THE LEGACY OF THE GREEKS 147 



tion of the pyramids, several thousand years before this era, 

 is sufficient evidence that for most practical concerns they 

 were not greatly inferior to our own. 



Some of their methods were roundabout. They calculated, 

 for example, the visual diameter of the sun from the time which 

 elapsed between the appearance of its edge above the horizon 

 to that in which its full disk was visible. They did this by 

 weighing the quantity of water which ran from one vessel into 

 another in the interval. Such means of observation seem to 

 us primitive. It is to be noted that they were fairly effective. 



They had applied mathematics to the problems of mechanics, 

 of optics, of acoustics. They understood the elements of musical 

 theory that a vibrating string divides successively into halves, 

 thirds, and so on, and that the notes of the scale are in simple 

 ratio to the fundamental tone. They understood the principle 

 of the lever ; they had developed fairly well the statics of bodies. 

 They had fairly well worked out the geometrical side of optical 

 theory. They knew that the sun appears before it is actually 

 above the horizon ; and from this Poseidonius was able to 

 calculate with a fair approximation the height of the earth's 

 atmosphere. Through the applications of geometrical optics, 

 they were able to solve the more essential questions which 

 pertain to the place of the earth in cosmos. Let us sum up 

 precisely what they knew : 



They understood that the earth is a sphere, and that it 

 hangs, so far as any one may see, in empty space. Their minds 

 had reached the conception that it rests on nothing. 



They understood the size of the earth, had fair ideas of its 

 variety of climate, had measured accurately the width of the 

 tropical zone. They knew in theory at least of the land of the 

 midnight sun. They discussed with enlightenment the question 

 of other habitable continents beyond the seas. They had fixed 

 with close approximation the distance of the moon, and realised 

 its great size. Some of them at least knew of the relations of 

 the moon to the tides. 



They understood something of the distance and grandeur 

 of the sun. They knew that it was a body far larger than the 

 earth. Two of them at least had more correct ideas, had made 

 better measures, than had any one before Cassini and Newton, 

 fifty years after the telescope was in general use. The sombre 

 reflections of Cicero and many another make it clear that the 



