U.S. patent application number 11/637877 was filed with the patent office on 2007-06-21 for combined titration and ph electrode for the preparation of liquid samples in particular for nmr spectroscopy.
This patent application is currently assigned to Bruker BioSpin GmbH. Invention is credited to Gudrun Hofmann, Martin Hofmann.
Application Number | 20070138011 11/637877 |
Document ID | / |
Family ID | 37711814 |
Filed Date | 2007-06-21 |
United States Patent
Application |
20070138011 |
Kind Code |
A1 |
Hofmann; Gudrun ; et
al. |
June 21, 2007 |
Combined titration and pH electrode for the preparation of liquid
samples in particular for NMR spectroscopy
Abstract
An electrode rod (1;21) for a pH meter, comprising a measuring
end (2; 22) for immersion into a liquid test sample (31), wherein
the measuring end (2; 22) has a pH measuring element, and wherein
electrical feed lines (5) in the electrode rod (1;21) extend
towards the pH measuring element, is characterized in that at least
one capillary (8, 9, 10; 23) for feeding a liquid into the test
sample (31) extends in the electrode rod (1; 21), and the at least
one capillary (8, 9, 10; 23) has an outlet opening (11, 12, 13; 24)
in the area of the measuring end (2; 22). The inventive electrode
rod facilitates and accelerates preparation of liquid test samples,
in particular, adjustment of a pH value for small amounts of test
samples or narrow sample containers.
Inventors: |
Hofmann; Gudrun;
(Rheinstetten, DE) ; Hofmann; Martin;
(Rheinstetten, DE) |
Correspondence
Address: |
KOHLER SCHMID MOEBUS
RUPPMANNSTRASSE 27
D-70565 STUTTGART
DE
|
Assignee: |
Bruker BioSpin GmbH
Rheinstetten
DE
|
Family ID: |
37711814 |
Appl. No.: |
11/637877 |
Filed: |
December 13, 2006 |
Current U.S.
Class: |
204/405 |
Current CPC
Class: |
G01N 27/286 20130101;
Y10T 436/116664 20150115 |
Class at
Publication: |
204/405 |
International
Class: |
G01N 27/26 20060101
G01N027/26 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 20, 2005 |
DE |
10 2005 060 866.3 |
Claims
1. An electrode rod for a pH meter, the electrode rod for immersion
into a liquid test sample, the rod comprising: a measuring end for
immersion into the liquid sample; a pH measuring element disposed
in said measuring end; electrical feed lines extending in the
electrode rod to said pH measuring element; and at least one
capillary extending within the electrode rod for feeding a fluid
into the sample, said capillary having an outlet opening proximate
said measuring end.
2. The electrode rod of claim 1, wherein several, 2, 3, or 4
capillaries are provided in the electrode rod, each having an
outlet opening in an area of said measuring end.
3. The electrode rod of claim 1, wherein said capillary is made
from glass, quartz glass of high purity, "fused silica", metal,
stainless steel, plastic material, PTFE (polytetrafuoroethylene),
or PEEK (polyetheretherketone).
4. The electrode rod of claim 1, wherein said pH measuring element
has a sensor chip or an ISFET (ion sensitive field effect
transistor) and a reference electrode.
5. The electrode rod of claim 1, further comprising a temperature
sensor disposed in an area of said measuring end.
6. The electrode rod of claim 1, wherein the electrode rod has an
outer diameter of between 2 mm and 7 mm in an area of said
measuring end.
7. The electrode rod of claim 1, wherein said capillary has an
inner diameter of between 50 .mu.m and 500 .mu.m.
8. The electrode rod of claim 1, wherein said measuring end is
pointed or bevelled.
9. The electrode rod of claim 1, wherein an outlet opening of a
lower capillary is closer to an end of the electrode rod than said
pH measuring element.
10. The electrode rod of claim 9, wherein outlet openings of other
capillaries are further away from an end of the electrode rod than
said outlet opening of said lower capillary.
11. Use of the electrode of claim 1 for adjusting a pH value of a
liquid test sample, wherein a titration liquid is supplied through
said at least one capillary.
12. The use of claim 11, wherein an acid is supplied through a
first capillary and a base is supplied through a second
capillary.
13. The use of claim 12, wherein a gas, an inert gas, nitrogen, a
noble gas, or air is supplied through a third capillary or through
a lower capillary.
