Abstract:
As previous processing of measurement in which gas to be measured containing, as gas components, carbon dioxide  13 CO 2  and carbon dioxide  12 CO 2 , is introduced into a cell, and in which the intensities of transmitted lights having wavelengths suitable for measurement of the respective gas components, are measured and then data-processed to measure the concentrations of the gas components, the air having a predetermined volume Va is sucked by a gas injection device  21 , a gas exhaust valve V 6  of a cell  11  is closed and the air stored in the gas injection device  21  is transferred to the cell  11  filled with the air at an atmospheric pressure, thereby to pressurize the cell inside. The pressure thus pressurized is measured as P. The cell volume Vc is subtracted from the product obtained by multiplying the sum. V0 of the volume Va and Vc the cell volume Vc, by the ratio P0/P in which P0 is the target pressure of the gas to be measured at which a calibration curve has been prepared for an isotope gas analysis and measurement, thus determining the one-time gas injection amount of the gas injection device  21 . Thus, measured concentration variations based on changes in atmospheric pressure can be corrected.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     After a medicine containing isotopes has been ad-ministered to a living body, the metabolic rate of the living body can be measured by measuring changes in concentration ratio of the isotopes. Accordingly, isotope analysis is utilized for disease diagnosis in the medical field.  
         [0003]     The present invention is achieved with attention focused on the difference in light absorption characteristics of isotopes, and relates to a gas injection amount determining method in isotope gas analysis for measuring the concentration ratio of isotope gases, and also relates to isotope gas analyzing and measuring method and apparatus.  
         [0004]     2. Description of Related Art  
         [0005]     It is generally known that bacteria called  Helicobacter pylori  (HP) are present in the stomach as the cause of gastric ulcer and gastritis.  
         [0006]     When HP is present in the patient&#39;s stomach, it is required to conduct a bacteria elimination treatment by administering an antibiotic substance. Accordingly, it is important whether or not HP is present in the patient. HP presents a strong urease activity and therefore dissolves urea into carbon dioxide and ammonia.  
         [0007]     On the other hand, carbon includes isotopes of which mass number is 13 and 14, in addition to 12. Out of these isotopes, the isotope  13 C having the mass number of 13 is not radioactive and is sable, thus causing the same to be readily handled.  
         [0008]     In this connection, when urea marked with the isotope  13 C is administered to a living body (patient), and the  13 C concentration, more specifically the concentration ratio between  13 CO 2  and  12 CO 2 , in the expired breath of the patient which is the final metabolic product, is measured, the presence/absence of HP can be made sure.  
         [0009]     However, the concentration ratio between  13 CO 2  and  12 CO 2  in the natural world, is as high as 1:100. It is therefore difficult to precisely measure the concentration ratio in the expired breath of the patient.  
         [0010]     Conventionally, it is known a method using infrared spectral diffraction as a method of obtaining the concentration ratio between  13 CO 2  and  12 CO 2  or the concentration of  13 CO 2  (See Japanese Patent Publication No. 61(1986)-42220 (B)).  
         [0011]     According to the method of Japanese Patent Publication No. 61(1986)-42220 (B), there are prepared two, long and short, cells having lengths such that the  12 CO 2  absorption in one cell is equal to the  13 CO 2  absorption in the other cell, and lights having wavelengths suitable for respective analyses are irradiated to the respective cells, and the intensities of the transmitted lights are measured. According to this method, the light absorption ratio at the concentration ratio in the natural field can be made 1, and if the concentration ratio undergoes a change, the light absorption ratio varies according to this change. Thus, the change in concentration ratio can be known.  
         [0012]     Even though there is adopted the method using infrared spectral diffraction above-mentioned, it is difficult to detect a slight change in concentration ratio.  
