UNIVERSITY OF CALIFORNIA PUBLICATIONS 
 
 IN 
 
 AGRICULTURAL SCIENCES 
 
 Vol. 4, No. 5, pp. 121-139, 1 text figure May 10, 1919 
 
 VAEIABILITY IN SOILS AND ITS SIGNIFICANCE 
 TO PAST AND FUTURE SOIL 
 INVESTIGATIONS 
 
 II. VARIATIONS IN NITROGEN AND CARBON IN FIELD 
 
 SOILS AND THEIR RELATION TO THE ACCURACY 
 
 OF FIELD TRIALS 
 
 BY 
 
 D. D. WAYNICK and L. T. SHAEP 
 
 Introduction 
 
 Investigations carried out under field conditions are subject to a 
 number of variables, all, or any one of which may serve to invalidate 
 the results which may be secured. The problem of adequate experi- 
 mental control is an exceedingly difficult one, and unlike many 
 experiments carried out in the laboratory none of the variables met 
 with in the field are capable of complete elimination. They may, 
 however, be allowed for, at least in so far as they are concerned with 
 the soil mass, if we know the magnitude of the variables met with. 
 The heterogeneity of the soil, even in experimental plots, has been 
 quite generally recognized as a factor which may render the data 
 secured from field plots open to more or less serious errors; but that 
 the soil may be so variable as to render the measurements made of 
 soil constituents of very questionable value has not been fully appreci- 
 ated. There are considerable data, gathered at various places, from 
 which very definite conclusions have been drawn without first making 
 allowance for the variables entering into the problem in hand. Unless 
 a high degree of certainty exists that the results secured in the first 
 trial will be obtained when the trial is repeated the experimental data 
 are of little value. 
 
122 University of California Publications in Agricultural Sciences [Vol. 4 
 
 The problem of variability in experimental trials with field crops 
 has formed the subject of a number of recent papers. 1 It is not 
 our purpose to enter into a discussion of the problem of the control 
 of field experiments from the crop standpoint. It is proposed, how- 
 ever, to consider the possible magnitudes of field variation in soils 
 and the bearing of such variation on field trials in which the soil 
 mass is the predominant factor. One of us has already taken up this 
 subject from the standpoint of nitrate production in soils, 5 and since 
 no data are obtainable which show the magnitude of the variation 
 in some of the constituents commonly measured in field soils it is of 
 very considerable interest to present data which have been obtained 
 from the viewpoint of the accurate control of the soil as a variable 
 factor. It must be understood in considering the data presented in the 
 following pages that the variations found and the statistical constants 
 computed are by no means absolute figures which can be taken bodily 
 and applied to any soil, but rather that they will serve to indicate the 
 extent and nature of the variations likely to be found in field soils, 
 together with the methods which it is hoped will prove of value in 
 allowing for such variations as are found in any soil. The point 
 has previously been made that variations in the soil within very 
 limited areas may be so great as to render results secured in the past, 
 with only a few samples taken from the area, of very limited value. 
 The data obtained, since the first paper was written, and presented 
 in this and the following papers make this viewpoint all the more 
 secure. 
 
 The present data were secured in connection with and preliminary 
 to a field study of biologic nitrogen fixation now being conducted by 
 this laboratory, and though incidental to that problem their bearing 
 upon the results which may finally be secured is so important as to 
 render their consideration from that viewpoint of much interest. This 
 is equally true of field experiments of a similar nature which have 
 been, or are being conducted elsewhere, and is the principal reason 
 for the presentation of the following data at the present time. 
 
 Methods 
 
 Two fields are concerned in the present study, one on the University 
 Farm al Davis and the other near the town of Oakley. The soils 
 of these two fields are of very different character, a silty clay loam 
 al Davis, and a blow sand at Oaklev. The total area sampled in each 
 
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 Pig. 1. Diagram of areas sampled, showing the locations from which the samples were taken. 
 
Digitized by the Internet Archive 
 
 in 2012 with funding from 
 
 University of California, Davis Libraries 
 
 http://archive.org/details/variabilityinsoi45wayn 
 
1919] WaynicTc-Sliarp : Variations in Nitrogen and Carbon in Field Soils 123 
 
 field is a little more than one and three-tenths acres. The fields were 
 both selected for their apparent uniformity, both being nearly level, 
 with no changes in the soil mass from one part of the field to another 
 great enough to be detected by the usual field methods. Both fields 
 were practically free from vegetation when selected, and before the 
 samplings were made (March, 1918) all extraneous material had been 
 carefully removed. Since the data presented in the previous paper 
 were the only data which would serve as any sort of a guide to the 
 number of samples necessary to secure the degree of accuracy desired, 
 and since it was necessary, further, to distribute the samples in such 
 a manner as to cover the entire area, the arrangement shown in 
 figure 1 was adopted. It will be noted that there are eighty samples 
 distributed at thirty-foot intervals over the entire area, forty samples 
 at fifteen-foot intervals taken from five different parts of the field, 
 these also uniformly distributed, and finally twelve samples taken 
 within one of the small areas, approximately one-forty-eighth of an 
 acre, in the center of the field. There are, then, one hundred samples 
 from each area under consideration. The entire number of samples 
 will be treated as one population, except in so far as they are useful 
 in showing the effect of the distance apart samples are taken upon 
 the variability, and, further, the relationship of the variability in 
 a given small area within a field to that of the entire field. It is 
 recognized that the data available at the present time on this last point 
 are limited, due to the small number of samples available, but they 
 are at least suggestive of the relationship between the two. 
 
 All the samples were taken uniformly with a three-inch soil auger 
 by foot sections. As soon as taken each foot section was thoroughly 
 mixed and approximately one-half of the sample placed in a quart 
 jar of the Mason type. When all the samples had been secured the 
 jars were placed in specially constructed boxes and shipped by express 
 to the laboratory at Berkeley. All the samples were there reduced to 
 the air-dry condition as rapidly as possible and passed through a two- 
 millimeter sieve. The determinations, as herein reported, were made 
 upon the mass of soil passing through a sieve of this size. 
 