14. The use of claim 12, wherein a buffer solution is supplied
through a fourth capillary.
15. A titration unit having the electrode rod of claim 2, the
titration unit further comprising: a pH meter connected to said pH
measuring unit; an acid reservoir; an acid pump connected to said
acid reservoir to pass acid to one of said capillary outlet
openings; a base reservoir; a base pump connected to said base
reservoir to pass base to an other one of said capillary outlet
openings; and means for controlling said acid pump and said base
pump to supply defined amounts of acid and base to the sample.
16. The titration unit of claim 15, wherein said controlling means
is designed to automatically, iteratively adjust a pH value of the
liquid test sample.
17. The titration unit of claim 15, further comprising a gas pump
to supply gas through a capillary or through a lower capillary,
wherein said controlling means drives said gas pump in such a
manner that gas can be supplied during and/or after supplying acid
and/or base.
18. The titration unit of claim 15, further comprising a buffer
reservoir and a buffer pump for supplying buffer solution from said
buffer reservoir through a capillary.
Description
[0001] This application claims Paris Convention priority of DE 10
2005 060 866.3 filed Dec. 20, 2005 the complete disclosure of which
is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] The invention concerns an electrode rod for a pH meter with
a measuring end for immersion into a liquid test sample, wherein
the measuring end comprises a pH measuring element, and wherein
electrical feed lines in the electrode rod extend towards the pH
measuring element.
[0003] An electrode rod of this type is disclosed e.g. in "IQ 240
Benchtop/Portable pH Meter" by I.Q. Scientific Instruments, Inc.,
San Diego, Calif., USA, 2001.
[0004] When substances, e.g. proteins, are measured using modern
methods of instrumental analytics, the measuring result is not only
influenced by the substance itself but also by the measuring
surroundings. In particular, in NMR spectroscopy of substances in
aqueous solution, the pH value considerably affects the obtained
spectra.
[0005] A correlation between the measuring result and the measuring
surroundings is sometimes possible, i.e. the influence of the
measuring surroundings can be extracted from the measuring result,
thereby obtaining information about the actual substance. It is
generally simpler and more accurate to examine the substance in
certain, defined measuring surroundings. Towards this end, the
measuring surroundings of the substance must be adjusted before the
measurement.
[0006] Solutions are particularly suited as measuring surroundings,
since the substance is homogeneously distributed therein and the
amount of a liquid test sample (that is the substance in a solution
in the measuring surroundings) can be easily adjusted.
[0007] As a first step, adjustment of the measuring surroundings
often includes adding a certain amount of a standard solution
and/or a buffer solution. In a further step, the pH value is in
general iteratively adjusted, typically to pH 7.0.
[0008] When a sufficient amount of the substance and therefore also
of the liquid test sample is available, the test sample is disposed
into a large sample container, e.g. a beaker in order to adjust the
pH value. An electrode rod of a pH meter and two pipettes for
adding acid and base are immersed into the test sample. Acid or
base is added until a desired pH value is obtained, which is
simultaneously measured by the pH meter. This method is illustrated
e.g. in the company leaflet "Basic Titrino 794" by Metrohm
Ionenanalytik.
[0009] In many applications of instrumental analytics, only small
amounts of the substance to be measured are available and hence
also of the liquid test sample, since the substance may generally
not be excessively diluted before measurement in order to produce
exact measuring results. Typical amounts of test sample for the
analysis of mouse urine using NMR spectroscopy are e.g. 0.5 to 2
ml. The liquid test sample, whose pH value is to be adjusted, is
thereby provided in a small and narrow sample container.
[0010] In this case, iterative adjustment of the pH value in
accordance with prior art is very difficult. An electrode rod of a
pH meter is initially immersed into the narrow sample container
holding the test sample, and the pH value is determined. The
electrode rod is then pulled out and a small amount of acid or base
is added to the test sample. The test sample is briefly mixed and
the electrode rod is subsequently immersed again to check the pH
value. The electrode rod is removed again and acid or base is added
in the required amounts. This is continued until the desired pH
value is reached.
[0011] Due to the narrow sample container (e.g. a 2 ml glass vial
with an opening width of approximately 5 mm), the electrode rod
(smallest available outer diameter 3.8 mm) cannot remain in the
sample container during titration of acid or base, since there is
not enough space for pipettes.
