1) - The present paper contains the results of the analysis of homogeneity in an experiment on the fertilization of the orange "Baía" (Washington Navel), in progress since 1932 in the Experiment Station of the Instituto Agronômico do Estado de São Paulo, at Limeira, São Paulo, Brasil. Such an experiment has to be divided into two phases': a preliminary period during which the trees remain without fertilizer in order to study their production and the homogeneity of the experimental plots, and the final period during which the different treatments are to be applied. The trees entered into production in 1938. It was decided to close up the first period after three harvestings, viz., in 1938, 1939 and 1940. The number of yields at our disposal remained thus very small. The trees, requiring urgent fertilization, began to be treated in 1941. 2) - Special care was taken while selecting a suitable, homogenous, minimum area of 233.600 sq. m. where to plot the experiment. Sour orange rootstocks from non selected seeds were subjected to a rigorous selection before budding. The buds were taken from two selected trees of heigh quality "Baía" variety. 3) - Every year the total number of fruits and their total weight in kg per tree were determined. These data were then subjected to a detailed statistical analysis, the results of which are presented in this paper. 4) - In spite of all precautions taken beforehand the plots proved to be highly heterogeneous. After some preliminary and afterwards discarded trials in grouping trees, the following sub-division of the whole experiment indicated in the graphs 2 and 3, was adopted : groups of 8 trees each, surrounded completely by a barrier of one row of other trees of "Baía" were considered as unit plots. 6 unit plots (or "parcelas") form a sub-bloc and 4 sub-blocs form a bloc. We have thus a total of 7 blocs, numbered I, II, etc.,all of equal size and form ; 7x4 = 28 sub-blocs ; 28x6 = 168 plots and finally 168 x 8 = 1344 trees. 5 of these trees had to be eliminated owing to poor development, thus 5 of the "parcelas" were left with 7 trees only. The results of the decomposition of the total errors in accordance with this subdivision are given in quadro I. 5) - The analysis of the variation within sub-blocs has been carried out both in a summarized form (quadro I) and individually (quadros II to V). The error "within" was decomposed into 3 parts : "between" of 6 trees each, "between" 6 lines or plots of 8 plants each and the remaining experimental error. In spite of the fact that all these errors "between" were statisticaly significant, the quotients were so small that they can be considered as without practical importance. Thus for all practical purposes, the sub-blocs may be considered as made up by homogenous uniform samples and the whole error within sub-blocs (4th line of quadro I) may be considered as a good estimate of the residual, inevitable experimental error. 6) - The variation between sub-blocs, within blocs, both considered jointly (3rd line of quadro I) and separatedly (quadro VI) is of higher order and the ft's are partially highly significant. In spite of this, these errors which may be considered as a reasonable measure of soil heterogeneity within blocs, do not indicate too great a lack of homogeneity. 7) - The variation between the seven blocs (2nd line of quadro I) is of such an order that it cannot be disregarded any more. A joint analysis of all blocs does not seem advisable. It cannot be decided yet whether a "confounding" of the 7 blocs, after application of the treatments, may be possible or not. In order to provide a method of checking the advisability of "confounding", test plots are to be reserved, one in each of the four sub-blocs of each bloc. 8) - The 4 x 7 = 28 test plots or controlls may possibly be used also to establish adjusted means which may serve in the comparison of treatment plots, localised between the test plots. The proposed distribution of these controlls is indicated in graph 2. Their arrangement will permit, in the future, a continuation of the analysis of soil heterogeneity over the whole area. 9) - As mentioned before about two thirds of the trees came from buds of one tree of "Baía" "1" and the remainder of another tree "2". The position of these two types of plants in the plots is given in the graph 2. An analysis has been carried out separatedly for these groups (quadro VII). Generally speaking, there is a slight tendency for mere variability in the larger group of experimental trees belonging to group "1". This might be due to the fact that these trees, in consequence of their greater number, are more likely to be planted in extremely diverging patches of the plots. Furthermore, there is a slight, but marked tendency of the trees of this group to be more productive than those of the smaller group. It is possible, of course, for these different tendencies of the group, to increase or to disappear after treatment. 