 Total nitrogen was determined on ten-gram samples of the Davis 
 soil, or twenty-gram samples of the Oakley soil, using the modification 
 of the Kjeldahl-Gunning method proposed by Hibbard. 2 Eight hun- 
 dred cubic centimeter Pyrex flasks were used in making all the 
 determinations, so that it was not necessary to transfer to copper 
 flasks for the final distillation. All the titrations were made with 
 
124 University of California Publications in Agricultural Sciences [Vol. 4 
 
 standard hydrochloric acid, 1 c.c. of which was equal to .54 milligrams 
 of nitrogen. Determinations for total carbon were made upon five 
 and ten gram samples, respectively, of the two soils by a modification 
 of the wet combustion method described by one of us elsewhere. 4 
 
 Limits of Accuracy of Methods for Nitrogen and Carbon 
 
 It is not proposed to take up a discussion of the accuracy of 
 experimental methods in general. Before experimental work with 
 field soils is undertaken the accuracy of the laboratory methods to be 
 used in the investigation should be known. This is true because, in 
 the first instance, any factors tending toward inaccurate results from 
 the laboratory standpoint are possible of elimination to a large extent, 
 and, in the second instance, the limitations of the laboratory method? 
 may finally define the limits of accuracy of results obtained in the 
 field. In the present study, all errors which may be termed accidental 
 have been eliminated so far as possible by careful attention to the 
 details of manipulation. 
 
 That determinations made upon the different portions of the same 
 sample may still differ considerably among themselves is shown by 
 an inspection of tables 1 and 2, where a number of determinations for 
 nitrogen and carbon are reported, all made upon the same soil sample. 
 The results presented here are of further interest in showing how 
 nearly values found for a composite sample may conform to the mean 
 of the individual samples making up that composite. The latter point 
 will be considered more at length later. 
 
 Table 1. — Variability of Determinations for Total Nitrogen made upon a 
 
 Uniform Soil Sample 
 
 
 Nitrogen 
 
 Deviation 
 
 
 
 Nitrogen 
 
 Deviation 
 
 No. 
 
 per cent 
 
 from mean 
 
 No. 
 
 
 per cent 
 
 from mean 
 
 1 
 
 .092 
 
 .004 
 
 16 
 
 
 .096 
 
 .000 
 
 2 
 
 .096 
 
 .000 
 
 17 
 
 
 .093 
 
 .003 
 
 3 
 
 .097 
 
 .001 
 
 18 
 
 
 .097 
 
 .001 
 
 4 
 
 .099 
 
 .003 
 
 19 
 
 
 .096 
 
 .000 
 
 5 
 
 .094 
 
 .002 
 
 20 
 
 
 .097 
 
 .001 
 
 6 
 
 .098 
 
 .002 
 
 21 
 
 
 .101 
 
 .005 
 
 7 
 
 .092 
 
 .004 
 
 22 
 
 
 .098 
 
 .002 
 
 8 
 
 .099 
 
 .003 
 
 23 
 
 
 .097 
 
 .001 
 
 9 
 
 .100 
 
 .004 
 
 24 
 
 
 .099 
 
 .003 
 
 10 
 
 .097 
 
 .003 
 
 25 
 
 
 .096 
 
 .000 
 
 11 
 
 .098 
 
 .002 
 
 
 
 
 
 
 
 12 • 
 
 .097 
 
 .001 
 
 Mean = 
 
 .0960 ± 
 
 .0030 .002 
 
 13 
 
 .092 
 
 .004 
 
 
 <r = 
 
 .0025 ± 
 
 .0002 
 
 14 
 
 .090 
 
 .000 
 
 C. 
 
 V.= 
 
 2.60 ± 
 
 0.24 
 
 15 
 
 .009 
 
 .on:; 
 
 
 
 
 
1919] Way nick-Sharp : Variations in Nitrogen and Carbon in Field Soils 125 
 
 Table 2. — Variability of Determinations for Total Carbon made upon a 
 
 Uniform Soil Sample 
 
 No. 
 
 Carbon 
 per cent 
 
 Deviation 
 from mean 
 
 No. 
 
 
 
 Carbon 
 per cent 
 
 
 Deviation 
 from mean 
 
 1 
 
 1.093 
 
 .012 
 
 11 
 
 
 
 1.081 
 
 
 .000 
 
 2 
 
 1.076 
 
 .005 
 
 12 
 
 
 
 1.093 
 
 
 .012 
 
 3 
 
 1.077 
 
 .004 
 
 13 
 
 
 
 1.076 
 
 
 .005 
 
 4 
 
 1.092 
 
 .011 
 
 14 
 
 
 
 1.073 
 
 
 .008 
 
 5 
 
 1.065 
 
 .016 
 
 15 
 
 
 
 1.082 
 
 
 .001 
 
 6 
 
 1.092 
 
 .011 
 
 16 
 
 
 
 1.069 
 
 
 .012 
 
 7 
 
 1.091 
 1.091 
 
 .010 
 .010 
 
 
 
 
 
 
 
 8 
 
 
 Mean 
 
 = 1.081 ± 
 
 .0015 
 
 .008 
 
 9 
 
 1.080 
 
 .001 
 
 
 
 cr 
 
 = .009 ± 
 
 .001 
 
 
 10 
 
 1.071 
 
 .010 
 
 
 C. 
 
 V. 
 