         [0013]     According to the isotope gas analyzing and measuring method above-mentioned, the concentration of carbon dioxide  13 CO 2  is obtained with the use of a calibration curve which determines the relationship between absorbance and concentration of  13 CO 2 . However, if the atmospheric pressure at which the calibration curve has beenprepared, is different from the atmospheric pressure at which the absorbance of carbon dioxide  13 CO 2  is measured, such difference may cause an error of measurement of  13 CO 2  concentration.  
         [0014]     Table 1 shows the results of measurement of CO 2  concentration obtained in the following manner. That is, a predetermined volume of air having a predetermined CO 2  concentration, was collected by a gas injection device at each of a plurality of atmospheric pressures, and was then injected into a cell. Each cell inside pressure was measured. Then, each absorbance was measured to measure the CO 2  concentration. The calibration curve used at this time was prepared at an atmospheric pressure of 1005 hPa.  
                                     TABLE 1                       Atmospheric   Cell           Pressure   Pressure       (hPa)   (Mpa)   CO 2  Concentration                                1005   0.402   2.995       964   0.385   2.874       892   0.357   2.536       858   0.347   2.445       799   0.323   2.245                  
 
         [0015]     According to Table 1, the cell inside pressures are naturally proportional to the atmospheric pressures, and the CO 2  concentrations which must originally be constant, are lowered according to the reduction in atmospheric pressure. Thus, the concentration varies with the variations of the atmospheric pressure.  
         [0016]     In measurement in which gas to be measured containing, as gas components, carbon dioxide  13 CO 2  and carbon dioxide  12 CO 2 , is introduced into a cell, and in which the intensities of transmitted lights having wavelengths suitable for measurement of the respective gas components, are measured and then data-processed to measure the concentrations of the gas components, it is an object of the present invention to provide a gas injection amount determining method in isotope gas analysis, and isotope gas analyzing/measuring method and apparatus, each of which can correct concentration variations resulting from the atmospheric pressure variations, thus improving the measuring precision.  
       SUMMARY OF THE INVENTION  
       [0017]     According to the present invention, a gas injection amount determining method in isotope gas analysis comprises the steps of: filling a cell with the air at an atmospheric pressure; operating a gas injection device so as to suck the air of a predetermined volume Va, the gas injection device being arranged to inject the gas to be measured into the cell; transferring the air stored in the gas injection device into the cell to pressurize the cell inside, and measuring the cell inside pressure P; and subtracting the cell volume Vc from the product obtained by multiplying the sum V 0  of the volume Va and the cell volume Vc, by the ratio P 0 /P in which P 0  is the target pressure of the gas to be measured in isotope gas analysis measurement, thus determining the one-time gas injection amount of the gas injection device.  
         [0018]     According to the method above-mentioned, when an isotope gas analysis measurement is conducted with the use of the one-time gas injection amount determined by multiplying the ratio P 0 /P with the standard volume or sum V 0  of the volume Va and the cell volume Vc, the gas to be measured can be measured at the target pressure P 0  of the gas to be measured. In other words, the cell inside pressure influenced by variations of the atmospheric pressure can be corrected.  
         [0019]     Accordingly, the measuring precision and the reproducibility are improved. Further, the measuring apparatus is not required to be made in large sizes.  
         [0020]     It is preferable that the cell volume Vc includes not only net volume of the cell, but also inner volumes of pipes, valves and pressure sensor which are in connection through the cell. With use of the above volume Vc, more precise measurement can be attained.  
         [0021]     The target pressure P 0  of the gas to be measured is preferably equal to the gas pressure at which a calibration curve for determining the relationship between absorbance and concentration of carbon dioxide  13 CO 2 , has been prepared.  
         [0022]     According to an isotope gas analyzing and measuring method of the present invention, gas to be measured having the volume determined by the gas injection amount determining method above-mentioned, is collected by a gas injection device, the gas thus collected is transferred into the cell to pressurize the cell inside, and the concentration of the carbon dioxide  13 CO 2  or the concentration ratio  13 CO 2 / 12 CO 2  is measured.  
