288 
Dr. Young's formula for expressing 
internal evidence of greater apparent correctness than either 
of the other bases, exhibiting a curve less irregular in its 
flexures, and generally intermediate between the others : it 
has also the advantage of exhibiting the duration of life as 
prolonged by the general introduction of vaccination : and 
when thus incorporated with the registers of two places in 
the country, each reduced to an equal supposed population, 
it must probably be sufficiently corrected for the errors that 
may be attributed to the effect of an afflux of settlers at an 
early age. The mean obtained in this manner might be em- 
ployed at once as a standard table without much inconvenience, 
but it still exhibits some minute but obvious irregularities, as 
an inspection of the line of stars in the diagram will show, 
principally perhaps from the want of skill or care with which 
the interpolations have been made by Dr. Price and others. 
The most effectual of all interpolations for harmonizing the 
various orders of differences, is to obtain a formula which 
shall extend with sufficient accuracy throughout the whole 
curve. It may be easily believed that it must be extremely 
difficult to find such an expression ; and that its form must 
be too complicated to be applied to any practical purpose 
throughout its extent. I have however drawn a curve which 
comes extremely near to the line of stars, and crosses it in 
10 or 12 different points, by means of the equation y = 368 
+ 10 x — 11 . (156 + 20 X x xY + 1 Tx~\ 6 
285 + a.o5** + z|~ j 
-5 • 5 (fo)'° + (£)”— 5500 (wf : y bein s the num - 
ber of deaths among 100000 persons, in the year that com- 
pletes the age x. 
