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efficients in the plane polarised wave, and that in consequence 
the rotations of the displacements and the elements of strain 
are the same as those in the original wave. As this seems 
to leave the question indefinite I examine the arbitrary por- 
tion of the expression and find that it only affects the integral 
result in terms depending upon the nature, form, and shape 
of the boundaries, and will in general enter them in such a 
way as to render them incapable of being experimentally 
determined, even if their mean value may not be zero. 
The terms which are definite and contribute the whole 
integral term (except so far as disturbing elements arise from 
the boundaries) are found to differ in several respects from 
those found by Professor Stokes and by Professor Rowland, 
and the points of difference are discussed at the end of the 
paper. The general question of diffraction at a finite aper- 
ture is not discussed, and the author intends to treat the 
question of the direction of vibration of plane polarised 
light in a future communication. 
I. 
In a paper On the solutions of the equations of vibration 
of light, &c.,” communicated to the Cambridge Philosophical 
Society, but not yet published, the author of this paper has 
shewn that the solution of the equation ^2 - = 0 can, on 
the hypothesis that the time only enters through the trigo- 
nometrical terms, be given in the form 
^ = I U-i + u _2 + 'W_3 + &c. I sin p[at - r) 
+ { v_i + v _2 + 'y _3 + &c. j- cos - r) 
where u_i and v_i are any homogeneous function whatever 
of X, y and x, of degree - 1, and where the terms of other 
degrees are to be derived by the laws. 
2^'y_a -r<[ ^u_i = 0 -r<^ = 0 &c. 'j 
2pit_g + r<] h_i - 0 4pw_3 + r<\ = 0 &c. / 
