210 O^ TH^' t>OCTUI\r.S OF CIIAXCE. 



a c 



will be greater tnan —7-7— ;, viz. the pro!)abiIity of the 

 ^ a c \-h (i ' -^ 



truth of a circumstance is greater if related by oj)c j'cr.son only, 

 tlian if related by two, when the second is in tlu; habit 01 relat- 

 ing a greater number of falsehoods than truths. 

 Cor. 7. Cor. 7. Lastly, if the relations be supposed to be inifohl, or, 



in other words, if it be supposed that .A and B are each about 

 to relate d circumstance, the probability tliat they will both" 



n c a c 



speak truth will be expressed r=nrz — ■ - — r r;- — r-r-,; 



(lA-b X c-\-d ac-{-a(l+(!C-\-Od 



a 

 for the probability of A's speakin^ truth would be — —,-, of 

 1 J 1 o «4-6' 



Xil. 



Farther licmarhs on the Doctrines of Change. Btj Opsimatit, 

 To Mr. NICHOLSON. 

 Sir, Odoher 7ih, 1808.- 



Not convinced -IL Beg to thank your correspondent iMr. B. IL for his i 



"C- 



ance* 



byacor:e»poa- ^^ on my letter respecting the Doctrines of Ch 

 dent s argu- •' 10 



nientsj obligingly inserted in your Philosophical Jour/uil for Sep- 



tember, although not productive of conviction on my.judg- 

 ment : — they strictly conform witli the systems of de Moivre 

 •cind 'rhomas Simpson, whose publications are the only works 

 on this subject, which 1 have seen. But as I fear not to have 

 made the path ol' reasoning, which leads to my deduction, a&- 

 plain as it admits J shall attempt to ^\o so iworc eii'ectually now, 

 provided rny humble essay docs not intrude on pages dedicatecJ 

 to the promulgation of so much more valuable information. 

 aa,l why. The variation of result arises^ as 3>Ir. C's remark observes, 



from six successive throws of one die being assumed equal to 

 1 simultaneous throw of 6" dice; which position, in my mind, 

 it completely subverts, though supported by the authority of 

 the above celebrated names. Let us compare 2 throws of 1 

 halfpenny with 1 throw of 2, as to their chances of a head's 



.bein» 