         [0023]     An isotope gas analyzing and measuring apparatus of the present invention is arranged to embody the isotope gas analyzing and measuring method above-mentioned, and comprises: a gas injection device for injecting gas into acell; gas transferring means for transferring the gas stored in the gas injection device into the cell; a pressure sensor for measuring the pressure of the gas housed in the cell; and gas injection amount determining means arranged such that the air having a predetermined volume Va is sucked by the gas injection device, that the air stored in the gas injection device is transferred to the cell filled with the air at an atmospheric pressure, thereby to pressurize the cell inside, that the cell inside pressure P is measured, and that the cell volume Vc is subtracted from the product obtained by multiplying the sum V 0  of the volume Va and the cell volume Vc, by the ratio P 0 /P in which P 0  is the target pressure of the gas to be measured in isotope gas analysis measurement, thus determining the one-time gas injection amount of the gas injection device; whereby gas to be measured having the volume determined by the gas injection amount determining means, is collected by the gas injection device, the gas thus collected is transferred into the cell filled with gas to be measured at an atmospheric pressure, and the concentration of carbon dioxide  13 CO 2  or the concentration ratio  13 CO 2 / 12 CO 2  is measured. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0024]      FIG. 1  is a block diagram illustrating the general arrangement of an isotope gas spectroscopic measurement apparatus;  
         [0025]      FIG. 2 ( a ) is a plan view of a gas injection device  21  for quantitatively injecting gas to be measured, and  FIG. 2 ( b ) is a front view of the gas injection device  21 ;  
         [0026]      FIG. 3 ( a ) and  FIG. 3 ( b ) are views illustrating gas flow passages at the time when a one-time gas injection amount is determined;  
         [0027]      FIG. 4 ( a ) and  FIG. 4 ( b ) are views illustrating gas flow passages at the time when a reference gas light amount measurement is conducted;  
         [0028]      FIG. 5 ( a ) and  FIG. 5 ( b ) are view illustrating gas flow passages at the time when a base gas light amount measurement is conducted; and  
         [0029]      FIG. 6 ( a ) and  FIG. 6 ( b ) are view illustrating gas flow passages at the time when a sample gas light amount measurement is conducted. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0030]     Referring to the attached drawings, the following description will discuss in detail an embodiment of the present invention in which after a urea diagnostic medicine marked with an isotope  13 C has been administered to a living body, the  13 CO 2  concentration of an expired breath of the living body is spectroscopically measured.  
         [0000]     I. Expired Breath Test  
         [0031]     First, an expired breath of a patient before a urea diagnostic medicine is administered, is collected in an expired breath bag. Then, a urea diagnostic medicine is orally administered to the patient. After the passage of about 20 minutes, an expired breath is collected in an expired breath bag in a manner similar to that before administration.  
         [0032]     The expired breath bags be-fore and after administration are respectively set to predetermined nozzles of an isotope gas spectroscopic measurement apparatus. Then, the following automatic measurement is conducted.  
         [0000]     II. Isotope Gas Spectroscopic Measurement Apparatus  
         [0033]      FIG. 1  is a block diagram illustrating the general arrangement of an isotope gas spectroscopic measurement apparatus.  
         [0034]     The expired breath bag containing the expired breath after administration (hereinafter referred to as “sample gas”), and the expired breath bag containing the expired breath before administration (hereinafter referred to as “base gas”), are respectively set to nozzles N 1  and N 2 . The nozzle N 1  is connected to an electromagnetic valve (hereinafter simply referred to as “valve”) V 4  through a metallic pipe (hereinafter simply referred to as “pipe”). The nozzle N 2  is connected to a valve V 3  through a pipe. A valve V 5  is connected to a pipe for taking in the air through a dust-proof filter  15 .  
         [0035]     On the other hand, a reference gas (In this embodiment, the air with CO 2  removed is used) supplied from a reference gas supply unit  30  (to be discussed later), is supplied to a valve V 1 .  
