Explanatory Notes 115 



physical ratios by any actual number, the author's text- 

 book of Arithmetic and Algebra for General Readers, 

 called Easy Mathematics (Macmillan), may be referred to, 

 in chapter xx and elsewhere. 



Page 26 



By the "degrees of freedom" of a body are meant the 

 independent modes of motion of which it is susceptible. 

 A rigid body has six degrees of freedom, which can be thus 

 enumerated: a translation or locomotion in each of three 

 directions, the three dimensions of space, up and down, to 

 and fro, right and left; and three rotations, viz., rotation 

 about each of these three directions considered as axes. 

 A particle however meaning a body of no size has only 

 three degrees of freedom; it can only move in the sense of 

 locomotion, it cannot spin ; or rather it may spin as much as 

 it likes and no one will care, its spinning will consume no 

 energy. A perfectly smooth sphere is in much the same 

 predicament; while a smooth dumb-bell has five degrees of 

 freedom, one of its rotations being ineffective. But a tun- 

 ing fork, or body susceptible of vibration, has many^ore 

 degrees of freedom than a rigid body can have; and inas- 

 much as molecules appear susceptible of vibration, as 

 evidenced by the spectra they emit, it might be supposed 

 that during their ordinary mutual collisions in a perfect 

 gas many of these vibratory movements would be called 

 out and take part in the action. If so, they would be 

 entitled to some of the energy. Indeed a mechanical 

 theory of Clerk Maxwell's proves that after a great number 

 of prefectly random collisions all the energy imparted to a 

 group of similar bodies will be equally shared, on an aver- 

 age, among all the degrees of freedom which they possess 

 (strictly speaking, among all the degrees of freedom which 

 are effective during collision). If, therefore, a given 

 quantity of energy, say heat, is imparted to a gas, it might 



