THE GROWTH OF PHYSICAL IDEAS 95 



remains constant is reversible, whereas one in which the 

 entropy increases must be irreversible. In dealing with the 

 transformation of energy, therefore, physicists use two vari- 

 ables: the energy involved and the entropy of the system. 

 In any transformation of energy for which ^ve wish to write 

 the equations, the first law of thermodynamics states that the 

 energy must remain constant after the transformation; that 

 is, the two sides of the equation must balance. The second 

 law of thermodynamics states that the entropy must increase 

 in carrying out the transformation. 



The attempt to reduce all laws to mechanical laws led to 

 the statistical theory of heat, formulated by Boltzmann and 

 very successfully applied to chemical problems by W^illard 

 Gibbs. The investigation of the states of matter (gaseous, 

 liquid, solid) and especially of its behavior at very low tem- 

 peratures (near the absolute zero) forms the basis of much 

 research in the field of thermodynamics. 



In the earliest speculations on the nature of light, Plato 

 and Aristotle held that light is derived from the eye, and 

 they pictured the eye as sending out something that inter- 

 cepted an object and so illuminated it. This idea, however, 

 was supplanted by the idea that the light was emitted from 

 the object seen; and much later it was realized that light is 

 emitted by such light sources as the sun and reflected to the 

 eye by objects seen. 



Lenses were known to the ancients. The use that was 

 made of them is not known. Possibly the crystal lenses that 

 have been found were considered to be merely ornamental, 

 although the fact that they would concentrate the rays from 

 the sun and would act as burning glasses is mentioned by 

 Aristophanes. In medieval times lenses were certainly used 

 as magnifying glasses to assist in reading. It is not a very 

 long step from the use of a lens in the hand to the produc- 

 tion of lenses in a mount that can be carried on the face and 

 thus to the invention of spectacles; but the invention of 

 spectacles must have been a most important step in increas- 

 ing the efficiency of those suffering from the small defects 