         [0036]     The valves V 1 , V 3 , V 4  and V 5  are connected to the gas injection device  21  for quantitatively injecting a reference gas, a sample gas or a base gas. The gas injection device  21  has a syringe shape having a piston and a cylinder. The piston is driven by a feed screw  21   e  connected to a pulse motor  21   f  in association with a nut  2   d  fixed to the piston (to be discussed later). The maximum gas injection amount of the gas injection device  21  is 40 ml.  
         [0037]     The gas injection device  21  is connected, through a valve V 2 , to a first sample cell  11   a  and a second sample cell  11   b.    
         [0038]     As shown in  FIG. 1 , the cell chamber  11  has the short first sample cell  11   a  for measuring the  12 CO 2  absorption, the long second sample cell  11   b  for measuring the  13 CO 2  absorption, and a dummy cell  11   c  containing gas which is not absorbed in the CO 2  absorbing range. Provision is made such that the first sample cell  11   a  and the second sample cell  11   b  communicate with each other, and that gas introduced into the first sample cell  11   a  enters, as it is, the second sample cell  11   b , and is then discharged through an exhaust valve V 6 .  
         [0039]     Disposed upstream of the exhaust valve V 6  is a pressure sensor  16  for measuring the gas pressure in the first sample cell  11   a  and the second sample cell  11   b . No restrictions are imposed on the detection method of this pressure sensor  16 , but there may be used for example a pressure sensor of the type in which the movement of a diaphragm is detected by a piezoelectric element.  
         [0040]     The first sample cell la has a capacity of about 0.085 ml, while the second sample cell  11   b  has a capacity of about 3.96 ml. More specifically, the first sample cell  11   a  has a length of 3 mm, the second sample cell  11   b  has a length of 140 mm, and the dummy cell  11   c  has a length of 135 mm. The cell chamber  11  is surrounded by an insulating material (not shown).  
         [0041]     There is also disposed an infrared light source device L having two light sources for irradiating infrared rays. Infrared rays may be generated by an optional method. For example, there may be used a ceramics heater (surface temperature of 700° C.) or the like. There is further disposed a chopper  22  for interrupting and passing infrared rays at predetermined intervals. The chopper  22  is rotated by a pulse motor  23 .  
         [0042]     Out of the infrared rays irradiated from the infrared light source device L, the light path formed by infrared rays passing through the first sample cell  11   a  and the dummy cell  11   c , is called a first light path L 1 , and the light path formed by infrared rays passing through the second sample cell  11   b , is called a second light path L 2  (See  FIG. 1 ).  
         [0043]     An infrared rays detector device for detecting the infrared rays having passed through the cells comprises: a first wavelength filter  24   a  and a first sensor element  25   a  disposed in the first light path; and a second wavelength filter  24   b  and a second sensor element  25   b  disposed in the second light path.  
         [0044]     For measuring the absorption of  12 CO 2 , the first wavelength filter  24   a  is designed to pass infrared rays having a wavelength of about 4280 nm which is the  12 CO 2  absorption wavelength range. For measuring the absorption of  13 CO 2 , the second wavelength filter  24   b  is designed to pass infrared rays having a wavelength of about 4412 nm which is the  13 CO 2  absorption wavelength range. The first and second sensor elements  25   a ,  25   b  are light-receiving elements for detecting infrared rays.  
         [0045]     The first wavelength filter  24   a , the first sensor element  25   a , the second wavelength filter  24   b , and the second sensor element  25   b  are maintained at a predetermined temperature by a temperature controlling block  27 .  
         [0046]     A fan  28  is disposed for discharging, to the outside of the apparatus, heat radiated from a Peltier element of the temperature controlling block  27 .  
         [0047]     Further, the isotope gas spectroscopic measurement apparatus has a reference gas supply unit  30  for supplying the air with CO 2  removed. The reference gas supply unit  30  is connected in series to a dust-proof filter  31  and a carbonic acid gas absorbing unit  36 .  
