160 ESSAY ON PROBABILITIES. 



w, and divide the product by E. Call the quotient t ; 

 then the value of H (Table I.) is the probability re- 

 quired. 



EXAMPLE. In 600 drawings, each of which may 

 be any thing between and 100., required the proba- 

 bility that the average of all the drawings shall lie 

 between 50 + 5 and 50 5. 



n 600, E = 100, k = 5 ; the square root of 6 times 

 600 is 60, and 5 times 60 divided by 100 is 3. The 

 first table does not contain values of t higher than 2 : 

 an event being almost certain, or of a very high pro- 

 bability when t is equal to 2. Table II., however, 

 furnishes us with an extension of Table I. ; the K oppo- 

 site to any value of t in that table. being always nearly 

 the H which belongs to half that value of t. Conse- 

 quently, the H belonging to t = 3, is the K belonging 

 to t = 6. But the second table only goes to t = 5 ; 

 in which case K is *999- It is then more than 999 to 

 1 that the average of the 600 drawings is within the 

 limits specified. If we take k = 1, in which case 

 t = '6, we find it is 3 to 2 that the average is con- 

 tained between 49 and 51. 



If then there were 600 infants born, and if it were 

 the law of human life that any individual is as likely to 

 die at one age as another, for any age not exceeding 100 

 years, even then, and with so much more scope for 

 fluctuation than is actually found, it would be more than 

 999 to 1 against the average life of the 600 infants 

 exceeding 55, or falling short of 45 years,; and more 

 than 3 to 2 that the same average should fall between 

 49 and 51 years. If such be the case, it is obvious that 

 the chances of fluctuation are much diminished by the 

 superior chances of death happening at some periods of 

 life rather than at others ; as well as by the smaller limits 

 of human life, which need not for any practical purpose 

 be supposed to extend as far as one hundred years. 



To suppose that the duration of human life is regu- 

 lated by no laws, would be to make an assumption of a 

 most monstrous character, a priori, and most evidently 



