On carrying out a plan for land amelioration, it is important to decide the sampling number which stands for the physical conditions of the field concerned. However, as sampling number is different under each places, we find it difficult to settle their representative value of soil physical properties. From the above point of view, we made a study about method of deciding the sampling number rationally by means of statistics. We chose 0.5 ha polder paddy field of Hachihama farm of Okayama University in Kojima Bay as a sampling farm, and examined water content and dry density of both surface and subsurface soil. Samplings were done with stainless samplers of φ75mm, φ50mm, φ25mm and 50 mm high respectively. These results are summarised as follows.
1) In the water content measurement, fluctuation is larger in case of weighing bottle than in case of constant volume sampler both in the surface and subsurface. And fluctuation is generally larger in the surface than in the subsurface.
2) In water content measurement, the necessary sampling number N_αs with the bottles requires about twice as many as that with the samplers. Also N_αs for surface soil requires about 1.5-1.6 times as many as for subsurface.
3) As to size of samplers, there's no differences among them, we have only to use a handy, both in water content and dry density measurement.
4) In dry density measurement, N_αs requires only about 50-60% of that of in measureing water content.
5) It became clear that in the polder paddy field, if α= 5% and ε= 5%, N_αs for estimating the population is about 10-17 for water content and about 7-10 for dry density.

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In this paper, to study the actual state of polder paddy soil in Kojima Bay, authors investigated the statistical problems of the sampling. From the statistical view point, for water content and dry density the following results were obtained:
1) the influence of ditches and unevenness of the surfacd of the field should be taken into account for water condition of the field.
2) Any sampler is allowable except weighing bottle.
3) It is necessary that sample density is large enough to catch the field characteristics. The numbers of samples from 1 point, when sampling is carefully performed, are 2-3 at least, and the space represented by them is about 5m sequare.
4) From Fig. 4 and Table 3, to know to take the distribution of water contents and dry densities of the whole field, we can see that dispersed sampling is much preferable to concentrated sampling.

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This study was done for the purpose of establishing the sampling method for the physical property measurement of soil in an area of heavy clay soil paddy-field with creek.
Statistical investigation both for water content distribution and apparent specific gravity in paddy-field was done, and soil layers taken for the measurement were surface soil, plowsole and subsoil. The results of the investigation are as follows;
1. In the surface soil layer, uniformity of physical properties is in progress, and the distribution of water content and apparent specific gravity seems to be normal. Risk ratio, α=5%; accuracy, ε=55, and minimum sample pieces required for the estimation of the population mean are less than 10.
2. In the subsoil layer, population of the larger value of water content and that of the smaller value are found, and both are in normal distribution. It is similar for apparent specific gravity, and these phenomena might be due to the remaining of the old soil properties still after the land reclamation.
3. The plowsole layer consists of populations of larger and smaller value of water content. As to the apparent specific gravity, on the other hand, the plowsole layer as a whole belongs to a normal population.
4. For surface soil, plowsule and subsoil layer, minimum sample pieces required for the apparent specific gravity determination may well be smaller in amount than those for the water content determination.

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The author has measured the moisture ratio and dry density of soil in a clayey paddy-field in Niigata prefecture, for two times-in April and September of 1969. In April it was done after the snow melting, and in September, after the rice harvest.
Sample number n, sample mean x, unbiased variance σ², standard deviation s, coefficient of variation C_v, and confidence intervals of means and variances are given in Table 1.
The measured values proved to be in normal distribution (Fig. 3). And there is no effect of sampling depth for the means and variances (Fig. 4, 5, 11, 12), while the difference of them by the sampling period are distinct.
The values of variance are very large even in the sampling of small sampling area less than 1 m². The coefficient of variation, C_v, is 3-6% for moisture ratio, and 5-9% for dry density. So we have to take 4-8 samples for moisture ratio and 7-15 samples for dry density, in order to gain a better accuracy in which the confidence intervals of means are less than 5% with the risk confidence coefficient of 95%(Fig. 6).

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The authors have measured moisture ratios in an alluvial sandy paddy-field in Chiba prefecture, for two times one in December 1969, and another in March 1970. Fine weather lasts from December to March in this district, and the ground is not covered with snow in the winter.
The length of the longer side of an usual paddy-field is 100m, and the shorter side is 30m. in length, and the measurement was done in a part of it (at an area of 100×16m). Numbers of sampling done at one point in each 2×2m section, were 400, and those of other concentrated sampling in some small area, were 30. The sampling depth was 0-5cm from the soil surface.
Sample number n, sample mean value x, unbiased variance σ², standard deviation s, coefficient of variation Cv, and confidence intervals of means and variances are given in the Table.
The distribution of values proved to be not in normal state (Fig. 3, 4, 5).
The value of Cv attained some 15%, and so, many samples are needed for getting a greater accuracy.