         [0048]     The carbonic acid gas absorbing unit  36  is arranged to use for example soda lime (a mixture of sodium hydroxide and calcium hydroxide), as a carbonic acid gas absorbing agent.  
         [0049]      FIG. 2 ( a ) is a plan view of a gas injection device  21  for quantitatively injecting gas to be measured, and  FIG. 2 ( b ) is a front view of the gas injection device  21 .  
         [0050]     The gas injection device  21  has a base stand  21   a , a cylinder  21   b  having a piston  21   c  disposed on the base stand  21   a , a movable nut  21   d  coupled to the piston  21   c , a feed screw  21   e  meshed with the nut  21   d , and a pulse motor  21   f  for rotating the feed screw  21   e , the nut  21   d , the feed screw  21   e  and the pulse motor  21   f  being disposed under the base stand  21   a.    
         [0051]     The pulse motor  21   f  is driven forwardly/reversely by a driving circuit (not shown). When the feed screw  21   e  is rotated by the rotation of the pulse motor  21   f , the nut  21   d  is moved back and forth according to the rotation direction. This causes the piston  21   c  to be moved back and forth to an optional position. It is there fore possible to optionally control both the introduction of gas to be measured, into the cylinder  21   b , and the discharge of the gas to be measured from the cylinder  21   b.    
         [0000]     III. Measuring Procedure  
         [0052]     The measuring process comprises the steps of determining a one-time gas injection amount, measuring the reference gas, measuring the base gas, measuring the reference gas, measuring the sample gas, and measuring the reference gas and the like. In FIGS.  3  to  5 , the arrows show the gas flowing.  
         [0000]     III-1. Determination of the One-Time Gas Injection Amount  
         [0053]     This gas injection amount determining step may be conducted at each measurement of a sample gas or at regular time intervals (e.g., every one hour).  
         [0054]     It is now supposed that the total of the first sample cell  11   a  volume and the second sample cell  11   b  volume is defined as Vc (a predetermined value). The volume Vc preferably not only includes the net volume of the sample cells  11   a ,  11   b , but also includes inner volumes of the pipes, valves and pressure sensor  16  which are connected through the sample cells  11   a ,  11   b . It is also supposed that the volume of the gas injection device  21  at the time when gas is injected by the gas injection device  21  to a predetermined scale thereof, is defined as Va. It is supposed that Vc+Va=V 0 . This volume V 0  is defined as a standard volume V 0 .  
         [0055]     The valve V 5  is opened, other valves are closed, and the air is sucked with the use of the gas injection device  21 . Then, the valve V 5  is closed, and the valve V 2  and the exhaust valve V 6  are opened. The air in the gas injection device  21  is injected into the first sample cell  11   a  and the second sample cell  11   b . Then, the valve V 2  is closed and the exhaust valve V 6  is closed. Thus, the air having the volume Vc at the atmospheric pressure is housed in the first sample cell  11   a  and the second sample cell  11   b.    
         [0056]     As shown in  FIG. 3 ( a ), the valve V 5  is opened, other valves are closed, and the air of volume Va is sucked with the use of the gas injection device  21 .  
         [0057]     As shown in  FIG. 3 ( b ), the valve V 5  is closed and the valve V 2  is opened to transfer the air in the gas injection device  21  into the first sample cell  11   a  and the second sample cell  11   b . Since the exhaust valve V 6  remains closed, the insides of the first sample cell  11   a  and the second sample cell  11   b  are pressurized.  
         [0058]     With the valve V 2  closed to stop the air movement, the pressure of the first sample cell  11   a  and the second sample cell  11   b  is measured by the pressure sensor  16 . This measured pressure value is defined as P.  
         [0059]     It is supposed that each calibration curve for determining the relationship between absorbance and concentration of each of carbon dioxide  13 CO 2  and carbon dioxide  12 CO 2 , has been prepared at a predetermined pressure P 0  (i.e., 4 atmospheric pressure). The calibration curve data and the value of the predetermined pressure P 0  are stored in an analysis computer of the isotope gas spectroscopic measurement apparatus.  
