Neste trabalho, realizado no Instituto Agronômico, determinou-se o tamanho da amostra para estudos de danos causados pela lagarta-da-espiga, Heliothis zea (Boddie), avaliados pelo método de Widstrom. Foram utilizados dados de dois experimentos de campo, com um cultivar resistente (Asteca Prolífico VRPE VII), um suscetível (híbrido duplo IAC Hmd 7974), o 'Maya XVI' e o híbrido simples HS 7777, em 1978/79 e 1979/80. O critério para estimar o tamanho da amostra foi de que esse tamanho permitisse detectar uma diferença de 10 ou de 20% da média geral entre médias de danos, em cultivares de milho, e avaliar o dano médio por cultivar com erro-padrão de 10 ou de 20% da média. Para definir o processo de amostragem, utilizou-se o método de componentes de variância, estimados a partir de dois modelos matemáticos. O tamanho da amostra foi bastante variável entre cultivares, sendo maior no resistente. Entre os possíveis tamanhos mínimos de amostra para detectar uma diferença de 10% da média geral entre médias de danos de tratamentos, podem ser utilizados seis blocos com quatro linhas de 24 plantas; para uma diferença de 20% de média, cinco blocos com três linhas de seis plantas são suficientes. Para estimar a média de danos por cultivar, com erro-padrão de 10% de média, são necessários sete blocos com quatro linhas de 30 plantas, no cultivar Asteca, e cinco blocos com duas linhas de 24 plantas nos cultivares Hmd 7974, HS 7777 e Maya e, com erro-padrão de 20% de média, cinco blocos de três linhas com doze plantas, no 'Asteca', e cinco blocos com duas linhas de seis plantas nos demais cultivares.

A study was made to determine the sample size for research on corn resistance to corn ear worm Heliothis zea (Boddie). The damage was measured using the Widstrom centimeter scale. The criteria used to select the sample sizes were such that a difference between two treatments of ten percent or twenty percent of the overall mean should be detected by the statistical test, and that each treatment mean can be estimated with a standard error of 0.10 y or a standard error of 0.20 y. The data were obtained from two field experiments, carried out in Instituto Agronômico, Campinas, State of São Paulo, Brazil. The treatments were: cultivar Asteca Prolífico VRPE VII, which is resistant to Heliothis zea; Hmd 7974, a susceptible double hybrid; cultivars Maya XVI and HS 7777. A randomized complete block design with ten replicates was used, and each plot consisted of four rows with 50 plants per row. The variance components method was used to define the type of sampling. The most important variance component was due to the variability among units within rows. The following minimum sample sizes can be used to detect the difference between two means: 6 blocks with 4 rows of 24 plants for a difference of 0.10 y and 5 blocks with 3 rows of 6 plants for a difference of 0.20 y. For estimating the mean damage with 0.10 y as the half confidence interval on the mean of the population, the following minimum sample sizes can be used: for cultivar Asteca, 7 blocks with 4 rows of 30 plants per row; for the hybrids Hmd 7974, HS 7777 and cultivar Maya, 5 blocks with 2 rows of 24 plants per row. If a 0.20 y is specified, as the half confidence interval on the mean, it can be used 5 blocks with 3 rows of 12 plants for cultivar Asteca and 5 blocks with 2 rows of 6 plants for the other three cultivars.

