JP2013164403A - Method and program for deriving specific gravity of aggregate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and program for deriving the specific gravity of an aggregate, in which a trouble for adjusting a sample in a saturated and surface-dry condition can be saved and an individual difference hardly occurs.SOLUTION: In a method for deriving the specific gravity of an aggregate, after the whole mass mof a vessel V1 in a first state of storing water and the aggregate in a wet state is measured, saline solution is added and a whole mass Mis measured. The specific gravity and concentration of the diluted saline solution are measured, and from the difference between the concentrations before and after dilution, a mass W of the water in the vessel V1 in the first state is derived. Consequently, the net mass and volume of a sample are derived, and the specific gravity of the sample is derived.

Description

  The present invention relates to an aggregate specific gravity deriving method and an aggregate specific gravity deriving program.

  The surface dry specific gravity test method for aggregate includes a fine aggregate specific gravity test method defined in Non-Patent Document 1 and a coarse aggregate specific gravity test method defined in Non-Patent Document 2.

  In the method of Non-Patent Document 1, in order to remove the surface water and adjust the surface of the aggregate soaked in water for 24 hours to absorb water, (1) the fine aggregate removed from the water is flattened. Spread it thinly on a flat surface, whilst sending warm air, occasionally stir and dry evenly. (2) When there is still some surface water on the surface of the fine aggregate, loosely stuff the fine aggregate into the flow cone, level the upper surface, and tap it 25 times with a stick, then flow cone Gently pull it up vertically. (3) At this time, when the fine aggregate cone is slumped for the first time, it is assumed that the surface is dry and saturated.

Furthermore, the aggregate sample thus brought to the surface dry saturation state is tested as follows. (1) Add water up to the fixed scale of the flask, and measure the mass (m ₀ ) at that time. (2) After emptying the water in the flask and weighing the sample (m2) adjusted to the surface dry saturated state to 0.1 g, the sample is put into the flask and water is added to the quantitative scale. (3) Roll the flask on a flat plate to drive out bubbles, then immerse in a water bath of 20 ± 0.2 ° C. (4) About 1 hour later, the sample is taken out, and water is further added to the quantitative scale, and the mass (m3) at that time is measured. (5) Table dry specific gravity of the fine aggregate will be calculated by the equation _{ds = m2 / (m 0 +} m2-m3). Here, ds: surface dry specific gravity, m ₀ : mass (g) of flask filled with water up to quantitative scale, m2: mass for specific gravity test (g), m3: flask filled up to quantitative scale with sample and water Mass (g).

Moreover, in the method of nonpatent literature 2, a representative thing is extract | collected among aggregate samples, (1) It wash | cleans sufficiently with water, and the dust etc. which are attached to the surface of a grain are removed. (2) Remove the water from the sample taken out of the water, roll it on a water-absorbent cloth, and wipe the visible water film. When the grains are large, wipe them one by one. The sample in such a state is tested as follows. (1) Weigh the sample mass m _s to 0.1 g. (2) Put the sample in a basket and immerse it in fresh water at 20 ± 0.2 ° C. to remove bubbles between the surface and the grains, and measure the apparent mass _mw of the sample in water. (3) The specific gravity is calculated by the formula D = m _s / (m _s −m _w ), rounding the 4th significant digit to 3 significant digits. D: surface specific gravity, m _s : mass (g) of sample, m _w : apparent mass of sample in water.

JIS A 1109 JIS A 1111

  According to the methods of Non-Patent Document 1 and Non-Patent Document 2 described above, although the work of adjusting the aggregate sample to the surface dry saturated state requires time and effort, the obtained surface dry saturated state varies depending on the individual. Is likely to occur. This is particularly noticeable in fine aggregate samples.

  An object of the present invention is to provide a method for deriving the specific gravity of an aggregate and a program for deriving the specific gravity of the aggregate, which saves the trouble of adjusting a sample to a surface dry saturated state and hardly causes individual differences.

The method for deriving the specific gravity of the aggregate according to the present invention includes a step of measuring a first mass which is a mass of the entire first container in a first state in which water and a wet aggregate are contained, Add the first liquid comprising an aqueous solution of a given substance in the first container in the first state, the first container, the step of the second state in which the liquid surface became height corresponding to the volume V ₁ Deriving the specific gravity of the second liquid that is the aqueous solution of the predetermined substance in the first container in the second state, and the second liquid concentration that is the concentration of the predetermined substance in the second liquid , A first liquid concentration that is a concentration of the predetermined substance in the first liquid, and a second mass that is a mass of the first liquid added when changing from the first state to the second state And the first state in the first state based on the second liquid concentration. Based on the step of calculating a third mass, which is the mass of water in the container, and the first liquid concentration, the second liquid concentration, the specific gravity, the first mass, the second mass, the third mass, and V ₁ , the bone And a step of calculating the specific gravity of the material in a surface dry saturated water state. In addition, the program of the present invention is the sum of the water and the wet aggregate when the aqueous solution of the predetermined substance is added to the first container containing water and the wet aggregate. Based on the mass, the predetermined volume, the concentration and mass of the added aqueous solution, and the concentration and specific gravity of the aqueous solution in the first container after the aqueous solution is added and diluted, the bone Let the computer function to calculate the specific gravity of the material.

  According to the present invention, an aqueous solution is added to a first container containing wet aggregate and water, and the mass of water in the first container can be derived based on the concentration change of the aqueous solution before and after the addition. Thereby, the net mass and volume of the aggregate are derived, and the specific gravity of the aggregate is calculated. Therefore, since it is not necessary to adjust the sample to a surface dry saturated state in advance, it is difficult to cause labor and individual differences, and the specific gravity of the aggregate can be accurately derived.

It is a flowchart which shows a part of flow of the measurement process in 1st Embodiment. It is a flowchart which shows another part of the flow of the measurement process in 1st Embodiment. It is the schematic which shows the state of two types of containers in the measurement process of FIG.1 and FIG.2. It is the flowchart which showed the flow of the calculation process in 1st Embodiment. It is data which shows the relationship between the estimated value regarding the measurement error of mass and temperature, and the difference between the masses of the water calculated with two types of calculation methods. It is a functional block diagram which shows the structure of the system which concerns on 2nd Embodiment.