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The experimental paddy field in this study is a field of volcanic ash soil named Kanto Loam and has been reclaimed for 2 years. The soil sampling in this paddy field was done at three layers-surface soil, plowsole and subsoil. And the soil samples were taken in series from the line of 50m, 30m and 1m length. Other samples were taken from the cross points of section 5×5m and 10×12.5m.
Summary of the discussion in this report was as follow:
(1) The characteristics of both cut and bank portion in paddy field were clearly different between them.
(2) The distribution of water contents (w) and dry densities (γd) were normal distribution mostly.
The greater parts of data that were denied their normality, however, proved normal when they were divided into two subgroup namely cut and bank group.
(3) Optimum size of sample was estimated as about 25cc for w sampling and about 125cc for γd sampling respectively. More volume than these optimum size could not decrease the variance of measured values. For γd measurement, sampling volume of smaller than 125cc increased the variance caused by cutting error of soil.

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In succession to the preceding report (VI), the required sampling numbers and the method of allocation were researched in this report.
(1) The required numbers calculated by non-stratified random sampling method, were dispersive depending on soil layers and sampling seasons. Especially, the required numbers for plowsole exceeded 100 samples, but in other layers the sufficient numbers were 20-50 samples and resulted precision and confidence coefficient were 5% and 95%.
On the local area in one paddy field, the required numbers were nearly equal to that required on the whole area concerned.
(2) The difference of characteristics between cut and bank portion were so clearly that the stratified sampling was desirable. But in many cases the border line of cut and bank is unknown, therefore, stratified sampling should be substituted by square mesh sampling (systematic sampling)
(3) Four allocation methods-equal interval sampling, zigzag sampling, block sampling, random sampling-were applied on the liner continuous sampling data. And it was cofirmed that x dispersion was the smallest in equal interval sampling (=square mesh sampling) and the largest in random sampling. The remaining two other methods were intermediate among fore them.

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The measured values of physical properties in soils vary with the location in the field. The authors studied the variances of soil moisture content and dry density of volcanic ash soil. The field was No.29 grazing land of Hokkaido Agricultural Experiment Station in Sapporo (see Fig.1). The measured areas were (a) 25m×20m, (b) 4m×4m, and (c) 2.5m×2m. The measured points of (a) were 30 intersecting-points across rectangular axes at intervals of 5m. The measured points of (b) were 25 coordinate-points with right-angled axes at intervals of lm, those of (c) were 30 intersecting-points across rectangular axes at intervals of 50cm (see Fig.2). The samplers used had diameters of 3cm, 5cm, and 7cm (each 5cm in height), respectively.
Results obtained are summarized as follows:
(1) The standard deviations of soil moisture content by weight percent at 5-10cm, 28-33cm, and 40-45cm depth were 2.83-5.27, 9.20-17.81, and 8.53-15.63, respectively. The variance of subsoil was larger than that of surface soil (see Table 3).
(2) The standard deviations of volumetric soil moisture content at 5-10cm, 28-33cm, and 40-45cm depth were 1.52-4.20, 2.70-6.76, and 2.43-4.90, respectively (see Table 5). The variances of volumetric moisture content were smaller than those of moisture content by weight percent. In this field, therefore, it is desireable to express soil moisture content by volumetric moisture content than by weight percent.
(3) The number of sampling necessary for volumetric moisture content at 5-10cm, 28-33cm, and 40-45cm depths by using 5cm diameter sampler were 2-4, 5-10, and 4-12, respectively (α=5%, ε= 5%) (see Table 5).
(4) The standard deviations of dry density at 5-10cm, 28-33cm, and 40-45cm depth were 0.028-0.052, 0.101-0.179, and 0.136-0.192, respectively (Table 7).
(5) The number of sampling for dry density at 5-10cm depth using 5cm diameter sampler was 2-4 by using Table 7, those of 28-33 cm and 40-45cm depth using 7cm diameter sampler were 23 and 43, respectively, by using Table 8 (α=5%, ε=5%).

