Mr. R. Moon on the Undnlatory Theory of Interference. 83 



done had it not been diffracted. Hence it can only be as a 

 physical fact, not as a dynamical principle, that this objection 

 can be urged. And taken in this point of view it can simply 

 amount to this, that in vacuo all spherical waves are originally 

 propagated with the same velocity, and that when unobstructed 

 such velocity will remain invariable, both which propositions 

 we admit in their fullest extent ; but this does not imply that 

 every possible variety of wave motion must be propagated with 

 uniform velocity (which in fact is perfectly incredible), and 

 until some proof to the contrary be given we shall consider 

 ourselves justified in assuming the case of broken or diffracted 

 waves to be an exception to the principle. 



The possibility of a change of form being once admitted, 

 it is easy to imagine how waves of the same length, but which 

 differ in the relative condensation and rarefaction of their 

 several parts, may effect such change with different degrees of 

 rapidity ; for the change of form depends entirely on the late- 

 ral extension of the waves, which in its turn must depend on 

 the degree of condensation and rarefaction of their different 

 parts. 



If, then, we have two such waves propagated at a short in- 

 terval from each other, the first of which is more retarded by 

 the diffraction than the second, they will ultimately intersect, 

 and so (the waves being nearly parallel) interference will be 

 produced. It is true that the intersection must take place at 

 a finite distance from the edge of the diffracting body, but it 

 is easy to suppose that this may be so small as to be inappre- 

 ciable by our senses. It is also evident that, as the waves will 

 continue to change their forms as they advance beyond the 

 object, the locus of their intersections will not be a straight 

 line, but will tend continually to diverge from the geometrical 

 shadow, and this divergence will constantly diminish as the 

 waves advance (since the relative change of the two fronts 

 with respect to each other must constantly diminish), and will 

 ultimately become insensible. Thus the line of interference 

 will approximate to the hyperbolic form. 



If the first two waves are followed by a third at about the 

 same interval from the second as the second is from the first, 

 and nearly the same relation obtain between the second and 

 third as between the first and second, the locus of the inter- 

 section of the second and third will nearly coincide with the 

 locus of intersection of the first and second, but the intersec- 

 tion of the first and third will take a different path, and thus a 

 second line of interference will occur. Also, this second line 

 of interference will lie without the first, for they must both 

 have the same sensible origin ; and as the relative change of 



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