88 
Proceedings of the Royal Society . 
obtained, by assuming, from experience, the value of U, and thence 
determining the value of v . The instance adopted was that of a 
man saying that out of a bag containing 99 white balls and one 
black, he has at the first trial drawn the black. In such a case, so 
long as there exists in our minds no suspicion of a motive for false- 
hood, the assertion is absolutely believed ; that is to say, we give to 
U the value unity. But p being the proper fraction U cannot 
equal 1 unless v = 1 ; that is to say, unless we consider human testi- 
mony, even to improbable events, as certainly truthful, in every case 
where there exists no suspicion of the action of a motive for false- 
hood. The suspicion of such motive at once prevents us from giving 
to U the value 1 ; that is, from receiving the assertion as absolutely 
true. If, for example, the man who drew the black ball was to 
gain L. 10 00 by our being persuaded that he had done so, we should 
not readily take his word for the fact that he had so succeeded. 
It was then noticed that the expression for the ultimate probability 
given by Laplace was 
vr + (1 — v) . (1 — r) 
vr + (1 — v) . (1 — r) + |”u . (1 — r) x r( 1 — v) 
where r represents the probability that the witness, though intend- 
ing to tell the truth, deceives himself. If in this expression 1 be 
opy 
substituted for (V) this formula coincides with —— — r — ? 
v ' pv -fe (1 — p) . 1 — v 
for all the cases treated in the paper are cases where there can be 
no reasonable suspicion that the witness is deceived. It was at the 
same time allowed that there are numerous cases where a suspicion 
of this, or some other disturbing force, may reasonably be suspected. 
But it was maintained that such cases, however numerous, are ex- 
ceptional, and are very few compared with those to which no sus- 
picion attaches : and that were this not the case, human tes- 
timony would be of no practical value, and human society could 
not subsist. The final inference was, that habitual credulity is less 
unreasonable than habitual incredulity ; that in the former the 
exception is sacrificed to the rule, in the latter the rule is sacrificed 
to the exception. 