[First Embodiment]
Hereinafter, a first embodiment which is an embodiment of the present invention will be described with reference to FIGS. The aggregate specific gravity deriving method according to the first embodiment is roughly divided into A. B. Measurement process It is divided into the calculation process. A. Based on the measurement values obtained in the measurement process, B.I. In the calculation step, the specific gravity of the aggregate is calculated. A. The measurement process includes the sample measurement process of FIG. 1 and the buoyancy correction value measurement process of FIG. In these measurement steps, an electronic balance is used for mass measurement. For the aqueous solution, a saline solution without heat of dilution is used. In the sample measurement process in FIG. 1, aggregates, measuring container V ₁ , measuring container V ₂ , distilled water, and saline are prepared. Saline, previously adjusted to the mass percent concentration P _0. The measuring container V ₁ has a volume up to the quantitative scale V ₁ , and the measuring container V ₂ has a volume up to the quantitative scale V ₂ smaller than V ₁ . The vessel V _1, mark line serves as a mark at a position corresponding to substantially the middle of the volume until quantitative scale is formed. Volume to mark the line of the container _{V 1} was a _{V m.} In this specification, when V ₁ and V ₂ are described alone, they indicate volume values, and when described as containers V ₁ and V ₂ , they indicate the names of the containers.

First, the aggregate is immersed in distilled water and left for 24 hours (step S1). Then removed bone material from distilled water, placed in a container V ₁ with water attached to the aggregate (step S2). Then, as shown in FIG. 3 (a), distilled water is added to the mark line of the container _{V 1} (step S3). The state at this time (first state) is shown in FIG. The container V ₁ containing aggregate and distilled water, distilled water and saline are immersed in a thermostatic water bath at a reference temperature (for example, 20 ± 0.2 ° C.) directly or in a container until immediately before measurement. The temperature is kept at this temperature. In addition, a constant temperature water tank uses a common thing in the following processes. The water in the thermostatic water tank has a sufficiently large heat capacity compared to the container used for measurement, and the container of the water tank itself is configured to keep the temperature constant. For this reason, the temperature in a constant temperature water tank does not change substantially during a measurement process.

Next, the mass (first mass) of the container V ₁ at the reference temperature containing the aggregate and distilled water is measured (step S4). The measured value is defined as m _2. Next, as shown in FIG. 3 (b), saline (first liquid) is added to the container A halfway between the mark line and the fixed scale, and after the bubbles are expelled, the container A is immersed in a constant temperature water bath for about 10 minutes. Then removed from the water bath, add more salt water to quantify the scale of the container V ₁ (step S5). Thus, the added salt solution mixed with distilled water contained in the container V _1, a dilute brine (second liquid). The state at this time (second state) is shown in FIG. Next, to measure the mass of the container _{V 1} of the state of FIG. 3 (c) (step S6). The measured value at this time is defined as _MN2 .

Then, the diluted brine in the vessel V _1, was transferred into the vessel V ₂ through a funnel and filter paper and stored in the container V ₂ until quantitative scale (step S6). The inside filter paper remains aggregate, only dilute brine is contained in a container V _2. The state at this time is shown in FIG. After that, it puts about 10 minutes pickled the container _{V 2} in a constant-temperature water bath. Accordingly, temperature changes in dilution saline is transferred to the container V ₂ is returned to the reference temperature.

Then, to measure the temperature of the dilution brine in the vessel V ₂ (step S7). An electronic thermometer is used for temperature measurement. The measured value is defined as t _1. B. In the calculation step, each value is calculated using t ₁ . Incidentally, t ₁ is not a dilution saline, may be used a measure of the temperature of the water in a thermostat bath may be used in which measured at different timing in the measurement step. Next, to measure the mass of the container _{V 2} in this state (step S8). The measured value is defined as R _2.

The buoyancy correction value measurement step in FIG. 2 includes the following step (1) and step (2). Steps (1) and (2) may be performed with the containers V ₁ and V ₂ emptied after performing the sample measurement step of FIG. In step (1), first, the empty container _{V 1,} accommodates only distilled water was 20 ± 0.2 ° C. in step S1 to quantitative scale (step S11). The state at this time is shown in FIG. Next, to measure the mass container _{V 1} of the this state (fourth mass) (step S12). The measured value at this time is Q _{(1) 2} . In step (2), first, the empty container _{V 2,} for accommodating only distilled water was 20 ± 0.2 ° C. in step S1 to quantitative scale (step S21). The state at this time is shown in FIG. Next, to measure the mass container _{V 2} in this state (sixth mass) (step S22). The measured value at this time is represented by Q _{(2) 2} .

Next, B. The calculation process will be described with reference to FIG. First, A. By subtracting Q _{(1) 2} from m ₂ and M _N2 acquired in the measurement process, m and M _N corrected for buoyancy are obtained as follows (step S30). Further, by subtracting Q _{(2) 2} from R ₂ , R corrected for buoyancy is obtained as in the following equation (step S30). In addition, m is the mass of the distilled water in the first state + sample, _MN is the mass of the diluted saline solution in the second state + the sample, and R is the mass (fifth mass) of the diluted saline in FIG. . .
(Mass calculation formula)
m = m ₂ −Q _{(1) 2} + V ₁ * ρ ₁ − (V ₁ −V _m ) * σ
M _N = M _N2 −Q _{(1) 2} + V ₁ * ρ ₁
R = R ₂ −Q _{(2) 2} + V ₂ * ρ ₁

Where ρ _{1 is} the specific gravity of distilled water and σ is the specific gravity of air. By subtracting Q _{(1) 2} etc. as in this formula, (b) the mass of the container can be removed from each measured value such as m ₂ , and (b) the volume of the container and the contents combined The amount by which the measured value becomes smaller than the actual mass due to the corresponding buoyancy can be corrected. In each equation, the third term on the right side is a term that compensates for the mass of distilled water that has been pulled too much by subtracting Q _{(1) 2} or the like. The fourth term of the first equation is, 3 states and Q ₍₁₎ Figure 3 state at the height of the water surface in the container V ₁ was the (e) corresponding to ₂ (b) corresponding to m ₂ Is a term that cancels out the difference in buoyancy corresponding to the difference in water surface height.

As the specific gravity ρ _{1 of} distilled water, the specific gravity table of Chappieus, which is used as the most accurate water density table at present, is used in this embodiment. The specific gravity σ of air in the fourth term of m is 0.0012 g / cm ³ at 20 ° C. and 1 atm. The specific gravity of air also varies with temperature and pressure, but since the value is small in the first place, errors due to differences in temperature and pressure are almost negligible.

