Evaluation of platelet number and function and fibrinogen level in patients bitten by snakes of the Bothrops genus

Platelet function and plasma fibrinogen levels were evaluated in 14 patients, 10 males and 4females, aged 13-59years bitten by Bothrops genus snakes. There was a statistical difference (p < 0.05) among plasma fibrinogen levels evaluated 24 and 48 hours after envenomation. There was a tendency towards normalization after 48 hours of treatment. The low platelet number was clear in 24-48 hour evaluations with a tendency towards normalization after 48 hours of treatment (p<0.05). Fibrinogen levels and fibrin degradation product (FDP) levels appeared to be altered in 83.33% of patients evaluated. The authors suggest that platelet hypoaggregation is related to decreased fibrinogen and increased FDP levels.

Experimental visceral leishmaniasis in high and low antibody - producer mice (selection IV-A)

Leishmaniasis is a typical parasite infection whose protective immunity depends on macrophage activation. Susceptibility to Leishmania donovani infection was compared in H (high antibody responder) and L (low antibody responder) mice from selection IV-A. H mice infected intravenously with 10(7) amastigotes of L. donovani were more susceptible to infection than their L counterparts. This higher susceptibility was characterized by a higher splenic and hepatic parasite burden. An increased splenic index was observed in both lines after sixty days of infection. This splenomegaly was caused, at least partially, by an increase in the number of splenic cells as determined by direct counts of cells from spleen. The results show that selection IV-A is susceptible to visceral leishmaniasis, with the H line being more susceptible than the L line.

Livros on-line da área médica

O trabalho indica alguns sites a serem considerados como alternativa para acesso gratuito a livros on-line disponíveis na Internet e destinados à área médica.

A SARIMA forecasting model to predict the number of cases of dengue in Campinas, State of São Paulo, Brazil

INTRODUCTION: Forecasting dengue cases in a population by using time-series models can provide useful information that can be used to facilitate the planning of public health interventions. The objective of this article was to develop a forecasting model for dengue incidence in Campinas, southeast Brazil, considering the Box-Jenkins modeling approach. METHODS: The forecasting model for dengue incidence was performed with R software using the seasonal autoregressive integrated moving average (SARIMA) model. We fitted a model based on the reported monthly incidence of dengue from 1998 to 2008, and we validated the model using the data collected between January and December of 2009. RESULTS: SARIMA (2,1,2) (1,1,1)12 was the model with the best fit for data. This model indicated that the number of dengue cases in a given month can be estimated by the number of dengue cases occurring one, two and twelve months prior. The predicted values for 2009 are relatively close to the observed values. CONCLUSIONS: The results of this article indicate that SARIMA models are useful tools for monitoring dengue incidence. We also observe that the SARIMA model is capable of representing with relative precision the number of cases in a next year.

The influence of carbohydrates in the interaction of Paracoccidioides brasiliensis with CCL-6 cells in vitro

INTRODUCTION: Little is known about the early events in the interaction between Paracoccidioides brasiliensis and its host. To understand the effect of carbohydrates in the interaction between the fungus and epithelial cell in culture, we analyzed the influence of different carbohydrate solutions on the adhesion of P. brasiliensis yeast cells to CCL-6 cells in culture. METHODS: Fungal cells were cultivated with the epithelial cell line, and different concentrations of D-fucose, N-acetyl-glucosamine, D-mannose, D-glucosamine, D-galactosamine, sorbitol and fructose were added at the beginning of the experiment. Six hours after the treatment, the cells were fixed and observed by light microscopy. The number of P. brasiliensis cells that were adhered to the CCL-6 monolayer was estimated. RESULTS: The number of adhesion events was diminished following treatments with D-fucose, N-acetyl-glucosamine, D-mannose, D-glucosamine and D-galactosamine as compared to the untreated controls. Sorbitol and fructose-treated cells had the same adhesion behavior as the observed in the control. P. brasiliensis propagules were treated with fluorescent lectins. The FITC-labeled lectins WGA and Con-A bound to P. brasiliensis yeast cells, while SBA and PNA did not. CONCLUSIONS: The perceptual of adhesion between P. brasiliensis and CCL-6 cells decreased with the use of D-mannose, N-acetyl-glucosamine and D-glucosamine. The assay using FITC-labeled lectins suggests the presence of N-acetyl-glucosamine, α-mannose and α-glucose on the P. brasiliensis cell surface. An enhanced knowledge of the mediators of adhesion on P. brasiliensis could be useful in the future for the development of more efficient and less harmful methods for disease treatment and control.