         [0060]     The analysis computer determines a one-time measuring gas volume V 0  (P 0 /P) with the use of the previously stored pressure P 0 , the measured pressure P and the standard volume V 0 . As shown by the following equation  1 ), the gas injection amount V of the gas injection device  21  is a value obtained by subtracting the cell volume Vc from V 0  (P 0 /P). In the equation (1), the volume Vc is subtracted because the first sample cell  11   a  and the second sample cell  11   b  already contain the gas to be measured having the volume Vc.
 
 V=V 0   ( P 0 /P )− Vc    (1)
 
         [0061]     The following description will discuss the equation (1). When the measured pressure P is equal to p 0 , the gas injection amount V is equal to Va. If the atmospheric pressure is high, the measured pressure P is higher than P 0 . At this time, the gas injection amount V may be set to a value smaller than Va. If the atmospheric pressure is low, the measured pressure P is lower than P 0 . At this time, the gas injection amount V maybe set to a value higher than Va. With such an operation, the CO 2  concentration can always be measured under conditions identical to those under which the calibration curve has been prepared.  
         [0000]     III-2. Reference Measurement  
         [0062]     A clean reference gas is flowed into the gas flow passages and the cell chamber  11  of the isotope gas spectroscopic measurement apparatus to wash the gas flow passages and the cell chamber  11 . At this time, the piston  21   c  is moved back and forth to wash the inside of the cylinder  21   b . A reference gas at an atmospheric pressure is housed in the first sample cell  11   a  and the second sample cell  11   b.    
         [0063]     In the reference measurement, the valve V 1  is opened, other valves are closed, and a reference gas is sucked with the use of the gas injection device  21 , as shown in  FIG. 4 ( a ).  
         [0064]     Then, as shown in  FIG. 4 ( b ), the valve V 1  is closed, and the valve V 2  and the exhaust valve V 6  are opened. While the reference gas in the gas injection device  21  is slowly flowed into the first sample cell  11   a  and the second sample cell  11   b  by controlling the gas injection device  21 , the light amount measurement is conducted by the sensor elements  25   a ,  25   b.    
         [0065]     The light amount thus obtained by the first sensor element  25   a  is recorded as  12 R 1 , and the light amount thus obtained by the second sensor element  25   b  is recorded as  13 R 1 .  
         [0000]     III-3. Base Gas Measurement  
         [0066]     The valve V 3  is opened, other valves are closed and the base gas is sucked with the use of the gas injection device  21 . Then, the valve V 3  is closed, the valve V 2  and the exhaust valve V 6  are opened, and the base gas in the gas injection device  21  is injected into the first sample cell  11   a  and the second sample cell  11   b . Thereafter, the exhaust valve V 6  is closed. Thus, the base gas at an atmospheric pressure is housed in the first sample cell  11   a  and the second sample cell  11   b.    
         [0067]     Then, the valve V 3  is opened, other valves are closed and the base gas having the volume V calculated according to the equation (1) is sucked from the expired breath bag by the gas injection device  21 , as shown in  FIG. 5 ( a ).  
         [0068]     After the base gas has been sucked, the valve V 3  is closed, and the valve V 2  is opened as shown in  FIG. 5 ( b ). The base gas is mechanically pushed out with the use of the gas injection device  21  to pressurize the first sample cell  11   a  and the second sample cell  11   b . This increases the pressure of the base gas in the first sample cell  11   a  and the second sample cell  11   b , to a value equal to the pressure P 0 .  
         [0069]     At this state, the valve V 2  is closed and the light amount is measured by the sensor elements  25   a ,  25   b.    
         [0070]     The light amount thus obtained by the first sensor element  25   a  is recorded as  12 B, and the light amount thus obtained by the second sensor element  25   b  is recorded as  13 B.  
