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1 - Análise do Brix Em três das variedades analisadas - F 29-7, Co. 285 e Tuc. 519, - a diferença entre o Brix do caldo das canas florescidas e das canas não florescidas foi estatisticamente insignificante. Apenas em uma variedade - Co. 312 - tivemos um resultado duvidoso. Em F 29-7 nota-se que o erro nas' canas florescidas é maior que nas não florescidas, o que parece indicar uma tendência a maior instabilidade do Brix com o florescimento. A diferença entre os dois erros é, poréxn, de significação duvidosa, embora o valor de P exceda bastante o limite de 5% de probabilidade, sem atingir o de 1%. 2 - Análise dos redutores Houve uma diferença sem significação em F 29-7 e Co. 285. Em Co. 312, porém, o resultado foi duvidoso e em Tuc. 519 foi significante, e em ambas estas variedades as canas não florescidas eram as mais ricas em redutores, o que merece ser salientado. Nota-se que o erro nas canas não florescidas é maior do que nas florescidas, o que indica uma estabilização de percentagem de redutores com o florescimento em F 29-7. A diferença entre os erros é, porém, de significação duvidosa, de sorte que só futuras pesquisas poderão esclarecer essa dúvida. 3 - Análise da pol Neste caso a diferença foi insignificante em F 29-7 e Co. 312 e duvidosa nas outras duas variedades. E nos casos de diferença duvidosa a pol foi maior no caldo das canas florescidas, o que é digno de destaque. O erro foi insignificantemente maior nas canas florescidas do que nas não florescidas. 4 - Análise das cinzas A diferença entre as médias foi insignificante em F 29-7 e Co. 312; foi duvidosa em Tuc. 519 e significante em Co. 285. Nos dois últimos casos a quantidade de cinzas foi maior no caldo das canas não florescidas do que no das florescidas. Nota-se, pelo erro, uma maior variação nas canas não florescidas, mas o teste F dá um resultado duvidoso, que exige novas pesquisas. 5 - Análise da acidez sulfúrica A diferença entre as médias foi insignificante em F 29-7 e Tuc. 519, tendo sido significante nas duas variedades restantes. Nestes dois últimos casos foi o caldo das canas florescidas favorecido com uma acidez menor do que o das não florescidas. O teste F foi absolutamente sem significação, o que significa que a variação é a mesma nas canas florescidas e não florescidas em F 29-7. 6 - Análise de litros de cadlo por quilo de cana A diferença entre as médias foi significante em F 29-7, Co. 285 e Co. 312, sempre com menor quantidade de caldo nas canas n florescidas. Em Tuc. 519 o resultado foi duvidoso, mas como se aproxima bastante do limite de 1% e concorda com os resultados obtidos nas outras variedades e ainda com a observação de medula seca nos gomos terminais das canas florescidas, como já foi dito atrás, esse resultado pode ser tomado como significante. O erro maior nas canas n florescidas e o teste F significante indicam que com o florescimento se estabiliza a relação litros de caldo por quilo de cana. 7 - Análise da fibra Neste caso os resultados foram análogos aos obtidos no caso da relação litros de caldo por quilo' de cana, como era de se esperar. De fato, em F 29-7, Co. 285 e Co. 312 as diferenças foram significantes. Em Tuc. 519 o resultado foi duvidoso, mas as mesmas considerações apresentadas no caso anterior nos levam a considerá-lo significante. Em todas as variedades analisadas as canas florescidas foram sempre mais ricas em fibra. O teste F foi insignificante, c que indica que não há diferença notável entre os erros. 8 - Análise do pêso Esta análise, que só foi feita em F 29-7, nos leva a concluir que o pequeno excesso de peso apresentado pelas canas florescidas n tem a menor significação. Como as nossas observações indicam para as canas florescidas maior comprimento e maior grossura, esse resultado evidencia um murchamente, o que é, aliás, confirmado pela diminuição da relação litros de caldo por quilo dé caria e pelo aumento da quantidade de fibra. Sobre o teste F já salientámos que êle neste caso nos indica que o peso das canas se estabiliza com o florescimento.

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In the present paper the behavior of the heterochromoso-mes in the course of the meiotic divisions of the spermatocytes in 15 species of Orthoptera belonging to 6 different families was studied. The species treated and their respective chromosome numbers were: Phaneropteridae: Anaulacomera sp. - 1 - 2n = 30 + X, n +15+ X and 15. Anaulacomera sp. - 2 - 2n - 30 + X, n = 15+ X and 15. Stilpnochlora marginella - 2n = 30 + X, n = 15= X and 15. Scudderia sp. - 2n = 30 + X, n = 15+ X and 15. Posldippus citrifolius - 2n = 24 + X, n = 12+X and 12. Acrididae: Osmilia violacea - 2n = 22+X, n = 11 + X and 11. Tropinotus discoideus - 2n = 22+ X, n = 11 + X and 11. Leptysma dorsalis - 2n = 22 + X, n = 11-J-X and 11. Orphulella punctata - 2n = 22-f X, n = 11 + X and 11. Conocephalidae: Conocephalus sp. - 2n = 32 + X, n = 16 + X and 16. Proscopiidae: Cephalocoema zilkari - 2n = 16 + X, n = 8+ X and 8. Tetanorhynchus mendesi - 2n = 16 + X, n = 8+X and 8. Gryliidae: Gryllus assimilis - 2n = 28 + X, n = 14+X and 14. Gryllodes sp. - 2n = 20 + X, n = 10- + and 10. Phalangopsitidae: Endecous cavernicola - 2n = 18 +X, n = 94-X and 9. It was pointed out by the present writer that in the Orthoptera similarly to what he observed in the Hemiptera the heterochromosome in the heterocinetic division shows in the same individual indifferently precession, synchronism or succession. This lack of specificity is therefore pointed here as constituting the rule and not the exception as formerly beleaved by the students of this problem, since it occurs in all the species referred to in the present paper and probably also m those hitherto investigated. The variability in the behavior of the heterochromosome which can have any position with regard to the autosomes even in the same follicle is attributed to the fact that being rather a stationary body it retains in anaphase the place it had in metaphase. When this place is in the equator of the cell the heterochromosome will be left behind as soon as anaphase begins (succession). When, on the contrary, laying out of this plane as generally happens (precession) it will sooner be reached (synchronism) or passed by the autosomes (succession). Due to the less kinetic activity of the heterochromosome it does not orient itself at metaphase remaining where it stands with the kinetochore looking indifferently to any direction. At the end of anaphase and sometimes earlier the heterochromosome begins to show mitotic activities revealed by the division of its body. Then, responding to the influence of the nearer pole it moves to it being enclosed with the autosomes in the nucleus formed there. The position of the heterochromosome in the cell is explained in the following manner: It is well known that the heterochromosome of the