Discontinuity in the Phenomena of Radiation 67 



molecular hypothesis, as a group of discrete particles, there is an 

 upper limit to the number of such types of motion, viz., the 

 number of particles itself. Be that as it may, we have the concept 

 of a string which may vibrate in certain simple fundamental 

 ways with frequencies which progress in the ratio of the whole 

 numbers. Thus if the fundamental vibration has a frequency 

 / times per sec, the others are 2/, 3./J 4/, etc. up to the limit 

 prescribed by the structure of the string. Any vibration of the 

 string, however complex its nature, can be considered as the sum 

 of a number of their simple vibrations, each one with an appropriate 

 amplitude or intensity. Hence these simple types of vibration 

 constitute the " degrees of freedom " of the string, and you will 

 observe that there are exactly n degrees of freedom whose 

 frequencies are not greater than n times that of the fundamental, 

 that is, the number below a certain frequency is proportional to 

 that frequency. Now let us make a further step. Consider a 

 stretched skin in the form of a square, instead of a string ; it has 

 also certain simple types of vibration which may be roughly 

 considered as a blend of those belonging to all the strings which 

 we could cut out of the skin by lines parallel to one pair of sides 

 with those belonging to strings cut out by lines parallel to the 

 other pair. This blending makes the total number of such 

 simple types, i.e., of degrees of freedom, whose frequencies are 

 not greater than a certain frequency to be proportional to the 

 square of that frequency. Finally, if we consider a cubical lump 

 of elastic material, its fundamental mode of vibration and all the 

 simple types constituting its " overtones " are a blend of three 

 sets of linear types, and it appears that the number of all the 

 simple types whose frequencies are not greater than a given 

 frequency is proportional to the cube of that frequency. Now, it 

 is this lump of elastic material which we are to take as our model 

 of the ether. The finite volume of ether enclosed within the 

 constant temperature walls is at any moment in a definite state 

 of agitation following on the transmission of vibrations through 

 it from the walls of the enclosure. This state of agitation is the 