 = .83 ± 
 
 .09 
 
 
 If a number of determinations are made upon a given sample and 
 the values so secured are arranged according to the frequency of their 
 occurrence it will be found that they group themselves after the man- 
 ner of a normal error curve. This fact has already been discussed 
 in connection with the determination of nitrates by the colorimetric 
 method and is introduced here because it serves as a background for 
 the consideration of limits of accuracy of the methods under dis- 
 cussion. Since a series of results such as given in table 1 or 2 do 
 follow a normal error curve, we are justified in using the statistical 
 constants calculated from them as a measure of the accuracy of our 
 methods. We have, for example, in the case of nitrogen, the mean 
 of twenty-five determinations, expressed as .0960 ± .0003%. This 
 mean is, then, probably correct to within ±0.31% of the actual 
 amount of nitrogen determined. If, however, but a single determina- 
 tion had been made it would have been subject to a probable error 
 of .0960 ± .0016% of ±1.66% of the amount of nitrogen found. 
 On the other hand, the probable error of the mean of one hundred 
 total nitrogen determinations amounts to ± .00016 %, or ± .016% of 
 the nitrogen present. It is evident, therefore, that the larger the 
 number of determinations made upon any given sample the greater 
 will be the accuracy of the mean of the determinations made, but only 
 in proportion to the square root of their number. It is possible on this 
 basis to determine the amount of nitrogen present in any soil with 
 a very high degree of accuracy, provided a sufficient number of deter- 
 minations can be made. This conception is derived from the fact that 
 what we have chosen to term the laboratory error is purely a matter 
 of chance. Therefore, a series of these errors, whether derived from 
 several determinations on a single sample or from individual deter- 
 minations on different samples, if plotted by classes, would be dis- 
 
126 University of California Publications in Agricultural Sciences [Vol. 4 
 
 tributed as a normal frequency curve in accordance with the laws 
 of chance. Computations of such a series of errors would yield the 
 same statistical constants whether the errors were from the deter- 
 minations made on a single sample or were secured from single 
 determinations made on separate samples. This point is of impor- 
 tance, and unless recognized before any determinations are made upon 
 soil taken from any experimental area, many determinations may 
 be made which will, in the final analysis, lend nothing to the final 
 accuracy of the results. This is true when we are dealing with the 
 mean of a representative number of determinations. The worker may 
 carry through his determination in duplicate or in triplicate, but such 
 a practice will only serve to satisfy him as to the accuracy of his own 
 manipulation, as such replications are of no value when a statistical 
 interpretation of the data as a whole is made. 
 
 That the laboratory error is small when compared with the 
 variation found in field samples is shown by the following data, which 
 have been computed on a "pounds per acre" basis, using 4,000,000 
 pounds as the weight of one acre foot of soil. If twenty-five samples 
 are taken the error which may be attributed to laboratory manipula- 
 tion amounts to plus or minus twelve pounds per acre, with an even 
 chance that our results are accurate to this amount. If we adopt a 
 thirty-to-one chance as the largest chance which we deem it safe to 
 take in order that our results will have a high degree of accuracy, the 
 lowest significant figure amounts to plus or minus thirty-eight pounds 
 per acre. In other words, with twenty-five determinations increases 
 or decreases in the nitrogen found must exceed this figure before they 
 reach a magnitude sufficiently great to be attributable to any treat- 
 ment which we have applied. On the same basis, the mean of our 
 total number of one hundred samples is probably accurate to within 
 twenty pounds per acre so far as the laboratory error itself is con- 
 cerned. However, when we consider that the error due to the varia- 
 tions in field samples amounts to two hundred and forty pounds per 
 acre on an even chance, or seven hundred and sixty pounds on a 
 thirty-to-one chance, it is seen that the laboratory error of twenty 
 pounds becomes relatively insignificant. When we are dealing with 
 the number of samples used in the present study, together with the 
 relatively large amount of nitrogen determined, in the case of the 
 Davis soil at least, it is evident that this laboratory error may be 
 safely disregarded. It is recognized, however, that there may be 
 instances in which the laboratory error may limit to a large degree 
 
1919] W ay niclc- Sharp : Variations in Nitrogen and Carbon in Field Soils 127 
 
 the accuracy to be expected from the use of a given number of field 
 samples. This might be true, for example, in a case in which the 
 total amount of nitrogen or any other element determined is so small 
 that the laboratory error becomes relatively of large magnitude. It 
 must always be borne in mind, however, that the curve representing 
 the laboratory errors and the one representing the errors due to 
 sampling are always parallel; that is, the- two variables always 
 decrease in the same ratio as the number of samples is increased. 
 
 The above discussion has been limited to a consideration of the 
 probable accuracy of the nitrogen determination, and it has been 
 treated somewhat at length because it is considered important that 
 there should be a clear understanding of the limitations of the 
 methods employed. The same mode of treatment might be followed 
 in discussing the limits of accuracy of the carbon determination. 
 These results will not be taken up in detail. Suffice it to say that 
 the laboratory error attributable to our method may be taken as 
 amounting to seventy-two pounds per acre on a thirty-to-one chance, 
 while the mean of one hundred samples has a probable error, on the 
 same basis, due to field variability, of approximately eight hundred 
 pounds per acre. 
 
 We have deemed it important to take up a discussion of the limits 
 of accuracy of the methods used in order that a false estimation of 
 the accuracy of the measurements made may not be assumed. Many 
 determinations have been reported in the past giving increases or 
 decreases in the constituents commonly measured in field soils without 
 consideration of the accuracy of the methods employed. For example, 
 the amount of nitrogen removed by an average crop of barley is 
 usually stated as about forty pounds per acre. We have shown that 
 by making twenty-five determinations on a single soil sample, we are 
 able, due to our laboratory errors, to determine nitrogen in amount 
 not less than plus or minus thirty-eight pounds per acre, which is 
 practically the same figure as given for the nitrogen removed by a 
 single crop. It is evident, therefore, that we are just able to deter- 
 mine the amount of nitrogen removed by a single crop from deter- 
 minations made upon the soil when the soil mass has been made as 
 uniform as it could be made experimentally and a large number of 
 determinations carried out on a soil so prepared. In other words, if 
 we ignore the variability of the field samples and consider only our 
 laboratory error it is found that the value for the nitrogen removed 
 by a single crop and that for the error due to laboratory manipulations 
 
128 University of California Publications in Agricultural Sciences [Vol. 4 
 
 is of nearly the same magnitude. When we take into account as well 
 the errors due to sampling in the field, it is evident that the differences 
 which must be secured before we can feel confident that the results 
 are reliable are very much larger. 
 