Evaluation of two sweeping methods for estimating the number of immature Aedes aegypti (Diptera: Culicidae) in large containers

Introduction Here, we evaluated sweeping methods used to estimate the number of immature Aedes aegypti in large containers. Methods III/IV instars and pupae at a 9:1 ratio were placed in three types of containers with, each one with three different water levels. Two sweeping methods were tested: water-surface sweeping and five-sweep netting. The data were analyzed using linear regression. Results The five-sweep netting technique was more suitable for drums and water-tanks, while the water-surface sweeping method provided the best results for swimming pools. Conclusions Both sweeping methods are useful tools in epidemiological surveillance programs for the control of Aedes aegypti.

New delivery systems for amphotericin B applied to the improvement of leishmaniasis treatment

Leishmaniasis is one of the six major tropical diseases targeted by the World Health Organization. It is a life-threatening disease of medical, social and economic importance in endemic areas. No vaccine is yet available for human use, and chemotherapy presents several problems. Pentavalent antimonials have been the drugs of choice to treat the disease for more than six decades; however, they exhibit high toxicity and are not indicated for children, for pregnant or breastfeeding women or for chronically ill patients. Amphotericin B (AmpB) is a second-line drug, and although it has been increasingly used to treat visceral leishmaniasis (VL), its clinical use has been hampered due to its high toxicity. This review focuses on the development and in vivo usage of new delivery systems for AmpB that aim to decrease its toxicity without altering its therapeutic efficacy. These new formulations, when adjusted with regard to their production costs, may be considered new drug delivery systems that promise to improve the treatment of leishmaniasis, by reducing the side effects and the number of doses while permitting a satisfactory cost-benefit ratio.

Effects of circular myotomy on the healing of esophageal suture anastomosis: an experimental study

For esophageal reconstruction in newborns with esophageal atresia, esophageal reunion with an end-to-end anastomosis is the ideal procedure, although it may result in leaks and strictures due to tension on the suture line, mainly in cases with a wide gap between the ends. Circular myotomy (Livaditis' procedure) is the best method to elongate the proximal esophageal pouch and reduce anastomotic tension. This experimental investigation in dogs was undertaken to attempt to verify that circular myotomy decreases the anastomotic leak rate in newborns with wide gap esophageal atresia, and to analyze whether the technique promotes morphologic changes in the anastomotic scar. A pilot study demonstrated that it is necessary to resect more than 8 cm (40% of the total esophageal length) in order to obtain high leak rates. In the experimental project, such resection was performed in dogs divided into two groups (control group, anastomosis only, and experimental group, anastomosis plus circular myotomy in the proximal esophageal segment). The animals were killed in the 14th postoperative day, submitted to autopsy, and were evaluated as to the presence of leaks and strictures, as well as to the features (macroscopic and microscopic aspects) of the anastomosis. Leak rates were the same in both groups. Morphometric analysis revealed that in animals in the experimental group, the anastomotic scar was thinner than the control animals, and the isolated muscular manchette distal to the site of myotomy was replaced by fibrous tissue. Correspondingly, a decreased number of newly formed small vessels were noted in the experimental animals, compared to control animals. We concluded that circular myotomy does not decrease the incidence of anastomotic leaks, and it also promotes deleterious changes in anastomotic healing.