[0012] For this reason, the laboratory equipment (electrode rod,
mixer, acid pipette, base pipette) must be removed and reinserted
from above the test sample a plurality of times during preparation
of a small amount of liquid test sample, which renders preparation
of such a test sample very time-consuming and therefore
expensive.
[0013] It is therefore the underlying purpose of the present
invention to facilitate and accelerate preparation of liquid test
samples, in particular adjustment of the pH value, for small
amounts of test sample and in narrow sample containers. Automation
of the preparation of the liquid test samples should also be
simplified.
SUMMARY OF THE INVENTION
[0014] This object is achieved by an electrode rod of the
above-mentioned kind, characterized in that at least one capillary
for feeding a liquid into the test sample extends in the electrode
rod, the at least one capillary having an outlet opening in the
area of the measuring end.
[0015] The inventive electrode permits maintenance of the electrode
rod immersed in a sample container in a test sample and at the same
time direct supply of a fluid, in particular, acid or base to the
test sample through the capillary of the electrode rod. Even when
the test sample is kept in a narrow container, the electrode rod
need not be removed in order to titrate the fluid. With the
inventive electrode rod, the laboratory equipment need not be moved
relative to the sample container during sample preparation between
pH measurement and titration. This facilitates and accelerates
iterative adjustment of the pH value of a test sample.
[0016] Automatic sample preparation only requires one single
movement of one single piece of laboratory equipment, i.e. the
inventive electrode rod, over the sample container and immerse it
into the test sample. The whole sample preparation, in particular,
complete titration may be performed while the inventive electrode
rod is immersed.
[0017] The electrode rod may subsequently be removed and (following
cleaning) be used in a further test sample in another sample
container. This facilitates automatic sample preparation.
[0018] The fact that the electrode rod must be immersed only once
for preparing the sample also reduces the danger of soiling the
test sample.
[0019] In a particularly preferred embodiment of the inventive
electrode rod, several, preferably 2, 3 or 4 capillaries are
provided in the electrode rod each having one outlet opening in the
area of the measuring end. The plurality of capillaries provides
the inventive electrode rod with a multitude of functions and saves
further operations for sample preparation. The capillaries are
provided, in particular, for acid, base, gas and buffer and/or
standard solution. Acid thereby means a solution having a smaller
pH value than the test sample, and a base means a solution having a
higher pH value than the test sample. The pH value may also be
corrected by the acid and base capillaries when the target value
has been overshot. The buffer/standard solution capillary saves one
further sample preparation step. The gas capillary permits faster,
more thorough and simpler mixing of the test sample.
[0020] In another preferred embodiment, the capillary/capillaries
is/are produced from glass, in particular, quartz glass of high
purity ("fused silica") or of metal, in particular, stainless steel
or plastic material, in particular PTFE (polytetrafuoroethylene) or
PEEK (polyetheretherketone). These materials are advantageous due
to their chemical resistance, and special steel and plastic
material are also advantageous due to their mechanical
stability.
[0021] In another preferred embodiment, the pH measuring element
has a sensor chip and a reference electrode, wherein the sensor
chip is preferably designed as an ISFET (ion sensitive field effect
transistor). This design of the sensor chip has proven to be
practical.
[0022] In one further preferred embodiment of the inventive
electrode rod, a temperature sensor is provided in the area of the
measuring end.
[0023] In another embodiment, the electrode rod has an outer
diameter of between 2 mm and 7 mm in the area of the measuring end.
These values are particularly suited for handling sample containers
for small amounts of test sample in the range between 0.5 and 2
ml.
[0024] In another advantageous embodiment, the
capillary/capillaries has/have an inner diameter of between 50
.mu.m and 500 .mu.m. These diameters are also adjusted for small
amounts of test samples.
[0025] One embodiment of the inventive electrode rod is
particularly preferred with which the measuring end tapers in a
pointed or bevelled fashion. Such a measuring end is suited to
penetrate through an upper sealing of a sample container, i.e. a
plastic diaphragm. No separate operation is required for opening a
sample container.