Neste trabalho, determinou-se o tamanho da amostra para estudos de danos causados pelo caruncho Sitophilus zeamais Motschulsky, avaliados pelos métodos da escala visual de notas e do número de grãos danificados em relação ao total de grãos. O critério adotado para estimar o tamanho da amostra foi de que esse tamanho permitisse detectar uma diferença de 10 ou de 20% da média geral entre médias de danos, em cultivares de milho, e avaliar o dano médio por cultivar com um erro-padrão de 10 ou de 20% da média. Discutiu-se, também, a eficiência dos dois métodos para avaliar o dano causado pelo caruncho. Foram utilizados dados de dois experimentos de laboratório, conduzidos nos anos agrícolas de 1978/79 a 1979/80, realizado no Instituto Agronômico, Campinas. O delineamento experimental foi de blocos casualizados com 10 repetições, sendo as parcelas formadas por cinco linhas de dez espigas. Os tratamentos estudados foram um cultivar resistente, Asteca Prolífico VRPE VII, um suscetível, o híbrido duplo IAC Hmd 7974, e os cultivares IAC Maya XVI e o híbrido simples HS 7777. Para definir o processo de amostragem, utilizou-se o método de componentes de variância. O tamanho da amostra foi bastante variável entre cultivares, sendo maior no cultivar resistente e, entre métodos de avaliação, maior no método de Davis. Entre os possíveis tamanhos de amostra para detectar uma diferença de 10% da média entre médias de danos de tratamentos, podem ser utilizados: seis blocos com seis linhas de dez espigas por linha, no método de Wiseman, e dez blocos com seis espigas, no método de Davis. Para diferença de 20% da média geral, podem ser empregados: seis blocos com duas linhas de sete espigas, no método de Wiseman, e seis blocos de uma linha de dez espigas, no método de Davis. Para estimar a média de dano por cultivar com erro-padrão equivalente a 0,10 y, os tamanhos de amostra indicados são os seguintes: (a) nas avaliações, pelo método de Wiseman, 270 espigas no 'Asteca' e 70 espigas nos cultivares Hmd 7974, HS 7777 e Maya; (b) nas avaliações pelo método de Davis, 450 espigas no 'Asteca' e cerca de 300 espigas nos demais. Para uma precisão menor, ou seja, erro-padrão de 0,20 y, pode-se estimar a média a partir dos seguintes tamanhos de amostra: (a) nas avaliações pelo método de Wiseman, cinco blocos com duas linhas de seis espigas, no 'Asteca', e cinco blocos com duas linhas de três espigas, nos demais cultivares; (b) nas avaliações pelo método de Davis, cinco blocos com três linhas de seis espigas, no 'Asteca', e cinco blocos com duas linhas de cinco espigas nos restantes.

A study was made to determine the adequate sample size for research on corn resistance to maize weevil, Sitophilus zeamais Motschulsky. To evaluate the damage, the techniques described by Wiseman et alii and by Davis et alii were used. The relative merits of these two methods are discussed. The criteria used to select the sample size was such that a difference between two treatments of ten percent and of twenty percent of the overall mean should be detected by the statistical test, and that each treatment mean could be estimated with a standard error of 0.10 y or 0.20 y. The data were obtained from two laboratory experiments, in 1978/79, and 1979/80, at Instituto Agronômico, Campinas, State of São Paulo, Brazil. The treatments were: cultivar Asteca Prolífico VRPE VII, which is resistant to Sitophilus zeamais, Hmd 7974, a susceptible double hybrid; cultivar Maya XVI and HS 7777. A randomized complete block design with ten replications was used and each plot consisted of five rows of ten ears. The variance components method was used to define the type of sampling. The following minimum sample sizes can be used to detect differences of ten percent of the overall mean, between two treatments means: 6 blocks with 6 rows of 10 ears for the Wiseman method and 10 blocks with 6 rows of 10 ears for the Davis method of evaluation. To detect differences of 0.20 y, it can be used 6 blocks with 2 rows of 7 ears for Wiseman method and 6 blocks with 1 row of 10 ears for the Davis method of evaluation. According to each method of damage evaluation the following minimum sample sizes can be used for estimating the mean damage with 0.10 y as the half confidence interval: a) by Wiseman method, 270 ears for cultivar Asteca, and 70 ears for the cultivars Maya, Hmd 7974 and HS 7777; b) by Davis method, 450 ears for cultivar Asteca, and 300 ears for the other three cultivars. To estimate the mean damage with a 0.20 y as the half confidence interval it can be used: a) by Wiseman method, for cultivar Asteca, 5 blocks with 2 rows of 6 ears; for cultivars Hmd 7974, HS 7777 and Maya, 5 blocks with 2 rows of 3 ears; b) by Davis method, for cultivar Asteca, 5 blocks with 3 rows of 6 ears and for the other three cultivars, 5 blocks with 2 rows of 5 ears.

