84 Mr. J. H. Jeans [March 80, 



covering the case of slow vibrations, the formula is of unit value, and 

 the partition is one of equality ; on the other hand, the formula 

 shows that vibrations of high frequency get no energy at all, so that 

 here we get the extreme case of failure of the law of equipartition. 

 It is extremely important for us that the theorem does fail in this 

 way, because if all the heat energy in the Avorld were to distiibute 

 itself equally over all the degrees of freedom in the world, as 

 required by the theorem of equipartition of energy, everything would 

 become frozen and dead within a small fraction of a second. 



Although the view has been opposed in the ])ast, there is now, I 

 think, no room for doubt that the failure of the theorem of 

 equipartition of energy must be interpreted in the most obvious and 

 direct way. The theorem is true subject only to the assumption that 

 the motion is governed by Newton's laws ; as a matter of experiment 

 the theorem is found' not to be true of high-frequency viljrations ; 

 therefore the motion of high-frequency vibrations is not governed 

 by Newton's laws. We must search for a new system of dynamical 

 laws which shall give the observed partition of energy. 



The formula xjie'' — 1), which is believed to give the true 

 partition of energy, was originally deduced by Planck from theoretical 

 considerations ; but the underlying conceptions were of such a strange 

 and novel nature that at first they gained but little credence. But 

 when the law of partition is known, it becomes merely a mathematical 

 problem to discover what laws of motion will result in this law of 

 partition. In 1911 I sliowed that this law of partition could only 

 result from laws substantially identical with those already assumed by 

 Planck. Shortly after, Poincare announced the same result, with 

 the important addition that the main nature of the laws would not be 

 altered by a slight variation in the observed law of partition. Planck 

 had assumed that energy was transmitted not by continuous processes 

 but by a system of jumps and jerks. It appears that the mere fact 

 that the energy is not divided equally among the different vibrations 

 is sufficient to show that there must be discontinuities of some kind 

 in the fundamental laws of motion. The particular type of discon- 

 tinuity which is found necessary to lead to the observed formula 

 xjif — 1) is expressed by Planck's equation 



e= llv. 



Here li is the same constant as occurs in the value of a*, v is the 

 frequency of the vibration in question, and e, equal to hv, is found 

 to be of the same physical dimensions as energy, and may be spoken 

 of as the "quantum" of energy associated with a vibration of 

 frequency v. The law of discontinuity is such that the vibration can 

 only gain or lose energy by whole quanta. Thus a vibration of 

 frequency v may have no energy at all, or one quantum, or two 

 quanta, but cannot for instance have half a quantum or \\ quanta — 

 the energy changes by discontinuous jumps. 



