140 INTRODUCTORY ADDRESS 



in keeping geometry pure from ideas which did not belong to it, it 

 failed to form what might otherwise have been the basis of physical 

 science. Its founders missed the discovery that methods similar to 

 those of geometric demonstration could be extended into other and 

 wider fields than that of space. Thus not only the development of 

 applied geometry, but the reduction of other conceptions to a rigorous 

 mathematical form was indefinitely postponed. 



Astronomy is necessarily a science of observation pure and simple, 

 in which experiment can have no place except as an auxiliary. The 

 vague accounts of striking celestial phenomena handed down by the 

 priests and astrologers of antiquity were followed in the time of the 

 Greeks by observations having, in form at least, a rude approach to 

 precision, though nothing like the degree of precision that the astro- 

 nomer of to-day would reach with the naked eye, aided by such 

 instruments as he could fashion from the tools at the command of 

 the ancients. 



The rude observations commenced by the Babylonians were 

 continued with gradually improving instruments, first by the 

 Greeks and afterward by the Arabs, but the results failed to afford 

 any insight into the true relation of the earth to the heavens. What 

 was most remarkable in this failure is that, to take a first step forward 

 which would have led on to success, no more was necessary than a 

 course of abstract thinking vastly easier than that required for work- 

 ing out the problems of geometry. That space is infinite is an unex- 

 pressed axiom, tacitly assumed by Euclid and his successors. Com- 

 bining this with the most elementary consideration of the properties 

 of the triangle, it would be seen that a body of any given size could 

 be placed at such a distance in space as to appear to us like a point. 

 Hence a body as large as our earth, which was known to be a globe 

 from the time that the ancient Phoenicians navigated the Mediter- 

 ranean, if placed in the heavens at a sufficient distance, would look 

 like a star. The obvious conclusion that the stars might be bodies 

 like our globe, shining either by their own light or by that of the sun, 

 would have been a first step to the understanding of the true system 

 of the world. 



There is historic evidence that this deduction did not wholly 

 escape the Greek thinkers. It is true that the critical student will 

 assign little weight to the current belief that the vague theory of 

 Pythagoras that fire was at the centre of all things implies a 

 conception of the heliocentric theory of the solar system. But the 

 testimony of Archimedes, confused though it is in form, leaves no 

 serious doubt that Aristarchus of Samos not only propounded the 

 view that the earth revolves both on its own axis and around the sun, 

 but that he correctly removed the great stumbling-block in the way 

 of this theory by adding that the distance of the fixed stars was 



