452 Waring. 



This result is obtained by equating the coefficients of the term 

 ^s-rj^r -^^ ^-j^g ^^Q members of Vandermonde's identity. 



The result is enunciated and printed so badly in Warings 

 work that some difficulty arose in settling what the result was and 

 how it had been obtained. 



836. I do not enter on that part of Waring's work which relates 

 to annuities. I am informed by Professor De Morgan that the late 

 Francis Baily mentions in a letter the following as the interesting 



parts of the work : — the series 8 — mS' -\ ^-^ S" — ...., the 



Problem III, and the observations on assurances payable imme- 

 diately at death. 



837. Another work by Waring requires a short notice ; it is 

 entitled A^i essay on the jirinciples of human knowledge. Cam- 

 bridge 1794. This is an octavo volume ; it contains the title-leaf, 

 then 240 pages, then 3 pages of Addenda, and a page containing 

 Corrige7ida. 



838. This work contains on pages 35 — 40 a few common theo- 

 rems of probability ; the first two pages of the Addenda briefly 

 notice the problem discussed by De Moivre and others about a 

 series of letters being in their proper places ; see Art. 281, and De 

 Moivre Prob. xxxv. Waring remarks that if the number of 

 letters is infinite the chance that they will occur all in their right 

 places is infinitesimal. He gives page 49 of his work as that on 

 which this remark bears, but it would seem that 49 is a misprint 

 for 41. 



839. Two extracts may be given from this book. 



I know that some mathematicians of the first class have endeavoured 

 to demonstrate the degree of probabihty of an event's happening 7^ times 

 from its having happened m preceding times; and consequently that 

 such an event will probably take place ; but, alas, the problem far ex- 

 ceeds the extent of human understanding : who can determine the time 

 when the sun will probably cease to run its present course ? Page 35. 



...I have myself wrote on most subjects in pure matliematics, and in 



