474, Cambridge Philosophical Society :— 
combinations involving a sign of inherent quantity, as follows :— 
By X..LM’Y is signified that X is an L of every M of Y. 
By X..L,MY it is signified that X is an L of none but Ms of Y. 
The contrary relation of L, not -L, is signified by 7. Thus X. LY is 
identical with X..7Y. ‘The converse of L is signified by L~*: thus 
X..LY is identical with Y..L7'X. ‘This is denominated the 
L-verse of X, and may be written LX by those who prefer to avoid 
the mathematical symbol. 
The attachment of the sign of inherent quantity to the symbols of 
relation is the removal of a difficulty which, so long as it lasted, pre- 
vented any satisfactory treatment of the syllogism. There is nothing 
more in X..LM/Y than in every M of Y is an L~’ of X, or 
MY))L~'X, X and Y being individuals; and nothing more in 
X..L,MY than in L~'X))MY, except only the attachment of the 
idea of quantity to the combination of the relation. 
When X is related to Y and Y to Z, a relation of X to Z follows: 
and the relation of X to Z is compounded of the relations of X to Y 
and Y to Z. And this is syllogism. Accordingly every syllogism 
has its inference really formed in the frst figure, with both premises 
affirmative. For example, Y.LX and Y..MZ are premises stated 
in the third figure: they amount to X..L7'Y and Y..MZ, 
giving X../~*MZ for conclusion. This affirmative form of conclu- 
sion may be replaced by either of the negative forms X .L~’M’Z or 
Re WL 
The arrangement of all the forms of syllogism, the discussion of 
points connected with the forms of conclusion, the extension from 
individual terms in relation to quantified propositions, the treatment 
of the particular cases in which relations are convertible, or transi- 
tive, or both—form the bulk of the paper, so far as it is not contro- 
versially directed against those who contend for the confinement of 
the syllogism to what Mr. De Morgan calls the onymatic form. 
An appendix follows the paper, on syllogism of transposed quan- 
tity, in which the number of instances included in one premise is 
equal to the whole number of existing instances of the concluding 
term in the other premise. 
Mr. J. H. Rohrs also read a paper ‘“‘ On the Motion of Bows, and 
thin Elastic Rods.” 
May 7.—The Rev. Professor Sedgwick made a communication 
“On the Succession of Organic Forms during long geological 
periods; and on certain Theories which profess to account for the 
origin of new species.” 
May 21.—The Public Orator read a paper ‘‘ On the Pronunciation 
of the Ancient and Modern Greek Languages.” 
He gave a rapid sketch of the ‘‘ Reuchlin and Erasmus” contro- 
versy in the sixteenth century, especially the part taken in it at 
Cambridge by Cheke, Smith, Ascham, and Bishop Gardiner; and 
then proceeded to show how the proper sounds of the Greek letters 
may be determined from the following sources ;—~ 
