344 Practical Comparison of 



7. But something much more simple than this is required for 

 practical purposes ; that is, if we attempt to apply a formula to the 

 detail of our computations ; and we may exhibit the basis of such 

 a formula to the eye by drawing a straight line from the Age to 

 the highest point of the Carlisle curve, and continuing it to the age 

 85 or 90 ; and it will be obvious, from inspection, that a triangle 

 like this approaches much nearer, between 10 and 80, to the cha- 

 racter of all the rapidly ascending lines of Carlisle, Finlaison, and 

 Deparcieux, than either Demoivre's horizontal line, or the slightly 

 irregular curve of Northampton ; and, from the employment of the 

 area of the triangle, the law derived from it may be called the 

 quadratic hypothesis. 



8. In other words, we find that many of the modern tables appear 

 to indicate, instead of a uniform decrement of life throughout the 

 full period of vitality, a decrement nearly proportional to the age 

 itself, and the quadratic hypothesis carries to its greatest possible 

 extent the exaggeration of the climacteric age, as I have before 

 denominated the age of the greatest mortality, which seems to have 

 been actually creeping upwards for the last century, though less 

 rapidly than has sometimes been supposed. Deparcieux made it 

 73, the Carlisle table 74, Mr. Finlaison 78, and Mr. Babbage's 

 reduction of the alleged mortality of the Equitable Office 82, though 

 my late computation upon the exponential hypothesis, derived from a 

 corrected report, makes it only about 75. Now, the triangle of the 

 quadratic hypothesis rises highest at its termination, and makes the 

 supposed climacteric the year of unavoidable death to those who 

 attain it. This is a peculiarity not very credible as a correct state- 

 ment of a matter of fact, though it requires little or no correction 

 when applied to the generality of results like those of the Carlisle 

 tables ; and, in other cases, its imperfections may probably be 

 remedied without difficulty. On the other hand, the true climacteric 

 of nature, as well as that of the geometrical hypothesis, is the year 

 of birth, while in the arithmetical hypothesis there is no climacteric 

 at any age. The mortahty of London in 1815, and the Northamp- 

 ton table, approach to the arithmetical hypothesis as having no 

 strongly marked climacteric after the year of birth, though they have 