Next, the mass N (second mass) of the saline solution added in step S5 of FIG. 1 is obtained by the following equation (step S32).
(N derivation formula)
N = M _N −m

Next, the specific gravity ρ ₂ of the diluted saline solution (see FIG. 3D) is obtained by the following equation (step S33).
(Ρ ₂ derivation)
ρ ₂ = R / V ₂ = (R ₂ −Q _{(2) 2} ) / V ₂ + ρ ₁

Next, the mass percent concentration of the diluted saline is calculated (step S34). In the present embodiment, the following Pt-ρ relational expression indicating the relationship among the saline solution concentration P, the temperature t, and the specific gravity ρ is used. A method for deriving this equation will be described later. By substituting t = t ₁ and ρ = ρ ₂ into the Pt-ρ relational expression, a quartic equation relating to P is obtained. The solution of the quartic equation relating to P is the concentration of the diluted saline solution (second liquid concentration). This concentration and _{P 2.}
(Pt-ρ relational expression)
ΣA _kl * P ^k * t ^l = ρ (k, l = 0 to 4)

  By the way, A. In the measurement process, errors occur in the measured values of temperature and mass. In step S35 and subsequent steps, the error value is evaluated. First, mathematical formulas used in the steps after S35 will be described as follows.

The error value of each measurement value is defined as follows.
(Error definition formula)
t ₁ = t ₀ + dt
m ₂ = m ₀ + (buoyancy error) + dm
M _N2 = M _N0 + (buoyancy error) + dM _N
R ₂ = R ₀ + (buoyancy error) + dR
N = N ₀ + dN
Q _{(1) 2} = Q ₍₁₎ 0+ (buoyancy error) + dQ ₁
Q _{(2) 2} = Q ₍₂₎ 0+ (buoyancy error) + dQ ₂
ρ ₁ = ρ ₀₁ + dρ ₁
ρ ₂ = ρ ₀₂ + dρ ₂
P ₂ = P ₀₂ + dP

Here, t ₀ , m ₀ , M _N0 , R ₀ , N ₀ , Q _{(1) 0} , Q _{(2) 0} , ρ ₀₁ , ρ ₀₂ , and P ₀₂ are true values obtained by removing errors from the measured values. Dt, dm, dM _N , dR, dN, dQ ₁ , dQ ₂ , dρ ₁ , dρ ₂ , and dP are errors caused by the measurement equipment. Among these, dm, dM _N , dR, dQ ₁ , and dQ ₂ are mass measurement errors by the electronic balance. dρ ₁ is an error in specific gravity due to a temperature error. That is, it depends on dt. Here, assuming that dt is sufficiently small, dρ ₁ is approximated to be linear with respect to dt. When the linear coefficient is k, dρ ₁ and ρ ₁ are expressed by the following ρ ₁ error equation.
(Ρ ₁ error formula)
dρ ₁ = k * dt
ρ ₁ = ρ ₀₁ + k * dt

When this error approximate expression 2 is substituted into the above ρ ₂ derivation expression, ρ ₂ is expressed as the following ρ ₂ error expression. Accordingly, ρ ₀₂ and dρ ₂ are also expressed as follows. It should be noted, it is a n≡dR-dQ _2.
(Ρ ₂ error formula)
ρ ₂ = (R ₀ −Q _{(2) 0} ) / V ₂ + ρ ₀₁ + k * dt + (dR−dQ ₂ ) / V ₂
ρ ₀₂ = (R ₀ −Q _{(2) 0} ) / V ₂ + ρ ₀₁
dρ ₂ = k * dt + n / V ₂

On the other hand, the weight percent concentration of dilute saline depends on both temperature and specific gravity. Both the temperature error dt and the specific gravity error dρ ₂ are sufficiently small, and the concentration error dP of the diluted saline is approximated to be linear with respect to both dt and dρ ₂ . In this case, when the linear coefficient related to dt is α and the linear coefficient related to dρ ₂ is β, dP is expressed as follows. In addition, as shown in the ρ ₂ error equation, dρ ₂ shows an error with k as a coefficient related to the temperature error, and an error related to n appears independently from the temperature error. The term n / V ₂ also appears.
(P error formula)
dP = β * dρ ₂ = β * (n / V ₂ + α * (− k + 1) * dt)

Meanwhile, when the mass of the distilled water in the vessel V ₁ of the first state (FIG. 3 (b)) (third mass) and W, the two equations below about W holds. In the container V ₁ in the first state, assuming that distilled water is added up to a quantitative scale instead of saline, the mass of distilled water added at this time is H.
(W + H) / ρ ₀₁ = (W + N) / ρ ₀₂
Holds. From this formula:
(W derivation formula 1)
W = (ρ ₀₁ * N−ρ ₀₂ * H) / (ρ ₀₂ −ρ ₀₁ )
Is obtained.

On the other hand, the mass N * P _{0 of the} salt obtained from the mass N of the added saline and its concentration P ₀ (first liquid concentration), and the dilution in the container V ₁ in the second state (FIG. 3C) Since the mass (N + W) of the saline solution and the mass P ₀₂ * (N + W) of the salt obtained from the concentration P ₀₂ are equal,
(W derivation formula 2)
W = (P ₀ / P ₀₂ −1) * N
Is obtained.

From the W derivation formula 1,
(H derivation formula)
H = [(ρ ₀₁ −ρ ₀₂ ) * W + ρ ₀₁ * N] / ρ ₀₂
Is obtained.

Substituting the above error definition formula, ρ ₁ error formula, ρ ₂ error formula and P error formula into these W derivation formula 1, W derivation formula 2 and H derivation formula,
(W error formula 1)
W = [(ρ ₁ −k * dt) * N− {ρ ₂ −k * dt−n / V ₂ } * H] / (ρ ₂ −ρ ₁ −n / V ₂ )
(W error formula 2)
W = [P ₀ / {P ₂ −β * (n / V ₂ −α * (− k + 1) * dt)} − 1] * N
(H error formula 1)
H = [(ρ ₁ −ρ ₂ + k * dt + n / V ₂ ) * W + (ρ ₁ −k * dt) * N] / (ρ ₂ −k * dt−n / V ₂ )
Get. Also, substituting W error equation 2 into H error equation 1,
(H error formula 2)
H = [(ρ ₁ −ρ ₂ + n / V ₂ ) * [P ₀ / {P ₂ −β * (n / V ₂ −α * (− k + 1) * dt)} − 1] * N + (ρ ₁ − k * dt) * N] / (ρ ₂ −k * dt−n / V ₂ )
Get. The above is the formula used in the processes after step 35.

  Next, step S35 and subsequent steps will be described. First, k, α, and β (change rate) are determined as follows (step S35). Since k and α are change rates of specific gravity with respect to minute temperature changes, in order to obtain these, a minute temperature change width Δt is appropriately set. In this embodiment, Δt is set based on the maximum error of the electronic thermometer used for temperature measurement. For example, when the maximum error of the electronic thermometer is Δ (> 0), Δt = + Δ or −Δ is set. Further, β is a change rate of density with respect to a minute change in specific gravity, and therefore a minute change width ΔP of density is appropriately set in order to obtain this. In the present embodiment, an arbitrary minute numerical value is set as ΔP.