[0026] In an advantageous embodiment, the outlet opening of a lower
capillary is closer to the end of the electrode rod than the pH
measuring element. This lower capillary is mainly suited as a gas
capillary. In an upright position of the electrode rod, i.e. the
measuring end faces downwards and is immersed into the test sample,
gas that rises from the outlet opening of the lower capillary can
be mixed with the test sample in the area around the pH measuring
element. This makes the pH measurement more reliable.
[0027] In a preferred further development of this embodiment, the
outlet openings of the other capillaries are further away from the
end of the electrode rod than the outlet opening of the lower
capillary. This also allows mixing through rising gas at the outlet
openings of the other capillaries (i.e. acid and base capillaries)
to accelerate titration.
[0028] The invention also concerns use of an inventive electrode
rod for adjusting the pH value of a liquid test sample, wherein a
titration liquid is supplied through the at least one capillary.
Change between titration and pH measurement is possible without
withdrawing the electrode rod. This facilitates and accelerates
adjustment of the pH value of the test sample.
[0029] In a preferred variant of the inventive application, an acid
is supplied through a first capillary and a base is supplied
through a second capillary. This permits correction of the pH value
when the target value has been overshot (e.g. on the acid side).
This is particularly useful when the acid or base is present in a
relatively high concentration such that excess amounts can
occur.
[0030] In a further preferred variant of the application, a gas, in
particular, an inert gas such as nitrogen, a rare gas or air is
supplied through a third capillary, in particular, the lower
capillary. The gas is mixed with the test sample in a simple and
reliable fashion, thereby accelerating adjustment of the balanced
conditions.
[0031] In another preferred variant of the application, a buffer
solution is supplied via a fourth capillary. The buffer solution
need not be supplied in a separate operation.
[0032] The present invention also concerns a titration unit
comprising an inventive electrode rod with at least two capillaries
in the electrode rod, a pH meter which is connected to the pH
measuring element, an acid reservoir and a base reservoir, two
pumps which may supply acid or base through one respective
capillary, and a control means which is designed to drive the pumps
such that defined amounts of acid or base are supplied to the
outlet openings. The titration unit facilitates sample preparation
of a liquid test sample, in particular, adjustment of the pH value,
wherein the electrode rod may remain in the sample container during
the entire sample preparation, even when it is narrow.
[0033] In a particularly preferred embodiment of the inventive
titration unit, the control unit is moreover designed to adjust the
pH value of a liquid test sample in an automatic, iterative
fashion. This embodiment minimizes the number of staff required for
sample preparation. The amount of acid or base that is supplied in
one titration step is preferably reduced when the difference
between the instantaneous pH value and the target pH value
decreases.
[0034] In another preferred embodiment, the titration unit also
comprises a gas pump which may supply gas through a third, in
particular, the lower capillary, and the control unit is designed
to drive the gas pump, such that gas may also be supplied during
and/or after supplying acid and/or base. This provides thorough
mixing of the test sample and a balanced pH value is reached more
quickly.
[0035] In another preferred embodiment, the titration unit also
comprises a buffer reservoir and a buffer pump which can supply the
buffer solution from the buffer reservoir through a fourth
capillary. With this titration unit, no separate operation for
supplying buffer solution is required. The buffer solution may also
be contained in or replaced by a standard solution for physical
measurement of the test sample.
[0036] Further advantages of the invention can be extracted from
the description and the drawing. The embodiments mentioned above
and below may be used in accordance with the invention either
individually or collectively in arbitrary combination. The
embodiments shown and described are not to be understood as
exhaustive enumerations, rather have exemplary character for
illustrating the invention.
[0037] The invention is shown in the drawing and explained in more
detail with reference to embodiments.
BRIEF DESCRIPTION OF THE DRAWING
[0038] FIG. 1a shows a schematic cross-sectional view of an
embodiment of an inventive electrode rod with three
capillaries;
[0039] FIG. 1b shows a schematic view on the measuring end of the
electrode rod of FIG. 1a;
[0040] FIG. 2a shows a schematic cross-sectional view of an
embodiment of an inventive electrode rod with four capillaries;
[0041] FIG. 2b shows a schematic view of the measuring end of the
electrode rod of FIG. 2a;
[0042] FIG. 3 shows a schematic view of the electrode rod of FIG.
