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This paper proves the following theorems on the gamma function: Theorem I The integral &#8747;O&#8734; t u e-t dt = &#915; ( u + 1 ) , where u, real or complex, is such that R (u) &gt; -1, will not change its value if we substitute z = Q (cos &#966; + i sen &#966;) for the real variable t, being jconstant and such that - &#928;/2 < &#966; < &#928;/2 , Theorem II The integral &#8747;-&#8734;&#8734; w2u + 1 e -w² dw = &#915; ( 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).

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The present work deals with the study of the effects of selfing and crossing in pures lines of okra inbred for five generations and the methods of breeding in this plant. This work is party of a large program of this Dept. to study heterosis in plants naturally self pollinated. The technic of selfing consists of tying with a string the floral bud before anthesis. To make controlled crosses, it is necessary to emasculate the flowers removing the anthers with small forceps, and to cover the flowers with a bag and wait for 1 or 2 days until the blooming. Also, the male parents are covered with paper bags prior to flowering. Finally, the pollen is brushed lightly over the stigma of the emasculated flowers and the females unit rebagged. The authors have tried without sucess the technic of soda fountain straw used for cotton. The treatments were: I) Fl of the cross pure-line x foreign variety (not improved by breeding). II) Fl of the cross pure-line x parental variety and III) pure-line 5 generations inbred. In order to compare the production of these three treatments, a randomized blocks with 4 replications was designed; since we had 6 families in each treatment, the total number was: 4 replications x 3 treatments x 6 families: = 72. Each familiy was planted in lines of 10 plants. Owing to the design devised, the present experiment corresponds to a split-plot. The analysis of variance of the number and the weight of the pods is given in tables 2 and 4, and shows the following: 1) The production expressed in both numbers and weights of the cross, - pure lines x foreign variety - was statistically smaller than the others treatments, i, e., the cross of pure-lines x parental variety and the pure-lines; 2) The production of the treatments pure-lines x parental variety and selfed purelines was the same. It was proved that the selfing do not produce harmful effects in okra, it was benefical, since after 5 inbred generations the production was the same when compared with Fl of the parental variety. Also, the methods of pure-lines are indicated to improve varieties of okra.

This paper deals with the estimation of milk production by means of weekly, biweekly, bimonthly observations and also by method known as 6-5-8, where one observation is taken at the 6th week of lactation, another at 5th month and a third one at the 8th month. The data studied were obtained from 72 lactations of the Holstein Friesian breed of the "Escola Superior de Agricultura "Luiz de Queiroz" (Piracicaba), S. Paulo, Brazil), being 6 calvings on each month of year and also 12 first calvings, 12 second calvings, and so on, up to the sixth. The authors criticize the use of "maximum error" to be found in papers dealing with this subject, and also the use of mean deviation. The former is completely supersed and unadvisable and latter, although equivalent, to a certain extent, to the usual standard deviation, has only 87,6% of its efficiency, according to KENDALL (9, pp. 130-131, 10, pp. 6-7). The data obtained were compared with the actual production, obtained by daily control and the deviations observed were studied. Their means and standard deviations are given on the table IV. Inspite of BOX's recent results (11) showing that with equal numbers in all classes a certain inequality of varinces is not important, the autors separated the methods, before carrying out the analysis of variance, thus avoiding to put together methods with too different standard deviations. We compared the three first methods, to begin with (Table VI). Then we carried out the analysis with the four first methods. (Table VII). Finally we compared the two last methods. (Table VIII). These analysis of variance compare the arithmetic means of the deviations by the methods studied, and this is equivalent to compare their biases. So we conclude tht season of calving and order of calving do not effect the biases, and the methods themselves do not differ from this view point, with the exception of method 6-5-8. Another method of attack, maybe preferrable, would be to compare the estimates of the biases with their expected mean under the null hypothesis (zero) by the t-test. We have: 1) Weekley control: t = x - 0/c(x) = 8,59 - 0/ = 1,56 2) Biweekly control: t = 11,20 - 0/6,21= 1,80 3) Monthly control: t = 7,17 - 0/9,48 = 0,76 4) Bimonthly control: t = - 4,66 - 0/17,56 = -0,26 5) Method 6-5-8 t = 144,89 - 0/22,41 = 6,46*** We denote above by three asterisks, significance the 0,1% level of probability. In this way we should conclude that the weekly, biweekly, monthly and bimonthly methods of control may be assumed to be unbiased. The 6-5-8 method is proved to be positively biased, and here the bias equals 5,9% of the mean milk production. The precision of the methods studied may be judged by their standard deviations, or by intervals covering, with a certain probability (95% for example), the deviation x corresponding to an estimate obtained by cne of the methods studied. Since the difference x - x, where x is the mean of the 72 deviations obtained for each method, has a t distribution with mean zero and estimate of standard deviation. s(x - x) = &#8730;1+ 1/72 . s = 1.007. s , and the limit of t for the 5% probability, level with 71 degrees of freedom is 1.99, then the interval to be considered is given by x ± 1.99 x 1.007 s = x ± 2.00. s The intervals thus calculated are given on the table IX.