Orthoptera is always at the periphery of the nucleus, just beneath the nuclear membrane. This position may be any in regard of the axis of the dividing cell, so that if one of the poles of the spindle comes to coincide with it, the heterochromosome will appear at this pole in the metaphasic figures. If, on the other hand, the angle formed by the axis of the spindle with the ray reaching the heterochromosome increases the latter will appear in planes farther and farther apart from the nearer pole until it finishes by being in the equatorial plane. In this way it is not difficult to understand precession, synchronism or succession. In the species in which the heterochromosome is very large as it generally happens in the Phaneropteridae, the positions corresponding to precession are much more frequent. This is due to the fact that the probabilities for the heterochromosome taking an intermediary position between the equator and the poles at the time the spindle is set up are much greater than otherwise. Moreover, standing always outside the spindle area it searches for a place exactly where this area is larger, that is, in the vicinity of the poles. If it comes to enter the spindle area, what has very little probability, it would be, in virtue of its size, propelled toward the pole by the nearing anaphasic plate. The cases of succession are justly those in which the heterochromosome taking a position parallelly to the spindle axis it can adjust its large body also in the equator or in its proximity. In the species provided with small heterochromosome (Gryllidae, Conocephalidae, Acrididae) succession is found much more frequently because here as in the Hemiptera (PIZA 1945) the heterochromosome can equally take equatorial or subequatorial positions, and, furthermore, when in the spindle area it does offer no sereous obstacle to the passage of the autosomes. The position of the heterochromosome at the periphery of the nucleus at different stages may be as I suppose, at least in part a question of density. The less colourability and the surface irregularities characteristic of this element may well correspond to a less degree of condensation which may influence passive movements. In one of the species studied here (Anaulacomera sp.- 1) included in the Phaneropteridae it was observed that the plasmosome is left motionless in the spindle as the autosomes move toward the poles. It passes to one of the secondary spermatocytes being not included in its nucleus. In the second division it again passes to one of the cells being cast off when the spermatid is being transformed into spermatozoon. Thus it is regularly found among the tails of the spermatozoa in different stages of development. In the opinion of the present writer, at least in some cases, corpuscles described as Golgi body's remanents are nothing more than discarded plasmosomes.

The study of pod corn seems still of much importance from different points of view. The phylogenetical importance of the tunicate factor as a wild type relic gene has been recently discussed in much detail by MANGELSDORF and REEVES (1939), and by BRIEGER (1943, 1944a e b). Selection experiments have shown that the pleiotropic effect of the Tu factor can be modified very extensively (BRIEGER 1944a) and some of the forms thus obtained permitt comparison of male and female inflorescences in corn and related grasses. A detailed discussion of the botanical aspect shall be given shortly. The genetic apect, finally, is the subject of the present publication. Pod corn has been obtained twice: São Paulo Pod Corn and Bolivia Pod Corn. The former came from one half ear left in our laboratory by a student and belongs to the type of corn cultivated in the State of São Paulo, while the other belongs to the Andean group, and has been received both through Dr. CARDENAS, President of the University at Cochabamba, Bolivia, and through Dr. H. C. CUTLER, Harvard University, who collected material in the Andes. The results of the studies may be summarized as follows: 1) In both cases, pod corn is characterized by the presence of a dominant Tu factor, localized in the fourth chromosome and linked with sul. The crossover value differs somewhat from the mean value of 29% given by EMERSON, BEADLE and FRAZER (1935) and was 25% in 1217 plants for São Paulo Pod Corn and 36,5% in 345 plants for Bolivia Pod Corn. However not much importance should be attributed to the quantitative differences. 2) Segregation was completely normal in Bolivia Pod Corn while São Paulo Pod Corn proved to be heterozygous for a new com uma eliminação forte, funcionam apenas 8% em vez de 50%. Existem cerca de 30% de "jcrossing-over entre o gen doce (Su/su) e o fator gametofítico; è cerca de 5% entre o gen Tu e o fator gametofítico. A ordem dos gens no cromosômio IV é: Ga4 - Tu - Sul. 3) Using BRIEGER'S formulas (1930, 1937a, 1937b) the following determinations were made. a) the elimination of ga4 pollen tubes may be strong or weak. In the former case only about 8% and in the latter 37% of ga4 pollen tubes function, instead of the 50% expected in normal heterozygotes. b) There is about 30,4% crossing-over between sul and ga4 and 5,3% between Tu and ga3, the order of the factors beeing Su 1 - Tu - Ga4. 4) The new gametophyte factor differs from the two others factors in the same chromosome, causing competition between pollen tubes. The factor Gal, ocupies another locus, considerably to the left of Sul (EMERSON, BEADLE AND FRAZSER, 1935). The gen spl ocupies another locus and causes a difference of the size of the pollen grains, besides an elimination of pollen tubes, while no such differences were observed in the case of the new factor Ga4. 5) It may be mentioned, without entering into a detailed discussion, that it seems remarquable that three of the few gametophyte factors, so far studied in detail are localized in chromosome four. Actuality there are a few more known (BRIEGER, TIDBURY AND TSENG 1938), but only one other has been localized so far, Ga2, in chromosome five between btl and prl. (BRIEGER, 1935). 6) The fourth chromosome of corn seems to contain other pecularities still. MANGELSDORF AND REEVES (1939) concluded that it carries two translocations from Tripsacum chromosomes, and BRIEGER (1944b) suggested that the tu allel may have been introduced from a tripsacoid ancestor in substitution of the wild type gene Tu at the beginning of domestication. Serious disturbances in the segregation of fourth chromosome factors have been observed (BRIEGER, unpublished) in the hybrids of Brazilian corn and Mexican teosinte, caused by gametophytic and possibly zygotic elimination. Future studies must show wether there is any relation between the frequency of factors, causing gametophyte elimination and the presence of regions of chromosomes, tranfered either from Tripsacum or a related species, by translocation or crossing-over.

