20 Prof. W. M. Thornton on the 



If they approach out of line in parallel paths and cohere, 

 the whole of their translational energy is converted into 

 rotational energy (an irreversible process in combustion), 

 and the molecule spins about the point of contact. In the 

 case of oblique incidence we may resolve into two com- 

 ponents and consider the energies before and after contact. 



Fig. 1. 



Before contact the total energy of each sphere is \{mv 2 + Io> 2 ), 

 I being its moment of inertia. The translational energy of 

 A parallel to B is J mv 2 sin 2 6 ; so that in union each sphere 

 loses by this amount, for this is the component causing 

 rotation about the point of cohesion. The total rotational 

 energy of the two before collision is Io> 2 ? after collision it 

 may reach Lo 2 + mv 2 sin 2 6. The mean value of sin 2 # is J ; 

 thus, since Ia> 2 was taken to be equal to mv 2 , the rotational 

 energy of the doublet formed is at most 1^ times the rota- 

 tional energy of its component before collision. 



The translational energy is before collision mv 2 ; afterwards 

 it is ^mv 2 (l — sin 2 0)+^mv 2 cos 2 0, for B loses a part of its 

 translational energy in combining with A and the vertical 

 component of the latter is unchanged. This expression is 

 equal to mv 2 cos 2 0, and in the mean to \mv 2 . Thus the 

 ratio of the total translational energy after collision (to 

 which the pressure of the gas is proportional), to that 

 immediately before collision is J; in other words, the resulting 

 pressure is only one half of that which would be obtained if 

 no new molecules were formed. The argument holds for com- 

 bining atoms of unequal mass, but with the same energy of 

 translation, as for example hydrogen and oxygen in complete 

 mixture. 



This excess of rotational over translation energy is not 

 permanent and is more or less rapidly equalized to pressure 

 and radiation ; but there is no experimental evidence other 

 than that derived from the velocity of an explosion wave, to 

 show its actual duration. The conditions in a travelling- 

 explosion wave are somewhat different from the explosion 

 at constant volume under consideration. Dixon has shown 