On line pre-concentration for simultaneous determination of low molecular weight organic acids and inorganic anions in Amazonian river water samples employing ion chromatography with conductivity detection

An ion chromatography procedure, employing an IonPac AC15 concentrator column was used to investigate on line preconcentration for the simultaneous determination of inorganic anions and organic acids in river water. Twelve organic acids and nine inorganic anions were separated without any interference from other compounds and carry-over problems between samples. The injection loop was replaced by a Dionex AC15 concentrator column. The proposed procedure employed an auto-sampler that injected 1.5 ml of sample into a KOH mobile phase, generated by an Eluent Generator, at 1.5 mL min-1, which carried the sample to the chromatographic columns (one guard column, model AG-15, and one analytical column, model AS15, with 250 x 4mm i.d.). The gradient elution concentrations consisted of a 10.0 mmol l-1 KOH solution from 0 to 6.5 min, gradually increased to 45.0 mmol l-1 KOH at 21 min., and immediatelly returned and maintained at the initial concentrations until 24 min. of total run. The compounds were eluted and transported to an electro-conductivity detection cell that was attached to an electrochemical detector. The advantage of using concentrator column was the capability of performing routine simultaneous determinations for ions from 0.01 to 1.0 mg l-1 organic acids (acetate, propionic acid, formic acid, butyric acid, glycolic acid, pyruvate, tartaric acid, phthalic acid, methanesulfonic acid, valeric acid, maleic acid, oxalic acid, chlorate and citric acid) and 0.01 to 5.0 mg l-1 inorganic anions (fluoride, chloride, nitrite, nitrate, bromide, sulfate and phosphate), without extensive sample pretreatment and with an analysis time of only 24 minutes.

Puberty in male collared peccary (Pecari tajacu) determined by quantitative analysis of spermatogenic cells

Biological studies are necessary for the management of wildlife in captivity, and knowledge of reproduction is one of the important features for increasing production. The objective of the research was to determine the age at which male collared peccaries reach puberty. Testicular samples of 15 animals, aged 7 to 16 months, distributed into five groups (G1, G2, G3, G4 and G5) were used. The testes showed considerably increased weight, length and width (p < 0.05) from G1 to G3, whereas, from this group onward, the development of this organ was slower. There was positive correlation (p < 0.001) between the following testicular parameters: weight and length (r = 0.97), weight and width (r = 0.88), length and width (r = 0.92). Regarding the diameter of seminiferous tubules, an increase was observed (p < 0.05) from G1 to G4. The total number of spermatogenic cells increased significantly (p < 0.05) until G3 and then it stabilized. There was also positive correlation between testis weight and tubular diameter (r = 0.99, p < 0.001), and testis weight and spermatogenic cells (r = 0.98, p < 0.001). The number of Sertoli cells decreased significantly (p < 0.05) from G1, when they were undifferentiated as support cells, to G5, when they occurred together with the complete line of spermatic cells. The results demonstrate that the reproductive development of peccaries can be classified into the following stages: impuberty (G1, 7-8 months); pre-pubertal (G2, 9-10 months); pubertal (G3, 11-12 months); post-pubertal 1 (G4, 13-14 months); and post-pubertal 2 (G5, 15-16 months). Based on the histological analyses, puberty in the male collared peccary was determined to occur between 11 and 12 months of age.

Hipometilação do LINE-1 está Associada ao Risco de Doença Cardíaca Coronariana na População Chinesa

