of reproduction. In VS, 216-7 (O-S)"''^-"' gives -7101, -5681, 

 •4445, -3556, -2845, -2276, -1821, -1457, -1165, -0929, whereof 

 some terms are found in the Table. 



In BR we have a symmetrical function on each side of 

 40-(42i); and the formula 1-50 sin (2^-35)1°, 80 gives for 

 18°, 36°; 54°, 72° the terms -4635, -8817, 12135, 1-4266, 

 1-5000: at 19— the argument 7° 12' yields 0-1880. With 

 respect to VR, the formula 3-4032(-78)''''*'-^' + -046(^-47-5) 

 —the latter for ages below 47i— yields 2-2532, 1-7345, 1-3805, 

 1-1550, 1-0298, 1-0127, -7899, -6161, -4806, -3748, -2924, &c. 



In BS, Table VII., three-eighths marry as Bjo S20 ; S19-29 and 

 B20-29 comprise half of this marrying group. In BS, Table VIII. 

 shows that up to 25, a spinster has the greatest chance of mar- 

 rying Boo- ; the maximum then proceeds diagonally, or in other 

 words, the equality of age preponderates. 



In VS, most spinsters take widowers who are their equals or 

 seniors by 5 years. 



In BR, widows older than 29, generally take bachelors younger 

 than themselves. 



In VR, the equality of age predominates. 



In Table IX., BS ; B18-29 mostly prefer S20-24; and the dif- 

 ference in age augments up to B^o, occasionally amounting to 

 20 years. The class VS exhibits the same increasing preference 

 for a younger S the older V is : but BR shows that B prefer R 

 of their own age, and VR that R is from 5 to 10 years younger 

 than V. 



These Tables offer many indications of geometrical progression, 

 which might be the case if these numbers resulted from data ex- 

 tending over many years. The constants of the formula must 

 certainly vary for different countries, from climatic and ethnolo- 

 gical causes ; and a country where very early marriages are in 

 vogue, and one where prudence defers most unions till the age 

 of 30, would exhibit marked contrasts. However, what has 

 been stated will probably suffice for showing the utility of these 

 deductions. 



S. M. Drach. 



Chelsea, Feb. Oct. 1858. 



P.S. I have added the quinquiseval sum b + b'^ + P + b'* + b^ ; 

 b^ ; the ratio of these numbers ; and the year corresponding to 

 the mean ; for every 0-1 value of the ratio b^. Thus if the quinqui- 

 seval ratio be '500, the average for z— corresponds to rr-f- 2-8603 

 years, its value for 2-5 years is -7071068-^-6726574 = 1-051214 

 of the average; reductions which ought to be regarded when 

 the ratios vary. Thus in Table III. 2S-^2Vj -081 7 corresponds 

 to 57-8603 years, -0412 to 62-8603 years, &c. ; and the values 

 for 57-5, 62-5 are 0859 and -0433. Corr. For N read D. 



