350 Lord Rayleigh on Light dispersed from 



than near the critical point, that is under conditions such that 

 the repulsive forces have just overcome the attractive forces 

 which hold the molecules in their places in the solid or 

 crystalline structure. 



The assumption of a co-volume, that is a space in which 

 the molecules as such are moving, does not seem to be at all 

 necessary so far as the additive relations are concerned. 

 Traube's theory is based upon this conception of liquid 

 structure, and since an unnecessary complication is thereby 

 introduced, it ceases to be significant. 



Municipal School of Technology, 



Victoria University, 



Manchester. 



XXX. On the Light dispersed from fine Lines ruled upon 

 Reflecting Surfaces or transmitted by very narrow Slits. By 

 Lord Rayleigh, O.M., Pres. R.S* 



THE problem of the incidence of plane waves upon a 

 cylindrical obstacle, whose radius is small in comparison 

 with the length of the waves and whose axis is parallel to 

 their plane, is considered in ' Theory of Sound,' § 343, also 

 Scientific Papers, iv. p. 314 ; but it is now desired to carry 

 the approximation further and also to make some applications. 

 On the other hand, we shall confine ourselves to the cases of 

 perfect reflexion where the boundary conditions are simplest. 

 The primary waves, travelling in the negative direction, 

 are represented by <j}=ze ik ^ ai+ *^, where a is the velocity of 

 propagation and k = 2tt/X, X being the wave-length. Dropping 

 the time-factor for brevity, we shall write 



(b = e ikx = e ikrcose = J (kr) + 2i J 1 (kr) cos 



+ ....+ 2i n J n {kr) cos nd + . . ., . . (1) 



J n being the Bessel's function usually so denoted, so that 



z n r £ 2 



J *( z ) = "2»r(n + 1) V~2(2n+2) 



+ 2.4=(2n + 2)(2n + 4) ""■'•/• ' ( 2 ) 



In (1) x and r are measured from the centre of the section 

 of the cylinder, whose length is supposed parallel to the axis 

 of z. 



* Communicated by the Author. 



