[ 4 ” ] 
this constancy; but we can have no reafon for thin Ic- 
ing that there are no caufes in nature which will ever 
inrerfere with the operations of the caufes from which 
this confiancy is derived, or no circumftances of the 
world in which it will fail. And if this is true, fup- 
pofing our only data derived from experience, we fhall 
find additional reafon for thinking thus if we ap- 
ply other principles, or have recourfe to fuch confi- 
derations as reafon, independently of experience, can 
fuggeft. 
-But I have gone further than I intended here ; and 
it is time to turn our thoughts to another branch of 
this fubjeft: I mean, to cafes where an experiment 
has fometimes lucceeded and fometimes failed. 
Here, again, in order to be as plain and explicit 
as pofiible, it will be proper to put the following- 
cafe, which is the eafieft and fimpleft I can think 
of. 
Let us then imagine a perlon prefent at the drawing 
of a lottery, who knows nothing of its fcheme or of 
the proportion of Blanks to Prizes in it. Let it further 
be fuppofed, that he is obliged to infer this from the 
number of blanks he hears drawn compared with the 
number of prizes j and that it is enquired what con- 
clufions in thefe circumftances he may reafonably 
make. 
Let him firft hear ten blanks drawn and one prize, 
and let it be enquired what chance he will have for be- 
ing right if he gueftes that the proportion of blanks to 
prizes in the lottery lies fomewhere between the pro- 
portions of 9 to i and n to i. 
Here taking X = x=z T %,p=io, q — 7, »=n, 
E = 1 1, the required chance, according to the firfi: 
rule^ 