Next, k, α, and β are obtained based on the temperature change width Δt and the concentration change width ΔP. Specifically, first, by assigning t = t ₁ −Δt to the t−ρ relational expression, the specific gravity ρ ₁ ′ when changed from t ₁ by Δt can be obtained. Using this, k can be obtained as follows.
(K derivation formula)
k = (ρ ₁ −ρ ₁ ′) / Δt

Similarly, α and β are obtained as follows. First, by substituting t _{= t} 1 -.DELTA.t, the P = _{P 2} to P-t-ρ relation, obtaining a density [rho ₂ ^A when changed from _{t 1} only Delta] t. On the other hand, by substituting P = P ₂ −ΔP and t = t ₁ into the Pt−ρ relational expression, the specific gravity ρ ₂ ^B when ΔP is changed from P ₂ is obtained.

Using the above, α and β can be obtained as follows.
(Αβ derivation formula)
α = (ρ ₂ −ρ ₂ ^A ) / Δt
β = ΔP / (ρ ₂ −ρ ₂ ^B )

  Next, an estimated value of dt (temperature error estimated value) and an estimated value of n (mass error estimated value) are set (step S36). The setting range of dt is determined based on the maximum error Δ of the electronic thermometer used for temperature measurement and the minimum display value. For example, when the maximum error is 0.3 ° C. and the minimum display value is 0.1 ° C., the minimum display value is 0.1 within the range of −0.3 ° C. to 0.3 ° C. based on the maximum error. Set in increments of ℃. That is, dt (estimated value) = − 0.3, −0.2, −0.1, 0.0, 0.1, 0.2, 0.3 ° C. is set. Similarly, n is determined based on the maximum error and the minimum display value of the electronic balance used for mass measurement. For example, n (estimated value) = − 0.3, −0.2, −0.1, 0.0, 0.1, 0.2, 0.3 g is set. According to the first embodiment described later, since the sign of both dt and n is determined, the number of combinations of estimated values is greatly reduced.

Next, when W represented by the W error equation 1 is set to W ₁ and W represented by the W error equation 2 is set to W ₂ , for each of the estimated values of dt and n set in step S36, dW≡W ₁ −W ₂ is calculated (step S37). Specifically, first, the combination of (dt, n) is variously changed within the set range, and is substituted into the H error equation 2 to obtain H. Next, W ₁ is calculated by substituting the obtained H into the W error equation 1, and W ₂ is calculated using the W error equation 2. Then, dW = W ₁ −W ₂ is calculated. Next, among the calculated dWs, a combination of (dt, n) whose dW value is closest to 0 is extracted as an appropriate error value combination (step S38).

Next, the specific gravity of the aggregate is calculated based on (dt, n) extracted in step S38 (step S39). Specifically, first, the extracted (dt, n) is substituted into the W error equation 2 to obtain W. Also, ρ ₀₂ is calculated by substituting the extracted (dt, n) into the above error equation for ρ ₂ . Then, the specific gravity ρs of the aggregate is obtained by using the following mathematical formula. The reason why W error equation 2 is used instead of W error equation 1 for calculating W is that both H and N are included in W error equation 1, and therefore both errors of H and N are included. On the other hand, since the W error equation 2 includes only N, the error is only derived from N and is more accurate.
(Aggregate derivation formula)
S = m−W
V _s = V ₁ − [P ₀ / {P ₂ −β * (n / V ₂ −α * (− k + 1) * dt)}] * N / ρ ₀₂
ρ _s = S / V _s

Here, S: mass of aggregate, V _s : volume of aggregate, ρ _s : specific gravity of aggregate. Note that V _{s in} the second formula of the aggregate derivation formula is derived as follows. In the container V ₁ in the second state, the mass of the diluted saline is expressed as N + W = (V ₁ −V _s ) * ρ ₀₂ . By substituting the W derivation formula 2 into this formula, the following formula is obtained.
(N derivation formula)
P ₀ / P ₀₂ * N = (V ₁ −V _s ) * ρ ₀₂
Therefore, V _s = V ₁ −P ₀ / P ₀₂ * N / ρ ₀₂ . If the above P error equation is substituted here, the second equation of the aggregate derivation equation is obtained.

(Derivation of specific gravity of distilled water)
The specific gravity table of Chappieus is used for the specific gravity of distilled water. The leftmost column of the table shows the integer part of the temperature, and the top row shows the decimal part of the temperature. The 4-digit numerical values in the table indicate the numerical values of the fourth to seventh decimal points of the specific gravity (g / cm ³ ). The numerical values from the first decimal place to the third decimal place of the specific gravity follow the numerical values in the second column from the left (for example, “0.999” from 0.0 to 16.9 ° C.). For example, if it is 20.3 ° C., in Table 1, the numerical value of the fourth to seventh decimal places in the specific gravity when the integer part of the temperature is 20 and the decimal part is 0.3 is “1395”. I understand that. Moreover, it turns out from the numerical value of the 2nd column from the left that the numerical value from the 1st decimal place to the 3rd decimal place is 0.998. From these, it can be seen that the specific gravity of water at 20.3 ° C. is 0.9981395 g / cm ³ .

(Derivation of Pt-ρ relational expression)
Hereinafter, a method for deriving the Pt-ρ relational expression will be described. The reason for using such an equation is to allow P, t, and ρ to be obtained with the highest possible accuracy when the data of the Pt-ρ relationship is limited. In particular, as shown in Appendix 2, when there is data only every 5 to 10 ° C. or every 2%, there is no choice but to adopt some means for complementing the data. In this embodiment, the Pt-ρ relational expression is derived from the data in Table 2 by the following method, so that P, t, and ρ can be obtained mutually with high accuracy even in a minute temperature range or concentration range. It is said. The numerical values other than the temperature and concentration in Table 2 are all specific gravity (g / cm ³ ) of saline.
ΣA _ki * P ^k * t ⁱ = ρ (k, i = 0 to 4)

First, in the above formula, the sum related to i is expanded and expressed as follows.
ΣB _k (t) * P ^k = ρ (k = 0 to 4)
However, B _k (t) = A _k0 + A _k1 * t + A _k2 * t ² + A _k3 * t ³ + A _k4 * t ⁴

Next, while fixing t, five different combinations regarding (P, ρ) are extracted from Table 2 and substituted into ΣB _k (t) * P ^k = ρ. For example, when t = 10 (° C.), (P, ρ) = (4, 1.02920), (8, 1.05907), (14, 1.10491), (18, 1.13643), (22 , 1.16891). Thereby, P = 4, 8, 14, 18, 28 (%) at t = 10 (° C.), another B ₀ (10), B ₁ (10), B ₂ (10), B ₃ (10), The five simultaneous linear equations for B ₄ (10) are obtained. By solving this equation, specific numerical values of the specific gravity B _k (10) (k = 0 to 4) of the quaternary expression of t at t = 10 (° C.) can be obtained.

