298 THE REALITIES OF MODERN SCIENCE 



The total energy possessed by the oscillators of one 

 mole of a substance will then depend upon their 

 natural frequencies, upon the number of molecules 

 in the mole, A 7 ", and upon the absolute temperature, T. 

 As the temperature is changed the energy changes 

 and the ratio of the change in energy to the change in 

 temperature is, of course, the specific heat. In terms 

 of h, /, N, and T both the average energy and the 

 specific heat l have been expressed by Einstein. These 

 formulae do not give calculated values of the specific 

 heat exactly in accord with the experimental values, 

 although the agreement is sufficient over a wide range 

 of temperatures to indicate that in the concepts of 

 energy quanta and of electronic oscillators, scientists 

 have much more than a hopeful clew to follow in their 

 study of matter and energy. Some modifications of 

 Einstein's equation have been suggested which adapt 

 it more nearly to the observed facts as to the specific 

 heat of solids, but these we shall not consider. 



To apply such a formula it is necessary to have 

 numerical values for h and /. The value of Planck's 

 constant, h, has been determined several times and is 

 fairly accurately known, as we shall see in the suc- 

 ceeding chapter. As to the frequency, /, of the natural 

 oscillation it should be noted that in general there would 

 be more than one natural frequency. (The total 



of external influences to dissipate the energy contributed to it in 

 producing the displacement. The opposite of a " natural ' ' vibration 

 is a "forced" one. A violin string when bowed receives energy and 

 vibrates at its natural frequency, but the drum of the ear of the 

 listener undergoes a forced vibration. 

 1Thn . r -O 



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