and Electric Waves upon Small Obstacles. 37 



■ — a term of order 1, to be added to that of zero order 

 given in (46). 



In general, the axis of the harmonic in (54) is inclined to 

 the direction of propagation of the primary waves; but there 

 are certain cases of exception. For example, v and to vanish 

 if the primary propagation be parallel to x (one of the 

 principal axes). Again, as for a sphere or a cube, Aj, B 2 , C 3 

 may be equal. 



We will now limit ourselves to the case of the ellipsoid, 

 and for brevity will further suppose that the primary waves 

 move parallel to x, so that v=w = 0. The terms correspond- 

 ing to u and v, if existent, are simply superposed. If, as 

 hitherto, <f>=e ikx , u = ik; so that by (14), <r being substituted 

 for fj/ and a' for /x, 



ik{<T-<r') 

 ^~Aira' + {<r-a')h ^ Jj 



In the intermediate region by (28) yjr= —TAx/r 3 , and thus at 

 a great distance 



*= ^ '> (56) 



or on substitution of the values of A and k, 



r ~ \V 4<7r</ + (<r-</)L' ' ' [ °' } 



Equations (46), (57) express the complete solution in the 

 case supposed. 



For an obstacle which is rigid and fixed, we may deduce 

 the result by supposing in our equations m'=co, <t' = cg. 

 Thus 



Certain particular cases are worthy of notice. For the 

 sphere L = f7r, and 



*~*5rt+ia- • • • w 



If the ellipsoid reduce to an infinitely thin circular disk of 

 radius c, T = and the term of zero order vanishes. The 

 term of the first order also vanishes if the plane of the disk 

 be parallel to x. If the plane of the disk be perpendicular to 



* 'Theory of Sound,' § 334. 