Similarly, specific numerical values of specific gravity B _k (t) (k = 0 to 4) are obtained for temperatures other than 10 ° C. For example, the specific gravity specific gravity B _k (20), B _k (25), B _k (30), B _k (40) for each of t = 20, 25, 30, 40 (° C.) is set to k = 0 to 0. Acquire for each of 4. Since B _k (t) = A _k0 + A _k1 * t + A _k2 * t ² + A _k3 * t ³ + A _k4 * t ⁴ holds, A _k0 , A _k1 , A _k2 , A for k = 0 to 4 respectively. Obtain five simultaneous linear equations for _k3 and _Ak4 . For example, the five simultaneous equations for k = 0 are as follows.
B ₀ (10) = A ₀₀ + A ₀₁ * 10 + A ₀₂ * 10 ² + A ₀₃ * 10 ³ + A ₀₄ * 10 ⁴
B ₀ (20) = A ₀₀ + A ₀₁ * 20 + A ₀₂ * 20 ² + A ₀₃ * 20 ³ + A ₀₄ * 20 ⁴
B ₀ (25) = A ₀₀ + A ₀₁ * 25 + A ₀₂ * 25 ² + A ₀₃ * 25 ³ + A ₀₄ * 25 ⁴
B ₀ (30) = A ₀₀ + A ₀₁ * 30 + A ₀₂ * 30 ² + A ₀₃ * 30 ³ + A ₀₄ * 30 ⁴
B ₀ (40) = A ₀₀ + A ₀₁ * 40 + A ₀₂ * 40 ² + A ₀₃ * 40 ³ + A ₀₄ * 40 ⁴

A ₀₀ , A ₀₁ , A ₀₂ , A ₀₃ , A ₀₄ are obtained by solving the above five simultaneous linear equations for k = 0. Similarly, A _k0 , A _k1 , A _k2 , A _k3 , and A _k4 are obtained for k = 1 to 4 by solving five simultaneous linear equations for k = 1, 2, 3, and 4, respectively. Can do. As described above, all A _ki can be determined by solving the five simultaneous linear equations with respect to k = 0, 1, 2, 3, and 4, respectively. Therefore, the Pt-ρ relational expression ΣA _ki * P ^k * t ⁱ = ρ (k, i = 0 to 4) can be specifically acquired.

(First embodiment)
Hereinafter, a first example according to a numerical simulation performed in accordance with the above-described embodiment will be described. In this simulation, each condition was assumed as follows. In the following, the condition described as [Premise] means that in an actual experiment, it corresponds to a known precondition before measurement.

(temperature)
t ₀ : 20.0 ° C

(Container) [Premise]
V ₁ : 2000.0 ml
V ₂ : 800.5 ml
V _m : 1000.0 ml
* However, in this embodiment, it is assumed that the height of the water surface in the first state is slightly below the mark line. The water volume of the container V ₁ of the up to the height of this time when the V _m0, can be calculated as follows. This value is unknown at the beginning of the experiment.
V _m0 = V ₁ − {(V ₁ −Vs) * ρ ₀₁ −W ₀ } / ρ ₀₁
= 988.884100422509ml

(Electronic thermometer) [Prerequisites]
Maximum error Δ: 0.3 ° C
Minimum display value: 0.1 ° C (2 decimal places are rounded off)

(Electronic scale) [Premise]
Minimum display value: 0.1 g (2 decimal places are rounded off)

(Tare: Container V ₁ ) [Premise]
Mass F ₁ : 850 g
Volume V _F1 : 425 cm ³

(Tare: Container V ₂ ) [Premise]
Mass F ₂ : 500 g
Volume V _F2 : 250 cm ³

(Aggregate sample)
Mass S ₀ : 1409.4 g
Volume V _s0 : 540.0 ml
Specific gravity ρ _s0 : 2.61 g / cm ³

(Distilled water)
W _0: 448.03394321538g
(Calculated along with N using V derivation 2 and N derivation from V ₁ , V _s0 , P ₀ , P ₀₂ , ρ ₀₂ )
ρ ₀₁ : 0.9982019 g / cm ³
(The specific gravity corresponding to t ₀ is derived from Table 1)

(Saline solution (before dilution))
P ₀ : 26.0% by weight [premise]
N ₀ : 1216.00921158462 g
(Calculated together with W ₀ from V ₁ , V _s0 , P ₀ , P ₀₂ , ρ _{02 using the} above W derivation 2 and N derivation)

(Diluted saline)
P ₀₂ : 19.0% by weight
ρ ₀₂ : 1.139812380 g / cm ³
(Calculated by substituting t ₀ and P ₀₂ into the Pt-ρ relational expression)

(Error value)
dt: + 0.3 ° C
dm: +0.1 g
dM _N : -0.1 g
dR: -0.1 g
dQ ₁ : -0.1 g
dQ ₂ : 0.1 g

According to the above condition values, A. In the measurement process, it is assumed that a measurement value including an error due to buoyancy and an error due to measurement equipment is obtained in the true value. In this case, each measured value is as follows. In the following description, D [x] represents a numerical value obtained by rounding off the decimal part of x with respect to x.
t ₁ = t ₀ + dt
= 20.3
m ₂ = D [S ₀ + W ₀ + F ₁ −σ * (V _m0 + V _F1 ) + dm]
= D [2705.8837331031]
= 2705.8
M _N2 = D [m ₀ + N ₀ + F ₁ −σ * (V ₁ + V _F1 ) + dM _N ]
= D [3920.5160748]
= 3920.5
R ₂ = D [V ₂ * ρ ₀₂ + F ₂ −σ * (V ₂ + V _F2 ) + dR]
= D [1411.05921019]
= 1411.1
Q _{(1) 2} = D [V ₁ * ρ ₀₁ + F ₁ −σ * (V ₁ + V _F1 ) + dQ ₁ ]
= D [2843.3938]
= 2843.4
Q _{(2) 2} = D [V ₂ * ρ ₀₁ + F ₂ −σ * (V ₁ + V _F2 ) + dQ ₂ ]
= D [1297.90002095]
= 1297.9

Next, assuming that the above measured values were obtained, B. In the calculation step, the specific gravity of the aggregate is calculated as follows. First, according to steps S30 to S33 of FIG. 4, the following mass values and specific gravity values are obtained.
m = m ₂ −Q _{(1) 2} + V ₁ * ρ ₁ − (V ₁ −V _m ) * σ
= 1857.479
M _N = M _N2 −Q _{(1) 2} + V ₁ * ρ ₁
= 3073.379
R = R ₂ −Q _{(2) 2} + V ₂ * ρ ₁
= 912.211
N = M _N −m
= 1215.9
ρ ₂ = R / V ₂ = (R ₂ −Q _{(2) 2} ) / V ₂ + ρ ₁
= 1.395551
Here, ρ ₁ = 0.9981395 g / cm ³ was used. This value is obtained by deriving the specific gravity corresponding to t = t ₀ + dt from Table 1.

