580 Br. G. Johnstone Stoney on 



is a complex one it may be resolved in various ways, into 

 simpler fields. In order that the resolution may be entitled 

 to be called a physical resolution, all the dynamical conditions 

 of the problem must be complied with. These include the 

 general dynamical conditions of motion, along with the 

 numerous special conditions which arise out of the definite 

 kind of physical causes that operates within the medium with 

 which we are dealing. The most useful of the general con- 

 ditions are the three following : — 



1. Each component field must be a solution of the funda- 



mental equation, which in the present case is 

 equation (9). 



2. The sum of the energies of the components must be 



equal to the energy of the complete event that is to be 

 resolved. 



3. The equation of Least Action must be complied with. 



Each of these is available as a criterion of physical resolu- 

 tions, being in so far a criterion that its not being true of any 

 given resolution demonstrates that this resolution is not a 

 physical resolution. By a physical resolution of one of the 

 complex fields that may result from a differential equation is 

 to be understood one in which, if some of the components 

 were absorbed, shifted aside, or in some other way withdrawn, 

 the others w^ould continue unchanged. A good example of a 

 physical resolution is the resolution of white light into its 

 various colours. This is a resolution which can be effected 

 by natural processes none of which need to import energy 

 into the system : indeed some (those which act by absorbing 

 some of the colours) withdraw energy from it. 



29. In the statement of the second condition it is essential 

 to insert the word " complete," inasmuch as what equation (9) 

 represents is the operation of physical causes inherent in the 

 medium, which are competent without external aid to propa- 

 gate undulations forward without loss of energy or change 

 of velocity. Now, a medium which fulfils the necessary 

 conditions completely will be a uniform medium subjected to 

 the following conditions : — 



A. It must not be acted upon by external sources of light 



or absorbers of light. 



B. It must not be subjected to boundary conditions, and 



will therefore be of unlimited extent. 



C. It must not emit or absorb light, but merely transmit 



it. 

 It is only in a medium which completely fulfils these con- 

 ditions that the progress of events will be in exact accordance 



