1895 - 96 .] 
Chairman's Opening Address. 
9 
also examines the several systems of vector analysis, which these 
critics believe to be superior to the quaternion system. His 
general conclusion is that the rival systems cannot compare in 
coherency, power, and flexibility, with quaternions, of which they 
are, at best, half-hearted imitations. 
Professor Cayley, in a paper entitled Co-ordinates versus 
Quaternions, has said that, while co-ordinates are applicable to the 
whole science of geometry, quaternions seem to be a particular and 
very artificial method for treating such parts of the science of 
3-dimensional geometry as are most naturally discussed by means 
of the rectangular co-ordinates. Professor Tait, on the other hand, 
holds that Cayley’s views are only applicable to Hamilton’s first 
conception of the quaternion, which was nothing more than a full 
development of imaginaries, but not to Hamilton’s subsequent con- 
ception of the quaternion as an organ of expression, giving simple, 
comprehensive, and transparently intelligible embodiment to the 
most complicated of real geometrical and physical relations. 
Amid his laborious, but happily hopeful, and so far successful 
work in developing the educational institutions of Cape Colony, 
Dr Muir has found time to continue his scientific researches. He 
has given us a paper on Sylvester’s Problem in Elimination, in 
dealing with which he has found an axisymmetric determinant, 
which is the square of its own primary co-axial minors. In 
another paper, he has shown that the difference between any two 
terms of the adjugate determinant is divisible by the original 
determinant. 
Although this Society is literary as well as scientific, we are not 
often favoured with literary communications. The only paper 
received during the past Session which might be classed as such is 
one by Professor D’Arcy Thompson on Ancient Symbolism. It is 
scientific, however, as well as literary — being an attempt to extract 
the hidden astronomical meaning “ from graven emblem, from 
symbolic monument, from the orientation of temple-walls, from the 
difficult interpretation of Hellenic names of Hero and Heroine, of 
solar god and lunar goddess, of mysterious monster and fabled 
bird, of celestial river and starry hill.” 
During the last and the preceding Session we have been favoured 
with addresses from Professor Flinders Petrie, Dr Munro, and 
