Discontinuity in the Phenomena of Radiation 69 



as ordinary matter. The frequencies cori^esponding to X-rays 

 are of the order 3 trillions per sec. 



To avoid much use of algebraic symbols let me make use of 

 graphical methods. The curve which I draw on the board is to 

 be interpreted thus. Lengths along the horizontal axis ai-e to be 

 considered as proportional to frequencies, so that a point on this 

 axis indicates a definite frequency. The lines drawn up from two 

 such points enclose with the axis and the curve a quasi-rectangu- 

 lar area. Now the curve is so drawn that this area is propor- 

 tional to the number of degrees of freedom in, say, 1 c.c. of the 

 ether whose frequencies lie between the limits indicated by the 

 two points. The area bounded by the curve and the axis up to 

 a particular vertical line is proportional to the cube of the length 

 along the axis up to this line, which agrees with the 

 rule concerning the number of degrees of freedom of the 

 ether mentioned above. The curve as a matter of fact 

 is a very well-known one, being a parabola. If we are then to 

 partition the energy of the ether in a constant temperature 

 enclosure equally between all the degrees of freedom, it follows 

 that the quasi-rectangular strips may be taken to be also propor- 

 tional to the amount of energy in the ether corresponding to 

 vibrations with frequencies between the limits indicated by the 

 two points ; and the whole energy in the ether is to be propor- 

 tional to the whole area under the curve up to the point 

 corresponding to the maximum frequency possible if we choose to 

 impose such a limit which, as I have stated, must be in the 

 trillions at least. Well, this conclusion is absolutely contradicted 

 by facts. It is possible to determine what is the partitioning of 

 the energy among the frequencies. A hollow vessel is maintained 

 at a steady temperature (by electric heating if the temperature is 

 very high). A small hole is opened in its wall, which permits 

 some of the radiation to emerge. This radiation is a fair sample 

 of that existing inside the vessel and can be analysed in the usual 

 way. It is known that this radiation, " full radiatio\i " as it is 

 called, is independent of the material of the walls so long as these 