Fundamentos: O nível de metilação global do ADN de leucócitos no sangue tem sido associado ao risco de doença arterial coronariana (DAC), com resultados inconsistentes em diferentes populações. Faltam dados semelhantes da população chinesa, onde diferentes fatores genéticos, de estilo de vida e ambientais podem afetar a metilação do ADN e sua relação com o risco de DCC. Objetivos: Analisar se a metilação global está associada ao risco de doença coronariana na população chinesa. Métodos: Foram incluídos um total de 334 casos de DCC e 788 controles saudáveis. A metilação global do ADN de leucócitos de sangue foi estimada por meio da análise das repetições do LINE-1 usando pirosequenciamento de bissulfito. Resultados: Em uma análise inicial restrita aos controles o nível do LINE-1 diminui significativamente com a idade avançada, colesterol total elevado, e diagnóstico de diabetes. Na análise de caso-controle, a redução da metilação do LINE-1 foi associada ao aumento do risco de DCC, tendo a análise por quartil revelado uma odds ratio (IC 95%) de 0,9 (0,6-1,4), 1,9 (1,3-2,9) e 2,3 (1,6 3.5) para o terceiro, segundo e primeiro (o mais baixo) quartil (P da tendência < 0,001), respectivamente, em comparação com o quarto (o mais alto) quartil. A metilação inferior (< mediana) do LINE-1 esteve associada a 2,2 vezes (IC 95% = 1,7-3,0) o aumento de risco de doença coronariana. As estimativas de risco de DCC menores relacionadas com o LINE-1 tenderam a ser mais fortes entre os indivíduos com maior tercil de homocisteína (P interação = 0,042) e naqueles com diagnóstico de hipertensão arterial (P interação = 0,012). Conclusão: A hipometilação do LINE-1 está associada ao risco de doença coronariana na população chinesa. Fatores de risco de DCC potenciais tais como a idade avançada, colesterol total elevado, e diagnóstico de diabetes podem ter impacto na metilação global do ADN, exercendo, portanto, o seu efeito sobre o risco de doença coronariana.

Investigation of Copy Number Variation in Children with Conotruncal Heart Defects

Background:Congenital heart defects (CHD) are the most prevalent group of structural abnormalities at birth and one of the main causes of infant morbidity and mortality. Studies have shown a contribution of the copy number variation in the genesis of cardiac malformations.Objectives:Investigate gene copy number variation (CNV) in children with conotruncal heart defect.Methods:Multiplex ligation-dependent probe amplification (MLPA) was performed in 39 patients with conotruncal heart defect. Clinical and laboratory assessments were conducted in all patients. The parents of the probands who presented abnormal findings were also investigated.Results:Gene copy number variation was detected in 7/39 patients: 22q11.2 deletion, 22q11.2 duplication, 15q11.2 duplication, 20p12.2 duplication, 19p deletion, 15q and 8p23.2 duplication with 10p12.31 duplication. The clinical characteristics were consistent with those reported in the literature associated with the encountered microdeletion/microduplication. None of these changes was inherited from the parents.Conclusions:Our results demonstrate that the technique of MLPA is useful in the investigation of microdeletions and microduplications in conotruncal congenital heart defects. Early diagnosis of the copy number variation in patients with congenital heart defect assists in the prevention of morbidity and decreased mortality in these patients.