The experiments reported were started as early as 1933, when indications were found in class material that the factor for small pollen, spl, causes not only differences in the size of pollen grains and in the growth of pollen tubes, but also a competition between megaspores, as first observed by RENNER (1921) in Oenothera. Dr. P. C. MANGELSDORF, who had kindly furnished the original seeds, was informed and the final publication delayed untill his publication in 1940. A further delay was caused by other circunstances. The main reason for the differences of the results obtained by SINGLETON and MANGELSDORF (1940) and those reported here, seems to be the way the material was analysed. I applied methods of a detailed statistical analysis, while MANGELSDORF and SINGLETON analysed pooled data. 1) The data obtained on pollen tube competition indicate .that there is about 3-4% of crossing-over between the su and sp factors in chromosome IV. The elimination is not always complete, but from 0 to 10% of the sp pollen tubes may function, instead of the 50% expected without elimination. These results are, as a whole, in accordance with SINGLETON and MANGELSDORF's data. 2) Female elimination is weaker and transmission determined as between 16 to 49,5%, instead of 50% without competition, the values being calculated by a special formula. 3) The variability of female elimination is partially genotypical, partially phenotypical. The former was shown by the difference in the behavior of the two progenies tested, while the latter was very evident when comparing the upper and lower halves of ears. For some unknown physiological reason, the elimination is generally stronger in the upper than in the lower half of the ear. 4) The female elimination of the sp gene may be caused theoretically, by either of two processes: a simple lethal effect in the female gametophyte or a competition between megaspores. The former would lead not only to the abortion of the individual megaspores, but of the whole uniovulate ovary. In the case of the latter, the abortive megaspore carrying the gene sp will be substituted in each ovule by one of the Sp megaspores and no abortion of ovaries may be observed. My observations are completely in favor of the second explication: a) The ears were as a whole very well filled except for a few incomplete ears which always appear in artificial pollinations. b) Row arrangement was always very regular. c) The number of kernels on ears with elimination is not smaller than in normal ears, but is incidentally higher : with elimnation, in back-crosses 354 kernels and in selfed ears 390 kernels, without elimination 310 kernels per ear. d) There is no correlation between the intensity of elimination and the number of grains in individual ears; the coefficient; of linear correlation, equal to 0,24, is small and insignificant. e) Our results are in complete disagreement whit those reported by SINGLETON and MANGELSDORF (1940). Since these authors present only pooled date, a complete and detailed analysis which may explain the cause of these divergences is impossible.

1) The first part deals with the different processes which may complicate Mendelian segregation and which may be classified into three groups, according to BRIEGER (1937b) : a) Instability of genes, b) Abnormal segregation due to distur- bances during the meiotic divisions, c) obscured segregation, after a perfectly normal meiosis, caused by elimination or during the gonophase (gametophyte in higher plants), or during zygophase (sporophyte). Without entering into detail, it is emphasized that all the above mentioned complications in the segregation of some genes may be caused by the action of other genes. Thus in maize, the instability of the Al factor is observed only when the gene dt is presente in the homozygous conditions (RHOADES 1938). In another case, still under observation in Piracicaba, an instability is observed in Mirabilis with regard to two pairs of alleles both controlling flower color. Several cases are known, especially in corn, where recessive genes, when homozigous, affect the course of meiosis, causing asynapsis (asyndesis) (BEADLE AND MC CLINTOCK 1928, BEADLE 1930), sticky chromosomes (BEADLE 1932), supermunmerary divisions (BEADLE 1931). The most extreme case of an obscured segregatiou is represented by the action of the S factors in self stetrile plants. An additional proof of EAST AND MANGELSDORF (1925) genetic formula of self sterility has been contributed by the studies on Jinked factors in Nicotina (BRIEGER AND MANGELSDORF (1926) and Antirrhinum (BRIEGER 1930, 1935), In cases of a incomplete competition and selection between pollen tubes, studies of linked indicator-genes are indispensable in the genetic analysis, since it is impossible to analyse the factors for gametophyte competition by direct aproach. 2) The flower structure of corn is explained, and stated that the particularites of floral biology make maize an excellent object for the study of gametophyte factors. Since only one pollen tube per ovule may accomplish fertilization, the competition is always extremely strong, as compared with other species possessing multi-ovulate ovaries. The lenght of the silk permitts the study of pollen tube competitions over a varying distance. Finally the genetic analysis of grains characters (endosperm and aleoron) simpliflen the experimental work considerably, by allowing the accumulation of large numbers for statistical treatment. 3) The four methods for analyzing the naturing of pollen tube competition are discussed, following BRIEGER (1930). Of these the first three are: a) polinization with a small number of pollen grains, b) polinization at different times and c) cut- ting the style after the faster tubes have passe dand before the slower tubes have reached the point where the stigma will be cut. d) The fourth method, alteration of the distatice over which competition takes place, has been applied largely in corn. The basic conceptions underlying this process, are illustrated in Fig. 3. While BRINK (1925) and MANGELSDORF (1929) applied pollen at different levels on the silks, the remaining authors (JONES, 1922, MANGELSDORF 1929, BRIEGER, at al. 1938) have used a different process. The pollen was applied as usual, after removing the main part of the silks, but the ears were divided transversally into halves or quarters before counting. The experiments showed generally an increase in the intensity of competition when there was increase of the distance over which they had to travel. Only MANGELSDORF found an interesting exception. When the distance became extreme, the initially slower tubes seemed to become finally the faster ones. 4) Methods of genetic and statistical analysis are discussed, following chiefly BRIEGER (1937a and 1937b). A formula is given to determine the intensity of ellimination in three point experiments. 