O presente trabalho teve como objetivo estudar as interações lineares, N' xP';N' x K'e P' x K', em quatro grupos de ensaios fatoriais 3³ de adubação de milho, com N, P e K, num total de 117 experimentos com 3.159 parcelas. Os grupos eram assim constituídos: Grupo 1: 53 ensaios, realizados em Ribeirão Preto (SP), utilizando-se as doses 0; 40 e 80 kg/ha de N, de P(2)0(5) e de K(2)0. Grupo 2: 41 ensaios, realizados no Estado do Rio de Janeiro, com as doses: 0, 30 e 60 kg/ha de N e de K(2)0 e 0; 60 e 120 kg/ha de P2Os. Grupo 3: 10 ensaios, realizados no Triângulo Mineiro, com as doses: 0; 75 e 150 kg/ha para os três nutrientes. Grupo 4: 13 ensaios, realizados: 7 no Triângulo Mineiro e 6 em Patos de Minas (MG), utilizando-se em ambos os subgrupos, as doses: 0; 60 e 120 kg/ha para os três nutrientes. Foi observado que somente as interações N' x P', referente às doses 0 e 1 no grupo 1, e P' x K', referente às doses 0 e 2 no grupo 2, foram significativas. É possível, pois, concluir com grande generalidade, que nos ensaios fatoriais 3³ de adubação de milho, quando se consideram doses moderadas de nutrientes, as interações são de importância secundária e, na grande maioria dos casos, são de pequena monta, quando comparadas aos efeitos principais dos nutrientes.

The present paper has in view the study of linear interactions N'xP';N'x K' and P' x K' in four groups of 3³ factorial experiments of fertilization of corn, with N, P and K, involving 117 experiments and 3,159 plots. The groups were: Group 1: 53 experiments, carried out in Ribeirão Preto (SP), with the following levels of nutrients: 0; 40 and 80 kg/ha of N, P2 0(5) and K2 O. Group 2: 41 experiments, carried out in the State of Rio de Janeiro, with the levels: 0; 30 and 60 kg/ha of both N and K(2)0, and 0; 60 and 120 kg/ha of P2Os. Group 3: 10 experiments carried out in the Region of Triângulo Mineiro (MG) with the levels: 0; 75 and 150 kg/ha for the 3 nutrients. Group 4: 13 experiments carried out: 7 of them in Triângulo Mineiro, and the other 6 in Patos de Minas (MG), using the levels: 0; 60 and 120 kg/ha for each of the 3 nutrients. It was observed that only the interaction N'xP' using the levels 0 and 1 in group 1, and P' x K' using the levels 0 and 2 in group 2, were significant at the 5% level of probability. Then, it is possible to conclude, with a wide generality, that in 3³ factorial experiments of fertilization of corn, for moderate levels of nutrients, the interactions have little importance. In most of the cases, interactions are secondary when compared with the main effects of nutrients.

No presente trabalho é feita a análise das quantidades de chuvas caídas em Campinas no período de 1890 a 1956, e medidas na sede do Instituto Agronômico. Além da análise dos totais anuais, destacaram-se para estudo os meses de janeiro, por ser o mais chuvoso, o de julho, por ser o mais sêco, e o de abril e outubro, por serem intermediários. Pelos resultados conclui-se que no período estudado a incidência dc chuvas, cm cada mês, é uni fenômeno puramente casual, sem nenhuma tendência secular.

A statistical analysis of rainfall data collected at Campinas from 1890 to 1956 was made. In addition to total rainfall, detailed studies were made of data from January and July, the wettest and driest months of the year, respectively, and of August and October, which are intermediary. The results obtained indicated that rainfall for the same months of the year was distributed at random over the period studied and did not show any secular trend.

