186 ANNUAL REJPORT SMITHSONIAN INSTITUTION, 1941 



In 1850 Maxwell placed a mathematical support under Faraday's 

 theories, to be followed by the experimental verification of Hertz. 



Joule (1818-89) found a mechanical equivalent for heat, namely, 

 energy, giving the world the first law of thermodynamics. 



Plank gave a description of radiation as incapable of emission in 

 aught but units, the quanta. In this quantum theory fractions of a 

 unit of energy simply do not exist. 



De Broglie and Schrodinger combined the energy theory of Einstein 

 with the quantum theory of Plank and compelled the joint wave- 

 particle view of the atom. (Since then the physicist has been accused 

 of teaching the wave theory on Monday, Wednesday, and Friday, 

 and the particle theory on Tuesday, Thursday, and Saturday.) 



Heisenberg proclaimed the doctrine that nature abhors not a 

 vacuum so much as it does accuracy and precision. 



Dirac extended the uncertainty principle of Heisenberg to the 

 entire realm of atomic physics. 



Pauli furnished us with his exclusion principle, 



Millikan and Cameron gave us cosmic radiation. 



Minkowski offered his space-time world. 



Einstein supplemented the Newtonian mechanics, proclaimed the 

 invariance of natural laws in inertial systems, the constancy of the 

 velocity of light, the abandonment of simultaneity, the identity of 

 mass and energy, claimed absolute motion incapable of detection, 

 related time and motion, connected space and matter. Gravitation, 

 that most elusive of concepts, appeared as the curvature, or crum- 

 pling, of a space-time continuum. But the electromagnetic fields 

 were not expressed in the field equations of general relativity. Later 

 came a field theory in which gravitation and electromagnetic radia- 

 tion were welded together. Only the expression of the atomic 

 structure in terms of the field theory was, and still is, missing. 



Here we are, and what a long way we have come. Let us examine 

 some of the high and low places along the path. Let us see again 

 something of the view from a few of the peaks and depressions along 

 the way. Let us inquire of Mathematics, the guide in this long and 

 fascinating journey. 



CONTINUITY 



Perhaps we never realize its subtlety until we really try to find 

 out the meaning of continuity. The writer of radio script uses the 

 term to refer to his product. We have heard his programs. Can 

 such an idea be hedged about with difficulty ? As is so often the case, 

 an understanding of the concept implies an understanding of its 

 opposite. The opposite of the continuous is the discrete. 



Long ago there lived an excellent gentleman named Zeno. It was 

 back in the time of the Pythagoreans, 600 years before Christ. This 



