o 



8 M. A. J. Angstrom on the Fi°aunhofer-lines 



nexion with the molecular phenomena of bodies, and it would 

 seem that the hypothesis, that thermometric heat belongs ex- 

 clusively to the body's own molecules, is unavoidable. 



§ 5. The question then becomes, What is the nature of that 

 oscillatory motion that constitutes thermometric heat? By a discus- 

 sion of the differential equations that obtain for wave-motion in 

 general, we easily arrive at the conclusion, that the molecular 

 elasticity of a medium cannot be sufficiently great to allow that 

 medium to assume an undulatory motion in which the periods 

 of oscillation are so short as those of light and heat. The 

 lengths of the waves would be so small as to be equal to, or at 

 least comparable with, the distances of the molecules, and in 

 that case no undulation is possible. In the case of one medium 

 in which we can observe the periods of oscillation, namely, the 

 case of the vibrations of sound, these periods are millions of 

 times greater than those of light and heat. 



If we assume, then, that thermometric heat consists in a motion 

 of the pendulum kind in the smallest constituent parts of the 

 body, and deduce the differential equations for these motions, we 

 obtain equations of the same kind as those which occur in the 

 theory of the secular perturbations of the planets, and, for de- 

 termining the time of an oscillation, we arrive at an equation 

 the degree of which is expressed by three times the number of 

 molecules within the sphere of attraction, and the roots of which 

 are real. The form of these differential equations, which obtain 

 for molecular oscillatory motion, must, however, be independent 

 of the external force whereby the particles are set in motion, 

 whence we may infer that the nature of the heat must be inde- 

 pendent of its source, and dependent exclusively on the body's own 

 molecular forces. It must be independent even of the body's 

 form and magnitude, provided the latter be greater than the 

 extent of the molecule's sphere of attraction. 



The number of vibratory motions possible is thus three times 

 the number of molecules contained within the sphere of attrac- 

 tion. It does not necessarily follow from this that all these dif- 

 ferent kinds of oscillatory motions always simultaneously exist 

 in the body, any more than that a sounding body should simul- 

 taneously assume the whole series of tones that can possibly be 

 produced from it. 



"When, however, the number of molecules within the sphere 

 of attraction is sufficiently great, the body ought, at a glowing 

 heat, to display a continuous spectrum, as is really in general the 

 case with solid bodies. That gases in general exhibit a discon- 

 tinuous spectrum is, according to our view of the nature of heat, 

 owing to the circumstance that there are but few molecules 

 within the sphere of attraction. 



