as- 



352 RADIATION OF ENERGY. 



One result of this view of the matter is that the principle of the conservati 

 of energy cannot be extended to empty space ; it must be limited in its application 

 to actual physical bodies. If we extend it to empty space, we assume that energy 

 is an entity and can exist independently of physical objects. This we have seen 

 is not true. If energy cannot exist by itself in free space many of the conclusions 

 of the modern German school are invalidated, for they are based on this 

 sumption. 



It will, of course, be possible to retain the mathematical expression for the 

 energy of space, considering the energy of space simply as a mathematical 

 concept, not expressing any reality, and using it simply in order that energy may 

 be a continuous function of space, just as we use magnetic or electric induction 

 in order to have a continuous function of the field with which to operate. 

 From this point of view, Poynting's theorem, expressing the radiant vector in 

 terms of the strength of the electric and magnetic fields, still has a meaning, 

 although a purely mathematical one. 



A difficulty in connection with the conception of the existence of energy in 

 free space independently of matter arises when we consider the absorption of 

 energy by matter. If matter and energy are independent entities of different kinds, 

 it is impossible to conceive of their having any effect upon each other. But 

 matter does acquire energy ; therefore energy cannot be an entity existing inde- 

 pendently of matter. 



§3. On the Different Types of Electrical Oscillators. 



Electrical oscillators as they occur in nature are of many different forms. 

 The best known of all of them, the Hertz oscillator, consists of two conducting 

 spheres connected by a conducting rod. In such an oscillator, to a first approxi- 

 mation, the capacity of the system can be taken as equal to one half of the 

 capacity of one of the spheres, and its inductance to that of the rod. The time 

 rate of radiation of energy from a Hertz oscillator is given by the formula 



dW 2 d?(el) 



fc 



2 > 



dt w dt 



where W is the energy of the oscillator, c is the velocity of light, e is the charge 

 on one sphere, and I is the distance between the spheres. The product of e and I 

 is called the electric moment of the oscillator. The rate of radiation of energy by 

 a Hertz oscillator is therefore proportional to the acceleration of its moment. 



Planck 1 and Lorentz 2 have based their electrical theories of radiation solely 

 upon an electronic oscillator of this type. The Hertz oscillator is, however, only 

 one of a large number of different types of oscillators. There are oscillators tha 

 are entirely closed ; there are those that are partially closed, such as are f orme 

 by the plates of a condenser; there is the linear oscillator, the spherical oscillator, 



Planck, Warmestrahlung. 



H. A. Lorentz, The Theory of Electrons 



