On a Simplification of the Theory of Vibratory Motions. 57 



build further conclusions on the existence of such selective 

 reflection. I will merely point out that if the reflecting-power 

 of incandescent gases for certain groups of rays is considerably 

 greater than for all others, this will not be without importance 

 for the spectroscopic investigation of heavenly bodies which, 

 like comets for instance, emit partly their own, partly reflected 

 light. If the light of such a body consists of single isolated 

 groups or shows narrower brighter bands on a continuous 

 dark spectrum, we are accustomed, according to our present 

 knowledge, to assume that the light of this discontinuous spec- 

 trum is entirely and exclusively emitted by the body as a self- 

 luminous one. If the body possesses a selective reflecting- 

 power, the above conclusion is not at once admissible. One 

 might even imagine, as the most extreme case, a non-luminous 

 very dense mass of gas in our solar system, possessing selec- 

 tive absorption, and consequently for many separate groups of 

 rays a power of selective reflection. Such a mass, intensely 

 illuminated by the sun, would, without being self-luminous, 

 show a discontinuous spectrum by reflection. 



Strassburgr, March 1880. 



VIII. Remarks on a Simplification of the Theory of Vibratory 

 Motions. By C. Cellerier*. 



THE motions in question are the oscillations of the particles 

 on both sides of their positions of equilibrium — that is 

 to say, those which constitute sound and light. To find their 

 law on the most general hypothesis, the excursions and the 

 molecular velocities at a fixed instant called the initial instant 

 are supposed to be given ; the unknowns are the projections 

 of those excursions upon three rectangular axes at any instant 

 whatever : they are functions of the time and of the position 

 of the particle. 



The equations of the motion are satisfied by taking for each 

 of them a sum of terms of the form a cos p(p — st), in which t 

 is the time, p the distance of the particle from a fixed plane, 

 and a, p, s constants. The motion represented by one of these 

 terms isolated is called a simple motion. 



At the initial instant each of the terms reduces to a cos pp ; 

 and the constants and the fixed plane corresponding to each 

 can be arranged so that their sum shall reproduce the initial 



* Translated from the Archives des Sciences Phtjsiqucs et Naturelles of 

 the Bibliotheque Universelle, June 5, 1880, pp. 549-553, having been com- 

 municated to the Societe de Physique et d'Histoire naturelle of Geneva 

 on June 3, 1880. 



