of Edinburgh, Session 1878-79. 
107 
Let U = a succession of states of the atmosphere at a given place, 
an individual state being of the length of a day. 
x — containing a thunderstorm, 
y = containing a hailstorm. 
Then the data are — 
X = p, xy = q- 
Hence, by means of the theorem proved 
_ - 0 - 
y = 1 + o'O ~p)> 
■ ■■ y>q, 
and < q + J - p. 
(2.) A says that B says that a certain event took place ; required 
the probability that the event did take place, yq and p 2 being A’s 
and B’s respective probabilities of speaking the truth. 
The solution of this problem recently gave rise to a great amount 
of discussion in the “ Educational Times.” No fewer than four 
different solutions are given, viz. : — 
Todhunter — 
PiPt + 0 - Pi) ( x " P 2 ) ■ 
Artemas Martin — 
Pl{i , 1^2 + ( 1 -Pi) (! -Pz)} ■ 
Woolhouse and American mathematicians — 
PlP2‘ 
Cayley— 
ihP2 + 0(1 - Pl ) (1 - p 2 ) + K(1 - P) (1 - rj, 
where /3 is the chance, on tlie supposition of the incorrectness of A's 
statement, that B told A that the event did not happen, and 1-/3 
that he did not tell him at all. k is the antecedent probability. 
Let U = statements of A about B’s statements about an event 
taking place. 
x = which truly reported a statement by B , 
y = which truly reported the event. 
