140 



LECTURES TO SCIENCE TEACHERS. 



From this time we have a long gap until we come to the age 

 of Galileo j but even in Greek times the simple ratios and 



Octave. 



Fifth. 



Fourth. 



eo|oo 



FIG. 1. Optical curves. The octave, fourth, and fifth. 



parts of the string were well known. I have placed these on 

 a diagram there just as a reminder, because we shall have to 

 speak again to-morrow of a different form of numerical calcu- 

 lation not involving ratios ; to-day I wish to bring before 

 you the ratios and nothing more. You can see how these 



