general solution ; and as it appears that r}i, Zi (standing for 
~ ^ etc.) do not identically satisfy 
^^^1 + ym + = 0. 
we make a step towards generality by adding the two forms 
of solution. In making this addition, Professor Rowland 
gives a physical reason founded upon the electro magnetic 
analogy, and an assumption of the equality of the energies. 
But, in the first place, if the original solution had been 
general, nothing would have been gained by the addition ; 
and secondly, the equality of the energies if it exists (I have 
attempted to prove it in the paper above quoted) depends 
upon the solution of the very equations here dealt with, 
and is true whatever particular solution of the equations is 
taken. Hence the argument of Professor Rowland is used 
to give a special form to his solution and does not really 
affect the equality of the energies at all. 
Now, passing to the resulting form of displacement in the 
diffraction problem (page 433), we may remove from the 
coefficients in it the portions corresponding to etc., as 
we have a method (just referred to) for deducing them from 
u-i, and replacing them when necessary; and I shall inter- 
change the coordinates so as to leave the coefficients easily 
comparable with those in the form I propose in this paper. 
We then get 
as the forms of the coefficients. 