         [0000]     III-4 Reference Measurement  
         [0071]     Again, the gas flow passages and the cells are washed, and the reference gas light amount measurement is conducted (See FIGS.  4  ( a ), ( b )). The light amount thus obtained by the first sensor element  25   a  is recorded as  12 R2, and the light amount thus obtained by the second sensor element  25   b  is recorded as  13 R2.  
         [0000]     III-5 Sample Gas Measurement  
         [0072]     The valve V 4  is opened, other valves are closed and the sample gas is sucked with the use of the gas injection device  21 . Then, the valve V 4  is closed, the valve V 2  and the exhaust valve V 6  are opened, and the sample gas in the gas injection device  21  is injected into the first sample cell  11   a  and the second sample cell  11   b . Thereafter, the exhaust valve V 6  is closed. Thus, the sample gas at an atmospheric pressure is housed in the first sample cell  11   a  and the second sample cell  11   b.    
         [0073]     Then, the valve V 4  is opened, other valves are closed and the sample gas having the volume V calculated according to the equation (1) is sucked from the expired breath bag by the gas injection device  21 , as shown in  FIG. 6 ( a ).  
         [0074]     After the sample gas has been sucked, the valve V 4  is closed, and the valve V 2  is opened, as shown in  FIG. 6 ( b ). The sample gas is mechanically pushed out with the use of the gas injection device  21  to pressurize the first sample cell  11   a  and the second sample cell  11   b . This increases the pressure of the sample gas in the first sample cell  11   a  and the second sample cell  11   b , to a value equal to the pressure P 0 .  
         [0075]     At this state, the valve V 2  is closed and the light amount is measured by the sensor elements  25   a ,  25   b.    
         [0076]     The light amount thus obtained by the first sensor element  25   a  is recorded as  12 S, and the light amount thus obtained by the second sensor element  25   b  is recorded as  13 S.  
         [0000]     III-6. Reference Measurement  
         [0077]     Again, the gas flow passages and the cells are washed, and the reference gas light amount measurement is conducted (See FIGS.  4  ( a ), ( b )).  
         [0078]     The light amount thus obtained by the first sensor element  25   a  is recorded as  12 R 3 , and the light amount thus obtained by the second sensor element  25   b  is recorded as  13 R 3 .  
         [0000]     IV Data Processing  
         [0000]     IV-1. Calculation of the Base Gas Absorbance Data  
         [0079]     First, both the absorbance  12 Abs(B) of  12 CO 2  and the absorbance  13 Abs (B) of  13 CO 2  in the base gas, are obtained with the use of (i) the transmitted light amounts  12 R 1 ,  13 R 1  of the reference gas, (ii) the transmitted light amounts  12 B,  13 B of the base gas, and (iii) the transmitted light amounts  12 R2,  13 R2 of the reference gas.  
         [0080]     Here, the absorbance  12 Abs(B) of  12 CO 2  is obtained by the following equation:
 
 12 Abs ( B )=−log [2 12   B /( 12   R 1+ 12   R 2)]
 
         [0081]     The absorbance  13 Abs(B) of  13 CO 2  is obtained by the following equation:
 
 13 Abs ( B )=−log [2 13   B /( 13   R 1+ 13   R 2)]
 
         [0082]     Thus, when calculating each absorbance, there is calculated the average value (R 1 +R2)/2 of the light amounts of reference measurements conducted before and after the absorbance calculation, and the absorbance is then calculated with the use of the average value thus obtained and the light amount obtained by the base gas measurement. Accordingly, the influence of drift (influence exerted to measurement by the passage of time) can be cancelled each other. Accordingly, the measurement can quickly be initiated without the need of waiting until the apparatus is brought into perfect thermal equilibrium after the apparatus has been stared (generally, several hours are required).  
