expressed by a New Formula. 



19 



Table IV. — Values of the finite differences A log A log P, ac- 

 cording to the New Formula, shown to be equal very nearly 

 to the reciprocals of the distances of the middle points from 

 the ideal zeros of life, even when the unit interval of age is so 

 large as 6 years in the period of Manhood. 



Interval 

 of age, 

 in units 



of 9 

 months 



or 6 

 yrs. from 

 zeros of 



life. 



AlogP 

 (in man- 

 hood). 



Log A log P. 



AlogAlogP. 



Reciprocal of 



last number, 



or 



1 



Distance 



from 



limits, 



in units 



of 9 

 months 



or 6 

 years. 



Age from birth. 



In child- 

 hood. 



In man- 

 hood. 



A log A log P 



15-14 



14-13 



13-12 



12-11 



11-10 



10- 9 



9- 8 



8- 7 



7- 6 



6- 5 



5- 4 



4- 3 



3- 2 



2- 1 



•0155187 

 •0182984 

 •0218526 

 •0264876 

 •0326755 

 •0411704 

 •0532338 

 •0711047 

 •0990406 

 •1459381 

 •2328676 

 •4196970 

 •9344010 

 3-3401550 



2-1908553 

 •2624131 

 •3395031 

 •4230426 

 •5142223 

 •6145851 

 •7261875 

 •8518983 

 •9958132 



1-1641687 

 •3671091 

 •6229359 

 •9705333 



o-5237666 



•0715578 

 •0770900 

 •0835395 

 •0911797 

 •1003628 

 •1116024 

 •1257108 

 •1439149 

 •1683555 

 •2029404 

 •2558268 

 •3475974 

 •5532333 



13-975 



12-972 



11-970 



10-967 



9-964 



8-960 



7-955 



6-948 



5-940 



4-927 



3-909 



2-877 



1-807 



14 



13 



12 



11 



10 



9 



8 



7 



6 



5 



4 



3 



2 



Years. 



8-25 

 7-50 

 6-75 

 600 

 5-25 

 4-50 

 3-75 

 3 00 

 2-25 

 1-50 

 •75 

 •00 

 -•75 



Years. 



18 

 24 

 30 

 36 

 42 

 48 

 54 

 60 

 66 

 72 

 78 

 84 

 90 



Table V. — Showing, for any quinquennial interval of age above 

 15 and less than 80 years, that there is no difference, appre- 

 ciable by observation, between the three quantities following, — 

 viz. the quinquennial ratio of the dying to the living, the hy- 

 perbolic logarithm of the quinquennial rate of decrement at the 

 middle of the interval, and the difference A log e P between the 

 hyperbolic logarithms of the numbers living at the beginning 

 and at the end of such interval. 



Interval of 

 age. 



One-fifth part 

 of quinquen- 

 nial ratio of 

 dying to 

 living. 



One-fifth part 

 of quinquen- 

 nia] rate of 

 decrement at 

 middle of 

 interval. 



One-fifth part of A log P. 



In hyp logs. 



In com logs. 



Years. 



15-20 

 20-25 

 25-30 

 30-35 

 35-40 

 40-45 

 45-50 

 50-55 

 55-60 

 60-65 

 65-70 

 70-75 

 75-80 

 80-85 



•00685 

 •00787 

 •00912 

 •01067 

 •01265 

 •01519 

 •01852 

 •02302 

 •02926 

 •03824 

 •05174 

 07321 

 •10993 

 •17882 



•00684 

 •00786 

 00911 

 •01067 

 •01264 

 •01517 

 •01850 

 •02300 

 •02924 

 •03823 

 •05178 

 •07344 

 •11091 

 •18333 



•00685 

 •00787 

 •00912 

 •01068 

 •01266 

 •01520 

 •01855 

 •02307 

 •02935 

 •03841 

 •05210 

 •07407 

 •11228 

 •18684 



•00297 

 •00342 

 •00396 

 •00464 

 •00550 

 •00660 

 •00806 

 •01002 

 •01275 

 •01668 

 •02263 

 •03217 

 •0-1876 

 •08115 



Note. — In the complete theoretical Table for annual inter- 



C2 