A aradura é a principal das operações agrícolas para o desenvolvimento das diversas culturas. A sua importância é conhecida desde as mais remotas eras. Assim, os romanos já tinham sua teoria sobre aradura. Desta forma o arado, a mais antiga das máquinas agrícolas, foi sempre motivo de atenção dos agricultores, fabricantes e técnicos em mecânica agrícola. A sua evolução foi bastante grande. O estudo do arado sob o ponto de vista agrícola e econômico, para exata aplicação da máquina, nas diversas condições de solo, é de máximo interêsse para a mecânica agrícola. Assim sendo, para orientar a correta aplicação do arado, o que constitui a presente tese, foi experimentado num solo arenoso, de características mecânicas (areia total 75,7%, argila 13,5 e lôdo 10,8%) a diversas profundidades de aração, (5, 10, 15, 20, 25, 30cm), plantando nos mesmos, milho para verificar o efeito na produção. Num terceiro ano de experiência, foi realizada uma experiência a mais, isto é, uma subsolagem a 40 cm. Foi plantado milho nos canteiros assim trabalhados, e que eram repetidos em número de 4, porque o milho é uma cultura muito frequente e de fácil contrôle. As experiências com as diversas profundidades, demostraram que nestas condições de solo, à medida que aumenta a profundidade, aumenta também a produção. Do exposto, conclui-se pela experimentação que para esse solo é aconselhável: fazer o arado trabalhar a maior profundidade em que comumente é empregado até o limite de 25 cm, que foi o valor máximo examinado.

Tomato roots heavily disfigured by root-knot nematodes were throughly mixed with soil. At various time intervals, samples were taken from the mixture and treated in closed containers by each of the folio wing nematicides: D.D., E.D.B. and M.B. The efficacy of the treatment was tested by setting indicator plants in the treated soil and by examining their roots for the presence of galls two months later. In other words, the ability of the three nematicides to penetrate nematode galls after various periods of rotting, which varied from 5 to 30 days was studied. The main conclusions drawn are as follows: a) no nematicide among the three listed above showed the ability for complete destruction of the nematodes protected inside the roots, for a number of small galls developed on the root system of the indicator plant in all treatments; b) smaller and less numerous galls were present on the roots of the indicator plants grown in soil treated after a rotting period of 30 days; c) however, the control obtained seems to be quite satisfactory economically, since the check plants grew poorly and have developed a very unhealthy root system. This is in accordance with STARK & LEAR (1947), LEAR (1951) and CICCARONE's (1951) statements. The results of the present experiments show again that awaiting for the rotting of galls of the root-knot nematodes is not indispensable for an economically convenient soil fumigation. Fields in which many fleshy infected roots from previous crops have been buried can be economically fumigated immediately, without any loss of time. Notwithstanding, when thick woody roots are present in the soil, the above statements may not hold true. This should constitute a new problem calling for further experiments. Another essay dealing with methyl bromide alone, consisted in treating cotton roots heavily disfigured by Meloidogyne incognita in a container (diameter = 28cm, height = 32 cm), which remained closed for five days. After the treatment, the roots were mixed with soil, in which tomato seedlings were planted. After a growing period of two months, the roots of the tomato plants were washed in running water and examined for the presence of galls. As an early infeccion was present in the root system of all plants, the inefficacy of the treatment has been proved.