5) The few facts are cited which give some indication about the physiological mechanism of gametophyte competition. They are four in number a) the growth rate depends-only on the action of gametophyte factors; b) there is an interaction between the conductive tissue of the stigma or style and the pollen tubes, mainly in self-sterile plants; c) after self-pollination necrosis starts in the tissue of the stigma, in some orchids after F. MÜLLER (1867); d) in pollon mixtures there is an inhibitory interaction between two types of pollen and the female tissue; Gossypium according to BALLS (1911), KEARNEY 1923, 1928, KEARNEY AND HARRISON (1924). A more complete discussion is found in BRIEGER 1930). 6) A list of the gametophyte factors so far localized in corn is given. CHROMOSOME IV Ga 1 : MANGELSDORF AND JONES (1925), EMERSON 1934). Ga 4 : BRIEGER (1945b). Sp 1 : MANGELSDORF (1931), SINGLETON AND MANGELSDORF (1940), BRIEGER (1945a). CHROMOSOME V Ga 2 : BRIEGER (1937a). CHROMOSOME VI BRIEGER, TIDBURY AND TSENG (1938) found indications of a gametophyte factor altering the segregation of yellow endosperm y1. CHROMOSOME IX Ga 3 : BRIEGER, TIDBURY AND TSENG (1938). While the competition in these six cases is essentially determined by one pair of factors, the degree of elimination may be variable, as shown for Ga2 (BRIEGER, 1937), for Ga4 (BRIEGER 1945a) and for Spl (SINGLETON AND MANGELSDORF 1940, BRIEGER 1945b). The action of a gametophyte factor altering the segregation of waxy (perhaps Ga3) is increased by the presence of the sul factor which thus acts as a modifier (BRINCK AND BURNHAM 1927). A polyfactorial case of gametophyte competition has been found by JONES (1922) and analysed by DEMEREC (1929) in rice pop corn which rejects the pollen tubes of other types of corn. Preference for selfing or for brothers-sister mating and partial elimination of other pollen tubes has been described by BRIEGER (1936). 7) HARLAND'S (1943) very ingenious idea is discussed to use pollen tube factors in applied genetics in order to build up an obstacle to natural crossing as a consequence of the rapid pollen tube growth after selfing. Unfortunately, HARLAND could not obtain the experimental proof of the praticability of his idea, during his experiments on selection for minor modifiers for pollen tube grouth in cotton. In maize it should be possible to employ gametophyte factors to build up lines with preference for crossing, though the method should hardly be of any practical advantage.

The general properties of POISSON distributions and their relations to the binomial distribuitions are discussed. Two methods of statistical analysis are dealt with in detail: X2-test. In order to carry out the X2-test, the mean frequency and the theoretical frequencies for all classes are calculated. Than the observed and the calculated frequencies are compared, using the well nown formula: f(obs) - f(esp) 2; i(esp). When the expected frequencies are small, one must not forget that the value of X2 may only be calculated, if the expected frequencies are biger than 5. If smaller values should occur, the frequencies of neighboroughing classes must ge pooled. As a second test reintroduced by BRIEGER, consists in comparing the observed and expected error standard of the series. The observed error is calculated by the general formula: δ + Σ f . VK n-1 where n represents the number of cases. The theoretical error of a POISSON series with mean frequency m is always ± Vm. These two values may be compared either by dividing the observed by the theoretical error and using BRIEGER's tables for # or by dividing the respective variances and using SNEDECOR's tables for F. The degree of freedom for the observed error is one less the number of cases studied, and that of the theoretical error is always infinite. In carrying out these tests, one important point must never be overlloked. The values for the first class, even if no concrete cases of the type were observed, must always be zero, an dthe value of the subsequent classes must be 1, 2, 3, etc.. This is easily seen in some of the classical experiments. For instance in BORKEWITZ example of accidents in Prussian armee corps, the classes are: no, one, two, etc., accidents. When counting the frequency of bacteria, these values are: no, one, two, etc., bacteria or cultures of bacteria. Ins studies of plant diseases equally the frequencies are : no, one, two, etc., plants deseased. Howewer more complicated cases may occur. For instance, when analising the degree of polyembriony, frequently the case of "no polyembryony" corresponds to the occurrence of one embryo per each seed. Thus the classes are not: no, one, etc., embryo per seed, but they are: no additional embryo, one additional embryo, etc., per seed with at least one embryo. Another interestin case was found by BRIEGER in genetic studies on the number os rows in maize. Here the minimum number is of course not: no rows, but: no additional beyond eight rows. The next class is not: nine rows, but: 10 rows, since the row number varies always in pairs of rows. Thus the value of successive classes are: no additional pair of rows beyond 8, one additional pair (or 10 rows), two additional pairs (or 12 rows) etc.. The application of the methods is finally shown on the hand of three examples : the number of seeds per fruit in the oranges M Natal" and "Coco" and in "Calamondin". As shown in the text and the tables, the agreement with a POISSON series is very satisfactory in the first two cases. In the third case BRIEGER's error test indicated a significant reduction of variability, and the X2 test showed that there were two many fruits with 4 or 5 seeds and too few with more or with less seeds. Howewer the fact that no fruit was found without seed, may be taken to indicate that in Calamondin fruits are not fully parthenocarpic and may develop only with one seed at the least. Thus a new analysis was carried out, on another class basis. As value for the first class the following value was accepted: no additional seed beyond the indispensable minimum number of one seed, and for the later classes the values were: one, two, etc., additional seeds. Using this new basis for all calculations, a complete agreement of the observed and expected frequencies, of the correspondig POISSON series was obtained, thus proving that our hypothesis of the impossibility of obtaining fruits without any seed was correct for Calamondin while the other two oranges were completely parthenocarpic and fruits without seeds did occur.

