28 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



sheets one over another, and proportional to the amount of the displacement of sliding. There 

 is no occasion to enter into any speculation as to the cause of this tangential force, nor to 

 entertain the question whether the luminiferous ether consists of distinct molecules or is mathe- 

 matically continuous, just as there is no occasion to speculate as to the cause of gravity in 

 calculating the motions of the planets. But we are absolutely obliged to suppose the existence 

 of such a force, unless we are prepared to throw overboard the theory of transversal vibrations, 

 as usually received, notwithstanding the multitude of curious, and otherwise apparently inex- 

 plicable phenomena which that theory explains with the utmost simplicity. Consequently we 

 are led to treat the ether as an elastic solid so far as the motions which constitute light are 

 concerned. It does not at all follow that the ether is to be regarded as an elastic solid when 

 large displacements are considered, such as we may conceive produced by the earth and 

 planets, and solid bodies in general, moving through it. The mathematical theories of fluids 

 and of elastic solids are founded, or at least may be founded, on the consideration of internal 

 pressures. In the case of a fluid, these pressures are supposed normal to the common surface 

 of the two portions whose mutual action is considered : this supposition forms in fact the 

 mathematical definition of a fluid. In the case of an elastic solid, the pressures are in general 

 oblique, and may even in certain directions be wholly tangential. The treatment of the 

 question by means of pressures presupposes the absence of any sensible direct mutual action of 

 two portions of the medium which are separated by a small but sensible interval. The state 

 of constraint or of motion of any element affects the pressures in the surrounding medium, and 

 in this way one element exerts an indirect action on another from which it is separated 

 by a sensible interval. 



Now the absence of prismatic colours in the stars, depending upon aberration, the absence 

 of colour in the disappearance and reappearance of Jupiter's Satellites in the case of eclipses, 

 and, still more, the absence of change of colour in the case of certain periodic stars, especially 

 the star Algol, shew that the velocity of light of different colours is, if not mathematically, at least 

 sensibly the same. According to the theory of undulations, this is equivalent to saying that in 

 vacuum the velocity of propagation is independent of the length of the waves. Consequently 

 the direct action of two elements of ether separated by a sensible interval must be sensibly 

 if not mathematically equal to zero, or at least must be independent of the disturbance; for, 

 were this not the case, the expression for the velocity of propagation would involve the length 

 of a wave. An interval is here considered sensible which is comparable with the length of a 

 wave. We are thus led to apply to the luminiferous ether in vacuum the ordinary equations 

 of motion of an elastic solid, provided we are only considering those disturbances which con- 

 stitute light. 



Let us return now to the case supposed at the beginning of this section. According to the 

 preceding explanation, we must regard the ether as an elastic solid, in which a series of 

 rectilinear transversal vibrations is propagated in a direction perpendicular to the. plane P. 

 The disturbance at any distance in front of this plane is really produced by the disturbance 

 continually transmitted across it ; and, according to the general principle of the superposition 

 of small motions, we have a perfect right to regard the disturbance in front as the aggregate 

 of the elementary disturbances due to the disturbance continually transmitted across the 