 When the results of past soil investigations are examined from 
 this viewpoint it will be found that most of them have been obtained 
 under conditions so imperfectly controlled or under variations in 
 sampling so inadequately taken into account, as to render the results 
 obtained of very questionable value. 
 
 Experimental Data 
 
 The experimental data for the two areas are reported in tables 3 
 and 4. It will be noted that the extreme range for nitrogen in the 
 Davis soil is from .077 to .124% and in the Oakley soil from .022 to 
 .063%, a difference between the extremes of about 60% in the first 
 soil and nearly 300% in the second. If we translate these figures into 
 a "pounds per acre" basis, we have a range of from 3100 to 5000 
 pounds in the first soil and from 900 to 2500 in the second soil. For 
 carbon the range is from 0.903 to 1.383% in the Davis soil and from 
 0.252 to 0.750% in the Oakley soil, a percentage difference between 
 the extremes of nearly the same magnitude as that given for nitrogen. 
 Expressed on the acre basis in the same manner as the nitrogen figures 
 given above, we have 36,000 to 55,000 pounds and 10,000 to 30,000 
 pounds respectively for the two soils. If but a single sample were 
 taken at random to represent these two areas, it can be readly seen 
 that a very inaccurate estimation of their nitrogen and carbon content 
 might be made. Further, it is probable that these differences between 
 samples taken from apparently uniform areas are quite as large 
 as any that may be found between different soil types. In fact, the 
 figures here presented are extremely interesting from that viewpoint, 
 in that, while it may be contended that different soil types, as usually 
 determined, have a range of values for total nitrogen, for instance, 
 not covered by another soil type, unless a large number of samples are 
 taken, it would be out of the question to distinguish between two soil 
 types on that basis. For example, in the two soils under consideration, 
 which are nearly as widely separated as soil types can be, one a silty 
 clay loam and the other a blow sand, the difference between the high 
 valne for nitrogen in one and the low value for nitrogen in the other 
 amounts to only .014%, or less than a third of the extreme range in 
 
1919] W ay nick- Sharp : Variations in Nitrogen and Carbon in Field Soils 129 
 
 either of these soils. This is a very small value when we take into 
 consideration the variability of the soil as a whole. In this connec- 
 tion, it is again emphasized that we are dealing with two very limited 
 areas, selected because of their apparent uniformity. 
 
 It will be noted that the coefficients of variability for both nitrogen 
 and carbon are 9.00% in the Davis soil, while in the Oakley soil they 
 are much in excess of this figure, being 21.87% for nitrogen and 
 21.11% for carbon. It will be recognized that the coefficients of 
 variability for the Davis soil as regards the two constituents here 
 measured are low, so that this area may be properly considered as 
 possessing a relatively high degree of uniformity. Just how true this 
 is as regards other constituents will be brought out in a subsequent 
 paper. The figures as here given may be used again to emphasize 
 the statement made in the introduction of this paper to the effect 
 that values found for one soil may be very misleading if an attempt 
 is made to apply them as an aid in forming a judgment of the probabk 
 variation to be found in another soil. 
 
 Effect of Distance on Variability of Samples 
 
 It has already been stated that because of the locations used in 
 sampling it is possible to arrange our data in such a manner that we 
 may calculate the statistical constants for any number of samples 
 taken at intervals of thirty, fifteen or ten feet. The samples taken 
 