1) The present paper deals with the mathematical basis and the relations of the different chance distributions. It is shown that the concepts of classical statistics may only be applied correctly when dealing with illimited populations where the number of variables is so large that it may be considered as infinite. After the attempts of LEXIS and HELMERT, a partial solution was found by KARL PEARSON and by STUDENT, until finally R. A. FISHER gave the general solution, solving the problem of statistical analysis in a general form and determining the chance distribution in small samples. 2) As a basis for the formulas, I am using always the relative deviate, which may be determined in two ways: the simple relative deviale: D= v-v/ δ ou D = v-v2/δ the compound relative deviate: D = + Σ (v - 2)²: o o = o1/ o o 3) The deviates are always defined by two degrees of freedom, nl for the dividend and n2 for the divisor. According to the values combined in any given case, we may distinguish four basic chance distributions which we shall call according to the respective authors: the distributions of GAUSS, STUDENT, PEARSON and FISHER. The mathematical definition and the corresponding degrees of freedom are given both in formulae 3-1 to 3-4 on pg. and in the lower part of Fig. 2. The upper part of Fig. 2. represents grafically these four distributions. The equations and the forma of the corresponding curves are discussed in detail. 4) The main differences between the simple and the compound relative deviate are discussed: a) Simple deviates have always a definite signe and are either positive or negative, according to the signe of the numerator. Correspondingly the distributions of GAUSS and STUDENT are symetrical with regards to the abscissa zero and extend on both sides of it untill plus and minus infinite. Compound deviates on the other side, have no definite sign, since the numerator is a square root. The distributions of PEARSON and FISHER, accordingly, are discontinuous for the value zero and,we obtain two identical and independent curves which go from zero to plus infinite, resp. from zero to minus infinite. b) Secondly when studying simple deviates we admitt that both positive and negative large deviates may occur in consequence of an increase in variability. Consequently we ha- ve to use, in the corresponding tests, bilateral limits of probability (Fig. 3). When analysing compound deviates, we are comparing one standard error with another, which may either be an ideal value or at least a better estimate. Admitting that only an increase of variability may occurr, we apply in tests, based on PEARSON'S or FISHER's distribuitions, only the upper (superior) unilateral limit of probability (Fig. 4). The tables thus far published, for these distributions contain the unilaeeral limits only. A more complete table, including bilateral limits, has been computed by myself and is already in press. 5) Discussing the relations of the four distribuitions, it is shown that mathematically their formulas can be easily transiormed from one to the other by changing the respective values of degrees of freedom. The application of a few principles of mathematics is sufficient, besides remembering that the distributions of PEARSON and FISHER correspond only to half a distribution of STUDENT and GAUSS. Thus it is shown: a) that for nl bigger than 30, the distribution of STUDENT is so near to that of GAUSS (or normal), to permitt its substitution. b) that for nl bigger than 30, the distribution of PEARSON becomes almost symetrical and may be substituted by a modified distribution of GAUSS (or normal) with mean equal to one and error standard. 1 : 2n1 c) That the distribution of FISHER with nl = n2 becomes more or less symetrical when both reach the limit of 50 or bester still 100, and than may be substituted by a modified distribution of GAUSS with mean one and error standard. 1 : n d) That the distributions of FISHER, when nl differs from n2, may be substituted either by the correspondent distribution of PEARSAN, if nl is small and n2 bigger than 100, or by a modified distribution of GAUSS with mean unity and error standard equal to when nl goes beyond 50 and n2 beyond 100 ou vice versa. 1 : 2n1n2 n1 + n2 6) The formulas, generally given in the litterature to characterize the different distribuitions are far from being uniform and use differents measures for the abcissa. Thus in the tests for FISHER's distribution, the natural logarithm for the deviate were used initially (FISER's z-test). Later on SNEDECOR (1937) recommended the square of the deviate (F-test) and BRIEGER (1937) the deviate itself (n- test). In the X2 test, based on PEARSON'S distribution, one generally uses the square of the compound deviate, multiplied by the degree of freedom n1. The t-test, based on STUDENT'S distribution, finally makes use of the simple deviate itself. The inevitabal algebric consequences of this variation of unitis of emasure is, that the severity and thus the statistical efficiency of the tests is not comparable. Decimals in the t-test and n-test correspond to hundreds in the F-test and to almost anything, depending upon the values of nl, in the X2-test. 7) In the last chapter a few rather complicated problems are discussed, which can be solved with approximation in practical tests, but wich are still unsolved from the theoretical point of view. We shall mention here only two of the questions raised: a)Analyzing the difference between a variable and its mean (or of a partial mean and a general mean), only the standard error of the first term is used generally, considering the other as a constant: D = v- v 6n Howewer with more justification both terms may be considered as variable und thus one should apply the formula : D. v-v δ2 - δ 2 0 The first mentioned simple value of D chould follow a distribution of STUDENT and its analysis thus does not present any difficulties. But in the second term we combine the term, v, with standard error o which should follow STUDENT'S distribution and the mean, V , with standard error o v which generally will follow the distribution of GAUSS. How shall we combine the requeriments of those two distribuitions simultaneously? BEHREND's test seems to give a solution, which however is not very easy to apply and which is not suficient when the second term follows also a distribution of STUDENT, but with different degree of freedom. b) The second problem arises in connection with the ana-ysis of variance in its