is
directly associated with the fibre length.
When a system is to be obtained, which shall render the equivalent content
in a number of fraction classes desired to be measured, the dependence of
the alternating voltage signal on the measuring geometry can be utilized.
By disposing the matrices below and solving the equation system
represented by them, the elements in K will represent the equivalent
content of fibres expressed preferably in mg/l of the predetermined length
fraction classes, i.e.
A K=U (1)
where the elements in the matrix A are the sensitivity coefficients
a.sub.ij for the different measuring geometries (rows) and length
fractions (columns), and where i stands for geometry and j stands for
length fraction. The elements in a row in the matrix A possibly may
consist of the sensitivity coefficients of the DC-signals. The elements in
the matrix K are the concentrations to be found of the different length
fraction classes. The matrix K is a column vector. The elements in the
matrix U are the linearized alternating voltage values from each of the
measuring geometries at measurements of the suspension, the content of
which is to be divided into classes. The matrix U is a column vector.
The input data obtained practically from the measurements, of course, will
be impaired by certain measuring errors. It is, therefore, very important
to use equations, which linearly are as independent as possible. In
practice, therefore, it is not suitable to directly solve a system with
measuring errors according to equation (1), but this equation is shown
only for illustrating the principle. The equation system in practice
should be built up, for example, according to the method of least squares.
When the matrix A is chosen non-square (redundancy system), the method of
least squares can be applied advantageously. The equation (1), therefore,
according to known mathematic methods should be converted to:
##EQU1##
Now the sensitivity coefficients a.sub.ij are to be found. An accurate
method in this respect is to pass fractions, which are representative of
each class and have known concentrations, through all measuring
configurations, and to repeat this until fractions representative of all
classes have been passed through. If, namely, a sample with mixed fraction
content is passed through one of the measuring configurations, the i:th
one, the following equation for the signal obtained can be drafted:
U.sub.i=conc.sub.1 a.sub.i1+conc.sub.2 a.sub.i2+ . . . +conc.sub.n a.sub.in
where conc.sub.1 is the concentration fibre content in the first class, and
conc.sub.n is the concentration fibre content in the last class. The
different coefficients a.sub.ij, thus, are obtained by the above run with
fractions with separate known class and known concentration. It is, thus,
apparent from the aforesaid that the entire fraction content is divided
into the number of fraction classes, which are desired to be measured. The
selected classes are adjoining each other, and the fibre fraction content
is covered to 100 percent.
This shows, that for obtaining an equation system providing full coverage
for the entire range with n fraction classes n-1 conditions are required.
This should indicate that it also is necessary to use a number of
measuring configurations of n-1.
It is possible, however, to manage with one less measuring configuration,
because the direct current signal from one of the measuring configurations
in fact yields one extra condition and can be used like an alternating
voltage signal received from a measuring configuration. The number of
measuring configurations used, therefore, can be reduced to n-2, even when
at experiments with the method preferably as many measuring configurations
are used as there are selected classes. It should be observed, that the
term different measuring configurations is to be understood as different
measuring head units with different measuring geometry, which implies that
not all elements in the different configurations must be different. It may
be sufficient, if one element, for example a diaphragm or a detector, is
varied. Multiple detectors, for example, can be used whereby one condition
can be obtained from the signal from a partial detector, and a second
condition can be obtained from the signal from the entire multiple
detector. The essential feature is, as mentioned above, that the different
measuring configurations yield different resolution relative to each
other.
There exist, of course, also other methods than the one described above for
obtaining the coefficients in the matrix A. It is possible, for example,
to run several different samples with known fraction content distributed
over different classes, and in this way, though more troublesome, to
obtain the different coefficients in the matrix A.
It is not necessary, of course, when building-up measuring apparatus to
carry out the relatively troublesome measuring of all coefficients in the
matrix A individually for each apparatus. This would render such apparatus
much more expensive. It can be sufficient to use coefficients obtained by
measurements of a prototype. In order to ensure that the separate
apparatus yield measuring results lying within permissible limits, one or
several media with a suitable fraction content can be run as reference
through the apparatus and be measured. Apparatus not fulfilling the
requirements are adjusted by adjusting especially the mechanical and
optical parts of the different measuring configurations. The coefficients
in the matrix A preferably are stored in a fixed memory, for example of
the type ROM, PROM or EPROM, in the calculation part of the apparatus. At
the manufacture it is in most cases cheapest to make these memories
identical.
In many cases it is not necessary, either, to calibrate the apparatus so as
to yield accurately correct values of the fraction content in every class,
and approximative values may be sufficient, because the apparatus often
are to be used to indicate changes in the fractionary composition of a
medium between different measurements. The apparatus in this case can be
said to be self-defining. Thus, as it is a question of comparative
measuring, the different coefficients can be chosen relatively
arbitrarily.
It is also obvious that the value, which the apparatus indicates for every
fraction class at a measuring, does not need to be the value of the
accurate fraction amount within the | | |
