420 



July 31. (Extraordinary Meeting.) 

 SIR Wm. R. HAMILTON, LL.D., President, in the Chair. 

 Resolved, — On the recommendation of Council, — That 

 the Treasurer be empowered to sell stock in the 3 per cent. 

 Consols, to the amount of £300, in order to pay Mr. Gill's 

 bill for printing Transactions to March 16, 1813, amount 

 ££64 lOs. 4d., and the rent of the Academy House to 31st 

 July, 1843. 



Resolved, — On the recommendation of Council, — That 

 the Treasurer be empowered to sell such 3^ per cent, stock, 

 being the Cunningham Fund, as shall amount to £50, to- 

 wards defraying the cost of medals. 



Sir WilHam Bethani presented to the Academy certain 

 casts from the sculptures on the inside of the tower of 

 Ardmore. 



Dr. Lloyd having taken the Chair, the President gave an 

 account of some researches in the Calculus of Probabilities. 



Many questions in the mathematical theory of probabili- 

 ties conduct to approximate expressions of the form 



o n t 



/ , dt e-'\ 



V TT J 



that is, 



P = B{t\ 



6 being the characteristic of a certain function which has been 

 tabulated by Encke in a memoir on the Method of Least 

 Squares, translated from the Berlin Ephemeris, in vol. ii. 

 part 7 of Taylor's Scientific Memoirs ; /^ being the proba- 

 bility sought, and t an auxiliary variable. 



Sir William Hamilton proposes to treat the equation 



P = 0{t) 

 as being in all cases rigorous, by suitably determining the 

 auxiliary variable t, which variable he proposes to call the 