Further, according to step S34, to obtain a P ₂ by solving the fourth order equation is obtained by substituting t ₁ and [rho ₂ to P-t-ρ relationship.
P ₂ = 18.99852021354179

Next, in step S35, k, α, and β are determined. In this embodiment, the following method for determining the sign of dt is adopted before these are determined. First, the following W ₂ ′, H ′, and W ₁ ′ values are obtained using the W derivation formulas 1 to H derivation formulas.
W ₂ ′ = (P ₀ / P ₂ −1) * N
= 449.260042780031
H = [(ρ ₁ −ρ ₂ ) * W ₂ ′ + ρ ₁ * N] / ρ ₂
= 1009.2633391431
W ₁ ′ = (ρ ₁ * N−ρ ₂ * H) / (ρ ₂ −ρ ₁ )
= 450.5767359033743

Therefore, W ₁ ′> W ₂ ′. According to a second embodiment to be described later, since it is known that dt> 0 when W ₁ ′> W ₂ ′, it can be determined that dt> 0 at this point.

Next, k, α, and β are determined. Since Δ = 0.3 and dt> 0 as described above, Δt = + Δ = + 0.3 is set. Further, ΔP = 0.0111 is set. From Table 1, at the measurement temperature t ₁ = 20.0 ° C., ρ ₁ ′ = 0.9982019. Therefore, k is obtained as follows.
k = (ρ ₁ −ρ ₁ ′) / Δt
= -0.000208

Also, t = t ₁ −Δt = 20.0, P = P ₂ is substituted into the Pt−ρ relational expression, and t = t ₁ , P = P ₂ −ΔP = 18.99741021354179 is changed to Pt By substituting into the -ρ relational expression, ρ ₂ ^A and ρ ₂ ^B are obtained.
ρ ₂ ^A = 1.13969482663652
ρ ₂ ^B = 1.13946298284840

Therefore, α and β are obtained.
α = (ρ ₂ −ρ ₂ ^A ) / Δt
= -0.000479027636666667
β = ΔP / (ρ ₂ −ρ ₂ ^B )
= 125.943300542582

  Next, in step S36, estimated values of dt and n are set using the W error equation 1, the W error equation 2, and the H error equation 2. In the W error equation 1, the W error equation 2, and the H error equation 2, since numerical values other than dt and n have already been determined, if dt and n can be determined, W and H can be obtained. First, by calculating dP as in the third embodiment below, it is possible to register n <0.

Next, a combination of estimated values of (dt, n) is set. As described above, since dt> 0 and n <0 are registered, the following settings are made.
(Dt, n) = (0,0), (0.1,0), (0.2,0), (0.3,0), (0, −0.1), (0.1, -0.1), (0.2, -0.1), (0.3, -0.1), (0, -0.2), (0.1, -0.2), (0 .2, -0.3), ...

In step S37, dW is calculated. Specifically, first, H for each combination is obtained using the H error equation 2, and then dW = W ₁ −W ₂ is calculated using the W error equation 1 and the W error equation 2. FIG. 5 shows the result. In FIG. 5, the reason why the value of H is two digits after the decimal point is that the value of N used in the calculation of H and W is one digit after the decimal point, so the accuracy of H is about one digit higher than N. This is because it is understood that it is sufficient to set to.

Next, in step S38, a combination having the smallest dW (dt, n) is extracted. As shown in FIG. 5, dW is smallest when n = −0.2 and dt = 0.3. Therefore, (dt, n) = (0.3, −0.2) is extracted. Here, since dt = 0.3 and n = dR−dQ ₂ = −0.2 are surely obtained from the initially assumed values of this simulation, an appropriate combination of error values can be extracted. I understand that.

Next, in step S39, the specific gravity of the aggregate is calculated.
W = [P ₀ / {P ₂ −β * (n / V ₂ −α * (− k + 1) * dt)} − 1] * N
= 448.0088798830441
S = m−W
= 1409.551500135696
V _s = V ₁ − [P ₀ / {P ₂ −β * (n / V ₂ −α * (− k + 1) * dt + α * dt)}] * N / (ρ ₂ −n / V ₂ −k * dt )
= 539.921684375262
ρ _s = S / V _s
= 2.610591556779117

Here, when the difference between the specific gravity of the obtained aggregate and the initial set value of this simulation is obtained, it becomes as follows, and this is the final error.
ρ _s −ρ _s0 = 0.0005915776711

When W is calculated using the W error formula 1 in step S39, the following is obtained.
W = [(ρ ₁ −k * dt) * N− {ρ ₂ −k * dt−n / V ₂ } * H] / (ρ ₂ −ρ ₁ −n / V ₂ )
= 447.208339895584

According to this, it can be seen that the above value using the W error equation 2 is closer to the initial setting value of this simulation, W ₀ = 448.0342932153.

(Second embodiment)
Hereinafter, a second embodiment according to another numerical simulation will be described. In the second embodiment, the following conditions are used.
t ₁ : 20.3 ° C.
t ₂ : 19.7 ° C.

