1''. Mr. K Exfi unite of the Degree of Legitimate [Jan. 18, 



diagonals trisect one another (orthoidal). The angles of an orthoidal 

 hexagon, other than equilateral, are not 120. The angles of the left- 

 hand hexagon fig. 1 ( 7) are 120, and its paracentric diagonals 

 do not trisect one another, as the diagram clearly shows. 



II. -An Estimate of the Degree of Legitimate Natality, as 

 shown in the Table of Natality compiled by the Author 

 from Observations made at Budapest." By JOSEPH 

 KoROsi, Member of the Hungarian Academy of Sciences, 

 Director of Municipal Statistics. Communicated by Sir 

 JAMES PAGET, F.R.S. Received December 28, 1893. 



(Abstract.) 



Both branches of the science of demography natality statistics as 

 well as mortality statistics originated on British soil. It was in 

 1665 that the Royal Society published the first work on these matters 

 (Graunt's "Observations"), whilst in 1693 Halley, by establishing 

 the first life table, laid the foundation of the scientific treatment 

 of mortality statistics. These tables of mortality showed for the 

 first time how to measure the probability of death for each year of 

 human age. The other branch of vital statistics is still in want of a 

 corresponding table of natality, showing the probability of birth for 

 each of the age-combinations of the parents. The table of natality is 

 not of so great scientific importance as the life table, as the probability 

 of death depends on natural laws, whilst the fertility, at least par- 

 tially, is influenced by voluntary causes also. But as the problems of 

 over-population or de-population are an effect of both forces, it is 

 worth while to study the law of these facts also. 



To reach this aim, I have tabulated the age of the 71,800 married 

 couples given in the Census of 1891, conforming to the single year- 

 combinations. The virtual number of these combinations as 45 pro- 

 ductive years of the male have to be combined with each of the 

 40 productive years of the female is about 2000. Knowing thus the 

 number of all age-combinations, I observed for four years (two before 

 and two after the Census) the 46,931 births amongst couples of 

 those ages ; I got thus, dividing the figures obtained by four, the 

 yearly probability of birth for each age-combination. 



As the legitimate natality is to be regarded as a resultant between 

 two distinct forces, the instinct of nature which urges towards multi- 

 plication and the forethought which causes moral restraint, it was 

 also desirable to get an insight into the march of the physiological 

 fertility alone. For this purpose I had to look out for couples in 

 whom the moral restraint is weakest or entirely absent. These con- 