 Table 3. — Total Nitrogen and Carbon in Various Samples of the Davis Soil 
 
 No. of 
 sample 
 1 
 
 Nitrogen 
 
 per cent 
 
 .104 
 
 Carbon 
 
 per cent 
 
 1.167 
 
 No. of 
 sample 
 
 18 
 
 Nitrogen 
 
 per cent 
 
 .099 
 
 Carbon 
 
 per cent 
 
 1.048 
 
 2 
 
 .086 
 
 1.048 
 
 19 
 
 .086 
 
 0.965 
 
 3 
 
 .080 
 
 0.958 
 
 20 
 
 .093 
 
 1.040 
 
 4 
 
 .092 
 
 1.069 
 
 21 
 
 .092 
 
 1.014 
 
 5 
 
 .099 
 
 1.071 
 
 22 
 
 .105 
 
 1.122 
 
 6 
 
 .098 
 
 1.132 
 
 23 
 
 .123 
 
 1.329 
 
 7 
 
 .107 
 
 1.124 
 
 24 
 
 .107 
 
 1.075 
 
 8 
 
 .117 
 
 1.195 
 
 25 
 
 .096 
 
 1.048 
 
 9 
 
 .105 
 
 1.059 
 
 26 
 
 .088 
 
 0.978 
 
 10 
 
 .093 
 
 1.084 
 
 27 
 
 .100 
 
 1.091 
 
 11 
 
 .086 
 
 1.077 
 
 28 
 
 .106 
 
 0.998 
 
 12 
 
 .091 
 
 0.997 
 
 29 
 
 .105 
 
 1.147 
 
 13 
 
 .082 
 
 0.896 
 
 30 
 
 .104 
 
 1.112 
 
 14 
 
 .105 
 
 1.198 
 
 31 
 
 • .110 
 
 1.154 
 
 15 
 
 .114 
 
 1.218 
 
 32 
 
 .115 
 
 1.244 
 
 16 
 
 .108 
 
 1.157 
 
 33 
 
 .093 
 
 0.997 
 
 17 
 
 .094 
 
 0.970 
 
 34 
 
 .103 
 
 1.052 
 
130 University of California Publications in Agricultural Sciences [Vol. 4 
 
 Table 3. 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 35 
 
 .101 
 
 36 
 
 .106 
 
 37 
 
 .103 
 
 38 
 
 .113 
 
 39 
 
 .110 
 
 40 
 
 .111 
 
 41 
 
 .093 
 
 42 
 
 .091 
 
 43 
 
 .096 
 
 44 
 
 .100 
 
 45 
 
 .097 
 
 46 
 
 .096 
 
 47 
 
 .104 
 
 48 
 
 .116 
 
 49 
 
 .093 
 
 50 
 
 .109 
 
 51 
 
 .107 
 
 52 
 
 .102 
 
 53 
 
 .106 
 
 54 
 
 .106 
 
 55 
 
 .118 
 
 56 
 
 .124 
 
 57 
 
 .101 
 
 58 
 
 .090 
 
 59 
 
 .101 
 
 60 
 
 .101 
 
 61 
 
 .098 
 
 62 
 
 .098 
 
 63 
 
 .107 
 
 64 
 
 .101 
 
 65 
 
 .086 
 
 66 
 
 .103 
 
 67 
 
 .088 
 
 68 
 
 .094 
 
 69 
 
 .100 
 
 70 
 
 .097 
 
 Carbon 
 per cent 
 
 1.045 
 
 1.019 
 
 1.120 
 
 1.215 
 
 1.202 
 
 1.167 
 
 1.007 
 
 0.973 
 
 1.100 
 
 1.135 
 
 1.052 
 
 1.034 
 
 1.090 
 
 1.252 
 
 0.993 
 
 1.180 
 
 1.126 
 
 1.153 
 
 1.256 
 
 1.250 
 
 1.254 
 
 1.383 
 
 0.973 
 
 1.001 
 
 0.973 
 
 1.120 
 
 1.051 
 
 1.101 
 
 1.195 
 
 1.254 
 
 1.088 
 
 1.137 
 
 1.009 
 
 1.078 
 
 1.173 
 
 1.071 
 
 {Continued) 
 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 71 
 
 .106 
 
 72 
 
 .116 
 
 73 
 
 .077 
 
 74 
 
 .090 
 
 75 
 
 .095 
 
 76 
 
 .093 
 
 77 
 
 .101 
 
 78 
 
 .104 
 
 79 
 
 .106 
 
 80 
 
 .116 
 
 81 
 
 .103 
 
 82 
 
 .091 
 
 83 
 
 .078 
 
 84 
 
 .091 
 
 85 
 
 .094 
 
 86 
 
 .096 
 
 87 
 
 .099 
 
 88 
 
 .107 
 
 89 
 
 .115 
 
 90 
 
 .103 
 
 91 
 
 .112 
 
 92 
 
 .116 
 
 93 
 
 .102 
 
 94 
 
 .098 
 
 95 
 
 .095 
 
 96 
 
 .097 
 
 97 
 
 .098 
 
 98 
 
 .099 
 
 99 
 
 .097 
 
 100 
 
 .103 
 
 Carbon 
 per cent 
 
 1.168 
 
 1.365 
 
 0.977 
 
 1.161 
 
 1.048 
 
 1.123 
 
 1.267 
 
 1.107 
 
 1.186 
 
 1.289 
 
 1.108 
 
 0.986 
 
 0.903 
 
 1.161 
 
 1.000 
 
 1.042 
 
 1.288 
 
 1.352 
 
 1.232 
 
 1.109 
 
 1.251 
 
 1.322 
 
 1.088 
 
 0.989 
 
 1.997 
 
 1.093 
 
 1.114 
 
 1.063 
 
 1.064 
 
 1.092 
 
 Mean = .100 ± .006 1.110 ± .007 
 
 A. D. = .006 .083 
 
 a~ .0090 ± .0006 .1000 ± .0005 
 
 C. V. = 9.00 ± 0.42 9.00 ± 0.42 
 
 Tarle 4. — Total Nitrogen and Carbon in Various Samples of the Oakley Soil 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 Carbon 
 per cent 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 Carbon 
 per cent 
 
 1 
 
 .042 
 
 .624 
 
 10 
 
 .032 
 
 .420 
 
 2 
 
 .032 
 
 .417 
 
 11 
 
 .024 
 
 .330 
 
 3 
 
 .027 
 
 .365 
 
 12 
 
 .024 
 
 .361 
 
 4 
 
 .022 
 
 .179 
 
 13 
 
 .031 
 
 .349 
 
 5 
 
 .029 
 
 .355 
 
 14 
 
 .032 
 
 .314 
 
 6 
 
 .026 
 
 .383 
 
 15 
 
 .033 
 
 .475 
 
 7 
 
 .027 
 
 .279 
 
 16 
 
 .042 
 
 .330 
 
 8 
 
 .031 
 
 .404 
 
 17 
 
 .042 
 
 .499 
 
 9 
 
 .042 
 
 .565 
 
 18 
 
 .028 
 
 .314 
 
1919] W ay nick-Sharp : Variations in Nitrogen and Carbon in Field Soils 131 
 
 
 
 Table 4.- 
 
 — (Continued) 
 