most simple form, i. e. the test "within-between". If we want to compare by a t-test the partial mean of one sample Va with the general mean v of the whole experiment, we must decide wether we should use standard error of this sample oa, based on np degrees of freedom or the error "within" oD which is a balanced mean value ot all the m individual sample errors. At the same time we have an alternative choice with regards to the degree of freedom: D = va - v/ Np n1 = 1/ n2 = n p ou D = va - v / δo/ n p = n1 = 1/ n2 = m. np Thus it is evident that the use of the value o D not only alters the value of the relative deviate D, but also the limits of probability to be applied which depend upon the degree of greedom. Howewer we must justify the substitution of the partial error o a by the error "within" oD and this should be done by determining wether the value o a: oD is due to chance only, i. e. that there is really no difference between the two errors from a statistical point of view. The necessary test howewer: D = δa /δ d n1 = np / n2 = m. n p generally does not allow a very decisive answer since the degree of freedom np is in most cases small. Whenever there is some reason to doubt wether the substitution is really justified, it seems to me reasonable to use the probably better estimate oD, instead of the individual sample error oa, while at the same time make allowances for doubts by not substituting the degrees of freedom: D = va - n / Bd Np n = 1 / n2 = nf A more complete formula naturally would be the following: D = va - v/ Bd N = 1 / N2... c) These too examples should be sufficient to show that there are still Important theoretical problems to be solved, in spite of the really very considerable progress achieved with regards to theory and methods of analysis of simple and compound relative deviates from uniform small or large, but always limited samples.

The authors studied the action of arsenic, in the form of lead arsenate and sodium arsenite, on cotton in white sandy soil of Piracicaba, State of S. Paulo, Brazil. The experiment was carried out in Mitscherlich pots, applying increasing quantities of the above mentioned compounds. The following conclusions were reached: sodium arsenite is more toxic than lead arsenate. 48 pounds per acre of lead arsenate and 16 pounds per acre of sodium arsenite reduced the vegetative development and the production of cotton. The roots were more seriously affected than the aerial parts. Sandy soils were sensitive to arsenic toxicity. The arsenic mobilization in the soil seems to depend upon factors such as, the a- cidity, the concentration of Fe2O3, CaO, P2O5 and soil colloids, both clay and humus components. The authors suggest, based on their own experiment and after a detailed study of the literature, the use of organic insecticids which may not leave toxic residues, rotation of crops, application of lime and reduction of arsenical sprays to a mini mum. Arsenic compounds should not be used in soils destined to the cultivation of food plants. Rice should not be planted in soils contaminated by arsenic compounds during several years of cotton cultivation. Future experiments are planed, using other soils such as "terra roxa", in Mitscherlich pots and in field plots.

1 - The morphology, occurrence use and genetics of functional lower flowers in spikelets of maize are discussed briefly. Normally only the upper flower in each spikelet of a maize ear develops and bears a grain but in the examples discussed the lower flower develops as well as the upper. 2 - The embryo in maize is usually turned toward the tip of the ear while that of the grain produced from the lower flower is turned toward the base. 3 - In North and Central America and most of South America ears in which grains are borne in the lower flower of the spikelets are rare. One exception is the sweet corn, "Country Gentleman", which bears grains in both flowers of most spikelets. In Brasil and Bolivia, however, ears with two grained spikelets are more common. If maize originated in South America, one would expect to find more varieties, and more primitive types near the center of origin. 4 - In Pointed Sao Paulo (Brazil) Pop Corn, Dr. BRIEGER found ears in which both flowers developed in some spikelets. In some spikelets both grains were of normal size, but more often either the lower or the upper grain was much smaller. 5 - In ears found by Dr. MARTIN CARDENAS some spikelets bear only grains from the lower flowers., a condition characteristic of the "Poaceae" and not the "Panicaceae", to which maize belogns. 6 - Many genes which influence tassel characters also influence the ears. Some of these control the formation of grains in the lower flower of the female spikelet. Most of the known genes affecting the lower spikelets are recessive, as are those in the Bolivian and Brazilian ears studied, and in "Country Gentleman". 7 - An example of paired spikelets was found in Dr. Brieger's tunicate material. In this case two complete spikelets appear where normally there would be only one. They are symetrical, and one of them thus is in a position opposite to the normal. The grains in both are borne in the upper flower. 8 - Studies on the maize spikelet are being continued. Dr. Gonçalves Drumond of the Escola Superior de Viçosa, Minas Gerais, recently found some ears of "Cateto", the common Brazilian orange flint, in which the lower flower was functional and he is studying this line. The most interesting material for further study appears to be that found by Dr. Brieger in his Pipoca Pontudo Paulista, for here there are varying degrees of development of both the upper and lower grains.

This paper deals with the preliminary results obtained with grasses and legumes tried as permanent pasture for poultry pasturage. Some informations of the species employed are given. Only a small number of species gave satisfactory results and the best ones were obtained with Bermuda grass, Cynodon dactylon Pers., (a green variety) in association with Ki-kuiú grass, Pennisetum clandestinum Chiov.. Other goods results obtained could be classified as follows: 2nd - Bermuda grass, Cynodon dactylon Pers., a green variety, named "Grama Seda". 3rd - Ki-kuiú grass, Pennisetum clandestinum Chiov.. 4th - Bahia grass, Paspalum notatum Flügge. 5th - One specie not yet classified. 6th - Bermuda grass, Cynodon dactylon Pers., a blue variety, named in this region "Grama Paulista". The giant variety of Bermuda grass did not give good results.

