[ 4°7 ] 
throw only fhews that it has the fide then thrown, 
without giving any reafon to think that it has it ana. 
one number of times rather than any other. It will 
appear, therefore, that after the firft throw and not 
before, we fhould be in the circumftances required 
by the conditions of the prefent problem, and that 
the. whole effedft of this throw would be to bring 
us into thefe circumftances. That is: the turning 
the fide firft thrown in any fubfequent fingle trial 
would be an event about the probability or improba- 
bility of which we could form no judgment, and 
of which we fhould know no more than that it 
lay fomewhere between nothing and certainty. With 
the fecond trial then our calculations muft begin ; 
and if in that trial the fuppofed folid turns again the 
fame fide, there will arife the probability of three 
to one that it has more of that fort of fides than of 
all others; or (which comes to the fame) that there 
is fomewhat in its conftitution difpofing it to turn that 
lide ofteneft : And this probability will increafe, in 
the manner already explained, with the number of 
times in which that fide has been thrown without 
failing. It fhould not, however, be imagined that any 
number of fuch experiments can give fufHcient reafon 
for thinking that it would never turn any other fide. 
For, fuppofe it has turned the fame fide in every 
trial a million of times. In thefe circumftances there 
would be an improbability that it had lefs than 
1.400.000 more of thefe fides than all others; but 
there would alfo be an improbability that it had above 
1.600.000 times more. The chance for the latter is 
exprelTed by raifed to the millioneth power 
fubftra&ed from unity, which is equal 10.4647 6cc.and 
G g g 2 the 
