of Edinburgh, Session 1878-79. 103 
Now it is well known that the alternant whose indices are in 
order 0, 1, 2, 3, .... is equal to the difference-product of its 
variables. In regard to every other alternant it is evident that it 
must contain the said difference-product as a factor, but what the 
co-factor should be is not so readily seen. In particular cases, 
doubtless, it can be found without much difficulty, but a general 
method of obtaining it has hitherto been a desideratum. Such a 
general method the author has discovered along with a number of 
less important results, bearing on the same special form of deter- 
minant. 
Monday , 7 th April 1879. 
Sir ALEXANDER GRANT, Bart., Vice-President, 
in the Chair. 
1. Professor Geddes’s Theory of the “ Iliad.” By 
Professor Blackie. 
(. Abstract .) 
Professor Blackie, after paying a high compliment to the erudition, 
ingenuity, and fine taste of the Aberdeen Hellenist, proceeded to 
give reasons why, in his opinion, the theory now broached, to the 
effect that certain books of the “ Iliad” were composed by the author 
of the “ Odyssey,” which author is to be considered as the real 
Homer, though not destitute of a certain plausibility, is untenable. 
The reasons were — (1.) The character of the minstrel as distinguished 
from the literary epos warrants the presumption that any small 
diversity in certain secondary characteristics of different sections of 
the poem, as we now have it, is a legitimate proof, not of diversity 
of authorship, but only of diversity of materials collected from 
different sources. (2.) The manner in which the minstrel epos was 
originally circulated, not as a separate literary composition to be 
read and studied, but as a sequence of easily separable cantos to be 
handed about and sung separately, rendered it, even when wrought 
into a finished artistic whole by the genius of a great singer, pecu- 
liarly liable to interpolations and variations of various kinds, which 
form no legitimate ground of induction with regard to the character 