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In this paper an account is given of the principal facts observer in the meiosis of Euryophthalmus rufipennis Laporte which afford some evidence in favour of the view held by the present writer in earlier publications regarding the existence of two terminal kinetochores in Hem ip ter an chromosomes as well as the transverse division of the chromosomes. Spermatogonial mitosis - From the beginning of prophase until metaphase nothing worthy of special reference was observed. At anaphase, on the contrary, the behavior of the chromosomes deserves our best attention. Indeed, the chromoso- mes, as soon as they begin to move, they show both ends pronouncedly turned toward the poles to which they are connected by chromosomal fibres. So a premature and remarkable bending of the chromosomes not yet found in any other species of Hemiptera and even of Homoptera points strongly to terminally localized kinetochores. The explanation proposed by HUGHES-SCHRADER and RIS for Nautococcus and by RIS for Tamalia, whose chromosomes first become bent late in anaphase do not apply to chromosomes which initiate anaphase movement already turned toward the corresponding pole. In the other hand, the variety of positions assumed by the anaphase chromosomes of Euryophthalmus with regard to one another speaks conclusively against the idea of diffuse spindle attachments. First meiotic division - Corresponding to the beginning of the story of the primary spermatocytes cells are found with the nucleus entirelly filled with leptonema threads. Nuclei with thin and thick threads have been considered as being in the zygotente phase. At the pachytene stage the bivalents are formed by two parallel strands clearly separated by a narrow space. The preceding phases differ in nothing from the corresponding orthodox ones, pairing being undoubtedly of the parasynaptic type. Formation of tetrads - When the nuclei coming from the diffuse stage can be again understood the chromosomes reappear as thick threads formed by two filaments intimately united except for a short median segment. Becoming progressively shorter and thicker the bivalents sometimes unite their extremities forming ring-shaped figures. Generally, however, this does not happen and the bivalents give origin to more or less condensed characteristic Hemipteran tetrads, bent at the weak median region. The lateral duplicity of the tetrads is evident. At metaphase the tetrads are still bent and are connected with both poles by their ends. The ring-shaped diakinesis tetrads open themselves out before metaphase, showing in this way that were not chiasmata that held their ends together. Anaphase proceeds as expected. If we consider the median region of the tetrads as being terminalized chiasmata, then the chromosomes are provided with a single terminal kinetochore. But this it not the case. A critical analysis of the story of the bivalents before and after the diffuse stage points to the conclusion that they are continuous throughout their whole length. Thence the chromosomes are considered as having a kinetochore at each end. Orientation - There are some evidences that Hemipteran chromosomes are connected by chiasmata. If this is true, the orientation of the tetrads may be understood in the following manner: Chiasmata being hindered to scape by the terminal kinetochores accumulate at the ends of the tetrads, where condensation begins. Repulsion at the centric ends being prevented by chiasmata the tetrads orient themselves as if they were provided with a single kinetochore at each extremity, taking a position parallelly to the spindle axis. Anaphase separation - Anaphase separation is consequently due to a transverse division of the chromosomes. Telophase and secund meiotic division - At telophase the kinetochore repeli one another following the moving apart of the centosomes, the chiasmata slip toward the acentric extremities and the chromosomes rotate in order to arrange themselves parallelly to the axis of the new spindle. Separation is therefore throughout the pairing plane. Origin of the dicentricity of the chromosomes - Dicentricity of the chromosomes is ascribed to the division of the kinetochore of the chromosomes reaching the poles followed by separation and distension of the chromatids which remain fused at the acentric ends giving thus origin to terminally dicentric iso-chromosomes. Thence, the transverse division of the chromosomes, that is, a division through a plane perpendicular to the plane of pairing, actually corresponds to a longitudinal division realized in the preceding generation. Inactive and active kinetochores - Chromosomes carrying inactive kinetochore is not capable of orientation and active anaphasic movements. The heterochromosome of Diactor bilineatus in the division of the secondary spermatocytes is justly in this case, standing without fibrilar connection with the poles anywhere in the cell, while the autosomes are moving regularly. The heterochromosome of Euryophthalmus, on the contrary, having its kinetochores perfectly active ,is correctly oriented in the plane of the equator together with the autosomes and shows terminal chromosomal connection with both poles. Being attracted with equal strength by two opposite poles it cannot decide to the one way or the other remaining motionless in the equator until some secondary causes (as for instances a slight functional difference between the kinetochores) intervene to break the state of equilibrium. When Yiothing interferes to aide the heterochromosome in choosing its way it distends itself between the autosomal plates forming a fusiform bridge which sometimes finishes by being broken. Ordinarily, however, the bulky part of the heterochromosome passes to one pole. Spindle fibers and kinetic activity of chromosomal fragments - The kinetochore is considered as the unique part of the chromosome capable of being influenced by other kinetochore or by the poles. Under such influence the kinetochore would be stimulated or activited and would elaborate a sort of impulse which would run toward the ends. In this respect the chromosome may be compared to a neüròn, the cell being represented by the kinetochore and the axon by the body of the chromosome. Due to the action of the kinetochore the entire chromosome becomes also activated for performing its kinetic function. Nothing is known at present about the nature of this activation. We can however assume that some active chemical substance like those produced by the neuron and transferred to the effector passes from the kinetochore to the body of the chromosome runing down to the ends. And, like an axon which continues to transmit an impulse after the stimulating agent has suspended its action, so may the chromosome show some residual kinetic activity even after having lost its kinetochore. This is another explanation for the kinetic behavior of acentric chromosomal fragmehs. In the orthodox monocentric chromosomes the kinetic activity is greater at the kinetochore, that is, at the place of origin of the active substance than at any other place. In chromosomes provided with a kinetochore at each end the entire body may become active enough to produce chromosomal fibers. This is probably due to a more or less uniform distribution and concentration of the active substance coming simultaneously from both extremities of the chromosome.

