A Letter to William Morgan, Esq. F.R.S. 339 



ting from <r = — — - to <r = + ~ 9 the time of an oscillation is 

 given by either of the following series : — 



cos* 



4 



or, 



LIX. A Letter to William Morgan, Esq. F.R.S. on the Ex- 

 perience of the Equitable Society. By A Correspondent. 



Dear Sir, 

 TJ AVING unfortunately failed, on some former occasions, of 

 "■"■ fully comprehending the meaning of your expressions, I 

 earnestly intreat your attention to a few remarks on your late 

 statement of the Experience of the Equitable Society, in order 

 that you may correct, if possible, the exaggerated conclu- 

 sions which appear to me to be fairly deducible from the num- 

 bers that you have published ; for I have no doubt that you 

 will unite with me in sincerely deprecating the dangerous con- 

 sequences, that would result from the hasty adoption of these 

 conclusions in the practice of life assurance, although they 

 may still be very useful as cautions deserving the attention of 

 the granters of annuities. 



Your table, lately published, stands thus : 



That is, 



[View of the Rise and Progress of the Equitable Society, 

 8vo 1828. p. 42.] 



1 . I have first to observe, that the numbers of the column 

 marked with an asterisc, which vary from 188 to 92, ought 

 all, according to Halley's earliest hypothesis, to be 1 00 ; and 

 according to Demoivre's correction of that hypothesis, to be 



2X2 86 only. 