         [0000]     IV-2. Calculation of Sample Gas Absorbance Data  
         [0083]     Then, both the absorbance  12 Abs(S) of  12 CO 2  and the absorbance  13 Abs (S) of  13 CO 2  in the sample gas are obtained with the use of (i) the transmitted light amounts  12 R 2 ,  13 R 2  of the reference gas, (ii) the transmitted light amounts  12 S,  13 S of the sample gas, and (iii) the transmitted light amounts  12 R 3 ,  13 R 3  of the reference gas.  
         [0084]     Here, the absorbance  12 Abs(S) of  12 CO 2  is obtained by the following equation:
 
 12 Abs( S )=−log [2 12   S /( 12   R 2+ 12   R 3)]
 
         [0085]     The absorbance  13 Abs(S) of  13 CO 2  is obtained by the following equation:
 
 13 Abs( S )=−log [2 13   S /( 13   R 2+ 13   R 3)]
 
         [0086]     Thus, when calculating an absorbance, there is calculated the average value of the light amounts of reference measurements conducted before and after the absorbance calculation, and the absorbance is then calculated with the use of the average value thus obtained and the light amount obtained by the sample gas measurement. Accordingly, the influence of drift can be cancelled each other.  
         [0000]     IV-3 Concentration Calculation  
         [0087]      12 CO 2  concentration and  13 CO 2  concentration are obtained with the use of calibration curves.  
         [0088]     As mentioned earlier, the concentration curves are prepared with the use of gas to be measured of which  12 CO 2  concentration is known and gas to be measured of which  13 CO 2  concentration is known.  
         [0089]     To obtain the calibration curve for  12 CO 2  concentration,  12 CO 2  absorbance data are measured with the  12 CO 2  concentration changed in the range of 0% to about 8%, and the data thus measured are plotted on a graph in which the axis of abscissas represents the  12 CO 2  concentration and the axis of ordinates represents the  12 CO 2  absorbance. Then, the curve is determined by the method of least squares.  
         [0090]     To obtain the calibration curve for  13 CO 2  concentration,  13 CO 2  absorbance data are measured with the  13 CO 2  concentration changed in the range of 0% to about 0.08%, and the data thus measured are plotted on a graph in which the axis of abscissas represents the  13 CO 2  concentration and the axis of ordinates represents the  13 CO 2  absorbance. Then, the curve is determined by the method of least squares.  
         [0091]     The curves approximated by quadratic equations are relatively less in error. Accordingly, the calibration curves approximated by quadratic equations are adopted in this embodiment.  
         [0092]     There are recorded the  12 CO 2  concentration of the base gas as  12 Conc (B), the  13 CO 2  concentration of the base gas as  13 Conc (B), the  12 C 2  concentration of the sample gas as  13 Conc (S), and the  13 CO 2  concentration of the sample gas as  13 Conc (S), these concentration data being obtained with the use of the calibration curves above-mentioned.  
         [0000]     IV-4 Calculation of the Concentration Ratios  
         [0093]     Then, each concentration ratio between 13CO 2  and  12 CO 2  is obtained. That is, the concentration ratio between  13 CO 2  and  12 CO 2  of the base gas is obtained by  13 Conc (B)/ 12 Conc (B), and the concentration ratio between  13 CO 2  and  12 CO 2  of the sample gas is obtained by  13 Conc (S)/ 12 Conc (S).  
         [0094]     The concentration ratios may also be defined as  13 Conc (B)/( 12 Conc (B)+ 13 Conc (B)) and as  13 Conc (S)/( 12 Conc (S)+ 13 Conc (S)). Since the  12 CO 2  concentrations are much greater than the  13 CO 2  concentrations, the concentration ratios obtained by these different calculation methods are substantially equal to each other.  
         [0000]     IV-5 Determination of  13 C Changed Portion  
         [0095]     The  13 C changed portion in comparison of the sample gas data with the base gas data, is calculated by the following equation:
 
Δ 13   C =[Sample Gas Concentration Ratio−Base Gas Concentration Ratio)]×10 3 /[Base Gas Concentration Ratio](Unit: permil).