Spermatogonial chromosomes of Pachylis laticornis and Pachylis pharaonis begin anaphasic movement with both ends turned toward the same pole, maintaining this form util they reach the poles. This is a proof that they are provided with one kinetochore at each end. Additional proof for a longitudinal division of each longitudinal half of the anaphase chromosomes of the primary sper- matocytes is presented against the idea of a previous end-toend pairing at metaphase. The longitudinal split of the chromosomes of the secondary spermatocytes which used to be considered as tertiary split is therefore a true secondary split. The heterochromosome in both species passes undivided to one pole in the first division of the spermatocyte. In Pachylis laticornis it appears connected with the poles by means of two fibrils detached from each extremity, what may be considered as indicating a rather premature longitudinal spliting. The behavior of the heterochromosome of Pachylis pharaonis is highly interesting and affords one of the most beautiful evidences in favour of the dicentricity of the chromosomes. Really, in metaphase the heterochromosome appears at the equator of the cell with a more or less round shape. In the beginning of anaphase it becomes fusiform. As anaphase proceeds it distends itself between the autosomal plates forming a long fusiform bridge or sends toward the plates a thick chromosomal thread. The bulky part of the heterochromosome as it passes to one side it reincorporates the substance of the thread in this side. The thread in the other side, which becomes generally thiner, is left with its kinetochore in the cell at this side. The heterochromosome therefore becomes terminally monocentric in the first division of the spermatocyte. Some figures, however, suggest that the heterochromossome from time to time may pass with both kinetochores to one of the cells, as ordinarily happens in the case of Pachylis laticornis. Summing up, other things apart the behavior of the heterochromosome in both species studied here puts out of doubt the question of the existence of two terminally located kinetochores.

The male of Eneoptera surinamensis (Orthoptera-Eneopteridae) is provided with 9 chromosomes, that is, with 3 pairs of autosomes and 3 sex chromosomes. Spermatogonia. - The autosomes of the spermatogonia are of the same size and U-shaped. One of the sex chromosomes approximately equalling the autosomes in size is telocentric, while the other two are much larger and V-shaped. One of the latter is smaller than the other. The sex chromosomes as showed in Figs. 1 and 2 are designated by X, Yl and Y2, X being the larger V, Yl the smaller one and Y2 the rod-shaped. Primary spermatocytes. - Before the growth period of the spermatocytes all the three sex chromosomes are visible in a state of strong heteropycnosis. X is remarkable in this stage in having two long arms well separated by a wide commissural segment. (Figs. 4, 5 and 6). During the growth period Y2 disappears, while X and Yl remain in a condensed form until metaphase. These may be separated from one another or united in the most varied and irregular manner. (Fig. 7 to 12). In the latter case the segments in contact seem to be always different so that we cannot recognize any homology of parts in the sense os genetics. At diplotene Y2 reappears together with the autosomal tetrads. X and Yl may again be seen as separate or united elements. (Figs. 13 and 14). At later diakinesis and metaphase the three sex chromosomes are always independent from each other, Y2 being typically rod-shaped, X and Yl V-shaped, X being a little larger than Yl. (Fig. 15 to 18). At metaphase the three condensed tetrads go to the equatorial plane, while the sex chromosomes occupy any position at both sides of this plane. In almost all figures which could be perfectly analysed X appeared at one side of the autosomal plate an Yl together with Y2 far apart at the other side. (Figs. 16 and 18). Only a few exception have been found. (Figs. 17 and 19). At anaphase X goes in precession to one pole, Yl and Y2 to the other (Figs. 20 and 21). As it is suggested by the few figures in which a localization of the sex chromosomes different from the normal has been observed, the possibility of other types of segregation of these elements cannot be entirely precluded. But, if this does happen, the resulting gametes should be inviable or give inviable zygotes. Early in anaphase autosomes and sex chromosomes divide longitudinally, being maintained united only by the kinetochore. (Figs. 20 and 21). At metaphase the three sex chromosomes seem to show no special repulsion against each other, X being found in the proximity of Yl or Y2 indifferently. At anaphase, however, the evidences in hand point to a stronger repulsion between X on the one side and both Ys on the other, so that in spite of the mutual repulsion of the latter they finish by going to the same pole. Secondary spermatocytes. - At telophase of the primary spermatocytes all the chromosomes enter into distension without disappearing of view. A nuclear membrane is formed around the chromosomes. All the chromosomes excepting Y2 which has two arms, are four-branched. (Fig. 22). Soon the chromosomes enter again into contraction giving rise to the secondary metaphase plate. Secondary spermatocytes provided as expected with four and five chromosomes are abundantly found. (Figs. 23 and 24). In the former all chromosomes are X-shaped while in the latter there is one which is V-shaped. This is the rod- shaped Y2. In the anaphase of the spermatocytes with four chromosomes all the chromosomes are V-shaped, one of them (X) being much larger than the others. In those with five there is one rod-shaped chromosome (Y2). (Fig. 25), Spermatids. Two classes of spermatids are produced, one with X and other with Yl and Y2. All the autosomes as well as Y2 soon enter into solution, X remaining visible for long time in one class and Yl in the other. (Figs. 26 and 27). Since both are very alike at this stage, one cannot distinguish the two classes of spermatids. Somatic chromosomes in the famale. - In the follicular cells of the ovary 8 chromosomes were found, two of which are much larger than the rest. (Figs. 29 and 30). These are considered as being sex chromosomes. CONCLUSION: Eneoptera surinamensis has a new type of sex-determining mechanism, the male being X Yl Y2 and the female XX. The sex chromosomes segregate without entering into contact at metaphase or forming group. After a review of the other known cases of complex sex chromosome mechanism the author held that Eneoptera is the unique representative of a true determinate segregation of sex chromosomes. Y2 behaving as sex chromosome and as autosome is considered as representing an intermediary state of the evolution of the sex chromosomes.