66 Mr. James Rice on 



elegant mathematical dress upon them, turned away somewhat 

 from such hard and fast physical ideas of radiation. Instead he 

 developed a system of equations based essentially on electro- 

 magnetism, which he claimed had to be satisfied by the par-ticular 

 physical property in the ether whose periodic variation accom- 

 panies the transmission of energy through space. Despite this 

 fact, his methods are quite consistent with the notion that a 

 finite body of the ether can possess degrees of freedom, and that 

 the average energy of any volume of the ether can be calculated 

 in a manner analogous to the calculations carried out for ordinary 

 matter. Furthermore his equations, whose importance in the 

 Physics of the last fifty years cannot be overestimated, are based 

 on the truth of Newtonian Dynamics, and ultimately involve an 

 equipartitioning of energy among the various degrees of freedom 

 of the ether iust as the Lagrange-Hamilton equations involve it 

 for the molecules of matter. The idea of degrees of freedom is 

 difficult enough for the non-mathematician to grasp in the case 

 even of such a tangible thing as solid matter. In the case of 

 the ether it appears very elusive indeed. It will perhaps be 

 best to illustrate by the older view of ethereal movement ; at all 

 events the conclusions are consistent with those developed by 

 means of Maxwell's equations. Consider a string stretched 

 between tAvo points. Such a string is capable of many ways of 

 simple vibration, several of which I illustrate by these drawings 

 on the board. First, it may vibrate as a whole between the 

 indicated forms ; then it may vibrate in two halves with 

 the middle point always at rest. It is kiiown that the frequency 

 of vibration of any point on the string is in the latter case double 

 what it is in the former, i.e., double the fundamental frequency. 

 Then it may vibrate in three different segments, with two 

 "nodes," and a frequency three times the fundamental; and so 

 on. Theoietically there is no limit to this exact division of the 

 string into so many parts with an accompanying simple type of 

 vibration, if we regard the string as a perfectly continuous piece 

 of matter. If, however, we regard it, as we must do on the 



