Maintenance of the Sun's Heat. 463 



tions, the aether/ according to our hypothesis/ being constituted 

 like air of given temperature. But the mode of its application 

 is in some respects different, as we shall presently see, in the 

 theory of the sun's heat. 



Reverting now to the mathematical theory of heat above 



referred to, it is first to be noticed that, according to that theory, 



the constituent atoms of substances are kept apart by a repulsion 



due to the dynamical action of vibrations reflected from their 



spherical surfaces. It is there shown mathematically that such 



vibrations propagated in the directions of the produced radii of 



an atom, and impinging on a neighbouring atom, may cause a 



permanent motion of translation of the latter, repelling it from 



the other. It is not, however, this effect that we are at present 



concerned with. We have rather to consider what modifications 



the impinging undulations are subject to in consequence of the 



inertia and constant spherical form of the atom on which they 



are incident. We will suppose that the undulations propagated 



from the first atom (without at present considering how they 



may have originated) are alike in all directions from its centre; 



in which case the velocity V and condensation a- at the time t 



and at the distance r from the centre are given by the known 



equations, 



V_f{r — Kat-\-c) f(r- K at + c) 



Kaa=. 



_f l (r-/cat + c) 



r 



Assuming generally that 



fir- teat + c) 1 V T . 2tt, "1 

 p — J5T ^\msm — (r-Kat + c)J 9 



we have also 



f'(r—tcat + c) 1 v r27rmr 2tt , 1 



~ T =^'\~ }r cos-(r- f cat + c)]. 



Since it may be inferred from experimental facts that the 

 radius of an atom must be very small compared to the mean in- 

 terval between adjacent atoms, and also that this mean interval 

 is very small compared to the values of X for waves of light and 

 heat the above expressions prove that the first term of the value 

 ot V has an extremely small ratio to the other at the surface of 

 the atom from which the waves radiate, and also a very small 

 ratio at the surface of the atom on which they impinge. 



This being premised, let us now consider the modifications 

 which the waves defined by the above equations undergo on en- 

 countering the adjacent atom, with especial reference to the 

 secondary waves which the presence of the atom eives rise to- 



212 



