262 The Rev. Prof. B. Powell on Circularly Polarized Light. 
reduce to w = sy, for the functions of all amplitudes greater 
than «+ 2(m — 1) would reduce to similar functions of 
amplitudes less than this. 
In the 15th Number of the Cambridge Mathematical Jour- 
nal, I very briefly pointed out the failure of some of M. Jacobi’s 
forms for w This the editor of that work was very reluctant 
toadmit; and in the 16th Number of the same I find a Note, 
bearing the signature C., intended as a refutation of what I 
had advanced. On this Note I must now make a few obser- 
vations, but after what has been done in this paper it will not 
be necessary to enter far into particulars. 
If the writer wished to compare my denominator with M. 
Jacobi’s, he should, for each particular form of w, have at- 
tempted to reduce them to the same quantity. His method 
gives the true one for the first value of », which proves to be 
mine, and affords no foundation for the inferences he has 
drawn from it. The true form would also be ascertained the 
moment it is proved, that when wu = a, v=H. And this is 
the important point ; if they differ, and when they differ, which 
is right. For the second value of w, the formule (1.), (2.) admit 
of reduction, as already shown. [The references are made to 
the note.| The third gives a factor infinite in the numerators 
of the second members of (1.), (2.) when «=, and is there- 
fore evidently inadmissible. For the last value of w, san w 
! 
1 ae : 
as Ee ee oe /—1; and these values the writer 
of the note has, evidently by mistake, taken for the values of 
sav,cav. For surely he never could prove, that when u = w 
the second member of (2.), divided by ¢ a ” w, is equal to unity. 
His last value of C therefore is wrong. I feel compelled to 
say that this Note is perfectly absurd at every step of it; and 
if the author had proved what he aimed at, and which is 
really true, it would have been nothing to the purpose. 
Denby, near Huddersfield, Jan. 5th, 1843. 
XLIV. On Mr. Earnshaw’s Deduction of a Property of Cir- 
cularly Polarized Light. By Professor Pows1u. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
jN a late Number of your Journal there appears a theoretical 
deduction by Mr. Earnshaw to this effect, that if circularly 
polarized light, right-handed, for example, fall on glass at a 
