of Edinburgh, Session 1878-79. 105 
after reading the book his opinion was modified. He thought 
Professor Geddes had strengthened the case for Grote’s theory, 
though not to the extent of proving an affirmative. 
Dr Donaldson concurred with the views of Professor Blackie. 
Professor Sellar, while having the greatest admiration for Professor 
Geddes’s knowledge and ingenuity, felt that he had done nothing in 
the way of enlightening those interested in the subject. 
Professor Blackie, in replying, observed that the Society were 
under obligations to Professor Geddes for having raised the question. 
2. The Principles of the Algebra of Logic. Part III. — Appli- 
cation to certain Problems in the Theory of Probability. 
By Dr Alexander Macfarlane. 
The Algebra of Logic, being the science of Necessity and Prob- 
ability, supplies a variety of methods of great power for solving 
problems in the theory of Probability. I propose to bring before 
the Society a few examples extracted from my work on the 
“ Principles of the Algebra of Logic,” which is about to be 
published. A large class of problems, some of which have created 
considerable diversity of opinion among mathematicians of 
eminence, can be solved by means of a single theorem. It con- 
sists in finding the arithmetical value of — . The meaning 
of this expression is shown by the diagram — 
The collection of individuals forming the subject of discourse 
is represented by the part of the page within the square, those 
which have a character x by the part inside the one circular line, 
and those which have the character y by the part inside the other 
