208 Prof. Challis on a Mathematical Theory of Heat. 



to the condensation at the other as tt- to -777, thatis^ as r^ to r'^, 



or as R2 to R'^. Hence, however small may be the condensa- 

 tion propagated from a single atom, the resulting condensation 

 from an aggregation of atoms in a spherical volume may be of 

 sensible magnitude at finite distances from the centre, if the 

 number of atoms in a given space be very great. The dynami- 

 cal effect of these compound waves on a given atom may be in- 

 vestigated in the same manner as the effect of the secondary 

 waves propagated from a single atom ; and a motion of transla- 

 tion will be found to result as before. But it is evident that 

 according to the distribution of the condensation about the 

 atom, resulting from propagation along its surface, the motion 

 of translation may either be from the centre of the waves, or be 

 neutralized by equality of the pressures on the two hemispheres, 

 or be towards the centre by an excess of pressure on the further 

 hemisphere. The full consideration of these cases I reserve for 

 a future opportunity. At present it will suffice to say that in 

 this manner it is conceivable that while the individual atoms 

 are repulsive to each other, an aggregation of atoms may give 

 rise to a controlling attraction. 



The last inference is important, on account of its bearing on 

 a theory of the different physical states of substances. A body 

 in a state of soliditij has an energetic attraction of aggregation ; 

 in liquids this attraction is only feebly in excess of the atomic 

 repulsion j and in gases, the atomic repulsion is in excess, the 

 density being small, and is controlled by some extraneous attrac- 

 tion, as that of gravity. In gaseous masses of great magnitude, 

 such as the atmospheres of comets appear to be, the solar rays 

 may produce a vast accumulation of heat by successive orders of 

 internal reflexions ; and it would be quite in accordance with this 

 theory if, under these circumstances, an attraction of aggregation 

 were generated sufficient to control the atomic repulsion. I 

 have, in fact, shown, in a communication recently made to the 

 Cambridge Philosophical Society, that most of the phsenomena 

 of Donati's comet, and in particular the production and direction 

 of the tail, admit of explanation on this hypothesis. 



Again, it may be remarked that the atomic repulsion from a 

 single atom of an aeriform substance may be nearly independent 

 of the density, on account of the comparatively large intervals 

 between the atoms. But in the case of liquids or solids, the 

 much greater proximity of the atoms to each other may give rise 

 to successive orders of reflexions, which would cause the inten- 

 sity of the compound waves reflected from a given atom to be 

 dependent on the number of atoms in a given space. In fact, a 

 difference between aeriform bodies and fluids or solids in this 



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