 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 Carbon 
 per cent 
 
 No. of 
 sample 
 
 Nitrogen 
 per cent 
 
 Carbon 
 per cent 
 
 19 
 
 .027 
 
 .402 
 
 63 
 
 .032 
 
 .466 
 
 20 
 
 .021 
 
 .428 
 
 64 
 
 .034 
 
 .450 
 
 21 
 
 .037 
 
 .421 
 
 65 
 
 .045 
 
 .647 
 
 22 
 
 .022 
 
 .308 
 
 66 
 
 .028 
 
 .384 
 
 23 
 
 .036 
 
 .345 
 
 67 
 
 .030 
 
 .480 
 
 24 
 
 .034 
 
 .345 
 
 68 
 
 .031 
 
 .362 
 
 25 
 
 .041 
 
 .524 
 
 69 
 
 .035 
 
 .498 
 
 26 
 
 .029 
 
 .377 
 
 70 
 
 .033 
 
 .407 
 
 27 
 
 .025 
 
 .382 
 
 71 
 
 .039 
 
 .577 
 
 28 
 
 .029 
 
 .450 
 
 72 
 
 .031 
 
 .431 
 
 29 
 
 .034 
 
 .453 
 
 73 
 
 .061 
 
 .947 
 
 30 
 
 .026 
 
 .292 
 
 74 
 
 .040 
 
 .589 
 
 31 
 
 .027 
 
 .345 
 
 75 
 
 .041 
 
 .612 
 
 32 
 
 .031 
 
 .450 
 
 76 
 
 .040 
 
 .636 
 
 33 
 
 .042 
 
 .507 
 
 77 
 
 .063 
 
 .750 
 
 34 
 
 .027 
 
 .314 
 
 78 
 
 .036 
 
 .478 
 
 35 
 
 .026 
 
 .341 
 
 79 
 
 .040 
 
 .587 
 
 36 
 
 .028 
 
 .252 
 
 80 
 
 .035 
 
 .516 
 
 37 
 
 .035 
 
 .319 
 
 81 
 
 .029 
 
 .368 
 
 38 
 
 .027 
 
 .346 
 
 82 
 
 .025 
 
 .361 
 
 39 
 
 .026 
 
 .368 
 
 83 
 
 .022 
 
 .329 
 
 40 
 
 .031 
 
 .524 
 
 84 
 
 .035 
 
 .409 
 
 41 
 
 .052 
 
 .450 
 
 85 
 
 .032 
 
 .558 
 
 42 
 
 .030 
 
 .314 
 
 86 
 
 .030 
 
 .384 
 
 43 
 
 .031 
 
 .396 
 
 87 
 
 .036 
 
 .380 
 
 44 
 
 .028 
 
 .381 
 
 88 
 
 .032 
 
 .497 
 
 45 
 
 .032 
 
 .502 
 
 89 
 
 .033 
 
 .436 
 
 46 
 
 .029 
 
 .404 
 
 90 
 
 .024 
 
 .312 
 
 47 
 
 .030 
 
 .480 
 
 91 
 
 .033 
 
 .396 
 
 48 
 
 .032 
 
 .382 
 
 92 
 
 .028 
 
 .366 
 
 49 
 
 .046 
 
 .426 
 
 93 
 
 .027 
 
 .407 
 
 50 
 
 .031 
 
 .718 
 
 94 
 
 .026 
 
 .338 
 
 51 
 
 .033 
 
 .456 
 
 95 
 
 .029 
 
 .314 
 
 52 
 
 .032 
 
 .488 
 
 96 
 
 .027 
 
 .360 
 
 53 
 
 .034 
 
 .443 
 
 97 
 
 .029 
 
 .396 
 
 54 
 
 .033 
 
 .450 
 
 98 
 
 .037 
 
 .435 
 
 55 
 
 .034 
 
 .516 
 
 99 
 
 .029 
 
 .382 
 
 56 
 
 .033 
 
 .352 
 
 100 
 
 .029 
 
 .347 
 
 57 
 
 .052 
 
 .742 
 
 
 
 
 
 
 58 
 
 .034 
 
 .461 
 
 Mean = 
 
 = .032 ± .005 
 
 .440 ± .007 
 
 59 
 
 .031 
 
 .475 
 
 A.D.= 
 
 = .007 
 
 .009 
 
 60 
 
 .031 
 
 .534 
 
 a - 
 
 = .0070 ± .0003 
 
 .115 ± .005 
 
 61 
 
 .031 
 
 .420 
 
 C.V.= 
 
 = 21.87 ± 1.03 
 
 25.11 ± 1.13 
 
 62 
 
 .032 
 
 .458 
 
 
 
 
 at the last two distances were not uniformly distributed over the 
 entire area but represent smaller areas within the larger. They are 
 none the less useful in forming an estimate of the relation which a 
 
132 University of California Publications in Agricultural Sciences [Vol.4 
 
 small area may bear to a larger area within which it is located, or, 
 as an interrogation, would we be justified in applying the value 
 obtained for nitrogen in a plot of %o °f an acre to tliat i R one acre • 
 In the case of the Davis soil we may answer this question in the 
 affirmative, since there is no significant difference between the mean 
 of amounts of nitrogen found in the total population as related to 
 the samples taken at either the fifteen or ten foot intervals as shown 
 in table 5. With the carbon determinations the differences are slight. 
 It will be noted, however, that the coefficients of variability of the 
 samples taken at ten foot intervals is only about one-third as large 
 as those found for the total population. With the Oakley soil, on the 
 other hand, there is a significant difference in the means for both total 
 nitrogen and total carbon for the samples taken at fifteen and at ten 
 foot intervals. In other words, in dealing with a soil as variable as 
 regards nitrogen and carbon as the Oakley soil we would not be justi- 
 fied in using the data obtained from a small area in the interpretation 
 of that secured from the larger. The coefficient of variability of the 
 samples taken at shorter intervals is significantly less than that cal- 
 culated from the total population, although the difference between the 
 two is less than half the coefficient of variability calculated for the 
 total population in either case. 
 
 These data emphasize again the point which was brought out in 
 the previous paper, that it is very unwise to judge an area even of 
 the size reported here by values obtained from a limited portion of 
 that area if the variations are of the magnitude reported for the 
 Oakley soil. Estimations so made may be far from the truth and if 
 extended in their application may lead to very erroneous conclusions. 
 Accuracy of Values Secured by Using Composite Soil Samples 
 
 From the standpoint of the amount of labor involved in making 
 determinations in the laboratory the compositing of a number of 
 individual samples is very desirable. Such a practice is permissible, 
 however, only when the variations amongst individual samples in the 
 area under consideration are known. When a larger area is broken up 
 into plots the compositing of a number of samples taken in a repre- 
 sentative manner from a small plot becomes almost necessary, since 
 otherwise the amount of work involved in making the determinations 
 on a large number of individual samples would be almost prohibitive. 
 To test this point, the determinations reported in tables 1 and 2 were 
 made on a composite sample, prepared by taking twenty grams from 
 each of the samples of the Davis soil, numbered from 2 to 26 inclusive. 
 
1919] W ay nick- Sharp : Variations in Nitrogen and Carbon in Field Soils 133 
 
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134 University of California Publications in Agricultural Sciences [Vol. 4 
 
 Just how closely the results agree is shown in table 6. In the case of 
 both nitrogen and carbon the probable error in the difference between 
 the two results is approximately equal to the difference between the 
 two results, hence the latter value is of no significance. 
 
