238 Prof. J. H. Jeans on Temperature-Radiation 



replacing R/J by its known value 2 x 10 ~ 2i , we find that X 

 must be of the order of 1*3 X 10 _8 Xo-3. For instance, for 

 water a=l : it follows that the mean distance apart of the 

 molecules of water must be comparable with 1*3 xlO -8 cm. 

 For air at atmospheric pressure, cr = *0002 : it follows that 

 the mean distance apart of the molecules of the atmosphere 

 must be comparable with 2 x 10~ 7 cm. If it were possible 

 to measure the energy of sether in temperature-equilibrium 

 with matter, we could determine the specific heat <7, and so 

 obtain a knowledge of the scale of structure of the sether 

 (ifanyj. 



Examples and Discussion of the "Normal State " in 

 continuous media. 



16. Before passing to further developments of the theory, 

 I have thought it permissible to illustrate the foregoing ideas 

 and concepts by a few mechanical illustrations. 



I. A Stretched String. 



17. Consider a dynamical system of which the kinetic and 

 potential energies are respectively given by 



21=™^^ + ... + ^), (10) 



2V= M {(^-^ f +(^- i *«) , + ..- + (^-^+i) f } 9 • (11) 

 and let n be very great. 



If x , .%, £c 2 , . . . #», # n +i are coordinates of particles con- 

 strained to remain always in the same straight line, the 

 system may be supposed to consist of a series of n + 2 

 collinear particles, each attracting (or repelling) its neighbour 

 according to the law of the direct distance, the two end 

 particles being fixed in position. With a slight change in 

 the meaning of the symbols, the system may be supposed to 

 consist of heavy particles connected by elastic strings. In 

 the limit when n is made infinite, the system will represent 

 a continuous one-dimensional elastic medium, or a stretched 

 string capable of performing longitudinal vibrations only. 



Regarding the system as a collection of particles, the pro- 

 perties of the u normal state " can be seen at once from an 

 examination of the energy-function. The velocities # l9 # 2 , . . . #«. 

 will be distributed according to Maxwell's law 



Ae~ hmu2 du, 



and, when n is infinite, the same can be shown to be true of 

 the differences # — # l5 x± — a: 2 , &c. Thus in the normal state, 