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We have studied statistically on the soil sampling for estimation of dry density and moisture content in the sandy soils. The samples are taken out of the pasture field (50 a.) and the paddy field (30 a.), and by the two methods;(1) the soil samples are obtained in the narrow place (about 1m. square: the concentration sampling), (2) the samples are collected from the extensive place (3m. square and 10m. square: the lattice sampling). The samplers employed are thin-wall samplers of diameter in 5cm. The sampling depths are 5-15cm.(the surface soil layer) and 30-45cm.(the subsoil layer).
Within this investigation, the distribution characteristics of dry density (γd) and moisture ratio (w) in the sandy soils are summarized as follows:
(1) In testing the distribution of γd and w onthe normal probability paper and X²-test, the dry density (γd) and moisture ratio (w) are distributed normally in the both fields.
(2) The coefficient of variation C_v (= s/x, wheres: standard deviation and x: mean) of dry density is within the range of 1.6-6.7%. In the range, the coefficieints are smaller in the subsoil layer than in the surface soil layer, and are smaller in the concentration sampling than in the lattice sampling.
(3) The coefficient of variation of moisture ratio is within the range of 5.3-18.7%. In the pasture field C_v in the subsoil layer is larger than in the surface soil layer. In the paddy field, conversely, C_v in the subsoil layer is smaller than in the surface layer.
From the study of coefficient of variation we estimated the necessary sampling number N (1-α: confidence coefficient and ε: degrees of error).
(1) For estimating dry density in terms of α= 5% and ε= 5%, in employing the concentration sampling, only one sample is sufficient in the pasture field, whereas 2-4 samples are necessary in the paddy field. And in the case of the lattice sampling, 4-5 samples are required in the pasture field (50 a.) and 4-6 samples in the paddy field (30 a.).
(2) On the sampling of moisture ratio (α= 5% and ε= 5%) many samples are necessary, 4-48 in the pasture field and 6-64 in the paddy field (Fig.8).

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We studied statistically the distribution characteristics of air and water permeability in sandy soils with the some method as reported in the previous paper.
The distribution of the measured value of air permeability (k_a) is summarized as follows:
(1) The frequency distribution of air permeability coefficient shows similar to the normal distribution. In testing the distribution of k_a on the normal probability paper and X²-test the hypothesis of the normal distribution cannot be abandoned.
(2) The range of scattering of air permeability coefficient is within 0.3-1.7cm./ sec. in the pasture field and the paddy field, respectively. The ratio of the maximum value to the minimum is 2 in the pasture field and 5 in the paddy field.
The distribution characteristics of water permeability (k_w) is summarized as follows:
(1) In the case of water permeability the deviation from the normal distribution is large. According to the result of X²-test, 4 in 12 cases cannot confirm the hypothesis of the normal distribution (α=5%). But, they are distributed log-normally.
(2) The range of scattering of water permeability coefficient is within (0.7-45) ×10^-3cm./ sec., and the ratio of the maximum value to the minimum reaches 40.
The coefficients of variation in both permeabilities are generally very large as compared with dry density and moisture ratio. And the coefficient of variation are larger in the paddy field than in the pasture field. The samplings of several hundreds for air permeability, and one thousand for water permeability are required to satisfy the statistical terms of α=5% and ε= 5%(Fig.12).

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To determine suitable number of sampling for the expected value in the population of water content (w%) and dry density (γd g/cm³) of gravelly sandy loam field, samplings were made with 50cm³ glass bottle (for water content only) and also with three stainless steel samplers which had the same height (5cm) and different diameter, i. e. 3. 6cm (φ36 sampler), 5.0cm (φ50 sampler) and 7.5cm (φ75 sampler). These tests were made at the site lying between grape trees planted at spaces of 4m square, and total number of sampling for each sampler was 48.
These data were treated statistically, and the necessary numbers of sampling (N_αs) at some risk (α%) and accuracy (ε%) were estimated from co-oxial correlation diagram about C_v (Coefficient of variation) and N_αs.
The following are clarified:
i. Each group of sampling with samplers of the same dimension belong to in the same population of normal distribution.
ii. For water content, only in the case of the φ75 sampler, it does not belong to the same population.(F-test)
And for dry density, there is no significant relationship between each group.
iii. Mean values of water content of each group in case of the bottle, φ36 and φ50 sampler have the same meaning by t-test. While for dry density, mean value of the φ75 sampler differs from two others.
iv. The φ75 sampler trends to show smaller value of water content and dry density than other smaller samplers.
v. The variation of water content in case of the φ75 sampler trends to become smaller than other groups, while for dry density with this sampler, the variation becomes rather large.
vi. Necessary numbers of sampling at 5% risk and 5% accuracy are as follows, for water content, (N_5.5) 34-35 (bottle, φ36 and φ50 sampler) 22 (φ75 sampler) for dry density, (N_5.5) 9-10 (φ36 and φ50 sampler) 12 (φ75 sampler) results the necessity of so many samplings in obtaining acourate data for water content and dry density of such field.

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The soil sampling operations based on the statistical method play an important role in the planning of land reclamation and quality control in earth work.
It is the purpose of this paper to summarizs 11 works in collaboration of the soil sampling operations.
As an example we take the data given in Table 1 and represented graphically in Fig. 2. Following are listed, in the first column, the number of works, in the second column, sampling place and sort of soil, in the third column, the size of soil sampler, in the rest column, the notation as follows:
w: moisture content (%), γd: dry density (g/cm³), x: mean value, Cv: coefficient of variation (%), N: numbers of sampling required, where α=5.%, ε=5%.

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