 It must be remembered, however, that we have made a large 
 number of determinations on the composite sample, so that we have 
 secured a much higher degree of accuracy than if but one or two 
 determinations had been made. The making of a composite sample 
 is, therefore, a justifiable procedure from the standpoint of the final 
 accuracy of the results secured; provided, of course, that enough 
 determinations are made upon the sample so that their mean will 
 accurately represent the soil mass, and, further, that the composite 
 itself represents equal amounts of the various individual samples 
 which have themselves been made as uniform as possible by thorough 
 mixing. 
 
 Table 6. — Showing the Eelation Between Determinations Made Upon 
 
 Individual Samples and on a Composite Sample made from the 
 
 Various Individual Samples 
 
 Mean Probable error of mean 
 
 * , , * , 
 
 Nitrogen Carbon Nitrogen Carbon 
 Determinations from compo- 
 site sample Nos. 2-26 in- 
 clusive 0960 1.081 .0003 .0015 
 
 Determinations on individ- 
 ual samples Nos. 2-26 in- 
 clusive 0940 1.075 .0015 .0058 
 
 Difference 0020 .006 .0015 .0059 
 
 Number of Field Samples Necessary to Secure the Degree 
 of Accuracy Desired 
 
 We may adopt as the limit of accuracy to be secured in any investi- 
 gation a value below which we attach no significance to our results. 
 The limiting values which may be taken will depend largely upon the 
 anticipated significance to be given to the results secured from the 
 experiment in hand. Further, the physical capacity of the laboratory 
 carrying on the experimental work will in many instances be the 
 factor limiting the number of samples and thus the probable accuracy 
 secured. When it is realized that the results obtained even by the 
 most careful laboratory procedure, carried out with a larger number 
 
1919] Waynich-Sharp : Variations in Nitrogen and Carbon in Field Soils 135 
 
 of samples than heretofore used, may still be in error to such a degree 
 that only large increases or decreases in soil constituents may be 
 measured with accuracy, the importance of using as many samples as 
 the capacity of the laboratory will permit becomes evident. 
 
 To emphasize the importance of a correct estimate of the number 
 of samples necessary to measure certain changes in carbon and nitro- 
 gen which may take place in the two soils under discussion, the values 
 given in table 7 have been calculated after the manner outlined in 
 a previous publication. 5 In the second column the differences which 
 we desire to measure are expressed on a "pounds per acre" basis, 
 while in the third column these differences are given on a basis of 
 percentage of soil, allowing 4,000,000 pounds per acre foot. In the 
 
 Table 7. — Estimate of the Number of Samples Eequired for Accurate 
 Measurement of Certain Changes in Nitrogen and Carbon 
 
 
 Limits of 
 
 Limits of 
 
 
 
 
 Davis Soil 
 
 accuracy 
 pounds 
 per acre 
 
 accuracy 
 
 percentage 
 
 basis 
 
 Odds 1-1 
 
 Odds 10-1 
 
 Odds 30- 
 
 Nitrogen 
 
 25 
 
 .0006 
 
 100 
 
 250 
 
 317 
 
 
 50 
 
 .0012 
 
 25 
 
 62 
 
 79 
 
 
 100 
 
 .0024 
 
 6 
 
 15 
 
 19 
 
 
 250 
 
 .0062 
 
 .9 
 
 2 
 
 3 
 
 
 500 
 
 .0125 
 
 .2 
 
 1 
 
 1 
 
 Carbon 
 
 25 
 
 .0006 
 
 12222 
 
 30555 
 
 38743 
 
 
 50 
 
 .0012 
 
 3055 
 
 7637 
 
 9684 
 
 
 100 
 
 .0024 
 
 764 
 
 1910 
 
 2425 
 
 
 250 
 
 .0062 
 
 114 
 
 285 
 
 361 
 
 
 500 
 
 .0125 
 
 28 
 
 70 
 
 88 
 
 Oakley Soil 
 
 
 
 
 
 
 Nitrogen 
 
 25 
 
 .0060 
 
 61 
 
 125 
 
 193 
 
 
 50 
 
 .0012 
 
 15 
 
 37 
 
 47 
 
 
 100 
 
 .0024 
 
 4 
 
 10 
 
 12 
 
 
 250 
 
 .0062 
 
 .6 
 
 1 
 
 2 
 
 
 500 
 
 .0125 
 
 .1 
 
 1 
 
 1 
 
 Carbon 
 
 25 
 
 .0006 
 
 16685 
 
 41712 
 
 52891 
 
 
 50 
 
 .0012 
 
 4170 
 
 10452 
 
 13218 
 
 
 100 
 
 .0024 
 
 1042 
 
 2605 
 
 3303 
 
 
 250 
 
 .0062 
 
 156 
 
 390 
 
 494 
 
 
 500 
 
 .0125 
 
 39 
 
 97 
 
 123 
 
 next three columns is stated the number of samples necessary to take 
 so that their mean will have a probable error no greater than that 
 given in columns two and three. The number of samples required 
 is listed under three headings, depending upon the chances we are 
 willing to take that our experimental results can be duplicated under 
 
136 University of California Publications in Agricultural Sciences [Vol. 4 
 
 the same conditions. With odds of one to one, the chances are even 
 that our experimental results are capable of duplication. With odds 
 of ten to one or thirty to one the chances are that in one hundred trials 
 ten and three of them, respectively, will not give the same results as 
 our original experiment. 
 
