70 ESSAY ON PROBABILITIES. 



Since it is very seldom necessary to use more than five 

 places of the table marked t, the sixth and seventh places, 

 and those which arise from them in the differences, are 

 separated from the rest by a blank space. The sixth 

 and seventh places are allowed to remain, on account of 

 the use which will hereafter be made of the differences 

 derived from them. 



In Table II. we find to five places only a column 

 marked K, and another marked A, containing the dif- 

 ferences of the former column. This is a modification 

 of the former table, the reason of which will hereafter 

 appear. In the meanwhile, however, observe that we 

 can directly find the value of H and K by these tables 

 only, when t is *QO or -01, &c. ; that is, when t is a 

 given decimal of two places. But supposing it required 

 to find H when t lies between two of the values in the 

 table; suppose, for instance, we ask what is H when 

 t = -47694 ? The method is as follows : 



QUESTION. What is the value of H (Table I.) 

 when t = '47694'., correct to five places of decimals ? 



RULE. 



Take out of Table I. the 

 value of H answering to the 

 two first decimal places and 

 the whole number preceding 

 them, if there be one. Retain 

 only five places of decimals. 



Take the figures of the first 

 difference (as far as the blank 

 space), and multiply them by 

 the remaining figures in the 

 value of t, and cut away as 

 many places from the result as 

 there were remaining figures. 



Add the figures in the last 

 result to the right hand of the 

 first, and the sum is the an- 

 swer required. 



;MrLIFJCATIOX. 



Opposite to *47 we find 

 49375 * 



Three figures remaining, 594. 



900x694 = 624600. 

 Cut away three figures, 

 625.* 



49375' 

 $& 



50000 

 When t= -47694, H= -50000. 



* Whenever decimal figures are rejected, if the first rejected be five or 

 upwards, the last retained is increased by a unit 