Num ensaio de adubação com N, P, K e estêrco (E) de mudas de eucalipto (Eucalyptus saligna Sm.) em "torrão paulista" nos viveiros da Cia. Paulista de Estrada de Ferro, em Rio Claro, SP, foi usado um delineamento fatorial de 3x3x3x2, com resultados estatisticamente significativos para N, P e estêrco. As alturas médias das mudas, em centímetros, 3(1/2) meses após a repicagem para os torrões, foram as seguintes. N0 42,4 ± 1,5 P0 56,4 ± 1,5 E0 54,9 ± 1,2 N1 62,8 ± 1,5 P1 58,4 ± 1,5 E1 64,0 ± 1,2 N2 73,2 ± 1,5 P2 63,6 ± 1,5 As médias de algumas combinações interessantes de tratamentos são dadas a seguir, em centímetros. N0PoK0Eo 41,3 ± 6,2 N2P2K0E1 83,0 ± 6,2 N2P0K0E0 59,6 ± 6,2 N2P2K2E1 87,4 ± 6,2 N2P2K0E0 64,0 ± 6,2

This paper deals with a3 X 3 X 3 X 2 factorial experiment with N, P, K, manure, applied to seedlings of Eucalyptus saligna Sm., planted in pots of the type known as "torrão paulista". Results were statistically significant for N, P and manure. The average heights of plants, 3½ months after planting in the pots were, in centimeters, the following: N0 42,4 ± 1,5 P0 56,4 ± 1,5 E0 54,9 ± 1,2 N1 62,8 ± 1,5 P1 58,4 ± 1,5 E1 64,0 ± 1,2 N2 73,2 ± 1,5 P2 63,6 ± 1,5 The averages corresponding to some more interesting treatment combinations are given below: N0PoK0Eo 41,3 ± 6,2 N2P2K0E1 83,0 ± 6,2 N2P0K0E0 59,6 ± 6,2 N2P2K2E1 87,4 ± 6,2 N2P2K0E0 64,0 ± 6,2

This paper deals with the study by orthogonal polynomials of trends in the mean annual and mean monthly temperatures (in degrees Centigrade) in Campinas (State of São Paulo, Brasil), from 1890 up to 1956. Only 4 months were studied (January, April, July and October) taken as typical of their respective season. For the annual averages both linear and quadratic components were significant, the regression equation being y = 19.95 - 0.0219 x + 0.00057 x², where y is the temperature (in degrees Centigrade) and x is the number of years after 1889. Thus 1890 corresponds to x = 1, 1891, to x = 2, etc. The equation shows a minimum for the year 1908, with a calculated mean y = 19.74. The expected means by the regression equation are given below. Anual temperature means for Campinas (SP, Brasil) calculated by the regression equation Year Annual mean (Degrees Centigrade) 1890 19.93 1900 10.78 1908 19.74 (minimum) 1010 19.75 1920 19.82 1930 20.01 1940 20.32 1950 20.74 1956 21.05 The mean for 67 years was 20.08°C with standard error of the mean 0.08°G. For January the regression equation was y = 23.08 - 0.0661 x + 0.00122 x², with a minimum of 22.19°C for 1916. The average for 67 years was 22.70°C, with standard error 0.12°C. For April no component of regression was significant. The average was 20.42°C, with standard error 0.13°C. For July the regression equation was of first degree, y = 16.01 + 0.0140X. The average for 67 years was 16.49°C, with standard error of the mean 0.14°C. Finally, for October the regression equation was y = 20.55 - 0.0362x + 0.00078x², with a minimum of 20.13°C for 1912. The average was 20.52°C, with standard error of the mean equal to 0.14°C.

The authors studied the rainfall in Pesqueira (Pernambuco, Brasil) in a period of 48 years (1910 through 1957) by the method of orthogonal polynomials, degrees up to the fourth having been tried. None of them was significant, so that it seems that no trend is present. The mean observed was 679.00 mm., with standard error of the mean 205.5 mm., and a 30.3% coefficient of variation. The 95% level of probability would include annual rainfall from 263.9 up to 1094.1mm.