 It will be noted that if we accept twenty-five pounds per acre as 
 our limiting value for nitrogen we must take no less than 317 samples 
 from the Davis soil or 193 samples from the Oakley soil with odds of 
 thirty to one. With carbon to be determined, no fewer than 38,743 
 and 52,891 samples, respectively, of the two soils must be taken. It 
 is at once evident that these samples are too numerous from the 
 standpoint of maintaining the integrity of the plot we are sampling 
 or the capacity of the laboratory to handle the samples. We must, 
 therefore, content ourselves with a lower degree of accuracy than 
 twenty-five pounds per acre. As we increase our limiting value 
 the necessary number of samples decreases very rapidly, so that 
 with a value of about one hundred pounds of nitrogen per acre we 
 require but nineteen samples of the Davis, or twelve samples of the 
 Oakley soil. For the investigation in hand we have taken eighty 
 pounds of nitrogen and eight hundred pounds of carbon per acre as 
 our limiting values, which makes it necessary to use twenty-eight 
 samples for nitrogen in the Davis soil and nineteen in the Oakley 
 soil, with forty-eight and forty-one samples, respectively, for carbon. 
 These values were chosen because this number of samples is within 
 the capacity of the laboratory to make the determinations when we 
 take into consideration the number of different plots under treatment. 
 It is true, then, that when the investigation is finished, we will know 
 that our results will not, with odds of thirty to one, have a probable 
 accuracy greater than the figures given above. With the chances but 
 even that we may be able to repeat our experiment and obtain the 
 same results as secured when the trial was originally carried out the 
 work involved in carrying through the original experiment is scarcely 
 justified. Even odds of ten to one leave a large chance for error when 
 attempts are made to repeat the experiment. We are hardly justified 
 in taking a larger chance than thirty to one, for our experimental 
 results will still probably fail of replication three times out of every 
 hundred trials. Some field experiments may not justify the work 
 involved in sampling to secure the degree of certainty desired in the 
 present experiment. This may be so if the results so secured are to 
 have a very limited application or are of a preliminary nature. In 
 
1919] Waynick-Sharp : Variations in Nitrogen and Carbon in Field Soils 137 
 
 general, however, it is felt that a larger chance than the one taken 
 in this experiment is hardly justified and may only lead to further 
 confusion in our interpretation of data secured through field experi- 
 mentation. 
 
 It will be noted that fractional values are given in four instances. 
 They are given only as the results of calculation as the taking of a 
 fraction of a sample is obviously impossible. It must be remembered, 
 however, that in using a small number of samples the laboratory error 
 may be great enough to invalidate the results secured unless a sufficient 
 number of determinations is made to reduce this error to a low value. 
 
 By the use of the method suggested for the calculation of the 
 number of samples necessary to secure any desired degree of accuracy, 
 two ends are attained. In the first place, the sampling of field soils 
 becomes not something to be done in a haphazard sort of way, but 
 rather a definite, practical procedure, the results of which may be 
 predicted with a high degree of certainty. In the second place, 
 much needless work may be avoided where more samples are taken 
 than are really necessary to ensure the degree of accuracy desired. 
 
 As we have already stated before, we do not think our data 
 sufficiently extensive to warrant a definite statement on the relation 
 between the total area reserved for experimental purposes and small 
 subdivisions made from that area. In general, it is probably true 
 that small areas are less variable than the larger areas within which 
 the former are located. That this may not always hold true is shown 
 by the data for the nitrate found in the field soil reported in a previous 
 paper, and, to a large extent, holds true for the data presented in 
 this paper for the Oakley soil. It is hoped that as our work progresses 
 with these two experimental plots we may secure data which will 
 be of value in interpreting the relation of small areas to larger, and 
 from such data we may likewise be able to correct, to a certain extent, 
 for the heterogeneity in field soils after the contingency method pro- 
 posed by Surface and Pearl. 3 
 
138 University of California Publications in Agricultural Sciences [Vol. 4 
 
 SUMMARY 
 
 Data are presented in the present paper showing the variations 
 found in total nitrogen and total carbon in two experimental areas, 
 located upon soils of widely different types. Statistical methods are 
 applied to the interpretation of the results obtained. The following 
 statements seem justified from the results secured: 
 
 1. The extreme variations between different samples in which 
 nitrogen and carbon were determined are of very considerable mag- 
 nitudes and show that the results secured with one or a few samples 
 would be likely to be unreliable. 
 
 2. It is unwise to attempt to apply the statistical constants cal- 
 culated for one area to other areas even though in themselves appar- 
 ently uniform since the respective variabilities may be very different. 
 
 3. Data are presented showing the making of a composite sample 
 to be fully justified after the variations in the area to be sampled are 
 known. 
 
 4. The relation of variations in a small area to differences between 
 soil types, based upon the constituents determined is discussed, and 
 the conclusion is drawn that only after very careful sampling may 
 such differences be determined with certainty. 
 
 5. The advantages of estimating the number of samples necessary 
 to secure any degree of accuracy are discussed. It is shown that a 
 higher degree of certainty in experimental work may be secured by so 
 doing, and also that in some instances needless labor may be elim- 
 inated. 
 
 In the past many erroneous conclusions have been drawn from 
 data secured in field experiments with soils, which it is hoped may be 
 avoided in the future by the application of the principles herein 
 outlined. 
 
1919] W ay niclc- Sharp : Variations in Nitrogen and Carbon in Field Soils 139 
 
 BIBLIOGRAPHY 
 
 i American Society of Agronomy. 
 
 Eeport of the Committee on Standardization of Field Experiments. Jour. 
 Amer. Soc. Agron., vol. 9, pp. 402-409, 1917. 
 
 2 Hibbard, P. L. 
 
 Notes on the Determination of Nitrogen by the Kjeldahl Method. Jour. Ind. 
 and Eng. Chem., vol. 2, pp. 463-466, 1910. 
 
 s Surface, Frank M., and Pearl, Eaymond. 
 
 A Method of Correcting for Soil Heterogenity in Variety Tests. Jour. Agr. 
 Ees., vol. V, no. 22, pp. 1039-1050, 1915. 
 
 4 Waynick, D. D. 
 
 A Modification of the Wet Combustion Method for Determining Total Carbon 
 in Soils. Jour. Ind. and Eng. Chem., May, 1918. 
 
 s Waynick, D. D, 
 
 Variability in Soils and Its Significance to Past and Future Soil Investiga- 
 tions. I. A Statistical Study of Nitrification in Soils. Univ. Calif. Publ. 
 Agri. Sci., vol. 3, no. 9, pp. 243-270, 1918.