2a which is immersed into a test sample in a sample container;
[0043] FIG. 4 shows a schematic view of a control means for an
inventive titration unit.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0044] The present invention provides an electrode rod for a pH
meter for measuring the pH value of a surrounding liquid test
sample, as well as adding at least one titration liquid to the test
sample through at least one capillary (a thin tube) which is
provided in the electrode rod. The electrode may remain in the
sample container, being immersed in the test sample during the
entire sample preparation of repeated, alternating pH measurements
and addition of fluid. An associated sample container which
contains the test sample and into which the inventive electrode rod
is immersed requires only one opening width which corresponds to
the outer cross-sectional dimensions of the electrode rod in the
area of its measuring end. In particular, no space is required for
separate titration pipettes. The inventive measuring electrode is
therefore particularly suited for preparing small amounts of test
sample which are required e.g. in NMR spectroscopy of body liquid
samples (urine, blood and the like). These small amounts of test
sample are stored in small sample containers which provide a volume
into which a pH measuring element can be immersed.
[0045] FIG. 1a shows a first embodiment of an inventive electrode
rod 1. The electrode rod 1 is substantially circular cylindrical.
The electrode rod 1 is not shown in its full length for reasons of
simplification. A pH measuring element is provided at one measuring
end 2, which tapers like a cone and comprises a sensor chip 3 and a
reference electrode 4. Electrical feed lines 5 inside the electrode
rod 1 extend to the sensor chip 3 and the reference electrode 4. A
temperature sensor 6 is provided at the lower tip of the measuring
end 2 which also has an electric feed line 7.
[0046] In the embodiment of FIG. 1a, three capillaries 8, 9, 10,
extend inside the electrode rod. A capillary 8 for an acid and a
capillary 9 for a base are disposed on opposing sides in the
electrode rod 1, close to the outer sleeve of the electrode rod 1.
This is intended to prevent neutralization of acid and base in the
capillaries 8, 9 through diffusion. A third capillary 10 is
provided for nitrogen gas. An outlet opening 11 of the third
capillary 10 is quite close to the tip of the measuring end 2. When
the electrode rod 1 is in an upright position which is the typical
position of use of the electrode rod (with the measuring end 2
facing vertically downwards), this outlet opening 11 is below the
outlet openings 12, 13 of the capillaries 8, 9 for acid and base
and also below the sensor chip 3, which is a substantial part of
the pH measuring element. When gas bubbles exit the outlet opening
11, they whirl the liquid test sample above them, in particular in
front of the other outlet openings 12, 13 and the sensor chip
3.
[0047] The electrode rod 1 has a cladding 14 of special steel which
provides the electrode rod 1 with sufficient stability for daily
use and, in particular, renders it unbreakable. The capillaries 8,
9, 10 are produced from quartz glass of high purity and have e.g.
an outer diameter of 360 .mu.m and an inner diameter of 220 .mu.m.
For typical titration, the acid and base should cover an operating
range of at least pH 4.01 to pH 7.00. In accordance therewith, the
acid in capillary 8 has a pH value of less than 4.01 and the base
in capillary 9 has a pH value of more than 7.00.
[0048] The overall electrode rod 1 is mounted to a robot arm which
can be preferably moved in all spatial directions X, Y, Z (not
shown). The electrode rod 1 may thereby be automatically moved
between the different positions of sample containers to thereby
test samples. A further robot arm may be provided for moving sample
containers (not shown).
[0049] A connection, e.g. a plug connection, to a flexible line
(not shown) is provided at the upper end 15 of the electrode rod 1.
The flexible line contains cables and hoses e.g. PTFE hoses in
order to connect the electrical feed lines 5, 7 and the capillaries
8, 9, 10 to a control means.
[0050] FIG. 1b shows a view from below of the measuring end 2 of
the electrode rod of FIG. 1a. The outlet openings 12, 13 of the
capillaries of acid and base have a maximum separation. The
cross-section of the electrode rod is circular.
[0051] FIGS. 2a and 2b show an embodiment of an electrode rod 21
and its measuring end 22 similar to FIGS. 1a, 1b. The electrode rod
21 has a further, fourth capillary 23 with an outlet opening 24
through which the buffer solution can be introduced into a test
sample. For this reason, the buffer solution which is typically
supplied before the pH value is adjusted in highly acidic or highly
basic test samples (the buffer capacity of the supplied buffer
solution is thereby exhausted) need not be supplied in a separate
step but may also be supplied via the electrode rod 21.
