226 



DANIEL BERNOULLI. 



Put q for - ; thus, da = — ^ dx ; 



^ s nin 



therefore 

 therefore 



and 



n log {mq — l)—x-\- constant ; 



^m^ 



s 



-1 =e^^^. 



m^ 



e " + 1 



To determine the constant C, we observe that when x 

 we have s = f ; thus, finally, 



= 0, 



s = 



m^ 



(m - 1) ^' + 1 



403. By this formula Daniel Bernoulli calculates a table on 

 the basis of Halley's table, derived from the Breslau Observations, 

 assuming that m and n each equal 8 ; Halley's table gives the 

 values of f corresponding to successive integer values of x, and 

 Daniel Bernoulli's formula then gives the values of s. The fol- 

 lowing is an extract from the table : 



