on the Undulatory Hypothesis of Light. 471 



matical Theory of Attractive Forces" contained in the Philosophi- 

 cal Magazine for November 1859), it will suffice for the present 

 purpose to say that it must be symmetrically distributed about 

 a straight line drawn in the direction of propagation through the 

 centre of the atom, that, in the case of waves of the magnitude 

 of those with which we are concerned in phenomena of light, the 

 excess of condensation, or rarefaction, is always on the hemisphe- 

 rical surface on which the waves directly impinge, and that this 

 excess is proportional to the incident condensation or rarefaction. 

 Hence the atom is continually urged in the direction of propa- 

 gation by a force which, to the degree of approximation with 

 which we propose to conduct this research, is proportional to the 

 condensation, and consequently to the velocity of the incident 

 waves. We will suppose this force to be 



£msin — - (bt— x + c) } 



A. 



b being the velocity of propagation in the diaphanous medium. 



In the foregoing reasoning it has been assumed that the atoms 

 of the medium are absolutely fixed. But according to our hypo- 

 thesis of the atomic constitution of bodies, the atoms are retained 

 in positions of stable equilibrium by the action of attractive and 

 repulsive forces. They will consequently be susceptible of move- 

 ment by the action of any extraneous force. This mobility of 

 the atoms will plainly have an effect on the amount of their re- 

 tardation of the movements of the setherial waves. For the com- 

 plete investigation of this retardation we ought, consequently, to 

 be acquainted with the laws and modes of action of the forces 

 which keep the atoms in equilibrium. The Theory of Molecular 

 Forces, of which I have explained the principles in the Philoso- 

 phical Magazine for February 1860, might, if fully carried out, 

 furnish these data. The present investigation will, however, be 

 conducted so as not to require a precise knowledge of the laws 

 of molecular forces, but only the admissible assumption that, as 

 each atom is acted upon by equilibrated forces, it will be put in 

 motion by the addition of the luminous undulations. We must 

 now endeavour to obtain on this assumption a mathematical ex- 

 pression for the velocity of each atom, in order to ascertain the 

 effect of the mobility of the atoms on the rate of transmission of 

 the waves. 



We have already found, for the case in which the atoms are 

 fixed, the expression 



km sin -— (bt — x + c) 



A, 



for the accelerative force, due to the action of the waves, by 

 which an atom at the distance x from a fixed plane is urged in 

 the direction of the propagation. If the atom be moving with 



