(22). 



186 Lord Kelvin on the Reflexion 



for trie present take the case of no interfacial slip, that is, equal 

 values of g, 7] on the two sides of the interface. Remarking 

 now that the argument of /for every one of the five waves is 

 t — ax where y = 0, we see that the condition of equality of 

 displacement on the two sides of the interface gives the 

 following equations : — ■ 



6(1-1') +oJ / =& / I / + aJ i TJ 



a (I + 1') + c J' = al J — c l J l f 



§ 12. As to the force-conditions at the interface, I have 

 already given, for ordinary elastic solid or fluid matter * on 

 the two sides of the interface, a complete solution of the 

 present problem in my paper f "On the Eeflexion and 

 Refraction of Light " in the ' Philosophical Magazine ' for 

 1888 (vol. xxvi.) ; nominally for the case of simple harmonic 

 wave-motion, but virtually including solitary waves as 

 expressed by an arbitrary function: and I need not now 

 repeat the work. At present let us suppose the surface-force 

 on each solid to be that which I have found it must be 

 for ether J, if magnetic force is due to rotational displace- 

 ment of ether, and the lines of magnetic force coincide with 

 axes of rotation of etherial 'substance. According to this 

 supposition the two components, Q (normal) and T (tan- 

 gential), of the mutual force between the mediums, which 

 must be equal on the two sides of the interface, are 



Q=«(f + ?) 



\dx dy) ™ 



\dx dy) '" J \dx dy. 



where k denotes for ether that which for the elastic solid we 

 have denoted by (k +■ fft), and suffixes indicate values for the 

 lower medium. If we begin afresh for ether, we may define 

 n as l/4«r of the torque required to hold unit of volume 

 of ether rotated through an infinitesimal angle us from its 



* The force-conditions for this case are as follows : — 



Normal cooiponent force equated for upper and lower mediums, 



C*-f.)«+a.5=(t -•»>,+*., (J) /S 



and taDg-ential forces equated, 



•ffi+fHS+D.- 



t In that paper B, A, and £ denote respectively the n, the k-\-pi, and 

 the p of the present paper. 

 J See first footnote to § 1. 



