30 GREAT MEN OF SCIENCE 



cannot exceed certain dimensions, since they would other- 

 wise collapse under their own weight. 



In the 'First Day' of the Dialogues a great deal concerning 

 sound vibrations and sounds is made clear in connection with 

 Pythagoras and previous remarks of musicians; thus the deter- 

 mination of the pitch of a note by its frequency, the relation 

 between the frequencies of harmonious and inharmonious 

 intervals, such as the octave, fifth, third, and second. The 

 dependence of the frequencies of strings upon their weight 

 and upon the tensile force is also completely understood. 

 We find a thorough treatment of the phenomena of resonance 

 which later became of such importance for the whole of 

 physics, and this perfect and exhaustive clarity at so early a 

 period astonishes us. 



At that time Galileo was also busy with the construction 

 of thermometers, which were the first appliances enabling 

 'warm' and 'cold' to be defined quantitatively. By observ- 

 ing the expansion with heat of air, water, and alcohol, he 

 strove to attain to a quantitative grasp of thermal phenomena, 

 and here also he took the path which, in full accordance with 

 the instructions given by Pythagoras, has always been the 

 necessary condition of progress. 



Galileo's first discoveries concerning me heavens were also 

 made in Padua, and in their comprehensive importance these 

 are fully on a par with his discoveries on motion. His eyes 

 gazed upon things never seen hitherto, and completely 

 unbelievable, as he turned a telescope towards the sky for the 

 first time. This new appliance, compounded of spectacle 

 glasses, had appeared in Holland, where the grinding of glass 

 lenses for use as spectacles had already been practised for 

 three hundred years, and with very great skill. ^ 



The tube with lenses very soon became widely known by 

 its astonishing powers with respect to objects on the earth; 



^ Evidence of much earlier use of lenses of glass and rock crystal, even 

 in antiquity, exists. 