[0052] FIG. 3 shows the electrode rod 21 of FIG. 2a which is
immersed into a liquid test sample 31. The test sample 31 is
contained in a sample container 32. The electrode rod 21 is
immersed into the test sample 31 until the entire measuring end 22,
in particular, all outlet openings 11, 12, 13, 24, the temperature
sensor 6 and the sensor chip 3 are surrounded by the liquid test
sample 31.
[0053] The opening of the sample container 32 is only somewhat
wider than the diameter of the electrode rod 21, such that the test
sample 31 cannot be reached, or only with great difficulty, with a
separate pipette when the electrode rod 21 is immersed. The largest
outer diameter d of the electrode rod 21 in the area of the
measuring end 22 is approximately 3.8 mm in the embodiment shown,
and the diameter OW of the opening of the sample container 32 is
approximately 5.0 mm. The sample container 32 may e.g. be an NMR
sample tube.
[0054] FIG. 4 schematically shows a control means 41 for an
inventive titration unit which comprises an electrode rod in
accordance with FIGS. 2a, 2b.
[0055] The control means 41 has a plug connection 42 with a
flexible line 42a which is connected to the inventive electrode rod
(not shown). A computer may be connected via a further plug
connection 51 which may receive or pass on data from/to the control
means 41.
[0056] Pumps 43, 44 for acid and base are provided in the control
means 41, which can pump acid and base, respectively, from an acid
reservoir 45 and a base reservoir 46 into the flexible line 42a and
thereby into the electrode rod and the test sample. A buffer pump
47 may moreover pump a buffer solution from a buffer reservoir 48
into the flexible line 42a. The pumps 43, 44, 47 are designed as
DNP gear pumps. A gas pump 49 may pump air from the surroundings
into the flexible line 42a. The flexible line 42a has four PTFE
hoses in order to separately guide the fluids.
[0057] The control means 41 receives information about the pH value
and the temperature of the test sample via the plug connection 42
to the electrode rod. The pH value and the temperature are
displayed on a display 50.
[0058] The control unit 41 provides for manual and also automatic
titration.
[0059] During manual operation, acid can be supplied to the test
sample via a key 52 "add". The amount of acid for each key
depression is displayed on a display 53 "step size" and can be
changed via the keys 54 "up/down". Typical acid volumes per
titration step are in a range between 1 and 10 .mu.l. The overall
acid volume added during one titration is displayed on a display 55
"total vol.". Base may be supplied to the test sample via a key 56
"add". The amount of base for each key depression is displayed on a
display 57 "step size" and may be changed via the keys 58
"up/down". Typical base volumes per titration step are also in a
range between 1 and 10 .mu.l. The overall volume of base added
during one titration is displayed on a display 59 "total vol.". The
gas pump 49 can be activated and deactivated via a key 60 "mix"
such that the test sample is mixed. The key 61 "get pH" up-dates
the pH measurement of the test sample. The pH meter of the
titration means may also be calibrated via a key 62 "calibr. pH".
Finally, buffer solution may be added to the test sample via a key
63 "add". The amount of buffer solution added per key depression is
displayed on a display 64 and can be changed via keys 65.
[0060] Automatic operation is preferably effected via a computer,
e.g. a PC which is connected to the control means 41 via the plug
connection 51. Software is run on the PC which controls the added
amounts of acid or base via control signals transmitted by the
computer to the control means 41 on the basis of a predetermined
target pH value in the computer and the read-out actual pH value.
With decreasing difference between the predetermined and actual pH
values, the acid or base is preferably added at a slower rate (i.e.
the added amount per titration step decreases).
[0061] In another embodiment of the control unit 41, a target pH
value may be predetermined at the control unit 41 itself, and
automatic titration may be started via a further key. The control
unit 41 itself then has sufficient computational resources.
[0062] Further functions may be provided on the control means 41
for automating sample preparation, in particular
[0063] rinsing of the titration unit (in particular, pumps, hoses
and capillaries) when the titration liquid is changed,
[0064] setting of the mixing time;
[0065] setting of the supply speed at the pumps;
[0066] cleaning of the electrode rod;
[0067] automatic calibration of the pH meter (in dependence on time
or on the number of measurements).
* * * * *