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The author carried out an experiment of watering of lettuce (Lactuca sativa L.) in the vegetable garden of the Escola Superior de Agricultura "Luiz de Queiroz", with soil of the type know as "terra roxa". Eight treatments, with 4 replications, were used, divided into 3 groups, as follows: Group A - Watering once a day, late, in the afternoon, with 5, 10 and 15 liters per square meter; Group B - Watering twice a day, with 10 and 15 liters per square meter, one half in the morning, one half late in the afternoon; Group C - Watering as in group A, but with a 0.1% Chilean nitrate of soda, every 3 days. The size of plots was 2,0 x 2,0 meters. The means obtained, with their respective standard errors, were the following: Group A- (4295 ± 53 gm.) 5 lit./sq.m. 4120 ± 92 gm. 10 lit./ sq. m. 4248 ± 92 gm. 15 lit./sq.m. 4518 + 92 gm. Group B- (4091 ± 65 gm.) 10 lit./sq.m. 3960 ± 92 gm. 15 lit./ sq. m. 4223 ± 92 gm. Group C- (4490 ± 53 gm.) 5 lit./ sq. m. 4300 ± 92 gm. 10 lit./sq.m. 4480 ± 92 gm. 15 lit./sq.m. 4690 ± 92 gm. Differences between groups, as well as within them were significant, even if within groups B the 5% probability level was not quite reached.

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Irish potato tubers imported from Holland and Germany were planted at the Instituto Agronômico Experiment Station, Campinas, in April, 1955. At digging time, in July, 1955, the tubers were found to be injured by nematodes belonging to the genus Ditylenchus. No visible symptoms were found on the plants during the growing season, since the nematodes did not attack the stems. However, prevailing weather conditions from April to July were not favorable for nema activities, with low temperature and rain precipitation. Therefore, it does not seem safe to assume that, as a rule, the nemas do not attack buds and stems, for further observations may reveal such an occurrence, as it has been reported in the literature. The injury was characterized by spots consisting of decaying brown tissue, the nematodes being found mainly between this and the uninjured tissue. Larvae and adults occurred simultaneously. Fourteen different potato varieties were attacked by the nematodes, the percentage of disfigured tubers ranging from 6 (vars. Irene, Barima and Tedria) to 38 (var. Stamm 456). Studies en the morphology cf the parasites disclosed that two different Ditylenchus forms were present, with Apheten-chus sp. and Aphelenchoides sp. associated with them. The writers have not yet drawn a final conclusion about the identification of the Ditylenchi. However, it was clearly seen that no form can be identified either with D. dipsaci or with D. destructor. Both forms have lateral fields made up of 6 incisures, what separates them from D. dipsaci. On the other hand, measurements as well as some details in the organization of the oesophagus make the identification with D. destructor quite impossible. As far as the origin of the parasites is concerned, the fact that they could not be determined either as D. dipsaci or as D. destructor emphasizes the possibility of being two native species, not introduced with the tubers imported.

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The pedigree of chickens homozygous for black plumage and naked and now obtained in the Poultry Department of the "Luiz de Queiroz" School of Agriculture, was traced in this paper. The animals will be used in the formation of the new local breed called "Piracicaba PPPP", (Pescoço Pelado Preta de Piracicaba), which we propose to start with selection of others morphological characters and mainly the economical ones: egg laying, early maturing and soft-meated chickens.

This paper deals with the inheritance of black, blue and blue-splashed plumage in poultry. The material analysed had its origin in the State of Goias, Brazil and the genetical data seems to indicate the interaction of a single pair of genes as in the Andalusian fowls and other blue breeds. The dominant gene for blue egg is also present in the material and selection is now being directed to isolate a breed with blue plumage and blue eggs, named "Tudo Azul", what in Portuguese means all blue (plumage and eggs) and corresponds, in braziliian slang, to the expression "O. K." used in the United States. The commercial possibility of the chickens, as judging by its, laying capacity, is emphasized.

The authors tried to check in this experiment the minimum of yellow corn necessary for preventing avitaminosis A in chickens. It was observed, in balanced ration with 50% of corn, that: a) 20% of dent and yellow grains and 30% of flint and white grains were insuficient to prevent avitaminosis A. b) 20% of flint and orange grains and 30% of flint and white grains or 40% of either colored grains and 10% of flint, and white grains did not show evident signs of avitaminosis A during the 12 weeks of the experiment. The ration containing 20% of flint and orange grains is pratically equivalent to the ration containing 40% of dent and yellow grains, regarding the content of pro-vitamina A. However, it was not possible to conclude if these dosage are sufficient to give the necessary vitamina A for normal development of the chickens since the table 3 seems to indicate a negative correlation between the amount of pigment in the ration and the mortality of the animals.