32 ILLINOIS ACADEMY OF SCIEN'CE 



the times considered are "all whatsoever." If, therefore, one 

 wishes to employ these definitions in the discussion of vari- 

 able motion he must take his time intervals indefinitely small. 



The invention of the well-known thermoscope which 

 Galileo employed in his lectures at Padua also belongs here; 

 for while it is not a true thermometer it doubtless led imme- 

 diately to those exquisite sealed instruments shortly after- 

 wards constructed by the Accademia del Cimento and still 

 preserved in the Tribuna di Galileo at Florence. The theory 

 of "dimensions," first stated by Fourier, was led up to in the 

 First Day of the Dialogues on Motion. 



The principle employed in his measurement of the density 

 of air(19) is one which is not only faultless in principle but 

 one which makes it plainly evident that Galileo had properly 

 conceived that idea of atmospheric pressure which, in the 

 hands of two of his students, led to the invention of the ba- 

 rometer, and, in the hands of von Guericke, to the air pump. 

 TorricelH knew well the Dialogues on Motion. 



ft. Finally. Galileo was an inspiring teacher and built 

 uj) at Padua a great school of physics. ^lany of his students 

 lodged under his own roof; helped him in his own garden; ate 

 at his own table. He had his own workshop and employed 

 his own mechanicians. Generous with his time, his energy 

 and his money, master of a fine literary style, endowed with a 

 keen sense of humor, familiar with the best that had been said 

 and thought in the world, standing in the front rank of inves- 

 tigators, is it any wonder that young men of talent hastened 

 to Padua from all parts of Europe? Could any higher com- 

 ])liment he paid to a teacher than the devotion exhibited by 

 the youthful Viviani. a lad in his 'teens, for his master already 

 some seventy years old and a "Prisoner in Arcetri?" If de- 

 ferred payments of the kind that teachers mostly depend upor 

 ever get as far as the next world, surely this courageous spirit 

 harried throughout his long life by poverty, ill-health and the 

 censorship of the church, must have been gratified by the 

 the work of the Accademia del Cimento which was, with the 

 exception of a single man. composed entirely of his students. 

 Mechanics was the one subject to which he was devoted con- 

 stantly and persistently throughout his life ; it was the sub- 

 ject of his earliest investigation when a young man at Pisa: 

 the subject upon which he lectured when in his prime at Pa- 

 dua ; the subject of his latest and most mature reflection at 

 Arcetri. His most important contribution to dynamics was 

 published in the seventy-third year of his age. 



If. in conclusion, I were asked to summarize in a single 

 sentence the principal contributions to the science of physics. 