The authors prove some approximate formulas for the computation of the mean and the standard error of quotients of two variates, correlated or uncorrelated, with not too high coefficient of variation. The formulas obtained are subsequently applied to some date on mensuration of horses of the Brazilian breed Mangalarga, by the eclectic system of LESBRE. The relsults obtained directly by the actual computation of the quotients as well as by means of the formulas with the aid of statistics of the numerators and the denominators are given in table 3, showing excellent agreement.

The author studies, with the aid of Mitscherlich's law, two experiments of sugar cane fertilization with vinasse. The first one, carried out in Piracicaba, State of S. Paulo, by ARRUDA, gave the following yields. No vinasse 47.0 tons/ha. 76.0 tons/ha. 250 c.m./ha. of vinasse 75.0 do. 112.0 do. 500 do. 90.0 do. 112.0 do. 1000 do. 98.0 do. 107.0 do. Data without NPK were appropriate for the fitting of the law, the equation of which was found to be: y = 100.8 [1 - 10 -0.00132 (x + 206) ], where y is measured in metric tons/hectare, and x in cubic meters/hectare. The optimum amount of vinasse to be used is given by the formula x* = 117.2 + 1 log w u , ______ ____ 0.00132 250 t being u the response to the standard dressing of 250 cubic meters/hectare of vinasse, w the price per ton of sugar cane, and t the price per cubic meter for the transportation of vinasse. In Pernambuco, a 3(4) NPK vinasse experiment gave the following mean yields: No vinasse 41.0 tons/hectare 250 cm./ha. of vinasse 108.3 do. 500 do. 134.3 do. The equation obtained was now y = 150.7 [1 - 10 -000165 (x + 84)], being the most profitable level of vinasse x* = 115.2 + 1 log w u , _______ ____ 0.00165 250 t One should notice the close agreement of the coefficients c (0.00132 in S. Paulo and 0.00165 in Pernambuco). Given the prices of Cr$ 20.00 per cubic meter for the transportation of vinasse (in trucks) and Cr$ 250.00 per ton of sugar cane (uncut, in the fields) the most profitable dressings are: 236 c.m./ha. of vinasse in S. Paulo, and 434 c.m./ha. in Pernambuco.

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

This paper deals with the estimation of the residual effect of fertilizers through the use of Mitscherlich's law. The formulas and reasonings now presented are a further development of those introduced previously by PIMENTEL GOMES (2). The new formulas allow the estimation of the residual effect h in cases where the experiments are carried out in the same plots for two or three subsequent years (or crops). In an experiment analysed as an example, the residual effect of calcium hydroxide was estimated to be h = 0.423, that is, about 42%, so that one should advise the use of frequent application of small amounts of lime instead of heavy quantities used at long intervals.

