314 ; REPORT—1905. 
of this Association upon the subject, will, some six or seven weeks hence, hold 
its last examination in which those methods are prescriptively required. The 
disestablishment of Euclid from tyranny over the youthful student on the conti- 
nent of Europe was effected before the end of the eighteenth century. , 
But it is time for me to pass on to the third of the centenaries with which 
the present year can be associated. Not so fundamental for the initiation of 
modern science as was the year in which the ‘Advancement of Learning’ was 
published, not so romantic in the progress of modern science as was the year in 
which Halley gave his prediction to the world, the year 1805 (turbulent as it was 
with the strife of Enropean politics) is marked hy the silent voices of a couple of 
scientific records. In that year Laplace published the last progressive instalment 
of his great treatise on Celestial Mechanics, the portion that still remained for the 
future being solely of an historical character; the great number of astronomical 
phenomena which he had been able to explain by his mathematical presentation 
of the consequences of the Newtonian theory would, by themselves, have been 
sufficient to give confidence in the validity of that theory. In that year also 
Monge published his treatise, classical and still to be read by all students of the 
subject, ‘The Application of Algebra to Geometry’; it is the starting point of 
modern synthetic geometry, which has marched in ample development since his 
day. These are but landmarks in the history of mathematical science, one of 
them indicating the completed attainment of a tremendous task, the other of 
them initiating a new departure; both of them have their significance in the 
progress of their respective sciences. 
When we contemplate the activity and the achievements of the century 
that has elapsed since the stages which have just been mentioned were 
attained in mathematical science, the amount, the variety, the progressive 
diligence, are little less than bewildering. It is not merely the vast develop- 
ment of all the sciences that calls for remark: no less striking is their detailed 
development, Each branch of science now has an enormous array of workers, a 
development rendered-more easily possible by the growing increase in the number 
of professional posts; and through the influence of these workers and their labours 
there is an ever-increasing body of scientific facts. Yet an aggregate of facts is 
not an explanatory theory any more necessarily than a pile of carefully fashioned 
stones is a cathedral; and the genius of a Kepler and a Newton is just as 
wbsolutely needed to evolve the comprehending theory as the genius of great 
architects was needed for the Gothic cathedrals of France and of England. Not 
infrequently it is difficult to make out what is the main line of progress in any 
one subject, let alone in a group of subjects; and though illumination comes from 
striking results that appeal, not merely to the professional workers, but also to 
unprofessional observers, this illumination is the exception rather than the rule. 
We can allow, and we should continue to allow, freedom of initiative in all 
directions. That freedom sometimes means isolation, and its undue exercise 
can lead to narrowness of view. In spite of the complex ramification of the 
sciences which it has fostered, it is a safer and a wiser spirit than that of uncon- 
genial compulsion, which can be as dogmatic in matters scientific as it can be in 
matters theological. Owing to the varieties of mind, whether in individuals or 
in races, the progress of thought and the growth of knowledge are not ultimately 
governed by the wishes of any individual or the prejudices of any section of 
individuals. Here, a school of growing thought may be ignored; there, it may 
be denounced as of no importance; somewhere else, it may be politely persecuted 
out of possible existence. But the here, and the there, and the somewhere else 
do not make up the universe of human activity ; and that school, like Galileo’s 
earth in defiance of all dogmatic authority, still will move. 
This complete freedom in the development of scientific thought, when the 
thought is applied to natural phenomena, is all the more necessary because of the 
ways of Nature, Physical nature cares nothing for theories, nothing for calcula- 
tions, nothing for difficulties, whatever their source; she will only give facts in 
answer to our questions, without reasons and without explanations; we may 
explain as we please and evolve laws as we like, without her help or her hindrance. 