10) - In an earlier paper, Brieger (1) has shown that trees of Coffea may be dividc-id into three groups according to the annual cycle of their production. One group shows during a period of 7 years a steady increase of yield, while in the others high and low production alternate regularly, with a maximum, either in even years (1934, 1936, 1938) or in uneven years (1933, 1935, 1937, 1939). The occurrence of one or other of these types is not conditioned by individual factors alone, but is dependent on the place a tree occupies in the experimental plot. The same behaviour was encountered in "Baía" orange. A comparison of the annual means of the sub-blocs or even blocs (quadro VIII) indicates that they follow one of three different types of annual cycles : 38 < 39 > 40; 38 <39 = 40 ; 38 <39 <40. The distribution of these types in the field is such as to indicate clearly that they are largely determined by some particularities of the plots. As shown by graph 3, the first type dominates in the left and upper part of the field and the third in the lower part, while the second occupies an aproximately diagonal and intermediate zone. 11) - Individual trees (quadro IX) seem to follow generally two types of cycles : 38 <39 > 40 or 38 <39 <40. When one or the other dominates or when they are nearly of equal frequency, the sub-bloc as a whole follows one or the other of these cycles or shows the intermediate behaviour : 38 < 39 = 40. In addition some trees follow another cycle 38 > 39 <40 and a few the intermediate cycle 38 < 39 = 40. About 10% (27 in 287) of the trees could not be classified as for their cycles. 12) - A test "between-within" (quadro X) for the classified trees in 6 sub-blocs showed that the separation was reasonably correct and that the residual errors generally were reduced by the separation. Furthermore, trees of the same type but in different sub-blocs are quite different in their production as shown bv the size of the errors between sub-blocs ijE'. Thus, the twofold effect of soil heterogeneity between sub-blocs clearly determinies at least partially the annual cycle and increases production. 13) - A test for interannual correlation of the production of trees belonging to the same annual cycle has been carried out, using a method explained elsewhere (1). The existence of a strong positive correlation is shown in quadro XI. Hence, trees which are better than others in one year tend to be better in following years. If the same test is applied to the data of quadro I, containing the production of all trees, without any separation of annual types, only an intermediate and positive correlation appears (quadro XII). The strong correlation which actually exists has been masked by the reunion of all trees of different and partially opposed annual cycles. 14) - A comparative analysis of the productivity of trees as measured by the weight of the fruits (in kg) has been carried out for one year only (1940). The results of the decomposition both for fruit weight and fruit number per tree are identical j as shown by the equality of the values of φ(quadro XIII). The parallel variation of mean fruit weight and mean fruit number in sub-blocs and blocs is also striking (quadro XIV). 15) - Analysis of correlation between fruit weight and fruit number per tree for all trees of three sub-blocs and also for the means of all sub-blocs gave a value of r equal to 1,00. The mean index weight number and the coefficient of regression are nearly equal and highly constant (quadro XV). The average weight of one fruit was reasonably constant in this experiment (0,26 kg with error standard of ± 0,03 kg). This may seem surprising in view of the negative correlation of mean diameter and number of fruit per tree established for the orange "Baianinha" (2). Unpublished data, however, indicate that such a correlation does not exist in "Baía". 16) - A study of the variation of the standard error σ and of the coefficient of variaion σ% per sub-bloc shows that not one of them is constant. With increasing size of the mean fruit number per tree, agrows from ± 25,44 to 75,86 and cr% decreases from nearly 100% to about 50% (quadro XVI). From a mean fruit number of ca. 100 fruits per tree onward, the decrease of the coefficient of correlation is only slight and it will probably reach the value of 40% with a mean fruit number per tree of 500, as determined by graficai interpolation (graph 4, upper half). On the other side the curve of the standard error (graph 4, lower half) tends to become a straight line and remains steadily increasing. In the analysis of the data after the application of fertilizers, in an experiment with highly variable mean fruit numbers per tree, like the present, it would be better to use coefficients of variation instead of standard errors.
