For over 150 years the statisticians and demographers have been interested in the incidence of twinning and other multiple maternities. The twinning research has grown alongside the increased quality of the registration of demographic data, especially birth and death data. Among the first scientists with special interest in the twinning one can observe Spengler (1848; Germany), Wappäus (1855; Germany), Veit (1855; Germany), Berg (1880; Sweden), and Drejer (1895; Norway). Of special interest for us were Strassmann (1889), Hellin (1895), Geissler (1889a b, 1896), Weinberg (1902) and Lommatzsch (1902, 1907), Zeleny, (1921). Strassmann and Hellin considered the relation between the rates of twins, triplets, quadruplets etc. In short, the proportions were considered to be , where p is the rate if twin maternities. This empirical observation, named as Hellin´s law, has later been an object of intensive studies. It has been an object of both support and criticism. Weinberg formulated his differential rule that the rate of dizygotic twinning is twice the rate of twin maternities with opposite sexes. The monozygotic twinning rate is the difference between the rates of same-sexed and of opposite-sexed twin sets. His rule is very simple but it is central when national twin registers are analysed. Weinberg´s differential rule has been a target for continuing studies. Geissler and Lommatzsch studied sibships ending with twin maternities. Although our main interest has been the incidence of twin maternities we have also been interested in general studies of the temporal and regional variation in both births and deaths. Before this project started January 1st 2008, we have several papers associated with the problems in this project (Eriksson & Fellman, 2004: Fellman & Eriksson, 2000, 2002, 2003, 2004, 2005, 2006a, 2006b, 2007). A central problem in research on twins is the estimation of the rates of monozygotic and dizygotic twin maternities. The estimation usually follows Weinberg´s differential rule. Although Weinberg´s rule has been the target for continuing discussions, the reliability of these assumptions has never been conclusively verified or rejected. In this study we analyse the accuracy of Weinberg´s rule by considering alternative attempts. Especially, we built a general likelihood function and showed that the maximum likelihood estimates differ only slightly from the rates obtained by Weinberg´s rule. In conclusion, our findings indicate that Weinberg´s differential rule is rather robust and, that in spite of its simplicity, it gives reliable results, when official birth registers are analysed. It is a common opinion that the stillbirth rate is higher among monozygotic (MZ) than among dizygotic (DZ) twins. We presented a method to estimate the stillbirth rates for MZ and DZ twins and identify the difference. We assumed that (a) Weinberg´s differential rule, including the assumption that the sex ratio is 100, (b) the stillbirth rates among opposite-sexed twins hold for all DZ twins and (c) the stillbirth rates estimated for MZ and DZ male and female twins yield for both sexes the observed total number of stillborn twins. Our methods are applied to data from Sweden, the Åland Islands, Saxony, and England and Wales. We observed that the ratio between the estimated stillbirth rates among MZ and DZ twins were on average 1.75, and the ratio among same-sexed and DZ (opposite-sexed) twins were on average 1.31. For Sweden and Saxony similar values were obtained, but for England and Wales the values were higher and for Åland lower. With exception of Åland, the estimated stillbirth rates were in all populations the lowest for DZ, medium for same-sexed and highest for MZ twins. We have considered data from the Åland Islands, 1650-1950. During the period 1650-1793 there were sub-periods with missing data for all parishes and the total data for the whole Åland for this period had to be estimated. The war-year 1809 shows a marked deficit of births. During the last decades of the 19th century the numbers of births increase markedly and after that show a strong decrease. After the 1930s births increased again. There is a markedly decreasing temporal trend in the seasonal variation of births for Åland as a whole but the general pattern remains mainly the same, having two peaks, one in March-April and one in September-October. For the period 1901-1950 the seasonal variation almost disappeared. The strength of the seasonal variation in the births shows regional differences but the general pattern is mainly the same. The outermost parish Kökar shows the strongest seasonal variation in births. The annual numbers of deaths show some marked peaks, especially in the war-year 1809. For both sexes there are marked peaks in this year indicating that the deaths were mainly caused by epidemic diseases. For mortality, a decreasing trend in the seasonal variation is observed during 1650-1750, but after 1751-1800 the strength in the seasonality shows an increasing trend and a sinusoidal pattern. In national birth registers, the secondary sex ratio, that is, the number of boys per 100 girls at birth is almost constant, at 106. An effective means of identifying discrepancies in the sex ratios is to investigate birth data compiled into sibships of different sizes. Over a century ago, the German scientists Geissler (1896) and Lommatzsch, 1907) considered sibships ending with twin sets. Their hypothesis was that in sibships ending with male-male twin pairs the sex ratio among previous births is higher than normal, while in sibships with female-female twin pairs the sex ratio is lower than normal. If the sibship ended with a male-female pair, then the sex ratio is almost normal. Consequently, a same-sex twin set indicated, in general, deviations in the sex ratio among the sibs within the sibship. Our analyses of their data yielded statistically significant results that support their statements. A relationship has been proposed to exist between individual outcomes (live or stillbirths) of twins in the same set. We analyzed this association between live births and stillbirths among individuals in different twin pairs. When national birth registers are analyzed, individuals in opposite-sexed twin sets can be identified and the correlation between individual outcomes estimated. However, full information about the individuals in same-sexed twin sets is not, as a rule, available, and consequently, only upper and lower limits of the correlation coefficients were obtained. The methods introduced were applied to data from Sweden, the Åland Islands, the Kingdom of Saxony, and England and Wales. Comparisons between the correlation coefficients among opposite-sexed twins and the lower bound of correlation coefficients among same-sexed twins indicated that in all populations studied a stronger association existed between twins in same-sexed than opposite-sexed twin pairs. For opposite-sexed twin sets, no general association between the correlation coefficient and the stillbirth rate was identified. In research on twinning and higher multiple maternities, Hellin´s law has played a central role because it is approximately correct, despite showing discrepancies that are difficult to explain or eliminate. It is named after Hellin, although he was not the first discoverer. We re-examined some old papers to provide an overview of the scientists who have contributed to the genesis and the improvements of this law. In addition, we considered more recent contributions in which Hellin´s law has been discussed and evaluated and we have mathematically proved that Hellin´s law does not hold as a general rule. References Berg, F. T. 1880. Om flerfostriga barnsbörder. Hygiea (Stockholm) 42, 331-342. Drejer, P. (1895). Om tvillinger (About twins). Tillægshefte til “Norsk Magazin for lægevidenskaben”. Februar 1895. Kristiania. 180pp. Geissler, A. (1889a). Beiträge zur Frage des Geschlechtverhältnisses der Geborenen. Zeitschrift des Königlichen Sächsischen Statistischen Bureaus, 35:1-24. Geissler, A. (1889b). Nachtrag zu dem Artikel „Das Geschlechtverhältniss bei der Kindern gleichen Stammes“ Zeitschrift des Königlichen Sächsischen Statistischen Bureaus, 35:56. Geissler, A. (1896). Zur Kenntnis der Geschlechtsverhältnisse bei Mehrlingsgeburten. Allgemeines Statistisches Archiv, III:537-544. Hellin, D. (1895). 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(1855). Beiträge zur Geburtshülflichen Statistik. Monatsschrift für Geburtskunde und Frauenkrankheiten. Bd 6 Heft 2:101-132. Wappäus, J. E. (1859) Algemeine Bevölkerungsstatistik. Vorlesungen (General population statistics. Lectures) Leipzig 1859, 581 pp. Zeleny, C. (1921). The relative numbers of twins and triplets. Science, 53:262-263.