6$ Prof. Max Planck : New Paths 



ways highly surprising results have been obtained. To heat 

 a piece of copper from —250° to —249°, i. e. by one degree, 

 we do not require the same quantity of heat as for heating- 

 it from 0° to 1°, but a quantity about thirty times less. If 

 we took the original temperature of the copper still lower, 

 the corresponding quantity ol heat would turn out many 

 times smaller, without any assignable limit. This fact not 

 only runs counter to our habitual ideas, but also is out of 

 harmony with the demands of the Classical Theory. For 

 although for more than 100 years we have learnt to dis- 

 tinguish between temperature and quantity of heat, yet we 

 were led by the Kinetic Theory of Matter to suppose that 

 these two quantities, even if not strictly proportional to each 

 other, preserved at all events a sensibly parallel course. 



The Quantum Hypothesis has entirely cleared up this 

 difficulty, and in addition has yielded another result of high 

 importance, viz. that the forces controlling the thermal oscil- 

 lations in a solid body are of the same kind as those which 

 control its elastic oscillations. With the help of the Quantum 

 Hypothesis, therefore, we can now calculate quantitatively 

 the thermal energy of a monatomic substance at various 

 temperature?, from its elastic properties, — a performance 

 which was far beyond the reach of the Classical Theory. 

 Hence arise a number of further questions which appear 

 verjr strange at first sight, — for instance, whether perhaps the 

 vibrations of a tuning-fork are not absolutely continuous 

 but are broken up into quanta. It is true that in acoustic 

 vibrations the energy quanta will be extremely small, on 

 account of their relatively low frequency. Thus, in the 

 middle a, they would amount to only 3 quadrillionths of a 

 unit of work in absolute mechanical measure. It would be 

 just as little necessary to alter the Theory of Elasticity on 

 that account as on account of the quite analogous circumstance 

 that it treats matter as perfectly continuous, whereas it is 

 really constituted atomistically, i. e. according to quanta. 

 But fundamentally the revolutionary aspect of the new con- 

 ception must be clear to everybody ; and although the nature 

 of dynamical quanta still remains somewhat puzzling, yet, 

 in view of the facts now known, it is difficult to doubt their 

 existence, in some form or other. For whatever we can 

 measure must exist. 



Thus in the light of recent investigation, the Physical 

 representation of the Universe exhibits an ever more intimate 

 correspondence between its various features, and also mani- 

 fests a certain peculiar structure whose refinement was 



