expressed by a New Formula. 11 



more rapid disppearance of the members of the classes suffering 

 the higher mortality. At the later ages of life, say for ages 

 above 65 years, the city population will nearly all have disap- 

 peared, and the national Table will be a representation of the 

 mortality of a population consisting, for the greater part, of 

 villagers. The mortality in advanced life will always be less 

 than that indicated by the true law derived from observations 

 on middle life. The apparent law is derived from the true law 

 subjected to continual changes through the increase, as age ad- 

 vances, of the proportion of lives of a superior class. At the 

 later ages of life an empirical law of mortality, such as is here- 

 after mentioned, may represent the apparent facts better than 

 they can be represented by the true law of mortality applicable 

 to classes formed of individuals equal in vital force at all ages 

 passed through. 



In Table I. hereunto annexed, is given the Life Table No. 3 

 for the male population of England, which was published in the 

 year 1864 by authority of the Registrar-General. This Table 

 has been offered and may be accepted as a correct representation 

 of the decrement of life, at all ages, observed during the 17 

 years 1838-54. The name of the constructor, Dr. William 

 Farr, is a sufficient guarantee for fidelity and correctness in con- 

 verting or transmuting the irregular numbers given by observa- 

 tion into their just equivalents expressed by the equable flow oi 

 a well-adjusted life Table. In this Table (I.) is expressed the 

 number living or surviving at different ages in relation to 1000 

 living at the age 12 years adopted as a basis. In adult life the 

 numbers living have been extracted from the original Table for 

 every fifth year of age. From the age of 1 year to 12 years the 

 intervals are annual. At ages under 1 year, the numbers living 

 have been extracted for the ages 0, one month, two months, 

 three months, and six months, — these comprising all the numbers 

 which have been obtained by direct observation. 



In Table I. a column has been added in which is contained a 

 life Table deduced from the new formula, and intended for com- 

 parison with the new English Life Table for males in the adjoin- 

 ing column. On inspection it will be seen that for all ages above 

 one month and less than 12 years, the new formula yields 

 results which are all but identical with the results of observation 

 as indicated by Dr. Farr. In devising and constructing theo- 

 retical Tables of mortality, the greatest difficulty has generally 

 been acknowledged to consist in finding any general law which 

 could satisfactorily represent the very rapidly changing mortality 

 iu early infancy. That such a law representing the facts in 

 early infancy should be contained in the new formula, is the 

 strongest attainable confirmation of the truth and applicability of 



