TKEMBLEY. 4:2 O 



Now there is nothing to hinder us from supposing the intervals 

 of time to be much shorter than a year ; thus n may be a large 

 number, and then 



(1 j = e'' nearly. 



The result thus agrees with that given by Daniel Bernoulli, see 

 Art. 402 : for the intervals in his theory may be much shorter than 

 a year. 



786. Hitherto we have used Daniel Bernoulli's hypotheses ; 

 Trembley however proceeds to a more general hypothesis. He 

 supposes that m and 7i are not constant, but vary from year to 

 year ; so that we may take m^ and oi^ to denote their values for the 

 x^^ year. There is no difficulty in working this hypothesis by 

 Trembley's method ; the results are of course more complicated 

 than those obtained on Daniel Bernoulli's simpler hypotheses. 



787. Trembley then compares the results he obtains on his 

 general hypothesis with a table which had been furnished by ob- 

 servations at Berlin during the years 1758 — 1774. The comparison 

 is effected by a rude process of approximation. The conclusions he 

 arrives at are that 7i is very nearly constant for all ages, its value 

 being somewhat less than 6 ; but m varies considerably, for it be- 

 gins by being equal to 6, and mounts up to 120 at the eleventh 

 year of age, then diminishes to 60 at the nineteenth year of 

 age, and mounts up again to 133 at the twenty-fifth year of age, 

 and then diminishes. 



Trembley also compares the results he obtains on his general 

 hypothesis with another table which had been furnished by obser- 

 vations at the Hague. It must be confessed that the values of m 

 and n deduced from this set of observations differ very much from 

 those deduced from the former set, especially the values of m. 

 The observations at Berlin were nearly five times as numerous as 

 those at the Hague, so that they deserved more confidence. 



788. In the volume for 1804 of the Memoires de VAcad..., 

 Berlin, which was published in 1807, there is a note by Trem- 

 bley himself on the memoir which we have just examined. 

 This note is entitled Eclaircissement relatif au Memoire sur la 