For each of the above conditions, ρ ₁ is derived using the t-ρ relational expression as follows.
(When t ₁ ) ρ ₁ = 0.9981395
(When t ₂ ) ρ ₁ = 0.9982633

Accordingly, each ρ ₂ is also derived as follows using the ρ ₂ derivation formula.
(When t ₁ ) ρ ₂ = 1.1395511
(When t ₂ ) ρ ₂ = 1.13996749

Substituting t ₁ or t ₂ or ρ ₂ into the tP-ρ relational expression and deriving P ₂ results in the following.
(When t ₁ )
P ₂ = 18.9985202
(At _{t 2)}
P ₂ = 18.949046

Using the P ₂ calculation result and the W derivation formula 1 and the W derivation formula 2, the following W ₁ ′ and W ₂ ′ are calculated, respectively.
(When t ₁ )
W ₁ ′ = (ρ ₁ * N−ρ ₂ * H) / (ρ ₂ −ρ ₁ )
= 449.28739
W ₂ ′ = (P ₀ / P ₂ −1) * N
= 449.26004
(At _{t 2)}
W ₁ ′ = (ρ ₁ * N−ρ ₂ * H) / (ρ ₂ −ρ ₁ )
= 449.446848
W ₂ ′ = (P ₀ / P ₂ −1) * N
= 451.06645

Thus, when the measured value is higher than the true value (20.0 ° C.) (when t ₁ ), the relationship of W ₁ ′> W ₂ ′ is greater than the true value (20.0 ° C.). When it is low (when t ₂ ), it is shown that the relationship of W ₁ ′ <W ₂ ′ is established. It is understood that such a shift in W ₁ ′ and W ₂ ′ is satisfied if it is in the vicinity of 20.0 ° C. For this reason, as long as the temperature setting of distilled water or saline is performed at 20.0 ° C., the measured value of temperature is higher than the true value (dt> 0) by verifying the magnitude relationship between W ₁ and W _2. It is understood that it is possible to determine whether it is low or low (dt <0).

(Third embodiment)
Hereinafter, a third embodiment according to another numerical simulation will be described. From the P error equation: dP = β * (− n / V ₂ + α * (− k + 1) * dt)

Further, dP is calculated as follows in each case of n = 0, 0.1, and −0.1 with dt = 0.1 fixed. The numerical values of the first embodiment were used for conditions other than n and dt.
When n = 0: dP = 0.00006034301249
When n = 0.1: dP = −0.00969987781419
When n = −0.1: dP = 0.021767380040

Here, in order to approach the true value of 19.0 from P ₂ = 18.99852 in the first embodiment, it is assumed that the sign of n is negative because the value of dP must be positive. The

[Second Embodiment]
The second embodiment according to the present invention is the same as that of the first embodiment. The present invention relates to an aggregate specific gravity derivation system that executes a calculation process. As shown in FIG. 6, the system includes a computer 100, and an input device 111 and an output device 112 connected to the computer 100. The computer 100 includes a CPU 101 that executes various types of information processing and a storage unit 103 that stores various types of data. The storage unit 103 includes a memory, a hard disk, and the like, and an area for storing program data and a work area for temporarily storing work data are secured. The input device 111 includes a keyboard, a mouse, and the like. Each measurement value in the measurement process is used to input to the computer 100. The output device 112 includes a display, a printer, and the like. The data input screen from the input device 111 and the B.B. The calculation result of the calculation process is output to the user.

The recording medium 121 is a medium such as a DVD-ROM, a CD-ROM, or a USB memory. A program for executing the calculation process is stored. The program includes data shown in Table 1 and data corresponding to A _ki that is a coefficient of the _Pt -ρ relational expression. Data corresponding to values that can be calculated in advance and are necessary for executing the calculation process are included. This program can be executed by the CPU 101 by being transferred from the recording medium 121 to the storage unit 103. CPU101 by executing various kinds of information processing according to a program stored in the storage unit 103, (1) conditions such as _{V 1} and _{V 2, m 2, M N2} , R 2 such measurements, such as, B. A process for allowing the user to input data necessary for executing the calculation process through the input device 111. (2) Based on the input data, B.I. Processing for executing steps S30 to S39 in the calculation step, (3) processing for causing the output device 112 to output the calculated data such as S, Vs, and ρs are executed. Note that the data related to the measured value is not input to the computer 100 via the input device 111, but the data related to the measured value recorded on the recording medium may be directly read out by the computer 100. Further, it may be transmitted from the outside to the computer 100 via a network.

(Modification)
In the above-described embodiment, in step S31, Q _{(1) 2} and Q _{(2) 2} are measured and subtracted from m ₂ or the like to correct an error due to buoyancy. However, when the error due to buoyancy is ignored, step S31 is not performed. When step S31 is not performed, m, M _N , R, and the like must be calculated using the tare mass (F ₁ , F ₂ ).

In the above-described embodiment, the concentration P ₂ of the diluted saline is set to B.I. In the calculation step, the temperature is calculated from the temperature t ₁ and the specific gravity ρ ₂ using the Pt-ρ relational expression. In the measurement step, the measurement may be performed directly using a concentration measuring device based on the measurement of electrical conductivity. In this case, the specific gravity ρ ₂ may be calculated from the measured concentration P ₂ and the temperature t ₁ using the Pt-ρ relational expression.

  In the above-described embodiment, the temperature and mass measurement errors are evaluated after step S35. However, when these errors are ignored, step S35 is not performed, and the measurement is performed using the formulas W derivation formulas 1 to H derivation formulas. It is only necessary to directly substitute the value and obtain the specific gravity of the aggregate.

  Further, the method of deriving the tP-ρ relational expression in the above-described embodiment (the above paragraphs 0044 to 0049) may be applied to an aqueous solution having pure sucrose, acetic acid, sulfuric acid, nitric acid or the like as a solute.