Estudos experimentais sôbre a origem do milho

1) It may seem rather strange that, in spite of the efforts of a considerable number of scientists, the problem of the origin of indian corn or maize still has remained an open question. There are no fossil remains or archaeological relics except those which are quite identical with types still existing. (Fig. 1). The main difficulty in finding the wild ancestor- which may still exist - results from the fact that it has been somewhat difficult to decide what it should be like and also where to look for it. 2) There is no need to discuss the literature since an excellent review has recently been published by MANGELSDORF and REEVES (1939). It may be sufficient to state that there are basically two hypotheses, that of ST. HILAIRE (1829) who considered Brazilian pod corn as the nearest relative of wild corn still existing, and that of ASCHERSON (1875) who considered Euchlaena from Central America as the wild ancestor of corn. Later hypotheses represent or variants of these two hypotheses or of other concepts, howewer generally with neither disproving their predecessors nor showing why the new hypotheses were better than the older ones. Since nearly all possible combinations of ideas have thus been put forward, it har- dly seems possible to find something theoretically new, while it is essential first to produce new facts. 3) The studies about the origin of maize received a new impulse from MANGELSDORF and REEVES'S experimental work on both Zea-Tripsacum and Zea-Euchlaena hybrids. Independently I started experiments in 1937 with the hope that new results might be obtained when using South American material. Having lost priority in some respects I decided to withold publication untill now, when I can put forward more concise ideas about the origin of maize, based on a new experimental reconstruction of the "wild type". 4) The two main aspects of MANGELSDORF and REEVES hypothesis are discussed. We agree with the authors that ST. HILAIRE's theory is probably correct in so far as the tunicata gene is a wild type relic gene, but cannot accept the reconstruction of wild corn as a homozygous pod corn with a hermaphroditic tassel. As shown experimentally (Fig. 2-3) these tassels have their central spike transformed into a terminal, many rowed ear with a flexible rachis, while possessing at the same time the lateral ear. Thus no explanation is given of the origin of the corn ear, which is the main feature of cultivated corn (BRIEGER, 1943). The second part of the hypothesis referring to the origin of Euchlaena from corn, inverting thus ASCHERSON's theory, cannot be accepted for several reasons, stated in some detail. The data at hand justify only the conclusion that both genera, Euchlaena and Zea, are related, and there is as little proof for considering the former as ancestor of the latter as there is for the new inverse theory. 5) The analysis of indigenous corn, which will be published in detail by BRIEGER and CUTLER, showed several very primitive characters, but no type was found which was in all characters sufficiently primitive. A genetical analysis of Paulista Pod Corn showed that it contains the same gene as other tunicates, in the IV chromosome, the segregation being complicated by a new gametophyte factor Ga3. The full results of this analysis shall be published elsewhere. (BRIEGER). Selection experiments with Paulista Pod Corn showed that no approximation to a wild ancestor may be obtained when limiting the studies to pure corn. Thus it seemed necessary to substitute "domesticated" by "wild type" modifiers, and the only means for achieving this substitution are hybridizations with Euchlaena. These hybrids have now been analysed init fourth generation, including backcrosses, and, again, the full data will be published elsewhere, by BRIEGER and ADDISON. In one present publication three forms obtained will be described only, which represent an approximation to wild type corn. 6) Before entering howewer into detail, some arguments against ST. HILAIRE's theory must be mentioned. The premendelian argument, referring to the instability of this character, is explained by the fact that all fertile pod corn plants are heterozygous for the dominant Tu factor. But the sterility of the homozygous TuTu, which phenotypically cannot be identified, is still unexplained. The most important argument against the acceptance of the Tunicata faetor as wild type relic gene was removed recently by CUTLER (not yet published) who showed that this type has been preserved for centuries by the Bolivian indians as a mystical "medicine". 7) The main botanical requirements for transforming the corn ear into a wild type structure are stated, and alternative solutions given. One series of these characters are found in Tripsacum and Euchlaena : 2 rows on opposite sides of the rachis, protection of the grains by scales, fragility of the rachis. There remains the other alternative : 4 rows, possibly forming double rows of female and male spikelets, protection of kernels by their glumes, separation of grains at their base from the cob which is thin and flexible. 