328 The Rev. Professor O'Brien on the 



Prof. MacCullagh has clearly shown that this statement must 

 be received with considerable limitation. On the whole I 

 think we have good reason to doubt the correctness of the 

 ^rst of the above hypotheses, both on the a priori ground 

 above stated, and because it appears to be capable of account- 

 ing for little more than the dispersion of light. 



5. The second hypotheses has not yet been taken up by any 

 writer upon physical optics, so far as I am aware, but it is de- 

 cidedly worthy of attention and leads to several important re- 

 sults. The object of the present communication is simply to 

 make a beginning in the application of this hypothesis to the 

 explanation of optical phasnomena, and to show that it may 

 possibly prove of much service in advancing the undulatory 

 theory of light. 



Let us suppose then that the amplitudes of the sethereal vi- 

 brations are large compared with the intervals between the 

 particles of transparent substances, and that consequently the 

 motion of each element of the aethereal fluid is resisted by 

 forces (the reactions of the material particles) which have this 

 peculiarity, that they depend simply upon the state of motion 

 of the element, but not upon its displacements from its equi- 

 librium position. 



6. Before we proceed, however, it will be necessary to make 

 a few general remarks upon the nature of resistances, reserving 

 mathematical details for a future communication. 



It is commonly assumed that, when a spherical particle 

 moves in a resisting medium, the force of resistance, at any 

 time, is a function simply of the velocity at that time, and acts 

 in a direction opposite to that of the motion. This must un- 

 doubtedly be true when the motion is uniform and rectilineal, 

 and very nearly true when the curvature of the path of the 

 particle is not great, and the variations of the velocity are 

 small compared with the velocity itself. But in general the 

 magnitude and direction of the resistance at any instant must 

 depend upon the magnitude and direction, not only of the ve- 

 locity at that instant, but also of the velocities with which the 

 particle was moving during a certain interval preceding that 

 instant. In other vi'ords, the magnitude and direction of the 

 resistance at any time must in general depend, not only upon 

 the velocity, but also upon the differential coefficients of the 

 velocity with respect to the time, and upon the curvature of 

 the path of the particle. The truth of this statement is mani- 

 fest from the fact, that the impulse given to the medium by 

 the particle at any instant produces more or less motion in the 

 medium, which must in some degree affect the subsequent 

 motion of a particle. We may not therefore assume that the 