A presente pesquisa foi realizada visando esclarecer dúvidas surgidas quando da determinação dos valores "T" (capacidade total do solo para bases de dupla troca), "S" (bases suscetíveis de dupla troca) e "H" (hidrogênio suscetível de dupla troca) de solos que receberam altas doses de vinhaça Tais valores, quando determinados pelo processo recomendado por A O. A. C. (2), desviam-se dos normais passando "S" (parte) a ser maior do que "T" (todo). Diversas porções de um mesmo solo depois de convenientemente preparadas foram tratadas em vasos de ferro zincado com doses crescentes de vinhaça como segue: Primeiro grupo (vasos 1, 2, 3 e 4): testemunhas; Sgundo grupo (vasos 5, 6, 7 e 8): incorporação de vinhaça em volume equivalente a 250.0001 por hectare; Terceiro grupo (vasos 9, 10, 11 e 12): idem ao anterior aumentando as dos»\s para 500.0001; Quarto grupo (vasos 13, 14, 15 e 16): idem com 750.0001; Quinto grupo (vasos 17, 18, 19 e 20): idem com 1.000.0001. Efetuada a incorporação e depois de sêcos ossolos à sombra, dos mesmos foram retiradas amostras (4 para cada tipo) para as respectivas análises. Estas compreenderam determinações de "T", "S" e "H" por diversos processos, baseados em lixiviação com acetato de amônio neutro e normal, com cloreto de amônio normal e cloreto de bário normal. Foram, ainda, efetuadas determinações para verificação de sais solúveis. Também foram verificados os índices pH e a possibilidade de volatilização de amoníaco durante os processos de lavagem dos solos com álcool concentrado para a retirada de excesso de reativo. Os resultados obtidos foram estudados estatisticamente revelando principalmente que a incorporação de vinhaça ao solo determina neste um aumento de seus valores "T", "S" e índice pH, e diminuição de "H". Revelaram ainda que nos solos tratados com altas doses de vinhaça o valor "T" não deve ser determinado com processos ligados a amônio-saturação (cloreto), uma vez que êste radical peptizando e solubilizando a matéria orgânica do solo faz com que se consigam valores aquém dos reais. Esta interferência é tão grande que pode conduzir ao absurdo de se ter "S" maior do que "T". Os catiônios bivalentes como cálcio e bário, apesar dos inconvenientes que apresentam, são os recomendados para êste caso.

This research aims to elucidate some doubts concerning the determination of the "T" value (total capacity of exchangeable base), the "S" value (exchangeable bases) and the "H" value (exchangeable hydrogen) in soils receiving heavy amounts of vinasse (waste product obtained in distilleries after the alcohol has been distilled off). In fact, it is known that in this case the values of "S" are sometimes larger than the corresponding values of "T", which is clearly absurd. Vinasse was applied to equal amounts of soil kept in iron pots. Four replications of the folowing treatments were obtained: 1st treatment: Control; 2nd treatment: Equivalent to 250.000 liters of vinasse per hectare; 3rd treatment: Equivalent to 500.000 liters of vinasse per hectare; 4th treatment: Equivalent to 750.000 liters of vinasse per hectare; 5th treatment: Equivalent to 1.000.000 liters of vinasse per hectare; Four samples were obtained from each of the 20 pots; after the soil was dried up in the shade "T", "S" and "H" were determined in each sample, by research methods including leaching with normal solution of amonium acetate, amonium chloride and barium chloride. Soluble salts and pH were determined also, and the possibility of loss of NH3 when washing the soil with alcohol was checked up and recognized to be non-existent. The data thus obtained were submitted to statistical analysis, which showed that indeed the values of "T", "S" and pH do augment with increasing amounts of vinasse, while "H" decreases. The authors concluded also that the methods using amonium saturation (either with amonium acetate or amonium chloride) should not be used for soils receiving large amounts of vinasse, since the peptization and solubilization of abundant organic matter leads then to underestimation of the value of "T". This underestimation is so serious that sometimes the value of "T" obtained is less than the corresponding value of "S" Therefore, bivalents cathions like calcium and barium are recommended for this case, notwithstanding their defects.

The authors studied the effects of calving time, season and time elapsed after calving on milk production of the Holstein Friesian Breed of the "Escola Superior de Agricultura "Luiz de Queiroz" (Piracicaba, Brasil), 180 lactation periods of 300 days were studied, with 15 calvings in each month. Statistical analysis of the data proved : 1. That calving in May, June, July or August, that is, in the driest months, the cows give a milk production 17,3% larger than calving in December, January, February, March or April. August is the best month for calving, and February is the worst. 2. Spring is the most favorable, and Autumn the most unfavorable season for milk production. 3. The decrease of milk production during the lactation period depends largely on calving time. But, on the whole, linear regression can be used as a good aproximation, with a correlation coefficient r = - 0,9926 and a monthly decrease, per month elapsed after calving, of 8,06 percent of the general mean. 4. Diagram 1 shows the effects of calving month on milk production. The limits of 5%, 1% and l%o of probabilities are given there.