8) Three successive stages in the reconstruction of wild corn, obtained experimentally, are discussed and illustrated, all characterized by the presence of the Tu gene. a) The structure of the Fl hybrids has already been described in 1943. The main features of the Tunicata hybrids (Fig. -8), when compared with non-tunicate hybrids (Fig. 5-6), consist in the absence of scaly protections, the fragility of the rachis and finally the differentiation of the double rows into one male and one female spikelet. As has been pointed out, these characters represent new phenotypic effects of the tunicate factor which do not appear in the presence of pure maize modifiers. b) The next step was observed among the first backcross to teosinte (Fig. 9). As shown in the photography, Fig. 9D, the features are essencially those of the Fl plants, except that the rachis is more teosinte like, with longer internodes, irregular four-row-arrangement and a complete fragility on the nodes. c) In the next generation a completely new type appeared (Fig. 10) which resembles neither corn nor teosinte, mainly in consequence of one character: the rachis is thin and flexible and not fragile, while the grains have an abscission layer at the base, The medium sized, pointed, brownish and hard granis are protected by their well developed corneous glumes. This last form may not yet be the nearest approach to a wild grass, and I shall try in further experiments to introduce other changes such as an increase of fertile flowers per spikelet, the reduction of difference between terminal and lateral inflorescences, etc.. But the nature of the atavistic reversion is alveadwy such that it alters considerably our expectation when looking for a still existing wild ancestor of corn. 9) The next step in our deductions must now consist in an reversion of our question. We must now explain how we may obtain domesticated corn, starting from a hypothetical wild plant, similar to type c. Of the several changes which must have been necessary to attract the attention of the Indians, the following two seem to me the most important: the disappearance of all abscission layers and the reduction of the glumes. This may have been brought about by an accumulation of mutations. But it seems much more probable to assume that some crossing with a tripsacoid grass or even with Tripsacum australe may have been responsible. In such a cross, the two types of abscission layer would be counterbalanced as shown by the Flhybrids of corn, Tripsacum and Euchlaena. Furthermore in later generations a.tu-allele of Tripsacum may become homozygous and substitute the wild tunicate factor of corn. The hypothesis of a hybrid origin of cultivated corn is not completely new, but has been discussed already by HARSHBERGER and COLLINS. Our hypothesis differs from that of MANGELSDORF and REEVES who assume that crosses with Tripsacum are responsible only for some features of Central and North American corn. 10) The following arguments give indirects evidence in support of our hypothesis: a) Several characters have been observed in indigenous corn from the central region of South America, which may be interpreted as "tripsacoid". b) Equally "zeoid" characters seem to be present in Tripsacum australe of central South-America. c) A system of unbalanced factors, combined by the in-tergeneric cross, may be responsible for the sterility of the wild type tunicata factor when homozygous, a result of the action of modifiers, brought in from Tripsacum together with the tuallele. d) The hybrid theory may explain satisfactorily the presence of so many lethals and semilethals, responsible for the phenomenon of inbreeding in cultivated corn. It must be emphasized that corn does not possess any efficient mechanism to prevent crossing and which could explain the accumulation of these mutants during the evolutionary process. Teosinte which'has about the same mechanism of sexual reproduction has not accumulated such genes, nor self-sterile plants in spite of their pronounced preference for crossing. 11) The second most important step in domestication must have consisted in transforming a four rowed ear into an ear with many rows. The fusion theory, recently revived byLANGHAM is rejected. What happened evidently, just as in succulent pXants (Cactus) or in cones os Gymnosperms, is that there has been a change in phyllotaxy and a symmetry of longitudinal rows superimposed on the original spiral arrangement. 12) The geographical distribution of indigenous corn in South America has been discussed. So far, we may distinguish three zones. The most primitive corn appears in the central lowlands of what I call the Central Triangle of South America: east of the Andies, south of the Amazone-Basin, Northwest of a line formed by the rivers São Prancisco-Paraná and including the Paraguay-Basin. The uniformity of the types found in this extremely large zone is astonishing (BRIEGER and CUTLER). To the west, there is the well known Andian region, characterized by a large number of extremely diverse types from small pop corn to large Cuszco, from soft starch to modified sweet corn, from large cylindrical ears to small round ears, etc.. The third region extends along the atlantic coast in the east, from the Caribean Sea to the Argentine, and is characterized by Cateto, an orange hard flint corn. The Andean types must have been obtained very early, and undoubtedly are the result of the intense Inca agriculture. The Cateto type may be obtained easily by crosses, for instance, of "São Paulo Pointed Pop" to some orange soft corn of the central region. The relation of these three South American zones to Central and North America are not discussed, and it seems essential first to study the intermediate region of Ecuador, Colombia and Venezuela. The geograprical distribution of chromosome knobs is rapidly discussed; but it seems that no conclusions can be drawn before a large number of Tripsacum species has been analysed.

A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.