Proceedings of the Royal Society. 87 
exists in writers to adopt one general standard of reference, tliat 
a critical examination like the present, which certainly does much 
towards throwing down the buildings of others, cannot fail to have 
great value, even should its own foundations not stand. This is 
not like a discovery in pure analysis, — the opening up of a royal road 
from one position to another, — so much as a survey of the ground, 
with a view to the assertion that the right road lies on this side, 
and not on that, of some given obstacle. In the name of the 
Council, I beg our Vice-President, Bishop Terrot, to take charge of 
this Medal for Professor Boole, and to express to him our wishes 
for his future success in the career to which he has devoted himself. 
Bishop Terrot is not, in this instance, a mere passive spectator, nor 
a mere hand to convey a reward from one party to another ; he 
stands in the light of a participator in the honour, and that to no 
small extent. The problem of combining two or more probabilities 
of the same event received from Bishop Terrot a solution in our 
Transactions two years since, to which the present paper is proba- 
bly due. Plere, for the first time, was given the form of the proba- 
bility or value of expectation due to entire ignorance, as an inde- 
terminate fraction. This result, as indeed the other conclusions of 
Bishop Terrot, the present paper satisfactorily confirms. Bishop 
Terrot, therefore, whilst I doubt not he will cheerfully transfer the 
award to Mr Boole, will still retain a share in the honour. 
The following Communications were then read : — 
1. On the Average Value of Human Testimony. By 
Bishop Terrot. 
The author began by some remarks upon the expression 
- — —7- — — 75 n or — — == U. Where p represents the 
pv + (1 — p) . (1 — v) pv + wq 
a priori probability of an event attested by a witness whose veracity, 
or the ratio of whose true assertions to the number of all his as- 
sertions is, v. He observed that U, or the ultimate probability of the 
asserted fact, depended upon the accuracy of the numerical value 
given to v , and that men have never such knowledge of their neigh- 
bours’ antecedents, as to assume this value with anything like an 
approximation to the truth. 
It was then suggested that a more definite result might be 