100 Computer 103 Storage Unit 111 Input Device 112 Output Device 121 Recording Medium

The method for deriving the specific gravity of the aggregate according to the present invention includes a step of measuring a first mass which is a mass of the entire first container in a first state in which water and a wet aggregate are contained, Add the first liquid comprising an aqueous solution of a given substance in the first container in the first state, the first container, the step of the second state in which the liquid surface became height corresponding to the volume V ₁ Deriving the specific gravity of the second liquid that is the aqueous solution of the predetermined substance in the first container in the second state, measuring the temperature of the second liquid, and in the second liquid Deriving the second liquid concentration, which is the concentration of the predetermined substance , from the specific gravity and temperature of the second liquid based on a known relationship between the concentration, specific gravity and temperature in the aqueous solution; A first liquid concentration that is a concentration of a predetermined substance, the first state From the second mass that is the mass of the first liquid added when the second state is added to the second state, and the mass of water in the first container in the first state based on the second liquid concentration Based on the step of calculating a third mass, the first liquid concentration, the second liquid concentration, the specific gravity of the second liquid, the first mass, the second mass, the third mass, and V ₁ A step of calculating the specific gravity of the aggregate in the surface dry saturated state , and the step of calculating the third mass, and the step of calculating the specific gravity of the aggregate in the surface dry saturated state. A step of setting a mass error estimation value relating to a mass measurement error and a temperature error estimation value relating to a temperature measurement error, a rate of change of the specific gravity of the aqueous solution relative to the temperature measurement error, and the aqueous solution corresponding to a temperature and mass measurement error Concentration change Calculating the rate, and setting the third mass expressed based on the first liquid concentration, the second liquid concentration, and the second mass to W1, and the liquid level on the first container in the first state There weight of additional water when adding water to a height corresponding to the volume V _1, the water specific gravity, the third mass is expressed based on the specific gravity and the second mass of the aqueous solution W2 And calculating the difference between W1 and W2 according to the mass error estimated value, the temperature error estimated value, and the rate of change, and the mass error estimated value and the temperature error estimated value. The step of extracting the combination that minimizes the difference between W1 and W2 calculated for the plurality of combinations is performed. Alternatively, the specific gravity deriving method of the aggregate of the present invention includes a step of measuring a first mass that is a mass of the entire first container in a first state in which water and a wet aggregate are accommodated, and Add the first liquid comprising an aqueous solution of a given substance in the first container is in said first state, said first container, a second state in which the liquid surface became height corresponding to the volume V ₁ Deriving a second liquid concentration that is a concentration of the predetermined substance in a second liquid that is an aqueous solution of the predetermined substance in the first container in the second state; and A first liquid concentration that is a concentration of the predetermined substance in one liquid, a second mass that is a mass of the first liquid added when changing from the first state to the second state, and the second liquid concentration A third mass that is the mass of water in the first container in the first state based on And calculating the first liquid concentration, the second liquid concentration, the specific gravity of the second liquid, the first mass, the second mass, the third mass and V ₁ based on the first liquid concentration, the second liquid concentration, the specific gravity of the second liquid , Calculating a specific gravity in a surface dry saturated water state, and the step of deriving the second liquid concentration includes any one of the first and second concentration deriving steps, and the first concentration deriving step comprises the steps of measuring the the step of transferring the second container while the second liquid is filtered, the second container total mass which accommodates the second liquid volume V ₂ of the first vessel, Deriving the specific gravity of the second liquid, and the second liquid concentration deriving step is a step of deriving the second liquid concentration using a concentration measuring device.

Claims (9)

Measuring a first mass that is a mass of the entire first container in a first state in which water and wet aggregate are contained;
Add the first liquid comprising an aqueous solution of a given substance in the first container is in said first state, said first container, a second state in which the liquid surface became height corresponding to the volume V ₁ And a process of
Deriving the specific gravity of a second liquid that is an aqueous solution of the predetermined substance in the first container in the second state;
Deriving a second liquid concentration that is a concentration of the predetermined substance in the second liquid;
A first liquid concentration that is a concentration of the predetermined substance in the first liquid; a second mass that is a mass of the first liquid added when the first state is changed to the second state; and Calculating a third mass that is a mass of water in the first container in the first state based on a liquid concentration;
Based on the first liquid concentration, the second liquid concentration, the specific gravity of the second liquid, the first mass, the second mass, the third mass, and V ₁ , the aggregate in a surface dry saturated state And a method for deriving the specific gravity of the aggregate. Measuring a fourth mass which is the mass of the entire first container containing only water;
The aggregate specific gravity deriving method according to claim 1, further comprising: calculating a correction value obtained by correcting an error due to buoyancy in the first mass based on the fourth mass. Deriving the second liquid concentration comprises:
Measuring a fifth mass is a second container total mass which accommodates the second liquid volume V _2,
Measuring a sixth mass is the second vessel the total mass containing the water by the volume V _2,
The aggregate specific gravity deriving method according to claim 1, further comprising: calculating a correction value obtained by correcting an error due to buoyancy in the fifth mass based on the sixth mass. Further comprising measuring the temperature of the second liquid;
In the step of deriving the second liquid concentration,
When the temperature is t and A _kl (k, l = 0, 1, 2, 3, 4) is a constant, the second liquid concentration is derived using the formula ΣA _kl * P ^k * t ^l = ρ. The method for deriving the specific gravity of the aggregate according to any one of claims 1 to 3. Setting a mass error estimate for mass measurement error and a temperature error estimate for temperature measurement error; and
Calculating a rate of change of the specific gravity of the aqueous solution with respect to a temperature measurement error, and a rate of change of the concentration of the aqueous solution with respect to a temperature and mass measurement error;
The first liquid concentration, the third mass is expressed based on the second liquid concentration and the second mass and W1, the liquid level in the first container is in said first state corresponds to the volume V ₁ W1 when W3 is the third mass represented based on the mass of water to be added until the height reaches, the specific gravity of water, the specific gravity of the aqueous solution, the specific gravity of the aqueous solution and the second mass Calculating a difference that occurs between W2 and the mass error estimated value, the temperature error estimated value, and the rate of change;
A step of extracting the combination that minimizes a difference between W1 and W2 calculated for a plurality of combinations of the mass error estimated value and the temperature error estimated value. The aggregate specific gravity deriving method according to claim 4.   When adding an aqueous solution of a predetermined substance up to a predetermined volume to a first container containing water and wet aggregate, the total mass of the water and wet aggregate, and the predetermined volume The specific gravity of the aggregate is calculated based on the concentration and mass of the added aqueous solution and the concentration and specific gravity of the aqueous solution in the first container after the aqueous solution is added and diluted. A program characterized by causing a computer to function.   The program according to claim 6, wherein the computer functions to calculate the concentration of the diluted aqueous solution based on the specific gravity and temperature of the diluted aqueous solution.   The mass W of the water in the first container before the aqueous solution is added is calculated based on the concentration and mass of the added aqueous solution and the concentration of the aqueous solution after the dilution. The program according to claim 6 or 7, characterized by causing a computer to function. Setting a mass error estimate for mass measurement error and a temperature error estimate for temperature measurement error; and
Calculating a rate of change of the specific gravity of the aqueous solution with respect to a temperature measurement error, and a rate of change of the concentration of the aqueous solution with respect to a temperature and mass measurement error;
W1 represented by the concentration and mass of the aqueous solution to be added, and the concentration of the diluted aqueous solution is W1, and the liquid level is in the first container before the aqueous solution is added. It is expressed based additional mass of water, water density, the mass of the aqueous solution having a specific gravity and the said additional said diluted the solution for adding water to a height corresponding to the volume V ₁ Calculating a difference generated between W1 and W2 according to the mass error estimated value, the temperature error estimated value, and the rate of change when W is W2.
And causing the computer to execute the step of extracting the combination that minimizes the difference between W1 and W2 calculated for a plurality of combinations of the mass error estimated value and the temperature error estimated value. The program according to claim 8.

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