THE FIRST IDEAS OF GRAVITATION 125 



a hundred times that of the moon ; he must have known it, 

 because an extensive commentary upon Eratosthenes was one 

 of his principal works. 



But the same limitations which forced Hipparchus to the 

 rejection of the heliocentric doctrines of Aristarchus, the same 

 indifference to the mechanics of the problem, the disregard of 

 considerations of relative weight and relative mass, would, it 

 is obvious, have guided his mind away from, rather than toward, 

 the problem of gravitation, the curious acceleration of the fall 

 of bodies, and its possible connection with the circular move- 

 ment of the planets. It is not so clear how this possible con- 

 nection could have escaped the Titan mind of Archimedes. 



It is to the great geometer of Syracuse that we attribute the 

 foundation of mechanics. The principle of the lever doubtless 

 had been known for thousands of years, perhaps tens ; but 

 it seems to have been Archimedes who worked out its theory 

 and made it the basis of a science. Concerned with the problem 

 of weight, the means of its determination, it was he perhaps of 

 all the ancients who must have come nearest to the distinc- 

 tion between weight and mass. He was profoundly interested 

 in considerations of gravitation. Not merely the method of 

 determination, but the idea of centres of gravity seems to have 

 been his. It was Archimedes, as we have seen, who gave the 

 explanation of why it is that upon a round earth the waters 

 of the ocean did not run down the sides and spill away. 



Strangely did he not see the implication. Since bodies 

 appear to be attracted towards the centre of a sphere, it follows 

 that at the centre of the sphere this attraction will be zero. 

 If it increases outward from the centre to the surface, what 

 reason is there to suppose that it stops at the surface ? Not 

 to the utmost height to which any of the huge engines Archi- 

 medes constructed might hurl a heavy body was there the 

 slightest evidence of the diminution of this force. The fall 

 of meteorites, evidently from great heights, and pretty obviously 

 under this same force of gravitation, carried the mind yet further 

 outwards into space. It seems incredible that such a mind, 

 working amid such problems and in contact with other minds 

 like those of Aristarchus and Eratosthenes, busy with the 

 measures of the moon and the sun, could not have made the 

 one further step. 



Yet, as we shall see, the same limitations hemmed that 



